1
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$P = \left[ {\matrix{ 1 & 0 \cr {{1 \over 2}} & 1 \cr } } \right]$$, then P50 is :
A
$$\left[ {\matrix{ 1 & 0 \cr {25} & 1 \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & {50} \cr 0 & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & {25} \cr 0 & 1 \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & 0 \cr {50} & 1 \cr } } \right]$$
2
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let X be a random variable such that the probability function of a distribution is given by $$P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$$. Then the mean of the distribution and P(X is positive and even) respectively are :
A
$${3 \over 8}$$ and $${1 \over 8}$$
B
$${3 \over 4}$$ and $${1 \over 8}$$
C
$${3 \over 4}$$ and $${1 \over 9}$$
D
$${3 \over 4}$$ and $${1 \over 16}$$
3
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $${}^n{P_r} = {}^n{P_{r + 1}}$$ and $${}^n{C_r} = {}^n{C_{r - 1}}$$, then the value of r is equal to :
A
1
B
4
C
2
D
3
4
JEE Main 2021 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y = y(x) be the solution of the differential

equation xdy = (y + x3 cosx)dx with y($$\pi$$) = 0, then $$y\left( {{\pi \over 2}} \right)$$ is equal to :
A
$${{{\pi ^2}} \over 4} + {\pi \over 2}$$
B
$${{{\pi ^2}} \over 2} + {\pi \over 4}$$
C
$${{{\pi ^2}} \over 2} - {\pi \over 4}$$
D
$${{{\pi ^4}} \over 4} - {\pi \over 2}$$
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