Trigonometry NDA PYQ Topic Wise (2016–2026)

Explore: All NDA topics · NDA Mathematics PYQs · NDA hub · Syllabus & pattern · NDA 2026

Answer first

Trigonometry PYQs (previous year questions) for NDA: Trigonometry (Mathematics) had 321 questions across the 42 official NDA papers we tagged (2016–2026), and appeared in 21 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Trigonometric Identities, Properties of Triangles, Trigonometric Equations.

Year-wise question count

Asked in 11 of 11 years.

Most-asked concepts

Sorted by the number of papers a concept appeared in.

How to practise Trigonometry PYQs

1. Start with the concepts at the top of the table. They have come back the most.
2. Solve one year’s Trigonometry questions from the official PDF against the clock, then check the answer listed below.
3. Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
4. Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.

Questions by year

Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.

NDA2026

• Q.26 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Possible value of α+β from a sec, tan, cot relation PDF
• Q.27 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Ratio of m and n for complementary angles with a tan relation PDF
• Q.28 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Relation between x = secθ - tanθ and y = cosecθ + cotθ PDF
• Q.29 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Product of sines of sub-multiple angles given cosθ PDF
• Q.30 (NDA (I) Mathematics) · MCQ · Maximum and Minimum Values: Value of x where cos x + √3 sin x is maximum PDF
• Q.31 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of sin2θ + cos2θ given cotθ in the fourth quadrant PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Expression in cos2α, cos2β given sums of sines and cosines are zero PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Half-angle expression when sinA = cosB + cosC PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Count correct identities for inverse functions of -x PDF
• Q.35 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of tan of an inverse-tan expression PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Perimeter of a triangle with angles in ratio 1:1:4 PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Expression in sides and angles of a triangle PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Smallest positive x solving a log equation in sin x and cos x PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Heights and Distances: Height of a plane from its distance and elevation of 67.5° PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Chord length of a unit circle subtending 45° at the centre PDF
• Q.78 (NDA (I) Mathematics) · MCQ · Maximum and Minimum Values: Maximum of sinA·sinB when 2A + 2B = π PDF
• Q.1 (NDA (II) Mathematics) · MCQ · Heights and Distances: H² + D² from depression angles to top and bottom of a tower PDF
• Q.2 (NDA (II) Mathematics) · MCQ · Heights and Distances: Relation between H and D for α = 15° and β = 45° PDF
• Q.3 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Ratio of longest to shortest side for angles in ratio 1:2:7 PDF
• Q.4 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of sinA·cosB for the same triangle PDF
• Q.5 (NDA (II) Mathematics) · MCQ · Properties of Triangles: sinA : sinB : sinC from ratios of sums of sides PDF
• Q.6 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Follow-up quantity for the same triangle PDF
• Q.7 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: tan A from tan of sum and difference values p and q PDF
• Q.8 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: tan B from the same p and q PDF
• Q.9 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of (1+tanA)(1+tanB) when A+B = π/4 PDF
• Q.10 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of (cotA-1)(cotB-1) when A+B = π/4 PDF
• Q.11 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of 6sin(π/18) - 8sin³(π/18) PDF
• Q.12 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of solutions of tan²θ + cot²θ = 2 in [0°, 360°) PDF
• Q.13 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of sin(tan⁻¹ 0.75) PDF
• Q.14 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: tan² of an inverse-cosine expression PDF
• Q.15 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Combination of tan and cot of large angles PDF

