AP EAPCET - 07 July 2022

b2+c2	a2	a2
b2	c2+a2	b2
c2	c2	a2+b2

b2+c2	a2	a2
b2	c2+a2	b2
c2	c2	a2+b2

If a matrix A satisfies the equation A3−6A2+11A−6I=0, then A−1 can be

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If a matrix A satisfies the equation A3−6A2+11A−6I=0, then A−1 can be

The rank of the matrix A=[

2	1	2
1	0	1
4	1	4

] is

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The rank of the matrix A=[

2	1	2
1	0	1
4	1	4

1	−2	2
2	−6	5
5	0	4

] then Adj A=

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If A=[

1	−2	2
2	−6	5
5	0	4

Let z and w be two distinct non-zero complex numbers if |z|2w−|w|2z=z−w, then

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Let z and w be two distinct non-zero complex numbers if |z|2w−|w|2z=z−w, then

If 1,ω,ω2 denote the cube roots of unity, then, the value of (1−ω+ω2)5+(1+ω−ω2)5 is

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If 1,ω,ω2 denote the cube roots of unity, then, the value of (1−ω+ω2)5+(1+ω−ω2)5 is

The values of θ, for which ‌

The values of θ, for which ‌

If α,β are the roots of ax2+bx+c=0, then the quadratic equation whose roots are √5α,√5β is

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If α,β are the roots of ax2+bx+c=0, then the quadratic equation whose roots are √5α,√5β is

If a2+b2+c2=1,a,b,c∈C, then the set of extreme values of ab+bc+ca is

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If a2+b2+c2=1,a,b,c∈C, then the set of extreme values of ab+bc+ca is

If 2,3,6 are the roots of the polynomial f(x)=x3+a2+bx+c, where a,b,c, ∈mathbb‌C. Then the value of a−c is

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If 2,3,6 are the roots of the polynomial f(x)=x3+a2+bx+c, where a,b,c, ∈mathbb‌C. Then the value of a−c is

If y2+z2=3yz,z2+x2=8zx,x2+y2=4xy, then the value of ‌

is

If y2+z2=3yz,z2+x2=8zx,x2+y2=4xy, then the value of ‌

is

The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

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The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through the point B. Moreover, no three lines (apart from the lines passing through A and B) pass through same point and no two are parallel. What is the number of points of intersection of the straight lines?

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In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through the point B. Moreover, no three lines (apart from the lines passing through A and B) pass through same point and no two are parallel. What is the number of points of intersection of the straight lines?

The sum of all possible numbers that can be formed by using the digits 2,3,5,7 without repetition of digits is

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The sum of all possible numbers that can be formed by using the digits 2,3,5,7 without repetition of digits is

If ‌nPr=‌(n−1)Pr+x.‌(n−1)P(r+1)‌‌∀n,r∈N and r≤n, then x=

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If ‌nPr=‌(n−1)Pr+x.‌(n−1)P(r+1)‌‌∀n,r∈N and r≤n, then x=

=

=

=

=

cos‌θ(cosec‌θ−sec‌θ)−cot‌θ=

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cos‌θ(cosec‌θ−sec‌θ)−cot‌θ=

Let ABC be an acute-angled triangle with area R Then √a2b2−4R2+√b2c2−4R2+√c2a2−4R2=

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Let ABC be an acute-angled triangle with area R Then √a2b2−4R2+√b2c2−4R2+√c2a2−4R2=

In a triangle ABC, if a=4,b=5 and c=7, then sin(A∕2)=

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In a triangle ABC, if a=4,b=5 and c=7, then sin(A∕2)=

In any triangle ABC,‌

=

In any triangle ABC,‌

=

In a triangle ABC, let ∠C=

π

2

. If r and R are respectively inradius and circumradius of ABC, then R+r=

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In a triangle ABC, let ∠C=

π

2

. If r and R are respectively inradius and circumradius of ABC, then R+r=

Let a=i+xj+k,b=i+j+k and |a+b|=|a|+|b| then

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Let a=i+xj+k,b=i+j+k and |a+b|=|a|+|b| then

If a=i+2j+3k,b=2i+3j+k,c=8i+13j+9k and xa+yb+zc=0, then ‌

xy

z2

=

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If a=i+2j+3k,b=2i+3j+k,c=8i+13j+9k and xa+yb+zc=0, then ‌

=

The vector x is perpendicular to the vectors a=3i+2j+2k,b=18i−22j−5k and makes an obtuse angle with j. If |x|=14, then x=

