AP EAPCET - 07 July 2022

If the system of simultaneous linear equations x+y−z=6,3x−y+z=2 and x+ky+z=−8 has a unique solution x=2,y=β,z=γ then the value of k satisfies the following quadratic equation

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If the system of simultaneous linear equations x+y−z=6,3x−y+z=2 and x+ky+z=−8 has a unique solution x=2,y=β,z=γ then the value of k satisfies the following quadratic equation

x	2	1
2	x	1
2	1	0

] and det(A3)=125, then x=

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If A=[

x	2	1
2	x	1
2	1	0

] and det(A3)=125, then x=

1	2
−2	1

] and B−1=[

1	1
0	2

]. If (AB−1)−1=[

a	b
c	d

], then 2b+5c+10d=

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Let A=[

1	2
−2	1

] and B−1=[

1	1
0	2

]. If (AB−1)−1=[

a	b
c	d

n	0	0
0	n	0
0	0	n

] and B=[

0	0	n
0	n	0
n	0	0

]. Then A2+B2+AB=

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Let A=[

n	0	0
0	n	0
0	0	n

] and B=[

0	0	n
0	n	0
n	0	0

Let z and w be two complex numbers such that z+iw=0 and Arg(zw)=π. Then ArgZ=

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Let z and w be two complex numbers such that z+iw=0 and Arg(zw)=π. Then ArgZ=

If the complex number z1,z2,0 are vertices of an equilateral triangle, then z12+z22=

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If the complex number z1,z2,0 are vertices of an equilateral triangle, then z12+z22=

Let z=x+ iy be a complex number with x,y∈ℤ. Then the area (in square units) of the rectangle whose vertices are the roots of the equation z⋅z3+z⋅z3=350 is

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Let z=x+ iy be a complex number with x,y∈ℤ. Then the area (in square units) of the rectangle whose vertices are the roots of the equation z⋅z3+z⋅z3=350 is

If 1,ω,ω2 are the cube roots of unity, then (2−ω)2(2−ω2)2(2−ω10)2(2−ω11)2=

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If 1,ω,ω2 are the cube roots of unity, then (2−ω)2(2−ω2)2(2−ω10)2(2−ω11)2=

Let f(x)=x2+1/x2 and g(x)=x−1/x for x∈R−{−1,0,+1} then, the local minimum of ‌

f(x)

g(x)

is

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Let f(x)=x2+1/x2 and g(x)=x−1/x for x∈R−{−1,0,+1} then, the local minimum of ‌

is

The range of the function f(x)=‌

x2+x+1

x2−x+1

is

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The range of the function f(x)=‌

is

Which of the following quadratic equations whose real roots x1,x2 satisfy the conditions x12+x22=5,3(x15+x25)=11(x13+x23) ?

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Which of the following quadratic equations whose real roots x1,x2 satisfy the conditions x12+x22=5,3(x15+x25)=11(x13+x23) ?

The remainder when the polynomial 2x5−3x4+5x3−3x2+7x−9 is divided by x2−x−3 is

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The remainder when the polynomial 2x5−3x4+5x3−3x2+7x−9 is divided by x2−x−3 is

If ‌nCr−1=36,‌nCr=84 and ‌nCr+1=126 then the value of nr2 is

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If ‌nCr−1=36,‌nCr=84 and ‌nCr+1=126 then the value of nr2 is

The total number of positive integral solutions (x,y,z) of xyz=24 is

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The total number of positive integral solutions (x,y,z) of xyz=24 is

Let P1,P2,...,P15 be 15 points on a circle. The number of distinct triangles formed by points Pi,Pj,Pk such that i+j+k≠15, is

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Let P1,P2,...,P15 be 15 points on a circle. The number of distinct triangles formed by points Pi,Pj,Pk such that i+j+k≠15, is

What is the sum of the first n-terms of the series, whose k-term is k!×k ?

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What is the sum of the first n-terms of the series, whose k-term is k!×k ?

, then the number of non-zero values in A,B,C,D is

, then the number of non-zero values in A,B,C,D is

The smallest integer n such that

The smallest integer n such that

sin(x+y)‌sec‌x‌sec‌y=

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sin(x+y)‌sec‌x‌sec‌y=

)=1, then the value of x in the interval [0,π]

)=1, then the value of x in the interval [0,π]

In △ABC, if 3‌sin‌A+4‌cos‌B=6 and 4‌sin‌B+3‌cos‌A=1, then the angle C is

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In △ABC, if 3‌sin‌A+4‌cos‌B=6 and 4‌sin‌B+3‌cos‌A=1, then the angle C is

If cosh(x−log‌3)=sinh‌x, then x=

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If cosh(x−log‌3)=sinh‌x, then x=

