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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true
The terms of an infinitely decreasing geometric progression in which all the terms are positive, the first term is $\mathbf{4}$, and the difference between third and fifth term is $\frac{32}{81}$, then which of the following is not true
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
For real numbers $x$ and $y, x R y \Leftrightarrow x-y+\sqrt{2}$ is an irrational number. Then the relation R is:
For real numbers $x$ and $y, x R y \Leftrightarrow x-y+\sqrt{2}$ is an irrational number. Then the relation R is:
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

Let $A=\{x: x=4 n+1, n \in Z, 0 \leq n<4\}$

$$\begin{aligned} & B=\{x: x=15 n+4, n \in N, n \leq 3\} \\ & C=\{x: x \text { is a prime number }, x \in A \cup B\} \end{aligned}$$

Then the cardinal number of set C is

Let $A=\{x: x=4 n+1, n \in Z, 0 \leq n<4\}$

$$\begin{aligned} & B=\{x: x=15 n+4, n \in N, n \leq 3\} \\ & C=\{x: x \text { is a prime number }, x \in A \cup B\} \end{aligned}$$

Then the cardinal number of set C is
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

If $ 2 y=\left[\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right]^2 \forall x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{d y}{d x}$ is equal to :

If $ 2 y=\left[\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right]^2 \forall x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{d y}{d x}$ is equal to :
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability of all five persons leaving at different floors is :
Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability of all five persons leaving at different floors is :
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
If $\cos A=\frac{3}{4}$, then $\left(32 \sin \frac{A}{2} \sin \frac{5 A}{2}\right)=$
If $\cos A=\frac{3}{4}$, then $\left(32 \sin \frac{A}{2} \sin \frac{5 A}{2}\right)=$
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & \cot ^{-1} \sqrt{3}\end{array}\right] \quad B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & -\tan ^{-1} \sqrt{3}\end{array}\right]$ and I is an identity matrix of order $2 \times 2$, then $A-B=$
If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & \cot ^{-1} \sqrt{3}\end{array}\right] \quad B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & -\tan ^{-1} \sqrt{3}\end{array}\right]$ and I is an identity matrix of order $2 \times 2$, then $A-B=$
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
The length of the latus rectum of a conic $49 y^2-16 x^2=784$ is
The length of the latus rectum of a conic $49 y^2-16 x^2=784$ is
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
The curve $4 y=3 x^4-2 x^2$ attains ----------- at the points $x=-\frac{1}{\sqrt{3}}$ and $x=\frac{1}{\sqrt{3}}$
The curve $4 y=3 x^4-2 x^2$ attains ----------- at the points $x=-\frac{1}{\sqrt{3}}$ and $x=\frac{1}{\sqrt{3}}$
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

The area of the region enclosed by the lines $2 x+y=10, y=1, y=5$ and the $y$-axis is

The area of the region enclosed by the lines $2 x+y=10, y=1, y=5$ and the $y$-axis is
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
$x=a(\theta+\sin \theta)$ and $y=a(1-\cos \theta)$ represents the equation of a curve. If $\theta$ changes at a constant rate $k$ then the rate of change of the slope of the tangent to the curve at $\theta=\frac{\pi}{3}$ is
$x=a(\theta+\sin \theta)$ and $y=a(1-\cos \theta)$ represents the equation of a curve. If $\theta$ changes at a constant rate $k$ then the rate of change of the slope of the tangent to the curve at $\theta=\frac{\pi}{3}$ is
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
The function $f(x)=\left\{\begin{array}{l}\frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ is discontinuous at
The function $f(x)=\left\{\begin{array}{l}\frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ is discontinuous at
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is
Integrating factor of the differential equation $\frac{d y}{d x}+y=\frac{x^3+y}{x}$ is
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

If $y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$,

then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$

If $y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$,

then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
If ${ }^{n+2} C_8:{ }^{n-2} P_4=57: 16$, then ' $n$ ' is
If ${ }^{n+2} C_8:{ }^{n-2} P_4=57: 16$, then ' $n$ ' is
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
Differentiate $\log _a x$ with respect to $a^x$
Differentiate $\log _a x$ with respect to $a^x$
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is
On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

A bag contains $(n+1)$ coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is $\frac{7}{12}$, then the value of $n$ is :

A bag contains $(n+1)$ coins. It is known that one of these coins has a head on both sides, whereas the other coins are fair. One of these coins is selected at random and tossed. If the probability that the toss results in heads is $\frac{7}{12}$, then the value of $n$ is :
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is

COMEDK 2025 Afternoon Shift Mathematics - Application of Derivatives Question 7 English

Quadrilateral PQRS is inscribed inside a rectangle of dimensions $10 \mathrm{~cm} \times 8 \mathrm{~cm}$. The value of ' $x$ ', if the area of the quadrilateral is minimum is

COMEDK 2025 Afternoon Shift Mathematics - Application of Derivatives Question 7 English
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
If $A=\left[\begin{array}{ccc}0 & -1 & 2 \\ 1 & 0 & 3 \\ -2 & -3 & 0\end{array}\right]$, then $A+2 A^T=$
If $A=\left[\begin{array}{ccc}0 & -1 & 2 \\ 1 & 0 & 3 \\ -2 & -3 & 0\end{array}\right]$, then $A+2 A^T=$
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

Simplified expression of

$1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ is :

Simplified expression of

$1-\frac{\sin ^2 y}{1+\cos y}+\frac{1+\cos y}{\sin y}-\frac{\sin y}{1-\cos y}$ is :
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
The length of the perpendicular from the point $P(1,-1,2)$ to the given line $\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z+2}{4}$ is
The length of the perpendicular from the point $P(1,-1,2)$ to the given line $\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z+2}{4}$ is
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt

The point on the line $x+y=4$ that lie at a unit distance from the line $4 x+3 y=10$ is

The point on the line $x+y=4$ that lie at a unit distance from the line $4 x+3 y=10$ is
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
The area of the region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
The area of the region bounded by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
If $A(\operatorname{adj} A)=\left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]$, then the value of $|A|+|\operatorname{adj} A|$ is equal to :
If $A(\operatorname{adj} A)=\left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]$, then the value of $|A|+|\operatorname{adj} A|$ is equal to :
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are $\frac{1}{2}, \frac{3}{10}$ and $\frac{1}{5}$ respectively. Each team gets 5 points for win, 3 points for draw and 0 points for loss in a game. After two games, find the probability that Jaipur has more points than Delhi.
In a kabaddi league, two matches are being played between Jaipur and Delhi. It is assumed that the outcomes of the two games are independent. The probability of Jaipur winning, drawing and losing the game against Delhi are $\frac{1}{2}, \frac{3}{10}$ and $\frac{1}{5}$ respectively. Each team gets 5 points for win, 3 points for draw and 0 points for loss in a game. After two games, find the probability that Jaipur has more points than Delhi.
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$
$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
If the mean of $4,7,2,8,6$ and $k$ is 7 . Then the mean deviation from the mean of these observations is
If the mean of $4,7,2,8,6$ and $k$ is 7 . Then the mean deviation from the mean of these observations is
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
$\int\limits_0^{\frac{\pi}{2}} \log \left(\frac{5+4 \sin x}{5+4 \cos x}\right) d x=$
$\int\limits_0^{\frac{\pi}{2}} \log \left(\frac{5+4 \sin x}{5+4 \cos x}\right) d x=$
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{4}}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}$
The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{4}}=\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{3}}$
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt

Evaluate the value of $(1.02)^8$ using binomial theorem up to two decimal places.

Evaluate the value of $(1.02)^8$ using binomial theorem up to two decimal places.
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$
$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$
Which of the following transformations reduce the differential equation $\frac{d z}{d x}+\frac{z}{x} \log z=\frac{z}{x^2}(\log z)^2$ into the form $\frac{d u}{d x}+P(x) u=Q(x)$
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
The least area of a circle circumscribing any right-angle triangle of area $\frac{9}{\pi}$ sq units is
The least area of a circle circumscribing any right-angle triangle of area $\frac{9}{\pi}$ sq units is
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
$\lim _\limits{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\left(\frac{\pi}{2}-\theta\right) \cos \theta}$ is equal to :
$\lim _\limits{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\left(\frac{\pi}{2}-\theta\right) \cos \theta}$ is equal to :
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
If for two events $A$ and $B, P(A-B)=\frac{1}{5}$ and $P(A)=\frac{3}{5}$ then $P(B / A)=$
If for two events $A$ and $B, P(A-B)=\frac{1}{5}$ and $P(A)=\frac{3}{5}$ then $P(B / A)=$
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then
$\int \frac{x}{(x-1)(x-2)^2} d x=a \log \left|\frac{x-1}{x-2}\right|+\frac{b}{(x-2)}+c$ then
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
The complex number $\frac{1+7 i}{(2-i)^2}$ lies in
The complex number $\frac{1+7 i}{(2-i)^2}$ lies in
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
If a function $f:[2, \infty) \rightarrow R$ defined by $f(x)=x^2-4 x+5$, then the range of $f$ is
If a function $f:[2, \infty) \rightarrow R$ defined by $f(x)=x^2-4 x+5$, then the range of $f$ is
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
The corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$, If objective function is $Z=p x+q y, p, q>0$ then the condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
The corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$, If objective function is $Z=p x+q y, p, q>0$ then the condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt

Three bags contain a number of red and white balls are as follows.

