Let $n\ge 2$ be a natural number and $0<\theta<\dfrac{\pi}{2}$. Then \[ \int \frac{\big(\sin^{n}\theta-\sin\theta\big)^{1/n}\,\cos\theta}{\sin^{\,n+1}\theta}\,d\theta \] is equal to (where $C$ is a constant of integration):

1

The mean of five observations is $5$ and their variance is $9.20$. If three of the five observations are $1,\,3,$ and $…

Topic: JEE Main 2019 (10 January Morning Shift)

2

If the system of equations$x + y + z = 5$$x + 2y + 3z = 9$$x + 3y + az = \beta$has infinitely many solutions, then $\be…

Topic: JEE Main 2019 (10 January Morning Shift)

1

Let $\vec a=2\hat i+\lambda_{1}\hat j+3\hat k$, $\vec b=4\hat i+(3-\lambda_{2})\hat j+6\hat k$, and $\vec c=3\hat i+6\h…

Topic: JEE Main 2019 (10 January Morning Shift)

2

In a class of $140$ students numbered $1$ to $140$, all even–numbered students opted Mathematics, those whose number is…

Topic: JEE Main 2019 (10 January Morning Shift)

3

If $5,\ 5r,\ 5r^{2}$ are the lengths of the sides of a triangle, then $r$ cannot be equal to:

Topic: JEE Main 2019 (10 January Morning Shift)

4

For each $t\in\mathbb{R}$, let $[t]$ be the greatest integer less than or equal to $t$. Then $\displaystyle \lim_{x\…

Topic: JEE Main 2019 (10 January Morning Shift)

5

Let&nbsp;&nbsp;$f\left( x \right) = \left\{ {\matrix{ {\max \left\{ {\left| x \right|,{x^2}} \right\}} &amp; {\left|…

Topic: JEE Main 2019 (10 January Morning Shift)

6

If the third term in the binomial expansion of $(1+x^{\log_{8}x})^{5}$ equals $2560$, then a possible value of $x$ is:

Topic: JEE Main 2019 (10 January Morning Shift)

7

Let $d\in\mathbb{R}$, and $A=\begin{bmatrix} -2 & 4+d & \sin\theta-2\\ 1 & \sin\theta+2 & d\\ 5 & 2\sin\theta-d & -\sin…

Topic: JEE Main 2019 (10 January Morning Shift)

8

If the line $3x+4y-24=0$ intersects the $x$-axis at the point $A$ and the $y$-axis at the point $B$, then the incentre …

Topic: JEE Main 2019 (10 January Morning Shift)

9

The sum of all two–digit positive numbers which, when divided by $7$, yield $2$ or $5$ as remainder is:

Topic: JEE Main 2019 (10 January Morning Shift)

10

Consider the quadratic equation $(c - 5)x^2 - 2cx + (c - 4) = 0,\ c \ne 5.$ Let $S$ be the set of all integral values…

Topic: JEE Main 2019 (10 January Morning Shift)