Choose the incorrect statement
Question: Choose the incorrect statement from the following. A good fuel is one which (a) is readily available (b) produces a large amount of heat (c) leaves behind many undesirable substances (d) burns easily in air at a moderate rate Solution: (c) A good fuel does not produce any harmful gases or leaves any residue after burning. So, incorrect statement is option (c)....
Read More →Which one among the following
Question: Which one among the following is considered as the cleanest fuel? (a) Cowdung cake (b) Petrol (c) Kerosene (d) Hydrogen gas Solution: (d) Hydrogen gas is considered as cleanest fuel. Unlike carbon based fuels, hydrogen produces no harmful by-products on combustion. Only energy and clean water are produced....
Read More →The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference.
Question: The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference. Solution: LetrbetheradiusandCbethecircumferenceofthecircleatanytimet.Then, $C=2 \pi r$ $\Rightarrow \frac{d C}{d t}=2 \pi \frac{d r}{d t}$ $\Rightarrow \frac{d C}{d t}=2 \pi \times 0.5$ $\left[\because \frac{d r}{d t}=0.5 \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d C}{d t}=\pi \mathrm{cm} / \mathrm{sec}$...
Read More →In villages, people use wood as fuel because
Question: In villages, people use wood as fuel because (a) it is considered to be an ideal fuel (b) of its easy availability and low cost (c) it is environment friendly (d) it catches fire easily Solution: (b) In villages, people use wood as fuel because of its easy availability and low cost....
Read More →The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference.
Question: The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference. Solution: LetrbetheradiusandCbethecircumferenceofthecircleatanytimet.Then, $C=2 \pi r$ $\Rightarrow \frac{d C}{d t}=2 \pi \frac{d r}{d t}$ $\Rightarrow \frac{d C}{d t}=2 \pi \times 0.5$ $\left[\because \frac{d r}{d t}=0.5 \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d C}{d t}=\pi \mathrm{cm} / \mathrm{sec}$...
Read More →The calorific value of a fuel is expressed
Question: The calorific value of a fuel is expressed in a unit called (a) kilojoule per litre (b) kilogram per millilitre (c) kilojoule per gram (d) kilojoule per kilogram Solution: (d) The calorific value of a fuel is expressed in the unit of kilojoule per kilogram (kJ/kg),...
Read More →The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter
Question: The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter Solution: LetxbethesideandPbetheperimeterofthesquareatanytimet. Then, $P=4 x$ $\Rightarrow \frac{d P}{d t}=4 \frac{d x}{d t}$ $\Rightarrow \frac{d P}{d t}=4 \times 0.1$ $\left[\because \frac{d x}{d t}=0.1 \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d P}{d t}=0.4 \mathrm{~cm} / \mathrm{sec}$...
Read More →Choose the incorrect statement
Question: Choose the incorrect statement from the following. Forest fires are usually due to (a) carelessness of humans (b) heat of Sun (c) cutting of trees (d) lightning strike Solution: (c) Forest fires are not due to cutting of trees,...
Read More →The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter
Question: The side of a square is increasing at the rate of 0.1 cm/sec. Find the rate of increase of its perimeter Solution: LetxbethesideandPbetheperimeterofthesquareatanytimet. Then, $P=4 x$ $\Rightarrow \frac{d P}{d t}=4 \frac{d x}{d t}$ $\Rightarrow \frac{d P}{d t}=4 \times 0.1$ $\left[\because \frac{d x}{d t}=0.1 \mathrm{~cm} / \mathrm{sec}\right]$ $\Rightarrow \frac{d P}{d t}=0.4 \mathrm{~cm} / \mathrm{sec}$...
Read More →Choose the correct statement about
Question: Choose the correct statement about inflammable substances from the following. They have (a) low ignition temperature and cannot catch fire easily (b) high ignition temperature and can catch fire easily (c) low ignition temperature and can catch fire easily (d) high ignition temperature and cannot catch fire easily Solution: (c) Inflammable substances have low ignition temperature and can catch fire easily....
Read More →The substance expected to have
Question: The substance expected to have the highest ignition temperature out of the following is (a) kerosene (b) petrol (c) coal (d) alcohol Solution: (c) Coal has the highest ignition temperature. Note The lowest temperature at which a substance catches fire and starts burning, is called its ignition temperature. Kerosene, petrol and alcohol have low ignition temperature....
Read More →The sides of an equilateral triangle are increasing at the rate of 2 cm/sec.
Question: The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms? Solution: LetxbethesideandAbetheareaoftheequilateraltriangleatanytimet.Then, $A=\frac{\sqrt{3}}{4} x^{2}$ $\Rightarrow \frac{d A}{d t}=2 \times \frac{\sqrt{3}}{4} x \frac{d x}{d t}$ $\Rightarrow \frac{d A}{d t}=\frac{\sqrt{3}}{2} \times 2 \times 10$ $\Rightarrow \frac{d A}{d t}=10 \sqrt{3} \mathrm{~cm}^{2} / \mathrm{sec}$...
Read More →The sides of an equilateral triangle are increasing at the rate of 2 cm/sec.
Question: The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. How far is the area increasing when the side is 10 cms? Solution: LetxbethesideandAbetheareaoftheequilateraltriangleatanytimet.Then, $A=\frac{\sqrt{3}}{4} x^{2}$ $\Rightarrow \frac{d A}{d t}=2 \times \frac{\sqrt{3}}{4} x \frac{d x}{d t}$ $\Rightarrow \frac{d A}{d t}=\frac{\sqrt{3}}{2} \times 2 \times 10$ $\Rightarrow \frac{d A}{d t}=10 \sqrt{3} \mathrm{~cm}^{2} / \mathrm{sec}$...
