4 Marks

Question 14 Marks

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is $\tan ^{-1}(0.5)$. Water is poured into it at a constant rate 5 cubic meter per minute. Find the rate at which the level of water rising at the instant when the depth of water in the tank is 10 meter.

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Question 24 Marks

The population of a village increase continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20,000 in 1999 and 25,000 in the year 2004, what will be the population of the village in 2009?

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Question 34 Marks

Solve the differential equation $y e^{\frac{x}{y}} d x=\left(x e^{\frac{x}{y}}+y^2\right) d y(y \neq 0)$.

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Question 44 Marks

Evaluate definite integral $\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x$.

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Question 54 Marks

Find the angle between two curves $y^2=4 a x$ and $x^2=4 b y$.

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Question 64 Marks

Using properties of determinant prove that$
\left|\begin{array}{ccc}
1 & 1+p & 1+p+q \\
2 & 3+2 p & 4+3 p+2 q \\
3 & 6+3 p & 10+6 p+3 q
\end{array}\right|=1
$

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Maths 4 Marks

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