AP EAPCET - 06 July 2022

x	1	2
2	4	x
−3	3	2

] is a singular matrix and the distinct values of x are x1 and x2, then x1+x2+x1x2=

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If A=[

x	1	2
2	4	x
−3	3	2

] is a singular matrix and the distinct values of x are x1 and x2, then x1+x2+x1x2=

If the system of simultaneous linear equations 3x−4y+kz+13=0,x+2y−z−9=0 and kx−y+3z+7=0 has a unique solution x=α,y=β,z=γ for k≠m and 2β−γ=8 then α+m =

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If the system of simultaneous linear equations 3x−4y+kz+13=0,x+2y−z−9=0 and kx−y+3z+7=0 has a unique solution x=α,y=β,z=γ for k≠m and 2β−γ=8 then α+m =

sin‌α	−cos‌α
cos‌α	sin‌α

] and A+A−1=I, then α=

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If A=[

sin‌α	−cos‌α
cos‌α	sin‌α

] and A+A−1=I, then α=

1	0	−1	−3
0	1	1	k−1
0	0	k−1	1

] and k∈R. Then the value of k, if exists, for which the rank of A is 2 , is

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Let A=[

1	0	−1	−3
0	1	1	k−1
0	0	k−1	1

] and k∈R. Then the value of k, if exists, for which the rank of A is 2 , is

For any complex number z, the minimum value of |z|+|z−1| is

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For any complex number z, the minimum value of |z|+|z−1| is

If the vertices A,B and C of an isosceles triangle ABC are respectively z1,z2 and z3 and if ∠C=90∘, then

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If the vertices A,B and C of an isosceles triangle ABC are respectively z1,z2 and z3 and if ∠C=90∘, then

If α1,α2,............α23 are the 23‌rd ‌ roots of unity, then α147+α247+⋯....+α2347=

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If α1,α2,............α23 are the 23‌rd ‌ roots of unity, then α147+α247+⋯....+α2347=

The sum of squares of roots of the equation x‌

The sum of squares of roots of the equation x‌

If a,b,c,d are real numbers such that a<b<c<d, then the roots of the equation (x−a)(x−c)+2(x−b)(x−d)=0 are

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If a,b,c,d are real numbers such that a<b<c<d, then the roots of the equation (x−a)(x−c)+2(x−b)(x−d)=0 are

If one root of the quadratic equation ax2+bx+c=0 is equal to the n‌th ‌ power of the other, then (acn)1/n+1+(anc)1/n+1=

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If one root of the quadratic equation ax2+bx+c=0 is equal to the n‌th ‌ power of the other, then (acn)1/n+1+(anc)1/n+1=

If a,b,c are distinct positive real numbers and a2+b2+c2=1, the the value of ab+bc+ca is

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If a,b,c are distinct positive real numbers and a2+b2+c2=1, the the value of ab+bc+ca is

In how many ways can the letters of the word "ASSASSNATION" can be arranged so that all S's are together?

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In how many ways can the letters of the word "ASSASSNATION" can be arranged so that all S's are together?

Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10, then the value of n is:

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Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1−Tn=10, then the value of n is:

The number of numbers between 2000 and 5000 that can be formed with the digits 0,1,2,3,4 (repetition of digits not allowed) and are multiple of 3 is:

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The number of numbers between 2000 and 5000 that can be formed with the digits 0,1,2,3,4 (repetition of digits not allowed) and are multiple of 3 is:

How many numbers between 10 and 10,000 can be formed by using the digits 1,2,3,4,5, if no digit is repeated in any number?

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How many numbers between 10 and 10,000 can be formed by using the digits 1,2,3,4,5, if no digit is repeated in any number?

If the equivalent partial fraction of ‌

, then the value of C is

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If the equivalent partial fraction of ‌

, then the value of C is

If θ is any angle, then sin2θcos2θ=

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If θ is any angle, then sin2θcos2θ=

(4cos29∘−3)(4cos2270−3)=

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(4cos29∘−3)(4cos2270−3)=

=

=

cos245∘+cos2135∘+cos2225∘+cos2315∘=

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cos245∘+cos2135∘+cos2225∘+cos2315∘=

Let θ∈R such that 3‌sinh(2θ)=13−3e2θ, then θ=

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Let θ∈R such that 3‌sinh(2θ)=13−3e2θ, then θ=

=

=

In a triangle ABC, if ∠A=60∘, then ‌

=

In a triangle ABC, if ∠A=60∘, then ‌

=

In a triangle ABC, if a‌cos‌A=b‌cos‌B, where a≠b, then △ABC is

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In a triangle ABC, if a‌cos‌A=b‌cos‌B, where a≠b, then △ABC is

The vectors a=2i+3j+6k and b are collinear and |b|=21, then b=

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The vectors a=2i+3j+6k and b are collinear and |b|=21, then b=

