Let f : R $ \to $R be a continuously differentiable function such that f(2) = 6 and f'(2) = ${1 \over {48}}$. If $\int\limits_6^{f\left( x \right)} {4{t^3}} dt$ = (x - 2)g(x), then $\mathop {\lim }\limits_{x \to 2} g\left( x \right)$ is equal to :
Previous 10 Questions — JEE Main 2019 (12 April Morning Shift)
Nearest first
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Let $S_n$ denote the sum of the first $n$ terms of an A.P. If $S_4=16$ and $S_6=-48$, then $S_{10}$ equals:
Topic: JEE Main 2019 (12 April Morning Shift)
The value of $\sin^{-1}\left(\dfrac{12}{13}\right)-\sin^{-1}\left(\dfrac{3}{5}\right)$ is equal to:
Topic: JEE Main 2019 (12 April Morning Shift)
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed w…
Topic: JEE Main 2019 (12 April Morning Shift)
If $B = \left[ {\matrix{
5 & {2\alpha } & 1 \cr
0 & 2 & 1 \cr
\alpha & 3 & { - 1}…
Topic: JEE Main 2019 (12 April Morning Shift)
. The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distin…
Topic: JEE Main 2019 (12 April Morning Shift)
The integral $\displaystyle \int \dfrac{2x^3 - 1}{x^4 + x} , dx$ is equal to :
(Here $C$ is a constant of integration)
Topic: JEE Main 2019 (12 April Morning Shift)
For $x \in (0, 3/2)$, let $f(x) = \sqrt{x}$, $g(x) = \tan x$ and $h(x) = \dfrac{1 - x^2}{1 + x^2}$.
If $\phi(x) = (h \c…
Topic: JEE Main 2019 (12 April Morning Shift)
If $\displaystyle \int_{0}^{\pi/2} \dfrac{\cot x}{\cot x + \cos \csc x} , dx = m(\pi + n)$, then $m \cdot n$ is equal to
Topic: JEE Main 2019 (12 April Morning Shift)
The equation $|z - i| = |z - 1|$, where $i = \sqrt{-1}$, represents :
Topic: JEE Main 2019 (12 April Morning Shift)
If $\alpha$ and $\beta$ are the roots of the equation $375x^2 - 25x - 2 = 0$, then
$\displaystyle \lim_{n \to \infty} \…
Topic: JEE Main 2019 (12 April Morning Shift)
Next 10 Questions — JEE Main 2019 (12 April Morning Shift)
Ascending by ID
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The equation $y = \sin x \sin (x + 2) - \sin^2 (x + 1)$ represents a straight line lying in:
Topic: JEE Main 2019 (12 April Morning Shift)
A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of 25 cm/…
Topic: JEE Main 2019 (12 April Morning Shift)
If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $\left[ {\matrix{
2 & 3 \cr
5…
Topic: JEE Main 2019 (12 April Morning Shift)
Let $\vec a = 3\hat i + 2\hat j + 2\hat k$ and $\vec b = \hat i + 2\hat j - 2\hat k$ be two vectors.
If a vector perpen…
Topic: JEE Main 2019 (12 April Morning Shift)
If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16…
Topic: JEE Main 2019 (12 April Morning Shift)
If the area (in sq. units) of the region ${(x,y):, y^{2}\le 4x,; x+y\le 1,; x\ge 0,; y\ge 0}$ is $a\sqrt{2}+b$, then $a…
Topic: JEE Main 2019 (12 April Morning Shift)
Consider the differential equation
$y^{2},dx+\left(x-\dfrac{1}{y}\right)dy=0.$
If $y=1$ when $x=1$, then the value of $…
Topic: JEE Main 2019 (12 April Morning Shift)
If the angle of intersection at a point where two circles with radii $5\text{ cm}$ and $12\text{ cm}$ intersect is $90^…
Topic: JEE Main 2019 (12 April Morning Shift)
The coefficient of $x^{18}$ in the product
$(1+x)(1-x)^{10}(1+x+x^{2})^{9}$ is:
Topic: JEE Main 2019 (12 April Morning Shift)
If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^{2}}$ is increasing in the interval $[0,3]$…
Topic: JEE Main 2019 (12 April Morning Shift)
