1
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
If the function f : R $$\to$$ R is defined by f(x) = |x| (x $$-$$ sin x), then which of the following statements is TRUE?
A
f is one-one, but NOT onto
B
f is onto, but NOT one-one
C
f is BOTH one-one and onto
D
f is NEITHER one-one NOR onto
2
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let the functions f : R $$\to$$ R and g : R $$\to$$ R be defined by

f(x) = ex $$-$$ 1 $$-$$ e$$-$$|x $$-$$ 1|

and g(x) = $${1 \over 2}$$(ex $$-$$ 1 + e1 $$-$$ x).

The the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and x = 0 is
A
$$(2 - \sqrt 3 ) + {1 \over 2}(e - {e^{ - 1}})$$
B
$$(2 + \sqrt 3 ) + {1 \over 2}(e - {e^{ - 1}})$$
C
$$(2 - \sqrt 3 ) + {1 \over 2}(e + {e^{ - 1}})$$
D
$$(2 + \sqrt 3 ) + {1 \over 2}(e + {e^{ - 1}})$$
3
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+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
$${{2 \over 5}}$$
4
JEE Advanced 2020 Paper 1 Offline
MCQ (Single Correct Answer)
+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
$${{1} \over {4}}$$
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