1
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\vec{a}=2 \hat{i}+\hat{j}-\hat{k}, \vec{b}=((\vec{a} \times(\hat{i}+\hat{j})) \times \hat{i}) \times \hat{i}$$. Then the square of the projection of $$\vec{a}$$ on $$\vec{b}$$ is:

A
$$\frac{1}{3}$$
B
$$\frac{1}{5}$$
C
2
D
$$\frac{2}{3}$$
2
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\overrightarrow{\mathrm{a}}=6 \hat{i}+\hat{j}-\hat{k}$$ and $$\overrightarrow{\mathrm{b}}=\hat{i}+\hat{j}$$. If $$\overrightarrow{\mathrm{c}}$$ is a is vector such that $$|\overrightarrow{\mathrm{c}}| \geq 6, \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=6|\overrightarrow{\mathrm{c}}|,|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $$\vec{a} \times \vec{b}$$ and $$\vec{c}$$ is $$60^{\circ}$$, then $$|(\vec{a} \times \vec{b}) \times \vec{c}|$$ is equal to:

A
$$\frac{3}{2} \sqrt{6}$$
B
$$\frac{9}{2}(6-\sqrt{6})$$
C
$$\frac{9}{2}(6+\sqrt{6})$$
D
$$\frac{3}{2} \sqrt{3}$$
3
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the area of the region $$\left\{(x, y): \frac{\mathrm{a}}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2,0<\mathrm{a}<1\right\}$$ is $$\left(\log _{\mathrm{e}} 2\right)-\frac{1}{7}$$ then the value of $$7 \mathrm{a}-3$$ is equal to :

A
1
B
0
C
2
D
$$-$$1
4
JEE Main 2024 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{P}(\alpha, \beta, \gamma)$$ be the image of the point $$\mathrm{Q}(3,-3,1)$$ in the line $$\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$$ and $$\mathrm{R}$$ be the point $$(2,5,-1)$$. If the area of the triangle $$\mathrm{PQR}$$ is $$\lambda$$ and $$\lambda^2=14 \mathrm{~K}$$, then $$\mathrm{K}$$ is equal to :

A
18
B
81
C
72
D
36
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12