JEE Main 2019 (Online) 8th April Evening Slot | Definite Integrals and Applications of Integrals Question 228 | Mathematics

JEE Main 2019 (Online) 8th April Evening Slot

MCQ (Single Correct Answer)

-1

Let S($$\alpha $$) = {(x, y) : y² $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ $$\alpha $$} and A($$\alpha $$) is area of the region S($$\alpha $$). If for a $$\lambda $$, 0 < $$\lambda $$ < 4, A($$\lambda $$) : A(4) = 2 : 5, then $$\lambda $$ equals

$$2{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$

$$2{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$

$$4{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$

$$4{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

If $$f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$$ and g(x) = log_ex, (x > 0) then the value of integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}} $$ is

log_e3

log_e2

log_e1

log_ee

JEE Main 2019 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the region
A = { (x, y) $$ \in $$ R × R| 0 $$ \le $$ x $$ \le $$ 3, 0 $$ \le $$ y $$ \le $$ 4, y $$ \le $$ x² + 3x} is :

$${{59} \over 6}$$

$${{26} \over 3}$$

$${{53} \over 6}$$

JEE Main 2019 (Online) 12th January Evening Slot

MCQ (Single Correct Answer)

-1

The integral $$\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,$$ log_e x dx is equal to :

$$ - {1 \over 2} + {1 \over e} - {1 \over {2{e^2}}}$$

$${3 \over 2} - e - {1 \over {2{e^2}}}$$

$${1 \over 2} - e - {1 \over {{e^2}}}$$

$${3 \over 2} - {1 \over e} - {1 \over {2{x^2}}}$$

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