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The vector x is perpendicular to the vectors a=3i+2j+2k,b=18i−22j−5k and makes an obtuse angle with j. If |x|=14, then x=

a,b are two vectors such that |a|=√3,|b|=√2. If x is a unit vector satisfying x×a=b then x=

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a,b are two vectors such that |a|=√3,|b|=√2. If x is a unit vector satisfying x×a=b then x=

The set of real values of λ for which the vectors λi−3j+5k and 2λi−λj+k are perpendicular to each other is

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The set of real values of λ for which the vectors λi−3j+5k and 2λi−λj+k are perpendicular to each other is

The standard deviation of first 10 multiples of 4 is

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The standard deviation of first 10 multiples of 4 is

From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is

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From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is

Person A can solve 90% of the problems given in the book and Person B can solve 70%. Then the probability that atleast one of them will solve the problem selected at random from the book is

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Person A can solve 90% of the problems given in the book and Person B can solve 70%. Then the probability that atleast one of them will solve the problem selected at random from the book is

A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is

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A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is

A person P speaks truth in 75% cases and another person R in 80% cases. Then the probability that they likely to contradict each other in narrating the same event is

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A person P speaks truth in 75% cases and another person R in 80% cases. Then the probability that they likely to contradict each other in narrating the same event is

During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is

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During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is

If X is a Poisson random variate with mean 3 , then P(|X−3|<2)=

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If X is a Poisson random variate with mean 3 , then P(|X−3|<2)=

A point P(x,y) is such that the sum of squares of its distances from (a,0) and (−a,0) is 2b2. The equation representing the locus of P is

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A point P(x,y) is such that the sum of squares of its distances from (a,0) and (−a,0) is 2b2. The equation representing the locus of P is

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are 3x+4y−4=0 and (2,2) respectively. Then, which of the following is another side of the triangle?

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Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are 3x+4y−4=0 and (2,2) respectively. Then, which of the following is another side of the triangle?

A point P on a line is at a distance of 4 units from the origin (0,0). If the line makes 60∘ with the negative direction of the x - axis, then P is

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A point P on a line is at a distance of 4 units from the origin (0,0). If the line makes 60∘ with the negative direction of the x - axis, then P is

Suppose ABOC is a rhombus in the first quadrant with O being the origin. If the vertices B and C of △ABC lie respectively on y=‌

4

3

x and y=0, and the side BC passes through (‌

), then the midpoint of BC is

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Suppose ABOC is a rhombus in the first quadrant with O being the origin. If the vertices B and C of △ABC lie respectively on y=‌

4

3

x and y=0, and the side BC passes through (‌

), then the midpoint of BC is

If ax2−34xy−5y2+2x+26y−5=0 represents a pair of straight lines, then the value of a is

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If ax2−34xy−5y2+2x+26y−5=0 represents a pair of straight lines, then the value of a is

The equations of the lines perpendicular to x2−5xy+4y2=0 and passing through (2,1) is

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The equations of the lines perpendicular to x2−5xy+4y2=0 and passing through (2,1) is

The straight line touching the circle x2+y2−2x−3=0 and remaining normal to the circle x2+y2−4y−6−0 is

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The straight line touching the circle x2+y2−2x−3=0 and remaining normal to the circle x2+y2−4y−6−0 is

The ratio of the areas of the greatest and the smallest circles touching (x±1)2+(y±1)2=1 is

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The ratio of the areas of the greatest and the smallest circles touching (x±1)2+(y±1)2=1 is

The equation of circle with centre (2,−3) and touching x-axis is

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The equation of circle with centre (2,−3) and touching x-axis is

In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is

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In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is

Suppose A (2,3) and B are the points of intersections of two circles. The points P lying on one circle and Q lying on the other circle are such that BP and BQ constitute the diameters of the circles. If the slopes of the radical axis and PQ are 3/4 and a/b respectively, then the value of 3a+4b is

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Suppose A (2,3) and B are the points of intersections of two circles. The points P lying on one circle and Q lying on the other circle are such that BP and BQ constitute the diameters of the circles. If the slopes of the radical axis and PQ are 3/4 and a/b respectively, then the value of 3a+4b is

If the directrix of the parabola x2+4y−6x+λ=0 is y+1=0, then which of the following is correct?

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If the directrix of the parabola x2+4y−6x+λ=0 is y+1=0, then which of the following is correct?

