List of top Mathematics Questions asked in CBSE Class XI

Name the octants in which the following points lie:
(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7).
The sum of first three terms of a G.P. is \(\frac{39}{10}\) and their product is 1. Find the common ratio and the terms.
A point is in the XZ plane. What can you say about its y-coordinate?

Find the equation for the ellipse that satisfies the given conditions:Major axis on the x-axis and passes through the points (4,3) and (6,2).

Prove that.  \(2sin^2 \frac{π}{6}+cosec^2 \frac{7π}{6}–cos^2 \frac{π}{3}=\frac{3}{2}\)

Prove that. \(sin^2 \frac{π}{6}+cos^2 \frac{π}{3}–tan^2 \frac{π}{4}=-\frac{1}{2}\)

Find the value of the trigonometric function tan \(\frac{19π}{3}.\)
A point is on the x-axis. What are its y-coordinates and z-coordinates?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?

Find the equation for the ellipse that satisfies the given conditions:Centre at (0,0), major axis on the y-axis and passes through the points(3,2) and (1,6). 

Find the equation of the line which passes through the points (-1, 1) and (2, -4).
Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

Find  \(sin \frac{x}{2},\,cos \frac{x}{2} \,and \,tan\,\frac{ x}{2}\, for \,sin\,\,x=\frac{1}{4}\) in quadrant II.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are: an = \(\frac{3}{6}\)
A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of:
(i) exactly 3 girls? 
(ii) atleast 3 girls? 
(iii) atmost 3 girls?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
Prove that  \(sin 3x + sin 2x – sin x = 4sin \,x cos\, \frac{x}{2} cos \frac{3x}{2}\)
Prove that \((cos\,x-cos\, y)^2 + (sin\,x – sin\,y)^2 = 4sin^2 \frac{x-y}{2}\)