Important Questions of Binomial Theorem Mathematics | Zigya

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11.

If the expansion in powers of x of the function fraction numerator 1 over denominator left parenthesis 1 minus ax right parenthesis left parenthesis 1 minus bx right parenthesis end fraction is a0 + a1x + a2x2 + a3x3 + … , then an is

  • fraction numerator straight b to the power of straight n minus straight a to the power of straight n over denominator straight b minus straight a end fraction
  • fraction numerator straight a to the power of straight n minus straight b to the power of straight n over denominator straight b minus straight a end fraction
  • fraction numerator straight a to the power of straight n plus 1 end exponent minus straight b to the power of straight n plus 1 end exponent over denominator straight b minus straight a end fraction
  • fraction numerator straight a to the power of straight n plus 1 end exponent minus straight b to the power of straight n plus 1 end exponent over denominator straight b minus straight a end fraction
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12.

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a2y2 + … , and a1 = a2 = 10, then (m, n) is

  • (20, 45)

  • (35, 20)

  • (45, 35)

  • (45, 35)

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13.

The value of integral subscript 1 superscript straight a left square bracket straight x right square bracket straight f apostrophe left parenthesis straight x right parenthesis space dx comma space straight a space greater than 1,where [x] denotes the greatest integer not exceeding x is

  • af(a) − {f(1) + f(2) + … + f([a])}

  • [a] f(a) − {f(1) + f(2) + … + f([a])}

  • [a] f([a]) − {f(1) + f(2) + … + f(a)}

  • [a] f([a]) − {f(1) + f(2) + … + f(a)}

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14.

If a1, a2, … , an are in H.P., then the expression a1a2 + a2a3 + … + an−1an is equal to

  • n(a1 − an)

  • (n − 1) (a1 − an)

  • na1an

  • na1an

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15.

If xm.yn = (x+y)m+n, then dy/dx is

  • y/x

  • x+y/xy

  • xy

  • xy

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16.

The coefficient of the middle term in the binomial expansion in powers of x of (1 +αx)4  and of (1−αx )6  is the same if α equals

  • -5/3

  • 3/5

  • -3/10

  • -3/10

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17. If space straight S subscript straight n space equals space sum from straight r equals 0 to straight n of fraction numerator 1 over denominator straight C presuperscript straight n subscript straight r end fraction space and space straight t subscript straight n space equals space sum from straight r equals space 0 to straight n of space straight r over straight C subscript straight r space then comma straight t subscript straight n over straight S subscript straight n space is
  • 1 half straight n
  • 1 half straight n minus 1
  • n-1

  • n-1

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18.

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


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19.

If log5xlogx3xlog3xy = logxx3, then y equals

  • 125

  • 25

  • 5/3

  • 243


20.

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

  • 684

  • - 171

  • 171

  • - 342


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