The foci of the ellipse 9x2+25y2=225 are

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The foci of the ellipse 9x2+25y2=225 are

If (1,2) is the focus, x+2y=0 is the directrix and √2 is the eccentricity of a hyperbola then the equation of the hyperbola is

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If (1,2) is the focus, x+2y=0 is the directrix and √2 is the eccentricity of a hyperbola then the equation of the hyperbola is

The locus of the point of intersection on the line √3x−y−4√3k=0 and √3kx+ky−4√3=0 for different real values of k is a hyperbola H. If e is the eccentricity of H then 4e2=

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The locus of the point of intersection on the line √3x−y−4√3k=0 and √3kx+ky−4√3=0 for different real values of k is a hyperbola H. If e is the eccentricity of H then 4e2=

If the centroid of a triangle with vertices (4,p,−3),(−1,−1,2) and (3,5,−8) is given by mid point of (1,4,−2) and (q. 2, -4), then p2+q2=

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If the centroid of a triangle with vertices (4,p,−3),(−1,−1,2) and (3,5,−8) is given by mid point of (1,4,−2) and (q. 2, -4), then p2+q2=

with Y and Z-axes respectively. Then the value of the sine of the angle made by the ray with X-axis is

with Y and Z-axes respectively. Then the value of the sine of the angle made by the ray with X-axis is

A plane meets the X,Y,Z - axes in A,B,C respectively. If the centroid of the triangle ABC is (2,−3,5) then the perpendicular distance from origin to the given plane is

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A plane meets the X,Y,Z - axes in A,B,C respectively. If the centroid of the triangle ABC is (2,−3,5) then the perpendicular distance from origin to the given plane is

=

=

4	−∞<x<−√5
x2−1	−√5≤x≤√5
4	√5≤x<∞

If k is the number of points where f(x) is not differentiable then k−2=

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f(x)={

4	−∞<x<−√5
x2−1	−√5≤x≤√5
4	√5≤x<∞

If k is the number of points where f(x) is not differentiable then k−2=

Assertion (A): f(x)=|x| is differentiable at x=a≠0 and continuous but not differentiable at x=0
Reason (R): If a function is differentiable at a point then it is continuous at that point. But converse is not true.

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Assertion (A): f(x)=|x| is differentiable at x=a≠0 and continuous but not differentiable at x=0
Reason (R): If a function is differentiable at a point then it is continuous at that point. But converse is not true.

then 2h(x)−f(x)−g(x)=

then 2h(x)−f(x)−g(x)=

Equation of tangent to the curve y=x+‌

4

x2

which is parallel to x-axis is

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Equation of tangent to the curve y=x+‌

4

x2

which is parallel to x-axis is

The normal to the curve y=f(x) at the points (3,4) makes an angle ‌

3π

4

with positive x-axis then f′(3)=

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The normal to the curve y=f(x) at the points (3,4) makes an angle ‌

3π

4

with positive x-axis then f′(3)=

The minimum distance of a point on the curve y=x2−4 from the origin is

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The minimum distance of a point on the curve y=x2−4 from the origin is

If an open cylinder of given surface area has maximum volume then its radius is

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If an open cylinder of given surface area has maximum volume then its radius is

If x+y=k,x>0,y>0 then x2+y2 is minimum. if

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If x+y=k,x>0,y>0 then x2+y2 is minimum. if

=

=

dx=Ax5+Bx3+Cx+K, then 5A+3B+C=

dx=Ax5+Bx3+Cx+K, then 5A+3B+C=

tan−1(f(x))+C, then f(x)=

tan−1(f(x))+C, then f(x)=

dx=

dx=

If f(x)=sin(tan−1x), then

If f(x)=sin(tan−1x), then

If a and b are respectively the order and degree of a differential equation y2(y′′)2+3x(y′)1∕3+x2y2=sin‌x, then

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If a and b are respectively the order and degree of a differential equation y2(y′′)2+3x(y′)1∕3+x2y2=sin‌x, then

An integrating factor of the differential equation (x2+1)‌

An integrating factor of the differential equation (x2+1)‌

If the general solution of ‌

)=f(y)+C, then f(e3)=

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If the general solution of ‌

)=f(y)+C, then f(e3)=

A physical quantity P is related to four observables a, b, c, and d as P‌

√ab⋅dα

√C

(α is constant) The percentage errors in a,b,c and d are 0.5% in each. If the percentage error in P is 2%, then α is

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A physical quantity P is related to four observables a, b, c, and d as P‌

√ab⋅dα

√C

(α is constant) The percentage errors in a,b,c and d are 0.5% in each. If the percentage error in P is 2%, then α is

A car is moving along a straight line is brought to a stop within a distance of 200m and in time 10s. The initial speed of the car is

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A car is moving along a straight line is brought to a stop within a distance of 200m and in time 10s. The initial speed of the car is

