GATE Questions and Answers with Explanation

Q:

Select a figure from the four alternatives that would complete the Figure Matrix.

1366338089-121484716755.jpg image

1366338089-131484716775.jpg image

(1) (2) (3) (4)

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

Answer & Explanation Answer: A) 4

Explanation:

Similar small figures are increasing by one in each of the bigger figure.

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Q:

An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing ?

A) Rs. 38000	B) Rs. 47000
C) Rs. 50000	D) Rs. 35000

Answer & Explanation Answer: C) Rs. 50000

Explanation:

Let 'x' be the amount he had in the bank.

=> 20/100(25/100(30/100(x))) = 750

x = 750 x 8000/120 = Rs. 50000

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Q:

It costs Rs. p each to send the first thousand messsages and Rs. q to send each subsequent one . If r is greater than 1,000, how many Rupees will it cost to send r messages ?

A) 1000 (r - p) + pq	B) 1000 p + qr
C) 1000 (r - q) + pr	D) 1000(p - q) + qr

Answer & Explanation Answer: D) 1000(p - q) + qr

Explanation:

We need to find the total cost to send r messsages, r > 1000.

The first 1000 messsages will cost Rs.p each (Or)

The total cost of first 1000 messsages = Rs.1000p

The remaining (r - 1000) messsages will cost Rs.q each (Or)

The cost of the (r - 1000) = Rs.(r - 1000)y

Therefore, total cost = 1000p + rq - 1000q

= 1000(p - q) + qr

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Q:

64 S on CB?

Answer

The given statement implies that 64 Squares on Carrom Board.

Workspace

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Q:

Two metallic plate of equal thickness and coefficient thermal conductivity K1 and K2 put together face to face. A common plate is constructed. What is equivalent K?

A) K1k2/k1+k2	B) 2k1k2/k1+k2
C) K1+k2/k1k2	D) None

Answer & Explanation Answer: B) 2k1k2/k1+k2

Explanation:

We know that,

The equivalent K = $\frac{L 1 + L 2}{\frac{L 1}{K 1} + \frac{L 2}{K 2}}$

where L1 & L2 are plate1 & Plate2 thicknesses, K1 & K2 are coefficient thermal conductivity of plate1 & Plate2 respectively.

But here L1 = L2 = L (say)

Then K = L+L/(L/K1 + L/K2) = $\frac{2 K 1 K 2}{K 1 + K 2}$

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Q:

How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ?

A) 59	B) 60
C) 61	D) 64

Answer & Explanation Answer: B) 60

Explanation:

The given digits are 1, 2, 3, 5, 7, 9

A number is even when its units digit is even. Of the given digits, two is the only even digit.Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.

Number of even numbers = ⁵P₃ = 60.

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Q:

Two letters are randomly chosen from the word TIME. Find the probability that the letters are T and M?

A) 1/4	B) 1/6
C) 1/8	D) 4

Answer & Explanation Answer: B) 1/6

Explanation:

Required probability is given by P(E) = $\frac{n (E)}{n (S)} = \frac{1}{4 C_{2}} = \frac{1}{6}$

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Q:

On a ruler's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the ruler live to be ?

A) 84 years	B) 72 years
C) 82 years	D) 64 years

Answer & Explanation Answer: A) 84 years

Explanation:

Let the age of ruler is x so that of son = x/2 (given)
Now according to the given condition
(x/6) + (x/12) + (x/7) + 5 + (x/2) + 4 = x
=> x = 84

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