1
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respectively, where O(0, 0, 0) is the origin. Let $$S\left( {{1 \over 2},{1 \over 2},{1 \over 2}} \right)$$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If p = SP, q = SQ, r = SR and t = ST, then the value of |(p $$ \times $$ q) $$ \times $$ (r $$ \times $$ t)| is ............
Your input ____
2
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let $$X = {({}^{10}{C_1})^2} + 2{({}^{10}{C_2})^2} + 3{({}^{10}{C_3})^2} + ... + 10{({}^{10}{C_{10}})^2}$$,

where $${}^{10}{C_r}$$, r $$ \in $${1, 2, ..., 10} denote binomial coefficients. Then, the value of $${1 \over {1430}}X$$ is ..........
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3
JEE Advanced 2018 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $${E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}$$ and


$${E_2} = \left\{ \matrix{ x \in {E_1}:{\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right) \hfill \cr is\,a\,real\,number \hfill \cr} \right\}$$

(Here, the inverse trigonometric function $${\sin ^{ - 1}}$$ x assumes values in $$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$.).

Let f : E1 $$ \to $$ R be the function defined by f(x) = $${{{\log }_e}\left( {{x \over {x - 1}}} \right)}$$ and g : E2 $$ \to $$ R be the function defined by g(x) = $${\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right)$$.

JEE Advanced 2018 Paper 2 Offline Mathematics - Functions Question 19 English
The correct option is :
A
P $$ \to $$ 4; Q $$ \to $$ 2; R $$ \to $$ 1 ; S $$ \to $$ 1
B
P $$ \to $$ 3; Q $$ \to $$ 3; R $$ \to $$ 6 ; S $$ \to $$ 5
C
P $$ \to $$ 4; Q $$ \to $$ 2; R $$ \to $$ 1 ; S $$ \to $$ 6
D
P $$ \to $$ 4; Q $$ \to $$ 3; R $$ \to $$ 6 ; S $$ \to $$ 5
4
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
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