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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
For \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), if \(A=\left[\begin{array}{cc}a & b \\ c & -a\end{array}\right]\) be such that A2= I, then:
For \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), if \(A=\left[\begin{array}{cc}a & b \\ c & -a\end{array}\right]\) be such that A2= I, then:
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If x = at4 and y = 2at2, then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) is equal to:
If x = at4 and y = 2at2, then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}\) is equal to:
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt

A random variable Xhas the following probability distribution:

X 0 1 2 otherwise
P(X) k 2k 3k 0

Then:

(A)\(\mathrm{k}=\frac{1}{6}\)

(B) \(P(X<2)=\frac{1}{2}\)

(C) \(\mathrm{E}(\mathrm{X})=\frac{3}{4}\)

(D) 

Choose the correct answer from the options given below:

A random variable Xhas the following probability distribution:

X 0 1 2 otherwise
P(X) k 2k 3k 0

Then:

(A)\(\mathrm{k}=\frac{1}{6}\)

(B) \(P(X<2)=\frac{1}{2}\)

(C) \(\mathrm{E}(\mathrm{X})=\frac{3}{4}\)

(D)

Choose the correct answer from the options given below:
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
If \(\left[\begin{array}{ll}1 & 3 \\ 4 & 5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right]=\left[\begin{array}{l}5 \\ 6\end{array}\right]\), then value of x is:
If \(\left[\begin{array}{ll}1 & 3 \\ 4 & 5\end{array}\right]\left[\begin{array}{l}x \\ 2\end{array}\right]=\left[\begin{array}{l}5 \\ 6\end{array}\right]\), then value of x is:
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Let f(x) = x3- 6x2+ 12x - 3, then at x = 2, f(x) has:
Let f(x) = x3- 6x2+ 12x - 3, then at x = 2, f(x) has:
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The integral of the function \(\frac{1}{9-4 x^2}\)is:
The integral of the function \(\frac{1}{9-4 x^2}\)is:
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
The interval, in which the function \(f(x)=\frac{3}{x}+\frac{x}{3}\) is strictly decreasing, is:
The interval, in which the function \(f(x)=\frac{3}{x}+\frac{x}{3}\) is strictly decreasing, is:
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

A pair of dice is rolled. If the two numbers appearing on them are different, the probability that Match List-I with List-II.

List-I
(Event)		List-II
(Probability)
(A)The sum of the numbers is greater than 11(I)0
(B)The sum of the numbers is 4 or less(Il)1/15
(C)The sum of the numbers is 4(llI)2/15
(D)The sum of the numbers is 7(Iv)3/15

Choose the correct answer from the options given below:

A pair of dice is rolled. If the two numbers appearing on them are different, the probability that Match List-I with List-II.

List-I
(Event)		List-II
(Probability)
(A)The sum of the numbers is greater than 11(I)0
(B)The sum of the numbers is 4 or less(Il)1/15
(C)The sum of the numbers is 4(llI)2/15
(D)The sum of the numbers is 7(Iv)3/15

Choose the correct answer from the options given below:
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
The value of \(\mathrm{I}=\int_0^{1.5}\left[x^2\right] \mathrm{d} x\), where [ ] denotes the greatest integer function, is:
The value of \(\mathrm{I}=\int_0^{1.5}\left[x^2\right] \mathrm{d} x\), where [ ] denotes the greatest integer function, is:
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

Maximise Z = 9x + 3y

Subject to the constraints: x + 3y ≤ 60, x - y ≤ 0, x ≥ 0, y ≥ 0

If x = A, y = B is the optimum solution of the given LPP, then the value of A + B is:

