AP EAPCET - 04 July 2022

2	−3
−4	1

], then (AT)2+(12A)T=

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If A=[

2	−3
−4	1

], then (AT)2+(12A)T=

If a,b,c are respectively the 5‌th ‌,8‌th ‌,13‌th ‌ terms of an arithmetic progression, then |

a	5	1
b	8	1
c	13	1

|=

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If a,b,c are respectively the 5‌th ‌,8‌th ‌,13‌th ‌ terms of an arithmetic progression, then |

a	5	1
b	8	1
c	13	1

|=

1	0	0
a	−1	0
b	c	1

] is such that A2=I, then

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If A=[

1	0	0
a	−1	0
b	c	1

] is such that A2=I, then

−2	x	1
x	1	1
2	3	−1

]. If the roots of the equation det‌A=0 are l, m then l3−m3=

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Let A=[

−2	x	1
x	1	1
2	3	−1

]. If the roots of the equation det‌A=0 are l, m then l3−m3=

Multiplicative inverse of the complex number (sin‌θ,cos‌θ) is

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Multiplicative inverse of the complex number (sin‌θ,cos‌θ) is

ik=x+iy⇒x100+x99y+x242y2+x97y3=

ik=x+iy⇒x100+x99y+x242y2+x97y3=

A true statement among the following identities is

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A true statement among the following identities is

=

=

If f(f(0))=0, where f(x)=x2+ax+b,b≠0 then a+b=

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If f(f(0))=0, where f(x)=x2+ax+b,b≠0 then a+b=

The sum of the real roots of the equation |x−2|2+|x−2|−2=0 is

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The sum of the real roots of the equation |x−2|2+|x−2|−2=0 is

If the difference between the roots of x2+ax+b=0 and that of the roots of x2+bx+a=0 is same and a≠b. then

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If the difference between the roots of x2+ax+b=0 and that of the roots of x2+bx+a=0 is same and a≠b. then

For what values of a∈Z, the quadratic expression (x+a)(x+1991)+1 can be factorised

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For what values of a∈Z, the quadratic expression (x+a)(x+1991)+1 can be factorised

If a set A has m - elements and the set B has n-elements, then the number of injections from A to B is

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If a set A has m - elements and the set B has n-elements, then the number of injections from A to B is

In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

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In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

The least value of n so that ‌(n−1)C3+‌(n−1)C4>‌nC3

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The least value of n so that ‌(n−1)C3+‌(n−1)C4>‌nC3

A natural number n such that n ! ends in exactly 1000 zeros is

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A natural number n such that n ! ends in exactly 1000 zeros is

If A+B+C=π,cos‌B=cos‌A‌cos‌C, then tan‌A‌tan‌C=

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If A+B+C=π,cos‌B=cos‌A‌cos‌C, then tan‌A‌tan‌C=

In a triangle ABC,(tan‌

In a triangle ABC,(tan‌

In a triangle ABC,2(bc‌cos‌A+ac‌cos‌B+ab‌cos‌C)=

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In a triangle ABC,2(bc‌cos‌A+ac‌cos‌B+ab‌cos‌C)=

If 4+6(e2x+1)‌tanh‌x=11‌cosh‌x+11‌sinh‌x, then x=

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If 4+6(e2x+1)‌tanh‌x=11‌cosh‌x+11‌sinh‌x, then x=

=2+√3 and ∠C=60∘. Then the measure of ∠A is

=2+√3 and ∠C=60∘. Then the measure of ∠A is

If a=2,b=3,c=4 in a triangle ABC, then cos‌C=

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If a=2,b=3,c=4 in a triangle ABC, then cos‌C=

In a triangle ABC,(b+c)‌cos‌A+(c+a)‌cos‌B+(a+b)‌cos‌C=

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In a triangle ABC,(b+c)‌cos‌A+(c+a)‌cos‌B+(a+b)‌cos‌C=

D,E,F are respectively the points on the sides BC,CA and AB of a △ABC dividing them in the ratio 2:3,1:2,3:1 internally. The lines BE and CF intersect on the line AD at P. If AP=x1⋅AB+y1.AC then x1+y1=

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D,E,F are respectively the points on the sides BC,CA and AB of a △ABC dividing them in the ratio 2:3,1:2,3:1 internally. The lines BE and CF intersect on the line AD at P. If AP=x1⋅AB+y1.AC then x1+y1=

