1
JEE Advanced 2020 Paper 1 Offline
+3
-1
Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x $$-$$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 $$-$$ 20x + 2020. Then the value of

ac(a $$-$$ c) + ad(a $$-$$ d) + bc(b $$-$$ c) + bd(b $$-$$ d) is
A
0
B
8000
C
8080
D
16000
2
JEE Advanced 2020 Paper 1 Offline
+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
3
JEE Advanced 2020 Paper 1 Offline
+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
$$(2 + \sqrt 3 ) + {1 \over 2}(e + {e^{ - 1}})$$
4
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
$${{2 \over 5}}$$
2023
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
EXAM MAP
Joint Entrance Examination