If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^{2}}$ is increasing in the interval $[0,3]$ and $M$ is the maximum value of $f$ in $[0,3]$ when $k=m$, then the ordered pair $(m,M)$ is equal to:

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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)

10

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)