GATE Questions and Answers with Explanation

Q:

H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 and 16 x 81 x 5 x 11 x 49 is :

A) 360	B) 180
C) 90	D) 120

Answer & Explanation Answer: B) 180

Explanation:

4 x 27 x 3125 = $2^{2} \times 3^{3} \times 5^{5}$ ;

8 x 9 x 25 x 7 = $2^{3} \times 3^{2} \times 5^{2} \times 7$

16 x 81 x 5 x 11 x 49 = $2^{4} \times 3^{4} \times 5 \times 11 \times 7^{2}$

H.C.F = $2^{2} \times 3^{2} \times 5$ = 180.

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Filed Under: HCF and LCM
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23 10672

Q:

Two trains of equal length are running on parallel lines in the same direction at 36 km/hr and 26 km/hr. The faster train passes the slower train in 36 sec. The length of each train is ?

A) 28 mts	B) 54 mts
C) 24 mts	D) 50 mts

Answer & Explanation Answer: D) 50 mts

Explanation:

Let the length of each train be x mts.

Then, distance covered = 2x mts.

Relative speed = 36 - 26 = 10 km/hr.

= 10 x 5/18 = 25/9 m/sec.

2x/36 = 25/9 => x = 50 mts.

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Filed Under: Problems on Trains
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8 10670

Q:

Bhim has assembled a basket of fruit as a holiday gift for each of his friends- Santosh, Tarun, Ujjwal, and Varun. A total of fifteen pieces of fruits-five apples, five oranges and five pears are distributed among the four baskets according to the following conditions: Santosh , Tarun and Ujjwal will each receive exactly two different types of fruit. Varun will receive only apples. Tarun will receive more pieces of fruit than Santosh. Each basket includes at least three pieces of fruit.

1. If Varun’s basket contains more pieces of fruit than Tarun’s basket, then Tarun’s basket must contain:
I. Four pieces of fruit.
II. At least one orange.
III. At least one pear.

(a) I only (b) III only (c) Botha I and II (d) Both II and III

2. If Ujjwal’s basket contains more pieces of fruit than Tarun’s basket, all of the following must be false EXCEPT:

(a) Only Varun will receive apple

(b) Varun will receive exactly four apple.

(c) Ujjwal will receive exactly two apple.

(d) Tarun will receive exactly four pear.

Answer

1. Answer (b)

Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.
At least one pear.

2. Answer (c)

Varun may receive no more than five pieces and Tarun may receive no fewer than four pieces. As a result, if Varun receives more pieces than Tarun, then Varun must receive five pieces, and Tarun must receive four pieces. Thus, statement (a) must be true. Since Varun will receive five pieces, none of the other three friends will receive any apple, accordingly, each of the other three friends must receive at least one orange and at least one pear. Thus, statement (b) and (d) must be true.

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Subject: Deriving Conclusions From Passages Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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10 10668

Q:

In how many ways can 100 soldiers be divided into 4 squads of 10, 20, 30, 40 respectively?

A) 1700	B) 18!
C) 190	D) None of these

Answer & Explanation Answer: D) None of these

Explanation:

$100 C_{10} + 90 C_{20} + 70 C_{30} + 40 C_{40} = \frac{100!}{10! x 20! x 30! x 40!}$

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Filed Under: Permutations and Combinations
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4 10651

Q:

What is needed for steering control on a PWC?

Answer

PWC refers to Personal Water Crafts.

To control steering on a PWC, the most needed requirement is to have power in which will allows the one using it to control the engine for it to stop or for it to move. Without power, the person using it could be out of balance or fail to start the engine. This is the basic requirement because even though it is shut off or the engine is off, the PWC is still on and it could still move without proper knowledge of the engine.

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Subject: Physics Exam Prep: AIEEE , Bank Exams , CAT , GATE
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3 10636

Q:

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate ?

A) Rs. 5422	B) Rs. 5489
C) Rs. 3972	D) Rs. 6145

Answer & Explanation Answer: C) Rs. 3972

Explanation:

Let p = Rs. 100.

Then, S.I is Rs. 50 and time = 5 years.

$∴ R = \frac{100 \times 50}{100 \times 5}$ = 10% p.a.

Now, p = Rs. 12,000 , T = 3 years and R = 10% p.a.

C.I. = Rs. $12000 \times \{{(1 + \frac{10}{100})}^{3} - 1\}$ = Rs. 3972

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Filed Under: Compound Interest
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7 10629

Q:

An amount doubles itself in 15 years. what is the rate of interest ?

A) 7.85 %	B) 9.41%
C) 6.66 %	D) 4.21 %

Answer & Explanation Answer: C) 6.66 %

Explanation:

Let the principle be Rs. P
As the amount double itself the interest is Rs. P too
So P = P x r x 15/100
=> r = 100/15 = 20/3 % = 6.66 %.

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Filed Under: Simple Interest
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5 10627

Q:

Cassock : Priest :: ? : Graduate

A) Gown	B) Tie
C) Cap	D) Coat

Answer & Explanation Answer: A) Gown

Explanation:

A Christian Priest wears cassock while a Graduate wears gown.

Hence, Cassock : Priest :: Gown : Graduate.

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Filed Under: Analogy
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5 10624

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