In a trapezium ABCD,BC=λAD and x=AC+BD. If x=pAD then p=

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In a trapezium ABCD,BC=λAD and x=AC+BD. If x=pAD then p=

|=c and CD is the median through the vertex C. Then CA⋅CD=

|=c and CD is the median through the vertex C. Then CA⋅CD=

If a=i+j+k,c=j−k,a×b=c and a⋅b=3 then b=

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If a=i+j+k,c=j−k,a×b=c and a⋅b=3 then b=

Let P be a real number and |P|≥2. If A,B,C are variable angles such that (√P2−4)‌tan‌A+P‌tan‌B+(√P2+4)‌tan‌C=6P, then the minimum value of tan2A+tan2B+tan2C=

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Let P be a real number and |P|≥2. If A,B,C are variable angles such that (√P2−4)‌tan‌A+P‌tan‌B+(√P2+4)‌tan‌C=6P, then the minimum value of tan2A+tan2B+tan2C=

If the variance of four numbers w,x,y and z is 9 , then the variance of 5w,5x,5y and 5z is

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If the variance of four numbers w,x,y and z is 9 , then the variance of 5w,5x,5y and 5z is

Two dice are rolled. Then, the probability that the total score is a prime number is

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Two dice are rolled. Then, the probability that the total score is a prime number is

An unbiased dice with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is:

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An unbiased dice with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is:

A bag contains 19 red balls and 19 black balls. Two balls are chosen at a time repeatedly and discarded if they are of the same color, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is:

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A bag contains 19 red balls and 19 black balls. Two balls are chosen at a time repeatedly and discarded if they are of the same color, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is:

An unbiased coin is tossed 3 times. If the third toss gets head, then the probability of getting at least one more head is

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An unbiased coin is tossed 3 times. If the third toss gets head, then the probability of getting at least one more head is

A discrete random variable X has the distribution B(15,p). Given that Var(X)=3.15. Then the two possible values of p are

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A discrete random variable X has the distribution B(15,p). Given that Var(X)=3.15. Then the two possible values of p are

When success is not an impossible event, then the mean of Binomial distribution is

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When success is not an impossible event, then the mean of Binomial distribution is

A variable line passing through (l,m) intersects the coordinate axes at the points A and B. If the lines drawn parallel to y-axis through A and parallel to x-axis through B meet at P, then the locus of P is

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A variable line passing through (l,m) intersects the coordinate axes at the points A and B. If the lines drawn parallel to y-axis through A and parallel to x-axis through B meet at P, then the locus of P is

The triangle with vertices at (−2,2),(2,−2) and (1,1) is

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The triangle with vertices at (−2,2),(2,−2) and (1,1) is

For the three points A(2,0),B(0,2) and P(1,1), suppose d is the algebraic sum of the distances of A and B from a line that passes through P. Then which of the following is correct?

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For the three points A(2,0),B(0,2) and P(1,1), suppose d is the algebraic sum of the distances of A and B from a line that passes through P. Then which of the following is correct?

Number of triangles formed by the lines x−y+3=0,2x−y+3=0,3x−y+2=0 and x+y−3=0 is

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Number of triangles formed by the lines x−y+3=0,2x−y+3=0,3x−y+2=0 and x+y−3=0 is

The two pairs of straight lines 12x2+7xy−12y2=0 and 12x2+7xy−12y2−x+7y−1=0 constitute a

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The two pairs of straight lines 12x2+7xy−12y2=0 and 12x2+7xy−12y2−x+7y−1=0 constitute a

The distance between the lines represented by 4x2+20xy+25y2+2x+5y−12=0 is equal to

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The distance between the lines represented by 4x2+20xy+25y2+2x+5y−12=0 is equal to

If the circle x2+y2+2αx+c=0 lies completely inside the circle x2+y2+2βx+c=0, then which of the following holds ?

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If the circle x2+y2+2αx+c=0 lies completely inside the circle x2+y2+2βx+c=0, then which of the following holds ?

If the line 3x−4y=1 touches the circle (x−1)2+(y+2)2=4 at (α,β), the values of α and β are

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If the line 3x−4y=1 touches the circle (x−1)2+(y+2)2=4 at (α,β), the values of α and β are

The equation of a tangent to the circle x2+y2=1, which is perpendicular to the line y=mx+1, is

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The equation of a tangent to the circle x2+y2=1, which is perpendicular to the line y=mx+1, is

If the equation ax2+by2+2hxy+2gx+2fy+c=0 represents a circle passing through the origin, then

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If the equation ax2+by2+2hxy+2gx+2fy+c=0 represents a circle passing through the origin, then

The radical centre of the circles x2+y2+3x+2y+1=0,x2+y2−x+6y+5=0 and x2+y2+5x−8y+15=0 is

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The radical centre of the circles x2+y2+3x+2y+1=0,x2+y2−x+6y+5=0 and x2+y2+5x−8y+15=0 is

The length of the latus rectum of the parabola (x−2)2+(y−3)2=‌

The length of the latus rectum of the parabola (x−2)2+(y−3)2=‌

The values of λ, for which (λ,λ−2) lies inside the ellipse 4x2+9y2=36 and outside the parabola y2=x, satisfy

