Question & Answer

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x² + y² = 9 is

Locus of mid point of the portion between the axes of  where p is constant is

The point of lines represented by 3ax² + 5xy + (a – 2)y² = 0 and ^ to each other for

The centres of a set of circles, each of radius 3, lie on the circle x² + y² = 25. The locus of any point in the set is

Locus of the centroid of the triangle whose vertices are (a cost, a sint), (b sint, –b cost) and (1, 0), where t is a parameter, is

A rifle man,who together with his rifle has a mass of 100 kg, stands on a smooth surface fires 10 shots horizontally. Each bullet has a mass 10 gm and a muzzle velocity of 800 m/s. What velocity does rifle man acquire at the end of 10 shots

A uniform rod of length 4 m and mass 20 kg is lying horizontal on the ground. The work done in keeping it vertical with one of its ends touching the ground, will be

If the pairs of straight lines x² – 2pxy – y² = 0 and x² – 2qxy – y² = 0 be such that each pair bisects the angle between the other pair, then

The work done by a person in carrying a box of mass 10 kg through a vertical height of 10 m is 4900 J. The mass of the person is

A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to (–k/r2), where k
is a constant. The total energy of the particle is

A bus of mass 1000 kg has an engine which produces a constant power of 50 kW. If the resistance to motion, assumed constant is 1000 N. The maximum speed at which the bus can travel on level road and the acceleration when it is travelling at 25 m/s, will respectively be?

A uniform chain is held on a frictionless table with one- fifth of its length hanging over the edge. If the chain has a length l and a mass m, how much work is required to pull the hanging part back on the table ?

A boy pulls a 5 kg block 20 metres along a horizontal sur- face at a constant speed with a force directed 45° above the horizontal. If the coefficient of kinetic friction is 0.20, how much work does the boy do on the block?

A square of side a lies above the x ­axis and has one vertex at the origin. The side passing through the origin makes an angle  with the positive direction of the x-­axis. The equation of its diagonal not passing through the origin is

The lines 2x – 3y= 5 and 3x – 4y= 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is

If the two circles (x – 1)² + (y – 3)² = r² and x² + y² – 8x + 2y + 8 = 0 intersect in two distinct points, then

The normal at the point (bt₁², 2bt₁) on a parabola meets the parabola again in the point (bt₂², 2bt₂), then

The foci of the ellipse  and the hyperbola  coincide. Then the value of b² is

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