Bag I: 3 red balls

Bag II: 2 red balls and 1 white ball

Bag III: 3 White balls

The probability that bag $i$ will be chosen and a ball is selected from it is $\frac{i}{6}, i=1,2,3$. If a white ball is selected, what is the probablity that it came from Bag III

Three bags contain a number of red and white balls are as follows.

Bag I: 3 red balls

Bag II: 2 red balls and 1 white ball

Bag III: 3 White balls

The probability that bag $i$ will be chosen and a ball is selected from it is $\frac{i}{6}, i=1,2,3$. If a white ball is selected, what is the probablity that it came from Bag III
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
The line $A B$ passes through the point $P(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5: 3$ by the point $P$. Given that the point A lies on $x$-axis and B lies on $y$-axis, then the $x$ intercept of the line is
The line $A B$ passes through the point $P(-4,3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5: 3$ by the point $P$. Given that the point A lies on $x$-axis and B lies on $y$-axis, then the $x$ intercept of the line is
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
If $Q(1,0,1)$ is the image of the point $P(a, b, c)$ in the line $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$ then $a+b+c$ is equal to :
If $Q(1,0,1)$ is the image of the point $P(a, b, c)$ in the line $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$ then $a+b+c$ is equal to :
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 500 .

The cost of 1 kg onion, 2 kg wheat and 3 kg rice is ₹ 300 .

The cost of 6 kg onion, 2 kg wheat and 3 kg rice is ₹ 575 .

The above situation can be represented in matrix form as $\mathrm{AX}=\mathrm{B}$. Then $\left|5 A^{-1}\right|=$

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 500 .

The cost of 1 kg onion, 2 kg wheat and 3 kg rice is ₹ 300 .

The cost of 6 kg onion, 2 kg wheat and 3 kg rice is ₹ 575 .

The above situation can be represented in matrix form as $\mathrm{AX}=\mathrm{B}$. Then $\left|5 A^{-1}\right|=$
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Let $A$ and $G$ denote the arithmetic mean and geometric mean of positive real numbers $5^x$ and $5^{1-x}$. Then the minimum value of the expression $5^x+5^{1-x}$ where $x \in R$ is
Let $A$ and $G$ denote the arithmetic mean and geometric mean of positive real numbers $5^x$ and $5^{1-x}$. Then the minimum value of the expression $5^x+5^{1-x}$ where $x \in R$ is
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
In a triangle $A B C$ the coordinate of the vertex $A$ is $(1,2)$. Equations of the median through $B$ and $C$ are respectively $x+y=5$ and $x=4$. Then the equation of side $\mathbf{A B}$ is
In a triangle $A B C$ the coordinate of the vertex $A$ is $(1,2)$. Equations of the median through $B$ and $C$ are respectively $x+y=5$ and $x=4$. Then the equation of side $\mathbf{A B}$ is
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The radius of the circle passes through the foci of a conic $\frac{x^2}{16}+\frac{y^2}{9}=1$ and has its centre at $(0,3)$, then the diameter of the circle is ---
The radius of the circle passes through the foci of a conic $\frac{x^2}{16}+\frac{y^2}{9}=1$ and has its centre at $(0,3)$, then the diameter of the circle is ---
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
If $A=\{1,2,4\} \quad B=\{2,4,5\} \quad C=\{2,5\}$ then $(A-B) \cap(B-C)=$
If $A=\{1,2,4\} \quad B=\{2,4,5\} \quad C=\{2,5\}$ then $(A-B) \cap(B-C)=$
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
$\int \frac{d x}{x \sqrt{4 x^2-9}}=$
$\int \frac{d x}{x \sqrt{4 x^2-9}}=$
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
In the interval $(0,1)$ the function $f(x)=x^2-x+1$ is
In the interval $(0,1)$ the function $f(x)=x^2-x+1$ is
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
If $|\vec{a}|=2 \sqrt{2}$ and $|\vec{b}|=3$ and angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$. If a parallelogram is constructed with adjacent sides $\vec{p}=2 \vec{a}-3 \vec{b}$ and $\vec{q}=\vec{a}+\vec{b}$ then the product of length of both the diagonals is :
If $|\vec{a}|=2 \sqrt{2}$ and $|\vec{b}|=3$ and angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$. If a parallelogram is constructed with adjacent sides $\vec{p}=2 \vec{a}-3 \vec{b}$ and $\vec{q}=\vec{a}+\vec{b}$ then the product of length of both the diagonals is :
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is
The value of $\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)$ is
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
The cofactor of the element $a_{21}$ in the expansion of $\Delta=\left|\begin{array}{ccc}1 & 4 & 4 \\ -3 & 5 & 9 \\ 2 & 1 & 2\end{array}\right|$ is
The cofactor of the element $a_{21}$ in the expansion of $\Delta=\left|\begin{array}{ccc}1 & 4 & 4 \\ -3 & 5 & 9 \\ 2 & 1 & 2\end{array}\right|$ is
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
If for real values of $x, \cos \theta=x+\frac{1}{x}$, then $X$
If for real values of $x, \cos \theta=x+\frac{1}{x}$, then $X$
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of
Solution of the differential equation $y \frac{d y}{d x}+x=0$ represents a family of
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt

The inequality representing the following graph is

COMEDK 2025 Afternoon Shift Mathematics - Sets and Relations Question 4 English

The inequality representing the following graph is

COMEDK 2025 Afternoon Shift Mathematics - Sets and Relations Question 4 English
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
Position vector of P and Q are $\hat{\imath}+3 \hat{\jmath}-7 \hat{k}$ and $5 \hat{\imath}-2 \hat{\jmath}+4 \hat{k}$ respectively. Then the cosine of the angle between $\overrightarrow{P Q}$ and y -axis is
Position vector of P and Q are $\hat{\imath}+3 \hat{\jmath}-7 \hat{k}$ and $5 \hat{\imath}-2 \hat{\jmath}+4 \hat{k}$ respectively. Then the cosine of the angle between $\overrightarrow{P Q}$ and y -axis is
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
Domain of the function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ for real valued of $x$ is
Domain of the function $f(x)=\sqrt{\sin ^{-1}(2 x)+\frac{\pi}{6}}$ for real valued of $x$ is
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Shortest distance between the lines $\vec{r}=(8+3 \lambda) \hat{\imath}-(9+16 \lambda) \hat{\jmath}+(10+7 \lambda) \hat{k}$ and $\vec{r}=15 \hat{\imath}+29 \hat{\jmath}+5 \hat{k}+\mu(3 \hat{\imath}+8 \hat{\jmath}-5 \hat{k})$ is
Shortest distance between the lines $\vec{r}=(8+3 \lambda) \hat{\imath}-(9+16 \lambda) \hat{\jmath}+(10+7 \lambda) \hat{k}$ and $\vec{r}=15 \hat{\imath}+29 \hat{\jmath}+5 \hat{k}+\mu(3 \hat{\imath}+8 \hat{\jmath}-5 \hat{k})$ is
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
$\lim _\limits{x \rightarrow 1} \frac{(\sqrt{x}-1)(2 x-3)}{2 x^2+x-3}$ is
$\lim _\limits{x \rightarrow 1} \frac{(\sqrt{x}-1)(2 x-3)}{2 x^2+x-3}$ is
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
An organic compound $\mathrm{A}\left(\mathrm{C}_5 \mathrm{H}_9 \mathrm{~N}\right)$ upon reaction with $\mathrm{Na} / \mathrm{Hg} / \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$ gives compound B . B reacts with $\mathrm{NaNO}_2 / \mathrm{HCl}$ at 274 K to form C with quantitative liberation of $\mathrm{N}_2$ gas. B also reacts with Hinsberg's reagent to form a compound which is soluble in alkali. Identify compound B.
An organic compound $\mathrm{A}\left(\mathrm{C}_5 \mathrm{H}_9 \mathrm{~N}\right)$ upon reaction with $\mathrm{Na} / \mathrm{Hg} / \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}$ gives compound B . B reacts with $\mathrm{NaNO}_2 / \mathrm{HCl}$ at 274 K to form C with quantitative liberation of $\mathrm{N}_2$ gas. B also reacts with Hinsberg's reagent to form a compound which is soluble in alkali. Identify compound B.
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

The $E_{M^{3+} / M^{2+}}^o$ values for $\mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}$ and Co are $-0.41,+1.57,+0.77$ and +1.97 V respectively.