The sides of a triangle ABC are given by a=3,b=5 and c=3. Then cos‌A=

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The sides of a triangle ABC are given by a=3,b=5 and c=3. Then cos‌A=

In a triangle ABC, if a=2,b=3 and sin‌A=

In a triangle ABC, if a=2,b=3 and sin‌A=

In a △ABC,a:b:c=4:5:6. The ratio of radius of the circumcircle to that of the incircle is

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In a △ABC,a:b:c=4:5:6. The ratio of radius of the circumcircle to that of the incircle is

PQRS is a quadrilateral and PQ=a,QR=b,SP=a−b,
M is the midpoint of QR and X is a point on SM such that SX=‌

4

5

SM. If SM=m(4a−b) and SX=n(4a−b), then m+n=

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PQRS is a quadrilateral and PQ=a,QR=b,SP=a−b,
M is the midpoint of QR and X is a point on SM such that SX=‌

4

5

SM. If SM=m(4a−b) and SX=n(4a−b), then m+n=

If C is the midpoint of the line segment AB and P is any point outside the line AB, then

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If C is the midpoint of the line segment AB and P is any point outside the line AB, then

a,b are non-collinear vectors, |a|=2√2,|b|=3 and the angle between a and b is 45∘. Then the lengths of the diagonals of the parallelogram whose adjacent sides are represented by the vectors 5a+2b and a−3b are

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a,b are non-collinear vectors, |a|=2√2,|b|=3 and the angle between a and b is 45∘. Then the lengths of the diagonals of the parallelogram whose adjacent sides are represented by the vectors 5a+2b and a−3b are

Two vertices of a triangle are at −i+3j and 2i+5j and its orthocenter is at i+2j. If the position vector of the 3‌rd ‌ vertex is ai+bj, then (a,b)=

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Two vertices of a triangle are at −i+3j and 2i+5j and its orthocenter is at i+2j. If the position vector of the 3‌rd ‌ vertex is ai+bj, then (a,b)=

If 3 vectors a,b,c are such that a≠0 and a×b=2(a×c),|a|=1,|c|=1,|b|=4 and angle between b and c is cos−1(

1

4

) and b−2c=λa, then λ=

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If 3 vectors a,b,c are such that a≠0 and a×b=2(a×c),|a|=1,|c|=1,|b|=4 and angle between b and c is cos−1(

1

4

) and b−2c=λa, then λ=

The range of the data 35,12,21,24,15,7,16,12,30,32,13,17 is

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The range of the data 35,12,21,24,15,7,16,12,30,32,13,17 is

If A and B are two independent events such that P(A)=0.3,P(B)=x and P(A∪B)=0.44, then x=

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If A and B are two independent events such that P(A)=0.3,P(B)=x and P(A∪B)=0.44, then x=

In a set of 30 games cards, 17 are white and rest are green. Out of 30,4 white and 5 green are marked IMPORTANT. If a card is chosen randomly from this set, the possibility of choosing a green card or an "IMPORTANT" card is

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In a set of 30 games cards, 17 are white and rest are green. Out of 30,4 white and 5 green are marked IMPORTANT. If a card is chosen randomly from this set, the possibility of choosing a green card or an "IMPORTANT" card is

In a toy factory, the machines A,B and C are used to manufacture 30%,40% and 30% of the output, respectively. The probabilities of toys made by machines A,B, and C to be defective are respectively 2%,3% and 1%. A toy is taken from the factory and is found to be defective. The probability that it was manufactured by the machine B is

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In a toy factory, the machines A,B and C are used to manufacture 30%,40% and 30% of the output, respectively. The probabilities of toys made by machines A,B, and C to be defective are respectively 2%,3% and 1%. A toy is taken from the factory and is found to be defective. The probability that it was manufactured by the machine B is

If a number is chosen at random from the set {1,2,3,...,100}, then the probability that the chosen number is a perfect cube is

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If a number is chosen at random from the set {1,2,3,...,100}, then the probability that the chosen number is a perfect cube is

Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poission distribution. The probability that all the 10 pages selected at random with no print mistakes is

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Suppose that a book of 600 pages contains 40 print mistakes. Assume that these errors are randomly distributed throughout the book and the number of errors per page follows a Poission distribution. The probability that all the 10 pages selected at random with no print mistakes is

The maximum value of the variance of Binomial distribution with parameters n and p is

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The maximum value of the variance of Binomial distribution with parameters n and p is

On the locus of the point P(x,y) equidistant from (3,0) and (0,4), if A and B are two points that satisfy 4x=3y and x=y respectively, then the distance between A and B is

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On the locus of the point P(x,y) equidistant from (3,0) and (0,4), if A and B are two points that satisfy 4x=3y and x=y respectively, then the distance between A and B is

