Question & Answer

A triangle with vertices (4, 0), (–1, –1), (3, 5) is

The equation of a circle with origin as a center and passing through equilateral triangle whose median is of length 3a is

 A chain of linear density 3 kg /m and length 8 m is lying on the table with 4 m of chain hanging from the edge. The work done in lifting the chain on the table will be ?

An automobile of mass m accelerates from rest. If the engine supplies a constant power P, the velocity at time t is given by

A force F =(7–2x+3x*x )N is applied on a 2kg mass which displaces it from x = 0 to x = 5 m. Work done in joule is ?

The work done in pulling a body of mass 5 kg along an inclined plane (angle 60) with coefficient of friction 0.2 through 2 m,will be?

A body is acted upon by a force F=-i+2j+3k.The work done by the force in displacing it from (0,0,0) to (0,0,4m) will be?

If the chord y = mx + 1 of the circle x² + y² = 1 subtends an angle of measure 45° at the major segment of the circle then value of m is

An object of mass 5 kg falls from rest through a vertical distance of 20 m and reaches a velocity of 10 m/s. How much work is done by the push of the air on the object ? (g = 10 m/s2).

The work done in lifting water from a well of depth 6 m using a bucket of mass 0.5 kg and volume 2 litre, will be

Two common tangents to the circle x² + y² = 2a² and parabola y² = 8ax are

The non­-zero vectors  are related   Then the angle between and  is

The vector  lies in the plane of the vectors  and  and bisects the angle between and . Then which one of the following gives possible values of  and ?

If  and  are unit vectors and  is the acute angle between them, then  is a unit vector for

The values of a, for which the points A, B, C with position vectors  and  respectively are the vertices of a right­ angled triangle at c are

If , where  and  any three vectors such that  then and  and  are

If  are non­coplanar vector and  is a real number then  for

Let a, b and c be distinct non­negative numbers. If the vectors  and  lie in a plane, then c is

Let  and 

Then  depends on

For any vector,  the value of  is equal to

If C is the mid point of AB and P is any point outside AB, then

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