Let $S$ and $S'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\triangle S'BS$ is a right-angled triangle with right angle at $B$ and area $(\triangle S'BS)=8$ sq. units, then the length of a latus rectum of the ellipse is:
Previous 10 Questions — JEE Main 2019 (12 January Evening Shift)
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The integral $\displaystyle \int \frac{3x^{13}+2x^{11}}{(2x^{4}+3x^{2}+1)^{4}},dx$ is equal to: (where $C$ is a constan…
Topic: JEE Main 2019 (12 January Evening Shift)
If the function $f$ given by $f(x)=x^3-3(a-2)x^2+3ax+7$, for some $a\in\mathbb{R}$, is increasing in $(0,1]$ and decrea…
Topic: JEE Main 2019 (12 January Evening Shift)
Let $Z$ be the set of integers. If $A={x\in Z:2(x+2)(x^2-5x+6)=1}$ and $B={x\in Z:-3
Topic: JEE Main 2019 (12 January Evening Shift)
If A = $\left[ {\matrix{
1 & {\sin \theta } & 1 \cr
{ - \sin \theta } & 1 & {\sin \…
Topic: JEE Main 2019 (12 January Evening Shift)
In a class of $60$ students, $40$ opted for NCC, $30$ opted for NSS and $20$ opted for both NCC and NSS. If one of thes…
Topic: JEE Main 2019 (12 January Evening Shift)
Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1|=9$ and $|z_2-3-4i|=4$. Then the minimum value of $|z_1-z_2…
Topic: JEE Main 2019 (12 January Evening Shift)
Let $f$ be a differentiable function such that $f(1)=2$ and $f'(x)=f(x)$ for all $x\in\mathbb{R}$. If $h(x)=f(f(x))$, t…
Topic: JEE Main 2019 (12 January Evening Shift)
If a straight line passing through the point $P(-3,4)$ is such that its intercepted portion between the coordinate axes…
Topic: JEE Main 2019 (12 January Evening Shift)
The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3, 4…
Topic: JEE Main 2019 (12 January Evening Shift)
The set of all values of $\lambda$ for which the system of linear equations$x-2y-2z=\lambda x$$x+2y+z=\lambda y$$-x-y=\…
Topic: JEE Main 2019 (12 January Evening Shift)
