##
If 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

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

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

##
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

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

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

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

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

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 ?

If are vectors such that then what will be ?

##
If 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

**.**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

##
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 ?

If then what will be ?

##
Consider A, B, C and D with position vectors 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

*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

*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?

*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

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*?

*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

*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

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?

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

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

*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?*

*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 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

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

*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

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 *x*^{2} + y^{2} – 2ay= 0, where *a* is an arbitrary constant is

*x*= 0, where

^{2}+ y^{2}– 2ay*a*is an arbitrary constant is

The differential equation for the family of curves *x ^{2} + y^{2} – 2ay*= 0, where

*a*is an arbitrary constant is

##
The solution of the differential equation 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

*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

If then the solution of the equation is

##
The differential equation whose solution is *Ax*^{2} +By^{2} = 1, where *A* and *B* are arbitrary constants is of

*Ax*= 1, where

^{2}+By^{2}*A*and

*B*are arbitrary constants is of

The differential equation whose solution is *Ax ^{2} +By^{2}* = 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

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

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 *P*^{2} : Q^{2} : R^{2} is

*P*is

^{2}: Q^{2}: R^{2}

The resultant of forces and is If is doubled, then is doubled. If the direction of is reversed, then is again doubled. Then *P ^{2} : Q^{2} : R^{2} *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, 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

*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?

*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?

*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

Area of the greatest rectangle that can be inscribed in the ellipse is

##
is equal to

is equal to

##
Let F : R 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

*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

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

If , , and then

##
The area enclosed between the curve y = log_{e}(x + e) and the coordinate axes is

*and the coordinate axes is*

_{e}(x + e)

The area enclosed between the curve y = log* _{e}(x + e)* and the coordinate axes is

##
The parabolas *y*^{2} = 4*x* and *x*^{2} = 4*y* divide the square region bounded by the lines *x* = 4, *y* = 4 and the coordinate axes. If S_{1}, S_{2}, S_{3} are respectively the areas of these parts numbered from top to bottomÍ¾ then S_{1} : S_{2} : S_{3} is

*y*4

^{2}=*x*and

*x*4

^{2}=*y*divide the square region bounded by the lines

*x*= 4,

*y*= 4 and the coordinate axes. If S

_{1}, S

_{2}, S

_{3}are respectively the areas of these parts numbered from top to bottomÍ¾ then S

_{1}: S

_{2}: S

_{3}is

The parabolas *y ^{2} = *4

*x*and

*x*4

^{2}=*y*divide the square region bounded by the lines

*x*= 4,

*y*= 4 and the coordinate axes. If S

_{1}, S

_{2}, S

_{3}are respectively the areas of these parts numbered from top to bottomÍ¾ then S

_{1}: S

_{2}: S

_{3}is

##
The value of is

The value of is

##
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

##
The value of a > 1, where [*x*] denotes the greatest integer not exceeding *x* is

*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

*F(x) = f(x) + f(1/x)*, where 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

*x*of the equation is

The solution for *x* of the equation is

##
equals

equals

##
The area enclosed between the curves *y*^{2} = x and *y = |x|* is

*y*and

^{2}= x*y = |x|*is

The area enclosed between the curves *y ^{2} = x* and

*y = |x|*is

##
Let and .

Then which one of the following is true?

Let and .

Then which one of the following is true?

##
The area of the plane region bounded by the curves *x + 2y*^{2} = 0 and *x + 3y*^{2} = 1 is equal to

*x + 2y*= 0 and

^{2}*x + 3y*= 1 is equal to

^{2}

The area of the plane region bounded by the curves *x + 2y ^{2}* = 0 and

*x + 3y*= 1 is equal to

^{2}##
Tha value of is

Tha value of is

##
The value of is

The value of is

##
If then A is

If then A is

##
If then A is

If then A is

##
If 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

*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

*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

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* = ln*x*, *y* = ln |*x|*, *y* = |ln*x|* and y = |ln |*x||* is

*y*= ln

*x*,

*y*= ln |

*x|*,

*y*= |ln

*x|*and y = |ln |

*x||*is

The area bounded by the curves *y* = ln*x*, *y* = ln |*x|*, *y* = |ln*x|* and y = |ln |*x||* is

##
The value of is

The value of is

##
What is the area of the region bounded by the curves *y = |x – 1|* and *y = 3 – |x|?*

*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) = x*^{2} . Then what is the value of the integral ?

