NDA Mathematics Previous Year Questions with Solutions

1

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is T equal to ?

NDA 2026 Solution View →

2

What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is decreasing ?

NDA 2026 Solution View →

3

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is S equal to ?

NDA 2026 Solution View →

4

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

NDA 2026 Solution View →

5

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the area bounded by the curves, the lines x=0 and x=1 ?

NDA 2026 Solution View →

6

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

NDA 2026 Solution View →

7

If 1- ₁₀2= ₁₀(5^x+4^x+3^x+2^x+1) , then what is a value of x ?

NDA 2026 Solution View →

8

What is the sum of the binary numbers (101101101)₂ and (100011)₂ ?

NDA 2025 Solution View →

9

For the following two (02) items: Let p = _ j=1 ^ n ₁₀ 2^j and q = _ j=1 ^ n ₁₀ 5^j . If p + q = 15 , then what is q - p equal to?

NDA 2025 Solution View →

10

What is the binary number equivalent to decimal number 1011?

NDA 2023 Solution View →

11

If x^3+y^3=(100010111)₂ and x+y=(11111)₂ , then what is (x-y)^2+x y equal to?

NDA 2022 Solution View →

12

What is (1110011)₂ (10111)₂ equal to?

NDA 2022 Solution View →

13

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n elements is 1024 , then what is the value of n ?

NDA 2026 Solution View →

14

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: Consider the following statements : I. (u+v

NDA 2026 Solution View →

15

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of u ?

NDA 2026 Solution View →

16

Consider the following inequalities : I. 1+4i>3+2i II. 2+3i III. 4+3i>3+4i where i= -1 How many of the above are valid ?

NDA 2026 Solution View →

17

If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 & r^2 & r^2 p^2 & q^2+r^2 & p^2 q^2 & q^2 & r^2+p^2 vmatrix equal to ?

NDA 2026 Solution View →

18

If , , are cube roots of -8 , then what is ^2 p^2+ ^2 q^2+ ^2 r^2 ^2 p^2+ ^2 q^2+ ^2 r^2 equal to ?

NDA 2026 Solution View →

19

What is the derivative of x |x| with respect to x , where x<0 ?

NDA 2026 Solution View →

20

Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val

NDA 2026 Solution View →

21

Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f g(x) , then which of the following statements is/are correct ? I. q(x) is continuous at x=0 . II. q(x) is differe

NDA 2026 Solution View →

22

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(x) g(x) ,dx equal to ?

NDA 2026 Solution View →

23

Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is the value of k ?

NDA 2026 Solution View →

24

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(4-x) g(4-x) ,dx equal to ?

NDA 2026 Solution View →

25

Let p=(x+y+z) and q=xyz . If vmatrix x & 1 & 1 1 & y & 1 1 & 1 & z vmatrix is positive, then which one of the following is correct ?

NDA 2026 Solution View →

26

Let f(x)= vmatrix 3x^2 & x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix where q is any constant, then what is d^2 dx^2 (f(x) ) at x=0 equal to ?

NDA 2026 Solution View →

27

If M= bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix , then what is the value of |M| ,| adj M| ?

NDA 2026 Solution View →

28

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is d^2y dx^2 ( dx dy )^2 equal to ?

NDA 2026 Solution View →

29

What is the solution of the differential equation ( dy dx )=p when y(0)=q ?

NDA 2026 Solution View →

30

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is the solution of the differential equation with y(0)=0 ?

NDA 2026 Solution View →

31

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ?

NDA 2026 Solution View →

32

If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ?

NDA 2026 Solution View →

33

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ?

NDA 2026 Solution View →

34

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the value of p ?

NDA 2026 Solution View →

35

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the difference between the eccentricities

NDA 2026 Solution View →

36

If any point on an ellipse is (3 , 5 ) , then what is the eccentricity of the ellipse?

NDA 2025 Solution View →

37

Consider the following statements in respect of the function f(x)=x in the interval (-1,1) : I. The function attains maximum value. II. The function attains minimum value. Which of

NDA 2026 Solution View →

38

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of intersection of the curves ?

NDA 2026 Solution View →

39

If 2f(x)+f(1-x)=x , then what is f(x) equal to ?