For which of these metals, the change in oxidation state from +2 to +3 is the easiest?

The $E_{M^{3+} / M^{2+}}^o$ values for $\mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}$ and Co are $-0.41,+1.57,+0.77$ and +1.97 V respectively.

For which of these metals, the change in oxidation state from +2 to +3 is the easiest?
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
Given are 4 pairs of covalent molecules. Identify the pair in which both molecules have the same shape.
Given are 4 pairs of covalent molecules. Identify the pair in which both molecules have the same shape.
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
Lead storage battery contains $4.25 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ which has a density of $1.24 \mathrm{~g} / \mathrm{ml}$. Calculate the molality of aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$.
Lead storage battery contains $4.25 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ which has a density of $1.24 \mathrm{~g} / \mathrm{ml}$. Calculate the molality of aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$.
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Which of the following is the correct name according to IUPAC rules?
Which of the following is the correct name according to IUPAC rules?
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The Enthalpy of combustion of 1.0 mole of a reactive metal X at $27^{\circ} \mathrm{C}$ and 1.0 bar pressure to form a solid oxide ( XO ) is $-601.83 \mathrm{~kJ} / \mathrm{mol}$. The Internal energy change for this reaction is ___________ kJ. $$\left(\mathrm{R}=8.314 \mathrm{j} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$$
The Enthalpy of combustion of 1.0 mole of a reactive metal X at $27^{\circ} \mathrm{C}$ and 1.0 bar pressure to form a solid oxide ( XO ) is $-601.83 \mathrm{~kJ} / \mathrm{mol}$. The Internal energy change for this reaction is ___________ kJ. $$\left(\mathrm{R}=8.314 \mathrm{j} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$$
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
The ionisation constant of the weak acid HF whose concentration is 0.1 M is $3.5 \times 10^{-4}$ The Equilibrium constant value for the reaction $\mathrm{F}^{-}+\mathrm{H}_2 \mathrm{O} \leftrightharpoons \mathrm{HF}+\mathrm{OH}^{-}$is _________ and the pH of aqueous solution of the weak acid is __________ .
The ionisation constant of the weak acid HF whose concentration is 0.1 M is $3.5 \times 10^{-4}$ The Equilibrium constant value for the reaction $\mathrm{F}^{-}+\mathrm{H}_2 \mathrm{O} \leftrightharpoons \mathrm{HF}+\mathrm{OH}^{-}$is _________ and the pH of aqueous solution of the weak acid is __________ .
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
An Alkene " X " on reaction with hot acidified $\mathrm{KMnO}_4$ gave a mixture of Ethanoic acid and Propanone. Identify " X ".
An Alkene " X " on reaction with hot acidified $\mathrm{KMnO}_4$ gave a mixture of Ethanoic acid and Propanone. Identify " X ".
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
Imagine an R - moiety of a pentapeptide molecule having one $-\mathrm{SH},-\mathrm{CONH}_2,-\mathrm{NH}_2$ groups each and two $-$COOH groups in the amino acids forming the pentapeptide. If the pH is maintained at 13.2, what would be the total number of negative charges on the pentapeptide?
Imagine an R - moiety of a pentapeptide molecule having one $-\mathrm{SH},-\mathrm{CONH}_2,-\mathrm{NH}_2$ groups each and two $-$COOH groups in the amino acids forming the pentapeptide. If the pH is maintained at 13.2, what would be the total number of negative charges on the pentapeptide?
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
An aqueous solution which contains $42 \%$ by weight $(\mathrm{w} / \mathrm{W})$ of a volatile liquid "A" of molar mass of $140 \mathrm{~g} / \mathrm{mol}$, has a vapour pressure of 2141.4 mm of Hg at $37^{\circ} \mathrm{C}$. What is the vapour pressure of the pure liquid " A "? Vapour pressure of water at $37^{\circ} \mathrm{C}$ is 2019.1 mm .
An aqueous solution which contains $42 \%$ by weight $(\mathrm{w} / \mathrm{W})$ of a volatile liquid "A" of molar mass of $140 \mathrm{~g} / \mathrm{mol}$, has a vapour pressure of 2141.4 mm of Hg at $37^{\circ} \mathrm{C}$. What is the vapour pressure of the pure liquid " A "? Vapour pressure of water at $37^{\circ} \mathrm{C}$ is 2019.1 mm .
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
What would be the cell potential for the Galvanic cell which is represented by the electrochemical reaction: $$ \begin{aligned} & 2 \mathrm{Cr}_{(\mathrm{S})}+3 \mathrm{Fe}^{2+}(0.02 \mathrm{M}) \rightarrow 2 \mathrm{Cr}^{3+}(0.2 \mathrm{M})+3 \mathrm{Fe} \\ & \mathrm{E}^0 \mathrm{Fe}^{2+} / \mathrm{Fe}=-0.42 \mathrm{~V} \quad \mathrm{E}^0 \mathrm{Cr}^{3+} / \mathrm{Cr}=-0.72 \mathrm{~V} \end{aligned} $$
What would be the cell potential for the Galvanic cell which is represented by the electrochemical reaction: $$ \begin{aligned} & 2 \mathrm{Cr}_{(\mathrm{S})}+3 \mathrm{Fe}^{2+}(0.02 \mathrm{M}) \rightarrow 2 \mathrm{Cr}^{3+}(0.2 \mathrm{M})+3 \mathrm{Fe} \\ & \mathrm{E}^0 \mathrm{Fe}^{2+} / \mathrm{Fe}=-0.42 \mathrm{~V} \quad \mathrm{E}^0 \mathrm{Cr}^{3+} / \mathrm{Cr}=-0.72 \mathrm{~V} \end{aligned} $$
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
The hydrogenation of Ethyne is carried out at 600 K . The same reaction when carried out in presence of a catalyst maintaining the same rate constant, the temperature required is only 400 K . If the catalyst lowers the Activation energy of the reaction by $20 \mathrm{~kJ} / \mathrm{mol}$, what is the value of $\mathrm{E}_{\mathrm{a}}$ ?
The hydrogenation of Ethyne is carried out at 600 K . The same reaction when carried out in presence of a catalyst maintaining the same rate constant, the temperature required is only 400 K . If the catalyst lowers the Activation energy of the reaction by $20 \mathrm{~kJ} / \mathrm{mol}$, what is the value of $\mathrm{E}_{\mathrm{a}}$ ?
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

Complete the following 2 reactions A \& B by choosing appropriate reactants $[\mathrm{X}] \&[\mathrm{Y}]$.

COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 5 English

Complete the following 2 reactions A \& B by choosing appropriate reactants $[\mathrm{X}] \&[\mathrm{Y}]$.

COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 5 English
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The time needed for completion of $80 \%$ is $y$ times the half-life period of a first order reaction. What is the value of $y$ ?
The time needed for completion of $80 \%$ is $y$ times the half-life period of a first order reaction. What is the value of $y$ ?
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
A current of 1.5 A is passed for 2 hours through an aqueous solution of $\mathrm{PdX} \mathrm{n}_{\mathrm{n}}$ where X is a monovalent anion. During the electrolysis process 2.977 g of Palladium metal gets deposited at the cathode. Calculate the charge on Pd ions. (Atomic mass of $\mathrm{Pd}=106.4 \mathrm{~g} / \mathrm{mol}$ ).
A current of 1.5 A is passed for 2 hours through an aqueous solution of $\mathrm{PdX} \mathrm{n}_{\mathrm{n}}$ where X is a monovalent anion. During the electrolysis process 2.977 g of Palladium metal gets deposited at the cathode. Calculate the charge on Pd ions. (Atomic mass of $\mathrm{Pd}=106.4 \mathrm{~g} / \mathrm{mol}$ ).
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

Choose the statements which are incorrect in the case of Lanthanoids.

A. $\mathrm{Ce}^{4+}$ is diamagnetic while $\mathrm{Sm}^{3+}$ is paramagnetic.

B. The atomic size of the transition metals having atomic number greater than 71 are very close to that of the elements above them.

C. Lanthanoids react with hot water forming water soluble $\mathrm{Ln}(\mathrm{OH})_3$ with the liberation of $\mathrm{O}_2$.

D. The general electronic configuration of Lanthanoids is $(n-2) \mathrm{f}^{1-14} 5 \mathrm{~d}^0 6 \mathrm{~s}^2$, where $n=6$.

Choose the statements which are incorrect in the case of Lanthanoids.

A. $\mathrm{Ce}^{4+}$ is diamagnetic while $\mathrm{Sm}^{3+}$ is paramagnetic.

B. The atomic size of the transition metals having atomic number greater than 71 are very close to that of the elements above them.

C. Lanthanoids react with hot water forming water soluble $\mathrm{Ln}(\mathrm{OH})_3$ with the liberation of $\mathrm{O}_2$.

