1
JEE Advanced 2018 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5.
(i) Let $$\alpha $$1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.
(ii) Let $$\alpha $$2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.
i) Let $$\alpha $$3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.
(iv) Let $$\alpha $$4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls such that both M1 and G1 are NOT in the committee together.
The correct option is
(i) Let $$\alpha $$1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.
(ii) Let $$\alpha $$2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.
i) Let $$\alpha $$3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.
(iv) Let $$\alpha $$4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls such that both M1 and G1 are NOT in the committee together.
The correct option is
2
JEE Advanced 2018 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60$$^\circ $$ at one of its vertices N. Let the area of the $$\Delta $$LMN be $$4\sqrt 3 $$.
List - I | List - II | ||
---|---|---|---|
P. | The length of the conjugate axis of H is | 1. | 8 |
Q. | The eccentricity of H is | 2. | $${4 \over {\sqrt 3 }}$$ |
R. | The distance between the foci of H is | 3. | $${2 \over {\sqrt 3 }}$$ |
S. | The length of the latus rectum of H is | 4. | 4 |
3
JEE Advanced 2018 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $${f_1}:R \to R,\,{f_2}:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R,\,{f_3}:( - 1,{e^{\pi /2}} - 2) \to R$$ and $${f_4}:R \to R$$ be functions defined by
(i) $${f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )$$,
(ii) $${f_2}(x) = \left\{ \matrix{ {{|\sin x|} \over {\tan { - ^1}x}}if\,x \ne 0,\,where \hfill \cr 1\,if\,x = 0 \hfill \cr} \right.$$
the inverse trigonometric function tan$$-$$1x assumes values in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$,
(iii) $${f_3}(x) = [\sin ({\log _e}(x + 2))]$$, where for $$t \in R,\,[t]$$ denotes the greatest integer less than or equal to t,
(iv) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$
(i) $${f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )$$,
(ii) $${f_2}(x) = \left\{ \matrix{ {{|\sin x|} \over {\tan { - ^1}x}}if\,x \ne 0,\,where \hfill \cr 1\,if\,x = 0 \hfill \cr} \right.$$
the inverse trigonometric function tan$$-$$1x assumes values in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$,
(iii) $${f_3}(x) = [\sin ({\log _e}(x + 2))]$$, where for $$t \in R,\,[t]$$ denotes the greatest integer less than or equal to t,
(iv) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$
4
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A particle of mass $$m$$ is initially at rest at the origin. It is subjected to a force and starts moving along the $$x$$-axis. Its kinetic energy $$K$$ changes with time as $$dK/dt = \gamma t,$$ where $$\gamma $$ is a positive constant of appropriate dimensions. Which of a positive constant of appropriate dimensions. Which of the following statement is (are) true?
Paper analysis
Total Questions
Chemistry
18
Mathematics
18
Physics
18
More papers of JEE Advanced
JEE Advanced 2023 Paper 2 Online
JEE Advanced 2023 Paper 1 Online
JEE Advanced 2022 Paper 2 Online
JEE Advanced 2022 Paper 1 Online
JEE Advanced 2021 Paper 2 Online
JEE Advanced 2021 Paper 1 Online
JEE Advanced 2020 Paper 2 Offline
JEE Advanced 2020 Paper 1 Offline
JEE Advanced 2019 Paper 2 Offline
JEE Advanced 2019 Paper 1 Offline
JEE Advanced 2018 Paper 2 Offline
JEE Advanced 2018 Paper 1 Offline
JEE Advanced 2017 Paper 2 Offline
JEE Advanced 2017 Paper 1 Offline
JEE Advanced 2016 Paper 2 Offline
JEE Advanced 2016 Paper 1 Offline
JEE Advanced 2015 Paper 2 Offline
JEE Advanced 2015 Paper 1 Offline
JEE Advanced 2014 Paper 2 Offline
JEE Advanced 2014 Paper 1 Offline
JEE Advanced 2013 Paper 2 Offline
JEE Advanced 2013 Paper 1 Offline
IIT-JEE 2012 Paper 2 Offline
IIT-JEE 2012 Paper 1 Offline
IIT-JEE 2011 Paper 1 Offline
IIT-JEE 2011 Paper 2 Offline
IIT-JEE 2010 Paper 1 Offline
IIT-JEE 2010 Paper 2 Offline
IIT-JEE 2009 Paper 2 Offline
IIT-JEE 2009 Paper 1 Offline
IIT-JEE 2008 Paper 2 Offline
IIT-JEE 2008 Paper 1 Offline
IIT-JEE 2007
IIT-JEE 2007 Paper 2 Offline
IIT-JEE 2006
IIT-JEE 2006 Screening
IIT-JEE 2005 Screening
IIT-JEE 2005
IIT-JEE 2004
IIT-JEE 2004 Screening
IIT-JEE 2003
IIT-JEE 2003 Screening
IIT-JEE 2002
IIT-JEE 2002 Screening
IIT-JEE 2001
IIT-JEE 2001 Screening
IIT-JEE 2000
IIT-JEE 2000 Screening
IIT-JEE 1999
IIT-JEE 1999 Screening
IIT-JEE 1998
IIT-JEE 1998 Screening
IIT-JEE 1997
IIT-JEE 1996
IIT-JEE 1995
IIT-JEE 1995 Screening
IIT-JEE 1994
IIT-JEE 1993
IIT-JEE 1992
IIT-JEE 1991
IIT-JEE 1990
IIT-JEE 1989
IIT-JEE 1988
IIT-JEE 1987
IIT-JEE 1986
IIT-JEE 1985
IIT-JEE 1984
IIT-JEE 1983
IIT-JEE 1982
IIT-JEE 1981
IIT-JEE 1980
IIT-JEE 1979
IIT-JEE 1978
JEE Advanced
Papers
2020
2019
1997
1996
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978