NDA2025

• Q.31 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Sum of sines of 35°, 25° and -95° PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Sum of pairwise products of three sine values PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Sum of squares of three sine values PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Maximum and Minimum: Minimum of |sinα - sin(α-90°)| PDF
• Q.35 (NDA (I) Mathematics) · MCQ · Maximum and Minimum: Maximum of |sinα - sin(α-90°)| PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Statements on a 3-5-7 triangle being obtuse PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Angle B of a triangle with sides 3, 5, 7 PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Area of a triangle with sides 3, 5, 7 PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Heights and Distances: Distance of first observation point from tower foot using 30°, 45°, 60° PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Heights and Distances: Height of tower in terms of b from three elevation angles PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Ratio p/q with p=tan2α-tanα and q=cotα-cot2α PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify p+q for tan and cot differences PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Express tan^2 α in terms of p and q PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: tanα when 2sinα+cosα=2 for acute α PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of 2sin2α+cos2α given 2sinα+cosα=2 PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Properties of Triangles: An angle of a triangle with side ratio 2:1 and angle ratio 3:1 PDF
• Q.47 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Statements about a triangle with given side and angle ratios PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Heights and Distances: Angle subtended by smoke above a chimney at an observer PDF
• Q.49 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: tan^-1 k + tan^-1(1/k) where k is a root of x^2-4x+1=0 PDF
• Q.50 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Solve tan^-1 k + tan^-1(1/2) = π/4 PDF
• Q.91 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Simplify sin^-1(x-4x^3/27) to a standard form PDF
• Q.25 (NDA (II) Mathematics) · MCQ · Sum to Product: Ratio (sinA+sinB)/(cosA+cosB) PDF
• Q.26 (NDA (II) Mathematics) · MCQ · Sum to Product: Simplify (p^2-q^2)/(p^2+q^2) for sine and cosine sums PDF
• Q.27 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of an expression in cosec 20° and cosec 70° PDF
• Q.28 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: (p^2+q^2)/(p^2 q^2) for cosec 20° and cosec 70° PDF
• Q.29 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of values of x+y from two cosine equations PDF
• Q.30 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of values of y-x from two cosine equations PDF
• Q.46 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of cot^-1 9 + cosec^-1(√41/4) PDF
• Q.47 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of θ satisfying given cot and cosec values together PDF
• Q.48 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: x^3+1/x^3 when x+1/x=2cosθ PDF
• Q.49 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of solutions of tan x + sec x = 2cos x in [0, π/2] PDF
• Q.50 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of tan of half of an inverse secant PDF

NDA2024

• Q.36 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of (√3cos10°-sin10°)/(sin25°cos25°) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of sin9°-cos9° PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Solve cos⁻¹x = sin⁻¹x PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Number of solutions of (sinθ-cosθ)^2=2 in (-π,π) PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Value of (cosA+cosB)/cos((A-B)/2) when C=60° PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Value of a root expression with cot of inverse cot PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of a sum of sine products PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Difference of two inverse tangents in a and b PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Condition on β for a trig-coefficient quadratic to have real roots PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Properties of Triangles: cos2A+cos2B+cos2C for a triangle with given sides PDF
• Q.47 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: f(α)f(β) for f=1/(1+tanθ) with α+β=5π/4 PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: cos(2α+2β) when tanα, tanβ are roots of a quadratic PDF
• Q.49 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of tan65°+2tan45°-2tan40°-tan25° PDF
• Q.50 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Nature of triangle from signs of cot and tan products PDF
• Q.21 (NDA (II) Mathematics) · MCQ · Inverse Trigonometry: sin⁻¹x+4cos⁻¹x given another inverse trig relation PDF
• Q.22 (NDA (II) Mathematics) · MCQ · Inverse Trigonometry: Value of cot^2(sec⁻¹2)+tan^2(cosec⁻¹3) PDF
• Q.23 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Area of a triangle with a/cosA = b/cosB = c/cosC PDF
• Q.24 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Nature of triangle when tanα, tanβ are roots of a quadratic PDF
• Q.25 (NDA (II) Mathematics) · MCQ · Properties of Triangles: 2a-b in terms of c for a triangle with given angles PDF
• Q.26 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of solutions of cot2x·cot3x=1 in (0,π) PDF
• Q.27 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: General solution of cos^100 x - sin^100 x = 1 PDF
• Q.28 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: cotA·cotB·cotC when tanA+tanB+tanC=k in a triangle PDF
• Q.29 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of sin12°·sin48° PDF
• Q.30 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Simplify (cos17°-sin17°)/(cos17°+sin17°) PDF
• Q.31 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: How many of tan22.5°, cot22.5° and their difference are irrational PDF
• Q.32 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: x+y+z from ratios with cosines of shifted angles PDF
• Q.33 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: (p+q)/(p-q) from p·tan(θ-30°)=q·tan(θ+120°) PDF
• Q.75 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Maximum value of a cos x + b sin x + c PDF

