Find the value of
Question: Find the value of $\sec \left(\frac{-25 \pi}{3}\right)$ Solution: To find: Value of $\sec \left(-\frac{25 \pi}{3}\right)$ We have, $\sec \left(-\frac{25 \pi}{3}\right)=\sec \frac{25 \pi}{3}$ $[\because \sec (-\theta)=\sec \theta]$ Putting = 180 $=\sec \frac{25 \times 180}{3}$ $=\sec \left[25 \times 60^{\circ}\right]$ $=\sec \left[1500^{\circ}\right]$ $=\sec \left[90^{\circ} \times 16+60^{\circ}\right]$ Clearly, $1500^{\circ}$ is in Ist Quadrant and the multiple of $90^{\circ}$ is even ...
Read More →Find the value of
Question: Find the value of $\cot \left(\frac{13 \pi}{4}\right)$ Solution: To find: Value of $\cot \frac{13 \pi}{4}$ We have $\cot \frac{13 \pi}{4}$ Putting $\pi=180^{\circ}$ $=\cot \left(\frac{13 \times 180^{\circ}}{4}\right)$ $=\cot \left(13 \times 45^{\circ}\right)$ $=\cot \left(585^{\circ}\right)$ $=\cot \left[90^{\circ} \times 6+45^{\circ}\right]$ $=\cot 45^{\circ}$ [Clearly, $585^{\circ}$ is in IIIrd Quadrant and the multiple of $90^{\circ}$ is even] $=1\left[\because \cot 45^{\circ}=1\rig...
Read More →Find the value of
Question: Find the value of $\tan \left(\frac{-25 \pi}{3}\right)$ Solution: To find: Value of $\tan \frac{-25 \pi}{3}$ We know that, $\tan (-\theta)=-\tan \theta$ $\therefore \tan \left(-\frac{25 \pi}{3}\right)=-\tan \left(\frac{25 \pi}{3}\right)$ $\tan \left(-\frac{25 \pi}{3}\right)=-\tan \left(\frac{25 \pi}{3}\right)=-\tan \left(8 \pi+\frac{1}{3} \pi\right)$ $=-\tan \left(4 \times(2 \pi)+\frac{1}{3} \pi\right)$ Value of $\tan \mathrm{x}$ repeats after an interval of $2 \pi$, hence ignoring $4 ...
Read More →Find the value of
Question: Find the value of $\cos \left(\frac{17 \pi}{2}\right)$ Solution: To find: Value of $\cos \frac{17 n}{2}$ $\cos \frac{17 \pi}{2}=\cos \left(8 \pi+\frac{1}{2} \pi\right)$ $=\cos \left(4 \times(2 \pi)+\frac{1}{2} \pi\right)$ Value of $\cos x$ repeats after an interval of $2 \pi$, hence ignoring $4 \times(2 \pi)$ $=\cos \left(\frac{1}{2} \pi\right)$ $=\cos \left(\frac{1}{2} \times 180^{\circ}\right)$ $=\cos 90^{\circ}$ $=0\left[\because \cos 90^{\circ}=1\right]$...
Read More →Find the value of
Question: Find the value of $\sin \left(\frac{31 \pi}{3}\right)$ Solution: To find: Value of $\sin \frac{31 \pi}{3}$ $\sin \frac{31 \pi}{3}=\sin \left(10 \pi+\frac{1}{3} \pi\right)$ $=\sin \left(5 \times(2 \pi)+\frac{1}{3} \pi\right)$ Value of $\sin x$ repeats after an interval of $2 \pi$, hence ignoring $5 \times(2 \pi)$ $=\sin \left(\frac{1}{3} \pi\right)$ $=\sin \left(\frac{1}{3} \times 180^{\circ}\right)$ $=\sin 60^{\circ}$ $=\frac{\sqrt{3}}{2}\left[\because \sin 60^{\circ}=\frac{\sqrt{3}}{2...
