1
BITSAT 2023
+3
-1

Water is being filled at the rate of $$1 \mathrm{~cm}^3 / \mathrm{s}$$ in a right circular conical vessel (vertex downwards) of height $$35 \mathrm{~cm}$$ and diameter $$14 \mathrm{~cm}$$. When the height of the water levels is $$10 \mathrm{~cm}$$, the rate (in $$\mathrm{cm}^2 / \mathrm{sec}$$) at which the wet conical surface area of the vessel increases is

A
$$\frac{\sqrt{26}}{10}$$
B
5
C
$$\frac{\sqrt{21}}{5}$$
D
$$\frac{\sqrt{26}}{5}$$
2
BITSAT 2022
+3
-1

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then the lengths of its side are

A
70 ft and 110 ft
B
80 ft and 120 ft
C
35 ft and 110 ft
D
35 ft and 120 ft
3
BITSAT 2022
+3
-1

A spherical balloon is filled with 4500$$\pi$$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72$$\pi$$ cubic meters per minute then the rate (in meters per minute) at which the radius of the balloon decreases 49 min after the leakage began is

A
$$\frac{9}{7}$$
B
$$\frac{7}{9}$$
C
$$\frac{2}{9}$$
D
9
4
BITSAT 2021
+3
-1

The slope of the tangent to the curve x = t2 + 3t $$-$$ 8, y = 2t2 $$-$$ 2t $$-$$ 5 at the point t = 2 is

A
$${7 \over 6}$$
B
$${5 \over 6}$$
C
$${6 \over 7}$$
D
1
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