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Q:

A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

A) 123/897	B) 23/67
C) 7/44	D) 12/45

Answer & Explanation Answer: C) 7/44

Explanation:

Here, n(E) = $7 C_{1} \times 5 C_{1} \times 5 C_{1}$

And, n(S) = $12 C_{1} * 11 C_{1} * 10 C_{1}$

P(S) = $\frac{7 * 6 * 5}{12 * 11 * 10}$ = 7/44

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Q:

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

A) 19/5525	B) 16/5525
C) 17/5525	D) 7/5525

Answer & Explanation Answer: B) 16/5525

Explanation:

Required probability:

$\frac{4 C_{1} * 4 C_{1} * 4 C_{1}}{52 C_{3}} = \frac{4 * 4 * 4}{22100} = \frac{16}{5525}$

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Q:

The cash realised on selling a 14% stock is Rs.106.25, brokerage being 1/4% is

A) 123	B) 106
C) 100	D) 156

Answer & Explanation Answer: B) 106

Explanation:

Cash realised= Rs. (106.25 - 0.25)
= Rs. 106.

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Filed Under: Stocks and Shares

Q:

In a race, the odd favour of cars P,Q,R,S are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of them wins the race.

A) 319/420	B) 27/111
C) 114/121	D) 231/420

Answer & Explanation Answer: A) 319/420

Explanation:

$P (P) = \frac{1}{4}, P (Q) = \frac{1}{5}, P (R) = \frac{1}{6}, P (S) = \frac{1}{7}$
All the events are mutually exclusive hence,

Required probability = P(P)+P(Q)+P(R)+P(S)

$\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}$ = $\frac{319}{420}$

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Q:

If x is chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?

A) 1/2	B) 2/3
C) 3/4	D) 4/3

Answer & Explanation Answer: B) 2/3

Explanation:

S ={(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)}
Total element n(S)=12

xy will be even when even x or y or both will be even.
Events of x, y being even is E.
E ={(1,6),(2,5),(2,6),(2,7),(3,6),(4,5),(4,6),(4,7)}
n(E) = 8

P(E)=n(E)n(S)=812 = 4/3

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Q:

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is neither a spade nor a Jack?

A) 9/13	B) 4/13
C) 10/13	D) 8/13

Answer & Explanation Answer: A) 9/13

Explanation:

There are 13 spade and 3 more jack

Probability of getting spade or a jack:
=13+352=1652=413

So probability of getting neither spade nor a jack:
=1−413 = 9/13

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Q:

A man sells Rs.5000, 12 % stock at 156 and uinvests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Rs. 70. How much of the proceeds were invested in each stock?

A) 4000	B) 4200
C) 4002	D) 4020

Answer & Explanation Answer: B) 4200

Explanation:

S.P of Rs. 5000 stock = $R s . (\frac{156}{100} * 5000)$ = Rs. 7800.

Income from this stock = $R s . (\frac{12}{100} * 5000)$ = Rs. 600.

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,

$(x * \frac{8}{90}) + (7800 - x) * \frac{9}{108} = [600 + 70]$

$\frac{4 x}{45} + \frac{7800 - x}{12} = 670 \Leftrightarrow x = 3600$

Therefore, Money invested in 8 % stock at 90 = Rs. 3600.

Money invested in 9 % at 108 = Rs. (7800-3600) = Rs. 4200.

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Filed Under: Stocks and Shares

Q:

A man buys Rs. 25 shares in company which pays 9 % dividend. The money invested is such that it gives 10 % on investment. At what price did he buy the shares?

A) 22.50	B) 22
C) 20.45	D) 12.50

Answer & Explanation Answer: A) 22.50

Explanation:

Suppose he buys each share for Rs. x.

Then, $R s . (25 * \frac{9}{100}) = (x * \frac{10}{10})$ or x = Rs. 22.50.

Cost of each share = Rs. 22.50.

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