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Trigonometry — JEE Mathematics MCQs

Master Trigonometry for JEE Main with free mathematics MCQs. Each question includes a detailed solution and instant feedback — practice at easy, medium, and hard difficulty levels to build exam-ready confidence.

16 practice questions with instant feedback and solutions.

Medium•Trigonometry
The equation of the plane passing through the point (1,1,1)(1,1,1) and perpendicular to the planes 2x+y−2z=52 x+y-2 z=5 and 3x−6y−2z=73 x-6 y-2 z=7, is
Easy•Trigonometry
The value of sin⁡30°+cos⁡60°\sin 30° + \cos 60° is:
Easy•Trigonometry
The value of sin²30° + cos²30° is:
Hard•Trigonometry
Let C1C_{1} and C2C_{2} be two biased coins such that the probabilities of getting head in a single toss are 23\frac{2}{3} and 13\frac{1}{3}, respectively. Suppose α\alpha is the number of heads that appear when C1C_{1} is tossed twice, independently, and suppose β\beta is the number of heads that appear when C2C_{2} is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x2−αx+βx^{2}-\alpha x+\beta are real and equal, is
Hard•Trigonometry
The value of ∫−π2π2x2cos⁡x1+exdx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^{2} \cos x}{1+e^{x}} d x is equal to
Hard•Trigonometry
Consider all rectangles lying in the region {(x,y)∈R×R:0≤x≤π2 and 0≤y≤2sin⁡(2x)} \left\{(x, y) \in \mathbb{R} \times \mathbb{R}: 0 \leq x \leq \frac{\pi}{2} \text { and } 0 \leq y \leq 2 \sin (2 x)\right\} and having one side on the xx-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
Hard•Trigonometry
Let a,ba, b and λ\lambda be positive real numbers. Suppose PP is an end point of the latus rectum of the parabola y2=4λxy^{2}=4 \lambda x, and suppose the ellipse x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 passes through the point PP. If the tangents to the parabola and the ellipse at the point PP are perpendicular to each other, then the eccentricity of the ellipse is
Hard•Trigonometry
Let S={x∈(−π,π):x≠0,±π2}S=\left\{x \in(-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}. The sum of all distinct solutions of the equation 3sec⁡x+cosec⁡x+2(tan⁡x−cot⁡x)=0\sqrt{3} \sec x+\operatorname{cosec} x+2(\tan x-\cot x)=0 in the set SS is equal to
Hard•Trigonometry
For any positive integer nn, define fn:(0,∞)→Rf_{n}:(0, \infty) \rightarrow \mathbb{R} as fn(x)=∑j=1ntan⁡−1(11+(x+j)(x+j−1)) for all x∈(0,∞) f_{n}(x)=\sum_{j=1}^{n} \tan ^{-1}\left(\frac{1}{1+(x+j)(x+j-1)}\right) \text { for all } x \in(0, \infty) (Here, the inverse trigonometric function tan⁡−1x\tan ^{-1} x assumes values in (−π2,π2)\left(-\frac{\pi}{2}, \frac{\pi}{2}\right). ) Then, which of the following statement(s) is (are) TRUE?
Hard•Trigonometry
Let PP be the image of the point (3,1,7)(3,1,7) with respect to the plane x−y+z=3x-y+z=3. Then the equation of the plane passing through PP and containing the straight line x1=y2=z1\frac{x}{1}=\frac{y}{2}=\frac{z}{1} is
Hard•Trigonometry
Consider a triangle Δ\Delta whose two sides lie on the xx-axis and the line x+y+1=0x+y+1=0. If the orthocenter of Δ\Delta is (1,1)(1,1), then the equation of the circle passing through the vertices of the triangle Δ\Delta is
Hard•Trigonometry
The general solution of sin⁡2x=cos⁡3x\sin 2x = \cos 3x is:
Medium•Trigonometry
[JEE Mains 2026] If (cos²48° - sin²12°)/(sin24° + cos6°) = p/q where p and q are coprime positive integers, then the value of p + q is:
Medium•Trigonometry
If a chord, which is not a tangent, of the parabola y2=16xy^{2}=16 x has the equation 2x+y=p2 x+y=p, and midpoint (h,k)(h, k), then which of the following is(are) possible value(s) of p,hp, h and kk ?
Medium•Trigonometry
If the function f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} is defined by f(x)=∣x∣(x−sin⁡x)f(x)=|x|(x-\sin x), then which of the following statements is TRUE?
Medium•Trigonometry
Let −π6<θ<−π12-\frac{\pi}{6}<\theta<-\frac{\pi}{12}. Suppose α1\alpha_{1} and β1\beta_{1} are the roots of the equation x2−2xsec⁡θ+1=0x^{2}-2 x \sec \theta+1=0 and α2\alpha_{2} and β2\beta_{2} are the roots of the equation x2+2xtan⁡θ−1=0x^{2}+2 x \tan \theta-1=0. If α1>β1\alpha_{1}>\beta_{1} and α2>β2\alpha_{2}>\beta_{2}, then α1+β2\alpha_{1}+\beta_{2} equals