JEE Main 2021 (Online) 25th February Evening Shift | Circle Question 61 | Mathematics

JEE Main 2021 (Online) 25th February Evening Shift

MCQ (Single Correct Answer)

-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 :

$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$

$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$

$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$

$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$

JEE Main 2021 (Online) 24th February Evening Shift

MCQ (Single Correct Answer)

-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 :

$${{69} \over {256}}$$

$${{71} \over {256}}$$

$$ - {{71} \over {256}}$$

$$ - {{69} \over {256}}$$

JEE Main 2020 (Online) 5th September Evening Slot

MCQ (Single Correct Answer)

-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 :

$${9 \over 5}$$

$${{24} \over 5}$$

$${{12} \over 5}$$

JEE Main 2020 (Online) 4th September Evening Slot

MCQ (Single Correct Answer)

-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 :

(–3, 1)

(1, –3)

(–1, 3)

(–3, 6)

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