List of practice Questions

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 \((cos\,x-cos\, y)^2 + (sin\,x – sin\,y)^2 = 4sin^2 \frac{x-y}{2}\)

Determine n if
(i) ²ⁿC_3: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 \((cos x+cos y)^2+(sin x – sin y)^2 = 4 cos^2\,\frac{x+y}{2}\)