*f(x)*be a function satisfying

*f*with

**'**(x) = f (x)*f*(0) = 1 and

*g(x)*be a function that satisfies

*f(x) + g(x) = x*. Then what is the value of the integral ?

^{2}

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) = x*. Then what is the value of the integral ?

^{2}##
If *f(y) = e*^{y}, *g(y) = y* Í¾ *y > *0 and , then

*f(y) = e*,

^{y}*g(y) = y*Í¾

*y >*0 and , then

If *f(y) = e ^{y}*,

*g(y) = y*Í¾

*y >*0 and , then

##
If *f(a + b – x)* = *f(x)*, then is equal to

*f(a + b – x)*=

*f(x)*, then is equal to

If *f(a + b – x)* = *f(x)*, then is equal to

##
Let and be the distinct roots of *ax*^{2} + bx + c = 0, then is equal to

*ax*, then is equal to

^{2}+ bx + c = 0

Let and be the distinct roots of *ax ^{2} + 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 cm^{3}/min. When the thickness of ice is 5 cm, then what will be the rate at which the thickness of ice decreases?

^{3}/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 cm^{3}/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 ?

*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 = x*^{2} – 5x + 6 at the points (2, 0) and (3, 0)?

*y = x*at the points (2, 0) and (3, 0)?

^{2}– 5x + 6

What will be the angle between the tangents to the curve *y = x ^{2} – 5x + 6* at the points (2, 0) and (3, 0)?

##
The set of points where 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 x^{m}**âˆ™** y^{n }= (x + y)^{m+n}, then *dy/dx* is

^{m}

**âˆ™**y

^{n }= (x + y)

^{m+n}, then

*dy/dx*is

If x^{m}**âˆ™** y^{n }= (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) = log*_{e} x on the interval [1, 3] is

*c*for which conclusion of Mean Value Theorem holds for the function

*f(x) = log*on the interval [1, 3] is

_{e}x

A value of *c* for which conclusion of Mean Value Theorem holds for the function *f(x) = log _{e} x* on the interval [1, 3] is

##
The function *f(x) = tan*^{-1}(sin x + cos x) is an increasing function in

*f(x) = tan*is an increasing function in

^{-1}(sin x + cos x)

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 ?

*f : R*be a function defined by

**R***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

*f : R / {0} R*given by

*x*= 0 by defining

*f(0)*as

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 *p*^{2} + q^{2} = 1, then the maximum value of *(p + q)* is

*p*and

*q*are positive real numbers such that

*p*= 1, then the maximum value of

^{2}+ q^{2}*(p + q)*is

If *p* and *q* are positive real numbers such that *p ^{2} + q^{2}* = 1, then the maximum value of

*(p + q)*is

##
How many real solutions does the equation* x*^{7} + 14x^{5} + 16x^{3} + 30x – 560 = 0 have?

*x*have?

^{7}+ 14x^{5}+ 16x^{3}+ 30x – 560 = 0

How many real solutions does the equation* x ^{7} + 14x^{5} + 16x^{3} + 30x – 560 = 0* have?

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Let

Then which one of the following is true?

Let

Then which one of the following is true?

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Suppose the cubic *x*^{3} – px + q has three distinct real roots where *p > 0 and q > 0*. Then which one of the following holds?

*x*has three distinct real roots where

^{3}– px + q*p > 0 and q > 0*. Then which one of the following holds?

Suppose the cubic *x ^{3} – px + q* has three distinct real roots where

*p > 0 and q > 0*. Then which one of the following holds?

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What is the value ?

What is the value ?

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equals

equals

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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

*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

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

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The normal to the curve x = a(cos+ 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

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What is the value of ?

What is the value of ?