Question & Answer

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

A particle acted by constant forces  and  is displaced from the point  to the point  What will be the total work done by the forces?

Two stones are projected from the top of a cliff h metres high, with the same speed u so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle of  to the horizontal then tan equals

A body travels a distance s in t seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration f and in the second part with constant retardation r. What will be value of t?

A bead of weight w can slide on the smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle  with the vertical then the tension of the thread and reaction of the wire on the bead are

The resultant of two forces Pn and 3n is a force of 7n. If the direction of 3n force were reversed, the resultant would be n. What will be the value of P?

ABC is a triangle, right angled at A. The resultant of the forces acting along AB, AC with magnitudes 1/AB and 1/AC respectively is the force along AD, where D is the foot of the perpendicular from A to BC. What will be the magnitude of the resultant?

A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance

A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance

The solution of the differential equation  is

The degree and order of the differential equation of the family of all parabolas whose axis is x-­axis, are respectively

The order and degree of the differential equation  are

If  then the solution of the equation is

The differential equation representing the family of curves  where c > 0, is a parameter, is of order and degree as follows

The solution of the differential equation is

The differential equation for the family of curves x² + y² – 2ay= 0, where a is an arbitrary constant is

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