JEE Main 2021 (Online) 24th February Morning Slot | Definite Integrals and Applications of Integrals Question 179 | Mathematics

JEE Main 2021 (Online) 24th February Morning Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$$ is equal to :

$${1 \over {15}}$$

$${2 \over 3}$$

$${3 \over 2}$$

JEE Main 2021 (Online) 24th February Morning Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the parabola y² = 9x, is :

$$12\pi - 3\sqrt 3 $$

$$24\pi + 3\sqrt 3 $$

$$24\pi - 3\sqrt 3 $$

$$12\pi + 3\sqrt 3 $$

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 :

$${8 \over 3}$$

$${4 \over 3}$$

$${7 \over 2}$$

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

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