D. The general electronic configuration of Lanthanoids is $(n-2) \mathrm{f}^{1-14} 5 \mathrm{~d}^0 6 \mathrm{~s}^2$, where $n=6$.
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
Larger number of oxidation states are exhibited by the actinoids than those of lanthanoids. The reason is:
Larger number of oxidation states are exhibited by the actinoids than those of lanthanoids. The reason is:
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

Given below are 2 statements: one Assertion and the other Reason. Which one of the following options is correct?

Assertion : Sulphur dioxide and Hydrogen peroxide can act as both oxidising and reducing agents but Nitric acid can act as only oxidising agent.

Reason : Sulphur and Oxygen can exhibit more than one stable oxidation states while Nitrogen does not.

Given below are 2 statements: one Assertion and the other Reason. Which one of the following options is correct?

Assertion : Sulphur dioxide and Hydrogen peroxide can act as both oxidising and reducing agents but Nitric acid can act as only oxidising agent.

Reason : Sulphur and Oxygen can exhibit more than one stable oxidation states while Nitrogen does not.
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

From among the 4 given compounds identify the compounds which possess a net dipole moment.

A. cis-1,2-Dichloroethene

B. Tetrachloromethane

C. o-Dichlorobenzene

D. trans 2,3-Dibromobut-2-ene

From among the 4 given compounds identify the compounds which possess a net dipole moment.

A. cis-1,2-Dichloroethene

B. Tetrachloromethane

C. o-Dichlorobenzene

D. trans 2,3-Dibromobut-2-ene
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt

Which is the correct order of increasing number of unpaired electrons in the following ions?

$$\mathrm{A}=\mathrm{Cr}^{2+}(\mathrm{Z}=24) \mathrm{B}=\mathrm{Cu}^{2+}(\mathrm{Z}=29) \quad \mathrm{C}=\mathrm{Ni}^{2+}(\mathrm{Z}=28) \mathrm{D}=\mathrm{Fe}^{3+}(\mathrm{Z}=26)$$

Which is the correct order of increasing number of unpaired electrons in the following ions?

$$\mathrm{A}=\mathrm{Cr}^{2+}(\mathrm{Z}=24) \mathrm{B}=\mathrm{Cu}^{2+}(\mathrm{Z}=29) \quad \mathrm{C}=\mathrm{Ni}^{2+}(\mathrm{Z}=28) \mathrm{D}=\mathrm{Fe}^{3+}(\mathrm{Z}=26)$$
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
Which one of the following is incorrect?
Which one of the following is incorrect?
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
A dilute solution of $\mathrm{K}_2 \mathrm{HgI}_4$ reagent is $95 \%$ ionised. What would be the approximate value of its van't Hoff factor?
A dilute solution of $\mathrm{K}_2 \mathrm{HgI}_4$ reagent is $95 \%$ ionised. What would be the approximate value of its van't Hoff factor?
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
For a hypothetical chemical reaction $\mathrm{A}_2+3 \mathrm{~B}_2+$ Heat $\cdots\rightarrow 2 \mathrm{AB}_3$, which one of the following combinations of state variables would support the spontaneity of the reaction at a particular temperature?
For a hypothetical chemical reaction $\mathrm{A}_2+3 \mathrm{~B}_2+$ Heat $\cdots\rightarrow 2 \mathrm{AB}_3$, which one of the following combinations of state variables would support the spontaneity of the reaction at a particular temperature?
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
Choose the incorrect statement from the following.
Choose the incorrect statement from the following.
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
Which one of the following compounds will give a yellow precipitate when reacted with $\mathrm{I}_2 / \mathrm{NaOH}$?
Which one of the following compounds will give a yellow precipitate when reacted with $\mathrm{I}_2 / \mathrm{NaOH}$?
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt

Identify X and Y formed in the following two reactions.

(i) Decan-1-ol $\xrightarrow{\text { Jones reagent }} \mathrm{X}$

(ii). Sodium salt of $\mathrm{X} \xrightarrow{\mathrm{NaOH} / \mathrm{CaO}, \Delta} \mathrm{Y}$

Identify X and Y formed in the following two reactions.

(i) Decan-1-ol $\xrightarrow{\text { Jones reagent }} \mathrm{X}$

(ii). Sodium salt of $\mathrm{X} \xrightarrow{\mathrm{NaOH} / \mathrm{CaO}, \Delta} \mathrm{Y}$
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
Choose the incorrect statement.
Choose the incorrect statement.
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt

Match A, B, C and D with the appropriate functions given.

Column I Functions
A. Oxidoreductase P. Malfunctioning leads to Addison's disease.
B. Phosphodiester bonds Q. Regulates responses to external stimuli.
C. Adrenal cortex R. Catalyses glycolysis.
D. Epinephrine S. Links nucleotides together.

Match A, B, C and D with the appropriate functions given.

Column I Functions
A. Oxidoreductase P. Malfunctioning leads to Addison's disease.
B. Phosphodiester bonds Q. Regulates responses to external stimuli.
C. Adrenal cortex R. Catalyses glycolysis.
D. Epinephrine S. Links nucleotides together.

Q.29 Correct
Q.29 In-correct
Q.29 Unattempt

Two statements, One Assertion and the other Reason, are given.

Which one of the following is the correct option?

Assertion: The acid strength of 4 compounds in the descending order is p- Nitrophenol > p-Methoxyphenol > Phenol > p-chlorophenol.

Reason: Electron withdrawing groups increase the acid strength while Electron donating groups decrease the acid strength of Phenol and its derivatives.

Two statements, One Assertion and the other Reason, are given.

Which one of the following is the correct option?

Assertion: The acid strength of 4 compounds in the descending order is p- Nitrophenol > p-Methoxyphenol > Phenol > p-chlorophenol.

Reason: Electron withdrawing groups increase the acid strength while Electron donating groups decrease the acid strength of Phenol and its derivatives.
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
Identify the incorrect statement.
Identify the incorrect statement.
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt

Arrange the following ions in the decreasing order of covalent double bonds formed by the transition metal with oxygen.

 

A. $=$ chromate $\mathrm{B}=$ permanganate $\mathrm{C}=$ dichromate

Arrange the following ions in the decreasing order of covalent double bonds formed by the transition metal with oxygen.

 

A. $=$ chromate $\mathrm{B}=$ permanganate $\mathrm{C}=$ dichromate
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt

Which one of the following structures in Column I does not have the correct IUPAC name as given in Column II.

S.No. Structure IUPAC name
A. $\left[\mathrm{CoBr}_2(\mathrm{en})_2\right] \mathrm{Cl}$ P. Dibromidodi-( ethan-1, 2 - diamine)cobalt (III) chloride
B. $\mathrm{Na}\left[\mathrm{PtBrCl}\left(\mathrm{NO}_2\right)\left(\mathrm{NH}_3\right)\right]$ Q. Sodium amminebromidochloridonitrito- N - palatinate(II)
C. $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_2\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}\right] \mathrm{SO}_4$ R. Tetraamminediaquachloridochromium (III) sulphate.
D. $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{PtCl}_4\right]$ S. Tetraammineplatinum (II) tetrachloridoplatinate (II)

Which one of the following structures in Column I does not have the correct IUPAC name as given in Column II.

S.No. Structure IUPAC name
A. $\left[\mathrm{CoBr}_2(\mathrm{en})_2\right] \mathrm{Cl}$ P. Dibromidodi-( ethan-1, 2 - diamine)cobalt (III) chloride
B. $\mathrm{Na}\left[\mathrm{PtBrCl}\left(\mathrm{NO}_2\right)\left(\mathrm{NH}_3\right)\right]$ Q. Sodium amminebromidochloridonitrito- N - palatinate(II)
C. $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_2\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}\right] \mathrm{SO}_4$ R. Tetraamminediaquachloridochromium (III) sulphate.
D. $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{PtCl}_4\right]$ S. Tetraammineplatinum (II) tetrachloridoplatinate (II)

Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
When $0.4 \mathrm{~g} \mathrm{CH}_3 \mathrm{COOH}$ is added to 40 g of Benzene to form a solution, the freezing point is depressed by $0.45^{\circ} \mathrm{C}$. If Acetic acid undergoes dimerisation in Benzene ( $\mathrm{K}_{\mathrm{f}}=5.12 \mathrm{~K} \mathrm{~kg} / \mathrm{mol}$ ) what is the percentage association of the acid in Benzene?
When $0.4 \mathrm{~g} \mathrm{CH}_3 \mathrm{COOH}$ is added to 40 g of Benzene to form a solution, the freezing point is depressed by $0.45^{\circ} \mathrm{C}$. If Acetic acid undergoes dimerisation in Benzene ( $\mathrm{K}_{\mathrm{f}}=5.12 \mathrm{~K} \mathrm{~kg} / \mathrm{mol}$ ) what is the percentage association of the acid in Benzene?
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
Two subatomic particles 1 and 2, with the same kinetic energies have their de- Broglie wavelengths as $\lambda_1 \& \lambda_2$ and masses as 3 m and 6 m respectively. Determine the ratio $\lambda_1: \lambda_2$.
Two subatomic particles 1 and 2, with the same kinetic energies have their de- Broglie wavelengths as $\lambda_1 \& \lambda_2$ and masses as 3 m and 6 m respectively. Determine the ratio $\lambda_1: \lambda_2$.
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt

Identify the product $(\mathrm{Y})$ formed in the given reaction and the name of the reaction where $(\mathrm{X}) \rightarrow(\mathrm{Y})$.

