CAT sample papers

Binomial Theorem practice questions

binomial theorem

Binomial Theorem Quiz:

Ques. The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification will be
(a) 202
(b) 51
(c) 50
(d) None of these
Ans. (b)

Related: Digestive system questions

Ques. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 –Tn = 21, then n equals
(a) 5
(b) 7
(c) 6
(d) 4
Ans. (b)

Ques. If A and B are the coefficients of xn in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then
(a) A = B
(b) A = 2B
(c) 2A = B
(d) None of these
Ans. (b)

Ques. The number 111……1 (91 times) is
(a) Not a prime
(b) An even number
(c) Not an odd number
(d) None of these
Ans. (a)

Related: permutation and combination quiz

Ques. In the expansion of (1 + x)5, the sum of the coefficient of the terms is
(a) 80
(b) 16
(c) 32
(d) 64
Ans. (c)

Ques. If p and q be positive, then the coefficients of xp and xq in the expansion of (1 + x)p + q will be
(a) Equal
(b) Equal in magnitude but opposite in sign
(c) Reciprocal to each other
(d) None of these
Ans. (a)

Ques. Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24)  is
(a) 12C6 + 3
(b) 12C6 + 1
(c) 12C6
(d) 12C6 + 2
Ans. (d)

Related: Relations and functions objective questions

Ques. The sum of all the coefficients in the binomial expansion of (x2 + x – 3)319 is
(a) 1
(b) 2
(c) – 1
(d) 0
Ans. (c)

Ques. If in the expansion of (1 + x)m (1 – x)n, the coefficient of  x and  x2 are 3 and – 6 respectively, then m is
(a) 6
(b) 9
(c) 12
(d) 24
Ans. (c)

Ques. Cube root of 217 is
(a) 6.01
(b) 6.04
(c) 6.02
(d) None of these
Ans. (a)

Related: wave optics quiz

Ques. If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n be in A.P., then n =
(a) 7 only
(b) 14 only
(c) 7 or 14
(d) None of these
Ans. (c)

Ques. If in the expression of (1 + x)m (1 – x)n, then coefficient  of x and x2 are 3 and – 6 respectively, then m is
(a) 6
(b) 9
(c) 12
(d) 24
Ans. (c)

Ques. In the expansion of (1 + x)n the sum of coefficients of odd powers of x is
(a) 2n + 1
(b) 2n – 1
(c) 2n
(d) 2n – 1
Ans. (d)

Ques. If the three consecutive coefficient in the expansion of (1 + x)n are 28, 56 and 70, then the value of n is
(a) 6
(b) 4
(c) 8
(d) 10
Ans. (c)

Related: Nuclear Chemistry Sample paper

Ques. In the expansion of (1 + x + x3 + x4)10, the coefficient of x4 is
(a) 40C4
(b) 10C4
(c) 210
(d) 310
Ans. (d)

Ques. The sum of coefficients in (1 + x – 3x2)2134 is
(a) – 1
(b) 1
(c) 0
(d) 22134
Ans. (b)

Ques. The expression {(x + (x3 – 1)1/2)5} + {x – (x3 – 1)1/2}5 is polynomial of degree
(a) 5
(b) 6
(c) 7
(d) 8
Ans. (c)

Related: objective questions on Quantum Numbers

Ques. If the coefficients of second, third and fourth term in the expansion of (1 + x)2n are in A.P., then 2n2 – 9n + 7 is equal to
(a) – 1
(b) 0
(c) 1
(d) 3/2
Ans. (b)

Ques. In the expansion of (1 + 3x + 2x2)6 the coefficient of x11 is
(a) 144
(b) 288
(c) 216
(d) 576
Ans. (d)

Ques. The sum of coefficients in the expansion of (x + 2y + 3z)8 is
(a) 38
(b) 58
(c) 68
(d) None of these
Ans. (c)

Related: Ratio and proportion quiz

Ques. The greatest integer which divides the number 101100 – 1, is
(a) 100
(b) 1000
(c) 10000
(d) 100000
Ans. (c)

Ques. If the second, third and fourth term in the expansion of (x + a)n are 240, 720 and 1080 respectively, then the value of n is
(a) 15
(b) 20
(c) 10
(d) 5
Ans. (d)

Ques. Given positive integers r > 1, m > 2, and that the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + r)2n are equal. Then
(a) n = 2r
(b) n = 2r + 1
(c) n = 3r
(d) none of these
Ans. (a)

Related: Percentage problems and solutions

Ques. If coefficient of (2r + 3)th  and (r – 1)th terms in the expansion of (1 + x)15 are equal, then value of r is
(a) 5
(b) 6
(c) 4
(d) 3
Ans. (a)

Ques. The coefficient of x5 in the expansion of (x2 – x – 2)5 is
(a) – 83
(b) – 82
(c) – 81
(d) 0
Ans. (c)

Ques. The coefficient of x5 in the expansion of (x + 3)6 is
(a) 18
(b) 6
(c) 12
(d) 10
Ans. (a)

Related: syllogism worksheet

Ques. The last digit in 7300 is
(a) 7
(b) 9
(c) 1
(d) 3
Ans. (c)

Ques. The digit in the unit place of the number (183!) + 3183 is
(a) 7
(b) 6
(c) 3
(d) 0
Ans. (a)

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Vishal Arora

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