Six teachers and six students have to sit around a circular table such that there is a teacher between any two students. The number of ways in which they can sit is
(a) 6 ! × 6 ! (b) 5 ! × 6 ! (c) 5 ! × 5 ! (d) None... View Article
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The greatest common divisor of 20C1, 20C3, …20C9 is
(a) 20 (b) 4 (c) 5 (d) None of these Solution: 20C1 = 20 20C3 = 20 × 19 ×... View Article
The expression nCr + 4.nCr-1 + 6.nCr – 2 + 4.nCr – 3 + nCr – 4 is equal to
(a) n + 4Cr (b) 2.n + 4Cr – 1 (c) 4.nCr (d) 11.nCr Solution: nCr + nCr-1 = n!/r!(n-r)!]... View Article
Total number of words that can be formed using all letters of the word FAILURE which neither begin with F nor end with E is equal to
(a) 3720 (b) 5040 (c) 3600 (d) 3480 Solution: The total number of words formed without any restriction = 7!... View Article
A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in this stock. There are 5 places in a row in his showcase. The number of different ways of displaying the three varieties of perfumes in the showcase is
(a) 6 (b) 50 (c) 150 (d) None of these Solution: Number of ways of displaying without restriction = 35... View Article
The number of permutations of the letters of the word HINDUSTAN such that neither the pattern ‘HIN’ nor ‘DUS’ nor ‘TAN’ appears are
(a) 166674 (b) 169194 (c) 166680 (d) 181434 Solution: There are 9 letters in HINDUSTAN in which N is repeated... View Article
Find the number of non negative solutions of the system of equations: a + b = 10, a + b + c + d = 21, a + b + c + d + e + f = 33, a + b + c + d + e + f + g + h = 46, and so on till a + b + c + d + … + x + y + z = 208.
(a) 22P10 (b) 22P11 (c) 23P13 (d) None of these Solution: Consider the equation a + b = 10 number... View Article
Find the number of non negative integral solutions of equation a + b + c + d = 20.
(a) 1800 (b) 1771 (c) 1770 (d) none of the above Solution: Number of non-negative integral solutions of the type... View Article
Find the number of non-negative integral solutions of the equation x + y + z = 10.
(a) 10C2 (b) 12C2 (c) 11C2 (d) 9C2 Solution: Number of non-negative integral solutions of the type of equations x1... View Article
There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is :
(a) 816 (b) 806 (c) 805 (d) 813 Solution: We need three non collinear points to form a triangle. The... View Article
The total number of 3-digit numbers, the sum of whose digits is even, is equal to
(a) 450 (b) 350 (c) 250 (d) 325 Solution: Let the three-digit number be n = pqr Sum of digits... View Article
The number of ways in which a mixed doubles game in tennis can be arranged from 5 married couples, if no husband and wife play in the same game, is
(a) 46 (b) 54 (c) 60 (d) None of these Solution: Given that there are 5 married couples. Let the... View Article
Let 1 ≤ m < n ≤ p. The number of subsets of the set A = {1, 2, 3, ……..p} having m, n as the least and the greatest elements respectively, is
(a) 2n-m-1-1 (b) 2n-m-1 (c) 2n-m (d) 2p-n+m-1 Solution: Given 1 ≤ m < n ≤ p A = {1,... View Article
n’ is selected from the set {1, 2, 3, …, 100} and the number 2n + 3n + 5n is formed. Total number of ways of selecting ‘n’ so that the formed number is divisible by 4, is equal to
(a) 50 (b) 49 (c) 48 (d) None of these Solution: If n is odd, 3n = 4λ1 – 1... View Article
If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is
(a) 85 (b) 100 (c) 120 (d) 240 Solution: The number of ways of selecting 3 persons from 12 people... View Article
All the words that can be formed using alphabets A, H, L, U, and R are written as in a dictionary (no alphabet is repeated). The rank of the word RAHUL is
(a) 71 (b) 72 (c) 73 (d) 74 Solution: No. of words starting with A are 4 ! = 24... View Article
A boat is to be manned by eight men of whom 2 can only row on the bow side and 1 can only row on stroke side, the number of ways in which the crew can be arranged is
(a) 4360 (b) 5760 (c) 5930 (d) None of these Solution: 2 men on the bow side can be arranged... View Article
A person invites a party of 10 friends at dinner and place them so that 4 are on one round table and 6 on the other round table. The number of ways in which he can arrange the guests is
(a) 10!/6! (b) 10!/24 (c) 9!/24 (d) none of these Solution: 6 friends are at one round table and the... View Article
A student performed the experiment to measure the speed of sound in air using the resonance air-column method. Two resonances in the air column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,
a) the intensity of the sound heard at the first resonance was more than that at the resonance b) the... View Article
The frequency of the fundamental note in a wire stretched under tension T is v. If the tension is increased to 25 T, then the frequency of the fundamental note will be
a) 25f b) 5f c) 10f d) f Answer: b) 5f Solution: The fundamental frequency f = (1/2L) √(T/m) (f’/f) = √(T’/T) = √(25T/T)... View Article
