JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 3 - MCQExams.com

In the expansion of (1 + 3x + 2x2)6 is , the coefficient of x11 is
  • 144
  • 288
  • 216
  • 576
  • 3 . 211
The coefficient of χ3 y4 z5 in the expansion of (χy + yz + χZ)6 is
  • 70
  • 60
  • 50
  • None of these
23n - 7n - 1 is divided by
  • 64
  • 36
  • 49
  • 25
If n is a positive integer, than n3 + 2n is divisible by
  • 2
  • 6
  • 15
  • 3
10n + 3(4n+2) + 5 is divisible by (n ∈ N)
  • 7
  • 5
  • 9
  • 17
If n ≥ 2 be and integer,
Maths-Binomial Theorem and Mathematical lnduction-11328.png
  • An = I and An-1 ≠ I
  • Am ≠ I for any positive integer m
  • A is not invertible
  • Am = 0 for a positive integer m
Which of following result is valid ?
  • (1 + χ)n > (1 + nχ), for all natural numbers n
  • (1 + χ)n ≥ (1 + nχ), for all natural numbers n, where χ > - 1
  • (1 + χ)n ≤ (1 + nχ), for all natural numbers na
  • (1 + χ)n < (1 + nχ), for all natural numbers na
If n is natural number, then
  • 12 + 22 + ...+n2 < n3/3
  • 12 + 22 + ...+n2 = n3/3
  • 12 + 22 + ...+n2 > n3
  • 12 + 22 + ...+n2 > n3/3
If a1 = 1 and an = nan-1 for all positive integers n ≥ 2, Then a5 is equal to
  • 125
  • 120
  • 100
  • 24
  • 6
(23n -will be divisible by (∀ n ∈N )
  • 25
  • 8
  • 7
  • 3
Using mathematical induction, the number an 's are defined by a0 = 1, an+1 = 3n2 + n + an, (n ≥Then, an is equal to
  • n3 + n2 + 1
  • n3 - n2 + 1
  • n3 - n2
  • n3 + n2

Maths-Binomial Theorem and Mathematical lnduction-11334.png
  • Statement I is correct, Statement II is correct; Statement II is correct explanation for statement I
  • Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement II
  • Statement I is correct, Statement II is incorrect
  • Statement I is not incorrect, statement II is correc
If P(n) = 2 + 4 + 6 +...+(2n), n ∈ N, then P(k) = K(k++ 2 implies P(K += (K + 1)(K ++ 2 is true for all K ∈ N. So, statement P(n) = n(n ++ 2 is true for
  • n ≥ 1
  • n ≥ 2
  • n ≥ 3
  • None of these
For n ∈ N, 10n-2 ≥ 8In, is
  • n > 5
  • n ≥ 5
  • n < 5
  • n > 8
Matrix A is such that A2 = 2A - I, where I is the identity matrix, then for n ≥ 2, An is equal to
  • nA - (n - 1)I
  • nA - I
  • 2n-1 A - (n -I
  • 2n-1 A - I
The last digit in 7300 is
  • 7
  • 9
  • 1
  • 3
Cube root of 217 is
  • 6.01
  • 6.04
  • 6.02
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11340.png

  • Maths-Binomial Theorem and Mathematical lnduction-11341.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11342.png

  • Maths-Binomial Theorem and Mathematical lnduction-11343.png
  • none of these
If (1 + aχ)n = 1 + 6χ + 27/2 χ2 + an χn, then the values of a and n are respectively
  • 2 , 3
  • 3 , 2
  • 3/2 , 4
  • 1 , 6
  • 3/2 , 6
The remainder left out when 82n – (62)2n+1 is divided by 9, is
  • 0
  • 2
  • 7
  • 8
In the expansion of
Maths-Binomial Theorem and Mathematical lnduction-11347.png
  • 20
  • - 20
  • 30
  • - 30
If in the expansion of (1 – χ)m (1 – χ)n, the coefficients of χ2 are 3 and – 6 respectively, then m is
  • 6
  • 9
  • 12
  • 24
The coefficient of χ2 in the binomial expansion of
Maths-Binomial Theorem and Mathematical lnduction-11350.png
  • 70/243
  • 60/423
  • 50/13
  • None of these
If χ is so small that χ3 and higher powers of χ may be neglected, then
Maths-Binomial Theorem and Mathematical lnduction-11352.png

  • Maths-Binomial Theorem and Mathematical lnduction-11353.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11354.png

