Let $\vec{a} = \hat{i} - \hat{j} + 2\hat{k}$ and let $\vec{b}$ be a vector such that  

$\vec{a} \times \vec{b} = 2\hat{i} - \hat{k}$ and $\vec{a} \cdot \vec{b} = 3$.  

Then the projection of $\vec{b}$ on the vector $\vec{a} - \vec{b}$ is :

1

The shortest distance between the lines  $\dfrac{x+7}{-6} = \dfrac{y-6}{7} = z$  and  $\d…

Topic: JEE Main 2022 (25 July Evening Shift)

2

Let the foci of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{7}=1$ and the hyperbola $\dfrac{x^{2}}{144}-\dfrac{y^{2}}{…

Topic: JEE Main 2022 (25 July Evening Shift)

3

If the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ meets the line $\dfrac{x}{7} + \dfrac{y}{2\sqrt{6}} = 1$ on th…

Topic: JEE Main 2022 (25 July Evening Shift)

4

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines  $L_1 : 3x - 4y + 12 = 0$, …

Topic: JEE Main 2022 (25 July Evening Shift)

5

Let $[t]$ denote the greatest integer less than or equal to $t$.  Then the value of the integral  $…

Topic: JEE Main 2022 (25 July Evening Shift)

6

If $A$ and $B$ are two events such that $P(A) = \tfrac{1}{3},\ P(B) = \tfrac{1}{5}$ and $P(A \cup B) = \tfrac{1}{2}$, t…

Topic: JEE Main 2022 (25 July Evening Shift)

7

$\lim_{x \to \tfrac{\pi}{4}} \dfrac{8\sqrt{2} - (\cos x + \sin x)^7}{\sqrt{2} - \sqrt{2}\sin 2x}$ is equal to

Topic: JEE Main 2022 (25 July Evening Shift)

8

The remainder when $(11)^{1011} + (1011)^{11}$ is divided by $9$ is

Topic: JEE Main 2022 (25 July Evening Shift)

9

The number of bijective functions $f:\{1,3,5,7,\ldots,99\}\to\{2,4,6,8,\ldots,100\}$ such that$f(3)\ge f(9)\ge f(15)\ge…

Topic: JEE Main 2022 (25 July Evening Shift)

10

The number of real values of $\lambda$, such that the system of linear equations$2x - 3y + 5z = 9$$x + 3y - z = -18$$3x…

Topic: JEE Main 2022 (25 July Evening Shift)

1

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in ascending order, is 6, then…

Topic: JEE Main 2022 (25 July Evening Shift)

2

$2 \sin\!\left(\tfrac{\pi}{22}\right) \sin\!\left(\tfrac{3\pi}{22}\right) \sin\!\left(\tfrac{5\pi}{22}\right) \sin\!\le…

Topic: JEE Main 2022 (25 July Evening Shift)