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Q:

Find the probability of selecting 2 woman when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A) 1/5	B) 1/7
C) 1/6	D) 1/9

Answer & Explanation Answer: C) 1/6

Explanation:

Out of 9 persons,4 can be choosen in $9 C_{4}$ ways =126.

Favourable events for given condition = $2 C_{2} * 7 C_{2}$ = 21.

So,required probability = 21/126 =1/6.

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Q:

A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?

A) 13/42	B) 17/42
C) 5/42	D) 3/14

Answer & Explanation Answer: B) 17/42

Explanation:

3 letters can be choosen out of 9 letters in $9 C_{3}$ ways.

More than one vowels ( 2 vowels + 1 consonant or 3 vowels ) can be choosen in $(4 C_{2} * 5 C_{1}) + 4 C_{3}$ ways

Hence,required probability = $\frac{(4 C_{2} * 5 C_{1}) + 4 C_{3}}{9 C_{3}}$ = 17/42

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Q:

Find the probability of selecting exactly 2 children when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A) 9/29	B) 10/21
C) 12/21	D) 14/19

Answer & Explanation Answer: B) 10/21

Explanation:

4 persons can be selected from 9 in $9 C_{4}$ ways =126

Fvaourable events = $4 C_{2} * 5 C_{2}$ =60

So,required probability = 60/126 = 10/21

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Q:

The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being 1/4%, is:

A) 108.25	B) 112.20
C) 124.75	D) 125.25

Answer & Explanation Answer: C) 124.75

Explanation:

For an income of Rs. 756, investment = Rs. 9000.

For an income of $R s . \frac{21}{2}$ , investment = $R s . \frac{9000}{756} \times \frac{21}{2}$ = Rs. 125.

For a Rs. 100 stock, investment = Rs. 125.

Market value of Rs. 100 stock = $R s . (125 - \frac{1}{4})$ = Rs. 124.75

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Filed Under: Stocks and Shares

Q:

Four persons are to be choosen from a group of 3 men, 2 women and 4 children. Find the probability of selecting 1 man,1 woman and 2 children.

A) 2/7	B) 3/7
C) 4/7	D) 3/7

Answer & Explanation Answer: A) 2/7

Explanation:

Total number of persons = 9

Out of 9 persons 4 persons can be selected in $9 C_{4}$ ways =126

1 man,1 woman and 2 children can be selected in $3 C_{1} * 2 C_{1} * 4 C_{1}$ ways =36

So,required probability = 36/126 =2/7

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Q:

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

A) 2 : 1	B) 3 : 2
C) 25 : 18	D) 27 : 20

Answer & Explanation Answer: C) 25 : 18

Explanation:

Volume of the large cube = $(3^{3} + 4^{3} + 5^{3})$ = 216 cu.cm.

Let the edge of the large cube be a.

So, $a^{3}$ = 216

=>a = 6 cm.

Required ratio = $\frac{6 (3^{2} + 4^{2} + 5^{2})}{6 (6^{2})} = \frac{25}{18}$

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Filed Under: Volume and Surface Area

Q:

A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:

A) 8.5%	B) 7.5%
C) 8%	D) 9%

Answer & Explanation Answer: C) 8%

Explanation:

By investing Rs. 1552, income = Rs. 128.

By investing Rs. 97, income = $R s . (\frac{128}{1552} \times 97)$ = Rs. 8.

Dividend = 8%

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Q:

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

A) 344.35 sq.cm	B) 462 sq.cm
C) 498.35 sq.cm	D) None of these

Answer & Explanation Answer: C) 498.35 sq.cm

Explanation:

h = 14 cm, r = 7 cm.

So, l = $[\sqrt{7^{2} + 14^{2}}] = \sqrt{245} = 7 \sqrt{5} c m$

Total surface area = $πrl + {πr}^{2}$ = $\frac{22}{7} \times 7 \times 7 \sqrt{5} + \frac{22}{7} \times 7 \times 7$

= $154 (\sqrt{5} + 1)$

= (3.236 x 154) sq.cm

= 498.35 sq.cm

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Filed Under: Volume and Surface Area

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