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

1

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)

2

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)

3

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)

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

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)

6

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)

7

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)

8

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

Topic: JEE Main 2019 (10 April Morning Shift)

9

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)

10

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)

1

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)

2

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)

3

If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ an…

Topic: JEE Main 2019 (10 April Morning Shift)

4

If $\displaystyle \lim_{x\to1}\frac{x^{4}-1}{x-1}=\lim_{x\to k}\frac{x^{3}-k^{3}}{x^{2}-k^{2}}$, then $k$ is:

Topic: JEE Main 2019 (10 April Morning Shift)

5

Let $f(x)=x^{2},\ x\in\mathbb{R}$. For any $A\subseteq\mathbb{R}$, define $g(A)={,x\in\mathbb{R}:\ f(x)\in A,}$. If $S=…

Topic: JEE Main 2019 (10 April Morning Shift)