1
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $${1 \over 2}$$ and probability of occurrence of 0 at the odd place be $${1 \over 3}$$. Then the probability that '10' is followed by '01' is equal to :
A
$${1 \over 18}$$
B
$${1 \over 3}$$
C
$${1 \over 9}$$
D
$${1 \over 6}$$
2
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$ \to $$ R be defined as f(x) = e$$-$$xsinx. If F : [0, 1] $$ \to $$ R is a differentiable function with that F(x) = $$\int_0^x {f(t)dt} $$, then the value of $$\int_0^1 {(F'(x) + f(x)){e^x}dx} $$ lies in the interval
A
$$\left[ {{{331} \over {360}},{{334} \over {360}}} \right]$$
B
$$\left[ {{{330} \over {360}},{{331} \over {360}}} \right]$$
C
$$\left[ {{{335} \over {360}},{{336} \over {360}}} \right]$$
D
$$\left[ {{{327} \over {360}},{{329} \over {360}}} \right]$$
3
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S1, S2 and S3 be three sets defined as

S1 = {z$$\in$$C : |z $$-$$ 1| $$ \le $$ $$\sqrt 2 $$}

S2 = {z$$\in$$C : Re((1 $$-$$ i)z) $$ \ge $$ 1}

S3 = {z$$\in$$C : Im(z) $$ \le $$ 1}

Then the set S1 $$\cap$$ S2 $$\cap$$ S3 :
A
has exactly three elements
B
is a singleton
C
has infinitely many elements
D
has exactly two elements
4
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of solutions of the equation

$${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}$$, for x$$\in$$[$$-$$1, 1], and [x] denotes the greatest integer less than or equal to x, is :
A
0
B
Infinite
C
2
D
4
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