If 
and 
are three non-coplanar vectors, then 
equals
and are three non-coplanar vectors, then equals
If and are three non-coplanar vectors, then equals
Let 
and 
If 
is a unit vector such that 
and 
then 
is equal to
and If is a unit vector such that and then is equal to
Let and If is a unit vector such that and then is equal to
The vectors 
and 
are the sides of a triangle ABC. The length of the median through A is
and are the sides of a triangle ABC. The length of the median through A is
The vectors and are the sides of a triangle ABC. The length of the median through A is
are three vectors, such that 
then 
is equal to
are three vectors, such that then is equal to
are three vectors, such that then is equal to
Let 
and 
be three non-zero vectors such that no two of these are collinear. If the vector 
is collinear with 
and 
is collinear with 
(
being some nonzero scalar) then 
equals
and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with ( being some nonzero scalar) then equals
Let and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with ( being some nonzero scalar) then equals
A particle is acted upon by constant forces 
and 
which displace it from a point 
to the point 
The work done in standard units by the forces is given by
and which displace it from a point to the point The work done in standard units by the forces is given by
A particle is acted upon by constant forces and which displace it from a point to the point The work done in standard units by the forces is given by
If 
are non-coplanar vectors and 
is a real number, then the vectors 
and 
are non-coplanar fo
are non-coplanar vectors and is a real number, then the vectors and are non-coplanar fo
If are non-coplanar vectors and is a real number, then the vectors and are non-coplanar fo
Let 
be such that 
If the projection 
along 
is equal to that of 
along and , are perpendicular to each other then 
equals
be such that If the projection along is equal to that of along and , are perpendicular to each other then equals
Let be such that If the projection along is equal to that of along and , are perpendicular to each other then equals
Let 
and 
be non-zero vectors such that 
If 
is the acute angle between the vectors 
and 
then 
equals
and be non-zero vectors such that If is the acute angle between the vectors and then equals
Let and be non-zero vectors such that If is the acute angle between the vectors and then equals
If 
are vectors such that 
then what will be 
?
are vectors such that then what will be ?
If are vectors such that then what will be ?
If 
are vectors show that 
and 
then angle between vector 
and 
is
are vectors show that and then angle between vector and is
If are vectors show that and then angle between vector and is
If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a . b + b . c + c . a|, given that 
If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a . b + b . c + c . a|, given that
then
then
then
and 
are two vectors and 
is a vector such that 
then what is 
?
and are two vectors and is a vector such that then what is ?
and are two vectors and is a vector such that then what is ?
If 
then what will be 
?
then what will be ?
If then what will be ?
Consider A, B, C and D with position vectors 
and 
respctively. Then ABCD is a
and respctively. Then ABCD is a
Consider A, B, C and D with position vectors and respctively. Then ABCD is a
Two points A and B move from rest along a straight line with constant acceleration f and f' respectively. If A takes msec. more than B and describes n units more than B in acquiring the same speed then
Two points A and B move from rest along a straight line with constant acceleration f and f' respectively. If A takes msec. more than B and describes n units more than B in acquiring the same speed then
A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s 2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/ s. Then when the lizard will catch the insect?
A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s 2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/ s. Then when the lizard will catch the insect?
A particle is projected from a point O with velocity u at an angle of 60º with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given b
A particle is projected from a point O with velocity u at an angle of 60º with the horizontal. When it is moving in a direction at right angles to its direction at O, its velocity then is given b
A particle has two velocities of equal magnitude inclined to each other at an angle q. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then q is
A particle has two velocities of equal magnitude inclined to each other at an angle q. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then q is
A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If g = 10 m/s 2, then the height above the point P from where the body began to fall is
A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4 s prior to passing through P. If g = 10 m/s 2, then the height above the point P from where the body began to fall is
A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. What will be the angle of projection?
A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. What will be the angle of projection?
A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point, Then tensions in the strings are
A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point, Then tensions in the strings are
A bead of weight w can slide on the smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle 
with the vertical then the tension of the thread and reaction of the wire on the bead are
with the vertical then the tension of the thread and reaction of the wire on the bead are
A bead of weight w can slide on the smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle with the vertical then the tension of the thread and reaction of the wire on the bead are
A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. What will be value of t?
A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. What will be value of t?
Two stones are projected from the top of a cliff h metres high, with the same speed u so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle of 
to the horizontal then tan equals
to the horizontal then tan equals
Two stones are projected from the top of a cliff h metres high, with the same speed u so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle of to the horizontal then tan equals
A particle acted by constant forces 
and 
is displaced from the point 
to the point 
What will be the total work done by the forces?
and is displaced from the point to the point What will be the total work done by the forces?
A particle acted by constant forces and is displaced from the point to the point What will be the total work done by the forces?
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity 
and the other from rest with uniform acceleration 
. Let 
be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time
and the other from rest with uniform acceleration . Let be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity and the other from rest with uniform acceleration . Let be the angle between their directions of motion. The relative velocity of the second particle with respect to the first is least after a time
A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km andBC= 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively
A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km andBC= 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively
A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30º and 45º respectively with the given velocity. Then the component along OB is
A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30º and 45º respectively with the given velocity. Then the component along OB is
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance
ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC with magnitudes 1/AB and 1/AC respectively is the force along AD, where D is the foot of the perpendicular from A to BC. What will be the magnitude of the resultant?
ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC with magnitudes 1/AB and 1/AC respectively is the force along AD, where D is the foot of the perpendicular from A to BC. What will be the magnitude of the resultant?
The resultant of two forces Pn and 3n is a force of 7n. If the direction of 3n force were reversed, the resultant would be 
n. What will be the value of P?
n. What will be the value of P?
The resultant of two forces Pn and 3n is a force of 7n. If the direction of 3n force were reversed, the resultant would be n. What will be the value of P?
The order and degree of the differential equation 
are
are
The order and degree of the differential equation are
The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively
The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively
The solution of the differential equation 
is
is
The solution of the differential equation is
If 
, x > 0 then dy/dx is
, x > 0 then dy/dx is
If , x > 0 then dy/dx is
The differential equation for the family of curves x2 + y2 – 2ay= 0, where a is an arbitrary constant is
The differential equation for the family of curves x2 + y2 – 2ay= 0, where a is an arbitrary constant is
The solution of the differential equation
is
is
The solution of the differential equation is
The differential equation representing the family of curves 
where c > 0, is a parameter, is of order and degree as follows
where c > 0, is a parameter, is of order and degree as follows
The differential equation representing the family of curves where c > 0, is a parameter, is of order and degree as follows
If 
then the solution of the equation is
then the solution of the equation is
If then the solution of the equation is
The differential equation whose solution is Ax2 +By2 = 1, where A and B are arbitrary constants is of
The differential equation whose solution is Ax2 +By2 = 1, where A and B are arbitrary constants is of
The differential equation of all circles passing through the origin and having their centres on the x-axis is
The differential equation of all circles passing through the origin and having their centres on the x-axis is
The differential equation of the family of circles with fixed radius 5 units and centre on the liney = 2 is
The differential equation of the family of circles with fixed radius 5 units and centre on the liney = 2 is
The solution of the differential equation 
satisfying the condition y(1) = 1 is
satisfying the condition y(1) = 1 is
The solution of the differential equation satisfying the condition y(1) = 1 is
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. What wil be the magnitude of the two forces?
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. What wil be the magnitude of the two forces?
A couple is of moment 
and the force forming the couple is 
. If is turned through a right angle, the moment of the couple thus formed is 
. If instead, the forces are turned through an angle 
then the moment of couple becomes
and the force forming the couple is . If is turned through a right angle, the moment of the couple thus formed is . If instead, the forces are turned through an angle then the moment of couple becomes
A couple is of moment and the force forming the couple is . If is turned through a right angle, the moment of the couple thus formed is . If instead, the forces are turned through an angle then the moment of couple becomes
The resultant of forces 
and 
is 
If is doubled, then is doubled. If the direction of is reversed, then is again doubled. Then P2 : Q2 : R2 is
and is If is doubled, then is doubled. If the direction of is reversed, then is again doubled. Then P2 : Q2 : R2 is
The resultant of forces and is If is doubled, then is doubled. If the direction of is reversed, then is again doubled. Then P2 : Q2 : R2 is
With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N. If they act at right angles, then their resultant is 3 N. Then what will be the forces?
With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N. If they act at right angles, then their resultant is 3 N. Then what will be the forces?
In a right angle 
A = 90º and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force 
has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then what will be the magnitude of F?
A = 90º and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then what will be the magnitude of F?
In a right angle A = 90º and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then what will be the magnitude of F?
Three forces 
and 
acting along IA, IB and IC, where I is the in centre of a 
are in equilibrium. Then 
is
and acting along IA, IB and IC, where I is the in centre of a are in equilibrium. Then is
Three forces and acting along IA, IB and IC, where I is the in centre of a are in equilibrium. Then is
ABC is a triangle. Forces 
acting along IA, IB and IC respectively are in equilibrium, where I is the incentre of 
Then what will be the P : Q : R?
acting along IA, IB and IC respectively are in equilibrium, where I is the incentre of Then what will be the P : Q : R?
ABC is a triangle. Forces acting along IA, IB and IC respectively are in equilibrium, where I is the incentre of Then what will be the P : Q : R?
The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is
The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is
Area of the greatest rectangle that can be inscribed in the ellipse 
is
is
Area of the greatest rectangle that can be inscribed in the ellipse is
is equal to
is equal to
is equal to
Let F : R 
R be a differentiable function having 
Then 
R be a differentiable function having Then
Let F : R R be a differentiable function having Then
Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the ordinates 
and 
is 
Then 
is
and is Then is
Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the ordinates and is Then is
If 
, 
, 
and 
then
, , and then
If , , and then
The area enclosed between the curve y = loge(x + e) and the coordinate axes is
The area enclosed between the curve y = loge(x + e) and the coordinate axes is
The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2 : S3 is
The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2 : S3 is
The value of 
is
is
The value of is
equals
equals
equals
What is the value of the integral, 
?
?
