JEE Questions for Maths Binomial Theorem And Mathematical Lnduction Quiz 7 - MCQExams.com

Coefficients of (2r + 4)th term and (r - 2)th term are equal in expansion of (1 + x)18 then r =_____
  • 4
  • 5
  • 6
  • 7

Maths-Binomial Theorem and Mathematical lnduction-11683.png
  • p = 3, n = 8
  • p = 2, n = 6
  • p = 3, n = 6
  • p = 3, n = 5
Sun of coefficients in expansion of (1 + x - 3x2)4331 is ____
  • 1
  • –1
  • 0
  • 24330

Maths-Binomial Theorem and Mathematical lnduction-11684.png

  • Maths-Binomial Theorem and Mathematical lnduction-11685.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11686.png

  • Maths-Binomial Theorem and Mathematical lnduction-11687.png

  • Maths-Binomial Theorem and Mathematical lnduction-11688.png

Maths-Binomial Theorem and Mathematical lnduction-11690.png

  • Maths-Binomial Theorem and Mathematical lnduction-11691.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11692.png

  • Maths-Binomial Theorem and Mathematical lnduction-11693.png
  • 1

Maths-Binomial Theorem and Mathematical lnduction-11695.png
  • 0
  • 129
  • 229
  • 178

Maths-Binomial Theorem and Mathematical lnduction-11697.png
  • 40
  • 5
  • 41
  • 8

Maths-Binomial Theorem and Mathematical lnduction-11698.png

  • Maths-Binomial Theorem and Mathematical lnduction-11699.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11700.png

  • Maths-Binomial Theorem and Mathematical lnduction-11701.png

  • Maths-Binomial Theorem and Mathematical lnduction-11702.png
If coefficient of 2nd, 3rd and 4th terms are in A.P for (1 + x)n then n =____
  • 28
  • 14
  • 7

  • Maths-Binomial Theorem and Mathematical lnduction-11703.png

Maths-Binomial Theorem and Mathematical lnduction-11704.png

  • Maths-Binomial Theorem and Mathematical lnduction-11705.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11706.png

  • Maths-Binomial Theorem and Mathematical lnduction-11707.png

  • Maths-Binomial Theorem and Mathematical lnduction-11708.png

Maths-Binomial Theorem and Mathematical lnduction-11709.png

  • Maths-Binomial Theorem and Mathematical lnduction-11710.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11711.png

  • Maths-Binomial Theorem and Mathematical lnduction-11712.png

  • Maths-Binomial Theorem and Mathematical lnduction-11713.png

Maths-Binomial Theorem and Mathematical lnduction-11714.png

  • Maths-Binomial Theorem and Mathematical lnduction-11715.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11716.png

  • Maths-Binomial Theorem and Mathematical lnduction-11717.png

  • Maths-Binomial Theorem and Mathematical lnduction-11718.png

Maths-Binomial Theorem and Mathematical lnduction-11719.png

  • Maths-Binomial Theorem and Mathematical lnduction-11720.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11721.png

  • Maths-Binomial Theorem and Mathematical lnduction-11722.png

  • Maths-Binomial Theorem and Mathematical lnduction-11723.png

Maths-Binomial Theorem and Mathematical lnduction-11724.png

  • Maths-Binomial Theorem and Mathematical lnduction-11725.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11726.png

  • Maths-Binomial Theorem and Mathematical lnduction-11727.png

  • Maths-Binomial Theorem and Mathematical lnduction-11728.png

Maths-Binomial Theorem and Mathematical lnduction-11729.png
  • 8
  • 9
  • 10
  • 11
coefficients of 5th, 6th and 7th terms are in A.P. for expansion of (1 + x)n then n = ____
  • 7 or 12
  • –7 or 14
  • 7 or 14
  • –7 or 12

Maths-Binomial Theorem and Mathematical lnduction-11731.png
  • 1151
  • 1152
  • 1153
  • 1154

Maths-Binomial Theorem and Mathematical lnduction-11733.png
  • 415
  • 416
  • 417
  • 418

Maths-Binomial Theorem and Mathematical lnduction-11735.png
  • 1
  • 5
  • 2
  • 6

Maths-Binomial Theorem and Mathematical lnduction-11737.png

  • Maths-Binomial Theorem and Mathematical lnduction-11738.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11739.png

  • Maths-Binomial Theorem and Mathematical lnduction-11740.png

  • Maths-Binomial Theorem and Mathematical lnduction-11741.png

Maths-Binomial Theorem and Mathematical lnduction-11742.png
  • 6
  • 7
  • 4
  • 5

Maths-Binomial Theorem and Mathematical lnduction-11743.png
  • 5
  • 6
  • 7
  • 8

Maths-Binomial Theorem and Mathematical lnduction-11745.png
  • 3
  • 4
  • 5
  • 6

Maths-Binomial Theorem and Mathematical lnduction-11746.png

  • Maths-Binomial Theorem and Mathematical lnduction-11747.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11748.png

  • Maths-Binomial Theorem and Mathematical lnduction-11749.png

  • Maths-Binomial Theorem and Mathematical lnduction-11750.png

Maths-Binomial Theorem and Mathematical lnduction-11751.png
  • 4
  • 7
  • 8
  • 9
If the sum of Co-efficient is 4096 in expansion of (x + y)n then the greatest Co-efficient is ______
  • 792
  • 924
  • 1594
  • 2990
Co-efficient of xr is denoted by ar in expansion of (x + 1)p+q then

