The polar equation of the circle of radius 5 and touching the initial line at the pole is

The circle with centre at and radius 2 is

Statement-I : If 
Statement-II :If 

Which of the above statements is true

If x, y are rational number such that  Then

A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is -

There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is -

If a, b, c are the three natural numbers such that a + b + c is divisible by 6, then a³ + b³ + c³ must be divisible by -

For x  R, let [x] denote the greatest integer  x, then value of++ +…+is -

The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1  x  5, 12  y  18, z  –1

Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -

In how many ways can we get a sum of at most 17 by throwing six distinct dice -

The number of non negative integral solutions of equation 3x + y + z = 24

Sum of divisors of 2⁵ ·3⁷ ·5³ · 7² is –

The length of the perpendicular from the pole to the straight line is

The condition for the lines and to be perpendicular is

If f : R →R; f(x) = sin x + x, then the value of (f^-1 (x)) dx, is equal to

Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is .