1
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Change Language
If (2021)3762 is divided by 17, then the remainder is __________.
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2
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Change Language
Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $$\alpha$$, only E2 occurs is $$\beta$$ and only E3 occurs is $$\gamma$$. Let 'p' denote the probability of none of events occurs that satisfies the equations
($$\alpha$$ $$-$$ 2$$\beta$$)p = $$\alpha$$$$\beta$$ and ($$\beta$$ $$-$$ 3$$\gamma$$)p = 2$$\beta$$$$\gamma$$. All the given probabilities are assumed to lie in the interval (0, 1).

Then, $$\frac{Probability\ of\ occurrence\ of\ E_{1}}{Probability\ of\ occurrence\ of\ E_{3}} $$ is equal to _____________.
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3
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Change Language
The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y $$ \le $$ 100 and 4x + 3y $$ \le $$ 75 for x $$ \ge $$ 0 and y $$ \ge $$ 0 is __________.
Your input ____
4
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
Change Language
If [ . ] represents the greatest integer function, then the value of


$$\left| {\int\limits_0^{\sqrt {{\pi \over 2}} } {\left[ {[{x^2}] - \cos x} \right]dx} } \right|$$ is ____________.
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