 # (11 Nov 2020) – Mathematical Reasoning, 1st & 2nd Shift NTA UGC NET JRF Question paper, Answer key

1. Find the wrong number in the series:
7, 8, 18, 57, 228, 1165, 6996

A. 1165
B. 57
C. 228
D. 18

Explanation: 7*1+1 = 7+1 =8
8*2+2 = 16+2=18
18*3+3 = 54+3=57
57*4+4 = 228+4=232 (not 228 )

2. In a park A, B, C, D, E and F are sitting. C is the brother of D’s husband and son of A. F is the daughter of D and sister of E.
(A)E is the grandson of A
(B) F is the daughter of C
(C) B is the father of F
(D) There are one son and one daughter in the group
(E) C is the uncle of E

(1)(A), (B) and (C) only
(2)(A), (C) and (E) only
(3)(B), (D) and (E) only
(4) (B), (C) and (D) only

3. In a 100 meters race, A beat B by 10 meter or 2 seconds. What is the speed of A?

(1) 5 Km/h
(2) 10 Km/h
(3) 15 Km/h
(4) 20 Km/h

Explanation: B can cover distance 10 M in 2 Sec
Speed of B= D/T= 10/2= 5 m/s
Total Distance= 100
Let Time by A to cover 100 m = x
Time by A to cover 100 m = x + 2
Speed of B= 5
100 = 5
X +2 100 = 5X + 10
X= 90/5 = 18
Speed of A= D/t= 100/18 m/s
In Km/h
100 x 18 = 20

4. In a `100m` race, A beats B by `20m` or 5 seconds. Find the speed of A

A 10 m/s
B 5 m/s
C 20 m/s
D 15 m/s

Explanation: B can cover distance 20 M in 5 Sec
Speed of B= 20/5= 4 m/s
Total Distance= 100
Let Time by A to cover 100 m = x
Time by A to cover 100 m = x + 5
Speed of B= 4
100 = 4
X +5 100 = 4X + 20
X= 80/4 = 20
Speed of A= D/t= 100/20 = 5m/s

5. Three pipes fill a tank in 4 hours. If two of them take 8 and 12 hours each to fill the tank, how many hours will the third pipe take to fill the tank?

(1) 6 hours
(2) 15 hours
(3) 18 hours
(4) 24 hours

Explanation: 1 + 1 + 1 = 1
8 12 x 4 1 + 1 – 1 = – 1
8 12 4 x 3 + 2 – 6 = 1
24 x x= 24

6. The ratio of ages of two persons A and B is 3 : 4 and that of ages of B and C is 4: 5. If the average of all three is 40 years, what is B’s age?

(1) 20 years
(2) 30 years
(3) 40 years
(4) 50 years

Explanation: Average of all three is 40 years
A+b+c= 40 x 3= 120
3:4:5
B= 4/12 x 120 = 40

7. If UGCNET = 35, then CSIRNET =

1. 42
2. 43
3. 44
4. 45

Explanation: Alphabet comes on UGCNET= 21+7+3+14+5+20= 70/2= 35
CSIRNET =3+19+9+18+14+5+20= 88/2= 44

8. The missing letters in the given letter series are:
BCE, CDG, DEI,_FGM

1. EFK
2. EGJ
3. EFH
4. EGH

9. A certain principal is invested at the annual rate of interest of 5% for 2 years. The difference between compound interest and simple interest is Rs.1 (Rupee one). What is the principal?

1. Rs.150
2. Rs.250
3. Rs.300
4. Rs.400

Explanation: 2 yr diff= P(r/100)^2
1 = P(25/10000)
P= 10000/25 = 400

10. Twenty times a positive integer is less than its square by 96. What is the integer?

1. 24
2. 20
3. 30
4. 14

Explanation: 24 x 20 = 480
24* 24= 576 – 96= 480
1. 