1
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circle of radius r, then r is equal to :
A
$${1 \over 4}$$
B
$${1 \over 2}$$
C
1
D
$${1 \over 3}$$
2
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $$\bot$$ OB. Then, the area of the triangle PQB (in square units) is :

A
24$$\sqrt 2$$
B
24$$\sqrt 3$$
C
26$$\sqrt 2$$
D
26$$\sqrt 3$$
3
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
A
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
B
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
C
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
D
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
4
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be $$\left( {{{10} \over 3},{7 \over 3}} \right)$$. If $$\alpha$$, $$\beta$$ are the roots of the equation $$a{x^2} + bx + 1 = 0$$, then the value of $${\alpha ^2} + {\beta ^2} - \alpha \beta$$ is :
A
$${{69} \over {256}}$$
B
$${{71} \over {256}}$$
C
$$- {{71} \over {256}}$$
D
$$- {{69} \over {256}}$$
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