NATA SERIES Mathematics
Algebra
39 previous year questions.
Volume: 39 Ques
Yield: High
High-Yield Trend
2
2025 19
2023 4
2021 12
2019 2
2017 Chapter Questions 39 MCQs
01
PYQ 2017
medium
mathematics ID: nata-201
The system of linear equations -2x+y+2=a, x-2y+z=b, x+y-2z=c have infinitely many solutions if
1
a=0, b=0, c=0
2
a+b=c
3
a+b+c=0
4
a+b-c=0
02
PYQ 2017
medium
mathematics ID: nata-201
If are non-zero, then the number of solutions of is:
1
6
2
8
3
9
4
infinite
03
PYQ 2019
medium
mathematics ID: nata-201
Find the value of logy(x4) if logx(y3) = 2
1
6
2
4
3
12
4
3
04
PYQ 2019
medium
mathematics ID: nata-201
How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?
1
24
2
25
3
23
4
26
05
PYQ 2019
medium
mathematics ID: nata-201
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?
1
30 days
2
40 days
3
60 days
4
70 days
06
PYQ 2019
medium
mathematics ID: nata-201
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
1
6
2
10
3
7
4
5
07
PYQ 2019
medium
mathematics ID: nata-201
Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?
1
38
2
55
3
35
4
62
08
PYQ 2019
medium
mathematics ID: nata-201
Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :
1
20
2
16
3
8
4
24
09
PYQ 2019
medium
mathematics ID: nata-201
The difference of two positive integers is 3 and the sum of their squares is 117. What are the numbers?
1
2,0
2
2/3,1
3
1,-2
4
6.9
10
PYQ 2019
medium
mathematics ID: nata-201
The sum of odd integers from 1 to 2001 is:
1
(1121)2
2
(1101)2
3
(1001)2
4
(1021)2
11
PYQ 2019
medium
mathematics ID: nata-201
The function given by: xmyn = (x + y)m+n is:
1
strictly increasing
2
strictly decreasing
3
constant
4
neither increasing nor decreasing
12
PYQ 2019
medium
mathematics ID: nata-201
The average age of 20 students in a class is 15 years. If the teacher’s age is including, the average increases by 1. What is the teacher’s age?
1
30 years
2
21 years
3
42 years
4
36 years
13
PYQ 2019
medium
mathematics ID: nata-201
Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find
1
0
2
1
3
2
4
3
14
PYQ 2019
easy
mathematics ID: nata-201
If a2-b2 = 8 and a*b = 2, find a4+b4.
1
4
2
8
3
72
4
64
15
PYQ 2021
medium
mathematics ID: nata-202
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child ?
16
PYQ 2021
medium
mathematics ID: nata-202
Find out the wrong number in the series.
2880, 480, 92, 24, 8, 4, 4
2880, 480, 92, 24, 8, 4, 4
17
PYQ 2021
medium
mathematics ID: nata-202
In an election, a candidate who gets 84 % of the votes is elected by a majority of 476 votes. What is the total number of votes polled ?
18
PYQ 2021
easy
mathematics ID: nata-202
When the digits within the number are multiplied with each other, the product of which of the following numbers is the lowest ?
435, 224, 823, 902
435, 224, 823, 902
19
PYQ 2023
medium
mathematics ID: nata-202
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number pair?
1
96 or 69
2
27 or 72
3
56 or 65
4
75 or 57
20
PYQ 2023
easy
mathematics ID: nata-202
The produce of a square field when sold at the rate of Rs. 1.50 per 100 sq. meters fetches Rs. 1350. What will be the cost of putting a fence all-round the field at the rate of 50 paise per meter?
1
Rs.549
2
Rs.575
3
Rs.600
4
Rs.675
21
PYQ 2023
medium
mathematics ID: nata-202
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 27. What is the difference between the two digits of that number?
1
9
2
6
3
12
4
3
22
PYQ 2023
medium
mathematics ID: nata-202
The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is
1
65
2
15
3
13
4
25
23
PYQ 2023
medium
mathematics ID: nata-202
In a 100 m race, A covers the distance in 36 seconds and B covers in 45 seconds. In this race, A beats B by___________?
1
20 m
2
25 m
3
22.5 m
4
9 m
24
PYQ 2023
medium
mathematics ID: nata-202
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
1
12 days
2
16 days
3
18 days
4
15 days
25
PYQ 2023
medium
mathematics ID: nata-202
If times the term of an A.P is the same as times the term, then find its term
1
0
2
11
3
14
4
18
26
PYQ 2023
medium
mathematics ID: nata-202
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:
1
5%
2
4.75 %
3
6%
4
7.8 %
27
PYQ 2023
medium
mathematics ID: nata-202
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:
1
49,56
2
33,42
3
26,56
4
34,54
28
PYQ 2023
medium
mathematics ID: nata-202
The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
29
PYQ 2023
medium
mathematics ID: nata-202
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
30
PYQ 2023
medium
mathematics ID: nata-202
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
31
PYQ 2023
medium
mathematics ID: nata-202
A small village, having a population of 5,000 requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m x 25m x 15 m. For how many days will the water in the tank last?
32
PYQ 2023
medium
mathematics ID: nata-202
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
33
PYQ 2023
medium
mathematics ID: nata-202
The average of 15 numbers is 18. The average of first 8 is 19 and the last 8 is 17, then what is the number?
34
PYQ 2023
medium
mathematics ID: nata-202
If (2,0) is a solution of linear equation 2x+3y=k, then what is the value of k?
35
PYQ 2023
medium
mathematics ID: nata-202
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
1
3
2
15
3
16
4
6
36
PYQ 2023
medium
mathematics ID: nata-202
The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
1
23
2
27
3
32
4
64
37
PYQ 2023
medium
mathematics ID: nata-202
A sum of money is to be distributed among Arun, Banu, Chinu, Dany in the proportion of 5: 2:4: 3 respectively. If C gets Rs. 1500 more than D, what is B's share?
1
Rs. 500
2
Rs. 3000
3
Rs. 900
4
Rs. 5000
38
PYQ 2025
medium
mathematics ID: nata-202
The ratio of ages of Rahul and Neha is 3:4. After 5 years, the ratio becomes 4:5. What are their current ages?
1
15 and 20
2
18 and 24
3
21 and 28
4
24 and 32
39
PYQ 2025
medium
mathematics ID: nata-202
The age ratio of two friends is 4:5. The difference in their ages is 6 years. What is the age of the younger friend?
1
18 years
2
20 years
3
24 years
4
30 years