NDA 2026 Solution View →

40

A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67 5^ . What is the height of the p

NDA 2026 Solution View →

NDA Mathematics PYQs with solutions

Trigonometric Ratios & Identities

Statistics

Probability

Sequences and Series

Three Dimensional Geometry

Quadratic Equation

Matrices

Determinants

Functions

Permutation and Combination

Differential Equations

Definite Integration

Differentiation

Vector Algebra

Continuity and Differentiability

Limits

Binomial Theorem

Indefinite Integration

Inverse Trigonometric Functions

Application of Derivatives

Basics of Mathematics

Area Under Curves

Complex Number

Ellipse

Binary Numbers

Heights and Distances

Trigonometric Equations

Hyperbola

Mathematical Induction

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is T equal to ?

What is the length of the longest interval in which the function f(x)=2 ^2 x-1 is decreasing ?

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is S equal to ?

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the area bounded by the curves, the lines x=0 and x=1 ?

Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

If 1- ₁₀2= ₁₀(5^x+4^x+3^x+2^x+1) , then what is a value of x ?

What is the sum of the binary numbers (101101101)₂ and (100011)₂ ?

For the following two (02) items: Let p = _ j=1 ^ n ₁₀ 2^j and q = _ j=1 ^ n ₁₀ 5^j . If p + q = 15 , then what is q - p equal to?

What is the binary number equivalent to decimal number 1011?

If x^3+y^3=(100010111)₂ and x+y=(11111)₂ , then what is (x-y)^2+x y equal to?

What is (1110011)₂ (10111)₂ equal to?

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n elements is 1024 , then what is the value of n ?

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: Consider the following statements : I. (u+v

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of u ?

Consider the following inequalities : I. 1+4i>3+2i II. 2+3i III. 4+3i>3+4i where i= -1 How many of the above are valid ?

If p , q , r are the cube roots of unity, then what is vmatrix p^2+q^2 & r^2 & r^2 p^2 & q^2+r^2 & p^2 q^2 & q^2 & r^2+p^2 vmatrix equal to ?

If , , are cube roots of -8 , then what is ^2 p^2+ ^2 q^2+ ^2 r^2 ^2 p^2+ ^2 q^2+ ^2 r^2 equal to ?

What is the derivative of x |x| with respect to x , where x<0 ?

Passage: Let f(x)= cases ax(x-1), & x 3 cases Given that f(x) is continuous for all x but not differentiable at x=1 . Further f'(x) is continuous at x=3 . Question: What is the val

Passage: Let f(x)= (x^2) and g(x)=x|x| for |x| Question: If q(x)=f g(x) , then which of the following statements is/are correct ? I. q(x) is continuous at x=0 . II. q(x) is differe

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(x) g(x) ,dx equal to ?

Passage: Let ₀^ 2 a x+b x (a+b)( x+ x) ,dx=k . Question: What is the value of k ?

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ₀^4 f(4-x) g(4-x) ,dx equal to ?

Let p=(x+y+z) and q=xyz . If vmatrix x & 1 & 1 1 & y & 1 1 & 1 & z vmatrix is positive, then which one of the following is correct ?

Let f(x)= vmatrix 3x^2 & x & - x 6 & -1 & 0 q & q^2 & q^3 vmatrix where q is any constant, then what is d^2 dx^2 (f(x) ) at x=0 equal to ?

If M= bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix , then what is the value of |M| ,| adj M| ?

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is d^2y dx^2 ( dx dy )^2 equal to ?

What is the solution of the differential equation ( dy dx )=p when y(0)=q ?

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is the solution of the differential equation with y(0)=0 ?

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ?

If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ?

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ?

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the value of p ?

Passage: The foci of the ellipse px^2+16y^2=16p and the foci of the hyperbola 25(81x^2-144y^2)=11664 coincide (assume p Question: What is the difference between the eccentricities

If any point on an ellipse is (3 , 5 ) , then what is the eccentricity of the ellipse?

Consider the following statements in respect of the function f(x)=x in the interval (-1,1) : I. The function attains maximum value. II. The function attains minimum value. Which of

Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of intersection of the curves ?

If 2f(x)+f(1-x)=x , then what is f(x) equal to ?

A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of 67 5^ . What is the height of the p