OABC is a tetrahedron. If D,E are the midpoints of OA and BC respectively, then DE=

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OABC is a tetrahedron. If D,E are the midpoints of OA and BC respectively, then DE=

If a+b+c=0 and |a|=7,|b|=5,|c|=3 then the angle between b and c is

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If a+b+c=0 and |a|=7,|b|=5,|c|=3 then the angle between b and c is

If P,Q are two points on the curve y=2x+2 in the rectangular Cartesian coordinate system such that OP⋅i=−1,OQ⋅i=2 then OQ−4OP=

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If P,Q are two points on the curve y=2x+2 in the rectangular Cartesian coordinate system such that OP⋅i=−1,OQ⋅i=2 then OQ−4OP=

If the equation of the plane passing through the point A(−2,1,3) and perpendicular to the vector 3i+j+5k is ax+by+cz+d=0 then ‌

a+b

c+d

=

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If the equation of the plane passing through the point A(−2,1,3) and perpendicular to the vector 3i+j+5k is ax+by+cz+d=0 then ‌

=

If the mean of the data p.6,6.7,8,11,15,16, is 3 times p, then the mean deviation of the data from its mean is

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If the mean of the data p.6,6.7,8,11,15,16, is 3 times p, then the mean deviation of the data from its mean is

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is

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In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is

For two events A and B, a true statement among the following is

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For two events A and B, a true statement among the following is

Five digit numbers are formed by using digits 1,2,3,4 and 5 without repetition. Then, the probability that the randomly chosen number is divisible by 4 is

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Five digit numbers are formed by using digits 1,2,3,4 and 5 without repetition. Then, the probability that the randomly chosen number is divisible by 4 is

A manager decides to distribute Rs. 20000 between two employees X and Y. He knows X deserves more than Y, but does not know how much more. So, he decides to arbitrarily break Rs. 20000 in to two parts and gives X the bigger part. Then, the chance that X gets twice as much as Y or more is

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A manager decides to distribute Rs. 20000 between two employees X and Y. He knows X deserves more than Y, but does not know how much more. So, he decides to arbitrarily break Rs. 20000 in to two parts and gives X the bigger part. Then, the chance that X gets twice as much as Y or more is

Which of the following is not a property of a Binomial distribution?

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Which of the following is not a property of a Binomial distribution?

In a Binomial distribution B(n,p), if the mean and variance are 15 and 10 respectively, then the value of the parameter n is

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In a Binomial distribution B(n,p), if the mean and variance are 15 and 10 respectively, then the value of the parameter n is

Suppose P and Q are the mid points of the sides AB and BC of a triangle where A(1,3),B(3,7) and C(7,15) are vertices. Then the locus of R satisfying AC2+QR2=PR2‌ is ‌

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Suppose P and Q are the mid points of the sides AB and BC of a triangle where A(1,3),B(3,7) and C(7,15) are vertices. Then the locus of R satisfying AC2+QR2=PR2‌ is ‌

Suppose △ABC is an isosceles triangle with ∠C=90∘,A=(2,3) and B=(4,5). Then the centroid of the triangle is

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Suppose △ABC is an isosceles triangle with ∠C=90∘,A=(2,3) and B=(4,5). Then the centroid of the triangle is

If the points of intersection of the coordinate axes and |x+y|=2 form a rhombus, then its area is

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If the points of intersection of the coordinate axes and |x+y|=2 form a rhombus, then its area is

Suppose, in triangle △ABC,x−y+5=0,x+2y=0 are respectively the equations of the perpendicular bisectors of the sides AB and AC. If A is (1,−2), the equation of the line joining B and C is

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Suppose, in triangle △ABC,x−y+5=0,x+2y=0 are respectively the equations of the perpendicular bisectors of the sides AB and AC. If A is (1,−2), the equation of the line joining B and C is

If the pair of straight lines 9x2+axy+4y2+6x+by−3=0 represents two parallel lines then

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If the pair of straight lines 9x2+axy+4y2+6x+by−3=0 represents two parallel lines then

A line passing through P(2,3) and making an angle of 30∘ with the positive direction of x-axis meets x2−2xy−y2=0 at A and B. Then the value of PA.PB is

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A line passing through P(2,3) and making an angle of 30∘ with the positive direction of x-axis meets x2−2xy−y2=0 at A and B. Then the value of PA.PB is

For any real number t, the point (‌

For any real number t, the point (‌

The area of the circle passing through the points (5,±2),(1,2) is

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The area of the circle passing through the points (5,±2),(1,2) is

