1
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
$$- {{69} \over {256}}$$
2
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
If the length of the chord of the circle,
x2 + y2 = r2 (r > 0) along the line, y – 2x = 3 is r,
then r2 is equal to :
A
$${9 \over 5}$$
B
$${{24} \over 5}$$
C
$${{12} \over 5}$$
D
12
3
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
The circle passing through the intersection of the circles,
x2 + y2 – 6x = 0 and x2 + y2 – 4y = 0, having its centre on
the line, 2x – 3y + 12 = 0, also passes through the point :
A
(–3, 1)
B
(1, –3)
C
(–1, 3)
D
(–3, 6)
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?
A
3x – 4y – 24 = 0
B
4x + 3y – 8 = 0
C
3x + 4y – 6 = 0
D
4x – 3y + 17 = 0
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