List of top Questions asked in CBSE Class XI

Prove that, cos ⁶ x = 32cos⁶ x-48cos⁴ x+18cos² x -1.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Prove that  \(\frac{cos4x+cos3x+cos2x}{sin4x+sin3x+sin2x}=cot\,3x\).

Prove that  \(\frac{sinx-sin3x}{sin^2x+cos^2x}=2\,sin\,x\).

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

Find the center and radius of the circle \(x^2+y^2-4x-8y-45=0\)    

If \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\), find x.

How many 4-digit numbers are there with no digit repeated?

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Prove that cos² 2x-cos² 6x = sin 4x sin 8x

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Evaluate \(\frac{n!}{\left(n-r\right)!}\), when 
(i) n = 6, r = 2 (ii) n = 9, r = 5

Prove that. sin(n+1) xsin(n+2)x+cos(n+1) xcos(n+2)x=cosx.

Compute \(\frac{8!}{6!\times2!}\)

Is 3! + 4! = 7! ?

Evaluate (i) 8! (ii) 4! - 3!

Prove that, \(\frac{tan(\frac{π}{4}-x)}{tan(\frac{π}{4}-x)}=(\frac{1+tan x}{1-tan x})^2.\)

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that. 
(i) repetition of the digits is allowed?
(ii) repetition of the digits is not allowed ?