A man walking briskly in rain with speed v must slant
[question] Question. A man walking briskly in rain with speed $v$ must slant his umbrella forward making an angle $\theta$ with the vertical. A student derives the following relation between $\theta$ and $v \cdot \tan \theta=v$ and checks that the relation has a correct limit: as $v \rightarrow 0, \theta \rightarrow 0$, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not, guess the corre...
Read More →Find two consecutive positive integers,
[question] Question. Find two consecutive positive integers, sum of whose squares is 365. [/question] [solution] Solution: Let the consecutive positive integers be x and x + 1. Given that $x^{2}+(x+1)^{2}=365$ $\Rightarrow x^{2}+x^{2}+1+2 x=365$ $\Rightarrow 2 x^{2}+2 x-364=0$ $\Rightarrow x^{2}+x-182=0$ $\Rightarrow x^{2}+14 x-13 x-182=0$ $\Rightarrow x(x+14)-13(x+14)=0$ $\Rightarrow(x+14)(x-13)=0$ Either $x+14=0$ or $x-13=0$ i.e., $x=-14$ or $x=13$ Since the integers are positive, $x$ can only...
Read More →When the planet Jupiter is at a distance of 824.7 million kilometers
[question] Question. When the planet Jupiter is at a distance of $824.7$ million kilometers from the Earth, its angular diameter is measured to be $35.72^{\prime \prime}$ of arc. Calculate the diameter of Jupiter. [/question] [solution] solution: Distance of Jupiter from the Earth, $D=824.7 \times 10^{6} \mathrm{~km}=824.7 \times 10^{9} \mathrm{~m}$ Angular diameter $=35.72^{\prime \prime}=35.72 \times 4.874 \times 10^{-6} \mathrm{rad}$ Diameter of Jupiter = d Using the relation, $\theta=\frac{d...
Read More →Find two numbers whose sum is 27
[question] Question. Find two numbers whose sum is 27 and product is 182. [/question] [solution] Solution: Let one number be x, then second number = 27 – x $x \times(27-x)=182$ $\Rightarrow 27 x-x^{2}=182$ $\Rightarrow x^{2}-27 x+182=0$ $\Rightarrow x^{2}-14 x-13 x+182=0$ $\Rightarrow x(x-14)-13(x-14)=0$ $\Rightarrow(x-13)(x-14)=0$ $\Rightarrow x=13$ or 14 $\Rightarrow 27 x=14$ or 13 Hence, the two marbles are 13 and 14 . [/solution]...
Read More →Represent the following situations mathematically.
[question] Question. Represent the following situations mathematically. (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. (ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of ...
Read More →Find the roots of the following quadratic equations by factorisation :
[question] Question. Find the roots of the following quadratic equations by factorisation : (i) $x^{2}-3 x-10=0$ (ii) $2 x^{2}+x-6=0$ (iii) $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$ (iv) $2 x^{2}-x+\frac{1}{8}=0$ (v) $100 x^{2}-20 x+1=0$ [/question] [solution] Solution: (i) $x^{2}-3 x-10=0$ $\Rightarrow x^{2}-5 x+2 x-10=0$ $\Rightarrow x(x-5)+2(x-5)=0$ $\Rightarrow(x+2)(x-5)=0$ $\Rightarrow x+2=0$ or $x-5=0$ $\Rightarrow x=-2$ or $x=5$ Hence, the two roots are $-2$ and 5 . (ii) $2 x^{2}+x-6=0$ $\Rightar...
Read More →By what means can the consumers express their solidarity?
[question] Question. By what means can the consumers express their solidarity? [/question] [solution] Solution: Consumers can express their solidarity by forming consumer groups that write articles or hold exhibitions against traders’ exploitation. These groups guide individuals on how to approach a consumer court, and they even fight cases for consumers. Such groups receive financial aid from the government to create public awareness. Participation of one and all will further strengthen consume...
Read More →Mention some of the rights of consumers and write a few sentences on each.
[question] Question. Mention some of the rights of consumers and write a few sentences on each. [/question] [solution] Solution: Some of the rights of consumers include the right to be informed, the right to choose, the right to seek redressal and the right to representation in consumer courts. Under the RTI Act of 2005, consumers can now even get information regarding the working of government departments. The right to choose allows a consumer to choose if he wishes to continue or discontinue t...
