1
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the hyperbola $$H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$$ pass through the point $$(2 \sqrt{2},-2 \sqrt{2})$$. A parabola is drawn whose focus is same as the focus of $$\mathrm{H}$$ with positive abscissa and the directrix of the parabola passes through the other focus of $$\mathrm{H}$$. If the length of the latus rectum of the parabola is e times the length of the latus rectum of $$\mathrm{H}$$, where e is the eccentricity of H, then which of the following points lies on the parabola?

A
$$(2 \sqrt{3}, 3 \sqrt{2})$$
B
$$\mathbf(3 \sqrt{3},-6 \sqrt{2})$$
C
$$(\sqrt{3},-\sqrt{6})$$
D
$$(3 \sqrt{6}, 6 \sqrt{2})$$
2
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the lines

$$\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$$ and

$$\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$$ be coplanar

and $$\mathrm{P}$$ be the plane containing these two lines.

Then which of the following points does NOT lie on P?

A
$$(0,-2,-2)$$
B
$$(-5,0,-1)$$
C
$$(3,-1,0)$$
D
$$(0,4,5)$$
3
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

A plane P is parallel to two lines whose direction ratios are $$-2,1,-3$$ and $$-1,2,-2$$ and it contains the point $$(2,2,-2)$$. Let P intersect the co-ordinate axes at the points $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ making the intercepts $$\alpha, \beta, \gamma$$. If $$\mathrm{V}$$ is the volume of the tetrahedron $$\mathrm{OABC}$$, where $$\mathrm{O}$$ is the origin, and $$\mathrm{p}=\alpha+\beta+\gamma$$, then the ordered pair $$(\mathrm{V}, \mathrm{p})$$ is equal to :

A
$$(48,-13)$$
B
$$(24,-13)$$
C
$$(48,11)$$
D
$$(24,-5)$$
4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let S be the set of all a $$\in R$$ for which the angle between the vectors $$ \vec{u}=a\left(\log _{e} b\right) \hat{i}-6 \hat{j}+3 \hat{k}$$ and $$\vec{v}=\left(\log _{e} b\right) \hat{i}+2 \hat{j}+2 a\left(\log _{e} b\right) \hat{k}$$, $$(b>1)$$ is acute. Then S is equal to :

A
$$\left(-\infty,-\frac{4}{3}\right)$$
B
$$\Phi $$
C
$$\left(-\frac{4}{3}, 0\right)$$
D
$$\left(\frac{12}{7}, \infty\right)$$
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