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Question 1:

In a circle with centre $\mathrm{O}, \mathrm{PR}$ and $\mathrm{QS}$ meet at the point $\mathrm{T}$, when produced, and $\mathrm{PQ}$ is a diameter. If $\angle R O S=42^{\circ}$, then the measure of $\angle P T Q$ is :

Question 2:

₹8,505 is divided among $P, Q$ and $R$ with their shares in the ratio of $1 \frac{1}{3}: 1$ $\frac{3}{4}: 2 \frac{1}{6}$. What is the difference of $P$ and $R$ 's shares (in ₹ )?.

Question 3:

Find the greatest number of four digits which is divisible by 14,30 and 42 .

Question 4:

The salaries of Ravi and Sumit are in the ratio 4: 5. If the salary of each is increased by ₹ 6,000 the new ratio becomes 35: 40. What will be Sumit's increased salary?

Question 5:

A man lent Rs. $\mathbf{4 5 0 0}$ at $30 \%$ compound interest per annum for 3 years. What is the difference between the interest earned by the man in the 2 nd year only and the interest earned by the man in the 3rd year only?

Question 6:

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 7:

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 8:

A policeman goes from his home to police station with his bike at a speed of $50 \mathrm{~km} / \mathrm{h}$, he is late by 30 minute. If he goes at $60 \mathrm{~km} / \mathrm{h}$, he is late by only 5 minute. Find the distance between his house and police station. (in $\mathrm{km}$ )

Question 9:

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 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 $40 \mathrm{~cm}$?