  • Maths-Binomial Theorem and Mathematical lnduction-11355.png

  • Maths-Binomial Theorem and Mathematical lnduction-11356.png
The largest coefficient in the expansion of (1 + χ)24 is
  • 24C24
  • 24C13
  • 24C12
  • 24C11
The term independent of in the expansion of
Maths-Binomial Theorem and Mathematical lnduction-11359.png
  • T7
  • T8
  • T9
  • T10
For r = 0,1,...,10 let Ar , Br and Cr denote, respectively the coefficient of χr in the expansion of (1 +χ)10, (1 +χ)20 and (1 +χ)30 . Then
Maths-Binomial Theorem and Mathematical lnduction-11361.png
  • B10 - C10
  • A10(B102 - C10A10)
  • 0
  • C10 - B10
Let (1 + χ)n = 1 + a1χ + a2χ2 + ...+ anχn. If a1 , a2 and a3 are in AP, then the value of n is
  • 4
  • 5
  • 6
  • 7
  • 8
n – 2Cr + 2n –2Cr –1 + 3n –2Cr – 2 is equal to
  • n+1Cr
  • nCr
  • n+1Cr+1
  • n –1Cr

Maths-Binomial Theorem and Mathematical lnduction-11365.png
  • Statement I is correct , Statement II is correct; Statement II is a correct explanation for statement I
  • Statement I is correct , Statement II is correct; Statement II is not correct explanation for statement I
  • Statement I is a correct, Statement II is incorrect
  • Statement I is incorrect, Statement II is correct

Maths-Binomial Theorem and Mathematical lnduction-11367.png

  • Maths-Binomial Theorem and Mathematical lnduction-11368.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11369.png

  • Maths-Binomial Theorem and Mathematical lnduction-11370.png
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11372.png
  • 2
  • 0
  • 1/2
  • 1
The sum of the last eight coefficients in the expansion of (1 + χ)15 is
  • 216
  • 215
  • 214
  • None of these
If nC12 = nC6, then nC2 is equal to
  • 172
  • 153
  • 306
  • 2556
The value of
Maths-Binomial Theorem and Mathematical lnduction-11376.png
  • 56C4
  • 56C3
  • 55C3
  • 55C4

Maths-Binomial Theorem and Mathematical lnduction-11378.png
  • 30C11
  • 60C10
  • 30C10
  • 65C55
If ak is the coefficient of χk in the expansion of (1 + χ + χ2) for k = 0,1,2,...2n then the value of
Maths-Binomial Theorem and Mathematical lnduction-11380.png
  • - a0
  • 3n
  • n . 3n+1
  • n . 3n
If 49n + 16n + p is divisible by 64 for all n ∈ N, then the least negative integral value of P is
  • - 2
  • - 3
  • - 4
  • - 1
Statement I For each number n, (n + 1)7 - n7 - 1 is divisible by 7
Statement II For each natural number n, n7 - n is divisible by 7.
  • Statement I is incorrect, Statement II is correct
  • Statement I correct, Statement II is correct; Statement II is correct explanation for Statement I
  • Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
  • Statement I is correct; Statement II is incorrect

Maths-Binomial Theorem and Mathematical lnduction-11384.png
  • An = 2n-1 A + (n - 1)I
  • An = nA + (n - 1)I
  • An = 2n-1 A - (n -I
  • An = nA - (n - 1)I
Total number of terms in expansion of (x + y + z + w)n, n ∈ N is

  • Maths-Binomial Theorem and Mathematical lnduction-11386.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11387.png

  • Maths-Binomial Theorem and Mathematical lnduction-11388.png

  • Maths-Binomial Theorem and Mathematical lnduction-11389.png

Maths-Binomial Theorem and Mathematical lnduction-11391.png
  • 0
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11392.png

  • Maths-Binomial Theorem and Mathematical lnduction-11393.png
  • none of these
The last digit of the number 17256 is
  • 1
  • 8
  • 6
  • 0

Maths-Binomial Theorem and Mathematical lnduction-11395.png
  • 5th
  • 51st
  • 7th
  • 6th
  • Both 3 and 4

Maths-Binomial Theorem and Mathematical lnduction-11397.png
  • b < a
  • a < b
  • |a| < |b|
  • |b| < |a|

Maths-Binomial Theorem and Mathematical lnduction-11399.png
  • 202
  • 51
  • 50
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11401.png
  • 252
  • 352
  • 452
  • 532
The larger of 9950 + 10050 and 10150 is
  • 9950 + 10050
  • Both are equal
  • 10150
  • None of these
(1 + x)n – nx – 1 divisible (where n ∈ N )
  • by 2x
  • by x2
  • by 2x3
  • All of these

Maths-Binomial Theorem and Mathematical lnduction-11405.png
  • 9
  • 0
  • 5
  • 10
0:0:1


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