If μ, ν and ω (all posi

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 Multiple Choice QuestionsMultiple Choice Questions

21.

If an infinite GP has the first term x and the sum 5, then which of the following is correct ?

  • x < - 10

  •  - 10 < x < 0

  • 0  < x < 10

  • x > 10


22.

Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

  • 2480

  • 2481

  • 2482

  • 2483


23.

The sum of the series 3 - 1 + 13 - 19 + ... = 

  • 209

  • 920

  • 94

  • 49


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24.

If μ, ν and ω (all positive) are the pth, qth and rth terms of a GP, then the determinant of the matrixlnμp1lnνq1lnωr1 is

  • 0

  • 1

  • (p - q)(q - r)(r - p)

  • lnμ × lnν × lnω


A.

0

 We know that of μ, ν and ω are in GP, then logμ, logν, logω are in A.P. lnμp1lnνq1lnωr1 = 0


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25.

Let T, be the rth term of an AP for r = 1, 2, 3, ... If for some distinct positive integers m and n we have Tm = 1/n and Tn = 1/m, then what is Tmn equal to ?

  • mn - 1

  • m - 1 + n - 1

  • 1

  • 0


26.

The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

  • 45360

  • 30240

  • 27216

  • 15120


27.

If sec (θ - α), secθ and sec (θ + α) are in AP, where cosα  1,  then  what  is  the  value  of sin(2θ) + cos α ?

  • 0

  • 1

  •  - 1

  • 12


28.

If the second term of a GP is 2 and the sum of its infinite terms is 8, then the GP is

  • 8, 2, 12, 18, ...

  • 10, 2, 25, 225, ...

  • 4, 2, 12, 122, ...

  • 6, 3, 32, 34, ...


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29.

If a, b, c are in AP or GP or HP, then a - bb - c = ?

  • ba or 1 or bc

  • ca or cb or 1

  • 1 or ab or ac

  • 1 or ab or  ca


30.

What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not allowed ?

  • 2664

  • 3882

  • 4044

  • 4444


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