If one side of an isosceles triangle is given by y=2 and the base is provided by the points (2,0) and (0,2), then its area (in sq. units) is

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If one side of an isosceles triangle is given by y=2 and the base is provided by the points (2,0) and (0,2), then its area (in sq. units) is

The straight line passing through (0,0) and the foot of perpendicular from (2,4) onto x+y−1=0 is

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The straight line passing through (0,0) and the foot of perpendicular from (2,4) onto x+y−1=0 is

If P(sin‌α,cos‌α) lies inside the triangle formed by the vertices (0,0),(√3∕2,0) and (0,√3∕2), then α lies in the interval

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If P(sin‌α,cos‌α) lies inside the triangle formed by the vertices (0,0),(√3∕2,0) and (0,√3∕2), then α lies in the interval

The triangle formed by x2−4xy+y2=0 and x+y+4‌sqrt‌6=0 is

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The triangle formed by x2−4xy+y2=0 and x+y+4‌sqrt‌6=0 is

The equation of bisectors of the angle between the lines given by 3x2+5xy+4y2=0 is

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The equation of bisectors of the angle between the lines given by 3x2+5xy+4y2=0 is

Suppose d1 and d2 are respectively the lengths of intercepts of the circle x2+y2=4 and x2+y2−10x−14y+65=0 on the line 2x−2y−3=0. Then which of the following is true?

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Suppose d1 and d2 are respectively the lengths of intercepts of the circle x2+y2=4 and x2+y2−10x−14y+65=0 on the line 2x−2y−3=0. Then which of the following is true?

If the point (2,λ) lies inside the circles x2+y2=13 and x2+y2+x−2y=14, λ lies in the set

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If the point (2,λ) lies inside the circles x2+y2=13 and x2+y2+x−2y=14, λ lies in the set

For different real non zero numbers x1,x2,x3 and x4, suppose the points (x1,‌

) lie on the boundary of a circle of radius 4. Then the value of x1x2x3x4 is

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For different real non zero numbers x1,x2,x3 and x4, suppose the points (x1,‌

) lie on the boundary of a circle of radius 4. Then the value of x1x2x3x4 is

The equation of the tangent to the circle x2+y2−9=0 making an angle 60∘ with the x-axis is

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The equation of the tangent to the circle x2+y2−9=0 making an angle 60∘ with the x-axis is

The equation of circle passing through (0,0) and cutting orthogonally the circles x2+y2+6x−15=0 and x2+y2−8y−10=0 is

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The equation of circle passing through (0,0) and cutting orthogonally the circles x2+y2+6x−15=0 and x2+y2−8y−10=0 is

For the parabola represented in the parametric form by x=t2+t+1 and y=t2−t+1. the length of latus rectum is

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For the parabola represented in the parametric form by x=t2+t+1 and y=t2−t+1. the length of latus rectum is

An ellipse has 6 and 2 as lengths of major and minor axes respectively. If the centre is at (5,6) and the major axis is along x−y+1=0, then the ellipse is

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An ellipse has 6 and 2 as lengths of major and minor axes respectively. If the centre is at (5,6) and the major axis is along x−y+1=0, then the ellipse is

=1, if the length of the transverse axis is 8 and the distance between the foci is 2√41, then the length of its latus rectum is

=1, if the length of the transverse axis is 8 and the distance between the foci is 2√41, then the length of its latus rectum is

If the product of the perpendicular distances from any point on the hyperbola ‌

=1 to its asymptotes is 6 and eccentricity of the hyperbola is √3, then the length of the conjugate axis of the hyperbola is

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If the product of the perpendicular distances from any point on the hyperbola ‌

=1 to its asymptotes is 6 and eccentricity of the hyperbola is √3, then the length of the conjugate axis of the hyperbola is

If the point (3,4,5) divides the line segment joining the points (1,2,3) and (4,5,6) in the ratio λ:1 then the point which divides the line segment joining the points (3,4,5) and (1,2,3) in the ratio −1:λ is

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If the point (3,4,5) divides the line segment joining the points (1,2,3) and (4,5,6) in the ratio λ:1 then the point which divides the line segment joining the points (3,4,5) and (1,2,3) in the ratio −1:λ is

Suppose (l1,m1,n1) and (l2,m2,n2) are the directional cosines of two lines and θ is the angle between them and cos‌θ=±(l1l2+m1m2+n1n2). Let A=(1,−2,3), B=(3,1,−3) and C=(−3,1,3) be the vertices of a triangle ABC. Then cos‌A=

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Suppose (l1,m1,n1) and (l2,m2,n2) are the directional cosines of two lines and θ is the angle between them and cos‌θ=±(l1l2+m1m2+n1n2). Let A=(1,−2,3), B=(3,1,−3) and C=(−3,1,3) be the vertices of a triangle ABC. Then cos‌A=

Let ax+by+cz+d=0 be the equation of a plane. Given that 4a+4b+c=0 and a+2b+c=0. Then d=

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Let ax+by+cz+d=0 be the equation of a plane. Given that 4a+4b+c=0 and a+2b+c=0. Then d=

=

=

Which of the following is differentiable at x=0 ?

