Let $[x]$ denote the greatest integer less than or equal to $x$. Then $\displaystyle \lim_{x\to 0}\frac{\tan(\pi\sin^{2}x)+\left(|x|-\sin(x[x])\right)^{2}}{x^{2}}$ :

1

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)

2

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)

3

If $x\log_e(\log_e x)-x^2+y^2=4\ (y>0)$, then $\left.\dfrac{dy}{dx}\right|_{x=e}$ is equal to :

Topic: JEE Main 2019 (11 January Morning Shift)

4

The outcome of each of 30 items was observed; 10 items gave an outcome $\dfrac{1}{2}-d$ each, 10 items gave outcome $\d…

Topic: JEE Main 2019 (11 January Morning Shift)

1

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)

2

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)

3

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)

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

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)

6

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)

7

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)

8

If $\displaystyle \int \frac{\sqrt{\,1-x^{2}\,}}{x^{4}}\,dx = A(x)\left(\sqrt{\,1-x^{2}\,}\right)^{m} + C$, for a suita…

Topic: JEE Main 2019 (11 January Morning Shift)

9

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)

10

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)