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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Inverse Trigonometrical Function PYQ

JEE MAIN PYQ
$\tan\!\left(2\tan^{-1}\!\tfrac{1}{5}+\sec^{-1}\!\tfrac{\sqrt{5}}{2}+2\tan^{-1}\!\tfrac{1}{8}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
Considering the principal values of the inverse trigonometric functions, $\sin ^{-1}\left(\frac{\sqrt{3}}{2} x+\frac{1}{2} \sqrt{1-x^2}\right),-\frac{1}{2}< x<\frac{1}{\sqrt{2}}$, is equal to





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
$ \text{If } 0 < x < \tfrac{1}{\sqrt{2}} \text{ and } \tfrac{\sin^{-1}x}{\alpha} = \tfrac{\cos^{-1}x}{\beta}, \text{ then the value of } \sin!\left(\tfrac{2\pi\alpha}{\alpha+\beta}\right) \text{ is :}$





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 July Evening Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\cot\!\left(\displaystyle\sum_{n=1}^{19}\cot^{-1}\!\left(1+\sum_{p=1}^{n}2p\right)\right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The sum of the infinite series $\cot^{-1}\left(\dfrac{7}{4}\right)+\cot^{-1}\left(\dfrac{19}{4}\right)+\cot^{-1}\left(\dfrac{30}{4}\right)+\cot^{-1}\left(\dfrac{67}{4}\right)+\cdots$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (4 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $S = \left\{ {x \in R:0 < x < 1\,\mathrm{and}\,2{{\tan }^{ - 1}}\left( {{{1 - x} \over {1 + x}}} \right) = {{\cos }^{ - 1}}\left( {{{1 - {x^2}} \over {1 + {x^2}}}} \right)} \right\}$.

If $\mathrm{n(S)}$ denotes the number of elements in $\mathrm{S}$ then :






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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Evening Shift) PYQ

Solution

JEE MAIN PYQ
The domain of the function $f(x)=\sin^{-1}!\big([,2x^{2}-3,]\big)+\log_{2}!\left(\log_{1/2}(x^{2}-5x+5)\right)$, where $[,\cdot,]$ is the greatest integer function, is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 July Evening Shift) PYQ

Solution

JEE MAIN PYQ
A possible value of $\tan \left( {{1 \over 4}{{\sin }^{ - 1}}{{\sqrt {63} } \over 8}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Evening Shift) PYQ

Solution

JEE MAIN PYQ
The set of all values of k for which ${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$, is the interval :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos^{-1}!\left(\dfrac{x^{2}-4x+2}{x^{2}+3}\right)$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos^{-1}(x)-2\sin^{-1}(x)=\cos^{-1}(2x)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $x * y = {x^2} + {y^3}$ and $(x * 1) * 1 = x * (1 * 1)$.

Then a value of $2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$ is :






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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
The domain of the function ${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

JEE MAIN PYQ
Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $\tan^{-1}(x)+\tan^{-1}(2x)=\dfrac{\pi}{4}$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (27 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $, then the value of tan p is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 August Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $\alpha>\beta>\gamma>0$, then the expression $\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^2\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^2\right)}{(\beta-\gamma)}\right\}+\cot ^{-1}\left\{\alpha+\frac{\left(1+\alpha^2\right)}{(\gamma-\alpha)}\right\}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
If 0 < x, y < $\pi$ and cosx + cosy $-$ cos(x + y) = ${3 \over 2}$, then sinx + cosy is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (25 February Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $y = {\tan ^{ - 1}}\left( {\sec {x^3} - \tan {x^3}} \right),{\pi \over 2} < {x^3} < {{3\pi } \over 2}$, then





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
All $x$ satisfying the inequality $(\cot^{-1}x)^2 - 7(\cot^{-1}x) + 10 > 0$ lie in the interval:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (11 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
$\displaystyle \cos\left(\sin^{-1}\frac{3}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{33}{65}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (28 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
If ${{{{\sin }^1}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}$; $0 < x < 1$, then the value of $\cos \left( {{{\pi c} \over {a + b}}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $x = \sqrt{2^{\csc^{-1} t}}$ and $y = \sqrt{2^{\sec^{-1} t}}$ $(\lvert t \rvert \ge 1)$, then $\dfrac{dy}{dx}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
Considering only the principal values of inverse functions, the set $A = \{x \ge 0 : \tan^{-1}(2x) + \tan^{-1}(3x) = \dfrac{\pi}{4}\}$





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
The value of ${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}} \right)}}} \right)$ is equal to





