GATE Questions

Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123 B) 113
C) 246 D) 945
 
Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. 

 

(i) 1 lady out of 4 and 4 gentlemen out of 6 

(ii) 2 ladies out of 4 and 3 gentlemen out of 6 

(iii) 3 ladies out of 4 and 2 gentlemen out of 6 

(iv) 4 ladies out of 4 and 1 gentlemen out of 6 

 

In case I the number of ways = C14×C46 = 4 x 15 = 60 

In case II the number of ways = C24×C36 = 6 x 20 = 120 

In case III the number of ways = C34×C26 = 4 x 15 = 60

In case IV the number of ways = C44×C16 = 1 x 6 = 6 

 

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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5 4866
Q:

Ram sell his goods 25% cheaper than Shyam and 25% dearer than Bram. How much % is Bram's good cheaper than Shyam ?

A) 60% B) 40%
C) 50% D) 30%
 
Answer & Explanation Answer: B) 40%

Explanation:

Lets say shyam sells at 100,

 

Since Ram sells 25% cheaper than Shyam,

 

Therefor Ram sells at less than 25% of100 or 75 rs.

 

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

 

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

 

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

 

Hence Brams Good is 40% cheaper than that of Shyam's good.

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13 4642
Q:

A number is increased by 20% and then decreased by 20%, the final value of the number is ?

A) increase by 2% B) decrease by 3%
C) decrease by 4% D) increase by 5%
 
Answer & Explanation Answer: C) decrease by 4%

Explanation:

Here, x = 20 and y = - 20
Therefore, the net % change in value
=x + y + xy100 %
20 + -20 + 20 × -20100%  or  - 4%

Since the sign is negative, there is a decrease in value by 4%.

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9 4640
Q:

is related to 81 in the same way as 64 is related to ____

A) 225 B) 425
C) 525 D) 625
 
Answer & Explanation Answer: D) 625

Explanation:

The relationship is xy  :  x+1y+1

 

Now , 64 = 43

 

So, required number = 4+13+1 = 54 = 625

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Filed Under: Analogy - Verbal Reasoning - Mental Ability
Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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88 4461
Q:

There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

A) 105 B) 7! x 6!
C) 7!/5! D) 420
 
Answer & Explanation Answer: A) 105

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room, 

 Then, 7C1 x 6C2 x 4C

= 7 x 15 x 1 = 105

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9 4427
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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44 4303
Q:

A letter is takenout at random from 'ASSISTANT'  and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A) 35/96 B) 19/90
C) 19/96 D) None of these
 
Answer & Explanation Answer: B) 19/90

Explanation:

ASSISTANTAAINSSSTT

STATISTICSACIISSSTTT

Here N and C are not common and same letters can be A, I, S, T. Therefore

 Probability of choosing A =  2C19C1×1C110C1 = 1/45 

 Probability of choosing I = 19C1×2C110C1 = 1/45

Probability of choosing S = 3C19C1×3C110C1 = 1/10

Probability of choosing T = 2C19C1×3C110C1 = 1/15

Hence, Required probability =   145+145+110+115= 1990 

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55 4219
Q:

5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?

A) 2880 B) 1440
C) 720 D) 2020
 
Answer & Explanation Answer: A) 2880

Explanation:

There are total 9 places out of which 4 are even and rest 5 places are odd.

 

4 women can be arranged at 4 even places in 4! ways.

 

and 5 men can be placed in remaining 5 places in 5! ways.

 

Hence, the required number of permutations  = 4! x 5! = 24 x 120 = 2880

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3 3961