COMEDK 2025 Afternoon Shift Chemistry - Compounds Containing Nitrogen Question 7 English

Identify the product $(\mathrm{Y})$ formed in the given reaction and the name of the reaction where $(\mathrm{X}) \rightarrow(\mathrm{Y})$.

COMEDK 2025 Afternoon Shift Chemistry - Compounds Containing Nitrogen Question 7 English
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
Choose the correct statement:
Choose the correct statement:
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
A transition metal M forms 4 homoleptic octahedral coordination compounds, $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D of the type $\left[\mathrm{MX}_6\right]^{z-}$ with monodentate ligands a, b, c and d respectively. These compounds absorb red. blue. yellow and blue-green light respectively. Which one of the options shows the correct order of decreasing ligand strength?
A transition metal M forms 4 homoleptic octahedral coordination compounds, $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D of the type $\left[\mathrm{MX}_6\right]^{z-}$ with monodentate ligands a, b, c and d respectively. These compounds absorb red. blue. yellow and blue-green light respectively. Which one of the options shows the correct order of decreasing ligand strength?
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
Which one of the following is the correct statement?
Which one of the following is the correct statement?
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt

(i) and (ii) are 2 chemical reactions carried out at TK.

(i). $\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{W}$ with $\mathrm{k}_1$ as rate constant.

(ii). $\mathrm{X} \rightarrow \mathrm{Z}+\mathrm{W}$ with $k_2$ as rate constant.

The Activation energy for reaction (ii) is 3 times that of reaction (i). What is the expression for $k_1$ ?

(i) and (ii) are 2 chemical reactions carried out at TK.

(i). $\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{W}$ with $\mathrm{k}_1$ as rate constant.

(ii). $\mathrm{X} \rightarrow \mathrm{Z}+\mathrm{W}$ with $k_2$ as rate constant.

The Activation energy for reaction (ii) is 3 times that of reaction (i). What is the expression for $k_1$ ?
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt

Which one of the following is the major product formed when the given reaction occurs?

COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 6 English

Which one of the following is the major product formed when the given reaction occurs?

COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 6 English
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
Toluene when reacted with $\mathrm{Cl}_2$ gas at 385 K forms a product X which undergoes further reaction with Sodium ethoxide to yield product Y . The structure of Y is ___________ .
Toluene when reacted with $\mathrm{Cl}_2$ gas at 385 K forms a product X which undergoes further reaction with Sodium ethoxide to yield product Y . The structure of Y is ___________ .
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
A dilute solution of an ionic compound $\mathrm{A}_3 \mathrm{~B}$ has an Osmotic pressure which is 6 times that of $0.02 \mathrm{M} \mathrm{MgCl}_2$. What is the molar concentration of $\mathrm{A}_3 \mathrm{~B}$ assuming that it undergoes complete dissociation in water?
A dilute solution of an ionic compound $\mathrm{A}_3 \mathrm{~B}$ has an Osmotic pressure which is 6 times that of $0.02 \mathrm{M} \mathrm{MgCl}_2$. What is the molar concentration of $\mathrm{A}_3 \mathrm{~B}$ assuming that it undergoes complete dissociation in water?
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
An organic compound " A " reacts with $\mathrm{Zn} / \mathrm{Hg}$ / Conc. HCl to form p-Xylene. It reduces Tollen's reagent and on oxidation with $\mathrm{KMnO}_4 / \mathrm{H}^{+}$it yields 1, 4-benzenedicarboxylic acid. Identify compound A.
An organic compound " A " reacts with $\mathrm{Zn} / \mathrm{Hg}$ / Conc. HCl to form p-Xylene. It reduces Tollen's reagent and on oxidation with $\mathrm{KMnO}_4 / \mathrm{H}^{+}$it yields 1, 4-benzenedicarboxylic acid. Identify compound A.
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
The first ionisation enthalpy of Al in $\mathrm{kJ} \mathrm{mol}^{-1}$ is: [Given the first ionisation enthalpy of $\mathrm{Na}, \mathrm{Mg}$ and Si in $\mathrm{kJ} \mathrm{mol}^{-1}$ are 497,738 and 787 respectively]
The first ionisation enthalpy of Al in $\mathrm{kJ} \mathrm{mol}^{-1}$ is: [Given the first ionisation enthalpy of $\mathrm{Na}, \mathrm{Mg}$ and Si in $\mathrm{kJ} \mathrm{mol}^{-1}$ are 497,738 and 787 respectively]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Choose the coordination compound which does not exhibit Optical activity.
Choose the coordination compound which does not exhibit Optical activity.
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt

Identify the reagents to be used to complete the given reaction.

COMEDK 2025 Afternoon Shift Chemistry - Haloalkanes and Haloarenes Question 2 English

Identify the reagents to be used to complete the given reaction.

COMEDK 2025 Afternoon Shift Chemistry - Haloalkanes and Haloarenes Question 2 English
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt

What is the standard electrode potential at 298 K for the reaction: $\mathrm{Cu}^{2+}+1 \mathrm{e}-\rightarrow \mathrm{Cu}^{+1}$ ?

Given: $\mathrm{E}_0 \mathrm{Cu}^{+1} / \mathrm{Cu}=0.5 \mathrm{~V} \quad \& \quad \mathrm{E}_0 \mathrm{Cu}^{+2} / \mathrm{Cu}=0.335 \mathrm{~V}$

What is the standard electrode potential at 298 K for the reaction: $\mathrm{Cu}^{2+}+1 \mathrm{e}-\rightarrow \mathrm{Cu}^{+1}$ ?

Given: $\mathrm{E}_0 \mathrm{Cu}^{+1} / \mathrm{Cu}=0.5 \mathrm{~V} \quad \& \quad \mathrm{E}_0 \mathrm{Cu}^{+2} / \mathrm{Cu}=0.335 \mathrm{~V}$
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
Which one of the following molecules attains greater stability on formation of its diatomic monovalent anion?
Which one of the following molecules attains greater stability on formation of its diatomic monovalent anion?
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt

The Standard Reduction potential at $25^{\circ} \mathrm{C}$ for $\left(\mathrm{MnO}_4\right)^{-1} / \mathrm{H}^{+}$is +1.49 V . The $\mathrm{E}^0$ values for four Metal ions :

(a). $\mathrm{Co}^{3+} / \mathrm{Co}^{2+}$

(b). $\mathrm{Cr}^{3+} / \mathrm{Cr}$

(c). $\mathrm{Au}^{3+} / \mathrm{Au}$ and

(d). $\mathrm{Ag}^{+} / \mathrm{Ag}$

are $+1.81 \mathrm{~V},-0.74 \mathrm{~V},+1.50 \mathrm{~V}$ and +0.8 V respectively. Identify two of them which cannot be oxidised by $\left(\mathrm{MnO}_4\right)^{-1} / \mathrm{H}^{+}$

The Standard Reduction potential at $25^{\circ} \mathrm{C}$ for $\left(\mathrm{MnO}_4\right)^{-1} / \mathrm{H}^{+}$is +1.49 V . The $\mathrm{E}^0$ values for four Metal ions :

(a). $\mathrm{Co}^{3+} / \mathrm{Co}^{2+}$

(b). $\mathrm{Cr}^{3+} / \mathrm{Cr}$

(c). $\mathrm{Au}^{3+} / \mathrm{Au}$ and

(d). $\mathrm{Ag}^{+} / \mathrm{Ag}$

are $+1.81 \mathrm{~V},-0.74 \mathrm{~V},+1.50 \mathrm{~V}$ and +0.8 V respectively. Identify two of them which cannot be oxidised by $\left(\mathrm{MnO}_4\right)^{-1} / \mathrm{H}^{+}$
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
The best method for the separation of $o$-nitrophenol and $p$-nitrophenol from their mixture is :
The best method for the separation of $o$-nitrophenol and $p$-nitrophenol from their mixture is :
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
For the reaction $\mathrm{A}_2+\mathrm{B}_2 \cdots \cdots>2 \mathrm{AB}, \Delta \mathrm{H}_{\mathrm{f}}=-400 \mathrm{~kJ} / \mathrm{mol}$. The bond dissociation enthalpies of $\mathrm{A}_2$, $\mathrm{B}_2$ and AB are in the ratio $1: 0.75: 1$. What is the bond dissociation enthalpy of $\mathrm{B}_2$ in $\mathrm{kJ} / \mathrm{mol}$ ?
For the reaction $\mathrm{A}_2+\mathrm{B}_2 \cdots \cdots>2 \mathrm{AB}, \Delta \mathrm{H}_{\mathrm{f}}=-400 \mathrm{~kJ} / \mathrm{mol}$. The bond dissociation enthalpies of $\mathrm{A}_2$, $\mathrm{B}_2$ and AB are in the ratio $1: 0.75: 1$. What is the bond dissociation enthalpy of $\mathrm{B}_2$ in $\mathrm{kJ} / \mathrm{mol}$ ?
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
The correct order of spin only magnetic moments among the following is: [Given: Atomic numbers: $\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27$ ]
The correct order of spin only magnetic moments among the following is: [Given: Atomic numbers: $\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27$ ]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
Choose the incorrect statement from the following.
Choose the incorrect statement from the following.
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt

Match the reactions in Column I with the correct products given in Column II

S.No. Column I S.NO. Column II
A. 1- Chloropropane $+(\mathrm{Zn} / \mathrm{HCl}) \rightarrow$ P. Propanone + Methanal
B. n- Hexane $+\left(\right.$ anh. $\left.\mathrm{AlCl}_3 / \mathrm{HCl}_{(\mathrm{g})}\right) \rightarrow$ Q. Propanone
C. 2- Methylpropene $+\left(\mathrm{O}_3 \& \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\right) \rightarrow$ R. Propane
D. Propyne $+\left(\mathrm{HgSO}_4 / \mathrm{H}_2 \mathrm{SO}_4\right.$ at 333 K$) \rightarrow$ S. 2-Methylpentane + 3-Methylpentane

Match the reactions in Column I with the correct products given in Column II

S.No. Column I S.NO. Column II
A. 1- Chloropropane $+(\mathrm{Zn} / \mathrm{HCl}) \rightarrow$ P. Propanone + Methanal
B. n- Hexane $+\left(\right.$ anh. $\left.\mathrm{AlCl}_3 / \mathrm{HCl}_{(\mathrm{g})}\right) \rightarrow$ Q. Propanone
C. 2- Methylpropene $+\left(\mathrm{O}_3 \& \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\right) \rightarrow$ R. Propane
D. Propyne $+\left(\mathrm{HgSO}_4 / \mathrm{H}_2 \mathrm{SO}_4\right.$ at 333 K$) \rightarrow$ S. 2-Methylpentane + 3-Methylpentane

Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
The rate constant for a zero order reaction $\mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$ is $6.0 \times 10^{-3} \mathrm{molL}^{-1} \mathrm{~s}^{-1}$. What would be the time taken for the initial concentration of A to decrease from 0.2 M to 0.024 M ?
The rate constant for a zero order reaction $\mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$ is $6.0 \times 10^{-3} \mathrm{molL}^{-1} \mathrm{~s}^{-1}$. What would be the time taken for the initial concentration of A to decrease from 0.2 M to 0.024 M ?
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
When one mole of a hydrocarbon $\mathbf{C}_{\mathbf{a}} \mathbf{H}_{\mathbf{b}}$ undergoes complete combustion, it requires 7.5 moles of $\mathrm{O}_2$ and results in the production of 6 moles of $\mathrm{CO}_2$. Calculate the values of $\mathbf{a}$ and $\mathbf{b}$.
When one mole of a hydrocarbon $\mathbf{C}_{\mathbf{a}} \mathbf{H}_{\mathbf{b}}$ undergoes complete combustion, it requires 7.5 moles of $\mathrm{O}_2$ and results in the production of 6 moles of $\mathrm{CO}_2$. Calculate the values of $\mathbf{a}$ and $\mathbf{b}$.
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
For the reaction $\mathrm{P}+\mathrm{Q} \leq \mathrm{R}+\mathrm{S}$, carried out at 298 K , the equilibrium constant was found to be 169 and the initial concentrations of all reactants and products was 1.0 M . What is the equilibrium concentration of the reactants?
For the reaction $\mathrm{P}+\mathrm{Q} \leq \mathrm{R}+\mathrm{S}$, carried out at 298 K , the equilibrium constant was found to be 169 and the initial concentrations of all reactants and products was 1.0 M . What is the equilibrium concentration of the reactants?
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt

Two statements, one Assertion and the other Reason are given. Choose the correct option.

Assertion: Heterocyclic compounds like Pyridine and Thiophene are non-aromatic compounds.

Reason: According to Huckel rule for a given compound to exhibit aromaticity, the molecule must be planar, cyclic system having delocalised $(4 n+2) \pi$ electrons.

Two statements, one Assertion and the other Reason are given. Choose the correct option.

Assertion: Heterocyclic compounds like Pyridine and Thiophene are non-aromatic compounds.

Reason: According to Huckel rule for a given compound to exhibit aromaticity, the molecule must be planar, cyclic system having delocalised $(4 n+2) \pi$ electrons.
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt

Match the reaction in Column I with the major product formed given in Column II.

  Column I - Reaction/conditions   Column II - Product
A. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 1 P. Pentan-2-ol
B. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 2 Q. 2-Hydroxybenzoic acid.
C. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 3 R. Phenol
D. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 4 S. 2-Methylpropan-1-ol

Match the reaction in Column I with the major product formed given in Column II.

  Column I - Reaction/conditions   Column II - Product
A. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 1 P. Pentan-2-ol
B. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 2 Q. 2-Hydroxybenzoic acid.
C. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 3 R. Phenol
D. COMEDK 2025 Afternoon Shift Chemistry - Alcohol, Phenols and Ethers Question 4 English 4 S. 2-Methylpropan-1-ol
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt

Two statements, one Assertion and the other Reason are given. Choose the correct option.

Assertion: For strong electrolytes the plot of Molar conductivity versus Concentration gives a straight line with slope equal to +A and intercept equal to $\lambda_{\mathrm{m}}$

Reason: For strong electrolytes, $\lambda_{\mathrm{m}}$ increases slowly with dilution due to increase in the distance between the ions and increase in ionic mobility

Two statements, one Assertion and the other Reason are given. Choose the correct option.

Assertion: For strong electrolytes the plot of Molar conductivity versus Concentration gives a straight line with slope equal to +A and intercept equal to $\lambda_{\mathrm{m}}$

Reason: For strong electrolytes, $\lambda_{\mathrm{m}}$ increases slowly with dilution due to increase in the distance between the ions and increase in ionic mobility
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
A circular coil of area $2 \sqrt{2} \mathrm{~cm}^2$ and resistance $2 \boldsymbol{\Omega}$ is arranged vertically in the east -west direction. A uniform magnetic field 0.2 T is set up across the plane in the north to east direction. Now the magnetic field is removed at a steady rate in 0.4 s What is the current developed in the coil?
A circular coil of area $2 \sqrt{2} \mathrm{~cm}^2$ and resistance $2 \boldsymbol{\Omega}$ is arranged vertically in the east -west direction. A uniform magnetic field 0.2 T is set up across the plane in the north to east direction. Now the magnetic field is removed at a steady rate in 0.4 s What is the current developed in the coil?
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
A car, starting from rest, accelerates at the rate (f) through a distance ( $S$ ), then continues at constant speed for some time $(t)$ and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance is $5 S$, then
A car, starting from rest, accelerates at the rate (f) through a distance ( $S$ ), then continues at constant speed for some time $(t)$ and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance is $5 S$, then
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' $v$ '. Then the mass ' $m$ ' of the charged particle is
A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' $v$ '. Then the mass ' $m$ ' of the charged particle is
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

COMEDK 2025 Afternoon Shift Physics - Semiconductor Devices and Logic Gates Question 4 English

Three ideal diodes and resistors connected to the cell of negligible internal resistance is as shown. Find the current passing through the $10 \Omega$ resistor.

