Question & Answer

Let  and  be non­-zero vectors such that  If  is the acute angle between the vectors  and   then  equals

Let  be such that   If the projection  along  is equal to that of  along  and ,  are perpendicular to each other then  equals

If  are non­-coplanar vectors and  is a real number, then the vectors  and  are non­-coplanar fo

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

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

 are three vectors, such that   then  is equal to 

The vectors  and   are the sides of a triangle ABC. The length of the median through A is

Let and  If  is a unit vector such that  and  then  is equal to

If  and  are three non-­coplanar vectors, then  equals

Consider A, B, C and D with position vectors    and  respctively. Then ABCD is a

If  then what will be ?

 and  are two vectors and  is a vector such that  then what is ?

 then

If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a . b + b . c + c . a|,  given that 

If  are vectors show that  and  then angle between vector  and   is

If  are vectors such that  then what will be ?

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 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 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 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 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 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?

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 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 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

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 acted by constant forces  and  is displaced from the point  to the point  What will be the total work done by the forces?

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 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 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

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?

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?

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

The solution of the differential equation  is

The degree and order of the differential equation of the family of all parabolas whose axis is x-­axis, are respectively

The order and degree of the differential equation  are

If  then the solution of the equation is

The differential equation representing the family of curves  where c > 0, is a parameter, is of order and degree as follows

The solution of the differential equation is

The differential equation for the family of curves x² + y² – 2ay= 0, where a is an arbitrary constant is

If , x > 0 then dy/dx 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

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?

Three forces  and acting along IA, IB and IC, where I is the in centre of a  are in equilibrium. Then  is

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?

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?

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

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 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?