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Which of the following is differentiable at x=0 ?

If y=tan(3tan−1x), then (1−3x2)‌

=

If y=tan(3tan−1x), then (1−3x2)‌

=

The curve y=ax3+bx2+cx+5 touches x-axis at P(−2,0), then c=

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The curve y=ax3+bx2+cx+5 touches x-axis at P(−2,0), then c=

The curves y=x2−1,y=8x−x2−9

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The curves y=x2−1,y=8x−x2−9

The perimeter of a sector is constant. If its area is to be maximum, the sectorical angle should be

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The perimeter of a sector is constant. If its area is to be maximum, the sectorical angle should be

The set of all x for which sin‌x≤x is

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The set of all x for which sin‌x≤x is

The function f(x)=2x3−9ax2+12a2x+1(a>0) attains its maximum and minimum at p and q respectively and p2=q. Then a=

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The function f(x)=2x3−9ax2+12a2x+1(a>0) attains its maximum and minimum at p and q respectively and p2=q. Then a=

If f(x) is anti derivative of g(x) and ∫f(x)g(x)(1+f2(x))dx=F(x), then F(x)=

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If f(x) is anti derivative of g(x) and ∫f(x)g(x)(1+f2(x))dx=F(x), then F(x)=

dx=

dx=

)=

)=

If ∫f(x)dx=F(x)+C, then ‌

If ∫f(x)dx=F(x)+C, then ‌

dx=

dx=

, then the substitution to be used to solve the differential equation ‌

by using separation of variables is

, then the substitution to be used to solve the differential equation ‌

by using separation of variables is

For the differential equation ‌

For the differential equation ‌

The differential equation of the family of circles passing through (0,0) and having centre on x - axis is

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The differential equation of the family of circles passing through (0,0) and having centre on x - axis is

The number of significant figures in quantity 0.00005041J is

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The number of significant figures in quantity 0.00005041J is

of the distance L with speed v1 and ‌

2

3

of the distance with speed v2. Then the average speed is

of the distance L with speed v1 and ‌

2

3

of the distance with speed v2. Then the average speed is

A ball is projected from ground into the air. At the height of 5m, its velocity is

)‌m‌s−1. The maximum height reached by the ball is (Acceleration due to gravity =10ms−2 )

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A ball is projected from ground into the air. At the height of 5m, its velocity is

)‌m‌s−1. The maximum height reached by the ball is (Acceleration due to gravity =10ms−2 )

A particle is moving along x-axis with velocity v=e−βx. At time t=0, the particle is

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A particle is moving along x-axis with velocity v=e−βx. At time t=0, the particle is

Consider three masses M1,M2 and M3(M1>M2>M3) are at rest on a horizontal plane as shown in the figure. Now the angle of inclination (θ) of the plane is gradually increased until the masses just begin to slide. (Assume the co-efficient of static friction between the masses and the surface is constant). Then the correct statement of the following is

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Consider three masses M1,M2 and M3(M1>M2>M3) are at rest on a horizontal plane as shown in the figure. Now the angle of inclination (θ) of the plane is gradually increased until the masses just begin to slide. (Assume the co-efficient of static friction between the masses and the surface is constant). Then the correct statement of the following is

A bar of mass m resting on a smooth horizontal plane starts moving due to a constant force F. In the process of its rectilinear motion the angle θ between the direction of this force and the horizontal varies as θ=kx, where k is a constant and x is the distance traversed by the bar from its initial position. The velocity (v) of the bar as a function of the angle θ is

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A bar of mass m resting on a smooth horizontal plane starts moving due to a constant force F. In the process of its rectilinear motion the angle θ between the direction of this force and the horizontal varies as θ=kx, where k is a constant and x is the distance traversed by the bar from its initial position. The velocity (v) of the bar as a function of the angle θ is

A block of mass 5kg starts up a 45∘ incline plane with initial kinetic energy of 100J. If the coefficient of friction between block and plane is 0.5 then the distance covered by the block before it stops is (Acceleration due to gravity =10ms−2 )

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A block of mass 5kg starts up a 45∘ incline plane with initial kinetic energy of 100J. If the coefficient of friction between block and plane is 0.5 then the distance covered by the block before it stops is (Acceleration due to gravity =10ms−2 )

A lift raises 50 passengers each having average weight 600N to a height of 100m at a constant speed in time T. If the average power of 15kW is required by the lift, then the value of T in seconds is