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (25 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $f(x) = {\sin ^{ - 1}}x$ and $g(x) = {{{x^2} - x - 2} \over {2{x^2} - x - 6}}$. If $g(2) = \mathop {\lim }\limits_{x \to 2} g(x)$, then the domain of the function fog is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (26 February Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $g(x) = f(x) + f(1 - x)$ and $f''(x) > 0, \; x \in (0, 1)$. If $g$ is decreasing in the interval $(0, \alpha)$ and increasing in the interval $(\alpha, 1)$, then $\tan^{-1}(2\alpha) + \tan^{-1}\!\left(\dfrac{1}{\alpha}\right) + \tan^{-1}\!\left(\dfrac{\alpha + 1}{\alpha}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (10 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
The domain of the function $f(x) = \sin^{-1}\!\left(\dfrac{|x|+5}{x^2+1}\right)$ is $(-\infty, -a] \cup [a, \infty)$. Then $a$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2 September 2020 (Morning) PYQ

Solution

JEE MAIN PYQ
$\tan^{-1}\!\left(\dfrac{1+\sqrt{3}}{3+\sqrt{3}}\right) + \sec^{-1}\!\left(\sqrt{\dfrac{8+4\sqrt{3}}{6+3\sqrt{3}}}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (24 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $\alpha=\cos^{-1}\left(\dfrac{3}{5}\right),\ \beta=\tan^{-1}\left(\dfrac{1}{3}\right)$ where $0<\alpha,\beta<\dfrac{\pi}{2}$, then $\alpha-\beta$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2\left(\frac{1}{2}\right)} + 1}{\tan\left(\frac{1}{2}\right)} \right) $ is equal to





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the inverse trigonometric functions take principal values then ${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (26 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
If ${\cos ^{ - 1}}\left( {{y \over 2}} \right) = {\log _e}{\left( {{x \over 5}} \right)^5},\,|y| < 2$, then :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy ${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $2y=\left(\cot^{-1}\frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x}\right)^{2},\ x\in\left(0,\frac{\pi}{2}\right)$, then $\dfrac{dy}{dx}$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
2$\pi $ - $\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \right)$ is equal to





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

JEE MAIN PYQ
$\sin^{-1}\left(\sin \frac{2\pi}{3}\right) + \cos^{-1}\left(\cos \frac{7\pi}{6}\right) + \tan^{-1}\left(\tan \frac{3\pi}{4}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\tan^{-1}\left[\dfrac{\sqrt{1+x^{2}}+\sqrt{1-x^{2}}}{\sqrt{1+x^{2}}-\sqrt{1-x^{2}}}\right]$, $|x|<\dfrac{1}{2}$, $x\neq0$, is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (8 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The sum of possible values of x for tan$-$1(x + 1) + cot$-$1$\left( {{1 \over {x - 1}}} \right)$ = tan$-$1$\left( {{8 \over {31}}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Morning Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (27 June Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $D$ be the domain of the function $f(x)=\sin^{-1}\!\left(\log_{3x}\!\left(\dfrac{6+2\log_{3}x}{-5x}\right)\right)$. If the range of the function $g: D \to \mathbb{R}$ defined by $g(x)=x-[x]$ (where $[x]$ is the greatest integer function) is $(\alpha,\beta)$, then $\alpha^{2}+\dfrac{5}{\beta}$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (12 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
The number of solutions of the equation ${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}$, for x$\in$[$-$1, 1], and [x] denotes the greatest integer less than or equal to x, is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (17 March Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the domain of the function $f(x)=\sin^{-1}!\left(\dfrac{x-1}{2x+3}\right)$ is $\mathbb{R}-(\alpha,\beta)$, then $12\alpha\beta$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
For $\alpha,\beta,\gamma\ne 0$, if $\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi$ and $(\alpha+\beta+\gamma)\,(\alpha+\beta-\gamma)=3\alpha\beta$, then $\gamma$ equals:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
A value of $x$ satisfying the equation $\sin!\big(\cot^{-1}(1+x)\big) = \cos!\big(\tan^{-1} x\big)$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2017 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $x = \dfrac{m}{n}$ $(m, n$ are co-prime natural numbers$)$ be a solution of the equation $\cos(2\sin^{-1}x) = \dfrac{1}{9}$ and let $\alpha, \beta$ $(\alpha > \beta)$ be the roots of the equation $mx^2 - nx - m + n = 0$. Then the point $(\alpha, \beta)$ lies on the line:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The range of $f(x)=4\sin^{-1}\!\left(\dfrac{x^2}{x^2+1}\right)$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (13 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $a=\sin^{-1}(\sin 5)$ and $b=\cos^{-1}(\cos 5)$, then $a^{2}+b^{2}$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (31 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The domain of the function $f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (31 August Evening Shift) PYQ