The ratio of the largest and shortest distances from the point (2,−7) to the circle x2+y2−14x−10y−151=0 is

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The ratio of the largest and shortest distances from the point (2,−7) to the circle x2+y2−14x−10y−151=0 is

A circle has its centre in the first quadrant and passes through (2,3). If this circle makes intercepts of length 3 and 4 respectively on x=2 and y=3, its equation is

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A circle has its centre in the first quadrant and passes through (2,3). If this circle makes intercepts of length 3 and 4 respectively on x=2 and y=3, its equation is

The image of the point (3,4) with respect to the radical axis of the circles x2+y2+8x+2y+10=0 and x2+y2+7x+3y+10=0 is

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The image of the point (3,4) with respect to the radical axis of the circles x2+y2+8x+2y+10=0 and x2+y2+7x+3y+10=0 is

Suppose a parabola passes through (0,4),(1,9) and (4,5) and has its axis parallel to the y-axis. Then the equation of the parabola is

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Suppose a parabola passes through (0,4),(1,9) and (4,5) and has its axis parallel to the y-axis. Then the equation of the parabola is

The focal distances of the point (‌

The focal distances of the point (‌

If the normal to the rectangular hyperbola x2−y2=1 at the point P(π/4) meets the curve again at Q(θ), then sec2θ+tan‌θ=

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If the normal to the rectangular hyperbola x2−y2=1 at the point P(π/4) meets the curve again at Q(θ), then sec2θ+tan‌θ=

If the vertices and foci of a hyperbola are respectively (±3,0) and (±4,0) then the parametric equations of that hyperbola are

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If the vertices and foci of a hyperbola are respectively (±3,0) and (±4,0) then the parametric equations of that hyperbola are

If x-coordinate of a point P on the line joining the points Q(2,2,1) and R(5,2,−2) is 4 , then the y-coordinate of P=

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If x-coordinate of a point P on the line joining the points Q(2,2,1) and R(5,2,−2) is 4 , then the y-coordinate of P=

If (2,3,c) are the direction ratios of a ray passing through the point C(5,q,1) and also the mid point of the line segment joining the points A(p,−4,2) and B(3,2,−4) then c⋅(p+7q)=

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If (2,3,c) are the direction ratios of a ray passing through the point C(5,q,1) and also the mid point of the line segment joining the points A(p,−4,2) and B(3,2,−4) then c⋅(p+7q)=

If the equation of the plane which is at a distance of 1/3 units from the origin and perpendicular to a line whose directional ratios are (1,2,2) is x+py+qz+r=0 then √p2+q2+r2=

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If the equation of the plane which is at a distance of 1/3 units from the origin and perpendicular to a line whose directional ratios are (1,2,2) is x+py+qz+r=0 then √p2+q2+r2=

If [⋅] denotes greatest integer function, then

]=

If [⋅] denotes greatest integer function, then

]=

If l,m(l<m) are roots of ax2+bx+c=0, then

=

If l,m(l<m) are roots of ax2+bx+c=0, then

=

f(x) exist, then the possible values for a and b are

f(x) exist, then the possible values for a and b are

If x≠0 and f(x) satisfies 8f(x)+6f(1/x)=x+5, then ‌

If x≠0 and f(x) satisfies 8f(x)+6f(1/x)=x+5, then ‌

))=

))=

, then at x=0,f(x) is

, then at x=0,f(x) is

The number of those tangents to the curve y2−2x3−4y+8=0 which pass through the point (1,2) is

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The number of those tangents to the curve y2−2x3−4y+8=0 which pass through the point (1,2) is

If the straight line x‌cos‌α+y‌sin‌α=p touches the curve (‌

)n=2 at the point (a,b) on it and ‌

If the straight line x‌cos‌α+y‌sin‌α=p touches the curve (‌

)n=2 at the point (a,b) on it and ‌

Condition that 2 curves y2=4ax,xy=c2 cut orthogonally is

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Condition that 2 curves y2=4ax,xy=c2 cut orthogonally is

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

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A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

Two particles P and Q located at the points P(t,t3−16t−3),Q(t+1,t3−6t−6) are moving in a plane, the minimum distance between the points in their motion is

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Two particles P and Q located at the points P(t,t3−16t−3),Q(t+1,t3−6t−6) are moving in a plane, the minimum distance between the points in their motion is