A ball is thrown upward from the top of a building at an angle of 30∘ to the horizontal and with an initial speed of 20ms−1. If the ball strikes the ground after 3s, then the height of the building is (acceleration due to gravity =10ms−2 )

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A ball is thrown upward from the top of a building at an angle of 30∘ to the horizontal and with an initial speed of 20ms−1. If the ball strikes the ground after 3s, then the height of the building is (acceleration due to gravity =10ms−2 )

A particle is moving on a circular path with a constant speed v. It's change of velocity as it moves from A to B in the figure is

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A particle is moving on a circular path with a constant speed v. It's change of velocity as it moves from A to B in the figure is

A box of mass 2kg is placed on a inclined plane that makes 30∘ with the horizontal. The coefficient of friction between the box and inclined plane is 0.2. A force F is applied on the box perpendicular to the incline to prevent the box from sliding down. The minimum value of F is
(acceleration due to gravity =10ms−2 )

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A box of mass 2kg is placed on a inclined plane that makes 30∘ with the horizontal. The coefficient of friction between the box and inclined plane is 0.2. A force F is applied on the box perpendicular to the incline to prevent the box from sliding down. The minimum value of F is
(acceleration due to gravity =10ms−2 )

Which of the following is true about the coefficient of static friction (µs) and the coefficient of kinematic friction (µk)

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Which of the following is true about the coefficient of static friction (µs) and the coefficient of kinematic friction (µk)

Two wooden blocks of mass M1 and M2 rest on a frictionless table. A bullet of mass m is fired at M1 with speed v which embedded in it and the two together finally collide with M2. Find the velocity of M2 after collision. [Ignore any energy loss and treat the problem to be one dimensional]

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Two wooden blocks of mass M1 and M2 rest on a frictionless table. A bullet of mass m is fired at M1 with speed v which embedded in it and the two together finally collide with M2. Find the velocity of M2 after collision. [Ignore any energy loss and treat the problem to be one dimensional]

An object of mass 20kg. is displayed by x=5t2m (here t is time) by the application of a force. Then the ratio of the work done in times 3s and 5s is

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An object of mass 20kg. is displayed by x=5t2m (here t is time) by the application of a force. Then the ratio of the work done in times 3s and 5s is

A uniform rod of length 60cm is placed with one end in contact with the horizontal table and is then inclined at an angle 30∘ to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is (acceleration due to gravity =10ms−2 )

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A uniform rod of length 60cm is placed with one end in contact with the horizontal table and is then inclined at an angle 30∘ to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is (acceleration due to gravity =10ms−2 )

A wheel undergoes a constant acceleration starting form rest at t=0. The angular velocity of the wheel is 3.14‌

rad

sec

when t=2s. The accelerator is abruptly ceased at t=20s. The number of revolutions, wheel makes in the interval t=0 to t=40s is

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A wheel undergoes a constant acceleration starting form rest at t=0. The angular velocity of the wheel is 3.14‌

rad

sec

when t=2s. The accelerator is abruptly ceased at t=20s. The number of revolutions, wheel makes in the interval t=0 to t=40s is

Assertion (A): In S.H.M kinetic and potential energy become equal when the distance is ‌

1

√2

times its amplitude
Reason (R): The potential energy of a particle executing S.H.M is periodic with time period being maximum at the extreme displacement.

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Assertion (A): In S.H.M kinetic and potential energy become equal when the distance is ‌

1

√2

times its amplitude
Reason (R): The potential energy of a particle executing S.H.M is periodic with time period being maximum at the extreme displacement.

A block of mass 100g is connected to an elastic spring of spring constant 450Nm−1 oscillates vertically. The block-spring system is in viscous surrounding medium with a damping constant 69.3gs−1. The time in which the amplitude of oscillations drop to half of its initial value.
[ take ln‌2=0.693]

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A block of mass 100g is connected to an elastic spring of spring constant 450Nm−1 oscillates vertically. The block-spring system is in viscous surrounding medium with a damping constant 69.3gs−1. The time in which the amplitude of oscillations drop to half of its initial value.
[ take ln‌2=0.693]

As shown in the figure, two spherical cavities are made in the uniform solid sphere of radius R. The boundaries of the cavities touch at the centre of the sphere. The centers of the cavities and the sphere lie on the x-axis. The mass of the solid sphere before the cavities were created was M. The gravitational force on a point mass m at a distance ' d ' away from the center of the solid sphere is

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As shown in the figure, two spherical cavities are made in the uniform solid sphere of radius R. The boundaries of the cavities touch at the centre of the sphere. The centers of the cavities and the sphere lie on the x-axis. The mass of the solid sphere before the cavities were created was M. The gravitational force on a point mass m at a distance ' d ' away from the center of the solid sphere is

