List of top Questions asked in CBSE Class XI

If f(x) = \(f(x)=\left\{\begin{matrix} mx^2+n, &\,\,\,\,x<0 \\   nx+m,&\,\,\,\, 0\leq x\leq1 \\   nx^3+m,&\,\,\,\, x>1  \end{matrix}\right.\). For what integers m and n does both \(\lim_{x\rightarrow 1}\)f(x) and \(\lim_{x\rightarrow 1}\) f(x) exist?

Find the derivative of x² – 2 at x = 10

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Find the value of x for which the points (x, -1), (2, 1) and (4, 5) are collinear.

A card is selected from a pack of 52 cards.
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.

Without using distance formula, show that points (-2, -1), (4, 0), (3, 3) and (-3, 2) are vertices of a parallelogram.

Expand the expression\( (\frac{2}{x} - \frac{x}{2})^5\).

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i)The student opted for NCC or NSS.
(ii)The student has opted neither NCC nor NSS.
(iii)The student has opted NSS but not NCC

Expand the expression \((2x - 3) ^6\).

Find the angle between the x-axis and the line joining the points (3, -1) and (4, -2).

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that 
(i) all will be blue. 
(ii) at least one will be green.

4 cards are drawn from a well–shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

If three point (h, 0), (a, b) and (0, k) lie on a line, show that \(\frac ah+ \frac bk=1\).

Expand the expression \((\frac{x}{3} + \frac{1}{x})^5\).

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
(i) P (2)   (ii) P (1 or 3)    (iii) P (not 3)

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.

There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?

Write the equations for the x and y-axes.

Find the equation of the line which passes through the point (-4, 3) with slope \(\frac 12\).

Find the equation of the line which passes though (0, 0) with slope m.