Consider the quadratic equation $(c - 5)x^2 - 2cx + (c - 4) = 0,\ c \ne 5.$ Let $S$ be the set of all integral values of $c$ for which one root of the equation lies in the interval $(0, 2)$ and its other root lies in the interval $(2, 3).$ Then the number of elements in $S$ is:

1

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)

2

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)

3

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)

4

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)

5

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

Topic: JEE Main 2019 (10 January Morning Shift)

6

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)

7

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)

8

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)

9

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)

10

Let $n\ge 2$ be a natural number and $0

Topic: JEE Main 2019 (10 January Morning Shift)

1

If the area enclosed between the curves $y = kx^2$ and $x = ky^2$, $(k > 0)$, is $1$ square unit, then $k$ is:

Topic: JEE Main 2019 (10 January Morning Shift)

2

A point P moves on the line $2x - 3y + 4 = 0.$ If $Q(1, 4)$ and $R(3, -2)$ are fixed points, then the locus of the ce…

Topic: JEE Main 2019 (10 January Morning Shift)

3

Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3|z_1| = 4|z_2|.$ If $z = \dfrac{3z_1}{2z_2} + \df…

Topic: JEE Main 2019 (10 January Morning Shift)

4

The shortest distance between the point $\left(\dfrac{3}{2},\,0\right)$ and the curve $y=\sqrt{x},\ (x>0)$, is:

Topic: JEE Main 2019 (10 January Morning Shift)

5

If \(\dfrac{dy}{dx}+\dfrac{3}{\cos^2 x}\,y=\dfrac{1}{\cos^2 x},\ x\in\left(-\dfrac{\pi}{3},\dfrac{\pi}{3}\right)\) and …

Topic: JEE Main 2019 (10 January Morning Shift)

6

Let \(f:\mathbb{R}\to\mathbb{R}\) be a function such that \[ f(x)=x^{3}+x^{2}f'(1)+x f'(2)+f''(3),\qquad x\in\mathbb{R}…

Topic: JEE Main 2019 (10 January Morning Shift)

7

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)