<delect id="55ttd"></delect>

<cite id="55ttd"><font id="55ttd"></font></cite>

Showing posts with label Indian Navy. Show all posts
Showing posts with label Indian Navy. Show all posts

## Friday, 20 December 2013

1. Which of the following statements is not correct?

A. log10 10 = 1
B. log (2 + 3) = log (2 x 3)
C. log10 1 = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3

Explanation:

(a) Since loga a = 1, so log10 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

log (2 + 3) log (2 x 3)

(c) Since loga 1 = 0, so log10 1 = 0.

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So, (b) is incorrect.

2    If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

A. 2.870

B. 2.967
C. 3.876

D. 3.912

Explanation:

3    If log 27 = 1.431, then the value of log 9 is:

Explanation:

log 27 = 1.431

log (33 ) = 1.431

3 log 3 = 1.431

log 3 = 0.477

log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.

4    If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10

log10 [5 (5x + 1)] = log10 [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3

5    The value of log2 16 is:

Explanation:

Let log2 16 = n.

Then, 2n = 16 = 24 n = 4.

log2 16 = 4.

Directions : In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.

1. 1, 4, 9, 16, 25, (...)

(a) 35

(b) 36 (Ans)

(c) 48

(d) 49

Ans : The numbers are 12, 22, 32, 42, 52.

∴ Missing number = 62 = 36.

2. 20, 19, 17, (...), 10, 5,

(a) 12

(b) 13

(c) 14 (Ans)

(d) 15

Ans :  The Pattern is -1, -2, ...

∴ Missing number = 17 - 3 = 14.

3. 2, 3, 5, 7, 11, (...), 17

(a) 12

(b) 13 (Ans)

(c) 14

(d) 15

Ans :  Clearly, the given series consists of prime numbers starting from 2. The prime number after 11 is 13. So, 13 is the missing number.

4. 6, 11, 21, 36, 56, (...)

(a) 42

(b) 51

(c) 81 (Ans)

(d) 91

Ans :  The pattern is + 5, + 10, + 15, + 20, .....

∴ Missing number = 56 + 25 = 81.

5. 1, 6, 13, 22, 33, (...)

(a) 44

(b) 45

(c) 46 (Ans)

(d) 47

Ans :  The pattern is + 5, + 7, + 9, + 11, ....

∴ Missing number = 33 + 13 = 46.

6. 3, 9, 27, 81, (...)

(a) 324

(b) 243 (Ans)

(c) 210

(d) 162

Ans :  Each term of the given series is obtained by multiplying its preceding term by 3.

∴ Missing number = 81 x 3 = 243.

7. 1, 9, 17, 33, 49, 73, (...)

(a) 97 (Ans)

(b) 98

(c) 99

(d) 100

Ans :  The pattern is + 8, + 8, + 16, + 16, + 24, ...

∴ Missing number = 73 + 24 = 97.

8. 2, 5, 9, (...), 20, 27,

(a) 14 (Ans)

(b) 16

(c) 18

(d) 24

Ans :  The pattern is + 3, + 4, ...

∴ Missing number = 9 + 5 = 14.

9. 5, 9, 17, 29, 45, (...)

(a) 60

(b) 65 (Ans)

(c) 68

(d) 70

Ans :  The pattern is + 4, + 8, + 12, + 16, ...

∴ Missing number = 45 + 20 = 65.

10. 3, 7, 15, 31, 63, (...)

(a) 92

(b) 115

(c) 127 (Ans)

(d) 131

Ans :  Each number in the series is the preceding number multiplied by 2 and then increased by 1.

Thus, (3 x 2) + 1 = 7, (7 x 2) + 1 = 15, (15 x 2) 1 = 31 and so on.

∴ Missing number = (63 x 2) + 1 = 127.