NDA Mathematics 2021 (II)
Attempt this free UPSC mock test for Mathematics. Part of the SaralUPSC Free UPSC Test Series 2025. Practice, analyze, and boost your score!
Questions
3-digit numbers are formed using the digits 1,…
A problem is given to three students A,…
ABCDEFGH is a cuboid with base ABCD.Let A(0,…
Consider a regular polygon with 10 sides. What…
Consider all the real roots of the equation…
Consider the digits 3, 5, 7, 9. What…
Consider the expansion of (1 + x)ⁿ. Let…
Consider the following in respect of the matrixA…
Consider the following relations for two events E…
Consider the following statements : 1. A line…
Two regression lines are given as 3x −…
Two regression lines are given as 3x -4y+8=0…
The two vertices of an equilateral triangle are…
Consider the following statements in respect of f(x)…
Consider the following statements in respect of relations…
Consider the following statements in respect of sets:…
The two ends of the latus rectum of…
Consider the following statements in respect of the…
Consider the following statements in respect of the…
Consider the following statements in respect of the…
Consider the following statements in respect of the…
Consider three sets X, Y and Z having…
For the set of numbers x, x, x+2,…
For what value of θ, where 0 <…
For what values of k is the system…
How many 4-letter words (with or without meaning)…
How many distinct matrices exist with all four…
How many terms are there in the expansion…
If (a + b) is perpendicular to a…
If 1/(b + c), 1/(c + a), 1/(a…
If A and B are two events such…
If C(n, 4), C(n, 5) and C(n, 6)…
If a + 3b = 3i − j…
If aₙ = n(n!), then what is a₁…
If f(x) = 2^x, then what is ∫2…
If f(x) = [x]/|x|, x ≠ 0, where…
If f(x) satisfies f(1) = f(4), then what…
If ∑(i=1 to 10) xᵢ = 110 and…
If ∫-2 to 2 f(x) dx = k,…
If ∫√(1 − sin 2x) dx = A…
If P(A|B) < P(A), then which one of…
If g is the geometric mean of 2,…
If i = √–1, then how many values…
Let f(x) = { 1 + x /…
If log₁₀ 2, log₁₀(2ˣ – 1), log₁₀(2ˣ +…
If log₁₀2 log₂10 + log₁₀(10ˣ) = 2, then…
If p = (1111⋯ up to n digits),…
If p and q are the non-zero roots…
A circle is passing through the points (5,…
If sin(A + B) = 1 and 2sin(A…
If sinθ and cosθ are the roots of…
If the function f(x) = x^2 – kx…
If the harmonic mean of 60 and x…
If the position vectors of A and B…
If the roots of the equation 4x² –…
Ifx = a / (b – c), y =…
If x, y, z are in GP, then…
If x² + x + 1 = 0,…
If y = (1 + x)(1 + x²)(1…
If y = cos x · cos 4x…
If z = x + iy, where i…
IfΔ = | a b c | | d e f | | g h i…
In a cricket match, a batsman hits a…
Let 4 sin²x = 3, where 0 ≤…
Let ABC be a triangle. If cos 2A…
Let S = {2, 3, 4, 5, 6,…
Let Sₖ denote the sum of first k…
Let a, b and c be three vectors…
Let a, b and c be unit vectors…
Let f(x) be a polynomial function such that…
Let p, q and 3 be respectively the…
Let sin x + sin y = cos…
Let sin⁻¹x + sin⁻¹y + sin⁻¹z = 3π/2…
Let the equation sec x·cosec x = p…
Seven white balls and three black balls are…
Suppose 20 distinct points are placed randomly on…
Suppose set A consists of first 250 natural…
The inverse of a matrix A is given…
The two vertices of an equilateral triangle are…
The locus of a point P(x, y, z)…
The mean of 10 observations is 5·5. If…
The number of spheres of radius r touching…
The quadratic equation 3x² – (k² + 5k)x…
The tangent to the curve x^2 = y…
The xy-plane divides the line segment joining the…
If| a – b a – b – c ||…
The equations of the sides AB, BC and…
A circle is passing through the points (5,…
What is lim (n → ∞) (aⁿ +…
What is the area bounded by y =…
The coordinates of three consecutive vertices of a…
What is the condition that f(x) = x^3…
What is the degree of the differential equation…
What is the derivative of e^(e^x) with respect…
What is the differential equation of y =…
The equations of the sides AB, BC and…
What is ∑ (iⁿ) from n = 1…
What is ∫ dx / [x(x² + 1)]…
What is ∫₀^{π/2} ln(cos x) dx equal to?
What is ∫₀^π ln(tan(x/2)) dx equal to?
The coordinates of three consecutive vertices of a…
What is the integral of f(x) = 1…
What is the maximum area of a rectangle…
The two ends of the latus rectum of…
What is the mean deviation of the first…
What is the mean of natural numbers contained…
The marks obtained by 60 students in a…
The marks obtained by 60 students in a…
What is the order of the differential equation…
What is the period of the function f(x)…
What is the probability that the roots of…
What is the range of the function f(x)…
What is the slope of the tangent of…
What is the value of the following determinant?|…
What is the value of the following?cot[sin⁻¹(3/5) +…
When the measure of central tendency is available…
If A = | 1 a | | 0 1…
Where does the tangent to the curve y…
Let A = | 0 2 | | –2 0…
Which one of the following is a square…