The region represented by $|x-y|\le 2$ and $|x+y|\le 2$ is bounded by a:

1

All the pairs $(x,y)$ that satisfy the inequality $2\sqrt{\sin^{2}x-2\sin x+5}\cdot\dfrac{1}{4\sin^{2}y}\le 1$ also sat…

Topic: JEE Main 2019 (10 April Morning Shift)

2

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^{2}+x\sin\theta-2\sin\theta=0,\ \theta\in\left(0,\df…

Topic: JEE Main 2019 (10 April Morning Shift)

3

If $a>0$ and $z=\dfrac{(1+i)^{2}}{,a-i,}$ has magnitude $\sqrt{\dfrac{2}{5}}$, then $\overline{z}$ is equal to:

Topic: JEE Main 2019 (10 April Morning Shift)

4

If $y=y(x)$ is the solution of the differential equation $\dfrac{dy}{dx}=(\tan x-y)\sec^{2}x,\ x\in\left(-\dfrac{\pi}{2…

Topic: JEE Main 2019 (10 April Morning Shift)

5

If the length of the perpendicular from the point $(\beta,0,\beta)\ (\beta\ne0)$ to the line, $\dfrac{x}{1}=\dfrac{y-1}…

Topic: JEE Main 2019 (10 April Morning Shift)

6

If ${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - …

Topic: JEE Main 2019 (10 April Morning Shift)

7

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the c…

Topic: JEE Main 2019 (10 April Morning Shift)

1

Let $f(x)=e^{x}-x$ and $g(x)=x^{2}-x,\ \forall x\in\mathbb{R}$. Then the set of all $x\in\mathbb{R}$ where the function…

Topic: JEE Main 2019 (10 April Morning Shift)

2

If $a_{1},a_{2},a_{3},\ldots,a_{n}$ are in A.P. and $a_{1}+a_{4}+a_{7}+\cdots+a_{16}=114$, then $a_{1}+a_{6}+a_{11}+a_{…

Topic: JEE Main 2019 (10 April Morning Shift)

3

The number of $6$-digit numbers that can be formed using the digits $0,1,2,5,7,9$ which are divisible by $11$ and no di…

Topic: JEE Main 2019 (10 April Morning Shift)

4

If for some $x\in\mathbb{R}$, the frequency distribution of the marks obtained by $20$ students in a test is:then the m…

Topic: JEE Main 2019 (10 April Morning Shift)

5

If the system of linear equations$x+y+z=5$$x+2y+2z=6$$x+3y+\lambda z=\mu,; (\lambda,\mu\in\mathbb{R})$has infinitely ma…

Topic: JEE Main 2019 (10 April Morning Shift)

6

Let $A(3,0,-1),; B(2,10,6)$ and $C(1,2,1)$ be the vertices of a triangle and $M$ be the midpoint of $AC$. If $G$ divide…

Topic: JEE Main 2019 (10 April Morning Shift)

7

Let $f:\mathbb{R}\to\mathbb{R}$ be differentiable at $c\in\mathbb{R}$ and $f(c)=0$. If $g(x)=|f(x)|$, then at $x=c$, $g…

Topic: JEE Main 2019 (10 April Morning Shift)

8

The value of $\displaystyle \int_{0}^{2\pi}\big\lfloor \sin 2x,(1+\cos 3x)\big\rfloor,dx$, where $[\cdot]$ denotes the …

Topic: JEE Main 2019 (10 April Morning Shift)

9

If $\displaystyle \int \frac{dx}{(x^{2}-2x+10)^{2}} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^{2}-2x…

Topic: JEE Main 2019 (10 April Morning Shift)

10

If$f(x) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr …

Topic: JEE Main 2019 (10 April Morning Shift)