If n is a positive integer, then  is from Mathematics Binomia

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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


A.

an irrational number

left parenthesis straight x plus straight a right parenthesis to the power of straight n space equals space to the power of straight n straight C subscript straight o space straight x to the power of straight n space plus to the power of straight n straight C subscript 1 straight x to the power of straight n minus 1 end exponent space straight a space plus to the power of straight n straight C subscript 1 straight x to the power of straight n minus 2 end exponent straight a squared space plus..... plus straight n space to the power of straight n straight C subscript straight n straight a to the power of straight n
and
left parenthesis straight x minus straight a right parenthesis to the power of straight n space equals space to the power of straight n straight C subscript straight o space straight x to the power of straight n space minus to the power of straight n straight C subscript 1 straight x to the power of straight n minus 1 end exponent space straight a space plus to the power of straight n straight C subscript 1 straight x to the power of straight n minus 2 end exponent straight a squared space plus..... plus left parenthesis negative 1 right parenthesis straight n space to the power of straight n straight C subscript straight n straight a to the power of straight n
left parenthesis square root of 3 plus 1 end root right parenthesis to the power of 2 straight n end exponent space equals space to the power of 2 straight n end exponent straight C subscript straight o space left parenthesis square root of 3 right parenthesis to the power of 2 straight n end exponent space plus to the power of 2 straight n end exponent straight C subscript 1 left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 1 end exponent space plus to the power of 2 straight n end exponent straight C subscript 2 space left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 2 end exponent space
plus........ plus to the power of 2 straight n end exponent straight C subscript 2 straight n end subscript left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 2 straight n end exponent

left parenthesis square root of 3 minus 1 end root right parenthesis to the power of 2 straight n end exponent space equals space to the power of 2 straight n end exponent straight C subscript straight o space left parenthesis square root of 3 right parenthesis to the power of 2 straight n end exponent space left parenthesis negative 1 right parenthesis to the power of 0 plus to the power of 2 straight n end exponent straight C subscript 1 left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 1 end exponent space left parenthesis negative 1 right parenthesis squared space plus
to the power of 2 straight n end exponent straight C subscript 2 space left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 2 end exponent left parenthesis negative 1 right parenthesis squared space plus........ plus to the power of 2 straight n end exponent straight C subscript 2 straight n end subscript left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 2 straight n end exponent left parenthesis negative 1 right parenthesis to the power of 2 straight n end exponent
Adding both the binomial expansions above, we get
left parenthesis square root of 3 plus 1 right parenthesis to the power of 2 straight n end exponent space minus space left parenthesis square root of 3 straight n end root minus 1 right parenthesis to the power of 2 straight n end exponent space equals space 2 left square bracket to the power of 2 straight n end exponent straight C subscript 1 left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 1 end exponent
plus to the power of 2 straight n end exponent straight C subscript 3 space left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 3 end exponent space plus to the power of 2 straight n end exponent straight C subscript 5 space left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus 5 end exponent space plus....... space plus to the power of 2 straight n end exponent straight C subscript 2 straight n minus 1 end subscript space left parenthesis square root of 3 right parenthesis to the power of 2 straight n minus left parenthesis 2 straight n minus 1 right parenthesis end exponent right square bracket
It is the irrational number because of odd power of square root of 3 appears in each of the terms.


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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
(21C110C1) + (21C210C2) + (21C310C3) + (21C410C4) + .... +
(21C1010C10) 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.

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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

159 Views

10.

The sum of the series 20C020C1 + 20C220C3 + …… - ….. + 20C10 is-

  • 20C10

  • 1 half straight C presuperscript 20 subscript 10
  • 0

  • 0

1417 Views

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