SSC CGL MATHS QUIZ-30

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 :

₹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 ₹ )?.

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?

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?

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?

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:

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 $\mathrm{km}$ )

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

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 $40 \mathrm{~cm}$?