If f(x)=∫x2cos2x(2xtan2x−2x−6‌tan‌x)dx and f(0)=π then f(x)=

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If f(x)=∫x2cos2x(2xtan2x−2x−6‌tan‌x)dx and f(0)=π then f(x)=

(x+√x)dx=e√x[Ax+B√x+C]+K, then A+B+C=

(x+√x)dx=e√x[Ax+B√x+C]+K, then A+B+C=

dx=A‌log‌tan‌x+B‌tan‌x+C then 4A−2B=

dx=A‌log‌tan‌x+B‌tan‌x+C then 4A−2B=

dx=

dx=

=

=

etan2θsin2θ‌tan‌θ‌d‌θ=

etan2θsin2θ‌tan‌θ‌d‌θ=

(|cos‌t|‌sin‌t+|sin‌t|‌cos‌t)dt=

(|cos‌t|‌sin‌t+|sin‌t|‌cos‌t)dt=

If f(x)=Max{sin‌x,cos‌x} and g(x)=Min{sin‌x,cos‌x}, then

If f(x)=Max{sin‌x,cos‌x} and g(x)=Min{sin‌x,cos‌x}, then

If l and m are order and degree of a differential equation of all the straight lines at constant distance of P units from the origin, then lm2+l2m=

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If l and m are order and degree of a differential equation of all the straight lines at constant distance of P units from the origin, then lm2+l2m=

If 2x−y+c‌log(|x−2y−4|)=k is the general solution of ‌

If 2x−y+c‌log(|x−2y−4|)=k is the general solution of ‌

By eliminating the arbitrary constants from y=(a+b)‌sin(x+c)−dex+e+f, the differential equation obtained is of order

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By eliminating the arbitrary constants from y=(a+b)‌sin(x+c)−dex+e+f, the differential equation obtained is of order

In SI units, kgm2s−2 is equivalent to which of the following?

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In SI units, kgm2s−2 is equivalent to which of the following?

An object moving along x-axis with a uniform acceleration has velocity

at x=3cm. After 2s if it is at x=−5cm, then its acceleration is

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An object moving along x-axis with a uniform acceleration has velocity

at x=3cm. After 2s if it is at x=−5cm, then its acceleration is

of magnitude 4N acts on an object of mass 1kg, at origin in a direction 30∘ above the positive x - axis. A second force

→

F2

of magnitude 4N acts on the same object in the direction of the positive y - axis. The magnitude of the acceleration of the object is nearly

of magnitude 4N acts on an object of mass 1kg, at origin in a direction 30∘ above the positive x - axis. A second force

→

F2

of magnitude 4N acts on the same object in the direction of the positive y - axis. The magnitude of the acceleration of the object is nearly

y=(Pt2−Qt3)m is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

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y=(Pt2−Qt3)m is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

A cricket ball of mass 50g having velocity 50cms−1 is stopped in 0.5s. The force applied to stop the ball is

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A cricket ball of mass 50g having velocity 50cms−1 is stopped in 0.5s. The force applied to stop the ball is

Two masses M1 and M2 are arranged as shown in the figure. Let ' a ' be the magnitude of the acceleration of the mass M1. If the mass of M1 is doubled and that of M2 is halved, then the acceleration of the system is (Treat all surfaces as smooth ; masses of pulley and rope are negligible )

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Two masses M1 and M2 are arranged as shown in the figure. Let ' a ' be the magnitude of the acceleration of the mass M1. If the mass of M1 is doubled and that of M2 is halved, then the acceleration of the system is (Treat all surfaces as smooth ; masses of pulley and rope are negligible )

A ball of mass 300g is dropped from a height 10m above a sandy ground. On reaching the ground, it penetrates through a distance 1.5m in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity =10ms−2 )

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A ball of mass 300g is dropped from a height 10m above a sandy ground. On reaching the ground, it penetrates through a distance 1.5m in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity =10ms−2 )

Two balls A and B, of masses M and 2M respectively collide each other. If the ball A moves with a speed of 150ms−1 and collides with ball B, moving with speed v in the opposite direction. After collision if ball A comes to rest and the coefficient of restitution is 1 (one), then the speed of the ball B before it collides with ball A is

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Two balls A and B, of masses M and 2M respectively collide each other. If the ball A moves with a speed of 150ms−1 and collides with ball B, moving with speed v in the opposite direction. After collision if ball A comes to rest and the coefficient of restitution is 1 (one), then the speed of the ball B before it collides with ball A is

A solid sphere of radius R has its outer half removed, so that its radius becomes (

R

2

). Then its moment of inertia about the diameter is

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A solid sphere of radius R has its outer half removed, so that its radius becomes (

R

2

). Then its moment of inertia about the diameter is

Which of the following is not true about vectors

?