One end of the steel rod is clamped to the roof and the other end is attached to a mass of 1000kg as shown in the figure. The length of the rod is 50cm and its cross-sectional area is 1000mm2. The change in the length of the rod due to the weight of the mass is (Young's modulus of steel =2×1011Nm−2 and acceleration due to gravity =10ms−2 )

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One end of the steel rod is clamped to the roof and the other end is attached to a mass of 1000kg as shown in the figure. The length of the rod is 50cm and its cross-sectional area is 1000mm2. The change in the length of the rod due to the weight of the mass is (Young's modulus of steel =2×1011Nm−2 and acceleration due to gravity =10ms−2 )

A circular film of a liquid has an area of 10cm2. If the work done in making its radius two times the initial radius is 8×10−3J, the surface tension of the liquid is (1+‌

1

a

)Nm−1. The value of α is

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A circular film of a liquid has an area of 10cm2. If the work done in making its radius two times the initial radius is 8×10−3J, the surface tension of the liquid is (1+‌

1

a

)Nm−1. The value of α is

A cylindrical tank having large diameter is filled with water to a height H. A hole of cross-sectional area 5cm2 in the tank allows water to drain out. If the water drains out at the rate of 2×10−3m3s−1, then the value of H is
(acceleration due to gravity =10ms−2 )

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A cylindrical tank having large diameter is filled with water to a height H. A hole of cross-sectional area 5cm2 in the tank allows water to drain out. If the water drains out at the rate of 2×10−3m3s−1, then the value of H is
(acceleration due to gravity =10ms−2 )

) at a pressure of 4atm is compressed adiabatically so that its temperature rises from 27∘C to 327∘C. The pressure of the gas in its final state is

) at a pressure of 4atm is compressed adiabatically so that its temperature rises from 27∘C to 327∘C. The pressure of the gas in its final state is

The change in the internal energy of 3 moles of a gas heated at constant volume from 20∘C to 40∘C is 1080J. The molar specific heat of the gas at constant volume in Jmol−1K−1 is

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The change in the internal energy of 3 moles of a gas heated at constant volume from 20∘C to 40∘C is 1080J. The molar specific heat of the gas at constant volume in Jmol−1K−1 is

A gas at 37‌∘C is compressed adiabatically to half of its volume, then the final temperature of the gas is
(Ratio of specific heat capacities of the gas is 1.5 )

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A gas at 37‌∘C is compressed adiabatically to half of its volume, then the final temperature of the gas is
(Ratio of specific heat capacities of the gas is 1.5 )

A vessel contains 3 moles of He,1 mole of Ar,5 moles of N2 and 3 moles of H2. If the vibrational modes are ignored, the total internal energy of the system of gases is

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A vessel contains 3 moles of He,1 mole of Ar,5 moles of N2 and 3 moles of H2. If the vibrational modes are ignored, the total internal energy of the system of gases is

A steel wire of length 1.25m is stretched between two rigid supports. The tension in the wire produces an elastic strain of 0.14%. The fundamental frequency of the wire is
(Density and Young's modules of steel are 7.7×103kgm−3 and 2.2×1011Nm−2 respectively)

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A steel wire of length 1.25m is stretched between two rigid supports. The tension in the wire produces an elastic strain of 0.14%. The fundamental frequency of the wire is
(Density and Young's modules of steel are 7.7×103kgm−3 and 2.2×1011Nm−2 respectively)

An optician prescribes a corrective lens of power +2D, then the focal length of the required convex lens is

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An optician prescribes a corrective lens of power +2D, then the focal length of the required convex lens is

A monochromatic light of wavelength 6000Å coming from a star is detected in a 100 inch telescope. The limit of resolution of the telescope is approximately

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A monochromatic light of wavelength 6000Å coming from a star is detected in a 100 inch telescope. The limit of resolution of the telescope is approximately

The distribution of some charges on two Gaussian surfaces A and B are as shown in the figure. If φA and φB are electric fluxes linked with the surfaces A and B respectively, then ‌

φA

φB

=

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The distribution of some charges on two Gaussian surfaces A and B are as shown in the figure. If φA and φB are electric fluxes linked with the surfaces A and B respectively, then ‌

=

The magnetic field due to current carrying circular loop of radius 6cm at a point on the axis at a distance of 8cm from centre is 27µT. The magnetic field at the centre of the current carrying loop is.

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The magnetic field due to current carrying circular loop of radius 6cm at a point on the axis at a distance of 8cm from centre is 27µT. The magnetic field at the centre of the current carrying loop is.

