JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 1 - MCQExams.com

The coefficient of χ5 in the expansion of (1 + χ2)5 (1 + χ)4 is
  • 30
  • 60
  • 40
  • None of the these
In the expansion of (2 – 3χ3)20 , if the ratio of 10th term to 11th term is 45/22, then χ is equal to
  • – (2/3)
  • –3/2

  • Maths-Binomial Theorem and Mathematical lnduction-11188.png

  • Maths-Binomial Theorem and Mathematical lnduction-11189.png
Given positive integers r > 1, n >2 and that the coefficient of (3r)th and (r + 2)th terms in the binomial expansion of (1+ x)2n are equal . Then
  • n = 2r
  • n = 2r + 1
  • n = 3r
  • none of these
If 21st and 22nd terms in the expansion of (1 + χ)44 are equal, then χ is equal to
  • 8/7
  • 21/22
  • 7/8
  • 23/24
If the coefficient of χ8 in (aχ2 + 1/bχ )13 is equal to the coefficient of χ–8 in(aχ – 1/bχ2 )13, then a and b will satisfy the relation
  • ab + 1 = 0
  • ab = 1
  • a = 1 – b
  • a+b = – 1
The coefficient of χ3 in the infinite series expansion of 2/(1– χ) (2 – χ), for |χ| < 1 is
  • – (1/16)
  • 15/8
  • – (1/8)
  • 15/16
If (a + bχ)–3 = 1/27 + (1/3)χ + ..., the the ordered pair (a, b) equals
  • (3, – 27)
  • (1, 1/3)
  • (3, 9)
  • (3, – 9)
The coefficient of three consecutive of (1 + χ)n+5 are in the ratio 5 : 10 : 14. Then, n is equal to (answer lies between 0 to 9 )
  • 1
  • 3
  • 4
  • 6

Maths-Binomial Theorem and Mathematical lnduction-11139.png
  • 0
  • 1
  • - 2
  • 3

Maths-Binomial Theorem and Mathematical lnduction-11141.png
  • 1/2 , 6
  • 6, 1/2
  • 2, 6
  • None of these
If eχ / 1 – χ = B0 + B1χ + B2χ2 +....+ Bnχn + ..., then Bn– Bn–1 equals
  • 1/n!
  • 1/(n – 1)!
  • 1/n! - (1/(n – 1)!)
  • 1

Maths-Binomial Theorem and Mathematical lnduction-11144.png
  • 5
  • 6
  • 7
  • 8
If rth and (r + 1)th terms in the expansion of (p + q)n are equal, then the value of (n + 1)q / r(p+q) is
  • 0
  • 1
  • 1/4
  • 1/2
If A and B are coefficients of χn in the expansion of (1 + χ )2n and (1 + χ )2n - 1 respectively, then A/B is equal
  • 4
  • 2
  • 9
  • 6
In the of (χ3 – 1/χ2)n , n ∈ N, if the sum of the coefficients of χ5 and χ10 is 0, then n is equal to
  • 25
  • 20
  • 15
  • None of these
5th term from the end in the expansion of
Maths-Binomial Theorem and Mathematical lnduction-11149.png
  • – 7920χ–4
  • 7920χ4
  • 7920χ–4
  • –7920χ4
The coefficient of pn qn in the expansion of [(1 + p) (1 + q) (p + q)] n is

  • Maths-Binomial Theorem and Mathematical lnduction-11151.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11152.png

  • Maths-Binomial Theorem and Mathematical lnduction-11153.png

  • Maths-Binomial Theorem and Mathematical lnduction-11154.png
If in the expansion of (a– 2b)n, the same of 5th and 6th terms is zero, then the value of a/b is
  • (n – 4)/ 5
  • 2(n – 4)/5
  • 5/(n – 4)
  • 5/2(n – 4)
79 + 97 is divided by
  • 128
  • 24
  • 64
  • 72
Sum of infinite series
Maths-Binomial Theorem and Mathematical lnduction-11158.png
  • 21/3
  • 41/3
  • 81/3
  • 21/5
The total number of terms in the expansion of (χ + y)100 + (χ – y)100 after simplification is
  • 51
  • 202
  • 100
  • 50
Let [χ] denotes the greatest integer less than or equal of χ. If χ = (√3 + 1)5, then [χ] is equal to
  • 75
  • 50
  • 76
  • 51
  • 152
If in the expansion of (1 + x)m (1 – x)n, the coefficients of x and x2 are 3 and – 6 respectively, then m is
  • 6
  • 9
  • 12
  • 24
If the coefficient of χ2 and χ3 in the expansion of (3 + aχ)9 is same, then the value of a is
  • 3/7
  • 7/3
  • 7/9
  • 9/7

Maths-Binomial Theorem and Mathematical lnduction-11164.png
  • 3
  • 0
  • - 3
  • 5

