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Question 1:

What is the ratio of the area of an equilateral triangle of side 2a units to that of a square, whose diagonal is 2a units?

Question 2:

A copper sphere of diameter $18 \mathrm{~cm}$ is drawn into a wire of diameter $4 \mathrm{~mm}$. The length of the wire, in metre is:

Question 3:

A field is in the form of a rectangle of length $18 \mathrm{~m}$ and width $15 \mathrm{~m}$ deep, in a corner of the field a pit is dug of area $7.5 \times 6$ and $0.8 \mathrm{~m}$ deep and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is:

Question 4:

If the simple interest on a certain sum of money borrowed for 4 years at $8.5 \%$ per annum exceeds the simple interest on the same sum for 3 years at $10.5 \%$ per annum by Rs. 1000 , then the sum borrowed is:

Question 5:

PQRS is a rectangle. The ratio of the sides PQ and $Q R$ is $4: 3$. If the length of the diagonal $\mathrm{PR}$ is $20 \mathrm{~cm}$, then what is the area (in $\mathrm{cm}^{2}$ ) of the rectangle?

Question 6:

A rectangular lawn of length $30 \mathrm{~m}$ and breadth $15 \mathrm{~m}$ is to be surrounded externally by a path which is $3 \mathrm{~m}$ wide. Find the cost of making the path at the rate of Rs.20 per $\mathrm{m}^{2}$.

Question 7:

The simplest value $\frac{3}{4} \div \frac{5}{8} \div \frac{3}{5}$ of $\frac{5}{6}$ of $\frac{7}{10}$ is:

Question 8:

If $x+\frac{1}{x}=3$ and $x^{2}+\frac{1}{x^{3}}=9$ Find the value of $x^{3}+\frac{1}{x^{2}}$?

Question 9:

A hollow cylinder is made up of steal. The difference in its outer and inner CSA is 132 $\mathrm{cm}^{2}$. Height of cylinder is $21 \mathrm{~cm}$ and sum of its inner and outer radius is also $21 \mathrm{~cm}$. Then find the TSA of the hollow cylinder (in $\mathrm{cm}^{2}$ )

Question 10:

How many small solid spheres of radius $5 \mathrm{~mm}$ can be made from a solid metallic cone of base radius $21 \mathrm{~cm}$ and height of $40 \mathrm{~cm}$?