Trigonometric Functions

JEE Advanced · Mathematics · 27 past questions

1. Q1 2026 Paper 1

   Let…

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2. Q2 2025 Paper 2

   Let…

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3. Q3 2024 Paper 1

   Let $\frac{\pi}{2}<x<\pi$ be such that $\cot x=\frac{-5}{\sqrt{11}}$. Then…

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4. Q4 2022 Paper 1

   Consider the following lists…

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5. Q5 2022 Paper 2

   Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}$. If…

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6. Q6 2022 Paper 2

   Let $PQRS$ be a quadrilateral in a plane, where $QR = 1$, $\angle PQR = \angle QRS = 70^\circ$…

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7. Q7 2021 Paper 2

   Consider a triangle $PQR$ having sides of lengths $p, q$ and $r$ opposite to the angles $P, Q$ and $R$…

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8. Q8 2020 Paper 1

   Let $f:[0,2]\longrightarrow\mathbb{R}$ be the function defined by…

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9. Q9 2018 Paper 1

   Let $a,b,c$ be three non-zero real numbers such that the equation…

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10. Q10 2017 Paper 2

    Let $\alpha$ and $\beta$ be nonzero real numbers such that…

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11. Q11 2017 Paper 2

    Let $O$ be the origin, and $\overrightarrow{OX}, \overrightarrow{OY}, \overrightarrow{OZ}$ be three unit…

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12. Q12 2016 Paper 1

    Let $-\frac{\pi}{6}<\theta<-\frac{\pi}{12}$. Suppose $\alpha_1$ and $\beta_1$ are the roots of the equation…

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13. Q13 2016 Paper 1

    Let $S=\left\{x\in(-\pi,\pi):x\neq0,\pm\frac{\pi}{2}\right\}$. The sum of all distinct solutions of the…

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14. Q14 2016 Paper 2

    The value of…

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15. Q15 2015 Paper 1

    The number of distinct solutions of the equation…

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16. Q16 2014 Paper 2

    For $x \in (0, \pi)$, the equation $\sin x + 2\sin 2x - \sin 3x = 3$ has

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17. Q17 2013 Paper 1

    The number of points in $(-\infty, \infty)$, for which $x^2 - x\sin x - \cos x = 0$, is

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18. Q18 2012 Paper 1

    Let $\theta,\varphi\in[0,2\pi]$ be such that…

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19. Q19 2011 Paper 1

    Let $P=\{\theta: \sin\theta-\cos\theta=\sqrt{2}\cos\theta\}$ and…

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20. Q20 2011 Paper 1

    The positive integer value of $n > 3$ satisfying the equation…

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21. Q21 2010 Paper 1

    If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths…

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22. Q22 2010 Paper 1

    The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ such that…

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23. Q23 2010 Paper 1

    The maximum value of the expression $\frac{1}{\sin^2\theta+3\sin\theta\cos\theta+5\cos^2\theta}$ is

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24. Q24 2010 Paper 1

    The number of all possible values of $\theta$, where $0 < \theta < \pi$, for which the system of equations…

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25. Q25 2009 Paper 1

    If…

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26. Q26 2009 Paper 2

    For $0<\theta<\frac{\pi}{2}$, the solution(s) of…

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27. Q27 2007 Paper 1

    The number of solutions of the pair of equations…

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