1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $${1 \over n}$$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

A
$${7 \over {{2^{11}}}}$$
B
$${7 \over {{2^{12}}}}$$
C
$${3 \over {{2^{10}}}}$$
D
$${{13} \over {{2^{12}}}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of $${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}} \right)}}} \right)$$ is equal to :

A
$$ - {\pi \over 4}$$
B
$$ - {\pi \over 8}$$
C
$$ - {{5\pi } \over {12}}$$
D
$$ - {{4\pi } \over 9}$$
3
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The line y = x + 1 meets the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$ at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)2 is equal to :

A
20
B
12
C
11
D
8
4
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1
Change Language

Let $$A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)$$ and $$B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)$$. Then the number of elements in the set {(n, m) : n, m $$\in$$ {1, 2, .........., 10} and nAn + mBm = I} is ____________.

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