1
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to :

A
575
B
$$-$$575
C
576
D
$$-$$576
2
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The set of values of k, for which the circle $$C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$$ lies inside the fourth quadrant and the point $$\left( {1, - {1 \over 3}} \right)$$ lies on or inside the circle C, is :

A
an empty set
B
$$\left( {6,{{65} \over 9}} \right]$$
C
$$\left[ {{{80} \over 9},10} \right)$$
D
$$\left( {9,{{92} \over 9}} \right]$$
3
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The shortest distance between the lines

$${{x - 3} \over 2} = {{y - 2} \over 3} = {{z - 1} \over { - 1}}$$ and $${{x + 3} \over 2} = {{y - 6} \over 1} = {{z - 5} \over 3}$$, is :

A
$${{18} \over {\sqrt 5 }}$$
B
$${{22} \over {3\sqrt 5 }}$$
C
$${{46} \over {3\sqrt 5 }}$$
D
$$6\sqrt 3 $$
4
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\overrightarrow a $$ and $$\overrightarrow b $$ be the vectors along the diagonals of a parallelogram having area $$2\sqrt 2 $$. Let the angle between $$\overrightarrow a $$ and $$\overrightarrow b $$ be acute, $$|\overrightarrow a | = 1$$, and $$|\overrightarrow a \,.\,\overrightarrow b | = |\overrightarrow a \times \overrightarrow b |$$. If $$\overrightarrow c = 2\sqrt 2 \left( {\overrightarrow a \times \overrightarrow b } \right) - 2\overrightarrow b $$, then an angle between $$\overrightarrow b $$ and $$\overrightarrow c $$ is :

A
$${\pi \over 4}$$
B
$$-$$ $${\pi \over 4}$$
C
$${{5\pi } \over 6}$$
D
$${{3\pi } \over 4}$$
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