Monica Capoor Solutions for Chapter: Annual Test Paper, Exercise 1: ANNUAL TEST PAPER

Given that $\sqrt[3]{175616}=56$ find the value of $\sqrt[3]{0.000175616}+\sqrt[3]{0.175616}+\sqrt[3]{175.616}$

On selling two cameras for $₹500$ each, a person made no loss or gain. If he had sold one camera at $25\%$ gain, then at what loss per cent did he sell the other camera? (Round off the answer upto $2$ decimal places).

During the first hour, the bacteria in a culture increased by $4\%$, during the second it diminished by $4\%$ and during the third hour it again increased by $5\%$. If the number of bacteria at the end of the third hour is $3.276\times {10}^{14},$ find the bacteria originally present in the sample. If the answer obtained is $3.125\times {10}^k$, then find the value of $k$.

In the given figure, if the area of the given hexagonal field $\mathrm{ABCDEF}$ in which $\mathrm{BP}, \mathrm{CQ}, \mathrm{ER}$ and $\mathrm{FS}$ are perpendicular to $\mathrm{AD}$ and $\mathrm{AP}=60 \mathrm{m}$, $\mathrm{AS} = 100 \mathrm{m}$, $\mathrm{AQ} =180 \mathrm{m}$, $\mathrm{AR} =210 \mathrm{m}$, $\mathrm{AD} = 270 \mathrm{m}$, $\mathrm{BP}=50 \mathrm{m}$, $\mathrm{CQ}=60 \mathrm{m}$, $\mathrm{ER}=40 \mathrm{m}$ and $\mathrm{FS}=60 \mathrm{m}$ is $k {\mathrm{m}}^2$, then find the value of $k$.

Water flows out through a circular pipe, whose internal diameter is $2 \mathrm{cm},$ at the rate of $0.8 \mathrm{m}$ per second into a cylindrical tank, the radius of whose base is $40 \mathrm{cm}.$ By how much will the level of water rise in one and a half hour?

A cistern can be filled by two inlet pipes $A$ and $B$ in $12$ hours and $8$ hours respectively. The full cistern can be emptied by an outlet pipe $C$ in$6$ hours. If all the pipes are opened at the same time, in how much time will the empty cistern be filled up?

An air balloon has two punctures. The first puncture alone would have deflated the balloon in $6$ minutes and the second alone would have deflated it in $9$ minutes. If the air leaks out at a constant rate, how long does it take both the punctures together to deflate the air balloon? Write the answer in a mixed fraction in the number of minutes.

Simplify: $\frac{x}{a^2-b^2}\times \frac{(a+b{)}^2}{a-b}÷\frac{ax+bx}{(a-b{)}^2}$