Monica Capoor Solutions for Chapter: Half-Yearly Test Paper (Based on Chapters 1–12), Exercise 1: HALF-YEARLY TEST PAPER (Based on Chapters 1-12)

A man invested $₹3500$, a part of it at an annual interest rate of $12\%$ and the rest at $14\%.$ If after a year, he received $₹450$ as annual interest, how much did he invest at each rate?
 

A fruit vendor buys some oranges at the rate of $₹5$ per orange. He also buys an equal number of bananas at the rate of $₹2$ per banana. He makes a profit of $20\%$ on oranges and $15\%$ on bananas. At the end of the day, all the fruits are sold out. His total profit is $₹390$. Find the number of oranges purchased.

If $\frac{3}{x-1}-\frac{1}{x-3}=\frac{2}{x-2}$, then the value of $x$ is $\frac{a}{2}$. Find the value of $a$.

Find the angle measure of $x$ in the given figure.

Three angles of a quadrilateral are in the ratio $2:3:7$. The mean of these angles is $64°$. Find the fourth angle.

In the given figure, $\mathrm{OC}$ and $\mathrm{OD}$ are bisectors of $\angle \mathrm{BCD}$ and $\angle \mathrm{ADC}$ respectively. If $\angle \mathrm{A}=110°$ and $\angle \mathrm{B}=x°$, find the value of $x$.

The diagonals of a quadrilateral are of lengths $10 \mathrm{cm}$ and $24 \mathrm{cm}$ If the diagonals bisect each other at right angles, find the length of each side of the quadrilateral. What special name can you give to this quadrilateral?

The following data consists of the hours spent each week watching television, as reported by a group of $38$ teenagers.

$$\begin{gathered} 4, 25, 6, 20, 18, 13, 3, 16, 0, 4, 19, 28, 11, \\ 7, 19, 3, 17, 15, 31, 27, 10, 6, 22, 18, 25, 8, \\ 5, 19, 12, 17, 20, 32, 9, 21, 25, 36, 17, 20 \end{gathered}$$

Construct a table to group this data using intervals of $0-5, 5-10\dots$ and so on.