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The values of λ, for which (λ,λ−2) lies inside the ellipse 4x2+9y2=36 and outside the parabola y2=x, satisfy

Let x2+y2=16 be the equation of the auxiliary circle of a hyperbola ‌

=1 and let (4√2,3) be a point on the hyperbola. Then the eccentricity of the hyperbola is

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Let x2+y2=16 be the equation of the auxiliary circle of a hyperbola ‌

=1 and let (4√2,3) be a point on the hyperbola. Then the eccentricity of the hyperbola is

The distance between the tangent lines to the hyperbola x2−2y2=18 which are perpendicular to the line y=x is

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The distance between the tangent lines to the hyperbola x2−2y2=18 which are perpendicular to the line y=x is

Let the centroid of a triangle formed by the points A(4,x,1),B(y,−5,2) and C(7,8,3) be G(3,5,2) and CG meet AB in F. Then F=

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Let the centroid of a triangle formed by the points A(4,x,1),B(y,−5,2) and C(7,8,3) be G(3,5,2) and CG meet AB in F. Then F=

If (l1,m1,n1) and (l2,m2,n2) are the direction cosines of two lines satisfying the relations l2+mn−6n2=0 and 2l−m+3n=0, then |l1l2|+|m1m2|=

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If (l1,m1,n1) and (l2,m2,n2) are the direction cosines of two lines satisfying the relations l2+mn−6n2=0 and 2l−m+3n=0, then |l1l2|+|m1m2|=

If (3,4,−7) is the foot of the perpendicular drawn from the point (−2,3,6) to the plane π then the sum of the intercepts made by the plane π on the x and y-axes is

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If (3,4,−7) is the foot of the perpendicular drawn from the point (−2,3,6) to the plane π then the sum of the intercepts made by the plane π on the x and y-axes is

)=

)=

((a−n)nx−tan‌x)‌sin‌n‌x

x2

=0, then minimum value of a is

((a−n)nx−tan‌x)‌sin‌n‌x

x2

=0, then minimum value of a is

=

=

\|x\|,	−∞<x<2
\|2x−4\|,	2≤x≤20.

x=a is a point where f(x) is continuous but not differentiable and x=b is a point where f(x) is not differentiable (a≠b). Then a+b=

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Let f(x)={

\|x\|,	−∞<x<2
\|2x−4\|,	2≤x≤20.

x=a is a point where f(x) is continuous but not differentiable and x=b is a point where f(x) is not differentiable (a≠b). Then a+b=

If x‌sin(α+y)=sin‌y and y=‌

If x‌sin(α+y)=sin‌y and y=‌

[. ] represents the greatest integer function. At x=−1,‌

[. ] represents the greatest integer function. At x=−1,‌

The angle between the tangents drawn at (0,0) to the curves y3−x2y+5y−2x=0 and x4−x3y2+5x+2y=0 is

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The angle between the tangents drawn at (0,0) to the curves y3−x2y+5y−2x=0 and x4−x3y2+5x+2y=0 is

The normal to the curve x=a(1+cos‌θ),y=a‌sin‌θ at θ always passes through a fixed point, then the fixed point is

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The normal to the curve x=a(1+cos‌θ),y=a‌sin‌θ at θ always passes through a fixed point, then the fixed point is

Two sides of a triangle are given. If the area of the triangle is maximum then the angle between the given sides is

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Two sides of a triangle are given. If the area of the triangle is maximum then the angle between the given sides is

For a particle moving on a straight line it is observed that the distance ' S ' at a time ' t ' is given by S=6t−‌

t3

2

. The maximum velocity during the motion is

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For a particle moving on a straight line it is observed that the distance ' S ' at a time ' t ' is given by S=6t−‌

t3

2

. The maximum velocity during the motion is

a, b, c, d, e, f, g, h be distinct elements in the set {−7,−5,−3,−2,2,4,6,13}. The minimum value of (a+b+c+d)2+(e+f+g+h)2 is

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a, b, c, d, e, f, g, h be distinct elements in the set {−7,−5,−3,−2,2,4,6,13}. The minimum value of (a+b+c+d)2+(e+f+g+h)2 is

∫√1+2‌cot‌x(cot‌x+cosecx)dx=

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∫√1+2‌cot‌x(cot‌x+cosecx)dx=

dx=

dx=

=

=

)

)

)dx=e−2log2e
Reason (R):

b

∫

a

ex(f(x)+f′(x))dx=ebf(b)−eaf(a)

)dx=e−2log2e
Reason (R):

b

∫

a

ex(f(x)+f′(x))dx=ebf(b)−eaf(a)

