Important Questions of Binomial Theorem Mathematics | Zigya

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191.

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + .....
If B – 2A = 100λ, then λis equal to

  • 496

  • 232

  • 248

  • 464


192.

If log5xlogx3xlog3xy = logxx3, then y equals

  • 125

  • 25

  • 5/3

  • 243


193.

In the expansion of (x - 1) (x - 2) ... (x - 18), the coefficient of x17 is

  • 684

  • - 171

  • 171

  • - 342


194.

1 + C1ncosθ + C2ncos2θ + ... + Cnncos equals

  • 2cosθ2ncos2

  • 2cos22

  • 2cos2nθ2

  • 2cos2θ2n


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195.

The number of irrational terms in the binomial expansion of 315 + 713100

  • 90

  • 88

  • 94

  • 95


196.

Let P(x) be a polynomial, which when divided by (x - 3) and (x - 5) leaves remainders 10 and 6, respectively. If the polynomial is divided by (x - 3) (x - 5), then the remainder is

  • - 2x + 16

  • 16

  • 2x - 16

  • 60


197.

the coefficient of x8 in ax2 + 1bx13 is equal to the coefficient of x- 8 in ax - 1bx213 then a and b will satisfy the relation

  • ab + 1 = 0

  • ab = 1

  • a = 1 - b

  • a + b = - 1


198.

Let 1 + x10 = r = 010crxT and r = 071 + x7 = drxT. If P = r = 05crxT and Q =  r = 03d2r + 1 , then PQ is equal to

  • 4

  • 8

  • 16

  • 32


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199.

The coefficient of xn in the expansion of e7x + exe3x is

  • 4n - 1 - - 2n - 1n!

  • 4n - 1 - 2n - 1n!

  • 4n -  2nn!

  • 4n + - 2nn!


200.

The number (101)100 - 1 is divisible by

  • 104

  • 106

  • 108

  • 1012


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