List of top Mathematics Questions asked in CBSE Class XI

Determine n if
(i)  2nC3:nC3 = 12: 1
(ii)  2nC3: nC3 = 11: 1
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Prove that \((cos x+cos y)^2+(sin x – sin y)^2 = 4 cos^2\,\frac{x+y}{2}\)
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i) words start with P and end with S,
(ii) vowels are all together,
(iii) there are always 4 letters between P and S?

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(\dfrac{x^2}{25}+\dfrac{y^2}{100}=1\).

 If  nC8 = nC2, find nC2.
\(2cos \frac{π}{13}cos\frac{9π}{13}+cos \frac{3π}{13}+cos \frac{5π}{13}=0\)
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?

Find r if

(i) 5Pr = 26Pr-1 

(ii) 5Pr = 6Pr-1

Prove that  \(\frac{cos4x+cos3x+cos2x}{sin4x+sin3x+sin2x}=cot\,3x\).
Prove that  \(\frac{sinx-sin3x}{sin^2x+cos^2x}=2\,sin\,x\).
Find n if n-1P3: nP3 = 1: 9.
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