Job Roles Questions and Answers

Q:

How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?

A) 129780	B) 1587600
C) 35600	D) None of these

Answer & Explanation Answer: B) 1587600

Explanation:

H L C N T A U I O

L N A I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants are together then the numberof arrangements = $\frac{7!}{2!}$ x 1/2! .

But the 7 consonants can be arranged themselves in $\frac{7!}{2!}$ x 1/2! ways.

Hence the required number of ways = ${(\frac{7!}{2! 2!})}^{2}$ = 1587600

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Filed Under: Permutations and Combinations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk , Analyst

8 19002

Q:

A Group consists of 4 couples in which each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?

A) 1152	B) 1278
C) 1296	D) None of these

Answer & Explanation Answer: A) 1152

Explanation:

Case I : MW MW MW MW

Case II: WM WM WM WM

Let us arrange 4 men in 4! ways, then we arrange 4 women in 4P4 ways at 4 places either left of the men or right of the men. Hence required number of arrangements

$4! \times 4 P_{4} + 4! \times 4 P_{4} = 2 \times 576 = 1152$

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Filed Under: Permutations and Combinations
Exam Prep: AIEEE , Bank Exams , CAT
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4 11097

Q:

The least value of the expression $2 l o g_{10} (x) - l o g_{x} (\frac{1}{100})$ for x>1 is:

A) 2	B) 3
C) 4	D) 5

Answer & Explanation Answer: C) 4

Explanation:

Hence the least value of is 4

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Filed Under: Logarithms
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

44 7239

Q:

The number of solutions of the equation $l o g_{\frac{x}{2}} (x^{2}) + 40 l o g_{4 x} (\sqrt{x}) - 14 l o g_{16 x} (x^{3}) = 0$ is:

A) 0	B) 1
C) 2	D) 3

Answer & Explanation Answer: D) 3

Explanation:

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Filed Under: Logarithms
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

14 4931

Q:

If $\log_{3} (30)$ = $\frac{1}{a}$ and $\log_{5} (30) = \frac{1}{b}$ then the value of $3 \log_{30} (2)$ is:

A) 3(1+a+b)	B) 2(1-a-b)
C) 3(1-a-b)	D) 3(1+a-b)

Answer & Explanation Answer: C) 3(1-a-b)

Explanation:

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Filed Under: Logarithms
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

25 6280

Q:

The greatest possible value of n could be $9^{n} < 10^{8}$ if, given that log 3 = 0.4771 and $n \in N$ :

A) 7	B) 8
C) 9	D) 10

Answer & Explanation Answer: B) 8

Explanation:

Taking Log to both sides

we get

n = 8

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Filed Under: Logarithms
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8 5791

Q:

Find x if

$l o g_{\frac{1}{\sqrt{2}}} (\frac{1}{\sqrt{8}}) = l o g_{2} (4^{x} + 1) . l o g_{2} (4^{x + 1} + 4)$

A) 0	B) 1
C) 2	D) None of these

Answer & Explanation Answer: A) 0

Explanation:

By trial and error method, when we substitute

x = 0

Both LHS and RHS are equal.

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Filed Under: Logarithms
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Analyst , Bank Clerk , Bank PO

24 11612

Q:

The value of x satisfying the following relation:

$\log_{\frac{1}{2}} (x) = \log_{2} (3 x - 2)$

A) 1/3	B) -1/3
C) 3	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

But at x=-1/3, log x is not defined.

The only admissible value of x is 1.

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Filed Under: Logarithms
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16 12191

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