25 capacitors each of capacitance 1µF are connected in series to a battery of 100V. The total charge stored on capacitors is

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25 capacitors each of capacitance 1µF are connected in series to a battery of 100V. The total charge stored on capacitors is

Two cells A and B are connected in the secondary circuit of a potentiometer one at a time and the balancing lengths are respectively 360cm and 420cm. If emf of A is 2.4V, the emf of the second cell B is

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Two cells A and B are connected in the secondary circuit of a potentiometer one at a time and the balancing lengths are respectively 360cm and 420cm. If emf of A is 2.4V, the emf of the second cell B is

A 8Ω resistor is connected to a battery that has an internal resistance of 0.2Ω. If the voltage across the battery (the terminal voltage) is 10V, then the emf of the battery is

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A 8Ω resistor is connected to a battery that has an internal resistance of 0.2Ω. If the voltage across the battery (the terminal voltage) is 10V, then the emf of the battery is

An infinitely long wire carrying 1 A current in the +Z direction is placed at (1cm,1cm ). Another wire carrying 1A in +x direction is placed at y=1cm. If the magnetic field due to this configuration at the origin is

→

B

. Let B0 be the magnitude of the field if only the wire at (1cm,1cm) was present, then ‌

is

An infinitely long wire carrying 1 A current in the +Z direction is placed at (1cm,1cm ). Another wire carrying 1A in +x direction is placed at y=1cm. If the magnetic field due to this configuration at the origin is

→

B

. Let B0 be the magnitude of the field if only the wire at (1cm,1cm) was present, then ‌

is

An observer at rest experiences an electric field due to a static charge. Later he starts moving away from it then the observer experiences.

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An observer at rest experiences an electric field due to a static charge. Later he starts moving away from it then the observer experiences.

A short magnetic needle is placed in a magnetic field B

). The needle experiences a torque of 0.06Nm. If the same magnetic needle is placed in a magnetic field 2B

), the torque experienced by it is

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A short magnetic needle is placed in a magnetic field B

). The needle experiences a torque of 0.06Nm. If the same magnetic needle is placed in a magnetic field 2B

), the torque experienced by it is

Assertion (A): When a circular coil, placed in a region with its plane parallel to a magnetic field, expands radially outwards, no emf is induced in it.
Reason (R): There is a constant magnet field in the perpendicular (to the plane of the coil) direction.

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Assertion (A): When a circular coil, placed in a region with its plane parallel to a magnetic field, expands radially outwards, no emf is induced in it.
Reason (R): There is a constant magnet field in the perpendicular (to the plane of the coil) direction.

A circuit containing inductance of ‌

1

6π

H and a resistance of 15Ω in series. If an AC voltage of 100V and 60Hz is applied to above circuit, then the current in the circuit and phase difference between voltage and current respectively are

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A circuit containing inductance of ‌

1

6π

H and a resistance of 15Ω in series. If an AC voltage of 100V and 60Hz is applied to above circuit, then the current in the circuit and phase difference between voltage and current respectively are

In a plane electromagnetic wave, UE and UB are average energy densities of electric field and magnetic field respectively, then the correct option in the following is

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In a plane electromagnetic wave, UE and UB are average energy densities of electric field and magnetic field respectively, then the correct option in the following is

Light of wavelength 1nm belongs to the following class of waves

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Light of wavelength 1nm belongs to the following class of waves

A particle of mass 1×10−30kg and electric change 1.6×10−19C has de-Broglie wavelength 660nm. Then kinetic energy of this particle is (Plank's constant, h=6.6×10−34J−s )

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A particle of mass 1×10−30kg and electric change 1.6×10−19C has de-Broglie wavelength 660nm. Then kinetic energy of this particle is (Plank's constant, h=6.6×10−34J−s )

For the logic gates shown below, the correct output is

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For the logic gates shown below, the correct output is

A radioactive element of mass 1kg after N years is left with only 125g. If the half life of the element is 12.5y, then the value of N is

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A radioactive element of mass 1kg after N years is left with only 125g. If the half life of the element is 12.5y, then the value of N is

A pure semiconductor crystal has 8×1028‌

‌ atoms ‌

m3

. It is doped by 2ppm concentration of pentavalent atoms. The number of holes formed in the semiconductor crystal is
(Intrinsic carrier concentration, ni=1×1016m−3 ).

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A pure semiconductor crystal has 8×1028‌

‌ atoms ‌

m3

. It is doped by 2ppm concentration of pentavalent atoms. The number of holes formed in the semiconductor crystal is
(Intrinsic carrier concentration, ni=1×1016m−3 ).