COMEDK 2025 Afternoon Shift Physics - Semiconductor Devices and Logic Gates Question 4 English

Three ideal diodes and resistors connected to the cell of negligible internal resistance is as shown. Find the current passing through the $10 \Omega$ resistor.
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
A coin is placed on a disc rotating with an angular velocity $\omega$. The co-efficient of friction between the disc and the coin is $\mu$. The maximum distance of the coin from the centre of the disc up to which it will rotate with the disc is
A coin is placed on a disc rotating with an angular velocity $\omega$. The co-efficient of friction between the disc and the coin is $\mu$. The maximum distance of the coin from the centre of the disc up to which it will rotate with the disc is
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
A beam of light parallel to the principal axis of a concave and convex lens, first passes through the concave lens of focal length 0.5 m and then through the convex lens of focal length 1.75 m . If the lenses are placed 1.25 apart, which of the given statement is true?
A beam of light parallel to the principal axis of a concave and convex lens, first passes through the concave lens of focal length 0.5 m and then through the convex lens of focal length 1.75 m . If the lenses are placed 1.25 apart, which of the given statement is true?
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
Three point charges $-1 C,+1 C,+1 C$ are placed at points $A, B, C$ respectively of a triangle $A B C$. What is the total potential energy of the system? [given $\mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm}$ and $\mathrm{BC}=3 \mathrm{~cm}$ ]
Three point charges $-1 C,+1 C,+1 C$ are placed at points $A, B, C$ respectively of a triangle $A B C$. What is the total potential energy of the system? [given $\mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm}$ and $\mathrm{BC}=3 \mathrm{~cm}$ ]
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt
When a body of refractive index $\boldsymbol{\mu}=\mathbf{1 . 4}$ is put into a liquid, the body becomes invisible. What would be the refractive index of the medium?
When a body of refractive index $\boldsymbol{\mu}=\mathbf{1 . 4}$ is put into a liquid, the body becomes invisible. What would be the refractive index of the medium?
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
What is the frequency ' $\nu$ ' of the electron in Bohr's first orbit of radius ' $r$ ' of the hydrogen atom?
What is the frequency ' $\nu$ ' of the electron in Bohr's first orbit of radius ' $r$ ' of the hydrogen atom?
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$. The cross-sectional area of the tap is $1 \mathrm{~cm}^2$. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 15 cm below the tap is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
Water from a tap emerges vertically downwards with an initial speed of $1.0 \mathrm{~ms}^{-1}$. The cross-sectional area of the tap is $1 \mathrm{~cm}^2$. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 15 cm below the tap is $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
A bullet of momentum $p$ is fired into a door and gets embedded exactly at the center of the door. The door is 1.0 m wide and weighs 12 kg . It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is :
A bullet of momentum $p$ is fired into a door and gets embedded exactly at the center of the door. The door is 1.0 m wide and weighs 12 kg . It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is :
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
A wind mill converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. The electrical power output P is related to the velocity of wind v as
A wind mill converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. The electrical power output P is related to the velocity of wind v as
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The value of universal gravitational constant was first determined by
The value of universal gravitational constant was first determined by
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is $2000 \times 10^{-6}$ weber. What is the induced emf in the secondary if the current through the primary increases at a rate of $0.2 \mathrm{As}^{-1}$ ?
A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is $2000 \times 10^{-6}$ weber. What is the induced emf in the secondary if the current through the primary increases at a rate of $0.2 \mathrm{As}^{-1}$ ?
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
To get 300 MW electric power for half an hour, how much mass is to be completely converted into energy?
To get 300 MW electric power for half an hour, how much mass is to be completely converted into energy?
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

The electric field versus distance graph is shown as given. Select the correct statement from the following.

E- electric field

R-radius

r - distance from the centre

COMEDK 2025 Afternoon Shift Physics - Electrostatics Question 6 English

The electric field versus distance graph is shown as given. Select the correct statement from the following.

E- electric field

R-radius

r - distance from the centre

COMEDK 2025 Afternoon Shift Physics - Electrostatics Question 6 English
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt
One end of a nylon rope of length 1 and diameter 10 mm is fixed to free limb. A monkey weighing 100 N jumps to catch the free end and stays there. The change in diameter of the rope is (Young's modulus of the wire is Y and Poisson Ratio is $\sigma$ )
One end of a nylon rope of length 1 and diameter 10 mm is fixed to free limb. A monkey weighing 100 N jumps to catch the free end and stays there. The change in diameter of the rope is (Young's modulus of the wire is Y and Poisson Ratio is $\sigma$ )
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt
Two spherical planets P and Q have the same uniform density $\rho$, and masses Mp and $\mathrm{MQ}_{\mathrm{Q}}$ and surface areas A and 4 A respectively. Another spherical planet $R$ also has the same uniform density $\rho$, and its mass is $\mathrm{Mp}+\mathrm{MQ}$. The escape velocities from these planets is
Two spherical planets P and Q have the same uniform density $\rho$, and masses Mp and $\mathrm{MQ}_{\mathrm{Q}}$ and surface areas A and 4 A respectively. Another spherical planet $R$ also has the same uniform density $\rho$, and its mass is $\mathrm{Mp}+\mathrm{MQ}$. The escape velocities from these planets is
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
What is the dimensional formula for electric flux?
What is the dimensional formula for electric flux?
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
The ratio of the number of turns of the primary coil to the secondary coil of an ideal transformer is $5: 1$. The primary is connected to 220 V supply. What is the output power of the transformer if the output resistance is $11 \Omega$ ?
The ratio of the number of turns of the primary coil to the secondary coil of an ideal transformer is $5: 1$. The primary is connected to 220 V supply. What is the output power of the transformer if the output resistance is $11 \Omega$ ?
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
The wire made of Phosphor bronze is used as the suspension strip in the moving coil galvanometer, because:
The wire made of Phosphor bronze is used as the suspension strip in the moving coil galvanometer, because:
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

