Let the set of all values of $p\in\mathbb{R}$, for which both the roots of the equation $x^{2}-(p+2)x+(2p+9)=0$ are negative real numbers, be the interval $(\alpha,\beta)$. Then $\beta-2\alpha$ is:

1

Let the system of equations :$ \begin{aligned} & 2 x+3 y+5 z=9 \\ & 7 x+3 y-2 z=8 \\ & 12 x+3 y-(4+\lambda) z=16-\mu \e…

Topic: JEE Main 2025 (7 April Morning Shift)

2

If for $\theta\in\left[-\dfrac{\pi}{3},0\right]$, the points $(x,y)=\big(3\tan(\theta+\tfrac{\pi}{3}),,2\tan(\theta+\tf…

Topic: JEE Main 2025 (7 April Morning Shift)

3

The remainder when $\big((64)^{(64)}\big)^{(64)}$ is divided by $7$ is:

Topic: JEE Main 2025 (7 April Morning Shift)

4

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81$…

Topic: JEE Main 2025 (7 April Morning Shift)

5

Let $y=y(x)$ be the solution curve of the differential equation $x(x^{2}+e^{x})^{2}dy+\big(e^{x}(x-2)y-x^{3}\big)dx=0, …

Topic: JEE Main 2025 (7 April Morning Shift)

6

$\displaystyle \lim_{x\to 0^{+}}\frac{\tan\big(5x^{1/5}\big),\ln(1+3x^{2})}{\big(\tan^{-1}(3\sqrt{2})\big),\big(e^{x\sq…

Topic: JEE Main 2025 (7 April Morning Shift)

7

Let $\triangle ABC$ be the triangle such that the equations of lines $AB$ and $AC$ are $3y-x=2$ and $x+y=2$, respective…

Topic: JEE Main 2025 (7 April Morning Shift)

8

The mean and standard deviation of $100$ observations are $40$ and $5.1$, respectively. By mistake one observation is t…

Topic: JEE Main 2025 (7 April Morning Shift)

9

Let P be the parabola, whose focus is $(-2,1)$ and directrix is $2 x+y+2=0$. Then the sum of the ordinates of the point…

Topic: JEE Main 2025 (7 April Morning Shift)

10

Let $C_1$ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let $C_2$ be the circle …

Topic: JEE Main 2025 (7 April Morning Shift)

1

Among the statements (S1): The set ${z\in\mathbb{C}\setminus{-i}:\ |z|=1\ \text{ and }\ \dfrac{z-i}{z+i}\ \text{is pur…

Topic: JEE Main 2025 (7 April Morning Shift)

2

The integral $\displaystyle \int_{0}^{\pi}\frac{(x+3)\sin x}{1+3\cos^{2}x}dx$ is equal to

Topic: JEE Main 2025 (7 April Morning Shift)

3

Let the line $L$ pass through $(1,1,1)$ and intersect the lines $\dfrac{x-1}{2} = \dfrac{y+1}{3} = \dfrac{z-1}{4}$ and …

Topic: JEE Main 2025 (7 April Morning Shift)

4

If the area of the region bounded by the curves $y = 4 - \dfrac{x^2}{4}$ and $y = \dfrac{x-4}{2}$ is equal to $\alpha$,…

Topic: JEE Main 2025 (7 April Morning Shift)

5

Let the angle $\theta,;0

Topic: JEE Main 2025 (7 April Morning Shift)

6

Let $x_1,x_2,x_3,x_4$ be in a geometric progression. If $2,7,9,5$ are subtracted respectively from $x_1,x_2,x_3,x_4$, t…

Topic: JEE Main 2025 (7 April Morning Shift)

7

If the shortest distance between the lines $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$ and $\dfrac{x}{1}=\dfrac{y}{\…

Topic: JEE Main 2025 (7 April Morning Shift)

8

Let $x=-1$ and $x=2$ be the critical points of the function $f(x)=x^{3}+ax^{2}+b\log_{e}|x|+1,;x\neq0$. Let $m$ and $M$…

Topic: JEE Main 2025 (7 April Morning Shift)