COMBINATORICS, BINOMIAL THEOREM & INTEREST

COMBINATORICS, BINOMIAL THEOREM & INTEREST

91. Find the number of words formed by permuting all the letters of SERIES 

a) 177 

b) 160 

 c) 156 

 d) 180 

 Ans. d 

92. The number of different signals which can be given from 6 flags of different colours 

taken one or more at a time is 

a) 1958 

b) 1956 

c) 16 

d) 64 

Ans. b 

93. The product of r consecutive positive integers is divisible by 

a) r! 

b) (r – 1)! 

c) ( r + 1)! 

d) None of these 

 Ans. a 

94. If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the 

number of arrangements of 2 objects, then the number of objects is 

a) 10 

b) 8 

c) 6 

d) None of these 

Ans. c 

95. From 8 gentlemen and 4 ladies, a committee of 5 is to be formed. In how many ways can 

this be done so as to include at least one lady? 

a) 736 

b) 728 

c) 280 

d) 792 

Ans. a 

96. How many 3 digit numbers with distinct digits can be formed such that the product of the 

digits is the cube of a positive integer? 

a) 21 

b) 24 

c) 36 

d) 30 

Ans. d 

97. The number of triangles that can be formed with 10 points as vertices, n of them being 

collinear, is 110. Then n is 

a) 3 

b) 4 

c) 5 

d) 6 

Ans. c 

98. The greatest possible number of points of intersection of 8 straight lines and 4 circles is 

a) 32 

b) 64 

c) 76 

d) 104 

Ans. c 

99. If 20Cr= 20Cr-10, then 18Cr is equal to 

a) 4896 

b) 816 

c) 1632 

d) None of these 

Ans. b 

100.The number of parallelograms that can be formed from a set of four parallel lines 

intersecting another set of three parallel lines is

a) 6 

b) 9 

c) 12 

d) 18 

Ans. d 

101. How many 10 digits numbers can be written by using the digits 1and 2 

 a)10C1 + 9C2 

b) 210 

 c) 10C2

 d) 10! 

 Ans. b 

102. In how many ways 4 men and 4 women can be seated in a row so that men and women 

are alternate? 

a) 28 

b) 36 

c) 4! 4! 

d) 2.4! 4! 

Ans. d 

103. At what rate% per annum will Rs 64000 become Rs68921 in 1.5 years interest being 

compounded half yearly? 

a) 4% 

b) 6% 

c) 5% 

d) 7% 

Ans. c 

104. Find the compound interest for Rs 10000 for 2 years at 5% per annum the interest being 

compounded annually. 

e) Rs 1000 

f) Rs 1025 

g) Rs 1050 

h) Rs 1100 

Ans. b 

105. In how much time will Rs 3000 amount to Rs 3993 at 40% p.a compounded quarterly. 

 a) 8 months 

 b) 6 months 

 c) 9months 

 d) 11 months 

Ans. c 

106. If nC12 +

 nC8 , then n = 

20 

12 

 6 

 30 

Ans. a 

107. The number of diagonals that can be drawn by joining the vertices of an octagon is 

20 

 28 

 8 

16 

 Ans. a 

108. Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with 

at least 4 bowlers? 

a) 265 

b) 263 

c) 264 

d) 275 

Ans. c 

109. How many numbers greater than 10 lakhs be formed from 2, 3, 0, 3, 4, 2, 3? 

 a) 420 

 b) 360 

 c) 400 

 d) 300 

 Ans. b 

110. The term without x in the expansion ( 2x – 1/2x² )12 is 

a) 495 

b) -495 

c) -7920 

d) 7920 

Ans. d 

111. The middle term of the expansion ( x -1/x )10 is 

a) -252 

b) -250 

c) -248 

d) -262 

Ans. a 

112. The coefficient of x-15 in the expansion of ( 3x² -a/3x³) is 

a) -42/27 a7

b) -40/27 a7

c) - 43/27 a6

d) -38/27 a6

Ans. b 

113. Find the 5th term in the expansion ( 1 -2x )-1 

 a) 15x3 

 b) 16x4 

 c) 17x5 

 d) 14x6 

 Ans. b 

114. The cube root of 127 up to four places of decimal are 

a) 5.0264 

b) 4.1468 

c) 5.0236 

d) 4.1648 

Ans. a 

115. Using binomial theorem expansion of ( 3x + 2y)

4 

 a) 72x4

 + 21x3

 y 

b) 81x4

 +216x3

 y + 216x2

y

2

 + 96xy3

 + 16y4

c) 81x4

 + 96x3

y + 16x2

y

2

 +216xy3

 + 81y4

d) 37x4

 + 43x3

y +16y4

 Ans. b 

116. Find the term independent of x in the expansion of (x² + 1/x)9

 

a) 6 th term 

b) 8th term 

c) 7 th term 

d) 8th term 

Ans c 

117. Find the 5th term from the end in the expansion of (x³/2 - 2/x²)9 

a) -252 x² 

b) -252 x³ 

c) -250 x² 

d) -250 x³ 

Ans. a 

118. If in the expansion of (1 + x)15 the coefficient of (2r +3)th and (r -1)th terms are equal 

then the value of r is 

a) 5 

b) 6 

c) 4 

d) 3 

Ans. a 

119. If in expansion of (1 +y)n the coefficient of the 5th, 6th and the 7th terms are in A.P the n is 

equal to 

a) 7, 11 

b) 7, 14

c) 8, 16

d) None of these

Ans. b 

120. If Ram has 3 tickets of a lottery for which 10 tickets were sold and 5 prizes are to be 

given, the probability that he will win at least one prize is 

 a) 7/12 

 b) 9/12 

 c) 1/12 

 d) 11/12 

Ans. d 

121. The probability of a bomb hitting a bridge is ½ and two direct hits are needed to destroy 

it. The least number of bombs required so that the probability of the bridge being destroyed is 

greater than 0.9 is 

a) 8 

b) 9 

c) 10 

d) 11 

Ans. b 

122. A natural number x is chosen at random from the first one hundred natural numbers. 

What is the probability that (x + 100/x) > 50 

a) 13/20 

b) 3/5

c) 9/20

d) 11/20

Ans. d 

123. The probability that a man will live 10 years is ¼ and the probability that his wife will 

live 10 more years is 1/3. Then the probability that neither will be alive in 10 years as 

a) 5/12 

b) 7/12

c) ½

d) 11/12

Ans. c 

124. In how many ways 6 rings of different type can be had in 4 fingers? 

a) 4000 

b) 4096 

c) 4069 

d) 4009 

Ans. b 

125. If probability P( n, r) =720 and combination C(n, r) =120 then r is 

24

a) 9 

b) 8 

c) 5 

d) 3 

Ans. d 

126. Find the number of non-congruent rectangles that can be found on a 

normal 8*8 chessboard 

 a) 24 

 b) 36 

 c) 48 

 d) None of these 

 Ans: b 

127. The number of positive integral solution of abc = 30 is 

 a) 27 

 b) 81 

 c) 243 

 d) None of these 

Ans: c 

128. Find the number of integral solutions of equation x + y + z + t = 29, x > 0 , y > 0 < z > 0 

and t > 0 

 a) 27C3 

 b) 28C3 

 c) 2600 

 d) 29C4 

Ans: c