Maths-Binomial Theorem and Mathematical lnduction-11166.png
  • 3k – 1
  • 3k
  • 3k + 1
  • 3k + 2

Maths-Binomial Theorem and Mathematical lnduction-11168.png
  • 128
  • 256
  • 512
  • 1024
The two consecutive terms in the expansion of (3 + 2χ)74 whose coefficients are equal, are
  • 11, 12
  • 7 , 8
  • 30 , 31
  • None of the above
The coefficients of χ in the expansion of (1 + χ) (1 + 2χ) (1 + 3χ)...(1 + 100χ) is
  • 5050
  • 10100
  • 5151
  • 4950
  • 1100
The coefficient of χ-10 in
Maths-Binomial Theorem and Mathematical lnduction-11171.png
  • – 252
  • 210
  • – (5!)
  • – 120
The coefficient of χn in expansion of (1 + 2χ + 3χ2 + ...)1/2 is
  • – 1
  • 0
  • 2
  • 1

Maths-Binomial Theorem and Mathematical lnduction-11174.png
  • 21
  • 23
  • 25
  • 27
The coefficient of χr in the expansion of (1 – χ)-2 is
  • r
  • r + 1
  • r + 3
  • r – 1
The coefficient of χ20 in the expansion of (1 + 3χ + 3χ2 + χ3 )20 is
  • 60C40
  • 30C20
  • 15C2
  • None of these
The coefficient of χn in the expansion of (1 + χ) (1 – χ)n is
  • (n – 1)
  • (–1)n (1 – n)
  • (– 1)n –1 (n – 1)2
  • (– 1)n –1 n
The coefficient of t24 in the expansion of (1 + t2 )12 (1 + t12) (1 + t24) is
  • 12C6 + 2
  • 12C5
  • 12C6
  • 12C7
The ninth term of the expansion (3χ – 1/2χ)8 is

  • Maths-Binomial Theorem and Mathematical lnduction-11180.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11181.png

  • Maths-Binomial Theorem and Mathematical lnduction-11182.png

  • Maths-Binomial Theorem and Mathematical lnduction-11183.png
In the expansion of (1 + χ + χ2 + χ3)6 , the coefficient of χ14 is
  • 130
  • 120
  • 128
  • 125
  • 115
The larger of 9950 + 10050 and 10150 is
  • 9950 + 10050
  • Both are equal
  • 10150
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11191.png

  • Maths-Binomial Theorem and Mathematical lnduction-11192.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11193.png

  • Maths-Binomial Theorem and Mathematical lnduction-11194.png

  • Maths-Binomial Theorem and Mathematical lnduction-11195.png
The expression {χ + (χ3 – 1)1/2 }5 + { χ – (χ3 - 1)1/2 }5 is a polynomial of degree
  • 5
  • 6
  • 7
  • 8
If the expression in powers of χ of the function
Maths-Binomial Theorem and Mathematical lnduction-11198.png

  • Maths-Binomial Theorem and Mathematical lnduction-11199.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11200.png

  • Maths-Binomial Theorem and Mathematical lnduction-11201.png

  • Maths-Binomial Theorem and Mathematical lnduction-11202.png
If the second term, in the expression
Maths-Binomial Theorem and Mathematical lnduction-11204.png
  • 4
  • 3
  • 12
  • 6
The coefficient of χ100 in the expression of
Maths-Binomial Theorem and Mathematical lnduction-11206.png

  • Maths-Binomial Theorem and Mathematical lnduction-11207.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11208.png

  • Maths-Binomial Theorem and Mathematical lnduction-11209.png

  • Maths-Binomial Theorem and Mathematical lnduction-11210.png
Coefficient of χ19 in the polynomial (χ –(χ – 2)...(χ –is equal to
  • 210
  • –210
  • 20!
  • None of these
The digit at the unit place in the number 192005 + 112005 – 92005 is
  • 2
  • 1
  • 0
  • 8
  • 9
For all integers n ≥ 1, which of the following is divisible by 9?
  • 8n + 1
  • 4n – 3n – 1
  • 32n + 3n + 1
  • 10n + 1

Maths-Binomial Theorem and Mathematical lnduction-11215.png
  • A = 1, B = 3, C = 4, D = 5
  • A = 2, B = 3, C = 4, D = 5
  • A = 3, B = 2, C = 4, D = 5
  • A = 2, B = 3, C = 1, D = 5
If in the expansion of (1 +χ )21, the coefficients of χr and χr+1 be equal, then r is equal to
  • 9
  • 10
  • 11
  • 12
If |χ| < 1/2, then the coefficient of χr in the expansion of
Maths-Binomial Theorem and Mathematical lnduction-11218.png
  • r2r
  • (2r - 1)2r
  • r 2 2r+1
  • (2r + 1)2r
0:0:1


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