$\displaystyle \lim_{x\to0}\frac{\sin^{2}x}{\sqrt{2}-\sqrt{1+\cos x}}$ equals:

1

The length of the perpendicular from the point $(2,-1,4)$ on the straight line $\displaystyle \frac{x+3}{10}=\frac{y-2}…

Topic: JEE Main 2019 (8 April Morning Shift)

2

The mean and variance of seven observations are $8$ and $16$, respectively. If five of the observations are $2,4,10,12,…

Topic: JEE Main 2019 (8 April Morning Shift)

3

The area (in sq. units) of the region $A={(x,y)\in\mathbb{R}\times\mathbb{R}\mid 0\le x\le3,\ 0\le y\le4,\ y\le x^2+3x}…

Topic: JEE Main 2019 (8 April Morning Shift)

4

If $f(x)=\dfrac{2-x\cos x}{2+x\cos x}$ and $g(x)=\log_e x,\ (x>0)$, then the value of the integral $\displaystyle \int_…

Topic: JEE Main 2019 (8 April Morning Shift)

5

If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function $f(x)=9x^4+12x^3…

Topic: JEE Main 2019 (8 April Morning Shift)

6

Let $O(0,0)$ and $A(0,1)$ be two fixed points. Then the locus of a point $P$ such that the perimeter of $\triangle AOP$…

Topic: JEE Main 2019 (8 April Morning Shift)

7

If $f(x)=\log_e\left(\dfrac{1-x}{1+x}\right),\ |x|

Topic: JEE Main 2019 (8 April Morning Shift)

8

Let $A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr …

Topic: JEE Main 2019 (8 April Morning Shift)

9

The sum of all natural numbers $n$ such that $100

Topic: JEE Main 2019 (8 April Morning Shift)

10

Let $A$ and $B$ be two non-null events such that $A\subset B$. Then, which of the following statements is always correc…

Topic: JEE Main 2019 (8 April Morning Shift)

1

A point on the straight line $3x+5y=15$ which is equidistant from the coordinate axes will lie only in:

Topic: JEE Main 2019 (8 April Morning Shift)

2

If $\alpha$ and $\beta$ be the roots of the equation $x^2-2x+2=0$, then the least value of $n$ for which $\left(\dfrac{…

Topic: JEE Main 2019 (8 April Morning Shift)

3

Let $y=y(x)$ be the solution of the differential equation $(x^2+1)^2\dfrac{dy}{dx}+2x(x^2+1)y=1$ such that $y(0)=0$. If…

Topic: JEE Main 2019 (8 April Morning Shift)

4

If $\cos(\alpha+\beta)=\dfrac{3}{5},\ \sin(\alpha-\beta)=\dfrac{5}{13}$ and $0

Topic: JEE Main 2019 (8 April Morning Shift)

5

The greatest value of $c\in\mathbb{R}$ for which the system of linear equations$x-cy-cz=0$$cx-y+cz=0$$cx+cy-z=0$has a n…

Topic: JEE Main 2019 (8 April Morning Shift)

6

$\displaystyle \int \frac{\sin\frac{5x}{2}}{\sin\frac{x}{2}},dx$ is equal to (where $c$ is a constant of integration):

Topic: JEE Main 2019 (8 April Morning Shift)

7

If $2y=\left(\cot^{-1}\frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x}\right)^{2},\ x\in\left(0,\frac{\pi}{2}\right)…

Topic: JEE Main 2019 (8 April Morning Shift)

8

All possible numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a time. The number of such numbers in…

Topic: JEE Main 2019 (8 April Morning Shift)

9

The sum of the squares of the lengths of the chords intercepted on the circle $x^{2}+y^{2}=16$, by the lines $x+y=n,\ n…

Topic: JEE Main 2019 (8 April Morning Shift)

10

Let $f:[0,2]\to\mathbb{R}$ be a twice differentiable function such that $f''(x)>0$ for all $x\in(0,2)$. If $\phi(x)=f(x…

Topic: JEE Main 2019 (8 April Morning Shift)