Find the number of ways in which 16 identical things can be distributed among 4 persons, if each person gets at least 3 things. (a) 15 (b) 25 (c) 35 (d) 40 Solution: Let a,b,c,d be the numbers of things distributed to each person such that... View Article
How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number? (a) 259 (b) 249 (c) 257 (d) 252 Solution: Numbers can be with 1 digit, 2 digits and 3 digits formed by 1, 2, 3, 4, 5,... View Article
A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is : (a) 40 (b) 41 (c) 16 (d) 32 Solution: The committee should include at least 1 lady. at least 1 old man and at most 2 young men.... View Article
Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place. (a) 12 (b) 14 (c) 16 (d) 24 Solution: The number of committees of 4 gentlemen = 4C4 = 1 The number of committees of... View Article
There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is (a) 105 (b) 315 (c) 630 (d) 450 Solution: 3 women can be selected in 7C3 ways and can be paired with 3 men in 3!... View Article
Three boys and three girls are to be seated around a table, in a circle. Among them, the boy X does not want any girl neighbour and the girls Y does not want any boy neighbour. The number of such arrangements possible is (a) 4 (b) 6 (c) 8 (d) None of these Solution: Consider the figure. 1, 2 and X are the three boys and 3, 4 and Y are three girls, Boy X will... View Article
The graph of the function y = f(x) is symmetrical about the line x = 2, then (a) f(x) = -f(-x) (b) f(2+x) = f(2-x) (c) f(x) = f(-x) (d) f(x+2) = f(x-2) Solution: Consider a graph symmetric with respect to line x = 2... View Article
Which of the following statements is incorrect. (a) x sgn x = |x| (b) |x| sgn x = x (c) x (sgn x) (sgn x) = x (d) |x| (sgn x)3 = |x| Solution: The signum function gives the sign for... View Article
Let f(x) = x/(1- x) and ‘a’ be a real number. If x0 = a, x1 = f(x0), x2 = f(x1), x3 = f(x2)……. If x2009 = 1, then the value of a is (a) 0 (b) 2009/2010 (c) 1/2009 (d) 1/2010 Solution: Given f(x) = x/(1- x) x0 = a, x1 = f(x0) = f(a) = a/(1-a) x2 = f(x1) =... View Article
If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x) = f(x) g(x/5) – g(x) f(x/3) (a) 177 (b) 222 (c) 433 (d) 1155 Solution: Given F(x) = f(x) g(x/5) - g(x) f(x/3) Period of f(x) = 7 Therefore... View Article
Let f(x) = [x], where [x] denotes the greatest integer less than or equal to x. If a = √(20112+2012), then the value of f(a) is equal to (a) 2010 (b) 2011 (c) 2012 (d) 2013 Solution: Given f(x) = [x], where [x] denotes the greatest integer less than or... View Article
If f and g are two functions defined as f(x) = x + 2, x ≤ 0; g (x) = 3, x ≥0, then the domain of f + g is (a) {0} (b) [0, ∞) (c) (-∞, ∞) (d) (-∞, 0) Solution: f(x) = x + 2, x ≤ 0 g(x) = 3, x... View Article
If f(x) = x/(x-1), then f(a)/f(a+1) is equal to: (a) f(a2) (b) f(1/a) (c) f(-a) (d) f(-a/a-1) Solution: Given f(x) = x/(x-1) f(a) = a/(a-1) f(a+1) = (a+1)/(a+1-1) = (a+1)/a... View Article
If a function F is such that F(0) = 2, F(1) = 3, F(x + 2) = 2 F(x) – F(x + 1) for x ≥ 0, then F(5) is equal to (a) -7 (b) -3 (c) 17 (d) 13 Solution: Given F(0) = 2, F(1) = 3 F(x + 2) = 2 F(x) - F(x + 1)....(i) Put x = 0 in... View Article
Which of the following functions are periodic? (a) f(x) = log x, x > 0 (b) f(x) = ex, x ∈ R (c) f(x) = x - [x], x ∈ R (d) f(x) = x + [x], x ∈ R Solution:... View Article