NDA2023

• Q.31 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: cos 2β when sin β is GM of sin α and cos α (official answer: A) PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: sec 2γ when tan γ is the AM of sin α and cos α (official answer: B) PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Heights and Distances: Possible distances of a point where a flagstaff on a pillar subtends a given angle (official answer: A) PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Heights and Distances: Possible value of tan of angle subtended by the pillar (official answer: C) PDF
• Q.35 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Perimeter of a triangle from AM of sines of its angles (official answer: C) PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Whether the triangle is right-angled or has angles in AP (official answer: C) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Minimum value of an expression in sin A (official answer: C) PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Angle A at which the expression in sin A is minimum (official answer: D) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Nature of a triangle from a relation among its sides (official answer: C) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Area of the triangle when c = 8 (official answer: C) PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Find n from incircle tangent lengths n, n+2, n+4 (official answer: C) PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Smallest side of the triangle with given incircle tangents (official answer: D) PDF
• Q.47 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Reduce a sum of six trig ratios equal to 7 to an equation in sin 2x (official answer: A) PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Evaluate a - b + 2c when sin 2x = a - b√c (official answer: D) PDF
• Q.53 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Least value of cot^2 θ + n^2 tan^2 θ + 2n (official answer: D) PDF
• Q.54 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Condition under which the expression is least (official answer: B) PDF
• Q.26 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Evaluate twice cot of an inverse cosine expression (official answer: C) PDF
• Q.27 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of p^-2 + q^-2 from inverse sec and cosec relation (official answer: A) PDF
• Q.28 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Evaluate 1 + sin^2 of an inverse trigonometric expression (official answer: A) PDF
• Q.29 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Value of an expression when tan and cot of related angles are equal (official answer: C) PDF
• Q.30 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: cos(α + 2β) from given tan α and sin β (official answer: C) PDF
• Q.73 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of p + q for products of cosines (official answer: C) PDF
• Q.74 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of pq for the products of cosines (official answer: A) PDF
• Q.75 (NDA (II) Mathematics) · MCQ · Multiple Angles: Value of pq for expressions in tan 3x and tan x (official answer: D) PDF
• Q.76 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of values of x where an expression vanishes (official answer: C) PDF
• Q.77 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Value of sin 3x + sin 3y given a trig relation (official answer: B) PDF
• Q.78 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Value of cos^2 x + cos^2 y for the same relation (official answer: B) PDF
• Q.79 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Value of a + b + √2c for angles in ratio 3:5:4 (official answer: C) PDF
• Q.80 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Ratio of squares of sides for angles in ratio 3:5:4 (official answer: A) PDF

NDA2022

• Q.26 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of cot^2 15 + tan^2 15 (official answer: B) PDF
• Q.27 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Angle B in a triangle from a trigonometric condition (official answer: dropped in the final key) PDF
• Q.28 (NDA (I) Mathematics) · MCQ · Compound Angles: tan 2B given alpha + beta and tan alpha (official answer: C) PDF
• Q.29 (NDA (I) Mathematics) · MCQ · Compound Angles: cos 2 theta from tan(45 + theta) = 1 + sin 2 theta (official answer: C) PDF
• Q.30 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of 1 + 4 sin theta when sin 2 theta = cos 3 theta (official answer: C) PDF
• Q.31 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Possible value of sin theta given tan theta (official answer: C) PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Sum of fourth powers of cosines of multiples of pi/8 (official answer: B) PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Difference of sin^2 of (pi/4 + theta) and (pi/4 - theta) (official answer: A) PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Heights and Distances: Height of a tower topped by a flagstaff from elevation angles (official answer: C) PDF
• Q.35 (NDA (I) Mathematics) · MCQ · Heights and Distances: Sun elevation relation when a tower shadow lengthens (official answer: B) PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Solve a sum of two inverse tangents for x (official answer: A) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Solve 3 sin^-1 x + cos^-1 x = pi (official answer: C) PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Compound Angles: Value of alpha + beta from a tangent relation (official answer: B) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Compound Angles: tan 10 theta given (1 + tan theta)(1 + tan 9 theta) = 2 (official answer: B) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Sum of sines from 0 to 360 degrees in 10-degree steps (official answer: B) PDF
• Q.86 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Value of an expression in perimeter, area and tan(A/2) (official answer: D) PDF
• Q.12 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Diameter of a circle inscribed in a regular 12-gon (official answer: C) PDF
• Q.40 (NDA (II) Mathematics) · MCQ · Heights and Distances: Height of a lamp post at the midpoint of a triangular plot side (official answer: C) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Heights and Distances: Distance related to a lamp post on a triangular plot (official answer: B) PDF
• Q.42 (NDA (II) Mathematics) · MCQ · Properties of Triangles: cos A + cos B + cos C for a triangle with given sides (official answer: D) PDF
• Q.43 (NDA (II) Mathematics) · MCQ · Heights and Distances: Height of the top of a leaning tower from two elevations (official answer: A) PDF
• Q.44 (NDA (II) Mathematics) · MCQ · Heights and Distances: cot of the inclination of a leaning tower (official answer: D) PDF
• Q.45 (NDA (II) Mathematics) · MCQ · Heights and Distances: Length of a leaning tower (official answer: B) PDF
• Q.46 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of cosec(-73 pi/3) (official answer: B) PDF
• Q.47 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Simplify a sum of cosines of multiples of pi/17 (official answer: A) PDF
• Q.48 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of tan of a half-angle expression (official answer: B) PDF
• Q.49 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of tan^-1 cot(cosec^-1 2) (official answer: D) PDF
• Q.50 (NDA (II) Mathematics) · MCQ · Properties of Triangles: cos 3C for a triangle with sides 4, 3, 2 (official answer: A) PDF
• Q.51 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of cos 36 - cos 72 (official answer: C) PDF
• Q.52 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: tan x + sin x given sec x in the fourth quadrant (official answer: B) PDF
• Q.53 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of tan^2 165 + cot^2 165 (official answer: B) PDF
• Q.54 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Product of sines with angles shifted by multiples of pi (official answer: D) PDF
• Q.55 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Number of solutions of a trigonometric equation on (0, 360) (official answer: A) PDF
• Q.79 (NDA (II) Mathematics) · MCQ · Maximum and Minimum Values: Maximum of a combination of sin and cos expressions (official answer: B) PDF

