List of practice Questions

A lot of 12 bulbs contains 4 defective bulbs. Three bulbs are drawn at random from the lot, one after the other. The probability that all three are non-defective is

In the given circuit the reading of voltmeter $V_1$ and $V_2$ are $300$ volts each. The reading of the voltmeter $V_3$ and ammeter $A$ are respectively

$\int 4 \cos \left(x + \frac{\pi}{6}\right) \cos 2x . \cos\left(\frac{5\pi}{6} + x\right)dx $

$B_1$, $B_2$ and $B_3$ are the three identical bulbs connected to a battery of steady e.m.f. with key $K$ closed. What happens to the brightness of the bulbs $B_1$ and $B_2$ when the key is opened?

A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 5 km an hour the journey would have taken 2 h less. The original speed of the train was

Select the alternative that logically follows the two given statements:
Some rocks are not tables.
Some rocks are balloons.

A, B, C, D and E sit on a long bench. C does not sit next to A or E. A and E have three persons sitting between them.
Who is sitting in the middle of the bench?

A, B, C, D and E sit on a long bench. C does not sit next to A or E. A and E have three persons sitting between them.
Who are sitting at the extreme ends of the bench?

Find the missing numbers in the following set

2	4	6	8	10
2	14	34	??	98

There are 6 volumes of books on a rack kept in order (such as, vol. 1, vol. 2 and so on). After some readers used them, their order got disturbed. The changes showed as follows:
Vol.5 was directly to the right of vol. 2
Vol 4 has vol. 6 to its left and both were not at Vol.3's place.
Vol.1 has Vol.3 on right and Vol.5 on left.
An even numbered volume is at Vol.5's place.
Find the order in which the books are kept now, from the four given alternatives:

All German philosophers, except for Marx, are idealists. From which of the following can the statements above be most properly inferred?

Ramaswami was studying for his examinations and the lights went off. It was around 1:00 a.m. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally went to sleep, the thick candle was twice as long as the thin one. For how long did Ramaswami study in candle light?

The numerator and denominator of a fraction is in the ratio 2:3.If 6 are subtracted from the numerator the value of the fraction becomes $\frac 23$ of the original fraction.The numerator of the original fraction is,

A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that. After spending 20 paise, the person counts the money. To his surprise, he has double the amount he wanted to
withdraw. Find X and Y. (1 Rupee = 100 Paise)

Four children A, B, C and D are having some chocolates each.
A gives B as many as he already has, he gives C twice of what C already has and he gives D thrice of what D already has.
Now, D gives ($\frac 18$)^th of his own chocolates to B.
Then A gives 10% chocolates he now owns to C and 20% to B.
Finally, all of them have 35 chocolates each. What is the original number of chocolates each had in the beginning?

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the fewest number of socks you can take from the drawer without looking and be sure to get a pair of the same color?

There are two similar figures below with some numbers. The left one is complete where as one number is missing in the right one. Find a suitable number to fill in place of the question mark.

A placement company has to assign 1000 SW personnel who are skilled in Java and Dot Net to a prospective outsourcing company. He finds that 750 are having Dot Net skills and 450 have Java skills. Some have skills in both Java and Dot Net. Find the numbers who have skills in both Java and Dot Net.

If profit is defined as the difference between the selling price and the average cost, and each bottle is sold for Rs. 510, what is the approximate percent profit earned by the firm?

The sum of the areas of two circles which touch each other externally is $ 153\pi $. If the sum of their radii is 15, find the ratio of the larger to the smaller radius.

Answer questions based on the following information:

An automobile company's annual sales of its small cars depends on the state of the economy as well as on whether the company uses some high profile individual as its brand ambassador in advertisements of its product. The state of the economy is "good", "okay" and "bad" with probabilities 0.3, 0.4 and 0.3 respectively. The company may choose a high profile individual as its brand ambassador in TV ads or may go for the TV ads without a high profile brand ambassador.

If the company fixes price at Rs. 3.5 lakh, the annual sales of its small cars for different states of the economy and for different kinds of TV ads are summarized in Table 1. The figures in the first row are annual sales of the small cars when the company uses a high profile individual as its brand ambassador in its TV ads and the ones in the second row are that when the company does not use any brand ambassador in TV ads, for different states of the economy.

