1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Consider the parabola with vertex $$\left( {{1 \over 2},{3 \over 4}} \right)$$ and the directrix $$y = {1 \over 2}$$. Let P be the point where the parabola meets the line $$x = - {1 \over 2}$$. If the normal to the parabola at P intersects the parabola again at the point Q, then (PQ)2 is equal to :
A
$${{75} \over 8}$$
B
$${{125} \over {16}}$$
C
$${{25} \over 2}$$
D
$${{15} \over 2}$$
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The numbers of pairs (a, b) of real numbers, such that whenever $$\alpha$$ is a root of the equation x2 + ax + b = 0, $$\alpha$$2 $$-$$ 2 is also a root of this equation, is :
A
6
B
2
C
4
D
8
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let Sn = 1 . (n $$-$$ 1) + 2 . (n $$-$$ 2) + 3 . (n $$-$$ 3) + ..... + (n $$-$$ 1) . 1, n $$\ge$$ 4.

The sum $$\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)} $$ is equal to :
A
$${{e - 1} \over 3}$$
B
$${{e - 2} \over 6}$$
C
$${e \over 3}$$
D
$${e \over 6}$$
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such that i +j + k $$\ne$$ 15, is :
A
12
B
419
C
443
D
455
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