Maths-
General
Easy
Question
Let f : R → R be a differentiable function satisfying f (x) = f (x – y) f (y) " x, y Î R and f ¢ (0) = a, f ¢ (2) = b then f ¢ (-2) is
The correct answer is:
Related Questions to study
physics-
Four identical metal butterflies are hanging from a light string of length 
at equally placed points as shown in the figure . The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle 
and 
is given by
Four identical metal butterflies are hanging from a light string of length at equally placed points as shown in the figure . The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle and is given by
physics-General
physics-
Initially the spring is undeformed. Now the force 'F' is applied to 'B' as shown in the figure . When the displacement of 'B' w.r.t 'A' is 'x' towards right in some time then the relative acceleration of 'B' w.r.t. 'A' at that moment is:
Initially the spring is undeformed. Now the force 'F' is applied to 'B' as shown in the figure . When the displacement of 'B' w.r.t 'A' is 'x' towards right in some time then the relative acceleration of 'B' w.r.t. 'A' at that moment is:
physics-General
physics-
Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.
Mass m shown in the figure is in equilibrium. If it is displaced further by x and released find its acceleration just after it is released. Take pulleys to be light & smooth and strings light.
physics-General
physics-
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is 
In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4m just after the system is released from rest is
physics-General
maths-
If S and 
are two foci of an ellipse 
+
= 1 
and P 
a point on it, then SP + P is equal to-
If S and are two foci of an ellipse += 1 and P a point on it, then SP + P is equal to-
maths-General
physics-
A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle 
with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration 'a'. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be 
respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:
A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration 'a'. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:
physics-General
physics-
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases if time required is same then in which case he has to exert more force. Assume pulleys and strings light.
In the figure shown, a person wants to raise a block lying on the ground to a height h. In both the cases if time required is same then in which case he has to exert more force. Assume pulleys and strings light.
physics-General
physics-
A rod of length 
is moving such that its ends A and B move in contact with the horizontal floor and vertical wall respectively as shown in figure. O is the intersection point of the vertical wall and horizontal floor. The velocity vector of the centre of rod C is always directed along tangent drawn at C to the –
A rod of length is moving such that its ends A and B move in contact with the horizontal floor and vertical wall respectively as shown in figure. O is the intersection point of the vertical wall and horizontal floor. The velocity vector of the centre of rod C is always directed along tangent drawn at C to the –
physics-General
maths-
The orthogonal projection of 
on 
are unit vectors along three mutually perpendicular directions )
The orthogonal projection of on are unit vectors along three mutually perpendicular directions )
maths-General
maths-
If S and are foci and A be one and of minor axis of ellipse 
+
= 1, then area of 
is-
If S and are foci and A be one and of minor axis of ellipse += 1, then area of is-
maths-General
maths-
Q is a point on the auxiliary circle corresponding to the point P of the ellipse 
= 1. If T is the foot of the perpendicular dropped from the focus S. onto the tangent to the auxiliary circle at Q then the SPT is -
Q is a point on the auxiliary circle corresponding to the point P of the ellipse = 1. If T is the foot of the perpendicular dropped from the focus S. onto the tangent to the auxiliary circle at Q then the SPT is -
maths-General
physics-
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration ' a ' vertically downward. The tension in the string is equal to :
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration ' a ' vertically downward. The tension in the string is equal to :
physics-General
physics-
Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find out the accelerations of both the blocks just after release:
Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find out the accelerations of both the blocks just after release:
physics-General
physics-
A light spring is compressed and placed horizontally between a vertical fixed wall and a block free to slide over a smooth horizontal table top as shown in the figure. The system is released from rest. The graph which represents the relation between the magnitude of acceleration ‘ a ‘ of the block and the distance ‘ x ‘ travelled by it (as long as the spring is compressed) is:
A light spring is compressed and placed horizontally between a vertical fixed wall and a block free to slide over a smooth horizontal table top as shown in the figure. The system is released from rest. The graph which represents the relation between the magnitude of acceleration ‘ a ‘ of the block and the distance ‘ x ‘ travelled by it (as long as the spring is compressed) is:
physics-General
physics-
A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is
A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is
physics-General