NDA2021

• Q.2 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Solve log of sin x to base cos x equal to 1 in first quadrant (official answer: C) PDF
• Q.6 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Number of integer k for which 2 sin x = 2k+1 has a solution (official answer: C) PDF
• Q.15 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify cot 2x cot 4x - cot 4x cot 6x - cot 6x cot 2x (official answer: C) PDF
• Q.16 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: sin x - cos x given tan x in second quadrant (official answer: D) PDF
• Q.17 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of a product of cosec and sec of specific angles (official answer: C) PDF
• Q.19 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Product tan 31 tan 33 tan 35 tan 57 tan 59 (official answer: C) PDF
• Q.21 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Number of solutions of sin^-1 x - cos^-1 x = pi/6 (official answer: B) PDF
• Q.22 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Evaluate (sin 24 + cos 66)(sin 24 - cos 66) (official answer: B) PDF
• Q.23 (NDA (I) Mathematics) · MCQ · Circular Measure: Length of a chord subtending 120 degrees in a unit circle (official answer: D) PDF
• Q.24 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Product (1+cot - cosec)(1+tan+sec) (official answer: B) PDF
• Q.25 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify a sum of fractions in tan and cot (official answer: A) PDF
• Q.26 (NDA (I) Mathematics) · MCQ · Circular Measure: Interior angle of a regular octagon (official answer: B) PDF
• Q.27 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: sin + cos given 7 sin + 24 cos = 25 (official answer: D) PDF
• Q.28 (NDA (I) Mathematics) · MCQ · Heights and Distances: Height of a flagstaff from a ladder and 75 degree elevation (official answer: D) PDF
• Q.29 (NDA (I) Mathematics) · MCQ · Heights and Distances: Shadow length change as sun elevation moves from 60 to 45 degrees (official answer: B) PDF
• Q.30 (NDA (I) Mathematics) · MCQ · Compound Angles: tan(45 + theta) given 3 cos = 4 sin (official answer: B) PDF
• Q.31 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Domain where tan^-1 x + cot^-1 x = pi/2 holds (official answer: A) PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Multiple Angles: cos 2A given tan A = 2 (official answer: A) PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Sum of acute angles of triangle with sides m, n, root(m^2+n^2+mn) (official answer: B) PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Area of triangle from two sides and included angle (official answer: C) PDF
• Q.23 (NDA (II) Mathematics) · MCQ · Periodicity: Period of ln(2 + sin^2 x) (official answer: B) PDF
• Q.24 (NDA (II) Mathematics) · MCQ · Compound Angles: Ratio tan A : tan B from sin(A+B) and sin(A-B) (official answer: D) PDF
• Q.28 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Power sum when three inverse sines total 3pi/2 (official answer: C) PDF
• Q.29 (NDA (II) Mathematics) · MCQ · Transformation Formulae: tan((x+y)/2) given sin x + sin y = cos x + cos y (official answer: A) PDF
• Q.31 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Cot of a sum of inverse sine and inverse cot (official answer: A) PDF
• Q.32 (NDA (II) Mathematics) · MCQ · Multiple Angles: tan 3x given 4 sin^2 x = 3 (official answer: C) PDF
• Q.35 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Smallest p for which sec x cosec x = p has a solution (official answer: C) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Triangle condition from sum of cos 2A, cos 2B, cos 2C (official answer: D) PDF