If f is continuous function and f(x+T)=f(x),∀x∈R, it is given that

f(t)dt(N is a natural number). Then

If f is continuous function and f(x+T)=f(x),∀x∈R, it is given that

f(t)dt(N is a natural number). Then

=k, then greatest integer less than or equal to k is

=k, then greatest integer less than or equal to k is

π2∕4(2‌sin‌√x+√x‌cos‌√x)dx=

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∫

0

π2∕4(2‌sin‌√x+√x‌cos‌√x)dx=

a,b,c,d are real numbers. The general solution of ‌

represents a family of straight lines, when

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a,b,c,d are real numbers. The general solution of ‌

represents a family of straight lines, when

=A‌log‌x+C is the general solution of (x‌sin‌

=A‌log‌x+C is the general solution of (x‌sin‌

Every curve represented by the general solution of ‌

=0 cuts every curve represented by the general solution of ‌

=0 at angle θ. Then 4θ−‌

π

2

=

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Every curve represented by the general solution of ‌

=0 cuts every curve represented by the general solution of ‌

=0 at angle θ. Then 4θ−‌

=

The expressions below give current I through an electronic component as a function of applied potential V. I0 and V0 are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?
a) I=I0(e‌

The expressions below give current I through an electronic component as a function of applied potential V. I0 and V0 are constants having dimensions of current and potential respectively. Which of the following are dimensionally incorrect?
a) I=I0(e‌

A ball is thrown upward from the ground with an initial speed of V. At the same instant, another ball is dropped from a building of height 20m. If the balls are at the same height after 0.8s, then the magnitude of V is (Take acceleration due to gravity =10ms−2 )

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A ball is thrown upward from the ground with an initial speed of V. At the same instant, another ball is dropped from a building of height 20m. If the balls are at the same height after 0.8s, then the magnitude of V is (Take acceleration due to gravity =10ms−2 )

In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has a radius 10m, then to achieve centripetal acceleration at a point on circumference as 10ms−2, its angular speed is

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In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has a radius 10m, then to achieve centripetal acceleration at a point on circumference as 10ms−2, its angular speed is

A player kicks a foot ball at an angle 30∘ with the horizontal with an initial speed 30ms−1. A second player standing at a distance of 21√3m from the first and in the direction of kick, starts running to catch the ball, at the same instant as kicked by first player. The minimum speed of second player to catch the ball before it hits the ground is
(Take acceleration due to gravity =10ms−2 )

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A player kicks a foot ball at an angle 30∘ with the horizontal with an initial speed 30ms−1. A second player standing at a distance of 21√3m from the first and in the direction of kick, starts running to catch the ball, at the same instant as kicked by first player. The minimum speed of second player to catch the ball before it hits the ground is
(Take acceleration due to gravity =10ms−2 )

A particle attached to a string of length r is moving on vertical circular path continuously. If the speed of the particle at the highest point is √7gr, then the ratio of the respective tension in the string holding it at the highest and the lowest points is (g-acceleration due to gravity)

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A particle attached to a string of length r is moving on vertical circular path continuously. If the speed of the particle at the highest point is √7gr, then the ratio of the respective tension in the string holding it at the highest and the lowest points is (g-acceleration due to gravity)

A boat of mass 700kg is travelling at a speed of 24ms−1 when its engine is shut off. The magnitude of frictional force f between boat and water is given as f=35v, where v is the speed in ms−1 and f is in newton. The speed of boat becomes 6ms−1 in time.

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A boat of mass 700kg is travelling at a speed of 24ms−1 when its engine is shut off. The magnitude of frictional force f between boat and water is given as f=35v, where v is the speed in ms−1 and f is in newton. The speed of boat becomes 6ms−1 in time.

A satellite is orbiting the earth. It's orbital radius is reduced to half of its initial value then the change in its total energy is

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A satellite is orbiting the earth. It's orbital radius is reduced to half of its initial value then the change in its total energy is

A force of 5N acts on a body initially at rest. If the instantaneous power due to the force at the end of the third second (t=3s) is 5W, then the mass of the body is

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A force of 5N acts on a body initially at rest. If the instantaneous power due to the force at the end of the third second (t=3s) is 5W, then the mass of the body is

m‌‌,...∞ are placed at x=1,2,3,...N,...∞ respectively. If the total mass is M then the centre of mass of the system is

m‌‌,...∞ are placed at x=1,2,3,...N,...∞ respectively. If the total mass is M then the centre of mass of the system is

A block of mass m is hanging by a rope tied to a rotating solid disc of mass M and radius R as shown in the figure. If α is the angular acceleration of the disc, then the linear acceleration of the block is
( g= acceleration due to gravity)

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A block of mass m is hanging by a rope tied to a rotating solid disc of mass M and radius R as shown in the figure. If α is the angular acceleration of the disc, then the linear acceleration of the block is
( g= acceleration due to gravity)

A particle undergoing simple harmonic motion has an amplitude of 10cm. When the particle is at a displacement of 6cm from the center, then the ratio of its kinetic energy to potential energy is

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A particle undergoing simple harmonic motion has an amplitude of 10cm. When the particle is at a displacement of 6cm from the center, then the ratio of its kinetic energy to potential energy is

