JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 4 - MCQExams.com

The greatest integer which divides the number 101100 – 1 is
  • 100
  • 1000
  • 10000
  • 100000
The approximate value of (1.0002)3000 is
  • 1.6
  • 1.4
  • 1.8
  • 1.2
The positive integer just greater than (1 + 0.0001)10000 is
  • 4
  • 5
  • 2
  • 3
The coefficients of two consecutive terms in the expansion of (1 + x)n will be equal, if
  • n is any integer
  • n is an odd integer
  • n is any integer
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11411.png
  • 0
  • n
  • – n
  • 2n
If n is positive integer and three consecutive coefficients in the expansion of (1 + x)n are in the ratio 6 : 33 : 110 , then n =
  • 4
  • 6
  • 12
  • 16
If the three consecutive coefficient in the expansion of (1 + x)n are 28,56 and 70, then the value of n is
  • 6
  • 4
  • 8
  • 10
The digit in the unit place of the number (183!) + 3183 is
  • 7
  • 6
  • 3
  • 0

Maths-Binomial Theorem and Mathematical lnduction-11416.png
  • 134 and 135
  • 135 and 136
  • 136 and 137
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11418.png
  • 42n+1
  • 42n
  • 42n –1
  • 4–2n

Maths-Binomial Theorem and Mathematical lnduction-11420.png
  • 196
  • 197
  • 198
  • 199
If number of terms in the expansion of (x – 2y + 3z)n are 45, then n =
  • 7
  • 8
  • 9
  • None of these
The number of integral terms in the expansion of (51/2 + 71/6)642 is
  • 106
  • 108
  • 103
  • 109

Maths-Binomial Theorem and Mathematical lnduction-11424.png
  • 7
  • 5
  • 9
  • 17

Maths-Binomial Theorem and Mathematical lnduction-11426.png
  • 25
  • 8
  • 7
  • 3

Maths-Binomial Theorem and Mathematical lnduction-11428.png
  • 25
  • 35
  • 45
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11430.png
  • 113
  • 123
  • 133
  • None of these
When 2301 is divided by 5, the least positive remainder is
  • 4
  • 8
  • 2
  • 6
For each n ∈ N, the correct statement is
  • 2n < n
  • n2 > 2n
  • n4 < 10n
  • 23n > 7n + 1
For any natural number n, 2n (n - 1)! > nn , if
  • n < 2
  • n > 2
  • n ≥ 2
  • Never
For every natural number n,n(n+is always
  • Even
  • Odd
  • Multiple of 3
  • Multiple of 4
For every positive integer n.2n < n! when
  • n < 4
  • n ≥ 4
  • n < 3
  • None of these
For every positive integral value of n, 3n > n3 when
  • n > 2
  • n ≥ 3
  • n ≥ 4
  • n < 4
For natural number n, (n!)2 > nn , if
  • n > 3
  • n > 4
  • n ≥ 4
  • n ≥ 3
If p is a prime number, then np - n is divisible by p when n is a
  • Natural number greater than 1
  • Irrational number
  • Complex number
  • Odd number

Maths-Binomial Theorem and Mathematical lnduction-11437.png
  • n > 1
  • n > 2
  • All n ∈ N
  • None of these
The remainder left out when 82n - (62)2n + 1 is divided by 9 is
  • 0
  • 2
  • 7
  • 8
79 + 97 is divisible by
  • 128
  • 24
  • 64
  • 72
The coefficients of xr in the expansion of (1 – x)–2 is
  • r
  • r + 1
  • r + 3
  • r – 1
if |x| < 1 then the coefficient of xn in the expansion of (1 + x + x2 + ...)2 will be
  • 1
  • n
  • n + 1
  • None of these
The approximate value of (7.995)1/3 correct to four decimal places is
  • 1.9995
  • 1.9996
  • 1.9990
  • 1.9991

Maths-Binomial Theorem and Mathematical lnduction-11442.png
  • x
  • (1 + x)1/3
  • (1 – x)1/3
  • (1 – x)–1/3
If y = 3x + 6x2 + 10x3 + ...., then the value of x in terms of y is
  • 1 – (1 – y)–1/3
  • 1 – (1 + y)1/3
  • 1 + (1 + y)–1/3
  • 1 – (1 + y)–1/3
If the sum of the coefficients in the expansion of (x + y)n is 1024, then the value of the greatest coefficient in the expansion is
  • 356
  • 252
  • 210
  • 120
49n + 16n – 1 is divisible by
  • 3
  • 19
  • 64
  • 29
When P is a natural number, then Pn + 1 + (P + 1)2n - 1 is divisible by
  • P
  • P2 + P
  • P2 + P + 1
  • P2 - 1

Maths-Binomial Theorem and Mathematical lnduction-11448.png
  • 2n - 1
  • 2n + 1
  • 0
  • None of these
The difference between an integers and its cube is divisible by
  • 4
  • 6
  • 9
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11451.png
  • –15/16
  • 15/16
  • –16/15
  • 16/15

Maths-Binomial Theorem and Mathematical lnduction-11453.png
  • 19
  • 20
  • 21
  • 22

Maths-Binomial Theorem and Mathematical lnduction-11454.png
  • 144
  • -132
  • -144
  • 132

Maths-Binomial Theorem and Mathematical lnduction-11455.png
  • 2
  • 1/2
  • 3
  • 4
If the coefficients of Tr ,Tr+1 ,Tr+2 , terms of (1 + x)14 are in A.P then r =
  • 6
  • 7
  • 8
  • 9

Maths-Binomial Theorem and Mathematical lnduction-11456.png
  • 9a2
  • 10a3
  • 10a2
  • 10a
The ratio of the coefficient of terms xn - r ar and xran - r in the binomial expansion of (x + a)n will be
  • x : a
  • x : r
  • x : n
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11457.png
  • – 20
  • 20
  • 30
  • – 30
The coefficient of x5 in the expansion of (x2 – x – 2)5 is
  • – 83
  • – 82
  • – 81
  • 0
Coefficient of x4 in loge(1 + 3x + 2x2) is

  • Maths-Binomial Theorem and Mathematical lnduction-11458.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11459.png

  • Maths-Binomial Theorem and Mathematical lnduction-11460.png
  • None of these
If the expansion of (1 + x)m (1 - x)n, the coefficient of x and x2 are 3 and -6 respectively, then m is
  • 6
  • 9
  • 12
  • 24
Coefficient of x10 in the expansion of (1 + x2 - x3)8 is
  • 456
  • 476
  • 412
  • 342
0:0:1


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