What is the value of the integral, ?
is equal to
is equal to
is equal to
is equal to
is equal to
is equal to
The value of 
a > 1, where [x] denotes the greatest integer not exceeding x is
a > 1, where [x] denotes the greatest integer not exceeding x is
The value of a > 1, where [x] denotes the greatest integer not exceeding x is
Let F(x) = f(x) + f(1/x), where 
then F(e) equals
then F(e) equals
Let F(x) = f(x) + f(1/x), where then F(e) equals
The solution for x of the equation 
is
is
The solution for x of the equation is
equals
equals
equals
The area enclosed between the curves y2 = x and y = |x| is
The area enclosed between the curves y2 = x and y = |x| is
Let 
and 
.
Then which one of the following is true?
and .
Let and .
Then which one of the following is true?
The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to
The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to
Tha value of 
is
is
Tha value of is
The value of 
is
is
The value of is
If 
then A is
then A is
If then A is
If then A is
then A is
If then A is
If 
and 
then the value of 
is
and then the value of is
If and then the value of is
The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is
The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is
What is the value of 
?
?
What is the value of ?
If y = f(x) makes +ve intercept of 2 and 0 unit x and y and encloses an area of 3/4 square unit with the axes then 
is
is
If y = f(x) makes +ve intercept of 2 and 0 unit x and y and encloses an area of 3/4 square unit with the axes then is
What is the value of 
?
?
What is the value of ?
The area bounded by the curves y = lnx, y = ln |x|, y = |lnx| and y = |ln |x|| is
The area bounded by the curves y = lnx, y = ln |x|, y = |lnx| and y = |ln |x|| is
The value of 
is
is
The value of is
What is the area of the region bounded by the curves y = |x – 1| and y = 3 – |x|?
What is the area of the region bounded by the curves y = |x – 1| and y = 3 – |x|?
Let f(x) be a function satisfying f'(x) = f (x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2 . Then what is the value of the integral 
?
?
Let f(x) be a function satisfying f'(x) = f (x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x2 . Then what is the value of the integral ?
If f(y) = ey, g(y) = y ; y > 0 and 
, then
, then
If f(y) = ey, g(y) = y ; y > 0 and , then
If f(a + b – x) = f(x), then 
is equal to
is equal to
If f(a + b – x) = f(x), then is equal to
Let 
and 
be the distinct roots of ax2 + bx + c = 0, then 
is equal to
and be the distinct roots of ax2 + bx + c = 0, then is equal to
Let and be the distinct roots of ax2 + bx + c = 0, then is equal to
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then what will be the rate at which the thickness of ice decreases?
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then what will be the rate at which the thickness of ice decreases?
If x is real, what is the maximum value of 
?
?
If x is real, what is the maximum value of ?
The function g(x) = x/2 + 2/x has a local minimum at
The function g(x) = x/2 + 2/x has a local minimum at
What will be the angle between the tangents to the curve y = x2 – 5x + 6 at the points (2, 0) and (3, 0)?
What will be the angle between the tangents to the curve y = x2 – 5x + 6 at the points (2, 0) and (3, 0)?
The set of points where 
is differentiable, is
is differentiable, is
The set of points where is differentiable, is
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length x. What will be the maximum area enclosed by the park?
A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length x. What will be the maximum area enclosed by the park?
If xm∙ yn = (x + y)m+n, then dy/dx is
If xm∙ yn = (x + y)m+n, then dy/dx is
A value of c for which conclusion of Mean Value Theorem holds for the function f(x) = loge x on the interval [1, 3] is
A value of c for which conclusion of Mean Value Theorem holds for the function f(x) = loge x on the interval [1, 3] is
The function f(x) = tan-1(sin x + cos x) is an increasing function in
The function f(x) = tan-1(sin x + cos x) is an increasing function in
Let f : R 
R be a function defined by f(x) = min {x + 1, |x| + 1}. Then which of the following is true ?
R be a function defined by f(x) = min {x + 1, |x| + 1}. Then which of the following is true ?
Let f : R R be a function defined by f(x) = min {x + 1, |x| + 1}. Then which of the following is true ?
The function f : R / {0} 
R given by
can be made continuous at x = 0 by defining f(0) as
R given by
The function f : R / {0} R given by
can be made continuous at x = 0 by defining f(0) as
If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is
If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is
How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have?
How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have?
Let 
Then which one of the following is true?
Let
Then which one of the following is true?
Suppose the cubic x3 – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
Suppose the cubic x3 – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
What is the value 
?
?
What is the value ?
equals
equals
equals
If f is a realvalued differentiable function satisfying |f(x) - f(y)| <= (x-y)2, x, y 
R and f(0) = 0, then f(1) equals
R and f(0) = 0, then f(1) equals
If f is a realvalued differentiable function satisfying |f(x) - f(y)| <= (x-y)2, x, y R and f(0) = 0, then f(1) equals
The normal to the curve x = a(cos
+ sin), y = a(sin – cos) at any point is such that
+ sin), y = a(sin – cos) at any point is such that
The normal to the curve x = a(cos+ sin), y = a(sin – cos) at any point is such that
What is the value of 
?
?
What is the value of ?