An object is executing simple harmonic motion with an angular frequency ω. If the maximum velocity is vmax then the maximum acceleration of the object is

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An object is executing simple harmonic motion with an angular frequency ω. If the maximum velocity is vmax then the maximum acceleration of the object is

An object is thrown directly away from the surface of the earth with an initial speed V. The object reaches upto a height of ‌

4

5

RE from earth's surface, where RE is radius of the earth. If the escape velocity of the object is VE then the value of ‌

V

VE

is

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An object is thrown directly away from the surface of the earth with an initial speed V. The object reaches upto a height of ‌

4

5

RE from earth's surface, where RE is radius of the earth. If the escape velocity of the object is VE then the value of ‌

is

Statement (A): For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero.
Statement (B) : The volume contraction of a metal cube of bulk modulus 140GPa, 10cm on a edge, when subjected to a hydraulic pressure of 7×106Pa is −0.05m3
Statement (C) : A spiral spring is stretched by a weight attached to it. The strain is tensile.

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Statement (A): For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero.
Statement (B) : The volume contraction of a metal cube of bulk modulus 140GPa, 10cm on a edge, when subjected to a hydraulic pressure of 7×106Pa is −0.05m3
Statement (C) : A spiral spring is stretched by a weight attached to it. The strain is tensile.

A hydraulic lift is shown in the figure. The radii of the movable pistons P1 and P2 are 2m \& 5m respectively. If a block of mass x is placed on P2 then the minimum mass that should be kept on P1 to lift the block on P2 is

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A hydraulic lift is shown in the figure. The radii of the movable pistons P1 and P2 are 2m \& 5m respectively. If a block of mass x is placed on P2 then the minimum mass that should be kept on P1 to lift the block on P2 is

A block of wood of volume V floats in water with half of its volume submerged. The same block floats in an oil with 0.8V volume submerged. If the density of water is 1000kgm−3, then the density of the oil is

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A block of wood of volume V floats in water with half of its volume submerged. The same block floats in an oil with 0.8V volume submerged. If the density of water is 1000kgm−3, then the density of the oil is

A metal block of mass 3.3kg is heated to a temperature of 400∘C and then block is placed on a large ice block. The specific heat of the metal is 0.4Jg−1K−1 and heat of fusion of water is 330Jg−1. The maximum amount of ice that can melt is

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A metal block of mass 3.3kg is heated to a temperature of 400∘C and then block is placed on a large ice block. The specific heat of the metal is 0.4Jg−1K−1 and heat of fusion of water is 330Jg−1. The maximum amount of ice that can melt is

An ideal monatomic gas expands at constant pressure. The work done by the gas on its environment is 200J, then the heat absorbed by the gas during the process is

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An ideal monatomic gas expands at constant pressure. The work done by the gas on its environment is 200J, then the heat absorbed by the gas during the process is

A container of 10L is filled with an ideal gas at a temperature of 27∘C at a pressure 12atm. The volume of the container is reduced to 6L and the temperature of the gas in increased by 30∘C, then the final pressure of the gas is

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A container of 10L is filled with an ideal gas at a temperature of 27∘C at a pressure 12atm. The volume of the container is reduced to 6L and the temperature of the gas in increased by 30∘C, then the final pressure of the gas is

Assertion (A): When an ideal gas is compressed adiabatically its temperature and the average kinetic energy of the gas molecules increase.

Reason (R) : The kinetic energy increases because of collisions of molecules with moving parts of wall only.

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Assertion (A): When an ideal gas is compressed adiabatically its temperature and the average kinetic energy of the gas molecules increase.

Reason (R) : The kinetic energy increases because of collisions of molecules with moving parts of wall only.

Two open organ pipes of lengths 50cm and 51cm are totally immersed in a medium. They are found to give 40 beats in 10s when each is sounding at its fundamental note. The speed of sound in this medium is

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Two open organ pipes of lengths 50cm and 51cm are totally immersed in a medium. They are found to give 40 beats in 10s when each is sounding at its fundamental note. The speed of sound in this medium is

A screen is placed 100cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. The focal length of the lens is

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A screen is placed 100cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. The focal length of the lens is

A light ray is incident from a medium of refractive index 2 into a medium of refractive index √3. The critical angle is

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A light ray is incident from a medium of refractive index 2 into a medium of refractive index √3. The critical angle is

Four charges, each charge q coloumb are placed at points (−1,0,0),(1,0,0),(0,−1,0) and (0,1,0) in the xy - plane. The distances along the axes are measured in meters. The magnitude of the electric field at the point z=1m on the z− axis is

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Four charges, each charge q coloumb are placed at points (−1,0,0),(1,0,0),(0,−1,0) and (0,1,0) in the xy - plane. The distances along the axes are measured in meters. The magnitude of the electric field at the point z=1m on the z− axis is

A capacitor of capacitance C1=10µF to charged using 9V battery. It is then removed from the battery and connected to another capacitor C2=20µF as shown in the figure. The charge on C2 after equilibrium has reached is

