In an examination hall, there are four rows of chairs. Each row has 8 chairs, one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that in each row all students belong to the same class should sit and that no two adjacent rows are allotted to the same class. In how many ways can these 32 students be seated?
2 x 16! x 16!
2 x 16! x 15!
2 x 15! x 15!
2 x 14! x 16!
Answer : Option A. Students can be adjusted in 16! x 16! ways. Rows can be adjusted in 2 ways. So the final answer will be the 1st option.
There are three events A, B and C, only one of which must happen. The odds are 8 to 3 against A, 5 to 2 against B. Find the odds against C.
43 : 34
43 : 77
34 : 43
77 : 43
Answer : Option A. P(A) = 3/11 & P(B) = 2/7 . So probability of happening of C = 1 – ( 3/11+ 2/7) = 34/77 . So the odds against C are 43:34.
1,496 cm3 of a metal is used to cast a pipe of length 28 cm. If the internal radius of the pipe is 8 cm, the outer radius of the pipe is
Answer : Option C. That will be = 22/7 x 28 x (r2- 82) = 1,496. Now solving for 'r' we get r = 9
A man is standing on the 8 m long shadow of a 6 m long pole. If the length of the man’s shadow is 2.4 m, then the height of the man is
Answer : Option B. 8 m shadow. Length of pole is = 6m. 2.4 m shadow will have = 6/8 x 2.4 = 1.8 m height of the man as answer.
In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. The age of the new boy is
14 years 8 months
16 years 4 months
17 years 10 months
Answer : Option A. Decrease of 20 x 2 = 40 months means that incoming boy has age 18 years – 40 months = 14 years and 8 months.
Two taps can separately fill a cistern in 10 minutes and 15 minutes, respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in
Answer : Option C. 1/6 - 1/x = 1/18 Try option in place of x and get answer as third option.
A boatman goes 2 km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. How long will he take to go 5 km in stationary water?
1 hour 15 minutes
Answer : Option C. In 1 hr he goes 2 km against the stream and with the current he will go 6 km in 1 hr. In still water he will go 4 km in 1 hr. So it will take 1.15 hr for 5 km.
A person travels 285 km in 6 hours in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hour. In the second part of the journey, he travels by train at the speed of 55 km per hour. How much distance did he travel by train?
Answer : Option B. Just go by options. In 3 hours he will travel 165 by train and By bus 120 km in next the 3 hours. So 2nd option.
If there are six periods in each working day of a school, in how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
Answer : Option B. Let us take a case where we have decided which specific subject has a double class. Now we have 6 periods and we have filled all of them up – but with one subject being repeated. These can be arranged in 6!/2! = 360 ways. Now any of the 5 subjects can be repeated. So total no. of possibilities is – 360 x 5 = 1800.
A monument has 50 cylindrical pillars each of diameter 50 cm and height 4 m. What will be the labour charges for getting these pillars cleaned at the rate of 50 paise per sq. m? (Use π = 3.14)
Answer : Option B. Direct formula putting = 2 x π x r x h x 50 ÷ ( 2 x 100) = 50 x 2 x 3.14 x 25 x 4 ÷ (2 x 100)
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