1
WB JEE 2024
+1
-0.25

The area bounded by the curves $$x=4-y^2$$ and the Y-axis is

A
16 sq. unit
B
$$\frac{32}{3}$$ sq. unit
C
$$\frac{16}{3}$$ sq. unit
D
32 sq. unit
2
WB JEE 2024
+1
-0.25

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

A
has at least one root in $$(1,2)$$
B
has no root in $$(1,2)$$
C
is not at all solvable
D
has infinitely many roots in $$(-2,1)$$
3
WB JEE 2022
+1
-0.25

If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to

A
$$C{e^{{{{x^2}} \over 2}}}$$ (where C is the constant of integration)
B
$$C{e^{{x^2}}}$$ (where C is the constant of integration)
C
$$C{e^{2{x^2}}}$$ (where C is the constant of integration)
D
$$C{e^{{{{x^2}} \over 3}}}$$ (where C is the constant of integration)
4
WB JEE 2022
+1
-0.25

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

A
$${{11} \over 9}$$ sq. unit
B
$${{32} \over 3}\sqrt 6$$ sq. unit
C
$${{16} \over 3}$$ sq. unit
D
$${{24} \over 5}$$ sq. unit
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