GATE Questions and Answers with Explanation

Q:

A person is asked to put in a basket one apple when ordered 'one', one guava when ordered 'two', one orange whe ordered 'three' and is asked to take out from the basket one apple and one guava both when ordered 'four'. The ordered sequence executed by the person is as follows :

1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4

1. How many apples will be there in the basket at the end of the above order sequence ?
(a) 4 (b) 3 (c) 2 (d) 1

2. How many fruits will be there in the basket at the end of the above order sequence ?
(a) 13 (b) 17 (c) 9 (d) 11

Answer

1. Answer (c)

Each time we order 1, one apple is added to the basket but each time when 4 is ordered, one apple is removed from it.

Required number of apples = number of 1's - number of 4's = 6 - 4 = 2

2. Answer (d)

Each time we order 1, 2 or 3, one fruit is added to the basket but when ever we order 4, two fruits are removed from it.

Required number = Number of 1's + Number of 2's + Number of 3's - 2 x (Number of 4's)

= 6 + 6 + 7 - (2x4)
= 19 - 8
= 11.

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Subject: Number, Ranking and Time Sequence Test Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE
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12 8482

Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

A) 1	B) 2
C) 4	D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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Filed Under: Logarithms
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30 8481

Q:

_ tu _ rt _ s _ _ usrtu _

A) rsutrr	B) rsurtr
C) rsurts	D) rtusru

Answer & Explanation Answer: C) rsurts

Explanation:

The series rtus/rtus/rtus/rtus. Thus, the pattern 'rtus' is repeated.

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Filed Under: Number Series
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22 8463

Q:

Which of the following is not a compound?

A) Brass	B) Quick lime
C) Marble	D) Soda ash

Answer & Explanation Answer: A) Brass

Explanation:

Among the given options Brass is not a compound. Since it is an alloy, it is a mixture. It is a mixture of copper and zinc.

Which_of_the_following_is_not_a_compound1558074260.jpg image

The smallest part of a compound is called a molecule. It has a unique composition that is always the same.

Compound is a substance that consists of two or more elements.

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Filed Under: Chemistry
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12 8451

Q:

Arun and Varun started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, Akhil joined them with Rs. 20,000. What will be Varun's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business ?

A) Rs. 7500	B) Rs. 4520
C) Rs. 8750	D) Rs. 6350

Answer & Explanation Answer: A) Rs. 7500

Explanation:

Arun : Varun : Akhil = (20000 x 24) : (15000 x 24) : (20000 x 18) = 4:3:3

B's share = 25000 x 3/10 = Rs. 7500.

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Filed Under: Partnership
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5 8451

Q:

An item is sold at a loss of 10%. Had it sold for Rs. 9 more, a profit of 25/2% would have gained. What is the cost price of the item?

A) Rs. 90	B) Rs. 75
C) Rs. 55	D) Rs. 40

Answer & Explanation Answer: D) Rs. 40

Explanation:

Let the cost price of the item = Rs. 50

Sold at 10% loss => for Rs. 50 loss S.P = Rs. 45

From the given data,

25/2 % gain if it is sold at Rs. 9 more

56.25 - 45 = 9

=> 11.25 = 9

=> 22.5 = 18

=> 45 = 36

=> 50 = ?

=> $C . P = \frac{50 x 36}{45} = 40$

Hence, the Cost price of the item = Rs. 40.

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Filed Under: Profit and Loss
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15 8444

Q:

There are 11 True or False questions. How many ways can these be answered ?

A) 11!/2	B) 1024
C) 11!	D) 2048

Answer & Explanation Answer: D) 2048

Explanation:

Given 11 questions of type True or False

Then, Each of these questions can be answered in 2 ways (True or false)

Therefore, no. of ways of answering 11 questions = $2^{11}$ = 2048 ways.

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Filed Under: Permutations and Combinations
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9 8435

Q:

Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420 ?

A) Rs. 2000	B) Rs. 2100
C) Rs. 1900	D) Rs. 2150

Answer & Explanation Answer: A) Rs. 2000

Explanation:

Given,
Compound rate, R = 10% per annum
Time = 2 years
C.I = Rs. 420
Let P be the required principal.
A = (P+C.I)
Amount, A = $P {(1 + (\frac{r}{100}))}^{n}$

(P+C.I) = $P {[1 + (\frac{10}{100})]}^{2}$

(P+420) = P[11/10][11/10]

P-1.21P = -420

0.21P = 420

Hence, P = 420/0.21 = Rs. 2000

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Filed Under: Compound Interest
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7 8424

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