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NDA Mathematics PYQs with solutions

Chapter-wise Mathematics previous year questions for NDA: 2,981 questions in 29 chapters. Largest chapters: Trigonometric Ratios & Identities (295), Statistics (236) and Probability (201). Open any question for options, correct answer and solution.

NDA Mathematics PYQs with solutions

NDA Mathematics chapters

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

Sample Mathematics questions

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,(π)/(4)] . Question: What is the area between the curve y= x and the x-axis in the interval

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,(π)/(4)] . Question: What is the area between the curve y= x and the x-axis in the interval

If 1- _ 10 2= _ 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.

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 and r^2 and r^2 p^2 and q^2+r^2 and p^2 q^2 and q^2 and r^2+p^2 vmatrix equal to ?

If α , β , γ are cube roots of -8 , then what is (α^2 p^2+β^2 q^2+γ^2 r^2)/(β^2 p^2+γ^2 q^2+α^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

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

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^ (π)/(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 and 1 and 1 1 and y and 1 1 and 1 and z vmatrix is positive, then which one of the following is correct ?

Let f(x)= vmatrix 3x^2 and x and - x 6 and -1 and 0 q and q^2 and 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|\,|adjM| ?

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=y_0 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 α, 5 α) , 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

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