GATE Questions and Answers with Explanation

Q:

Simplify the following equation

$\frac{[{(K - L)}^{2} - {(K + L)}^{2}]}{4 K}$ = a/b

A) K = b /a	B) bL = -a
C) KL = 1	D) aK = -b

Answer & Explanation Answer: B) bL = -a

Explanation:

$\frac{[(K - L)^{2} - {(K + L)}^{2}]}{4 K} = \frac{a}{b} \frac{(K^{2} + L^{2} - 2 K L) - (K^{2} + L^{2} + 2 K L)}{4 K} = \frac{a}{b}$

=> - 4KL/4K = a/b

=> L = - a/b

=> bL = -a

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Q:

What is the next number in the given Number Series?

5, 24, 94, 279, ?

A) 587	B) 554
C) 489	D) 499

Answer & Explanation Answer: B) 554

Explanation:

The given number series follows a pattern that

5 x 5 – 1 = 24

24 x 4 – 2 = 94

94 x 3 – 3 = 279

279 x 2 – 4 = 554

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Q:

Re-arrange the following sentences into a meaningful paragraph.

(A) comes into effect from today. The bank's savings account rate was 3.5 per cent during March 2003 to May 2011 for all savings bank account customers

(B) The bank's decision comes two days ahead of RBI's monetary policy meet and is likely to trigger

(C) with deposits of above Rs 1 crore, it said in a statement. The two-tier savings bank account interest rate

(D) to 3.5 per cent, lowest in six years, a decision that will impact 90 per cent of its customers

(E) The country's largest lender however will continue to pay 4 per cent interest on savings bank accounts

(F) SBI today cut interest rate on savings bank account deposits up to Rs 1 crore by 0.5 per cent

(G) rate war among peers. SBI's savings bank account base is of around Rs 9 lakh crore.

A) BDFACEG	B) BFDCAGE
C) EGACDFB	D) FDBGECA

Answer & Explanation Answer: D) FDBGECA

Explanation:

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32 130553

Q:

Find the next two numbers in the sequence

4, 12, 6, 18, 12, 26, 30, ?, ?

A) 36 & 90	B) 90 & 41
C) 45 & 36	D) 41 & 36

Answer & Explanation Answer: A) 36 & 90

Explanation:

the next 2 number in series we need to divide the series into 2 different series

First series : 4 , 6, 12, 30 ??

Second Series : 12,18,26, ??

So we need to see for the pattern for those series in order to find the next two number , we can do this by finding the difference or division , multiplication logic whatever may apply :

Pattern of Series 1 :

6 divide 4 : 1.5

Next number i.e 12 divided by 6=2

Next number i.e 30 divided by 12 =2.5

So series is going in multiples of 1.5, 2, 2.5, 3 , so on

So first series will look like

4 , 6, 12, 30, 30x3 =90

Pattern of Series 2 : 12,18,26, ??

Its simple Adding numbers with iterative logic (i.e 6, 8, then followed by 10, 12)

Series will be like 12,18,26,36.

For the next two numbers : Series will be like 4, 12, 6, 18, 12, 26, 30, 36, 90

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Q:

Simplify the fraction?

5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17)

A) -4 (1/17)	B) 5 (2/17)
C) -2 (1/17)	D) 3 (3/17)

Answer & Explanation Answer: A) -4 (1/17)

Explanation:

Given fraction is 5 (2/7) - 3 (1/14) - 2 (1/14) - 1 (1/7) = ? + 3 (1/17)

It can be written as

(5 - 3 - 2 - 1) + (2/7 - 1/14 - 1/14 - 1/7) = ? + 3 (1/17)

-1 + 0 - 3 (1/17) = ?

=> ? = -4 (1/17)

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7 129569

Q:

What is the next number of the following sequence ?

21, 77, 165, 285, ......

A) 404	B) 415
C) 426	D) 437

Answer & Explanation Answer: D) 437

Explanation:

The series follow the rule,

21 = $5^{2}-4$
77 = $9^{2} - 4$
165 = $13^{2} - 4$
285 = $17^{2} - 4$

5,9,13,17,21,(+4)...
In the same way next no. will be
$21^{2} - 4$ = 441 - 4 = 437

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50 129445

Q:

Find the Odd One Out?

4, 6, 12, 30, 81, 315.

A) 6	B) 12
C) 81	D) 315

Answer & Explanation Answer: C) 81

Explanation:

Given the number series is 4, 6, 12, 30, 81, 315.

Here it follows a pattern that

4

4 x 1.5 = 6

6 x 2 = 12

12 x 2.5 = 30

30 x 3 = 90 not equals to 81

90 x 3.5 = 315

Hence the odd one in the series is 81.

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Q:

Select the four statements about Plasmodium that are true.

A) Inside an infected mosquito, haploid gametes fuse, forming a diploid zygote that develops into an oocyst

B) Plasmodium cells infect two specific types of cells in humans.

C) Inside an infected mosquito, haploid gametes fuse, forming a haploid zygote that develops into an oocyst.

D) When a mosquito bites a human with malaria, diploid Plasmodium cells enter the mosquito.

E) Plasmodium cells are transferred to humans through mosquito saliva.

F) The life cycle of Plasmodium involves only haploid forms.

G) The complete life cycle of Plasmodium requires two hosts.

A) A, B, E, G	B) A, C, F, G
C) B, C, D, F	D) None of the above

Answer & Explanation Answer: A) A, B, E, G

Explanation:

Plasmodium is a genus of unicellular eukaryotes that are obligate parasites of vertebrates and insects.

From the above given options, A, B, E, G are TRUE regarding Plasmodium.

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