1
WB JEE 2022
+2
-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

A
$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
B
$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
C
$$f\left( {{4 \over 3}} \right) < {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) < {2 \over 3}$$
D
$$f\left( {{4 \over 3}} \right) > {4 \over 3}$$ and $$f\left( {{2 \over 3}} \right) > {2 \over 3}$$
2
WB JEE 2021
+1
-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
A
y = x
B
y = 2x
C
y = $${3 \over 2}$$ x
D
y = $${2 \over 3}$$ x
3
WB JEE 2021
+2
-0.5
The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the straight line y = 2 is
A
$${{20\sqrt 2 } \over 3}$$ sq. unit
B
$$10\sqrt 5$$ sq. unit
C
$${{10\sqrt 3 } \over 7}$$ sq. unit
D
$$10\sqrt 2$$ sq. unit
4
WB JEE 2020
+1
-0.25
If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = }$$
A
2$$\pi a$$
B
$$\pi a$$
C
$${1 \over 2}\pi a$$
D
$${1 \over 4}\pi a$$
EXAM MAP
Medical
NEET