Which of the following is not true about vectors

?

A body is executing S.H.M. At a displacement ' x ' its potential energy is 9J and at a displacement ' y ' its potential energy is 16J. The potential energy at displacement (x+y) is

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A body is executing S.H.M. At a displacement ' x ' its potential energy is 9J and at a displacement ' y ' its potential energy is 16J. The potential energy at displacement (x+y) is

As shown in the figure, an iron block A of volume 0.25m3 is attached to a spring S of unstretched length 1.0m and hanging to the ceiling of a roof. The spring gets stretched by 0.2m. This block is removed and another block B of iron of volume 0.75m3 is now attached to the same spring and kept on a frictionless incline plane of 30∘ inclination. The distance of the block from the top along the incline at equilibrium is

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As shown in the figure, an iron block A of volume 0.25m3 is attached to a spring S of unstretched length 1.0m and hanging to the ceiling of a roof. The spring gets stretched by 0.2m. This block is removed and another block B of iron of volume 0.75m3 is now attached to the same spring and kept on a frictionless incline plane of 30∘ inclination. The distance of the block from the top along the incline at equilibrium is

A uniform solid sphere of radius R produces a gravitational acceleration of a0 on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes ‌

a0

4

is

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A uniform solid sphere of radius R produces a gravitational acceleration of a0 on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes ‌

is

In a hydraulic lift, compressed air exerts a force F on a small piston of radius 3cm. Due to this pressure the second piston of radius 5cm lifts a load of 1875kg. The value of F is
(Acceleration due to gravity =10ms−2 )

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In a hydraulic lift, compressed air exerts a force F on a small piston of radius 3cm. Due to this pressure the second piston of radius 5cm lifts a load of 1875kg. The value of F is
(Acceleration due to gravity =10ms−2 )

In a U-shaped tube the radius of one limb is 2mm and that of other limb is 4mm. A liquid of surface tension 0.03Nm−1, density 1500kgm−3 and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is
(Acceleration due to gravity =10ms−2 )

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In a U-shaped tube the radius of one limb is 2mm and that of other limb is 4mm. A liquid of surface tension 0.03Nm−1, density 1500kgm−3 and angle of contact zero is taken in the tube. The difference in the heights of the levels of the liquid in the two limbs is
(Acceleration due to gravity =10ms−2 )

A steady flow of a liquid of density ρ is shown in figure. At point i, the area of cross-section is 2A and the speed of flow of liquid is √2ms−1. At point 2 , the area of cross-section is A. Between the points 1 and 2 , the pressure difference is 100Nm−2 and the height difference is 10cm. The value of ρ is
(Acceleration due to gravity =10ms−2 )

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A steady flow of a liquid of density ρ is shown in figure. At point i, the area of cross-section is 2A and the speed of flow of liquid is √2ms−1. At point 2 , the area of cross-section is A. Between the points 1 and 2 , the pressure difference is 100Nm−2 and the height difference is 10cm. The value of ρ is
(Acceleration due to gravity =10ms−2 )

A metal tape is calibrated at 25∘C. On a cold day when the temperature is −15∘C, the percentage error in the measurement of length is (Coefficient of linear expansion of metal =1×10−5‌∘C−1 )

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A metal tape is calibrated at 25∘C. On a cold day when the temperature is −15∘C, the percentage error in the measurement of length is (Coefficient of linear expansion of metal =1×10−5‌∘C−1 )

A gas is expanded from an initial state to a final state along a path on a P−V diagram. The path consists of
(i) an isothermal expansion of work 50J,
(ii) an adiabatic expansion and
(iii) an isothermal expansion of work 20J. If the internal energy of gas is changed by −30J, then the work done by gas during adiabatic expansion is

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A gas is expanded from an initial state to a final state along a path on a P−V diagram. The path consists of
(i) an isothermal expansion of work 50J,
(ii) an adiabatic expansion and
(iii) an isothermal expansion of work 20J. If the internal energy of gas is changed by −30J, then the work done by gas during adiabatic expansion is