Read More →Read the paragraph and
Question: Read the paragraph and answer the questions following it. Water is essential for life. Without water there would be no life. We usually take water as granted for its purity, but we must ensure the quality of water. Pollution of water originates from human activities. Through different paths, pollution reaches to groundwater. Easily identified source or place of pollution is called as point source, e.g. municipal and industrial discharge pipes, where pollutants enter the water source. N...
Read More →How can we reduce,
Question: How can we reduce, reuse and recycle water? Solution: The various ways to conserve water (or save water) at home are as follows: (i) Reduce While brushing our teeth, bathing etc, we should not keep our taps on. We should turn off the tap immediately after use. The leaking taps should be repaired immediately. (ii)Reuse Water used for washing vegetables, rice, pulses and fruits can be used for gardening. (iii)Recycle Dirty water can be recycle after purification....
Read More →Explain the traditional ways
Question: Explain the traditional ways of purifying water to make it fit for drinking. Solution: The various traditional ways of purifying water to make it fit for drinking are as follows: (i) By filtering This is a physical method of removing impurities. A popular household water filter is a candle type water filter. (ii)By boiling When water is heated, it boils at a temperature of 100C. At this high temperature, all the harmful microorganisms (or germs) present in water are killed and it becom...
Read More →Solve this
Question: If $\sec x=-2$ and $\pix\frac{3 \pi}{2}$ find the values of all the other five trigonometric functions. Solution: Given: $\sec x=-2$ Given that: $\pix\frac{3 \pi}{2}$ So, x lies in IIIrd Quadrant. So, sin and cos will be negative but tan will be positive. Now, we know that $\cos x=\frac{1}{\sec x}$ Putting the values, we get $\cos x=\frac{1}{-2}$ (i) We know that, $\cos ^{2} x+\sin ^{2} x=1$ Putting the values, we get $\left(-\frac{1}{2}\right)^{2}+\sin ^{2} x=1$ [Given] $\Rightarrow \...
Read More →We should plant trees and nurture
Question: We should plant trees and nurture the ones already present in the neighbourhood. Why? Solution: We should plant more trees and also nurture the existing trees in our neighbourhood because trees reduce air pollution by absorbing excess carbon dioxide from the air. Thus, planting more trees will mitigate global warming. All of us should participate in programmes such as Van Mahotsav in which lakhs of trees are planted in the month of July every year....
Read More →It is said, ‘CO2 contributes to
Question: It is said, CO2contributes to global warming. Explain. Solution: Plants utilise C02 from the atmosphere for photosynthesis, thereby decreasing the amount of CO2in the air. Deforestation leads to an increase in the amount of CO2in the air because the number of trees which consume CO2, is reduced. Human activities, thus contribute to the accumulation of CO2in the atmosphere. CO2traps heat and does not allow it to escape jnto space. As a result, the average temperature of the earths atmos...
Read More →Why is it advised that industries
Question: Why is it advised that industries should switch over to cleaner fuels such as CNG and LPG in the Taj Mahal zone in Agra? Solution: Pollutants in air are discolouring white marble of Taj Mahal. The Mathura Oil Refinery near Agra as well as various industries in and around Agra are emitting gaseous pollutants such as sulphur dioxide and nitrogen dioxide into the air which cause acid rain. Acid rain react with the carbonates present in marble (calcium carbonate) and limestone of a monumen...
Read More →What do CFCs stand for?
Question: What do CFCs stand for? Name some devices where CFCs are used. Why CFCs are considered as pollutants? Solution: CFCs stands for chlorofluorocarbons. These are the chemical compounds made of chlorine, fluorine and carbon elements. CFCs are used in refrigerators, air conditioners and aerosol sprays. CFCs are considered as pollutants because these are depleting the useful ozone layer of the upper atmosphere. This happens as follows : CFCs released into the air, goes up and ultimately reac...
