1
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the foci of the ellipse $$\frac{x^{2}}{16}+\frac{y^{2}}{7}=1$$ and the hyperbola $$\frac{x^{2}}{144}-\frac{y^{2}}{\alpha}=\frac{1}{25}$$ coincide. Then the length of the latus rectum of the hyperbola is :

A
$$\frac{32}{9}$$
B
$$\frac{18}{5}$$
C
$$\frac{27}{4}$$
D
$$\frac{27}{10}$$
2
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The shortest distance between the lines $$\frac{x+7}{-6}=\frac{y-6}{7}=z$$ and $$\frac{7-x}{2}=y-2=z-6$$ is :

A
$$2 \sqrt{29}$$
B
1
C
$$\sqrt{\frac{37}{29}}$$
D
$$\frac{\sqrt{29}}{2}$$
3
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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 :

A
$$\frac{2}{\sqrt{21}}$$
B
$$2 \sqrt{\frac{3}{7}}$$
C
$$ \frac{2}{3} \sqrt{\frac{7}{3}} $$
D
$$\frac{2}{3}$$
4
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

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

A
11.5
B
10.5
C
12
D
11
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