NDA2020

• Q.19 (NDA (I & II) Mathematics) · MCQ · Multiple Angles: tan²A given tan 3A / tan A = K (official answer: B) PDF
• Q.20 (NDA (I & II) Mathematics) · MCQ · Multiple Angles: Interval where K cannot lie (official answer: A) PDF
• Q.21 (NDA (I & II) Mathematics) · MCQ · Properties of Triangles: Sine-rule statements in a trapezium (official answer: C) PDF
• Q.22 (NDA (I & II) Mathematics) · MCQ · Properties of Triangles: Length AB of the trapezium (official answer: A) PDF
• Q.23 (NDA (I & II) Mathematics) · MCQ · Compound Angles: θ from tan θ in terms of cos 17° and sin 17° (official answer: B) PDF
• Q.24 (NDA (I & II) Mathematics) · MCQ · Multiple Angles: A + 2B from two conditions on acute angles (official answer: D) PDF
• Q.25 (NDA (I & II) Mathematics) · MCQ · Multiple Angles: Simplify an expression in sin 3x and cos 3x (official answer: A) PDF
• Q.26 (NDA (I & II) Mathematics) · MCQ · Trigonometric Functions: Range of y = 2 + cos x (official answer: D) PDF
• Q.27 (NDA (I & II) Mathematics) · MCQ · Trigonometric Ratios: Value of 8 cos 10° cos 20° cos 40° (official answer: B) PDF
• Q.28 (NDA (I & II) Mathematics) · MCQ · Trigonometric Ratios: Value of cos 48° - cos 12° (official answer: B) PDF
• Q.29 (NDA (I & II) Mathematics) · MCQ · Properties of Triangles: Statements on right-angled and isosceles triangles (official answer: B) PDF
• Q.30 (NDA (I & II) Mathematics) · MCQ · Properties of Triangles: Statements on triangle types from given conditions (official answer: B) PDF
• Q.31 (NDA (I & II) Mathematics) · MCQ · Trigonometric Identities: tan²x from a weighted sin² and cos² relation (official answer: A) PDF
• Q.32 (NDA (I & II) Mathematics) · MCQ · Trigonometric Identities: Express (d - a)/(b - d) as a trig ratio of y (official answer: C) PDF
• Q.33 (NDA (I & II) Mathematics) · MCQ · Trigonometric Identities: Value of p²/q² from related conditions (official answer: B) PDF
• Q.34 (NDA (I & II) Mathematics) · MCQ · Trigonometric Identities: Ratio of differences of tn = sinⁿθ + cosⁿθ (official answer: A) PDF
• Q.35 (NDA (I & II) Mathematics) · MCQ · Trigonometric Identities: Value of t1² - t2 (official answer: B) PDF
• Q.36 (NDA (I & II) Mathematics) · MCQ · Trigonometric Ratios: Value of t10 at θ = 45° (official answer: C) PDF
• Q.37 (NDA (I & II) Mathematics) · MCQ · Trigonometric Ratios: sin α + cos β for α = β = 15° (official answer: D) PDF
• Q.38 (NDA (I & II) Mathematics) · MCQ · Trigonometric Ratios: sin 7α - cos 7β for α = β = 15° (official answer: D) PDF
• Q.39 (NDA (I & II) Mathematics) · MCQ · Compound Angles: sin(α + 1°) + cos(β + 1°) for α = β = 15° (official answer: dropped in the final key) PDF
• Q.40 (NDA (I & II) Mathematics) · MCQ · Compound Angles: tan((x - y)/2) from a sum relation (official answer: C) PDF
• Q.43 (NDA (I & II) Mathematics) · MCQ · Compound Angles: cot(α + β) when cot α, cot β are roots of a quadratic (official answer: B) PDF
• Q.96 (NDA (I & II) Mathematics) · MCQ · Maximum and Minimum Values: Minimum of 3 cos(A + π/3) (official answer: A) PDF

