If the shortest distance between the lines $\dfrac{x-\lambda}{2}=\dfrac{y-4}{3}=\dfrac{z-3}{4}$ and $\dfrac{x-2}{4}=\dfrac{y-4}{6}=\dfrac{z-7}{8}$ is $\dfrac{13}{\sqrt{29}}$, then a value of $\lambda$ is:1

1

Let $y=y(x)$ be the solution curve of the differential equation $\sec y,\dfrac{dy}{dx}+2x\sin y=x^{3}\cos y$, with $y(1…

Topic: JEE Main 2024 (8 April Evening Shift)

1

There are three bags $X,Y,Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-r…

Topic: JEE Main 2024 (8 April Evening Shift)

2

The area of the region in the first quadrant inside the circle $x^{2}+y^{2}=8$ and outside the parabola $y^{2}=2x$ is e…

Topic: JEE Main 2024 (8 April Evening Shift)

3

Let $\vec{a}=4\hat{i}-\hat{j}+\hat{k}$, $\vec{b}=11\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $(\vec{…

Topic: JEE Main 2024 (8 April Evening Shift)

4

If the line segment joining the points $(5,2)$ and $(2,a)$ subtends an angle $\dfrac{\pi}{4}$ at the origin, then the a…

Topic: JEE Main 2024 (8 April Evening Shift)

5

If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathr…

Topic: JEE Main 2024 (8 April Evening Shift)

6

Let $\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}$. Then $\mathrm{e}^\alpha$…

Topic: JEE Main 2024 (8 April Evening Shift)

7

If the system of equations $x+4y-z=\lambda,; 7x+9y+\mu z=-3,; 5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\…

Topic: JEE Main 2024 (8 April Evening Shift)

8

Let $f(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if …

Topic: JEE Main 2024 (8 April Evening Shift)

9

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\dfrac{70}{3}$ and …

Topic: JEE Main 2024 (8 April Evening Shift)

10

$\mathrm{a}, \mathrm{b}>0$, let $f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x< 0 \\ 3, &…

Topic: JEE Main 2024 (8 April Evening Shift)