## Sunday, 10 February 2013

### GATE-2013 Solutions (General Aptitude)(EC/EE/IN)

1. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is
(A)30   (B)36   (C)40   (D)24
Sol:
This is a simple formula based one.
Average speed = total distance/ total time
Total distance = 8+6+16 = 30 km
Total time taken = 3 quarters of an hour = ¾ hr
Average speed = total distance/ total time = 30/(3/4) = 40 kmph
Ans: C

2. Find the sum to n terms of the series 10+84+734+….
(A)9(9n+1)/10 + 1        (B) 9(9n-1)/8 + 1          (C) 9(9n-1)/8 + n          (D) 9(9n-1)/8 + n2
Sol:
Check from the options by substituting n = 1,2…
For n=1, all options are right
For n=2, sum must be 10+84=94.
Only option D is correct for this and we can bank on that…
Ans: D

3. The set of values of p for which the roots of the equation 3x2+2x+p(p-1)=0 are of opposite sign is

(A)(-∞,0)         (B)(0,1)            (C)(1,∞)          (D)(0,∞)

Sol:

This is a question on quadratic equations funda.

For ax2+bx+c=0,

if the two roots are of different signs, their product must be –ve => c/a < 0

=> p(p-1)/3 < 0 => p(p-1) < 0 => 0 < p < 1

Ans: B

4. What is the chance that a leap year, selected at random, will contain 53 Saturdays?

(A)2/7  (B)3/7  (C)1/7  (D)5/7

Sol:

A leap year has 366 days => 365/7 weeks = 52 weeks + 2 days

=> For a leap year to have 53 Saturdays, either one of the first two days of first week of the year (Jan 1st or 2nd) must be a Saturday. So the probability is 2 out of 7

Ans: A

5. In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 410C and of Tuesday to Thursday was 430C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in oC on Thursday was

(A)40   (B)43   (C)46   (D)49

Sol:

Let the temperatures on Monday,Tuesday,Wednesday and Thursday is M,T,W and Th respectively.

The mean temperature of Monday to Wednesday was 410C => (M+T+W)/3 = 41

=> M+T+W = 123        ---(1)

The mean temperature of Tuesday to Thursday was 430C=> (T+W+Th)/3 = 43

=> T+W+Th = 129        ---(2)

(2)-(1) => Th-M = 6     ---(3)

temperature on Thursday was 15% higher than that of Monday => Th = 1.15*M   ---(4)

From 93) and (4), 0.15M = 6 => M = 6/0.15 => Th = 1.15*6/0.15 = 46
Ans: C
6. They were requested not to quarrel with others.
Which one of the following is the closest in meaning to the word quarrel?
(A)   make out         (B) call out      (C) dig out       (D) fall out

Ans: D

7. Statement   You can always give me a ring whenever you need

Which one of the following is the inference from the above statement?
(A)   Because I have a nice caller tune
(B)   Because I have a better telephone facility
(C)   Because a friend in need is a friend in deed
(D)  Because you need not pay towards the telephone bills when you give me a ring

Explanation:

All the other options except (C) can be easily eliminated as they are illogical
Ans: C

8. Statement There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists and so on.

Which one of the following is the best inference from the above statement?

(A)The emergence of colonial India led to our independence

(B)Nationalism in India is emerged in the context of colonialism

(C)Nationalism in India is homogeneous
(D)Nationalism in India is heterogeneous

Explanation: As the movement is in different forms, we can say that nationalism is heterogeneous
Ans: D

9. Choose the grammatically CORRECT sentence:

(A) Two and two add four       (B) Two and two become four

(C) Two and two are four       (D) Two and two make four

Explanation: This is a question on English usage and 'make' makes sense here
Ans: D

10. Complete the sentence:
Dare ______ mistakes.

(A)   commit            (B) to commit  (C) committed (D) committing
Ans: A