Let $0<\theta<\frac{\pi}{2}$. If the eccentricity of the hyperbola $\dfrac{x^2}{\cos^2\theta}-\dfrac{y^2}{\sin^2\theta}=1$ is greater than $2$, then the length of its latus rectum lies in the interval:

1

If $\cos^{-1}\!\left(\dfrac{2}{3x}\right)+\cos^{-1}\!\left(\dfrac{3}{4x}\right)=\dfrac{\pi}{2}\ \ (x>\dfrac{3}{4})$, th…

Topic: JEE Main 2019 (9 January Morning Shift)

2

The maximum volume (in $\mathrm{m}^3$) of the right circular cone having slant height $3\,\mathrm{m}$ is:

Topic: JEE Main 2019 (9 January Morning Shift)

3

The system of linear equations$x + y + z = 2$$2x + 3y + 2z = 5$$2x + 3y + (a^2 - 1)z = a + 1$then:

Topic: JEE Main 2019 (9 January Morning Shift)

4

For any $\theta \in \left(\frac{\pi}{4}, \frac{\pi}{2}\right)$, the expression $3(\cos \theta - \sin \theta)^4 + 6(\s…

Topic: JEE Main 2019 (9 January Morning Shift)

5

Let $A = \{\theta \in (-\frac{\pi}{2}, \pi) : \frac{3 + 2i \sin \theta}{1 - 2i \sin \theta} \text{ is purely imaginary}…

Topic: JEE Main 2019 (9 January Morning Shift)

6

Let $a_1, a_2, \ldots, a_{30}$ be an A.P., $S = \sum_{i=1}^{30} a_i$ and $T = \sum_{i=1}^{15} a_{(2i-1)}$. If $a_…

Topic: JEE Main 2019 (9 January Morning Shift)

1

If $y=y(x)$ is the solution of the differential equation $x\dfrac{dy}{dx}+2y=x^{2}$, satisfying $y(1)=1$, then $y\!\lef…

Topic: JEE Main 2019 (9 January Morning Shift)

2

If $A=\begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{bmatrix}$, then the matrix $A^{-50}$ when …

Topic: JEE Main 2019 (9 January Morning Shift)

3

For $x \in \mathbb{R} - \{0,1\}$, let $f_1(x)=\dfrac{1}{x}$, $f_2(x)=1-x$, and $f_3(x)=\dfrac{1}{1-x}$ be three given f…

Topic: JEE Main 2019 (9 January Morning Shift)

4

Axis of a parabola lies along the x–axis. If its vertex and focus are at distances $2$ and $4$ respectively from the or…

Topic: JEE Main 2019 (9 January Morning Shift)

5

$\displaystyle \lim_{y\to 0}\frac{\sqrt{\,1+\sqrt{1+y^{4}}\,}-\sqrt{2}}{y^{4}}$:

Topic: JEE Main 2019 (9 January Morning Shift)

6

If $a,b,c$ be three distinct real numbers in G.P. and $a+b+c=xb$, then $x$ cannot be:

Topic: JEE Main 2019 (9 January Morning Shift)

7

If the fractional part of the number $\left\{\dfrac{2^{403}}{15}\right\}$ is $\dfrac{k}{15}$, then $k$ is equal to:

Topic: JEE Main 2019 (9 January Morning Shift)

8

Five students of a class have an average height $150\ \mathrm{cm}$ and variance $18\ \mathrm{cm}^2$. A new student, who…

Topic: JEE Main 2019 (9 January Morning Shift)

9

Let f : R $ \to $ R be a function defined as $f(x) = \left\{ {\matrix{ 5 &amp; ; &amp; {x \le 1} \cr {a + bx} …

Topic: JEE Main 2019 (9 January Morning Shift)

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For x2 $ \ne $ n$\pi $ + 1, n $ \in $ N (the set of natural numbers), the integral $\int {x\sqrt {{{2\sin ({x^2} - 1) …

Topic: JEE Main 2019 (9 January Morning Shift)