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A capacitor of capacitance C1=10µF to charged using 9V battery. It is then removed from the battery and connected to another capacitor C2=20µF as shown in the figure. The charge on C2 after equilibrium has reached is

Two parallel plate capacitors 8µF each are connected in parallel to a 10V battery. The plate separation in one of the capacitor is reduced to 40% of its initial value. The increase in the total charge stored on the capacitors is

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Two parallel plate capacitors 8µF each are connected in parallel to a 10V battery. The plate separation in one of the capacitor is reduced to 40% of its initial value. The increase in the total charge stored on the capacitors is

A metal wire of 1cm length and 1mm radius has a resistance of 3×10−3Ω. If a wire of the same metal of length 3cm and radius 0.5mm is drawn, the resistance of the wire

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A metal wire of 1cm length and 1mm radius has a resistance of 3×10−3Ω. If a wire of the same metal of length 3cm and radius 0.5mm is drawn, the resistance of the wire

A galvanometer has a coil of resistance 100Ω showing a full scale deflection at 50µA. The resistance that should be added to use it as an ammeter of range 10mA is

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A galvanometer has a coil of resistance 100Ω showing a full scale deflection at 50µA. The resistance that should be added to use it as an ammeter of range 10mA is

Two infinitely long wires are placed at (1cm,1cm) and (+1cm,−1cm) with 1A current in each and in the same directions perpendicular to x−y plane. Let the magnetic field due to these current carrying wires at the origin be

→

B

. If B0 is the magnitude of the field if only one of them was present, then ‌

is

Two infinitely long wires are placed at (1cm,1cm) and (+1cm,−1cm) with 1A current in each and in the same directions perpendicular to x−y plane. Let the magnetic field due to these current carrying wires at the origin be

→

B

. If B0 is the magnitude of the field if only one of them was present, then ‌

is

A particle of mass 1×10−27kg and charge 1×10−16C enters the uniform magnetic field within the solenoid, at speed 1000ms−1. The velocity vector makes an angle 60∘ with the axis of solenoid. The solenoid has 5000 turns along its length and carries current 5A. The number of revolutions the particle makes along the helical path within the solenoid by the time it emerges from solenoid's opposite end is

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A particle of mass 1×10−27kg and charge 1×10−16C enters the uniform magnetic field within the solenoid, at speed 1000ms−1. The velocity vector makes an angle 60∘ with the axis of solenoid. The solenoid has 5000 turns along its length and carries current 5A. The number of revolutions the particle makes along the helical path within the solenoid by the time it emerges from solenoid's opposite end is

Resonance frequency of LCR series AC circuit is f0. Now inductance is reduced to ‌

1

4

times and capacitance is increased to 16 times, then the resonance frequency becomes

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Resonance frequency of LCR series AC circuit is f0. Now inductance is reduced to ‌

1

4

times and capacitance is increased to 16 times, then the resonance frequency becomes

A long solenoid is carrying a current I=I0‌sin(ωt), having N turns per unit length and radius R. A square loop is placed inside the solenoid with its plane perpendicular to the solenoid axis, and its corners touching the solenoid. Now the e mf induced in the square coil

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A long solenoid is carrying a current I=I0‌sin(ωt), having N turns per unit length and radius R. A square loop is placed inside the solenoid with its plane perpendicular to the solenoid axis, and its corners touching the solenoid. Now the e mf induced in the square coil

µF capacitor is connected to a 250V,50HzAC supply. Then the rms current of the circuit is

µF capacitor is connected to a 250V,50HzAC supply. Then the rms current of the circuit is

A short bar magnet placed in a horizontal plane has its axis aligned along north-south direction. Null points are found on the axis of the magnet at 20cm from the center of magnet. The earth's magnetic field at the place is B and angle of dip is 0∘. If the total magnetic field on the normal bisector of the magnet 20cm from the center of the magnet is 0.6G, then the magnitude of B is

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A short bar magnet placed in a horizontal plane has its axis aligned along north-south direction. Null points are found on the axis of the magnet at 20cm from the center of magnet. The earth's magnetic field at the place is B and angle of dip is 0∘. If the total magnetic field on the normal bisector of the magnet 20cm from the center of the magnet is 0.6G, then the magnitude of B is

Microwaves are used in the following

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Microwaves are used in the following

The electric field associated with a mono chromatic light wave is given by E=E0‌sin[(1.57×107m−1)(x−ct)], then the stopping potential when this light is used in a photoelectric experiment with the metal having work function 1.9eV is [Planck's constant, h=6.64×10−34Js ]

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The electric field associated with a mono chromatic light wave is given by E=E0‌sin[(1.57×107m−1)(x−ct)], then the stopping potential when this light is used in a photoelectric experiment with the metal having work function 1.9eV is [Planck's constant, h=6.64×10−34Js ]

Statement (A): As one considers orbits with higher values of n in hydrogen atom, the electric potential energy of the atom increases.