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A lift raises 50 passengers each having average weight 600N to a height of 100m at a constant speed in time T. If the average power of 15kW is required by the lift, then the value of T in seconds is

If the earth suddenly shrinks to ‌

1

64

of its original volume, while keeping the same mass, then the duration of the day will be
[Assume earth is a perfect sphere]

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If the earth suddenly shrinks to ‌

1

64

of its original volume, while keeping the same mass, then the duration of the day will be
[Assume earth is a perfect sphere]

A wheel is rotating freely at some angular speed. A second wheel initially at rest and with thrice the rotational inertia of the first, is suddenly coupled to the first wheel. The fraction of the original rotational kinetic energy lost is

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A wheel is rotating freely at some angular speed. A second wheel initially at rest and with thrice the rotational inertia of the first, is suddenly coupled to the first wheel. The fraction of the original rotational kinetic energy lost is

There is a planet which is 8 times massive and 27 times denser than the earth. If g′ and g are the accelerations due to gravity on the surfaces of the planet and the earth respectively then

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There is a planet which is 8 times massive and 27 times denser than the earth. If g′ and g are the accelerations due to gravity on the surfaces of the planet and the earth respectively then

Position of a 3kg mass moving along the x-axis is given by x=0.3‌cos(ωt)‌m. If K(t) denotes the kinetic energy at time t,

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Position of a 3kg mass moving along the x-axis is given by x=0.3‌cos(ωt)‌m. If K(t) denotes the kinetic energy at time t,

A rubber band catapult has initial length 2cm and cross-sectional area 5mm2. It is stretched to 2cm and then released to project a stone of mass of 20g. The Velocity of projected stone is
(Young's modulus of rubber =5×108Nm−2 )

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A rubber band catapult has initial length 2cm and cross-sectional area 5mm2. It is stretched to 2cm and then released to project a stone of mass of 20g. The Velocity of projected stone is
(Young's modulus of rubber =5×108Nm−2 )

Two wires made of same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If x is the increase in the length of the first wire, then the increase in the length of the second wire is

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Two wires made of same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If x is the increase in the length of the first wire, then the increase in the length of the second wire is

A large tank open to atmosphere at top and filled with water, develops a small hole in the side at a point 20m below the water level. If the rate of flow of water from the hole is 3×10−3m3/min then the area of hole is
(Acceleration due to gravity =10ms−2 )

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A large tank open to atmosphere at top and filled with water, develops a small hole in the side at a point 20m below the water level. If the rate of flow of water from the hole is 3×10−3m3/min then the area of hole is
(Acceleration due to gravity =10ms−2 )

The movable cylindrical pistons P1 and P2 of a hydraulic lift are of radii 2m and R respectively. A body of mass 32kg on piston P2 is supported by a body of mass 2kg placed on piston P1. The value of R is

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The movable cylindrical pistons P1 and P2 of a hydraulic lift are of radii 2m and R respectively. A body of mass 32kg on piston P2 is supported by a body of mass 2kg placed on piston P1. The value of R is

The coefficient of volume expansion of a material is 5×10−4‌∘C−1. The fractional change in its density for a 40∘C rise in temperature is nearly

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The coefficient of volume expansion of a material is 5×10−4‌∘C−1. The fractional change in its density for a 40∘C rise in temperature is nearly

A gaseous mixture consists of 4g oxygen and 4g of helium. The ratio ‌

CP

CV

of mixture is (CP and CV are molar specific heats of the mixture at constant pressure and at constant volume respectively).

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A gaseous mixture consists of 4g oxygen and 4g of helium. The ratio ‌

CP

CV

of mixture is (CP and CV are molar specific heats of the mixture at constant pressure and at constant volume respectively).

One mole of an ideal monatomic gas undergoes the process A→B→C→D→A as shown in the graph. The work done during the process is

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One mole of an ideal monatomic gas undergoes the process A→B→C→D→A as shown in the graph. The work done during the process is

The volume of a gas at 30∘C temperature and 760mm of Hg pressure is 100cc. Then its volume at the same temperature and 400mm of Hg is

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The volume of a gas at 30∘C temperature and 760mm of Hg pressure is 100cc. Then its volume at the same temperature and 400mm of Hg is

Two trains A and B are moving towards each other with speeds 72knhl−1 and 36kmh−1 respectively. The train-A whistles at 640Hz frequency. Before the trains meet, frequency of sound heard by a passenger in Train-B is ( Speed of sound in air =340ms−1 )

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Two trains A and B are moving towards each other with speeds 72knhl−1 and 36kmh−1 respectively. The train-A whistles at 640Hz frequency. Before the trains meet, frequency of sound heard by a passenger in Train-B is ( Speed of sound in air =340ms−1 )