Solution

JEE MAIN PYQ
The domain of the function ${\cos ^{ - 1}}\left( {{{2{{\sin }^{ - 1}}\left( {{1 \over {4{x^2} - 1}}} \right)} \over \pi }} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (29 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $\cos^{-1}\!\left(\dfrac{2}{3x}\right)+\cos^{-1}\!\left(\dfrac{3}{4x}\right)=\dfrac{\pi}{2}\ \ (x>\dfrac{3}{4})$, then $x$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
The number of real roots of the equation ${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4}$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Morning Shift) PYQ

Solution

JEE MAIN PYQ
${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$ is equal to : (The inverse trigonometric functions take the principal values)





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (1 September Evening Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\tan \left( {2{{\tan }^{ - 1}}\left( {{3 \over 5}} \right) + {{\sin }^{ - 1}}\left( {{5 \over {13}}} \right)} \right)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (20 July Evening Shift) PYQ

Solution

JEE MAIN PYQ
Let $a_1=1,\,a_2,\,a_3,\,a_4,\ldots$ be consecutive natural numbers. Then $\tan^{-1}\!\left(\dfrac{1}{1+a_1a_2}\right)+\tan^{-1}\!\left(\dfrac{1}{1+a_2a_3}\right)+\cdots+\tan^{-1}\!\left(\dfrac{1}{1+a_{2021}a_{2022}}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (30 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
$ \alpha = \tan\left(\frac{5\pi}{16} \sin\left(2\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right) $ $ \beta = \cos\left(\sin^{-1}\left(\frac{4}{5}\right) + \sec^{-1}\left(\frac{5}{3}\right)\right) $ where the inverse trigonometric functions take principal values. Then, the equation whose roots are $ \alpha $ and $ \beta $ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (30 June Morning Shift) PYQ

Solution

JEE MAIN PYQ
Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of $16\!\left((\sec^{-1}x)^2+(\csc^{-1}x)^2\right)$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (22 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $\sin^{-1}\!\left(\dfrac{\alpha}{17}\right)+\cos^{-1}\!\left(\dfrac{4}{5}\right)-\tan^{-1}\!\left(\dfrac{77}{36}\right)=0,\ 0<\alpha<13$, then $\sin^{-1}(\sin\alpha)+\cos^{-1}(\cos\alpha)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Morning Shift) PYQ

Solution

JEE MAIN PYQ
If $\cos^{-1}x-\cos^{-1}\left(\dfrac{y}{2}\right)=\alpha$, where $-1\le x\le1,\ -2\le y\le2,\ x\le\dfrac{y}{2}$, then for all $x,y$, the value of $4x^{2}-4xy\cos\alpha+y^{2}$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (10 April Evening Shift) PYQ

Solution

JEE MAIN PYQ
If $x=\sin^{-1}(\sin 10)$ and $y=\cos^{-1}(\cos 10)$, then $y-x$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (9 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
If the domain of the function $f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{{2x - 1} \over 2}} \right)} }}$ is the interval ($\alpha$, $\beta$], then $\alpha$ + $\beta$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (22 July Evening Shift) PYQ

Solution

JEE MAIN PYQ
If S is the sum of the first 10 terms of the series ${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right) + {\tan ^{ - 1}}\left( {{1 \over {13}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {21}}} \right) + ....$then tan(S) is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 5 September 2020 (Morning) PYQ

Solution

JEE MAIN PYQ
Let $(a,b)\subset(0,2\pi)$ be the largest interval for which $\sin^{-1}(\sin\theta)-\cos^{-1}(\sin\theta)>0,\ \theta\in(0,2\pi)$, holds. If $\alpha x^{2}+\beta x+\sin^{-1}(x^{2}-6x+10)+\cos^{-1}(x^{2}-6x+10)=0$ and $\alpha-\beta=b-a$, then $\alpha$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (31 January Evening Shift) PYQ

Solution

JEE MAIN PYQ
The value of $\sin^{-1}\left(\dfrac{12}{13}\right)-\sin^{-1}\left(\dfrac{3}{5}\right)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution

JEE MAIN PYQ
Let $\tan^{-1}y=\tan^{-1}x+\tan^{-1}\left(\dfrac{2x}{1-x^{2}}\right)$, where $|x|<\dfrac{1}{\sqrt{3}}$. Then a value of $y$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2015 (Offline) PYQ

Solution

JEE MAIN PYQ
Let $S$ be the set of all solutions of the equation $\cos^{-1}(2x)-2\cos^{-1}\!\big(\sqrt{1-x^{2}}\big)=\pi,\ x\in\left[-\dfrac{1}{2},\,\dfrac{1}{2}\right]$. Then $\displaystyle \sum_{x\in S} 2\sin^{-1}(x^{2}-1)$ is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (1 February Morning Shift) PYQ

Solution


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