	Good	Okay	Bad
With brand ambassador	100000	80000	50000
Without brand ambassador	80000	50000	30000

Table 1

Without knowing what exactly will be the state of the company in the coming one year, the company will either have to sign a TV ad contract with some high profile individual, who will be the company's brand ambassador for its small car for the next one year, or go for a TV ad without featuring any high profile individual. It incurs a cost of Rs. 3.45 lakh (excluding the payment to the brand ambassador) to put a car on the road.

When the company's profit is uncertain, the company makes decisions on the basis of its expected profit. If the company can earn a profit x_i with probability p_i (the probability depends on the state of economy), then the expected profit of the company is:

∑ (x_i × p_i)

Answer the questions based on the data given in Table 2.
Cost and price data for Portland cement manufactured by Paharpur Cement and Bahsin Cement, for four consecutive quarters, are given in Table 2:

	Paharpur Cement		Bahsin Cement
	Cost (as % of sales revenue)	Price (Rs./bag)	Cost (as % of sales revenue)	Price (Rs./bag)
Oct – Dec 2008	92.11	352	94.21	438
Jan – Mar 2009	87.56	304	91.34	440
Apr – Jun 2009	91.03	340	89.96	430
Jul – Sep 2009	90.42	322	90.38	434

Formulas:
Sales Revenue = Price × Sales Quantity
Profit = Sales Revenue − Cost
Profit Rate = Profit ÷ Sales Quantity

The retail prices of flowers, consumer expenditure on flowers and sales of flowers for the calendar year 2009, in Phoolgaon, a small town with a population of 70,000, is summarized in Table 3:

Months	Price (retail) of roses (Rs./dozen)	Average consumer expenditure on roses and carnations (Rs.)	Total consumer expenditure on roses (Rs.)	Sales of carnations (dozens)
Jan	99	47.4	1136916	13848
Feb	112.5	51.9	1051650	20486
Mar	135	49.5	1137915	12928
Apr	130.5	51.6	1135310	14021
May	126	59.4	1116612	18774
Jun	157.5	55.8	979020	17579
Jul	144	56.4	1188432	17521
Aug	117	54.0	940446	20355
Sep	126	55.5	1287900	16031
Oct	162	55.6	772884	22897
Nov	189	52.8	597240	19128
Dec	166.5	56.4	977688	18859

Table 3

Answer the questions based on the information given below:

Madhubala Devi, who works as a domestic help, received Rs. 2500 as Deepawali bonus from her employer. With that money she is contemplating purchase of one or more among 5 available government bonds - A, B, C, D and E.

To purchase a bond Madhubala Devi will have to pay the price of the bond. If she owns a bond she receives a stipulated amount of money every year (which is termed as the coupon payment) till the maturity of the bond. At the maturity of the bond she also receives the face value of the bond.

Price of a bond is given by:
\[ P = \left[ \sum_{t=1}^{T} \frac{C}{(1+R)^t} \right] + \frac{F}{(1+R)^T} \]

where C is coupon payment on the bond, which is the amount of money the holder of the bond receives annually; F is the face value of the bond, which is the amount of money the holder of the bond receives when the bond matures (over and above the coupon payment for the year of maturity). T is the number of years in which the bond matures;
R = 0.25, which means the market rate of interest is 25%.

Among the 5 bonds the bond A and another two bonds mature in 2 years, one of the bonds matures in 3 years, and the bond D matures in 5 years.

The coupon payments on bonds A, E, B, D and C are in arithmetic progression, such that the coupon payment on bond A is twice the common difference, and the coupon payment on bond B is half the price of bond A.

The face value of bond B is twice the face value of bond E, but the price of bond B is 75% more than the price of bond E. The price of bond C is more than Rs. 1800 and its face value is same as the price of bond A. The face value of bond A is Rs. 1000.

Bond D has the largest face value among the five bonds.

OABC is a square where O is the origin and AB = 1. Consider the set of points S = (x_i, y_i) in the square such that x_i + y_i ≤ 1.

Let P(x₁, y₁) and Q(x₂, y₂) be two such points. Two operations addition (+) and multiplication (·) on S are defined as:

P + Q = (x₁ + x₂ − x₁x₂, y₁y₂)

P · Q = (x₁x₂, y₁ + y₂ − y₁y₂)