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Q:

If the letters of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word VERMA is :

A) 108	B) 117
C) 810	D) 180

Answer & Explanation Answer: A) 108

Explanation:

The number of words beign with A is 4!

The number of words beign with E is 4!

The number of words beign with M is 4!

The number of words beign with R is 4!

Number of words beign with VA is 3!

Words beign with VE are VEAMR

VEARM

VEMAR

VEMRA

VERAM

VERMA

Therefore, The Rank of the word VERMA = 4 x 4! + 3! + 6 = 96 + 6 + 6 =108

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Filed Under: Permutations and Combinations
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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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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
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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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Q:

If $A = \frac{l o g_{3} (2187)}{5}$ and $B = l o g_{243} (2187)$ , then which one of the following is correct?

A) A	B) A=B
C) A>B	D) can't be determined

Answer & Explanation Answer: B) A=B

Explanation:

Given $A = \frac{\log_{3} (2187)}{5} a n d B = \log_{243} (2187)$

$B = \log_{3^{5}} (2187) = \frac{\log_{3} (2187)}{5}$

=> A

Therefore, A = B

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Filed Under: Logarithms
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Q:

A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 50% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?

A) 1.5 lakh	B) 1.1 lakh
C) 1.2 lakh	D) 1.65 lakh

Answer & Explanation Answer: B) 1.1 lakh

Explanation:

Total cost of 4 cars = 1+2 = 3 lakh

Total S.P of 4 cars = 3 x 1.5 = 4.5 lakh ( $S i n c e S . P = \frac{(100 + G a i n %)}{100} x C . P$ )

S.P of 1 car = 1.2 lakh

S.P of rest 3 cars = 4.5 - 1.2 = 3.3 lakh

Average S.P of all the 3 cars = 1.1 lakh

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Filed Under: Profit and Loss
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Q:

A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 250 more than A :

A) Rs. 6000	B) Rs. 7250
C) Rs. 5000	D) None of these

Answer & Explanation Answer: B) Rs. 7250

Explanation:

A B C

investment 3x 4x 5x

Rate of return 6y% 5y% 4y%

Return $\frac{18 x y}{100} \frac{20 x y}{100} \frac{20 x y}{100}$

Total = (18+20+20) = $\frac{58 x y}{100}$

B's earnings - A's earnings = $\frac{2 x y}{100}$ = 250

Total earning = $\frac{58 x y}{100}$ = 7250

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Filed Under: Profit and Loss
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Q:

Rahul went to purchase a Nokia mobile handset, the shopkeeper told him to pay 20% tax if he asked the bill. Rahul manages to get the discount of 5% on the actual saleprice of the mobile and he paid the shopkeeper Rs. 3325 without tax. Besides he manages to avoid to pay 20% tax on the already discounted price, what is the amount of discount that he has gotten?

A) 750	B) 375
C) 875	D) 525

Answer & Explanation Answer: C) 875

Explanation:

CP = 100, SP (with tax) =120

New SP = 100 - 5 = 95

Effective discount = 120 - 95 = 25

So, at SP of 95 ----> discount = 25

and at SP of 3325 -----> discount = $\frac{25}{95} \times 3325 = 875$

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Filed Under: Profit and Loss
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