Maximise Z = 9x + 3y

Subject to the constraints: x + 3y ≤ 60, x - y ≤ 0, x ≥ 0, y ≥ 0

If x = A, y = B is the optimum solution of the given LPP, then the value of A + B is:
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
The area (in square units) of the region bounded by curves y = x and y = x3 is:
The area (in square units) of the region bounded by curves y = x and y = x3 is:
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
The solution region of the inequality 2x + 4y ≤ 9 is:
The solution region of the inequality 2x + 4y ≤ 9 is:
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
If p, q, r are distinct, then value of \(\left|\begin{array}{lll}p & p^2 & 1+p^3 \\ q & q^2 & 1+q^3 \\ r & r^2 & 1+r^3\end{array}\right|\) is:
If p, q, r are distinct, then value of \(\left|\begin{array}{lll}p & p^2 & 1+p^3 \\ q & q^2 & 1+q^3 \\ r & r^2 & 1+r^3\end{array}\right|\) is:
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The degree and order of the differential equation\(\left(\frac{d^2 y}{d x^2}\right)^{4 / 5}=10 \frac{d y}{d x}+2\) are:
The degree and order of the differential equation\(\left(\frac{d^2 y}{d x^2}\right)^{4 / 5}=10 \frac{d y}{d x}+2\) are:
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The particular solution of the differential equation (y - x2y)dy = (1 - x3)dx with y(0) = 1, is:
The particular solution of the differential equation (y - x2y)dy = (1 - x3)dx with y(0) = 1, is:
Q.1 Correct
Q.1 In-correct
Q.1 Unattempt
Relation R on the set A = {1, 2, 3, ..........., 13, 14} defined as R = {(x, y) : 3x - y = 0} is:
Relation R on the set A = {1, 2, 3, ..........., 13, 14} defined as R = {(x, y) : 3x - y = 0} is:
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt
If \(A=\left[\begin{array}{rr}2 & 3 \\ 1 & -4\end{array}\right]\) and \(B=\left[\begin{array}{rr}1 & -2 \\ -1 & 3\end{array}\right]\), then B-1 A-1 is equal to:
If \(A=\left[\begin{array}{rr}2 & 3 \\ 1 & -4\end{array}\right]\) and \(B=\left[\begin{array}{rr}1 & -2 \\ -1 & 3\end{array}\right]\), then B-1 A-1 is equal to:
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
If (cos x)y= (sin y)x then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) is:
If (cos x)y= (sin y)x then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) is:
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt
A particle moves along the curve 6x = y3+ 2. The points on the curve at which the x coordinate is changing 8 times as fast as y coordinate are:
A particle moves along the curve 6x = y3+ 2. The points on the curve at which the x coordinate is changing 8 times as fast as y coordinate are:
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt
Area of the parallelogram, whose adjacent sides are given by the vectors \(\overrightarrow{\mathrm{a}}=2 \hat{i}-\hat{j}+5 \hat{k}\) and \(\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+2 \hat{k}\), is:
Area of the parallelogram, whose adjacent sides are given by the vectors \(\overrightarrow{\mathrm{a}}=2 \hat{i}-\hat{j}+5 \hat{k}\) and \(\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+2 \hat{k}\), is:
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt
The angle between the lines \(\vec{r}=3 \hat{i}-2 \hat{j}+1 \hat{k}+\mu(4 \hat{i}+6 \hat{j}+12 \hat{k})\) and \(\overrightarrow{\mathrm{r}}=7 \hat{i}-3 \hat{j}+9 \hat{k}+\lambda(5 \hat{i}+8 \hat{j}-4 \hat{k})\) is:
The angle between the lines \(\vec{r}=3 \hat{i}-2 \hat{j}+1 \hat{k}+\mu(4 \hat{i}+6 \hat{j}+12 \hat{k})\) and \(\overrightarrow{\mathrm{r}}=7 \hat{i}-3 \hat{j}+9 \hat{k}+\lambda(5 \hat{i}+8 \hat{j}-4 \hat{k})\) is:
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt
If P(A) = 0.4, P(B) = 0.8 and P(A|B) = 0.6, then P(A ∪ B) is:
If P(A) = 0.4, P(B) = 0.8 and P(A|B) = 0.6, then P(A ∪ B) is:
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

Let f : \(\mathbb{R} \rightarrow \mathbb{R}\) be defined as f(x) = 10 - x2, then:

Let f : \(\mathbb{R} \rightarrow \mathbb{R}\) be defined as f(x) = 10 - x2, then:
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
The domain of f(x) = cos-17x is:
The domain of f(x) = cos-17x is:
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt
For a, b > 0, if \(\mathrm{P}=\left[\begin{array}{cc}0 & -\mathrm{a} \\ 2 \mathrm{a} & \mathrm{b}\end{array}\right]\) and \(\mathrm{Q}=\left[\begin{array}{cc}\mathrm{b} & \mathrm{a} \\ -\mathrm{b} & 0\end{array}\right]\) are two matrices such that \(P Q=\left[\begin{array}{ll}2 & 0 \\ 3 & 8\end{array}\right]\), then the value of (a + b)ab is:
For a, b > 0, if \(\mathrm{P}=\left[\begin{array}{cc}0 & -\mathrm{a} \\ 2 \mathrm{a} & \mathrm{b}\end{array}\right]\) and \(\mathrm{Q}=\left[\begin{array}{cc}\mathrm{b} & \mathrm{a} \\ -\mathrm{b} & 0\end{array}\right]\) are two matrices such that \(P Q=\left[\begin{array}{ll}2 & 0 \\ 3 & 8\end{array}\right]\), then the value of (a + b)ab is:
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt
If \(\mathrm{A}=\left[\begin{array}{cc}2 & 4 \\ x & \frac{-1}{2}\end{array}\right]\) and A is singular, then x is equal to:
If \(\mathrm{A}=\left[\begin{array}{cc}2 & 4 \\ x & \frac{-1}{2}\end{array}\right]\) and A is singular, then x is equal to:
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt
If \(y=\frac{1}{\sqrt{1-4 \sin ^2 x \cos ^2 x}}\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\)
If \(y=\frac{1}{\sqrt{1-4 \sin ^2 x \cos ^2 x}}\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\)
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt
The value of \(\int_{-1}^1\left|\tan ^{-1} x\right| d x\) is:
The value of \(\int_{-1}^1\left|\tan ^{-1} x\right| d x\) is:
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt
The area (in square units) bounded by the curve y = |x - 2| between x = 0, y = 0 and x = 5 is:
The area (in square units) bounded by the curve y = |x - 2| between x = 0, y = 0 and x = 5 is:
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt
The area (in square units) enclosed between the curve x2= 4y and the line x = y is:
The area (in square units) enclosed between the curve x2= 4y and the line x = y is:
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt
If the solution of differential equation \(\frac{d y}{d x}=\frac{a x+3}{2 y+5}\) represents a circle, then a is equal to:
If the solution of differential equation \(\frac{d y}{d x}=\frac{a x+3}{2 y+5}\) represents a circle, then a is equal to:
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt

Match List-I with List-II:

List-IList-II
(A)\(4 \hat{i}-2 \hat{j}-4 \hat{k}\)(I)A vector perpendicular to both \(\hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{i}+2 \hat{j}+3 \hat{k}\)
(B)\(-4 \hat{i}-4 \hat{j}+2 \hat{k}\)(lI)Direction ratios are-2, 1, 2
(C)\(2 \hat{i}-4 \hat{j}+4 \hat{k}\)(Ill)Angle with the vector \(\hat{i}-2 \hat{j}-\hat{k}\) is \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\)
(D)\(4 \hat{i}-\hat{j}-2 \hat{k}\)(Iv)Dot product with \(-2 \hat{i}+\hat{j}+3 \hat{k}\) is 10

Choose the correct answer from the options given below:

Match List-I with List-II:

List-IList-II
(A)\(4 \hat{i}-2 \hat{j}-4 \hat{k}\)(I)A vector perpendicular to both \(\hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{i}+2 \hat{j}+3 \hat{k}\)
(B)\(-4 \hat{i}-4 \hat{j}+2 \hat{k}\)(lI)Direction ratios are-2, 1, 2
(C)\(2 \hat{i}-4 \hat{j}+4 \hat{k}\)(Ill)Angle with the vector \(\hat{i}-2 \hat{j}-\hat{k}\) is \(\cos ^{-1}\left(\frac{1}{\sqrt{6}}\right)\)
(D)\(4 \hat{i}-\hat{j}-2 \hat{k}\)(Iv)Dot product with \(-2 \hat{i}+\hat{j}+3 \hat{k}\) is 10

Choose the correct answer from the options given below:
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

A die is thrown three times. Events A and B are defined as below

A: 6 on the third throw

B: 4 on the first and 5 on the second throw

The probability of Agiven that Bhas already occurred, is:

A die is thrown three times. Events A and B are defined as below

A: 6 on the third throw

B: 4 on the first and 5 on the second throw

The probability of Agiven that Bhas already occurred, is:
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt
Let A be a matrix such that A2= I, where I is an identity matrix, then (I + A)4- 8A is equal to:
Let A be a matrix such that A2= I, where I is an identity matrix, then (I + A)4- 8A is equal to:
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
For \(f(x)=\int \frac{\mathrm{e}^x}{\sqrt{4-\mathrm{e}^{2 x}}} \mathrm{~d} x\), if the point \(\left(0, \frac{\pi}{2}\right)\)satisfies y = f(x), then the constant of integration of the given integral is:
For \(f(x)=\int \frac{\mathrm{e}^x}{\sqrt{4-\mathrm{e}^{2 x}}} \mathrm{~d} x\), if the point \(\left(0, \frac{\pi}{2}\right)\)satisfies y = f(x), then the constant of integration of the given integral is:
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt

The equation of line passing through origin and parallel to the line \(\overrightarrow{\mathbf{r}}=3 \hat{i}+4 \hat{j}-5 \hat{k}+\mathrm{t}(2 \hat{i}-\hat{j}+7 \hat{k})\), where t is a parameter, is:

