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.

JEE Advanced 2018 Paper 2 Offline Mathematics - Permutations and Combinations Question 7 English
The correct option is
A
P $$ \to $$ 4; Q $$ \to $$ 6; R $$ \to $$ 2; S $$ \to $$ 1
B
P $$ \to $$ 1; Q $$ \to $$ 4; R $$ \to $$ 2; S $$ \to $$ 3
C
P $$ \to $$ 4; Q $$ \to $$ 6; R $$ \to $$ 5; S $$ \to $$ 2
D
P $$ \to $$ 4; Q $$ \to $$ 2; R $$ \to $$ 3; S $$ \to $$ 1
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
A
P $$ \to $$ 4 ; Q $$ \to $$ 2 ; R $$ \to $$ 1 ; S $$ \to $$ 3
B
P $$ \to $$ 4 ; Q $$ \to $$ 3 ; R $$ \to $$ 1 ; S $$ \to $$ 2
C
P $$ \to $$ 4 ; Q $$ \to $$ 1 ; R $$ \to $$ 3 ; S $$ \to $$ 2
D
P $$ \to $$ 3 ; Q $$ \to $$ 4 ; R $$ \to $$ 2 ; S $$ \to $$ 1
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) $${f_4}(x) = \left\{ \matrix{ {x^2}\sin \left( {{1 \over x}} \right)\,if\,x \ne 0 \hfill \cr 0\,if\,x = 0 \hfill \cr} \right.$$

JEE Advanced 2018 Paper 2 Offline Mathematics - Limits, Continuity and Differentiability Question 33 English
A
P $$ \to $$ 2 ; Q $$ \to $$ 3 ; R $$ \to $$ 1 ; S $$ \to $$ 4
B
P $$ \to $$ 4 ; Q $$ \to $$ 1 ; R $$ \to $$ 2 ; S $$ \to $$ 3
C
P $$ \to $$ 4 ; Q $$ \to $$ 2 ; R $$ \to $$ 1 ; S $$ \to $$ 3
D
P $$ \to $$ 2 ; Q $$ \to $$ 1 ; R $$ \to $$ 4 ; S $$ \to $$ 3
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?
A
The force applied on the particle is constant
B
The speed of the particle is proportional to time
C
The distance of the particle from the origin increases linearly with time
D
The force is conservative
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