A beam of light is incident from air on the surface of a liquid. The angle of incidence is θ and the angle of refraction is α. If the critical angle for liquid when surrounded by air is θc then sin‌θc is

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A beam of light is incident from air on the surface of a liquid. The angle of incidence is θ and the angle of refraction is α. If the critical angle for liquid when surrounded by air is θc then sin‌θc is

In Young's double slit experiment. light of wavelength 480nm is incident on two slits separated by a distance of 4×10−4m. If a thin plate of thickness 1.4×10−6m and refractive index ‌13/7 is placed between one of the slits and screen. the phase difference introduced at the position of central maxima is

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In Young's double slit experiment. light of wavelength 480nm is incident on two slits separated by a distance of 4×10−4m. If a thin plate of thickness 1.4×10−6m and refractive index ‌13/7 is placed between one of the slits and screen. the phase difference introduced at the position of central maxima is

Three charges +5q, Q and −2q are kept along a straight line in the same order such that, +5q and −2q charges are at a distance of ‌

from the charge Q respectively. If the net force on the charge −2q is zero, then Q is

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Three charges +5q, Q and −2q are kept along a straight line in the same order such that, +5q and −2q charges are at a distance of ‌

from the charge Q respectively. If the net force on the charge −2q is zero, then Q is

A capacitor has capacitance C0 when there is no dielectric between it's plates. 2 slabs of dielectric constant K1,K2 respectively with area equal to area of plates but thickness half of the distance between the plates are placed in between the plates. Then the new capacitance is

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A capacitor has capacitance C0 when there is no dielectric between it's plates. 2 slabs of dielectric constant K1,K2 respectively with area equal to area of plates but thickness half of the distance between the plates are placed in between the plates. Then the new capacitance is

In a parallel plate capacitor, if 1012 electrons pass from one plate to another, a potential difference of 10V is developed across the plates. The capacitance of the capacitor is

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In a parallel plate capacitor, if 1012 electrons pass from one plate to another, a potential difference of 10V is developed across the plates. The capacitance of the capacitor is

The current i in the circuit given below is

Q.108 Correct

Q.108 In-correct

Q.108 Unattempt

Two wires A and B of same material having length LA,LB and radii RA,RB and drift velocity VA,VB respectively carries same current. If LA=LB and RA=2RB then the value of (‌

Two wires A and B of same material having length LA,LB and radii RA,RB and drift velocity VA,VB respectively carries same current. If LA=LB and RA=2RB then the value of (‌

A long solenoid having 100 turns per cm carries a current of ‌

4

π

A. At the centre of it is placed a coil of 200 turns of cross sectional area 25cm2 having its axis parallel to the field produced by the solenoid. When the direction of the current in the solenoid is reversed with in 0.04s, the induced emf in the coil is

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A long solenoid having 100 turns per cm carries a current of ‌

4

π

A. At the centre of it is placed a coil of 200 turns of cross sectional area 25cm2 having its axis parallel to the field produced by the solenoid. When the direction of the current in the solenoid is reversed with in 0.04s, the induced emf in the coil is

A particle of charge 1.0×10−16C moves through a uniform magnetic field

)‌T. The particle velocity at some instant is

)‌m‌s−1 and the magnetic force acting on it is 3×10−16

∧

k

N. The magnitude of B∘ is

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A particle of charge 1.0×10−16C moves through a uniform magnetic field

)‌T. The particle velocity at some instant is

)‌m‌s−1 and the magnetic force acting on it is 3×10−16

∧

k

N. The magnitude of B∘ is

A short bar magnet produces a magnetic field of 6.4×10−5T at a distance of 20cm from the center of the magnet on the normal bisector of the magnet. The magnetic field produced by this magnet at a distance of 40cm from the center of the magnet on the axis, is

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A short bar magnet produces a magnetic field of 6.4×10−5T at a distance of 20cm from the center of the magnet on the normal bisector of the magnet. The magnetic field produced by this magnet at a distance of 40cm from the center of the magnet on the axis, is

A solenoid has the length 1m and the area of cross section 0.02m2. If no. of turns in the solenoid is 5000 then the self inductance of the solenoid is

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A solenoid has the length 1m and the area of cross section 0.02m2. If no. of turns in the solenoid is 5000 then the self inductance of the solenoid is

A 100µF capacitor is connected to a 100V,50HzAC supply. The rms value of the current is

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A 100µF capacitor is connected to a 100V,50HzAC supply. The rms value of the current is

A bulb of power 660W radiates uniformly in all directions. The pressure exerted by the radiation on the surface at a distance of 5m is

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A bulb of power 660W radiates uniformly in all directions. The pressure exerted by the radiation on the surface at a distance of 5m is

