If $\displaystyle \int \frac{\sqrt{\,1-x^{2}\,}}{x^{4}}\,dx = A(x)\left(\sqrt{\,1-x^{2}\,}\right)^{m} + C$, for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant of integration, then $(A(x))^{m}$ equals :

1

Let $\vec{a}=\hat{i}+2\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\lambda\hat{j}+4\hat{k}$ and $\vec{c}=2\hat{i}+4\hat{j}+(\lam…

Topic: JEE Main 2019 (11 January Morning Shift)

2

The sum of the real values of $x$ for which the middle term in the binomial expansion of $\left(\dfrac{x^{3}}{3}+\dfrac…

Topic: JEE Main 2019 (11 January Morning Shift)

3

The maximum value of the function $f(x)=3x^{3}-18x^{2}+27x-40$ on the set $S=\{x\in\mathbb{R}: x^{2}+30\le 11x\}$ is :

Topic: JEE Main 2019 (11 January Morning Shift)

4

The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A$, $B$ and the origin.…

Topic: JEE Main 2019 (11 January Morning Shift)

5

If one real root of the quadratic equation $81x^{2}+kx+256=0$ is cube of the other root, then a value of $k$ is :

Topic: JEE Main 2019 (11 January Morning Shift)

6

A square is inscribed in the circle $x^{2}+y^{2}-6x+8y-103=0$ with its sides parallel to the coordinate axes. Then the …

Topic: JEE Main 2019 (11 January Morning Shift)

7

If $y(x)$ is the solution of the differential equation $\dfrac{dy}{dx}+\left(\dfrac{2x+1}{x}\right)y=e^{-2x},\ x>0,$ w…

Topic: JEE Main 2019 (11 January Morning Shift)

8

Let $[x]$ denote the greatest integer less than or equal to $x$. Then $\displaystyle \lim_{x\to 0}\frac{\tan(\pi\sin^{…

Topic: JEE Main 2019 (11 January Morning Shift)

9

Let $A=\begin{pmatrix} 0 & 2q & r\\ p & q & -r\\ p & -q & r \end{pmatrix}$. If $AA^{T}=I_{3}$, then $|p|$ is :

Topic: JEE Main 2019 (11 January Morning Shift)

10

The area (in sq. units) of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is :

Topic: JEE Main 2019 (11 January Morning Shift)

1

If the system of linear equations  $2x+2y+3z=a$  $3x-y+5z=b$  $x-3y+2z=c$  wher…

Topic: JEE Main 2019 (11 January Morning Shift)

2

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\dfrac{27}…

Topic: JEE Main 2019 (11 January Morning Shift)

3

The value of the integral $\displaystyle \int_{-2}^{2}\frac{\sin^{2}x}{[x]+\tfrac{1}{2}}\,dx$ (where $[x]$ denotes the …

Topic: JEE Main 2019 (11 January Morning Shift)

4

Two integers are selected at random from the set $\{1,2,\ldots,11\}$. Given that the sum of selected numbers is even, t…

Topic: JEE Main 2019 (11 January Morning Shift)

5

Let $f\left( x \right) = \left\{ {\matrix{ { - 1} & { - 2 \le x < 0} \cr {{x^2} - 1,} & {0 \le x \le…

Topic: JEE Main 2019 (11 January Morning Shift)

6

Let $\left(-2-\dfrac{1}{3}i\right)^{3}=e^{\frac{x+iy}{2\pi i}}\ (i=\sqrt{-1})$, where $x$ and $y$ are real numbers, the…

Topic: JEE Main 2019 (11 January Morning Shift)

7

Let $f_k(x)=\dfrac{1}{k}\left(\sin^{k}x+\cos^{k}x\right)$ for $k=1,2,3,\ldots$ Then for all $x\in\mathbb{R}$, the value…

Topic: JEE Main 2019 (11 January Morning Shift)

8

Let $a_{1},a_{2},\ldots,a_{10}$ be a G.P. If $\dfrac{a_{3}}{a_{1}}=25$, then $\dfrac{a_{9}}{a_{5}}$ equals

Topic: JEE Main 2019 (11 January Morning Shift)

9

Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=\dfrac{x}{1+x^{2}},\ x\in\mathbb{R}$. Then the range of $f$ is :

Topic: JEE Main 2019 (11 January Morning Shift)