Statement (B): In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.

Statement (C): The orbital picture in Bohr's model of the hydrogen atom was consistent with the uncertainty principle.

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Statement (A): As one considers orbits with higher values of n in hydrogen atom, the electric potential energy of the atom increases.

Statement (B): In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.

Statement (C): The orbital picture in Bohr's model of the hydrogen atom was consistent with the uncertainty principle.

A radioactive substance has a half life of 108 years and an activity of 104Bq. The number of atoms of this substance present is

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A radioactive substance has a half life of 108 years and an activity of 104Bq. The number of atoms of this substance present is

The logic gates in which all the inputs must be low to get a high output are

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The logic gates in which all the inputs must be low to get a high output are

The maximum amplitude of an AM wave is found to be 20V while its minimum amplitude is 4V. The modulation index is

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The maximum amplitude of an AM wave is found to be 20V while its minimum amplitude is 4V. The modulation index is

The spectral series formed when electrons of excited hydrogen atoms return to the third orbit from higher energy orbits is

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The spectral series formed when electrons of excited hydrogen atoms return to the third orbit from higher energy orbits is

The incorrect set of quantum numbers (n,1,m,s) for an electron in 3p orbital is

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The incorrect set of quantum numbers (n,1,m,s) for an electron in 3p orbital is

Identify the elements x and z in the following representation. ( Sb= antimony)

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Identify the elements x and z in the following representation. ( Sb= antimony)

The successive ionization enthalpies of an element X in (kJmol−1) are 1012,1907 , 2955,4955,6275 and 21.260 respectively, the element X is

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The successive ionization enthalpies of an element X in (kJmol−1) are 1012,1907 , 2955,4955,6275 and 21.260 respectively, the element X is

The correct order of dipole moment of the molecules NH3 (I), BF3 (II), H2O (III), NF3(IV) is

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The correct order of dipole moment of the molecules NH3 (I), BF3 (II), H2O (III), NF3(IV) is

The number of sp2,sp3 hybridised carbons in cumene, respectively are:

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The number of sp2,sp3 hybridised carbons in cumene, respectively are:

The ratio of rates of diffusion of Helium (He) to Hydrogen (H2)

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The ratio of rates of diffusion of Helium (He) to Hydrogen (H2)

Equivalent weights of KMnO4 and K2Cr2O7 in acidic medium are respectively. (Molecular weight of KMnO4=MA and Molecular weight of K2Cr2O7=MB )

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Equivalent weights of KMnO4 and K2Cr2O7 in acidic medium are respectively. (Molecular weight of KMnO4=MA and Molecular weight of K2Cr2O7=MB )

The mass % of carbon in C57H110O6 is

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The mass % of carbon in C57H110O6 is

Enthalpy of formation of CO(g),CO2(g),N2O(g) and N2O4(g) are −110,−393,81, 9.7kJmol−1 respectively. Calculate ∆rH for the following reaction.
N2O4(g)+3CO(g)→N2O(g)+3CO2(g)

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Enthalpy of formation of CO(g),CO2(g),N2O(g) and N2O4(g) are −110,−393,81, 9.7kJmol−1 respectively. Calculate ∆rH for the following reaction.
N2O4(g)+3CO(g)→N2O(g)+3CO2(g)

For a reaction to be spontaneous, the required conditions are

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For a reaction to be spontaneous, the required conditions are

Identify the correct statements from the following
a) The ionic product of water at 100∘C is <10−14.
b) pH of a solution decreases with increasing temperature.
c) NaH2PO4 on hydrolysis gives a basic solution.
d) NH3 can act both as Bronsted acid and base.

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Identify the correct statements from the following
a) The ionic product of water at 100∘C is <10−14.
b) pH of a solution decreases with increasing temperature.
c) NaH2PO4 on hydrolysis gives a basic solution.
d) NH3 can act both as Bronsted acid and base.

1L of 0.02M aqueous HCl is mixed with 1L of 0.01M aqueous H2SO4 solution. Assuming complete dissociation and no change in the volume upon mixing, the pH of resultant solution is (log102=0.3)

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1L of 0.02M aqueous HCl is mixed with 1L of 0.01M aqueous H2SO4 solution. Assuming complete dissociation and no change in the volume upon mixing, the pH of resultant solution is (log102=0.3)

The mass of hydrogen (in grams) present in 1.0L of pure water of density 1.0gcm−3 is

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The mass of hydrogen (in grams) present in 1.0L of pure water of density 1.0gcm−3 is

The maximum covalency and highest oxidation state possible of an element with Z=13 are respectively

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The maximum covalency and highest oxidation state possible of an element with Z=13 are respectively

Identify A,B,C,&D in the reactions (I), (II)
(I) xCl2+

yNaOH

(cold, dil)

→A+B+H2O(l)
(II) xCl2+

Identify A,B,C,&D in the reactions (I), (II)
(I) xCl2+

yNaOH

(cold, dil)

→A+B+H2O(l)
(II) xCl2+

Which of the following behaves as a Lewis acid?