NDA2019

• Q.26 (NDA (I) Mathematics) · MCQ · Maximum and Minimum Values: Least value of 25cosec²x + 36sec²x (official answer: D) PDF
• Q.31 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of a ratio of products of sines and cosines (official answer: A) PDF
• Q.32 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Express tan 54° in terms of sin 9° and cos 9° (official answer: C) PDF
• Q.33 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Find θ from a rotation-of-axes identity (official answer: C) PDF
• Q.34 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Find A from the same rotation identity (official answer: B) PDF
• Q.35 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Find B from the same rotation identity (official answer: A) PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Compound Angles: cos(α - β) given cos(θ - α) and cos(θ - β) (official answer: A) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Compound Angles: Value of sin²(α - β) + 2ab cos(α - β) (official answer: A) PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Multiple Angles: cos²2α given sin α + cos α = p (official answer: C) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of sin⁻¹(4/5) + sec⁻¹(5/4) - π/2 (official answer: D) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Inverse Trigonometric Functions: Find x from an inverse trigonometric equation (official answer: B) PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Compound Angles: θ + φ given tan θ = 1/2 and tan φ = 1/3 (official answer: C) PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Multiple Angles: sin(A/2) sin(3A/2) given cos A = 3/4 (official answer: B) PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Value of tan 75° + cot 75° (official answer: B) PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Product of cosines from 46° to 135° (official answer: B) PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Multiple Angles: sin θ given sin 2θ = cos 3θ (official answer: B) PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Compound Angles: Relation of p, q when roots are tan 19° and tan 26° (official answer: A) PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify an expression in tan α, tan β and secants (official answer: A) PDF
• Q.49 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Relation between cosec θ - cot θ and its reciprocal form (official answer: B) PDF
• Q.50 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Side ratio of a triangle with angles in ratio 1:2:3 (official answer: C) PDF
• Q.96 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: cos θ - sin θ given sin θ + cos θ = √2 cos θ (official answer: C) PDF
• Q.97 (NDA (I) Mathematics) · MCQ · Measurement of Angles: Minor arc length of a chord in a circle (official answer: A) PDF
• Q.98 (NDA (I) Mathematics) · MCQ · Trigonometric Ratios: Quadrant of θ from signs of sin and tan (official answer: C) PDF
• Q.100 (NDA (I) Mathematics) · MCQ · Heights and Distances: Elevation angles of a tower from two points (official answer: A) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of 4 sec θ + 4 tan θ from cosec θ (official answer: B) PDF
• Q.42 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Bounds on cos θ + sec θ and tan θ + cot θ (official answer: C) PDF
• Q.43 (NDA (II) Mathematics) · MCQ · Heights and Distances: Flagstaff height from a ladder's elevation (official answer: C) PDF
• Q.44 (NDA (II) Mathematics) · MCQ · Measurement of Angles: Chord length of a unit circle for angle θ (official answer: C) PDF
• Q.45 (NDA (II) Mathematics) · MCQ · Inverse Trigonometric Functions: Value of tan(2 tan⁻¹(1/3)) (official answer: B) PDF
• Q.61 (NDA (II) Mathematics) · MCQ · Maximum and Minimum Values: Minimum of a²/cos²x + b²/sin²x (official answer: A) PDF
• Q.62 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Angle A when angles are in AP and sides in given ratio (official answer: D) PDF
• Q.63 (NDA (II) Mathematics) · MCQ · Compound Angles: cot(A - B) from given differences (official answer: A) PDF
• Q.64 (NDA (II) Mathematics) · MCQ · Compound Angles: Simplify sin(α+β) - 2 sin α cos β + sin(α-β) (official answer: A) PDF
• Q.65 (NDA (II) Mathematics) · MCQ · Compound Angles: tan(A - B) given 2 tan A = 3 tan B = 1 (official answer: C) PDF
• Q.66 (NDA (II) Mathematics) · MCQ · Trigonometric Ratios: Value of cos 80° + cos 40° - cos 20° (official answer: C) PDF
• Q.67 (NDA (II) Mathematics) · MCQ · Properties of Triangles: tan A + tan B in a right-angled triangle (official answer: D) PDF
• Q.68 (NDA (II) Mathematics) · MCQ · Multiple Angles: Simplify cot(A/2) - tan(A/2) (official answer: D) PDF
• Q.69 (NDA (II) Mathematics) · MCQ · Multiple Angles: Simplify cot A + cosec A (official answer: B) PDF
• Q.70 (NDA (II) Mathematics) · MCQ · Compound Angles: Sum of products of tan 25°, tan 15°, tan 50° (official answer: B) PDF