The temperature of the sink of a Carnot engine is 250K. In order to increase the efficiency of the Carnot engine from 25% to 50%, the temperature of the sink should be increased by

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The temperature of the sink of a Carnot engine is 250K. In order to increase the efficiency of the Carnot engine from 25% to 50%, the temperature of the sink should be increased by

In non-rigid diatomic molecule with an additional vibrational mode

©

In non-rigid diatomic molecule with an additional vibrational mode

Speed of sound in air near room temperature is approximately

©

Speed of sound in air near room temperature is approximately

The radii of curvature of a double convex lens are 4cm and 8cm. If the refractive index of the material of the lens is 1.5, the focal length of the lens is nearly

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The radii of curvature of a double convex lens are 4cm and 8cm. If the refractive index of the material of the lens is 1.5, the focal length of the lens is nearly

When monochromatic light of wavelength 600nm is used in Young's double slit experiment, the fifth order bright fringe is formed at 6mm from the central bright fringe on the screen. If the experiment is conducted with light of wavelength 400nm from the central bright fringe, the third order bright fringe will be located at

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When monochromatic light of wavelength 600nm is used in Young's double slit experiment, the fifth order bright fringe is formed at 6mm from the central bright fringe on the screen. If the experiment is conducted with light of wavelength 400nm from the central bright fringe, the third order bright fringe will be located at

A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass m and charge −q performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is

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A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass m and charge −q performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is

Assertion (A): In a region of constant potential, the electric field is zero and there can be no charge inside the region.
Reason (R): According to Gauss law, charge inside the region should be zero if electric field is zero.

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Assertion (A): In a region of constant potential, the electric field is zero and there can be no charge inside the region.
Reason (R): According to Gauss law, charge inside the region should be zero if electric field is zero.

Statement (A): Inside a charged hollow metal sphere, E=0,V≠0. (E - electric field, V - electric potential)
Statement (B): The work done in moving a positive charge on an equipotential surface is zero.
Statement (C): When two like charges are brought closer, their mutual electrostatic potential energy will increase.

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Statement (A): Inside a charged hollow metal sphere, E=0,V≠0. (E - electric field, V - electric potential)
Statement (B): The work done in moving a positive charge on an equipotential surface is zero.
Statement (C): When two like charges are brought closer, their mutual electrostatic potential energy will increase.

An electron takes 40×103s to drift from one end of a metal wire of length 2m to its other end. The area of cross-section of the wire is 4mm2 and it is carrying a current of 1.6A. The number density of free electrons in the metal wire is

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An electron takes 40×103s to drift from one end of a metal wire of length 2m to its other end. The area of cross-section of the wire is 4mm2 and it is carrying a current of 1.6A. The number density of free electrons in the metal wire is

The current ' i ' in the circuit shown in the figure is

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The current ' i ' in the circuit shown in the figure is

A toroid has a non ferromagnetic core of inner radius 24cm and outer radius 25cm. around which 4900 turns of a wire are wound. If the current in the wire is 12A. the magnetic field inside the core of the toroid is

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A toroid has a non ferromagnetic core of inner radius 24cm and outer radius 25cm. around which 4900 turns of a wire are wound. If the current in the wire is 12A. the magnetic field inside the core of the toroid is

A steel wire of length l and magnetic moment M is bent into a semicircular arc of radius R. The new magnetic moment is

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A steel wire of length l and magnetic moment M is bent into a semicircular arc of radius R. The new magnetic moment is

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 30∘ with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3G. Then the magnitude of the earth's magnetic field at the location is

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A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 30∘ with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3G. Then the magnitude of the earth's magnetic field at the location is

A circular coil has 100 turns, radius 3cm and resistance 4Ω. This coil is co-axial with a solenoid of 200 turns/cm and diameter 4cm. If the solenoid current is decreased from 2 A to zero in 0.04s, then the current induced in the coil is

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A circular coil has 100 turns, radius 3cm and resistance 4Ω. This coil is co-axial with a solenoid of 200 turns/cm and diameter 4cm. If the solenoid current is decreased from 2 A to zero in 0.04s, then the current induced in the coil is

Capacitive reactance of a capacitor in an AC circuit is 3kΩ. If this capacitor is connected to a new AC source of double frequency, the capacitive reactance will become

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Capacitive reactance of a capacitor in an AC circuit is 3kΩ. If this capacitor is connected to a new AC source of double frequency, the capacitive reactance will become