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Which of the following behaves as a Lewis acid?

The hybridization of elements present in Fullerene and graphite are respectively

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The hybridization of elements present in Fullerene and graphite are respectively

The major products P and Q of the following reactions respectively are
II. n− Pentyl bromide ‌

Zn/H+

────▶

P
II. n− Pentyl bromide ‌

Q

The major products P and Q of the following reactions respectively are
II. n− Pentyl bromide ‌

Zn/H+

────▶

P
II. n− Pentyl bromide ‌

Q

Z is an aromatic compound with substituents P&Q. What are P&Q ?

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Z is an aromatic compound with substituents P&Q. What are P&Q ?

A cubic lattice has atoms of A at the body centre, atoms of B at the corners of the cube and atoms C at all the face centers. What is its formula?

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A cubic lattice has atoms of A at the body centre, atoms of B at the corners of the cube and atoms C at all the face centers. What is its formula?

Which of the following molecular formula and type of defect are correct for the following statement?
"In FeO crystal, some Fe2+ ions are missing and the loss of positive charge is made up by the presence of Fe3+ ions"

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Which of the following molecular formula and type of defect are correct for the following statement?
"In FeO crystal, some Fe2+ ions are missing and the loss of positive charge is made up by the presence of Fe3+ ions"

At 298K, vapour pressures of two pure liquids A and B are 200 and 400mmHg respectively, If mole fractions of A and B in solution are 0.7 and 0.3 respectively. What is the mole fraction of B in vapour phase?

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At 298K, vapour pressures of two pure liquids A and B are 200 and 400mmHg respectively, If mole fractions of A and B in solution are 0.7 and 0.3 respectively. What is the mole fraction of B in vapour phase?

The freezing point depression of a solution containing 0.6g of urea (molar mass =60gmol−1) in 100g of benzene (in K) is (Kf of CH3COOH=4.0KKgmolK−1)

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The freezing point depression of a solution containing 0.6g of urea (molar mass =60gmol−1) in 100g of benzene (in K) is (Kf of CH3COOH=4.0KKgmolK−1)

The standard Gibbs energy change for Daniel cell reaction is
Zn(s)+Cu2+(aq)→Zn2+(aq)+Cu(s)
ECell∘=1.1V

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The standard Gibbs energy change for Daniel cell reaction is
Zn(s)+Cu2+(aq)→Zn2+(aq)+Cu(s)
ECell∘=1.1V

In a first order reaction, the concentration of the reactant is reduced from 0.6molL−1 to 0.2molL−1in5min. What is the rate constant of the reaction? (log‌3=0.4771)

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In a first order reaction, the concentration of the reactant is reduced from 0.6molL−1 to 0.2molL−1in5min. What is the rate constant of the reaction? (log‌3=0.4771)

Assertion (A):- The aggregate of carboxylate ions of fatty acids form a spherical shape
Reason (R): - Soap helps in emulsification and washing away of oils

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Assertion (A):- The aggregate of carboxylate ions of fatty acids form a spherical shape
Reason (R): - Soap helps in emulsification and washing away of oils

In the following reaction for the preparation of gold sol, a, b, c, x,y, and z are a

AuCl3+bHCHO+cH2O→xAu( sol )+yHCO2H+zHCl

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In the following reaction for the preparation of gold sol, a, b, c, x,y, and z are a

AuCl3+bHCHO+cH2O→xAu( sol )+yHCO2H+zHCl

Which of the following compound has reducing character?

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Which of the following compound has reducing character?

Assertion (A): All noble gases are monatomic.
Reason (R): All noble gases have very low melting and boiling points.

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Assertion (A): All noble gases are monatomic.
Reason (R): All noble gases have very low melting and boiling points.

Which of the following f - block element exhibits the highest oxidation state?

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Which of the following f - block element exhibits the highest oxidation state?

The correct order about the number of unpaired electrons present in the following complexes is

The correct order about the number of unpaired electrons present in the following complexes is

Which of the following is not true about the denaturation of protein?

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Which of the following is not true about the denaturation of protein?

Statement-I : Despite having aldehyde group, glucose does not give Schiff test
Statement-II : Glucose exists in α‌&‌β crystalline forms

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Statement-I : Despite having aldehyde group, glucose does not give Schiff test
Statement-II : Glucose exists in α‌&‌β crystalline forms

Identify the major product formed when propene is treated with hydrogen chloride followed by Swarts reaction

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Identify the major product formed when propene is treated with hydrogen chloride followed by Swarts reaction

Identify the product P from the following sequence of reactions?

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Identify the product P from the following sequence of reactions?

When ethanol is treated with sulphuric and at 413K the reaction involved in it is

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When ethanol is treated with sulphuric and at 413K the reaction involved in it is

Identify the major product of the following reaction

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Identify the major product of the following reaction

Identify the product formed in the following reaction sequence

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Identify the product formed in the following reaction sequence

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