# (01 & 09 Oct 2020) – Mathematical Reasoning, 2nd & 1st Shift NTA UGC NET JRF Question paper, Answer key

1. A man reaches his office 30 minutes late if he walks by 2/3 rd of his routine speed. What is the time he usually takes to reach the office?

1. 30 minutes
2. 90 minutes
3. 60 minutes
4. 45 minutes
एक व्यक्ति अपने कार्यालय में 30 मिनट देरी से पहुंचता है यदि वह अपनी नियमित गति के 2/3 से चलता है। वह आमतौर पर कार्यालय पहुंचने में कितना समय लेता है?

Explanation: 2/3 rd of his routine speed
usual speed: 3:2
usual time: 2: 3 (inverse relation)
As per Allegation difference 1 = 30
usual time ration2 = 30 x 2 = 60

2. If January 1, 2007, was a Monday, then January 1, 2008, is a:

1. Sunday
2. Monday
3. Tuesday
4. Wednesday

Explanation: Just 1 add in same day next year

3. Given below are two statements.

Statement I: The mean is the numerical average and is found by adding up all the values and dividing the sum by the number of values
Statement II: The mean of the following wages is 16000
i) 12000 ii) 10000 iii) 23000 iv) 15000

1. Both Statement I and Statement Il are true
2. Both Statement I and Statement Il are false
3. Statement I is correct but Statement Il is false
4. Statement I is incorrect but Statement Il is true

Explanation: 60000/4= 15000

4. The radii of the top and bottom of a bucket of slant height 45cm are 28cm and 7 cm respectively. The curved surface area of the bucket is:

(A) 4950 cm2
(B) 4951 cm2
(C) 4952 cm2
(D) 4953 cm2
तिरछी ऊँचाई 45cm की एक बाल्टी के ऊपर और नीचे की त्रिज्याएँ क्रमशः 28cm और 7cm हैं। बाल्टी का वक्र पृष्ठीय क्षेत्रफल है:

Explanation: (C.S.A/L.S.A)= Frustum: Π(r+R)l
Curved surface area of the bucket = π (28 + 7) X 45
Curved surface area of the bucket = 4950 cm2

5. What part of 1/12 is 3/8 ?

1) 3/7
2) 4/3
3) 1/12
4) 9/2

Explanation: X= 3/8×12

6. Given below are two statements.

Statement I: If you know the length of two sides of a right angled triangle then the length of the third side can not be found.
Statement II: The internal angles of a triangle add up to 180°.

1 Both Statement I and Statement II are true
2 Both Statement I and Statement II are false
3 Statement I is correct but Statement II is false
4 Statement I is incorrect but Statement II is true

Explanation: Properties of a triangle (given in explanation of 40).

7. The given equation becomes correct after interchanging two signs. One of the four alternatives under it specifies the interchange of signs in the equation which when made will make the equation correct.
Find the correct alternative?
9 + 5 / 4 x 3- 6 =12

(1) + and –
(2) / and x
(3) + and x
(4) – and –

Explanation: Interchange divide by multiply and x with / will give 12 ans.

8. If the day before yesterday was Friday, what will be the third day after the day after tomorrow?

(1) Friday
(2) Saturday
(3) Thursday
(4) Wednesday

Explanation: Friday, Saturday (today), Sunday (tomorrow), Monday (day after tomorrow), Tuesday 1 Wed 2 Thursday 3 Friday

9. Rajiv, Sanjiv and Vijay join a running race. The distance is 1500 meters. Rajiv beats Sanjiv by 30 meters and Vijay by 100 meters. By how much could Sanjiv beat Vijay over the full distance if they both ran as before?

(1) 72.3 meters
(2) 71.5 meters
(3) 71.4 meters
(4) 70.2 meters
राजीव, संजीव और विजय दौड़ती हुई दौड़ में शामिल होते हैं। दूरी 1500 मीटर है। राजीव ने संजीव को 30 मीटर और विजय को 100 मीटर से हराया। यदि वे दोनों पहले की तरह दौड़े तो संजीव विजय को कितनी दूर से हरा सकता है?

Explanation: Sanjiv runs 1470 metres while Vijay runs 1400 metres.
Sanjiv speed as compare of Vijay= 1400/1470
At the same rate Sanjiv runs 1500 metres whilst Vijay runs 1500 x 1400 / 1470 Meters Or 1428.6 metres
Hence Sanjiv ought to beat Vijay by 71.4 metres.

10. Find the odd one out in following sequence : 1, 5, 14, 30, 50, 55, 91
A. 14
B. 50
C. 30
D. 55

Explanation: 1² = 1; 1² + 2² = 1 + 4 = 5; 1²+ 2² + 3²= 1 + 4 + 9= 14
1²+ 2² + 3² + 4²= 1 + 4 + 9 + 16 = 30
1²+ 2² + 3² + 4² + 5²= 55
1²+ 2² + 3² + 4² + 5² + 6² = 91
50 is not correct in series