The minimum size of an antenna for transmitting electromagnetic waves at 1500MHz is

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The minimum size of an antenna for transmitting electromagnetic waves at 1500MHz is

Work function (W∘ ) values of six metals (in eV ) are given below:

The work function of a metal M is 6.3eV. The wave length of the incident radiation required to just eject the electrons from its surface (in nm) is

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The work function of a metal M is 6.3eV. The wave length of the incident radiation required to just eject the electrons from its surface (in nm) is

In which of the following, elements are correctly arranged in the decreasing order of their second ionization enthalpies.

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In which of the following, elements are correctly arranged in the decreasing order of their second ionization enthalpies.

Identify the element which has highest second ionization enthalpy

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Identify the element which has highest second ionization enthalpy

The general formula of the compound formed when a metal (M) of group - 1 reacts with non metal (x) of group −16 is

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The general formula of the compound formed when a metal (M) of group - 1 reacts with non metal (x) of group −16 is

Arrange the following species in the decreasing order of their bond orders.

Arrange the following species in the decreasing order of their bond orders.

20mL of gas A and 10mL of gas B diffuses through a porous membrane separately in 1 minute. If the vapor density of B is X, what is the vapor density of A ?

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20mL of gas A and 10mL of gas B diffuses through a porous membrane separately in 1 minute. If the vapor density of B is X, what is the vapor density of A ?

If the total electricity required to deposit 1 mole of a metal M is equal to that of 10.7 amperes of current for 10 hours. The equivalent weight of the metal is (atomic weight =Mu )

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If the total electricity required to deposit 1 mole of a metal M is equal to that of 10.7 amperes of current for 10 hours. The equivalent weight of the metal is (atomic weight =Mu )

Identify the correct statements from the following.
(i). For adiabatic process, ∆U=W‌adiabatic ‌
(ii). Work is a path function.
(iii). Volume is an extensive property.

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Identify the correct statements from the following.
(i). For adiabatic process, ∆U=W‌adiabatic ‌
(ii). Work is a path function.
(iii). Volume is an extensive property.

The standard molar enthalpy of vaporisation (∆‌vap ‌H∘) of A,B and C liquids is 23.3, 41 and 29kJmol−1 respectively. The correct order of dipole-dipole attractive forces in these liquids is:

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The standard molar enthalpy of vaporisation (∆‌vap ‌H∘) of A,B and C liquids is 23.3, 41 and 29kJmol−1 respectively. The correct order of dipole-dipole attractive forces in these liquids is:

At 25∘C, the solubility product of MCl is 1×10−10. What is its molar solubility in 0.1MNaCl solution at same temperature?

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At 25∘C, the solubility product of MCl is 1×10−10. What is its molar solubility in 0.1MNaCl solution at same temperature?

The solubility products of NiS,ZnS,CdS and HgS are 4.7×10−5,1.6×10−24,8×10−27 and 4×10−53 respectively. An aqueous solution contains Ni2+,Zn2+,Cd2+, and Hg2+ of equal concentration. H2S gas was passed into this solution very slowly. The first and the last ions that precipitate as sulphides are respectively

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The solubility products of NiS,ZnS,CdS and HgS are 4.7×10−5,1.6×10−24,8×10−27 and 4×10−53 respectively. An aqueous solution contains Ni2+,Zn2+,Cd2+, and Hg2+ of equal concentration. H2S gas was passed into this solution very slowly. The first and the last ions that precipitate as sulphides are respectively

Hydration enthalpy of which of the following ions is highest?

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Hydration enthalpy of which of the following ions is highest?

Identify the correct statements from the following:
(a) Alkali metals are strong reducing agents.
(b) KO2 is a diamagnetic oxide.
(c) Lithium chloride exists as LiCl. 2H2O

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Identify the correct statements from the following:
(a) Alkali metals are strong reducing agents.
(b) KO2 is a diamagnetic oxide.
(c) Lithium chloride exists as LiCl. 2H2O

Aluminium chloride in acidified aqueous solution gives a complex ion ' X '. The hybridization of central atom in X is

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Aluminium chloride in acidified aqueous solution gives a complex ion ' X '. The hybridization of central atom in X is

Bond enthalpy of Ge-Ge bond is 260kJmol−1. The bond ethalpies of Si-Si and Sn− Sn bonds in kJmol−1 are respectively,

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Bond enthalpy of Ge-Ge bond is 260kJmol−1. The bond ethalpies of Si-Si and Sn− Sn bonds in kJmol−1 are respectively,

