JEE Main 2020 (Online) 6th September Evening Slot | Definite Integrals and Applications of Integrals Question 182 | Mathematics

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JEE Main 2020 (Online) 6th September Evening Slot

MCQ (Single Correct Answer)

-1

The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :

e(4e + 1)

e(2e – 1)

e(4e – 1)

4e² – 1

JEE Main 2020 (Online) 6th September Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region enclosed
by the curves y = x² – 1 and y = 1 – x² is equal to :

$${8 \over 3}$$

$${4 \over 3}$$

$${7 \over 2}$$

$${{16} \over 3}$$

JEE Main 2020 (Online) 6th September Morning Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region
A = {(x, y) : |x| + |y| $$ \le $$ 1, 2y² $$ \ge $$ |x|}

$${1 \over 6}$$

$${5 \over 6}$$

$${1 \over 3}$$

$${7 \over 6}$$

JEE Main 2020 (Online) 6th September Morning Slot

MCQ (Single Correct Answer)

-1

If I₁ = $$\int\limits_0^1 {{{\left( {1 - {x^{50}}} \right)}^{100}}} dx$$ and
I₂ = $$\int\limits_0^1 {{{\left( {1 - {x^{50}}} \right)}^{101}}} dx$$ such
that I₂ = $$\alpha $$I₁ then $$\alpha $$ equals to :

$${{5051} \over {5050}}$$

$${{5050} \over {5051}}$$

$${{5050} \over {5049}}$$

$${{5049} \over {5050}}$$

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