Fusion reaction is more energetic than fission reaction because

Fusion reaction is more energetic than fission reaction because
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
Which physical quantity has the unit joule / tesla?
Which physical quantity has the unit joule / tesla?
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
In to a uniform transverse magnetic field, two charged particles having the same mass and charge enter and move in two different circular paths. The ratio of the radii of curvatures of the circular paths is $1: 4$. What would be the ratio of their respective velocities?
In to a uniform transverse magnetic field, two charged particles having the same mass and charge enter and move in two different circular paths. The ratio of the radii of curvatures of the circular paths is $1: 4$. What would be the ratio of their respective velocities?
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from $273^{\circ} \mathrm{C}$ to $473^{\circ} \mathrm{C}$ at constant volume is
The heat required to increase the temperature of 4 moles of a mono-atomic ideal gas from $273^{\circ} \mathrm{C}$ to $473^{\circ} \mathrm{C}$ at constant volume is
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
Rods $A$ and $B$ have their lengths in the ratio $1: 2$. Their thermal conductivities are $K_1$ and $K_2$ respectively. The temperatures at the ends of each rod are $\mathrm{T}_1$ and $\mathrm{T}_2$. If the rate of flow of heat through the rods is equal, the ratio of area of cross section of $A$ to that of $B$ is
Rods $A$ and $B$ have their lengths in the ratio $1: 2$. Their thermal conductivities are $K_1$ and $K_2$ respectively. The temperatures at the ends of each rod are $\mathrm{T}_1$ and $\mathrm{T}_2$. If the rate of flow of heat through the rods is equal, the ratio of area of cross section of $A$ to that of $B$ is
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
The square of resultant of two equal electric field vectors is three times their product. Angle between them is
The square of resultant of two equal electric field vectors is three times their product. Angle between them is
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
The nucleus of oxygen atom contains 8 protons and 8 neutrons. What is the mass defect in amu? [Given Mass of proton $=1.00727 \mathrm{amu}$ Mass of neutron $=1.00866 \mathrm{amu}$ and the mass of oxygen nucleus $=15.99053 \mathrm{amu}$. ]
The nucleus of oxygen atom contains 8 protons and 8 neutrons. What is the mass defect in amu? [Given Mass of proton $=1.00727 \mathrm{amu}$ Mass of neutron $=1.00866 \mathrm{amu}$ and the mass of oxygen nucleus $=15.99053 \mathrm{amu}$. ]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $\mathrm{T}_2$ by releasing the piston suddenly. If $L$ and $2 L$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is
A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $\mathrm{T}_2$ by releasing the piston suddenly. If $L$ and $2 L$ are the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
Time period of oscillation of a mass suspended from a spring is T . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, the fractional change in time period is
Time period of oscillation of a mass suspended from a spring is T . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, the fractional change in time period is
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Ten cells, each having internal resistance $1 \Omega$ and emf 1.5 V are connected in series. But unknowingly 3 cells are connected wrongly in series. The effective internal resistance and emf of the series combination are respectively:
Ten cells, each having internal resistance $1 \Omega$ and emf 1.5 V are connected in series. But unknowingly 3 cells are connected wrongly in series. The effective internal resistance and emf of the series combination are respectively:
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
A galvanometer of $50 \Omega$ resistance is converted into an ammeter using a shunt resistance of $10 \Omega$. If the same resistance is used to convert the same galvanometer in to a voltmeter, what would be the ratio of the resistance of the ammeter to the resistance of the voltmeter?
A galvanometer of $50 \Omega$ resistance is converted into an ammeter using a shunt resistance of $10 \Omega$. If the same resistance is used to convert the same galvanometer in to a voltmeter, what would be the ratio of the resistance of the ammeter to the resistance of the voltmeter?
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
A gun is used to fire a bullet at an angle of $30^{\circ}$ and at $60^{\circ}$ respectively. The ratios of heights and Ranges reached by the bullet are
A gun is used to fire a bullet at an angle of $30^{\circ}$ and at $60^{\circ}$ respectively. The ratios of heights and Ranges reached by the bullet are
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
Diamond is considered as an insulator because
Diamond is considered as an insulator because
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
A ray of light is travelling from glass of refractive index $\frac{3}{2}$ to water of refractive Index $\frac{4}{3}$. What is the minimum angle of incidence for which no light enters in to the water?
A ray of light is travelling from glass of refractive index $\frac{3}{2}$ to water of refractive Index $\frac{4}{3}$. What is the minimum angle of incidence for which no light enters in to the water?
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
An ideal gas is expanding such that $P T^2=$ constant. The coefficient of volume expansion of the gas is
An ideal gas is expanding such that $P T^2=$ constant. The coefficient of volume expansion of the gas is
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
The focal lengths of the objective and eyepiece of a compound microscope are 1 cm and 10 cm respectively. Length of the tube is 25 cm . If the final image is formed at infinity , the magnifying power of the microscope is :
The focal lengths of the objective and eyepiece of a compound microscope are 1 cm and 10 cm respectively. Length of the tube is 25 cm . If the final image is formed at infinity , the magnifying power of the microscope is :
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would
If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface would
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
The resistance of the conductor is $\sqrt{3} \Omega$ the angle made by the V-I graph with the voltage axis is $\theta$
The resistance of the conductor is $\sqrt{3} \Omega$ the angle made by the V-I graph with the voltage axis is $\theta$
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
A body weighing 125 kg just slides down a rough inclined plane that rises 1 m in every 2 m . What is the coefficient of friction?
A body weighing 125 kg just slides down a rough inclined plane that rises 1 m in every 2 m . What is the coefficient of friction?
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
In which of the following circuit do we find the current and voltage in phase?
In which of the following circuit do we find the current and voltage in phase?
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
When a dielectric slab of dielectric constant $\mathrm{k}=2$ is used to fill the space between the plates of a parallel plate capacitor, the capacitance of the capacitor is found to be $20 \mu \mathrm{~F}$. What will be the capacitance when the slab is replaced with air?
When a dielectric slab of dielectric constant $\mathrm{k}=2$ is used to fill the space between the plates of a parallel plate capacitor, the capacitance of the capacitor is found to be $20 \mu \mathrm{~F}$. What will be the capacitance when the slab is replaced with air?
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
de Broglie wave length associated with an electron accelerated through a potential difference ' V ' is ' $\lambda$ '. If the accelerating potential is halved, what will be the new wave length associated with the charged particle?
de Broglie wave length associated with an electron accelerated through a potential difference ' V ' is ' $\lambda$ '. If the accelerating potential is halved, what will be the new wave length associated with the charged particle?
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
An open pipe is in second harmonic with frequency $f_1$. One end of the tube is closed and frequency is increased to $f_2$ and it resonates again with nth harmonic. For what value of n , the ratio of $\frac{f_1}{f_2}$ is $\frac{4}{5}$ ?
An open pipe is in second harmonic with frequency $f_1$. One end of the tube is closed and frequency is increased to $f_2$ and it resonates again with nth harmonic. For what value of n , the ratio of $\frac{f_1}{f_2}$ is $\frac{4}{5}$ ?
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
Across the 220 V source of internal resistance $20 \Omega$, how many lamps of $40 \mathrm{~W}, 100 \mathrm{~V}$ can be connected in parallel so that all the lamps may glow with full brightness.
Across the 220 V source of internal resistance $20 \Omega$, how many lamps of $40 \mathrm{~W}, 100 \mathrm{~V}$ can be connected in parallel so that all the lamps may glow with full brightness.
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
In the expression $\mathrm{P}=\mathrm{El}^2 \mathrm{~m}^{-5} \mathrm{G}^{-2}$ where $\mathrm{E}, 1, \mathrm{~m}$ and G represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of P are
In the expression $\mathrm{P}=\mathrm{El}^2 \mathrm{~m}^{-5} \mathrm{G}^{-2}$ where $\mathrm{E}, 1, \mathrm{~m}$ and G represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of P are
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
The separation between C and O atoms in CO is 0.12 nm . The distance of C atom from the centre of mass is
The separation between C and O atoms in CO is 0.12 nm . The distance of C atom from the centre of mass is
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
An EM wave of frequency $5 \times 10^9 \mathrm{~Hz}$ falls normally on a rectangular slit of width 3 cm . What is the total angular width of the central maxima?
An EM wave of frequency $5 \times 10^9 \mathrm{~Hz}$ falls normally on a rectangular slit of width 3 cm . What is the total angular width of the central maxima?
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
Two wires A and B made of same material having length 10 cm and 40 cm respectively are connected in parallel to the same source of emf 10 V . What will be the ratio of the drift velocity of the electrons in the wire $A$ to the drift velocity in the wire $B$ ?
Two wires A and B made of same material having length 10 cm and 40 cm respectively are connected in parallel to the same source of emf 10 V . What will be the ratio of the drift velocity of the electrons in the wire $A$ to the drift velocity in the wire $B$ ?
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
When a metallic spherical shell of radius 20 cm is charged, the potential on its surface is found to be 5 V . The potential at a point 10 cm from the centre of the spherical shell is :
When a metallic spherical shell of radius 20 cm is charged, the potential on its surface is found to be 5 V . The potential at a point 10 cm from the centre of the spherical shell is :
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
What is the maximum wave length of EM radiation required to move an electron from the valance band to conduction band of a semiconductor? [Given :Energy gap $\mathrm{E}_{\mathrm{g}}=1.98 \times 10^{-19} \mathrm{~J}$; Planck's constant $h=6.6 \times 10^{-34} \mathrm{Js}$ ]
What is the maximum wave length of EM radiation required to move an electron from the valance band to conduction band of a semiconductor? [Given :Energy gap $\mathrm{E}_{\mathrm{g}}=1.98 \times 10^{-19} \mathrm{~J}$; Planck's constant $h=6.6 \times 10^{-34} \mathrm{Js}$ ]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
What should be the value of the inductance of the coil which is to be connected to 220 V , 50 Hz supply so that maximum current of $3 \sqrt{2} A$ flows through the circuit ?
What should be the value of the inductance of the coil which is to be connected to 220 V , 50 Hz supply so that maximum current of $3 \sqrt{2} A$ flows through the circuit ?
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
In the Young's double slit experiment, when a monochromatic light is used, fringe width obtained is 1 mm . If the wave length is halved and the slit width is doubled, what will be the new fringe width?
In the Young's double slit experiment, when a monochromatic light is used, fringe width obtained is 1 mm . If the wave length is halved and the slit width is doubled, what will be the new fringe width?
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
A monochromatic light of wave length $6000^{\circ} \mathrm{A}$ is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in $A$ is $\frac{1}{2}$ that of $B$. If the refractive index of $A$ is $\frac{4}{3}$, find the refractive index of $B$.
A monochromatic light of wave length $6000^{\circ} \mathrm{A}$ is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in $A$ is $\frac{1}{2}$ that of $B$. If the refractive index of $A$ is $\frac{4}{3}$, find the refractive index of $B$.
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
By connecting two given capacitors, a technician was able to make two new capacitors having the effective capacitance $12.5 \mu \mathbf{F}$ and $2 \mu \mathbf{F}$. What would be the capacitance of the given capacitors?
By connecting two given capacitors, a technician was able to make two new capacitors having the effective capacitance $12.5 \mu \mathbf{F}$ and $2 \mu \mathbf{F}$. What would be the capacitance of the given capacitors?
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
A rectangular coil of length 10 cm and breadth 9 cm carries a current of 10 A . A long straight conductor carrying a current of 20 A is placed 1 cm from the coil parallel to its length and in the same plane of the coil. What will be the net force acting on the straight conductor?
A rectangular coil of length 10 cm and breadth 9 cm carries a current of 10 A . A long straight conductor carrying a current of 20 A is placed 1 cm from the coil parallel to its length and in the same plane of the coil. What will be the net force acting on the straight conductor?
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
For a short magnet, the magnetic field on the axial line at a distance 10 cm from its centre is $1.6 \mathrm{~m} \times 10^{-7} \mathrm{~T}$. What is the magnetic field on its equatorial line at the same distance 10 cm from its centre?
For a short magnet, the magnetic field on the axial line at a distance 10 cm from its centre is $1.6 \mathrm{~m} \times 10^{-7} \mathrm{~T}$. What is the magnetic field on its equatorial line at the same distance 10 cm from its centre?
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
What is the kinetic energy of the electron in the nth level, moving in a plane under the influence of a magnetic field ' B '? [ m -mass of electron; h - Planck's constant; e- electronic charge]
What is the kinetic energy of the electron in the nth level, moving in a plane under the influence of a magnetic field ' B '? [ m -mass of electron; h - Planck's constant; e- electronic charge]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
Which of the following statement is wrong regarding the photo electric effect.
Which of the following statement is wrong regarding the photo electric effect.
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
What is the velocity of light in vacuum if the velocity of light in a medium of refractive index 1.2 is ' v ' $\mathrm{ms}^{-1}$ ?
What is the velocity of light in vacuum if the velocity of light in a medium of refractive index 1.2 is ' v ' $\mathrm{ms}^{-1}$ ?
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