Let f(x) = 5 – |x – 2| and g(x) = |x + 1|, x $ \in $ R. If f(x) attains maximum value at $\alpha $ and g(x) attains minimum value at $\beta $, then $\mathop {\lim }\limits_{x \to -\alpha \beta } {{\left( {x - 1} \right)\left( {{x^2} - 5x + 6} \right)} \over {{x^2} - 6x + 8}}$ is equal to :
Previous 10 Questions — JEE Main 2019 (12 April Evening Shift)
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A straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the…
Topic: JEE Main 2019 (12 April Evening Shift)
If $\alpha, \beta$ and $\gamma$ are three consecutive terms of a non-constant G.P. such that the equations
$\alpha x^{2…
Topic: JEE Main 2019 (12 April Evening Shift)
If $a_{1}, a_{2}, a_{3}, \dots$ are in A.P. such that $a_{1} + a_{7} + a_{16} = 40$,
then the sum of the first 15 terms…
Topic: JEE Main 2019 (12 April Evening Shift)
The term independent of $x$ in the expansion of
$\left(\dfrac{1}{60} - \dfrac{x^{8}}{81}\right)\left(2x^{2} - \dfrac{3}…
Topic: JEE Main 2019 (12 April Evening Shift)
Let $a \in \left(0, \dfrac{\pi}{2}\right)$ be fixed.
If
$\displaystyle \int \dfrac{\tan x + \tan a}{\tan x - \tan a} , …
Topic: JEE Main 2019 (12 April Evening Shift)
The general solution of the differential equation (y2
– x3)dx – xydy = 0 (x $ \ne $ 0) is :
(where c is a constant of i…
Topic: JEE Main 2019 (12 April Evening Shift)
If the area (in sq. units) bounded by the parabola $y^{2}=4\lambda x$ and the line $y=\lambda x,\ \lambda>0$, is $\dfra…
Topic: JEE Main 2019 (12 April Evening Shift)
Let $A, B$ and $C$ be sets such that $\varnothing \ne A\cap B \subseteq C$. Which of the following statements is not tr…
Topic: JEE Main 2019 (12 April Evening Shift)
Next 10 Questions — JEE Main 2019 (12 April Evening Shift)
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Let z $ \in $ C with Im(z) = 10 and it satisfies ${{2z - n} \over {2z + n}}$ = 2i - 1 for some natural number n. Then :
Topic: JEE Main 2019 (12 April Evening Shift)
A value of $\theta \in \left( {0,{\pi \over 3}} \right)$, for which
$\left| {\matrix{
{1 + {{\cos }^2}\theta } &am…
Topic: JEE Main 2019 (12 April Evening Shift)
$\lim_{x\to 0}\dfrac{x+2\sin x}{\sqrt{x^{2}+2\sin x+1}-\sqrt{\sin^{2}x-x+1}}$ is:
Topic: JEE Main 2019 (12 April Evening Shift)
The derivative of ${\tan ^{ - 1}}\left( {{{\sin x - \cos x} \over {\sin x + \cos x}}} \right)$, with respect to ${x \ov…
Topic: JEE Main 2019 (12 April Evening Shift)
A value of $\alpha$ such that
$\displaystyle \int_{\alpha}^{\alpha+1} \dfrac{dx}{(x+\alpha)(x+\alpha+1)} = \log_e\left(…
Topic: JEE Main 2019 (12 April Evening Shift)
An ellipse, with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$, passes through which of the following poi…
Topic: JEE Main 2019 (12 April Evening Shift)
A group of students comprises of $5$ boys and $n$ girls. If the number of ways in which a team of $3$ students can rand…
Topic: JEE Main 2019 (12 April Evening Shift)
A person throws two fair dice. He wins Rs. $15$ for throwing a doublet (same numbers on the two dice), wins Rs. $12$ wh…
Topic: JEE Main 2019 (12 April Evening Shift)
A circle touching the $x$-axis at $(3,0)$ and making an intercept of length $8$ on the $y$-axis passes through the poin…
Topic: JEE Main 2019 (12 April Evening Shift)