A light of intensity 12Wm−2 incidents on a black surface of area 4cm2. The radiation pressure on the surface is

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A light of intensity 12Wm−2 incidents on a black surface of area 4cm2. The radiation pressure on the surface is

The electric field (E) and magnetic field (B) of an electromagnetic wave passing through vacuum are given by
E=E0‌sin(kx−ωt)
B=B0‌sin(kx−ωt)
Then the correct statement among the following is

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The electric field (E) and magnetic field (B) of an electromagnetic wave passing through vacuum are given by
E=E0‌sin(kx−ωt)
B=B0‌sin(kx−ωt)
Then the correct statement among the following is

In a photoelectric experiment light of wavelength 800nm produces photoelectrons with the smallest de Broglie wavelength of 1nm. Light of 400nm produces photoelectrons with smallest de Broglie wavelength of 0.5nm. Then the work function of the metal used in the experiment is nearly

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In a photoelectric experiment light of wavelength 800nm produces photoelectrons with the smallest de Broglie wavelength of 1nm. Light of 400nm produces photoelectrons with smallest de Broglie wavelength of 0.5nm. Then the work function of the metal used in the experiment is nearly

A hydrogen atom at the ground level absorbs a photon and is excited to n=4 level. The potential energy of the electron in the excited state is

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A hydrogen atom at the ground level absorbs a photon and is excited to n=4 level. The potential energy of the electron in the excited state is

The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 6 fermi is

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The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 6 fermi is

Consider the statements In a semi conductor
(A) There are no free electrons at 0K.
(B) There are no free electrons at any temperature
(C) The number of free electrons increases with temperature.
(D) The number of free electrons is less than that in a conductor.

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Consider the statements In a semi conductor
(A) There are no free electrons at 0K.
(B) There are no free electrons at any temperature
(C) The number of free electrons increases with temperature.
(D) The number of free electrons is less than that in a conductor.

A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by 1% and 3% respectively, the modulation index is changed by

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A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are increased by 1% and 3% respectively, the modulation index is changed by

The maximum number of electrons present in an orbital with n=4,l=3 is

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The maximum number of electrons present in an orbital with n=4,l=3 is

Which quantum number provides information about the shape of an orbital?

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Which quantum number provides information about the shape of an orbital?

In which of the following, elements are arranged in the correct order of their electron gain enthalpies.

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In which of the following, elements are arranged in the correct order of their electron gain enthalpies.

In second period of the long form of the periodic table an element X has second lowest first ionization enthalpy and element Y has second highest first ionization enthalpy values. What are X and Y ?

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In second period of the long form of the periodic table an element X has second lowest first ionization enthalpy and element Y has second highest first ionization enthalpy values. What are X and Y ?

The set of molecules in which the central atom is not obeying the octet rule is

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The set of molecules in which the central atom is not obeying the octet rule is

The formal charges of atoms (1), (2) and (3) in the ion [

The formal charges of atoms (1), (2) and (3) in the ion [

From the following plots, find the correct option.

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From the following plots, find the correct option.

How many grams of Mg is required to completely reduce 100ml,0.1MNO3− solution using the following reaction
NO3−+Mg⟶Mg2++NH3

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How many grams of Mg is required to completely reduce 100ml,0.1MNO3− solution using the following reaction
NO3−+Mg⟶Mg2++NH3

What is the oxidation state of S in the sulphur containing product of the following reaction?
SO32−(aq)+Br2(l)+H2O→

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What is the oxidation state of S in the sulphur containing product of the following reaction?
SO32−(aq)+Br2(l)+H2O→

Observe the following properties:
Volume, enthalpy, density, temperature, heat capacity, pressure, internal energy. The number of extensive properties in the above list is

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Observe the following properties:
Volume, enthalpy, density, temperature, heat capacity, pressure, internal energy. The number of extensive properties in the above list is

Which of the following expression is correct

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Which of the following expression is correct

The pH of 0.01N lime water is

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The pH of 0.01N lime water is

The empirical formula of Calgon is

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The empirical formula of Calgon is

The pair of elements that form both oxides and nitrides, when burnt in air are

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The pair of elements that form both oxides and nitrides, when burnt in air are

Among P4,S8 and N2, the elements which undergo disproportionation when heated with NaOH solution

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Among P4,S8 and N2, the elements which undergo disproportionation when heated with NaOH solution

Identify the correct statements about the anomalous behavior of Boron
I. Boron trihalides can form dimeric structures.
II. Boron shows +1 as stable oxidation state
III. Maximum covalency of Boron is four.
IV. Boron does not form BF6‌6− ion.

