GATE Questions and Answers with Explanation

Q:

A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

A) 1/4	B) 1/2
C) 3/4	D) 7/12

Answer & Explanation Answer: C) 3/4

Explanation:

Let A, B, C be the respective events of solving the problem and $A, B, C$ be the respective events of not solving the problem. Then A, B, C are independent event

$∴ A, B, C$ are independent events

Now, P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

$P (A) = \frac{1}{2}, P (B) = \frac{2}{3}, P (C) = \frac{3}{4}$

$∴$ P( none solves the problem) = P(not A) and (not B) and (not C)

= $P (A \cap B \cap C)$

= $P (A) P (B) P (C)$ $[∵ A, B, C a r e I n d e p e n d e n t]$

= $\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4}$

= $\frac{1}{4}$

Hence, P(the problem will be solved) = 1 - P(none solves the problem)

= $1 - \frac{1}{4}$ = 3/4

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Filed Under: Probability
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1018 208357

Q:

Choose the Antonym of the given word from the following options

'Jettison'

A) Salvage	B) Submerge
C) Repent	D) Descend

Answer & Explanation Answer: A) Salvage

Explanation:

'Jettison' means to discard and 'salvage' means to rescue something discarded. Hence, 'salvage' is the word which is farthest in meaning to the given word 'Jettison'.

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Filed Under: Analogy
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46 204028

Q:

Correct the given sentence gramatically.

Shreya, who she is my best friend, is a singer.

A) Shreya, she who is my best friend, is a singer.	B) Shreya, who is my best friend, is a singer.
C) Shreya, is my best friend, who she is a singer.	D) All of the above

Answer & Explanation Answer: B) Shreya, who is my best friend, is a singer.

Explanation:

The relative pronoun acts as the subject or object of the relative clause. It replaces words like she, he, him, her, they, them etc.

It is, therefore, wrong to repeat the pronoun in the relative clause.

Hence, the correct sentence is Shreya, who is my best friend, is a singer.

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Filed Under: English
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65 202667

Q:

Correction of sentences:

What your Sirname is?

A) What your Sirname?	B) What is your Sirname?
C) Your Sirname is what?	D) None of the above

Answer & Explanation Answer: B) What is your Sirname?

Explanation:

'What is your Sirname?' is the correct sentence of the given sentence in English grammar.

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Filed Under: English
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22 200306

Q:

Crack the code & Unlock the Key ?

A) 062	B) 602
C) 042	D) 204

Answer & Explanation Answer: C) 042

Explanation:

From all the hints given,

only 042 satisfies and it unlocks the key.

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Filed Under: Number Puzzles
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1259 180586

Q:

Simplify the following :

$\frac{37^{3} + 35^{3} + 28^{3} - 3 x 37 x 35 x 28}{37^{2} + 35^{2} + 28^{2} - 37 x 35 - 35 x 28 - 37 x 28}$ ?

A) 100	B) 1
C) 4	D) 0

Answer & Explanation Answer: A) 100

Explanation:

Given $\frac{37^{3} + 35^{3} + 28^{3} - 3 x 37 x 35 x 28}{37^{2} + 35^{2} + 28^{2} - 37 x 35 - 35 x 28 - 37 x 28}$

It is in the form of

$\frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a^{2} + b^{2} + c^{2} - a b - b c - c a}$ = a + b + c

Here a = 37, b = 35 & c = 28

=> a + b + c = 37 + 35 + 28 = 100

Therefore, $\frac{(37)^{3}+(35)^{3}+(28)^{3}-3x37x35x28}{(37)^{2}+(35)^{2}+(28)^{2}-37x35-35x28-37x28}$ = 100

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Filed Under: Simplification
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20 172706

Q:

The following sentence contains which type of conjunction?

"She is not only a great singer but also an exceptional dancer."

A) Phrasal	B) Subordinating
C) Correlative	D) Coordinating

Answer & Explanation Answer: C) Correlative

Explanation:

A conjunction is a word that joins words, clauses, phrases or sentences.

For example but, and, or, nor, yet for, so, although, since, because, unless, when, where, while, etc.

There are four types of conjunctions:

1. Subordinating Conjunction

2. Correlative Conjunction

3. Phrasal Conjunction

4. Coordinating Conjunction

In the given sentence, "She is not only a great singer but also an exceptional dancer" Not Only But Also is a type of Correlative conjunction.

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Filed Under: English
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9 171014

Q:

Which pair of atoms has the highest electronegativity difference?

(Calcium's electronegativity is 1.0

Fluorine's electronegativity is 4.0

Hydrogen's electronegativity is 2.2

Sodium's electronegativity is 0.93)

A) F-F	B) Ca-F
C) H-F	D) Na-F

Answer & Explanation Answer: D) Na-F

Explanation:

F-F = 4 - 4 = 0

Ca-F = 4 - 1 = 3.0

H-F = 4 - 2.2 = 1.8

Na-F = 4 - 0.93 = 3.07

Hence, the highest electronegativity difference is in Na-F.

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Filed Under: Chemistry
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12 158646

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