Previous year questions with solutions · 2024 – 2026
| Year | Questions | Papers | Avg / paper | Weightage |
|---|---|---|---|---|
| 2026 | 20 | 19 | 1.1 | 4.21% ▼ 13% vs last year |
| 2025 | 23 | 19 | 1.2 | 4.84% ▲ 32.1% vs last year |
| 2024 | 22 | 20 | 1.1 | 3.67% |
Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is .
Three persons enter in a lift at the ground floor. The lift will go up to 10th floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to .
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is .
Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5-digit numbers having product of its digits equal to 20 . Then n(S) + n(P) is equal to
Let ABC be a triangle. Consider four points p1, p2, p3, p4 on the side AB, five points p5, p6, p7, p8, p9 on the side BC, and four points p10, p11, p12, p13 on the side AC. None of these points is a vertex of the triangle ABC. Then the total number of pentagons, that can be formed by taking all the vertices from the points p1, p2, , p13, is
Let S = \(m, n) : m, n \1, 2, 3, , 50\\. If the number of elements (m, n) in S such that 6m + 9n is a multiple of 5 is p and the number of elements (m, n) in S such that m + n is a square of a prime number is q, then p + q is equal to .
For n 2, let Sn denote the set of all subsets of \1, 2, , n\ with no two consecutive numbers. For example \1, 3, 5\ S6, but \1, 2, 4\ S6. Then n(S5) is equal to
Let m and n, (m<n), be two 2-digit numbers. Then the total number of pairs (m, n), such that (m, n)=6, is .
All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by Wn. Let the probability P(Wn) of choosing the word Wn satisfy P(Wn) = 2 P(Wn-1), n > 1. If P(CDBEA) = 2 2 -1, , N, then + is equal to
If the number of seven-digit numbers, such that the sum of their digits is even, is m n 10n; m, n \1, 2, 3, , 9\, then m + n is equal to
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is .
The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .
Let S=\p1,p2 ,p10\ be the set of first ten prime numbers. Let A=S P, where P is the set of all possible products of distinct elements of S. Then the number of all ordered pairs (x,y), x S, y A, such that x divides y, is .
The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is .
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is .
The number of integers, between 100 and 1000 having the sum of their digits equal to 14, is .
The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to .
The number of ways of getting a sum 16 on throwing a dice four times is .
There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .
The number of elements in the set S=\(x, y, z): x, y, z , x+2y+3z=42, x, y, z 0\ equals .
The lines L1, L2, ,L20 are distinct. For n=1,2,3, ,10 all the lines L2n-1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set \L1, L2, ,L20\ is equal to .
The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .
In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is .
All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is .