Question & Answer

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?

The solution of the differential equation  satisfying the condition y(1) = 1 is

The differential equation of the family of circles with fixed radius 5 units and centre on the liney = 2 is

The differential equation of all circles passing through the origin and having their centres on the x-­axis is

The differential equation whose solution is Ax² +By² = 1, where A and B are arbitrary constants is of

The value of  is

The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁, S₂, S₃ are respectively the areas of these parts numbered from top to bottom; then S₁ : S₂ : S₃ is

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is

If , ,  and  then

Let f(x) be a non­-negative continuous function such that the area bounded by the curve y = f(x), x-­axis and the ordinates  and is  Then  is

Let F : R  R be a differentiable function having  Then 

 is equal to

Area of the greatest rectangle that can be inscribed in the ellipse   is

Tha value of  is

The area of the plane region bounded by the curves x + 2y² = 0 and x + 3y² = 1 is equal to

Let  and .

Then which one of the following is true?

The area enclosed between the curves y² = x and y = |x| is

 equals

The solution for x of the equation  is

Let F(x) = f(x) + f(1/x), where  then F(e) equals

The value of  a > 1, where [x] denotes the greatest integer not exceeding x is

 is equal to

 is equal to

What is the value of the integral,  ?

 equals

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x­-axis is

If  and  then the value of  is

If  then A is

If  then A is

The value of  is

If f(a + b – x) = f(x), then  is equal to

If f(y) = e^y, g(y) = y ; y > 0 and , then

Let f(x) be a function satisfying f'(x) = f (x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x² . Then what is the value of the integral  ?

What is the area of the region bounded by the curves y = |x – 1| and y = 3 – |x|?

The value of  is

The area bounded by the curves y = lnx, y = ln |x|, y = |lnx| and y = |ln |x|| is

What is the value of ?

If y = f(x) makes +ve intercept of 2 and 0 unit x and y and encloses an area of 3/4 square unit with the axes then  is

What is the value of ?

Suppose the radius of earth is half of its present value (Mass remaining unchanged). The value of g at a height equal to the final radius is 10x m/s2. Find the value of x.

Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)

Two spherical planets P and Q have the same uniform density , masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density  and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. ThenTwo spherical planets P and Q have the same uniform density, masses MP and MQ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density  and its mass is (MP + MQ). The escape velocities from the planets P, Q and R, are VP, VQ and VR, respectively. Then