  • Maths-Binomial Theorem and Mathematical lnduction-11752.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11753.png

  • Maths-Binomial Theorem and Mathematical lnduction-11754.png
  • None
If co-efficients of (r + 2)th term and 3r th term are equal in expansion of (1 + x)2n, n, r ϵ N, r > 1, n > 2 then n =______
  • 3r
  • 3r + 1
  • 2r
  • 2r + 1

Maths-Binomial Theorem and Mathematical lnduction-11755.png
  • 33
  • 34
  • 35
  • 32
s(k) : 1 + 3 + 5 +----- + (2k -= 3 + k2 then which statement is true ?
  • s(k) ⇒ s (k - 1)
  • s(k) ⇒ s (k + 1)
  • s (is true
  • Result is proved by Principle of Mathematical induction

Maths-Binomial Theorem and Mathematical lnduction-11756.png

  • Maths-Binomial Theorem and Mathematical lnduction-11757.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11758.png

  • Maths-Binomial Theorem and Mathematical lnduction-11759.png

  • Maths-Binomial Theorem and Mathematical lnduction-11760.png
The Co-efficient of xn in the expansion of (1 + x) (1– x)n is
  • (–1)n–1 (n – 1)2
  • (–1)n (1 – n)
  • n – 1
  • (–1)n–1 n
If the co-efficients of rth, (r +th and (r +th terms in the biromial expansion of (1 + y)m are in A.P. then m and r satisfy the equation
  • m2 – m (4r + 1)+4r2 – 2 = 0
  • m2 – (4r – 1)m + 4r2 + 2 = 0
  • m2 – (4r – 1)m + 4r2 – 2= 0
  • m2 – (4r + 1)m + 4r2 + 2 = 0

Maths-Binomial Theorem and Mathematical lnduction-11762.png

  • Maths-Binomial Theorem and Mathematical lnduction-11763.png
  • ab = 1
  • a – b = 1
  • a + b = 1

Maths-Binomial Theorem and Mathematical lnduction-11764.png

  • Maths-Binomial Theorem and Mathematical lnduction-11765.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11766.png

  • Maths-Binomial Theorem and Mathematical lnduction-11767.png

  • Maths-Binomial Theorem and Mathematical lnduction-11768.png

Maths-Binomial Theorem and Mathematical lnduction-11769.png

  • Maths-Binomial Theorem and Mathematical lnduction-11770.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11771.png

  • Maths-Binomial Theorem and Mathematical lnduction-11772.png

  • Maths-Binomial Theorem and Mathematical lnduction-11773.png

Maths-Binomial Theorem and Mathematical lnduction-11774.png
  • a (≤ 100
  • a(> 100
  • a(≤ 100
  • a(> 100
  • Both 1 and 4

Maths-Binomial Theorem and Mathematical lnduction-11776.png

  • Maths-Binomial Theorem and Mathematical lnduction-11777.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11778.png

  • Maths-Binomial Theorem and Mathematical lnduction-11779.png

  • Maths-Binomial Theorem and Mathematical lnduction-11780.png

Maths-Binomial Theorem and Mathematical lnduction-11782.png

  • Maths-Binomial Theorem and Mathematical lnduction-11783.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11784.png

  • Maths-Binomial Theorem and Mathematical lnduction-11785.png

  • Maths-Binomial Theorem and Mathematical lnduction-11786.png

Maths-Binomial Theorem and Mathematical lnduction-11788.png
  • 2e
  • 2e - 1
  • 2e + 1
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11790.png

  • Maths-Binomial Theorem and Mathematical lnduction-11791.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11792.png

  • Maths-Binomial Theorem and Mathematical lnduction-11793.png
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11795.png

  • Maths-Binomial Theorem and Mathematical lnduction-11796.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11797.png

  • Maths-Binomial Theorem and Mathematical lnduction-11798.png

  • Maths-Binomial Theorem and Mathematical lnduction-11799.png

Maths-Binomial Theorem and Mathematical lnduction-11801.png
  • An irrational number
  • An odd positive integer
  • An even positive integer
  • A rational number other than positive integers

Maths-Binomial Theorem and Mathematical lnduction-11803.png
  • 32
  • 33
  • 34
  • 35

Maths-Binomial Theorem and Mathematical lnduction-11805.png
  • 1
  • 5
  • 25
  • 100

Maths-Binomial Theorem and Mathematical lnduction-11807.png
  • True for all n > 1
  • Not true for any n
  • True for all n ∈ N
  • None of these

Maths-Binomial Theorem and Mathematical lnduction-11809.png
  • n > 1
  • n ≥ 1
  • n > 2
  • n ≥ 2
Let P(n) denote the statement that n2 + n is odd. It is seen that P(n) ⇒ P(n + 1), Pn is true for all
  • n > 1
  • n
  • n > 2
  • None of these
If P(n) = 2 + 4 + 6 + ... + 2n, n ∈ N, then P(k) = k(k ++ 2 ⇒ P(k += (k +(k ++ 2 for all k ∈ N. So we can conclude that P(n) = n(n ++ 2 for
  • All n ∈ N
  • n > 1
  • n > 2
  • Nothing can be said
The fourth term in the expansion of (1 - 2x)3/2 will be

  • Maths-Binomial Theorem and Mathematical lnduction-11811.png
  • 2)
    Maths-Binomial Theorem and Mathematical lnduction-11812.png

  • Maths-Binomial Theorem and Mathematical lnduction-11813.png

  • Maths-Binomial Theorem and Mathematical lnduction-11814.png
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