Inner and outer radii of a spool are r and R respectively. A thread is wound over its inner surface and placed over a rough horizontal surface. Thread is pulled by a force F as shown in fig. then in case of pure rolling

Two identical circular loops are moving with same kinetic energy one rolls & other slides. The ratio of their speed is :

A disc of radius R is rolling purely on a flat horizontal surface, with a constant angular velocity. The angle between the velocity and acceleration vectors of point P is

A thin rod of length L is placed at angle to vertical on a frictionless horizontal floor and released. If the center of mass has acceleration = A, and the rod an angular acceleration = at initial moment, then

If is a real-valued differentiable function satisfying and f(0)=0, then f(1) equals

If f(x) = then:

where represents the integral part function, then:

Which of the following function(s) has/have removable discontinuity at

Consider the function f(x)= where {x} denotes the fractional part function. Which one of the following statements is NOT correct?

Statement-I : If , then

is equal to

is equal to-

Statement The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+…+(361+380+400) is 8000.
Statement - II : , for any natural number n.

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately.

The negation of the statement "If I become a teacher, then I will open a school", is :

The value of the definite integral is

So here we used the concept of integrals and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the minimum and maximum method which makes problem to solve easily. So the answer is non of these.