(A) \(\frac{x}{2}=\frac{y}{-1}=\frac{z}{7}\)

(B) \(\overrightarrow{\mathrm{r}}=\mathrm{m}(12 \hat{i}-6 \hat{j}+42 \hat{k})\); where m is the parameter

(C) \(\overrightarrow{\mathbf{r}}=(12 \hat{i}-6 \hat{j}+42 \hat{k})+\mathrm{s}(0 \hat{i}-0 \hat{j}+0 \hat{k})\); where s is the parameter

(D) \(\frac{x-3}{0}=\frac{y-4}{0}=\frac{z+5}{0}\)

(E) \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)

Choose the correct answer from the options given below:

The equation of line passing through origin and parallel to the line \(\overrightarrow{\mathbf{r}}=3 \hat{i}+4 \hat{j}-5 \hat{k}+\mathrm{t}(2 \hat{i}-\hat{j}+7 \hat{k})\), where t is a parameter, is:

(A) \(\frac{x}{2}=\frac{y}{-1}=\frac{z}{7}\)

(B) \(\overrightarrow{\mathrm{r}}=\mathrm{m}(12 \hat{i}-6 \hat{j}+42 \hat{k})\); where m is the parameter

(C) \(\overrightarrow{\mathbf{r}}=(12 \hat{i}-6 \hat{j}+42 \hat{k})+\mathrm{s}(0 \hat{i}-0 \hat{j}+0 \hat{k})\); where s is the parameter

(D) \(\frac{x-3}{0}=\frac{y-4}{0}=\frac{z+5}{0}\)

(E) \(\frac{x}{3}=\frac{y}{4}=\frac{z}{5}\)

Choose the correct answer from the options given below:
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt

\(A=\left[\begin{array}{rrr}0 & \alpha & \beta \\ -\alpha & 0 & \gamma \\ -\beta & -\gamma & 0\end{array}\right]\) is a

(A) square matrix

(B) diagonal matrix

(C) symmetric matrix

(D) skew-symmetric matrix

Choose the correct answer from the options given below:

\(A=\left[\begin{array}{rrr}0 & \alpha & \beta \\ -\alpha & 0 & \gamma \\ -\beta & -\gamma & 0\end{array}\right]\) is a

(A) square matrix

(B) diagonal matrix

(C) symmetric matrix

(D) skew-symmetric matrix

Choose the correct answer from the options given below:
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
The integrating factor of the differential equation \(\left(y \log _{\mathbf{e}} y\right) \frac{d x}{d y}+x=2 \log _{\mathbf{e}} y\) is:
The integrating factor of the differential equation \(\left(y \log _{\mathbf{e}} y\right) \frac{d x}{d y}+x=2 \log _{\mathbf{e}} y\) is:
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt

Optimise Z = 3x + 9y subject to the constraints:

x + 3y ≤ 60, x + y ≥ 10, x ≤ y, x ≥ 0, y ≥ 0, then

Optimise Z = 3x + 9y subject to the constraints:

x + 3y ≤ 60, x + y ≥ 10, x ≤ y, x ≥ 0, y ≥ 0, then
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt

Minimise Z = -50x + 20y

subject to the constraints: 2x - y ≥ -5, 3x + y ≥ 3, 2x - 3y ≤ 12, x ≥ 0, y ≥ 0.

Then which of the following is/are true:

(A) Feasible region is unbounded.

(B) Z has no minimum value.

(C) The minimum value of Z is 100.

(D) The minimum value of Z is -300.

Choose the correct answer from the options given below:

Minimise Z = -50x + 20y

subject to the constraints: 2x - y ≥ -5, 3x + y ≥ 3, 2x - 3y ≤ 12, x ≥ 0, y ≥ 0.

Then which of the following is/are true:

(A) Feasible region is unbounded.

(B) Z has no minimum value.

(C) The minimum value of Z is 100.

(D) The minimum value of Z is -300.

Choose the correct answer from the options given below:
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
If the system of linear equations x + y + z = 2, 2x + y - z = 3 and 3x + 2y + kz = 4 has a unique solution, then:
If the system of linear equations x + y + z = 2, 2x + y - z = 3 and 3x + 2y + kz = 4 has a unique solution, then:
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
The function f(x) = ||x| + 1 - x| is:
The function f(x) = ||x| + 1 - x| is:
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt

Match List-I with List-II.