The equation that represents magnetic field of a plane electromagnetic wave which is propagating along x-direction with wavelength 10mm and maximum electric field 60Vm−1 in y-direction is (c - speed of light)

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The equation that represents magnetic field of a plane electromagnetic wave which is propagating along x-direction with wavelength 10mm and maximum electric field 60Vm−1 in y-direction is (c - speed of light)

The average number of photons emitted per second by a laser of power 6.6×10−3W producing a light of wavelength 600nm is (Planck's constant, h=6.6×10−34Js )

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The average number of photons emitted per second by a laser of power 6.6×10−3W producing a light of wavelength 600nm is (Planck's constant, h=6.6×10−34Js )

A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is

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A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is

The correct statement of the following is

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The correct statement of the following is

Consider the following statements
Statement (A): The resistance of an ideal diode in forward biased condition is zero.
Statement (B): In a half wave rectifier, the load current flows only for every half cycle of the input signals.
Statement (C) : In the breakdown region, a zener diode behaves as a constant voltage source.

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Consider the following statements
Statement (A): The resistance of an ideal diode in forward biased condition is zero.
Statement (B): In a half wave rectifier, the load current flows only for every half cycle of the input signals.
Statement (C) : In the breakdown region, a zener diode behaves as a constant voltage source.

The frequency band for uplink satellite communication in the following is

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The frequency band for uplink satellite communication in the following is

The ratio of radii of second orbit of hydrogen atom to fourth orbit of He+ion is

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The ratio of radii of second orbit of hydrogen atom to fourth orbit of He+ion is

The velocity of the electron in Bohr's first orbit is x×106ms. The deBroglie wave length associated with it (in nm) is (me=9×10−31kg,h=6.6×10−34Js )

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The velocity of the electron in Bohr's first orbit is x×106ms. The deBroglie wave length associated with it (in nm) is (me=9×10−31kg,h=6.6×10−34Js )

The molecule which has more number of lone pair of electrons than the bond pair of electrons in its central atom is

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The molecule which has more number of lone pair of electrons than the bond pair of electrons in its central atom is

Arrange the following in the correct order of their bond orders.

Arrange the following in the correct order of their bond orders.

The element with the electronic configuration [Kr]4d105s0 is

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The element with the electronic configuration [Kr]4d105s0 is

Among the ions O2−,Na+,F−,N3−,Mg2+ the ions with smallest and largest radii are respectively

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Among the ions O2−,Na+,F−,N3−,Mg2+ the ions with smallest and largest radii are respectively

The ratio of rate of diffusion of SO2 to CH4 is

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The ratio of rate of diffusion of SO2 to CH4 is

A reaction gas mixture contains 50%,30%,20% of A,B and C by volume, respectively. The mixture undergoes the following reactions.
1. A+2B⟶P1
2. 4P1+3C⟶P2 P1 and P2 are two products of the reactions.
Choose the correct answer if the reaction completes.

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A reaction gas mixture contains 50%,30%,20% of A,B and C by volume, respectively. The mixture undergoes the following reactions.
1. A+2B⟶P1
2. 4P1+3C⟶P2 P1 and P2 are two products of the reactions.
Choose the correct answer if the reaction completes.

Which of the following does not show disproportionation reaction?

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Which of the following does not show disproportionation reaction?

Which of the following conditions are not suitable for a spontaneous reaction?

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Which of the following conditions are not suitable for a spontaneous reaction?

Which of the following are extensive properties?
(A) Heat capacity
(B) Entropy
(C) Gibbs Energy
(D) Concentration
(E) Vapour pressure.

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Which of the following are extensive properties?
(A) Heat capacity
(B) Entropy
(C) Gibbs Energy
(D) Concentration
(E) Vapour pressure.

For the formation of NH3(g) from its constituent elements, which of the relation between the reaction quotient (Q) and equilibrium constant (KC) is correct for the backward reaction

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For the formation of NH3(g) from its constituent elements, which of the relation between the reaction quotient (Q) and equilibrium constant (KC) is correct for the backward reaction

The conjugate base of NH4+is

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The conjugate base of NH4+is

In long form of periodic table, the d-block element which forms interstitial hydride is

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In long form of periodic table, the d-block element which forms interstitial hydride is

The bond order values of anions of sodium peroxide and potassium super oxide are respectively.

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The bond order values of anions of sodium peroxide and potassium super oxide are respectively.