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Identify the correct statements about the anomalous behavior of Boron
I. Boron trihalides can form dimeric structures.
II. Boron shows +1 as stable oxidation state
III. Maximum covalency of Boron is four.
IV. Boron does not form BF6‌6− ion.

The hybridizations of carbon in graphite, diamond and C60 are respectively

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The hybridizations of carbon in graphite, diamond and C60 are respectively

The major product of the following reaction is

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The major product of the following reaction is

Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list.

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Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list.

Match List I with List II

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Match List I with List II

Which of the following solids is not a molecular solid?

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Which of the following solids is not a molecular solid?

A solution containing 6.0g of urea is isotonic with a solution containing 10g of a non-electrolytic solute X. The molar mass of X( in gmolm−1 ) is

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A solution containing 6.0g of urea is isotonic with a solution containing 10g of a non-electrolytic solute X. The molar mass of X( in gmolm−1 ) is

x%(w/v) solution of urea is isotonic with 4%(w/v) solution of a non-volatile solute of molar mass 120gmol−1. The value of x is

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x%(w/v) solution of urea is isotonic with 4%(w/v) solution of a non-volatile solute of molar mass 120gmol−1. The value of x is

38.6 amperes of current is passed for 100 seconds through an aqueous CuSO4 solution using platinum electrodes. The mass of copper consumed from the solution and volume of gas liberated at STP are respectively (molar mass of Cu=63.54g mol−1 ).

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38.6 amperes of current is passed for 100 seconds through an aqueous CuSO4 solution using platinum electrodes. The mass of copper consumed from the solution and volume of gas liberated at STP are respectively (molar mass of Cu=63.54g mol−1 ).

The time required for completion of 93.75% of a first order reaction is x minutes. The half life of it (in minutes) is

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The time required for completion of 93.75% of a first order reaction is x minutes. The half life of it (in minutes) is

The macromolecular colloids of the following are
I. Starch solution
II. Sulphur sol
III. Synthetic detergent
IV. Synthetic rubber

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The macromolecular colloids of the following are
I. Starch solution
II. Sulphur sol
III. Synthetic detergent
IV. Synthetic rubber

Assertion (A) :- Animal skins are colloidal in nature
Reason (R) :- Animal skin has positively charged particles.

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Assertion (A) :- Animal skins are colloidal in nature
Reason (R) :- Animal skin has positively charged particles.

In the reaction of phosphorous with conc. HNO3, the oxidized and reduced products respectively are

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In the reaction of phosphorous with conc. HNO3, the oxidized and reduced products respectively are

Which of the following is formed when SO3 is absorbed by concentrated H2SO4

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Which of the following is formed when SO3 is absorbed by concentrated H2SO4

Assertion (A): Transition metals and their complexes show catalytic activity.

Reason (R): The activation energy of a reaction is lowered by the catalyst.

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Assertion (A): Transition metals and their complexes show catalytic activity.

Reason (R): The activation energy of a reaction is lowered by the catalyst.

The crystal filed theory is successful in explaining which of the following?
I. Ligands as point charges:
II. Formation and structures of complexes.
III. colour;
IV. Magnetic properties: V. covalent character of metal-ligand bonding.

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The crystal filed theory is successful in explaining which of the following?
I. Ligands as point charges:
II. Formation and structures of complexes.
III. colour;
IV. Magnetic properties: V. covalent character of metal-ligand bonding.

Pernicious anemia is caused due to deficiency of which vitamin?

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Pernicious anemia is caused due to deficiency of which vitamin?

Which of the following vitamins cannot be stored in the body?

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Which of the following vitamins cannot be stored in the body?

Finkelstein reaction is used for the synthesis of

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Finkelstein reaction is used for the synthesis of

Which among the following will have highest density?

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Which among the following will have highest density?

Identify the major product (Y) from the following reaction

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Identify the major product (Y) from the following reaction

An aryl carboxylic acid on treatment with sodium hydrogen carbonate liberates a gaseous molecule. Identify the gas molecule liberated.

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An aryl carboxylic acid on treatment with sodium hydrogen carbonate liberates a gaseous molecule. Identify the gas molecule liberated.

Identify the major product of the following reaction

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Identify the major product of the following reaction

Identify the major product of the following reaction

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Identify the major product of the following reaction

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