Let 1 + x + x29 = a0 +&

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is

  • 216

  • 192

  • 120

  • 120

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2.

If m is the AMN of two distinct real numbers l and n (l,n>1) and G1, G2, and G3 are three geometric means between l and n, then straight G subscript 1 superscript 4 space plus 2 straight G subscript 2 superscript 4 space plus space straight G subscript 3 superscript 4 equals

  • 4l2 mn

  • 4lm2n

  • 4 lmn2

  • 4 lmn2

238 Views

3.

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

  • 8 . 6C4 . 7C4

  • 6 . 7 . 8C4

  • 6 . 8 . 7C4

  • 6 . 8 . 7C4

178 Views

4.

The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-

  • 12!/3!(4!)3

  • 12!/3!(3!)4

  • 12!/(4!)3

  • 12!/(4!)3

181 Views

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5.

The value  of straight C presuperscript 50 subscript 4 space plus sum from straight r space equals 1 to 6 of straight C presuperscript 56 minus straight r end presuperscript subscript 3 space is

  • straight C presuperscript 55 subscript 4
  • straight C presuperscript 55 subscript 3
  • straight C presuperscript 56 subscript 3
  • straight C presuperscript 56 subscript 3
181 Views

6.

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

  • 120

  • 480

  • 360

  • 360

186 Views

7.

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

  • 5

  • 8C3
  • 38

  • 38

190 Views

8.

The number of all numbers having 5 digits, with distinct digits is

  • 99999

  • 9 × P49

  • P510

  • P49


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9.

The greatest integer which divides (p + 1) (p + 2) (p + 3) .... (p + q) for all p E N and fixed q  N is

  • p!

  • q!

  • p

  • q


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10.

Let 1 +x + x29 = a0 +a1x +a2x2 +... + a18x18. Then,

  • a0 +a2 +... +a18 = a0 +a3 + ... + a17

  • a0 + a2 +... + a18 is even

  • a0 + a2 +... + a18 is divisible by 9

  • a0 + a2 +... + a18 is divisible by 3 but not by 9


B.

a0 + a2 +... + a18 is even

1 +x + x29 = a0 +a1x +a2x2 +... + a18x18

Put x = -1, we get

1 - 1 + 19 =  a0 +a1 +a2 +... + a18

 1 =  a0 +a1 +a2 +... + a18    ...(i)

Put x = 1, we get

1 + 1 + 19 =  a0 +a1 +a2 +... + a18

 39 =  a0 +a1 +a2 +... + a18   ...(ii)

On adding equation (i) and (ii), we get

39 + 1 = 2(a0 +a1 +a2 +... + a18)

 a0 +a1 +a2 +... + a18 = 39 + 12

                                      = 19683 + 12 = 196842

                                      = 9842, which is even number.


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