GATE Questions

Q:

Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?

A) 120 B) 256
C) 192 D) 244
 
Answer & Explanation Answer: C) 192

Explanation:

We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.

 

The number can be 4 digited but greater than 4000 or 5 digited.

 

Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x P34 = 3 x 24 = 72. 

 

5 digited numbers = P55 = 5! = 120 

So the total numbers greater than 4000 = 72 + 120 = 192

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Filed Under: Permutations and Combinations
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21 14993
Q:

A scientist who studies water is called a

A) Geographer B) Herpetologist
C) Archeologist D) Hydrologist
 
Answer & Explanation Answer: D) Hydrologist

Explanation:

A person or scientist who studies on water is called as Hydrologist. Since the study of water and its properties is known as Hydrology, the persons who deals with this field are known as Hydrologists.

 

Geographer :

A scientist who studies Earth's natural environment and how human society uses the natural environment.

 

Herpetologist :

A person who studies reptiles and amphibians.

 

Archeologist :


Someone who studies people and what they did in the past from the things they left behind.

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Filed Under: General Awareness
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17 14978
Q:

What will come in place of the question mark in the series below?

7, 4.5, 5.5, 12, 49, ?

A) 393 B) 396
C) 354 D) 367
 
Answer & Explanation Answer: A) 393

Explanation:

Ans. 
4.5 = 7 x 0.5 + 1
5.5 = 4.5 x 1 + 1
12 = 5.5 x 2 + 1
49 = 12 x 4 + 1
? = 49 x 8 + 1, i.e. ? = 393

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Filed Under: Numbers
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2 14882
Q:

8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :

A) 8/39 B) 15/39
C) 12/13 D) None of these
 
Answer & Explanation Answer: B) 15/39

Explanation:

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize) 

 

 = 1-16C1× 14C1×12C1×10C116C4=1539

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Filed Under: Probability
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64 14867
Q:

A periscope works by the principle of

A) Total internal reflection B) Refraction
C) Diffraction D) Reflection & Refraction
 
Answer & Explanation Answer: A) Total internal reflection

Explanation:

A periscope is an optical instrument that uses a system of prisms, lenses, or mirrors to reflect images through a tube.

 

 per11526634345.jpg image

 

Light from a distant object strikes the top mirror and is then reflected at an angle of 90 degrees down the periscope tube. At the bottom of the periscope, the light strikes another mirror and is then reflected into the viewer’s eye.

 

Hence, A periscope works by the principle of Total internal reflection.

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Filed Under: Physics
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38 14810
Q:

Square units 13 by 9 of an office area is

A) 97 B) 117
C) 107 D) 127
 
Answer & Explanation Answer: B) 117

Explanation:

Square units 13 by 9 of an office means office of length 13 units and breadth 9 units.

 

Now its area is 13x 9 = 117 square units or units square.

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Filed Under: Area
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24 14762
Q:

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8cm and breadth 7cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?

A) 55.12 cm B) 22.54 cm
C) 42.51 cm D) 38.57 cm
 
Answer & Explanation Answer: D) 38.57 cm

Explanation:

We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm
Therefore, side of the square is = 1/4 x 60 = 15cm
Circumference of the required semicircle = πr + 2r = 227× 152 + 2×152 = 23.57 + 15 = 38.57cm.

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6 14762
Q:

217 x 217 + 183 x 183 = ?

A) 84521 B) 87487
C) 80578 D) 78458
 
Answer & Explanation Answer: C) 80578

Explanation:

2172+1832

 

= 200+172+200-172

 

It is in the form of a+b2+a-b2=2a2+b2

 

= 2(40000 + 289) = 80578.

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Filed Under: Simplification
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20 14686