Read More →If a person’s clothes catch fire,
Question: If a persons clothes catch fire, the best way to extinguish the fire is to (a) throw water on the clothes (b) use fire extinguisher (c) cover the person with a woollen blanket (d) cover the person with a polythene sheet Solution: (c) Cover the person with a woollen blanket so that the supply of air to the burning clothes is cut off and hence, the burning (or fire) stops....
Read More →On placing an inverted tumbler over a burning candle,
Question: On placing an inverted tumbler over a burning candle, the flame extinguishes after some time. This is because of non-availability of (a) oxygen (b) water vapours (c) carbon dioxide (d) wax Solution: (a) The flame extinguishes because of non-availability of oxygen. Air or oxygen is necessary for combustion....
Read More →The volume of a sphere is increasing at 3 cubic centimeter per second.
Question: The volume of a sphere is increasing at 3 cubic centimeter per second. Find the rate of increase of the radius, when the radius is 2 cms. Solution: LetrbetheradiusandVbethevolumeofthesphereatanytimet.Then, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$ $\Rightarrow \frac{d r}{d t}=\frac{1}{4 \pi r^{2}} \frac{d V}{d t}$ $\Rightarrow \frac{d r}{d t}=\frac{3}{4 \pi(2)^{2}} \quad\left[\because r=2 \mathrm{~cm}\right.$ and $\left.\frac{d V}{d t}=3 \mathr...
Read More →The volume of a sphere is increasing at 3 cubic centimeter per second.
Question: The volume of a sphere is increasing at 3 cubic centimeter per second. Find the rate of increase of the radius, when the radius is 2 cms. Solution: LetrbetheradiusandVbethevolumeofthesphereatanytimet.Then, $V=\frac{4}{3} \pi r^{3}$ $\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$ $\Rightarrow \frac{d r}{d t}=\frac{1}{4 \pi r^{2}} \frac{d V}{d t}$ $\Rightarrow \frac{d r}{d t}=\frac{3}{4 \pi(2)^{2}} \quad\left[\because r=2 \mathrm{~cm}\right.$ and $\left.\frac{d V}{d t}=3 \mathr...
Read More →The substance that does
Question: The substance that does not burn with flame is (a) LPG (b) camphor (c) dry grass (d) charcoal Solution: (d) Charcoal is a solid fuel which does not vaporise on heating. So, charcoal does not burn by producing a flame. It only glows on combustion....
Read More →Which of the following
Question: Which of the following is not a combustible substance? (a) Camphor (b) Glass (c) Straw (d) Alcohol Solution: (b) Those substances which do not burn are called non-combustible substance. Some of the non-combustible substances are stone, glass, cement, soil, sand, iron nails, etc....
Read More →If a particle moves in a straight line such that the distance travelled in time t is given by
Question: If a particle moves in a straight line such that the distance travelled in time $t$ is given by $s=t^{3}-6 t^{2}+9 t+8$. Find the initial velocity of the particle. Solution: $s=t^{3}-6 t^{2}+9 t+8$ $\Rightarrow \frac{d s}{d t}=3 t^{2}-12 t+9$ Initial velocity $=$ Velocity at $t=0$ $\Rightarrow \frac{d s}{d t}=3(0)^{2}-12(0)+9$ $\Rightarrow \frac{d s}{d t}=9$ units/unit time...
Read More →Which one of the following
Question: Which one of the following has the highest calorific value? (a) Kerosene (b) Biqgas (c) LPG (d) Petrol Solution: (c) LPG has the highest calorific value, i.e. 55000 kJ/kg. It means that if 1 kg of LPG is burnt completely, then it will produce 55000 kilojoules of heat energy. Note Calorific value 45000 kJ/kg 35000 to 40000 kJ/kg 45000 kJ/kg...
Read More →A substance which reacts with oxygen
Question: A substance which reacts with oxygen giving heat is called a combustible substance. Which one of the following is a combustible substance? (a) Iron nail (b) Glass (c) Stone piece (d) Wood Solution: (d) Wood is a combustible substance. It is a solid fuel and produces smoke during combustion....
Read More →Find the sum of the series:
Question: Find the sum of the series: $\left(2^{3}+4^{3}+6^{3}+8^{3}+\ldots\right.$ to $n$ terms $)$ Solution: In the given question we need to find the sum of the series. For that, first, we need to find the nth term of the series so that we can use summation of the series with standard identities and get the required sum. The series given is $\ldots 2^{3}+4^{3}+6^{3}+8^{3}+\ldots$ to $n$ terms. The series can be written as, $\left[(2 \times 1)^{3},(2 \times 2)^{3},\right.$, $\left.(2 \times 3)...
Read More →Water is flowing into a vertical cylindrical tank
Question: Water is flowing into a vertical cylindrical tank of radius 2 ft at the rate of 8 cubic/minute. The rate at which the water level is rising, is _______________. Solution: Lethbe the water level in the cylindrical tank at timetminutes. Radius of the cylinder,r= 2 ft $\therefore$ Volume of the water in the cylindrical tank at time $t, V=\pi r^{2} h=\pi \times(2)^{2} \times h$ $V=4 \pi h$ Differentiating both sides with respect tot, we get $\frac{d V}{d t}=4 \pi \times \frac{d h}{d t}$ No...
Read More →What steps woulcLyou suggest
Question: What steps woulcLyou suggest for the judicious use of fuels? Solution: (i) We should use fossil fuels only when absolutely necessary. (ii) We can also use natural gas as a substitute. The reserves of natural gas discovered by us have gone up ten times within 20 years. (iii) Alternative sources of energy such as solar, wind and biomass should be used in place of fossil fuels....
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