NDA2018

• Q.36 (NDA (I) Mathematics) · MCQ · Compound Angles: Value of x+y from given sines (official answer: C) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify (sin5x−sin3x)/(cos5x+cos3x) (official answer: C) PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Value of sin105°+cos105° (official answer: C) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Angle B from sides and sin A (official answer: B) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Principal value of an inverse trigonometric expression (official answer: C) PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Compound Angles: Angle x when tangents of triangle angles are in GP (official answer: A) PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Relation between inscribed and central angles (official answer: A) PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Heights and Distances: Sun's elevation from flagstaff shadow (official answer: A) PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Value of tan⁻¹(1/4)+tan⁻¹(3/5) (official answer: B) PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Heights and Distances: Height of a balloon's centre from subtended angle (official answer: A) PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Compound Angles: tanx/tany from a sine ratio (official answer: A) PDF
• Q.47 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Relation of α and β when sine and cosine sums are zero (official answer: B) PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Condition for a unique value of cos(A/2) (official answer: C) PDF
• Q.49 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Sum of sines when cosines sum to zero (official answer: B) PDF
• Q.50 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Point where a trigonometric expression is maximum (official answer: A) PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Period of a sine function (official answer: D) PDF
• Q.36 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Simplify a trigonometric expression (official answer: C) PDF
• Q.37 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value when sec(θ−α), secθ, sec(θ+α) are in AP (official answer: A) PDF
• Q.38 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: sin2A−sin2B−sin2C when A+B+C=180° (official answer: D) PDF
• Q.39 (NDA (II) Mathematics) · MCQ · Heights and Distances: Length of bridge from balloon's depression angle (official answer: B) PDF
• Q.40 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Fourth-quadrant angle satisfying a tan–cot equation (official answer: A) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Heights and Distances: Height of hill from building elevations (official answer: B) PDF
• Q.42 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Solutions of cosec x + cot x = √3 (official answer: B) PDF
• Q.43 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Product of cosine expressions for a given θ (official answer: B) PDF
• Q.44 (NDA (II) Mathematics) · MCQ · Trigonometric Functions: secα·secβ when cosα, cosβ are roots of 4x²−3=0 (official answer: A) PDF
• Q.45 (NDA (II) Mathematics) · MCQ · Inverse Trigonometry: Solutions of tan⁻¹2x + tan⁻¹3x = π/4 (official answer: A) PDF
• Q.50 (NDA (II) Mathematics) · MCQ · Trigonometric Functions: Range of sin²θ+cos⁴θ (official answer: B) PDF
• Q.104 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Statements when sinθ is HM and sinφ is AM of sinα, cosα (official answer: C) PDF

NDA2017

• Q.15 (NDA (I) Mathematics) · MCQ · Compound Angles: cot(α+β) when cotα, cotβ are roots of a quadratic (official answer: B) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: cos(A/3) for an angle between 450° and 540° (official answer: D) PDF
• Q.40 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Value of 1/sin10° − √3/cos10° (official answer: D) PDF
• Q.41 (NDA (I) Mathematics) · MCQ · Heights and Distances: Distance of boat from 100 m lighthouse (official answer: C) PDF
• Q.42 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Point where sin(x+π/6)+cos(x+π/6) is maximum (official answer: A) PDF
• Q.43 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Product of sines of multiples of π/18 (official answer: C) PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Simplify a trigonometric expression (official answer: A) PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Compound Angles: tan(θ+α)+2tanα given sinθ=3sin(θ+2α) (official answer: B) PDF
• Q.46 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Value of tan 18° (official answer: A) PDF
• Q.47 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Relation of x, y, z in GP with tan⁻¹ values in AP (official answer: A) PDF
• Q.48 (NDA (I) Mathematics) · MCQ · Compound Angles: tan 2α from tan(α+β) and tan(α−β) (official answer: A) PDF
• Q.49 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Angle-sum identities in a triangle ABC (official answer: B) PDF
• Q.50 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: sinθcosθ given secθ−cosecθ=4/3 (official answer: B) PDF
• Q.29 (NDA (II) Mathematics) · MCQ · Compound Angles: Relation of a, b, c when tan(P/2), tan(Q/2) are roots (official answer: C) PDF
• Q.31 (NDA (II) Mathematics) · MCQ · Heights and Distances: Height of cloud from elevation and reflection depression (official answer: B) PDF
• Q.32 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of tan9°−tan27°−tan63°+tan81° (official answer: D) PDF
• Q.33 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of √3 cosec20° − sec20° (official answer: A) PDF
• Q.34 (NDA (II) Mathematics) · MCQ · Compound Angles: sin x given parts A, B with tanA:tanB = p:q (official answer: D) PDF
• Q.35 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Range of A for which a sine-cosine identity holds (official answer: B) PDF
• Q.36 (NDA (II) Mathematics) · MCQ · Heights and Distances: Relations between tower and pole heights from elevations (official answer: C) PDF
• Q.37 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Product of half-angle cotangents when a+c=2b (official answer: B) PDF
• Q.38 (NDA (II) Mathematics) · MCQ · Trigonometric Equations: Interval where √(1−sin2A) = −(sinA+cosA) (official answer: C) PDF
• Q.39 (NDA (II) Mathematics) · MCQ · Properties of Triangles: Nature of triangle from a sine/cosine squares ratio (official answer: A) PDF
• Q.40 (NDA (II) Mathematics) · MCQ · Inverse Trigonometry: Principal value range of sin⁻¹x (official answer: B) PDF
• Q.84 (NDA (II) Mathematics) · MCQ · Trigonometric Functions: Match expressions with their maximum values (official answer: B) PDF

