If the ratio of AM to GM of two positive numbers a and b is 5 : 3

Subject

Mathematics

Class

NDA Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If n  N, then 121n - 25n + 1900n -  - 4n is divisible by which one of the following ?

  • 1904

  • 2000

  • 2002

  • 2006


2.

If n = 2007!, then what is 1log2n + 1log3n + 1log4n + ... + 1log2017n = ?

  • 0

  • 1

  • n2

  • n


3.

In the expansion of (1 + x)43, if the coefficients of (2r + 1)th and (r + 2)th terms are equal, then what is the value of r (r  1) ?

  • 5

  • 14

  • 21

  • 22


4.

What is the principal argument of (- 1 - i), where i =  - 1 ?

  • π4

  • - π4

  •  - 3π4

  • 3π4


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5.

Let α and β be real numbers and z be a complex number. If z2 + αz + β = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that :

  • β   - 1, 0

  • β = 1

  • β  1, 

  • β  0, 1


6.

Let A and B be subsets of X and C = (A  B')  (A'  B), where A' and B' arecomplements of A and B respectively in X. What is C equal to?

  • (A  B') - (A  B')

  • A'  B - A'  B

  • A  B - A  B

  • A'  B' - A'  B' 


7.

How many numbers between 100 and 1000 can beformed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed ?

  • 35

  • 53

  • 120

  • 60


8.

The number of non-zero integral solutions of the equation   1 - 2ix = 5x is :

  • Zero (No solution)

  • One

  • Two

  • Three


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9.

If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to :

  • 3 : 5

  • 2 : 9

  • 9 : 1

  • 5 : 3


C.

9 : 1

AM = a + b2GM = abGiven, AMGM = 53a + b2 × ab = 53Apply Componendo and Dividendoa + b +2aba + b - 2ab = 5 + 35 - 3a + b2a - b2 = 82 = 4a + ba - b = 21Again apply Componendo and Dividendoab = 2 + 12 - 1ab = 31    ab = 91


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10.

If the coefficients of am and an in the expansion of (1+ a)m + n are α and β, then which one of the following is correct ?

  • α = 2β

  • α = β

  • 2α = β

  • α = m + nβ


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