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/sec, then the rate (in cm/sec) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1m above the ground is:
Previous 10 Questions — JEE Main 2019 (12 April Morning Shift)
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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)
Let f : R $ \to $R be a continuously differentiable function such that f(2) = 6 and f'(2) = ${1 \over {48}}$. If $\int\…
Topic: JEE Main 2019 (12 April Morning Shift)
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)
Next 10 Questions — JEE Main 2019 (12 April Morning Shift)
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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 5cm and 12cm intersect is $90^\circ$, then the len…
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)
