WB JEE 2024 | Application of Integration Question 10 | Mathematics

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WB JEE 2024

MCQ (Single Correct Answer)

-0.25

Consider the function $$\mathrm{f}(x)=(x-2) \log _{\mathrm{e}} x$$. Then the equation $$x \log _{\mathrm{e}} x=2-x$$

has at least one root in $$(1,2)$$

has no root in $$(1,2)$$

is not at all solvable

has infinitely many roots in $$(-2,1)$$

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is

$${{11} \over 9}$$ sq. unit

$${{32} \over 3}\sqrt 6 $$ sq. unit

$${{16} \over 3}$$ sq. unit

$${{24} \over 5}$$ sq. unit

WB JEE 2022

MCQ (Single Correct Answer)

-0.5

Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} } $$ and f (0) = 0. Then

$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$

$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$

$$f\left( {{4 \over 3}} \right) < {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) < {2 \over 3}$$

$$f\left( {{4 \over 3}} \right) > {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) > {2 \over 3}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

The straight the through the origin which divides the area formed by the curves y = 2x $$-$$ x², y = 0 and x = 1 into two equal halves is

y = x

y = 2x

y = $${3 \over 2}$$ x

y = $${2 \over 3}$$ x

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