The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4} \sin^{4}x \left(1 + \log\left(\dfrac{2 + \sin 2x}{2 - \sin 2x}\right)\right),dx$ is :
Previous 10 Questions — JEE Main 2018 (15 April Morning Shift)
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In a triangle $ABC$, coordinates of $A$ are $(1,2)$ and the equations of the medians through $B$ and $C$ are respective…
Topic: JEE Main 2018 (15 April Morning Shift)
Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$ where $f\left( …
Topic: JEE Main 2018 (15 April Morning Shift)
If $\overrightarrow a ,\,\,\overrightarrow b ,$ and $\overrightarrow C $ are unit vectors such that $\overrightarrow a…
Topic: JEE Main 2018 (15 April Morning Shift)
The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then…
Topic: JEE Main 2018 (15 April Morning Shift)
A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black ba…
Topic: JEE Main 2018 (15 April Morning Shift)
If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of
$3\sin^{2}(A+B)-1…
Topic: JEE Main 2018 (15 April Morning Shift)
If the tangents drawn to the hyperbola $4y^{2}=x^{2}+1$ intersect the co-ordinate axes at the distinct points $A$ and $…
Topic: JEE Main 2018 (15 April Morning Shift)
The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for al…
Topic: JEE Main 2018 (15 April Morning Shift)
Consider the following two binary relations on the set $A = {a, b, c}$ :
$R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c)…
Topic: JEE Main 2018 (15 April Morning Shift)
If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-…
Topic: JEE Main 2018 (15 April Morning Shift)
Next 10 Questions — JEE Main 2018 (15 April Morning Shift)
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The area (in sq. units) of the region
${(x,y)\in \mathbb{R}^{2} : x \ge 0,\ y \ge 0,\ y \ge x-2 \text{ and } y \le \sqr…
Topic: JEE Main 2018 (15 April Morning Shift)
If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3\ \text{cm}$, then the curved sur…
Topic: JEE Main 2018 (15 April Morning Shift)
If $f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$ (x $ \in $ R $-${1, $-$ 2}), then $\int f \left( x \right)dx$ …
Topic: JEE Main 2018 (15 April Morning Shift)
Let $S={(\lambda,\mu)\in\mathbb{R}\times\mathbb{R}: f(t)=(\lvert\lambda\rvert e^{\lvert t\rvert}-\mu)\cdot\sin(2\lvert …
Topic: JEE Main 2018 (15 April Morning Shift)
If $x^{2} + y^{2} + \sin y = 4$, then the value of $\dfrac{d^{2}y}{dx^{2}}$ at the point $(-2,0)$ is :
Topic: JEE Main 2018 (15 April Morning Shift)
If $f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2\sin x & x^{2} & 2x \\ \tan x & x & 1 \end{vmatrix}$, then $\lim_{x \to 0…
Topic: JEE Main 2018 (15 April Morning Shift)
