# GATE Questions

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

Explanation:

$ASSISTANT\to AAINSSSTT$

$STATISTICS\to ACIISSSTTT$

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

Probability of choosing A =  $\frac{{2}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{1}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/45

Probability of choosing I = $\frac{1}{{9}_{{C}_{1}}}×\frac{{2}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/45

Probability of choosing S = $\frac{{3}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{3}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/10

Probability of choosing T = $\frac{{2}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{3}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/15

Hence, Required probability =

55 4292
Q:

The third proportional to 9 and 12 is ?

 A) 14 B) 16 C) 18 D) 20

Explanation:

Let the third proportion to 9 & 12 be 'x'.

=> 9:12 = 12 :p

=> p = 12x12/9 = 16.

12 4053
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

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

3 3996
Q:

The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is :

 A) Rs. 560 B) Rs. 530 C) Rs. 500 D) Rs. 514

Explanation:

110% of S.P. = Rs. 616

S.P. = (616 x 100)/110 = Rs. 560

C.P = (110 x 560)/112 = Rs. 500

10 3843
Q:

A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in    ?

 A) 20 hrs B) 28 hrs C) 36 hrs D) 40 hrs

Explanation:

1/8 - 1/x = 1/10

=> x = 40 hrs

11 3786
Q:

A Certain sum of money an amounts to Rs 2500 in a span Of 5 years and further to Rs.3000 in a span of 7 years at simple interest The sum is ?

 A) Rs. 1800 B) Rs. 2000 C) Rs. 1400 D) Rs. 1250

Explanation:

2500 in 5th year and 3000 in 7th year
So in between 2 years Rs. 500 is increased => for a year 500/2 = 250
So, per year it is increasing Rs.250 then in 5 years => 250 x 5 = 1250
Hence, the initial amount must be 2500 - 1250 = Rs. 1250

8 3632
Q:

The calendar for the year 1988 is same as which upcoming year ?

 A) 2012 B) 2014 C) 2016 D) 2010

Explanation:

We already know that the calendar after a leap year repeats again after 28 years.

Here year 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.

41 3555
Q:

How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?

 A) 129780 B) 1587600 C) 35600 D) None of these

Explanation:

H   L   C   N    T    A   U   I   O

L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$x 1/2! .

But the 7 consonants  can be arranged themselves in  $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$ x 1/2! ways.

Hence the required number of ways = ${\left(\frac{7!}{2!2!}\right)}^{2}$ = 1587600