If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $\left[ {\matrix{ 2 & 3 \cr 5 & { - 1} \cr } } \right]$, then AB is equal to :

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

If $B = \left[ {\matrix{ 5 & {2\alpha } & 1 \cr 0 & 2 & 1 \cr \alpha & 3 & { - 1}…

Topic: JEE Main 2019 (12 April Morning Shift)

8

. 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)

9

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)

10

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)

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)