List-I
(Function)		List-II
(Interval in which function is increasing)
(A)\(\frac{x}{\log _{\mathrm{e}} x}\)(I)(-∞, -2) ∪ (2, ∞)
(B)\(\frac{x}{2}+\frac{2}{x}, x \neq 0\)(lI)\(\left(-\frac{\pi}{4}, \frac{\pi}{4}\right)\)
(C)xx, x > 0(llI)\(\left(\frac{1}{\mathrm{e}}, ∞\right)\)
(D)sinx - cosx(IV)(e, ∞)

Choose the correct answer from the options given below:

Match List-I with List-II.

List-I
(Function)		List-II
(Interval in which function is increasing)
(A)\(\frac{x}{\log _{\mathrm{e}} x}\)(I)(-∞, -2) ∪ (2, ∞)
(B)\(\frac{x}{2}+\frac{2}{x}, x \neq 0\)(lI)\(\left(-\frac{\pi}{4}, \frac{\pi}{4}\right)\)
(C)xx, x > 0(llI)\(\left(\frac{1}{\mathrm{e}}, ∞\right)\)
(D)sinx - cosx(IV)(e, ∞)

Choose the correct answer from the options given below:
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
The value of \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\mathrm{~d} x}{1+\tan ^{18} x}\) is:
The value of \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\mathrm{~d} x}{1+\tan ^{18} x}\) is:
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt

If the angle between \(\overrightarrow{\mathrm{a}}=2 y^2 \hat{i}+4 y \hat{j}+\hat{\mathrm{k}}\) and\(\overrightarrow{\mathrm{b}}=7 \hat{i}-2 \hat{j}+y \hat{\mathrm{k}}\) is obtuse, then:

If the angle between \(\overrightarrow{\mathrm{a}}=2 y^2 \hat{i}+4 y \hat{j}+\hat{\mathrm{k}}\) and\(\overrightarrow{\mathrm{b}}=7 \hat{i}-2 \hat{j}+y \hat{\mathrm{k}}\) is obtuse, then:
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
Two events X and Y are such that \(P(X)=\frac{1}{3}, P(Y)=n\) and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of n is:
Two events X and Y are such that \(P(X)=\frac{1}{3}, P(Y)=n\) and the probability of occurrence of at least one event is 0.8. If the events are independent, then the value of n is:
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
The shortest distance (in units) between the lines \(\frac{1-x}{1}=\frac{2 y-10}{2}=\frac{z+1}{1}\) and \(\frac{x-3}{-1}=\frac{y-5}{1}=\frac{z-0}{1}\) is:
The shortest distance (in units) between the lines \(\frac{1-x}{1}=\frac{2 y-10}{2}=\frac{z+1}{1}\) and \(\frac{x-3}{-1}=\frac{y-5}{1}=\frac{z-0}{1}\) is:
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
The value of λ for which the lines \(\frac{2-x}{3}=\frac{3-4 y}{5}=\frac{z-2}{3}\) and \(\frac{x-2}{-3}=\frac{2 y-4}{3}=\frac{2-z}{λ}\) are perpendicular is:
The value of λ for which the lines \(\frac{2-x}{3}=\frac{3-4 y}{5}=\frac{z-2}{3}\) and \(\frac{x-2}{-3}=\frac{2 y-4}{3}=\frac{2-z}{λ}\) are perpendicular is:
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt

Let Aand Bare two independent events such that \(P(A)=\frac{3}{5}\) and \(P(B)=\frac{4}{9}\).

Match List-I with List-II

List-IList-II
(A)P(A ∩ B)(I)\(\frac{\mathrm{2}}{5}\)
(B)P(A | B)(Il)\(\frac{4}{15}\)
(C)P(A' | B)(Ill)\(\frac{3}{5}\)
(D)P(A' ∩ B')(IV)\(\frac{2}{9}\)

Choose the correct answer from the options given below:

Let Aand Bare two independent events such that \(P(A)=\frac{3}{5}\) and \(P(B)=\frac{4}{9}\).

Match List-I with List-II

List-IList-II
(A)P(A ∩ B)(I)\(\frac{\mathrm{2}}{5}\)
(B)P(A | B)(Il)\(\frac{4}{15}\)
(C)P(A' | B)(Ill)\(\frac{3}{5}\)
(D)P(A' ∩ B')(IV)\(\frac{2}{9}\)

Choose the correct answer from the options given below:
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
If \(\mathrm{P}=\left[\begin{array}{rr}5 & 3 \\ -1 & -2\end{array}\right]\) satisfies the equation P2- 3P - 7l = 0, where I is an identity matrix of order 2, then P-1 is:
If \(\mathrm{P}=\left[\begin{array}{rr}5 & 3 \\ -1 & -2\end{array}\right]\) satisfies the equation P2- 3P - 7l = 0, where I is an identity matrix of order 2, then P-1 is:
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