1
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Change Language
Let the curve y = y(x) be the solution of the differential equation, $${{dy} \over {dx}}$$ = 2(x + 1). If the numerical value of area bounded by the curve y = y(x) and x-axis is $${{4\sqrt 8 } \over 3}$$, then the value of y(1) is equal to _________.
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2
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E. If the length of EB is $$\alpha$$ + $${\sqrt 3 }$$ $$\beta$$, where $$\alpha$$, $$\beta$$ are integers, then $$\alpha$$ + $$\beta$$ is equal to ____________.
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3
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Change Language
Let f : R $$ \to $$ R be a continuous function such that f(x) + f(x + 1) = 2, for all x$$\in$$R.

If $${I_1} = \int\limits_0^8 {f(x)dx} $$ and $${I_2} = \int\limits_{ - 1}^3 {f(x)dx} $$, then the value of I1 + 2I2 is equal to ____________.
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4
JEE Main 2021 (Online) 16th March Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let f : (0, 2) $$ \to $$ R be defined as f(x) = log2$$\left( {1 + \tan \left( {{{\pi x} \over 4}} \right)} \right)$$. Then, $$\mathop {\lim }\limits_{n \to \infty } {2 \over n}\left( {f\left( {{1 \over n}} \right) + f\left( {{2 \over n}} \right) + ... + f(1)} \right)$$ is equal to ___________.
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