Read More →In the following statements,
Question: In the following statements, the underlined words are jumbled up. Write them in their correct form.(a) Air contains 78%ginrotenand 21%gonexy. (b) Vehicles produce high level of pollutants like carbon dioxide, nitrogen oxides,nobrac moondexiandmosek. (c) Carbon dioxide,thaneme,nitrous oxide and water vapour are known asheengrouse sesga. (d) Gangotri glacier in Himalaya has started melting because oflablog ringwam. (e) Whenever harmful substances such aswagese,toxic chemicals, silt, etc ...
Read More →State whether the following statement are True/False.
Question: State whether the following statement are True/False. (i) We can survive for sometime without air but we cannot survive even for a few minutes without food. (ii)A brick kiln emits lot of smoke and other harmful gases causing air pollution. (iii)Carbon monoxide is produced by complete burning of fuels such as coal, petrol, diesel. (iv)Chlorination is a commonly used chemical method for killing germs in water. (v) Water which is suitable for drinking is called soft water. Solution: (i) F...
Read More →Fill in the blanks with the help of words
Question: Fill in the blanks with the help of words given in bracket after each sentence. (a) When air is contaminated by. substances which have a .effect on both the. and.it is referred to as. (air pollution, harmful, living, unwanted, non-living, pollutants) (b) Many.are responsible for causing .pollution. Petroleum.are a major source of.pollutants like.and . (sulphur dioxide, refineries, industries, nitrogen dioxide, gaseous, liquid, people, air) (c) ,While.your teeth, leaving the.running may...
Read More →The level of air pollution is higher
Question: The level of air pollution is higher at a busy traffic intersection. Why? Solution: A large number of automobiles stop for a short period at red light throughout the day and release a large quantity of gases (due to burning of petrol and diesel) which create air pollution. Motor vehicles are the major cause of air pollution in big cities....
Read More →A lot of dry leaves are collected
Question: A lot of dry leaves are collected in a school garden and are burnt every day. Do you think that it is right to do so? If not, what should be done to dispose off the dry leaves? Solution: It is not right to burn dry leaves as it causes air pollution. The right way to dispose off the dry leaves is to convert them into compost by burying in a pit....
Read More →Name any two water pollutants
Question: Name any two water pollutants which are toxic for .both plants and animals. Solution: Lead and arsenic are two water pollutants which are toxic for both plants and animals....
Read More →Combustion of fossil fuels generates
Question: Combustion of fossil fuels generates a lot of air pollution. Can you suggest any two alternative sources of energy which do not cause any pollution? Solution: Combustion of fossil fuels generates a lot of air pollution. Solar energy and wind energy : are two alternative sources of energy which do not cause any pollution....
Read More →The quality of air at various locations
Question: The quality of air at various locations is monitored regularly by government and other agencies. In what way can you use these data? Solution: The quality of air at various locations is monitored regularly by government and other agencies. These data can be used to generate awareness about air pollution among people....
Read More →Name two gases which are
Question: Name two gases which are mainly responsible for acid rain. Solution: Sulphur dioxide and nitrogen dioxide are the two gases mainly responsible for acid rain....
Read More →Name any two sources which causes
Question: Name any two sources which causes air pollution due to Suspended Particulate Matter (SPM). Solution: Two sources which cause air pollution are as follows : (i) Automobiles which bum diesel and petrol, produce SPM which remain suspended in air and reduce visibility. When inhaled, they cause diseases. (ii)Industrial activities like manufacturing of steel and mining give out SPM which also pollute the atmosphere....
Read More →Name the chemicals which are used in refrigerators,
Question: Name the chemicals which are used in refrigerators, air conditioners and damage ozone layer when released in air. Solution: Chlorofluorocarbons (CFCs) are the chemical compounds made of chlorine, fluorine and carbon elements, which are used in refrigerators, air conditioners and aerosol sprays, and damage ozone layer when released in air....
Read More →Which of the following is not a greenhouse
Question: Which of the following is not a greenhouse gas? (a) Nitrogen gas (b) Water vapour (c) Methane gas (d) Carbon dioxide Solution: (a) Carbon dioxide, methane and water vapour are greenhouse gases. But the main constituents of the atmosphere nitrogen and oxygen are not greenhouse gases....
Read More →