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 perpendicular to both the vectors $\vec a+\vec b$ and $\vec a-\vec b$ has magnitude $12$, then one such vector is:
Previous 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)
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)
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)
Next 10 Questions — JEE Main 2019 (12 April Morning Shift)
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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
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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)
