List of top Mathematics Questions asked in CBSE Class XI

In a lottery, person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [Hint: order of the numbers is not important.]

A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is (i) a vowel (ii) a consonant

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.

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 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.

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.

A coin is tossed twice, what is the probability that atleast one tail occurs?

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.

State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii)A and B are mutually exclusive and exhaustive
(iii) A=B′
(iv)A and C are mutually exclusive
(v)A and B′ are mutually exclusive.
(vi) A′,B′,C are mutually exclusive and exhaustive.

Given a G.P. with a = 729 and 7^th term 64, determine S₇.

Find the 20th and n th terms of the G.P. \(\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8} \),......

IQ of a person is given by the formula \(IQ = \frac{MA}{CA}×100, \) Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it.The resulting mixture is to be more than 4% but less than 6% boric acid.If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by \(F = \frac{9}{5}C + 32\,\, ?\)

Solve the inequalities and represent the solution graphically on number line: 5(2x –7) – 3(2x+3) ≤ 0, 2x+19 ≤ 6x+47.

Solve the following inequalities and represent the solution graphically on number line: 3x –7 > 2(x-6), 6-x > 11-2x.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{x^2cos(\frac{\pi}{4})}{sin\,x}\)

Find the range of each of the following functions.
(i) f(x) = 2 - 3x, x ∈ R, x> 0.
(ii) f(x) = x²+ 2, x, is a real number.
(iii) f(x) = x, x is a real number

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (4x+5sinx)(3x+7cosx)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax²+ sin x)(p+qcos x)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (x²+1) cosx

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): x⁴(5sinx - 3cosx)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a+b\,sin\,x}{c+d\,cos\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sec\,x-1}{sec\,x+1}\)

Expand using Binomial Theorem \(( 1+ \frac{X}{2} - \frac{2}{X})^4, X≠0\)