JEE Main 2021 (Online) 27th August Evening Shift | Definite Integrals and Applications of Integrals Question 116 | Mathematics

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-1

The area of the region bounded by the parabola (y $$-$$ 2)² = (x $$-$$ 1), the tangent to it at the point whose ordinate is 3 and the x-axis is :

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-1

The value of the integral $$\int\limits_0^1 {{{\sqrt x dx} \over {(1 + x)(1 + 3x)(3 + x)}}} $$ is :

$${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 2}} \right)$$

$${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 6}} \right)$$

$${\pi \over 8}\left( {1 - {{\sqrt 3 } \over 6}} \right)$$

$${\pi \over 4}\left( {1 - {{\sqrt 3 } \over 2}} \right)$$

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

If $${U_n} = \left( {1 + {1 \over {{n^2}}}} \right)\left( {1 + {{{2^2}} \over {{n^2}}}} \right)^2.....\left( {1 + {{{n^2}} \over {{n^2}}}} \right)^n$$, then $$\mathop {\lim }\limits_{n \to \infty } {({U_n})^{{{ - 4} \over {{n^2}}}}}$$ is equal to :

$${{{e^2}} \over {16}}$$

$${4 \over e}$$

$${{16} \over {{e^2}}}$$

$${4 \over {{e^2}}}$$

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

$$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx} $$ is equal to :

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