1
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.

Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve
A
(x + y)2 = 3xy
B
x2/3 + y2/3 = 24/3
C
x2 + y2 = 2xy
D
x2 + y2 = x2y2
2
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on Paragraph "A", the question given below is one of them)

The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is
A
$${3 \over {40}}$$
B
$${1 \over 8}$$
C
$${7 \over 40}$$
D
$${1 \over 5}$$
3
JEE Advanced 2018 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on Paragraph "A", the question given below is one of them)

For i = 1, 2, 3, 4, let Ti denote the event that the students Si and Si+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event $${T_1} \cap {T_2} \cap {T_3} \cap {T_4}$$ is
A
$${1 \over {15}}$$
B
$${1 \over {10}}$$
C
$${7 \over {60}}$$
D
$${1 \over {5}}$$
4
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
The potential energy of a particle of mass $$m$$ at a distance $$r$$ from a fixed point $$O$$ is given by $$V\left( r \right) = k{r^2}/2,$$ where $$k$$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $$R$$ about the point $$O$$. If $$v$$ is the speed of the particle and $$L$$ is the magnitude of its angular momentum about $$O,$$ which of the following statements is (are) true?
A
$$v = \sqrt {{k \over {2m}}} R$$
B
$$v = \sqrt {{k \over m}} R$$
C
$$L = \sqrt {mk} {R^2}$$
D
$$L = \sqrt {{{mk} \over 2}} {R^2}$$
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