NDA2016

• Q.9 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Maximum value of 4(sin²θ+cos⁴θ) (official answer: D) PDF
• Q.10 (NDA (I) Mathematics) · MCQ · Trigonometric Functions: Minimum value of 4(sin²θ+cos⁴θ) (official answer: D) PDF
• Q.11 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Whether f(θ)=2 and f(θ)=7 have solutions (official answer: C) PDF
• Q.36 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Product of sines of half angles given cos-sum condition (official answer: C) PDF
• Q.37 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Product of cosines of half-angle expressions in a triangle (official answer: D) PDF
• Q.38 (NDA (I) Mathematics) · MCQ · Compound Angles: tan(α+β) when tanα, tanβ are roots of a quadratic (official answer: D) PDF
• Q.39 (NDA (I) Mathematics) · MCQ · Compound Angles: sin(α+β)secα secβ from roots of a quadratic (official answer: B) PDF
• Q.44 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Minimum k for k sin x+cos2x=2k−7 to have a solution (official answer: B) PDF
• Q.45 (NDA (I) Mathematics) · MCQ · Trigonometric Equations: Maximum k for k sin x+cos2x=2k−7 to have a solution (official answer: D) PDF
• Q.76 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Statements on inverse tangent and inverse sine identities (official answer: B) PDF
• Q.77 (NDA (I) Mathematics) · MCQ · Inverse Trigonometry: Statements on tan⁻¹x+tan⁻¹(1/x) and sin⁻¹x+cos⁻¹y (official answer: D) PDF
• Q.89 (NDA (I) Mathematics) · MCQ · Properties of Triangles: Statements on tangent relations in triangles (official answer: B) PDF
• Q.90 (NDA (I) Mathematics) · MCQ · Trigonometric Identities: Ratio A/B of trigonometric expressions in degrees (official answer: C) PDF
• Q.41 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Equivalent forms of sinA+2sin2A+sin3A (official answer: C) PDF
• Q.42 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Product of sin70°sin50° and cos60°cos80° (official answer: A) PDF
• Q.43 (NDA (II) Mathematics) · MCQ · Trigonometric Functions: Sum of cosines when sum of four sines equals 4 (official answer: A) PDF
• Q.44 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Product (1+cos π/8)(1+cos 3π/8)… (official answer: D) PDF
• Q.45 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: (x sinθ − y cosθ)² given x cosθ + y sinθ = z (official answer: A) PDF
• Q.46 (NDA (II) Mathematics) · MCQ · Inverse Trigonometry: Value of cos(2cos⁻¹0.8) (official answer: D) PDF
• Q.47 (NDA (II) Mathematics) · MCQ · Heights and Distances: Height of hill from elevations at top and bottom of building (official answer: B) PDF
• Q.48 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: sin 81° in surds given sin 18° (official answer: A) PDF
• Q.49 (NDA (II) Mathematics) · MCQ · Heights and Distances: Speed of boat from change in angle of depression (official answer: B) PDF
• Q.50 (NDA (II) Mathematics) · MCQ · Trigonometric Identities: Value of a tan/cot expression in degrees (official answer: B) PDF

Other Mathematics topics

• Algebra PYQs
• Matrices and Determinants PYQs
• Analytical Geometry (2D and 3D) PYQs
• Differential Calculus PYQs
• Integral Calculus and Differential Equations PYQs
• Vector Algebra PYQs
• Statistics and Probability PYQs

FAQ

How many Trigonometry questions come in NDA?

In the official papers we tagged: 31 in 2026 (2 papers), 32 in 2025 (2 papers), 28 in 2024 (2 papers), 29 in 2023 (2 papers), 34 in 2022 (2 papers), 28 in 2021 (2 papers), 24 in 2020 (1 paper), 39 in 2019 (2 papers), 28 in 2018 (2 papers), 25 in 2017 (2 papers) and 23 in 2016 (2 papers). That is 321 questions in all, about 13% of Mathematics.

Which Trigonometry topics repeat in NDA?

Asked in the most papers: Trigonometric Identities, Properties of Triangles, Trigonometric Equations. The concept table lists every one with its count.

Are these official NDA questions?

Yes. Every question is from an official NDA paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.