List of top Questions asked in CBSE Class XI

Using Binomial Theorem, evaluate \((96)^3\).

Find the equation of the line that passes though \((2, 2\sqrt 3)\) and is inclined with the x-axis at an angle of 75°.

Out of \(100\) students, two sections of \(40\) and \(60\) are formed. If you and your friend are among the \(100\) students, what is the probability that (a) you both enter the same sections? (b) you both enter the different sections?

Expand the expression \((x+ \frac{1}{x})^6\).

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

In a certain lottery, \(10,000\) tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy(a) one ticket (b) two tickets (c) Ten tickets?

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

A die is thrown, find the probability of the following events:(i) A prime number will appear,(ii) A number greater than or equal to \(3\) will appear,(iii) A number less than or equal to one will appear,(iv) A number more than \(6\) will appear,(v) A number less than 6 will appear.

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

Write the equations for the x and y-axes.

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?

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)

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

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

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

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.

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

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

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

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

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

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?

If the function f(x) satisfies \(\lim_{x\rightarrow 1}\) \(\frac{f(x)-2}{x^2-1}\) =\(\pi\), evaluate \(\lim_{x\rightarrow 1}\) f(x).

Expand the expression \((1- 2x)^ 5\).

Two dice are thrown. The events A, B, and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die.C: getting the sum of the numbers on the dice ≤ 5 Describe the events (i) A'(ii)not B(iii)A or B(iv) A and B(v)A but not C(vi)B or C(vii)B and C(viii)\(A∩B'∩C'\)