The equation of the straight line passing through the point (4, 3) and making intercepts on the co ordinate axes whose sum is –1 is
Let A(2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is
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 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
A particle moves in the X-Y plane under the influence of a force such that its linear momentum is p(t ) = A[i cos(kt ) - j sin(kt )] , where A and k are constants. The angle between the force and the momentum is?
A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is u . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 u, then N is
A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 , then N is
When 30.0 g of a nonvolatile solute having the empirical formula CH20 of water ,the solution freezes it-1.16°C. What is the molecular formula of solute
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 ?
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
Let be such that If the projection along is equal to that of along and , are perpendicular to each other 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