1
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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
$${{1} \over {4}}$$
2
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Change Language
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
$${{\pi \sqrt 3 } \over 2}$$
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
4
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Change Language
Let M be a 3 $$ \times $$ 3 invertible matrix with real entries and let I denote the 3 $$ \times $$ 3 identity matrix. If M$$-$$1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?
A
M = I
B
det M = 1
C
M2 = I
D
(adj M)2 = I
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