The sum of the series 20C0 – 20C1 + 20C2 – 20C3 + …… - �

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of coefficients of integral powers of x in the binomial expansion of left parenthesis 1 minus 2 square root of straight x right parenthesis to the power of 50 space is

  • 1 half left parenthesis 3 to the power of 50 space plus space 1 right parenthesis
  • 1 half left parenthesis 30 to the power of 50 right parenthesis
  • 1 half left parenthesis 30 to the power of 50 minus 1 right parenthesis
  • 1 half left parenthesis 30 to the power of 50 minus 1 right parenthesis
360 Views

2.

If (10)9 +2 (11)2(10)7 + .....+10 (11)9 = K(10)9, then k is equal to

  • 121/10

  • 441/100

  • 100

  • 100

192 Views

3.

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

  • 17/35

  • 13/35

  • 11/35

  • 11/35

168 Views

4.

The term independent of  x in open parentheses fraction numerator straight x plus 1 over denominator straight x to the power of 2 divided by 3 end exponent minus straight x to the power of 1 divided by 3 end exponent space plus 1 end fraction minus fraction numerator straight x minus 1 over denominator straight x minus straight x to the power of 1 divided by 2 end exponent end fraction close parentheses to the power of 10 is 

  • 4

  • 120

  • 18

  • 18

171 Views

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5.

If n is a positive integer, then open parentheses square root of 3 plus 1 close parentheses to the power of 2 straight n end exponent minus space left parenthesis square root of 3 minus 1 right parenthesis to the power of 2 straight n end exponent space is

  • an irrational number

  • an odd positive integer

  • an even positive integer

  • an even positive integer

170 Views

6.

The coefficient of x7 in the expansion of (1 - x - x2 +x3)6 is :

  • 144

  • -132

  • -144

  • -144

174 Views

7.

The value of
(21C1 – 10C1) + (21C2 – 10C2) + (21C3 – 10C3) + (21C4 – 10C4) + .... +
(21C10 – 10C10) is

  • 220 – 210

  • 221 – 211

  • 221 – 210

  • 221 – 210

1178 Views

8. Statement space minus 1 space colon space sum from straight r space equals space 0 to straight n of space left parenthesis straight r plus 1 right parenthesis space to the power of straight n straight C subscript straight r space equals space left parenthesis straight n plus 2 right parenthesis 2 to the power of straight n minus 1 end exponent
Statement space minus space 2 colon thin space sum from straight r equals 0 to straight n of space left parenthesis straight r plus 1 right parenthesis space to the power of straight n straight C subscript straight r straight x to the power of straight r space equals space left parenthesis 1 plus straight x right parenthesis to the power of straight n space plus space nx space left parenthesis 1 plus straight x right parenthesis to the power of straight n minus 1 end exponent
  • Statement −1 is false, Statement −2 is true

  • Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

  • Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

  • Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

154 Views

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9.

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals

  • 5/n −4

  • 6 /n −5

  • n -5 /6

  • n -5 /6

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10.

The sum of the series 20C0 – 20C1 + 20C2 – 20C3 + …… - ….. + 20C10 is-

  • – 20C10

  • 1 half straight C presuperscript 20 subscript 10
  • 0

  • 0


B.

1 half straight C presuperscript 20 subscript 10

(1 + x)20 = 20C0 + 20C1x + … + 20C10x10 + …+ 20C20x20
put x = − 1,
0 = 20C0 − 20C1 + … − 20C9 + 20C10 − 20C11 + … + 20C20
0 = 2 (20C0 − 20C1 + … − 20C9) + 20C10
⇒ 20C0 − 20C1 + … + 20C10 =1 half straight C presuperscript 20 subscript 10

1417 Views

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