Identify the molecules which have sp- hybridized carbon(s) from the list given under.
I. Ethane nitrile,
II. Buta-1, 3-diene,
III. Propa-1, 2-diene,
TV. Ethyne V. Benzene

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Identify the molecules which have sp- hybridized carbon(s) from the list given under.
I. Ethane nitrile,
II. Buta-1, 3-diene,
III. Propa-1, 2-diene,
TV. Ethyne V. Benzene

The decreasing order of acidic nature of the following compounds is

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The decreasing order of acidic nature of the following compounds is

The density of Na is 0.613gcm−3. If the edge length of unit cell of Na is 5A0, the effective number of atoms of Na per unit cell is (Atomic weight of Na=23u )

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The density of Na is 0.613gcm−3. If the edge length of unit cell of Na is 5A0, the effective number of atoms of Na per unit cell is (Atomic weight of Na=23u )

Ag crystallizes in fcc lattice. What is the total number of tetrahedral voids present in 540g of Ag metal? (NA= Avagadro number; Ag atomic weight =108gmol−1)

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Ag crystallizes in fcc lattice. What is the total number of tetrahedral voids present in 540g of Ag metal? (NA= Avagadro number; Ag atomic weight =108gmol−1)

3.1g of a compound. ' X ' (molar mass =62gmol−1 ) is dissolved in 19.5g of other compound, Y (molar mass =78gmol−1 ). The ratio of mole fractions of X and Y in the solution is

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3.1g of a compound. ' X ' (molar mass =62gmol−1 ) is dissolved in 19.5g of other compound, Y (molar mass =78gmol−1 ). The ratio of mole fractions of X and Y in the solution is

For which of the following liquid mixtures ∆mixH=0 and ∆mixV=0 ?

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For which of the following liquid mixtures ∆mixH=0 and ∆mixV=0 ?

The standard Gibbs energy (∆G0) for the following reaction is A(s)+B2+(aq)⇌A2+(aq)+B(s),Kc=1012 at 250C(Kc=‌ equilibrium constant ‌)

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The standard Gibbs energy (∆G0) for the following reaction is A(s)+B2+(aq)⇌A2+(aq)+B(s),Kc=1012 at 250C(Kc=‌ equilibrium constant ‌)

What is the concentration (in mol L−1 ) of the product after 20s in the following reaction.
Given that A→3B, rate =k[A]∘

Freundlich adsorption isotherm fails at which of the following condition?

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Freundlich adsorption isotherm fails at which of the following condition?

The no. of positively and negatively charged sols respectively in the following are
TiO2, blood, CdS,Cu,Ag, Clay, SiO2,Fe2O3.

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The no. of positively and negatively charged sols respectively in the following are
TiO2, blood, CdS,Cu,Ag, Clay, SiO2,Fe2O3.

Arrange the following oxides in correct order of their acidic character.

Arrange the following oxides in correct order of their acidic character.

Which of the following represents correct order of oxidizing power of halogens with water

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Which of the following represents correct order of oxidizing power of halogens with water

Which of the following elements are not regarded as transition elements?

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Which of the following elements are not regarded as transition elements?

The hybridization of metals involved in the following complexes, respectively are

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The hybridization of metals involved in the following complexes, respectively are

Hydrolysis of nucleic acid gives nitrogenous base sugar and_____________

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Hydrolysis of nucleic acid gives nitrogenous base sugar and_____________

Sugar present in DNA is

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Sugar present in DNA is

The rate of reaction of t-butyl bromide and NaOH in water depends on the concentration of

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The rate of reaction of t-butyl bromide and NaOH in water depends on the concentration of

The product formed in the given reaction is

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The product formed in the given reaction is

Which of the following reactions takes places when tertiary butanol passed over heated copper at 573K.?

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Which of the following reactions takes places when tertiary butanol passed over heated copper at 573K.?

Identify the major product from the following reaction sequence.

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Identify the major product from the following reaction sequence.

With reference to the carbonyl group which statement(s) is/are correct?
a) Carbonyl Carbon is electrophilic
b) Carbonyl Carbon is nucleophilic
c) Carbonyl Oxygen is electrophilic
d) Carbonyl Oxygen is nucleophilic

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With reference to the carbonyl group which statement(s) is/are correct?
a) Carbonyl Carbon is electrophilic
b) Carbonyl Carbon is nucleophilic
c) Carbonyl Oxygen is electrophilic
d) Carbonyl Oxygen is nucleophilic

Hydrolysis of the minor product formed from the reaction of 1-Bromo propane and ethanolic KCN given

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Hydrolysis of the minor product formed from the reaction of 1-Bromo propane and ethanolic KCN given

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