1
JEE Advanced 2020 Paper 1 Offline
+3
-1
Let a, b and $$\lambda$$ be positive real numbers. Suppose P is an end point of the latus return of the
parabola y2 = 4$$\lambda$$x, and suppose the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is
A
$${1 \over {\sqrt 2 }}$$
B
$${{1 \over 2}}$$
C
$${{1 \over 3}}$$
D
$${{2 \over 5}}$$
2
JEE Advanced 2020 Paper 1 Offline
+3
-1
Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are $${{2 \over 3}}$$ and $${{1 \over 3}}$$, respectively. Suppose $$\alpha$$ is the number of heads that appear when C1 is tossed twice, independently, and suppose $$\beta$$ is the number of heads that appear when C2 is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x2 $$-$$ ax + $$\beta$$ are real and equal, is
A
$${{40} \over {81}}$$
B
$${{20} \over {81}}$$
C
$${{1} \over {2}}$$
D
$${{1} \over {4}}$$
3
JEE Advanced 2020 Paper 1 Offline
+3
-1
Consider the rectangles lying the region

$$\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.$$ and $$\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}$$

and having one side on the X-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is
A
$${{3\pi \over 2}}$$
B
$$\pi$$
C
$${\pi \over {2\sqrt 3 }}$$
D
$${{\pi \sqrt 3 } \over 2}$$
4
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let the function f : R $$\to$$ R be defined by f(x) = x3 $$-$$ x2 + (x $$-$$ 1)sin x and let g : R $$\to$$ R be an arbitrary function. Let fg : R $$\to$$ R be the product function defined by (fg)(x) = f(x)g(x). Then which of the following statements is/are TRUE?
A
If g is continuous at x = 1, then fg is differentiable at x = 1
B
If f g is differentiable at x = 1, then g is continuous at x = 1
C
If g is differentiable at x = 1, then fg is differentiable at x = 1
D
If f g is differentiable at x = 1, then g is differentiable at x = 1
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