Statement A: - In general, the ionization potential value decreases on moving down in the group.
Statement B:- The1st ionization potential of sodium is greater from that of potassium
Correct answer is

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Statement A: - In general, the ionization potential value decreases on moving down in the group.
Statement B:- The1st ionization potential of sodium is greater from that of potassium
Correct answer is

The percentage of abundance of three elements X,Y and Z in the earth's crust are about 27.7,8.3 and 46.0 by mass respectively. X,Y and Z are

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The percentage of abundance of three elements X,Y and Z in the earth's crust are about 27.7,8.3 and 46.0 by mass respectively. X,Y and Z are

The two stable isotopes of carbon present in the naturally occurring carbon are

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The two stable isotopes of carbon present in the naturally occurring carbon are

Which of the following compounds do not have sp3 carbon atom(s)?
I. Acetone
II. Acetic acid
III. Buta-1, 3-diene
IV. Propyne
V. Naphthalene

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Which of the following compounds do not have sp3 carbon atom(s)?
I. Acetone
II. Acetic acid
III. Buta-1, 3-diene
IV. Propyne
V. Naphthalene

The major product ' B ' of the following reaction sequence is

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The major product ' B ' of the following reaction sequence is

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Q.141 Correct

Q.141 In-correct

Q.141 Unattempt

The ratio of effective number of atoms in a unit cell of fcc and bcc lattices is

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The ratio of effective number of atoms in a unit cell of fcc and bcc lattices is

A cubic lattice has A atoms at the body center, B atoms at the corners, C atoms at half of the face centers. The formula of the lattice is

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A cubic lattice has A atoms at the body center, B atoms at the corners, C atoms at half of the face centers. The formula of the lattice is

The molality and molarity of a solution of a glucose in water which is labeled as 10% (w\/w) are respectively (density of solution =1.2gmL−1 )

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The molality and molarity of a solution of a glucose in water which is labeled as 10% (w\/w) are respectively (density of solution =1.2gmL−1 )

1.8g of glucose (molar mass 180gmol−1 ) is dissolved in 0.1kg of water. The freezing point of the solution ( in ‌∘C ) is
(Kf‌ for water ‌=1.86Kkgmol−1)

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1.8g of glucose (molar mass 180gmol−1 ) is dissolved in 0.1kg of water. The freezing point of the solution ( in ‌∘C ) is
(Kf‌ for water ‌=1.86Kkgmol−1)

The energy conversion involved in a galvanic cell is

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The energy conversion involved in a galvanic cell is

If the rate of disappearance of N2O5 in the following reaction is 1.2X−5molL−1s−1, the rate of production of NO2( in molL−1s−1) is
2N2O5(g)→4NO2(g)+O2(g)

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If the rate of disappearance of N2O5 in the following reaction is 1.2X−5molL−1s−1, the rate of production of NO2( in molL−1s−1) is
2N2O5(g)→4NO2(g)+O2(g)

Assertion (B) :- Finely divided charcoal can act as an adsorbent
Reason (R): - Finely divided material has small surface area

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Assertion (B) :- Finely divided charcoal can act as an adsorbent
Reason (R): - Finely divided material has small surface area

The correct statements with respect to dialysis of colloidal solution are
I. Colloidal particles can pass through the membrane
II. Animal bladder can be used as membrane
III. Cellophane is not used as membrane
IV. Ions or small molecules can diffuse through membrane into water

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The correct statements with respect to dialysis of colloidal solution are
I. Colloidal particles can pass through the membrane
II. Animal bladder can be used as membrane
III. Cellophane is not used as membrane
IV. Ions or small molecules can diffuse through membrane into water

Which of the following is Indian saltpetre?

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Which of the following is Indian saltpetre?

In the following unbalanced reaction, the product formed is Al2O3+NaOH(aq)+H2O→

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In the following unbalanced reaction, the product formed is Al2O3+NaOH(aq)+H2O→

The outer electronic configuration of "Pd" is

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The outer electronic configuration of "Pd" is

The IUPAC name of the following complex is [Co(NH2CH2CH2NH2)2Br2]Br

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The IUPAC name of the following complex is [Co(NH2CH2CH2NH2)2Br2]Br

Which of the following is not a RNA?

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Which of the following is not a RNA?

Hydrolysis of which disaccharide in presence of enzyme maltase give glucose only?

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Hydrolysis of which disaccharide in presence of enzyme maltase give glucose only?

SN1 reactions are generally carried out in which type of the solvents?

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SN1 reactions are generally carried out in which type of the solvents?

Identify the major product formed from the following

Q.157 Correct

Q.157 In-correct

Q.157 Unattempt

Identify the correct trend of acidic strength for the given alcohols

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Identify the correct trend of acidic strength for the given alcohols

Identify P and Q respectively of the following reaction

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Identify P and Q respectively of the following reaction

Which of the following can undergo disproportion reaction on heating with Conc. Alkali?

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Which of the following can undergo disproportion reaction on heating with Conc. Alkali?

Identify the major product from the following reaction sequence

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Identify the major product from the following reaction sequence

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