NDA Mathematics 2015 (I)
Attempt this free UPSC mock test for Mathematics. Part of the SaralUPSC Free UPSC Test Series 2025. Practice, analyze, and boost your score!
Questions
(1 − sinA + cosA)² is equal to
(x³ − 1) can be factorised as where…
A force F = 3i + 4j –…
A line passes through (2, 2) and is…
A set of annual numerical data, comparable over…
At what value of x does f(x) attain…
Consider the following functions: 1.f(x) = x³, x…
Consider the following in respect of two non-singular…
Consider the following statements in respect of the…
Consider the following statements: 1.y = (e^x +…
Consider the following statements: 1.f(x) = [x], where…
Consider the following statements: 1. The general solution…
Consider the following statements: 1.The function attains local…
Consider the integral Iₘ = ∫₀^π (sin 2m…
For each non-zero real number x, let f(x)…
Given that the vectors a⃗ and b⃗ are…
How many words can be formed using all…
If A = [2 7] [1 5]then what is A…
If (11101011)₂ is converted to decimal system, then…
If |a⃗| = 7, |b⃗| = 11 and…
If 1, ω, ω² are the cube roots…
If 2p + 3q = 18and 4p² + 4pq −…
If A = {x : x is a…
If A and B are two events such…
If A ⊆ B, then which one of…
If E(θ) = [ cosθ sinθ ] [ −sinθ cosθ ] then…
If G(x) = √(25 − x²), then what…
If X = [3 −4] B = [5 2] and A =…
If a + b + c = 0,…
If a + b || a – b,…
If f(x) = log₅((1 + x)/(1 − x)),…
If log₁₀2, log₁₀(2ˣ − 1) and log₁₀(2ˣ +…
If m and n are the roots of…
If z = (2(1 + 2i)) / (3 +…
In a class of 60 students, 45 students…
In a triangle ABC, a = (1 +…
In an examination, the probability of a candidate…
In solving a problem that reduces to a…
In throwing of two dice, the number of…
Let A = [x + y y] B = [2 −1] and C…
Let A = {1, 2, 3, 4, 5,…
Let A = {x, y, z} and B…
Let X be the set of all persons…
Let Z be the set of integers and…
Let α, β, γ be distinct real numbers.…
Let θ be a positive angle. If the…
The adjacent sides AB and AC of a…
The angle of elevation of the top of…
The angles of elevation of the top of…
The area of a triangle, whose vertices are…
The correlation coefficient between two variables X and…
The decimal number (127.25)₁₀, when converted to binary…
The equation of the line joining the origin…
The hyperbola x²/a² − y²/b² = 1 passes…
The equation tan⁻¹(1 + x) + tan⁻¹(1 − x)…
The length of perpendicular from the origin to…
The matrix [0 −4 + i] [4 + i 0]…
The mean and the variance in a binomial…
The mean and the variance of 10 observations…
The ‘less than’ ogive curve and the ‘more…
The mean of five numbers is 30. If…
The perpendicular distance between the straight lines 6x…
The point on the parabola y² = 4ax…
The value of [1 1 1] [1 1 + x 1] [1 1 1 + y] is
Two cards are drawn successively without replacement from…
Two men hit at a target with probabilities…
Two similar boxes Bi (i = 1, 2)…
The projections of a directed line segment on…
What are the direction ratios of the line…
What are the intercepts made by the plane…
Consider the parametric equationx = a(1 – t²)…
Consider the integral Iₘ = ∫₀^π (sin 2m…
Consider the integral Iₘ = ∫₀^π (sin 2m…
Consider the integral Iₘ = ∫₀^π (sin 2m…
What is [cosθ / (1 − tanθ)] − [sinθ…
What is [sin(π/6) 1 − cos(π/6)]³ [sin(π/6) 1 − cos(π/6)] where i…
Consider the parametric equationx = a(1 – t²)…
Consider the parametric equationx = a(1 – t²)…
What is ∫ dx / √(x² + a²)…
What is ∫ x e^x dx / (x…
f(x) = (α cos x)/(π − 2x) if…
The integral ∫ dx / (a cos x…
Let α be the root of the equation…
Let α be the root of the equation…
What is the area of the region bounded…
What is the area of the region bounded…
Consider the line x = √3 y and…
What is the area of the region in…
Consider the triangle ABC with vertices A(-2, 3),…
Consider the triangle ABC with vertices A(-2, 3),…
What is the derivative of tan⁻¹(√(1 + x²)…
What is the equation of the plane ABC?…
What is the equation of the plane passing…
Consider the triangle ABC with vertices A(-2, 3),…
What is the length of one of the…
What is the length of the line segment…
The projections of a directed line segment on…
Consider the function f(x) = 0.75x⁴ − x³…
What is the minimum value of f(x)? Consider…
What is the real part of (sin x…
What is the solution of the differential equation…
What is the solution of the differential equation…
What is the solution of the differential equation…
What is the square root of i, where…
What is the sum of the series 0.5 +…
What is the value of A? Given that…
What is the value of A? Given that…
What is the value of B? Given that…
Given that lim (x→∞) [ (2 + x²)…
Given a functionf(x) = -1 if x ≤…
f(x) = -1 if x ≤ 0f(x) =…
What is the value of α? f(x) =…
Consider x = tan⁻¹(1/5), y = tan⁻¹(1/70) and…
Consider x = tan⁻¹(1/5), y = tan⁻¹(1/70) and…
Consider x = tan⁻¹(1/5), y = tan⁻¹(1/70) and…
What is Σ (r = 0 to n)…
What is α equal to? The integral ∫…
Which of the following statements is/are correct in…
Which one of the following matrices is an…
Which one of the following measures of central…