Read More →What legal measures were taken by the government to empower the consumers in India?
[question] Question. What legal measures were taken by the government to empower the consumers in India? [/question] [solution] Solution: Legal measures taken by the government to empower consumers in India are plenty. First and foremost being the COPRA in 1986. Then, in October 2005, the Right to Information Act was passed, ensuring citizens all information about the functioning of government departments. Also, under COPRA, a consumer can appeal in state and national courts, even if his case ha...
Read More →Suppose you buy a bottle of honey and a biscuit packet.
[question] Question. Suppose you buy a bottle of honey and a biscuit packet. Which logo or mark you will have to look for and why? [/question] [solution] Solution: While buying a bottle of honey or a biscuit packet, the logo or mark one will have to look for is ISI or Agmark. These are logos certifying the quality of goods in the market. Only those producers are allowed to use these marks who follow certain quality standards set by the organisations issuing these certifications. Thus, if a bottl...
Read More →Compare the use of manure and fertilizes in maintainig soil fertility.
[question] Question. Compare the use of manure and fertilizes in maintainig soil fertility. [/question] [solution] Solution: Manures increase soil fertility by enriching the soil with organic matter and nutrients as it isn prepared by the decomposition of animal excreta and plant wastes. On the other hand, fertilizers are mostly inorganic compounds whose excessive use is harmful to the symbiotic micro-organisms living in soil. Their excessive use also reduces soil fertility. Hence, fertilizers a...
Read More →Describe some of your duties as consumers if you visit a shopping complex in your locality.
[question] Question. Describe some of your duties as consumers if you visit a shopping complex in your locality. [/question] [solution] Solution: Some of my duties as a consumer if I visit a shopping complex include checking expiry dates of the products I wish to purchase, paying only the maximum retail price printed on the goods, preventing shopkeepers from duping me with defective products, and registering a complaint with a consumer forum or court in case a seller refuses to take responsibili...
Read More →How do plants get nutrients?
[question] Question. How do plants get nutrients? [/question] [solution] Solution: Nutrients found in the soil get dissolved in the water from rain and irrigation. This water is absorbed by the roots of plants and transported to different parts of the plants. [solution]...
Read More →What are macro-nutrients and why are they called macro-nutrients?
[question] Question. What are macro-nutrients and why are they called macro-nutrients? [/question] [solution] Solution: Macro-nutrients are Nitrogen, Phosphorus, Potassium, Calcium, Magnesium, Sulphur.Theyare required in large quantities to plants and are therefore called macro-nutrients. [/solution]...
Read More →What is the rationale behind the enactment of Consumer Protection Act 1986?
[question] Question. What is the rationale behind the enactment of Consumer Protection Act 1986? [/question] [solution] Solution: The rationale behind the enactment of Consumer Protection Act of 1986 is to protect the consumer against unethical and unfair trade practices. Also, it recognises the consumer’s right to be informed, right to choose, right to seek redressal and right to represent himself/herself in consumer courts. [/solution]...
Read More →What are the desirable agronomic characteristics for crop improvements?
[question] Question. What are the desirable agronomic characteristics for crop improvements? [/question] [solution] Solution: (a) Tallness and profuse branching are desirable characters for fodder crops. (b) Dwarfness is desired in cereals, so that less nutrients are consumed by plant body. [/solution]...
Read More →Represent the following situations in the form of quadratic equations :
[question] Question. Represent the following situations in the form of quadratic equations : (i) The area of a rectangular plot is $528 \mathrm{~m}^{2}$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot. (ii) The product of two consecutive positive integers is 306. We need to find the integers. (iii)Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to...
Read More →Mention a few factors which cause exploitation of consumers.
[question] Question. Mention a few factors which cause exploitation of consumers. [/question] [solution] Solution: Exploitation of consumers is caused by a variety of factors. Producers are always looking for easy ways to increase profits. Adulterated or low-quality goods have less production costs, and if the consumer is unaware or illiterate, it is easy to cheat him/her. Also, shopkeepers brush off their responsibility by claiming that the manufacturer is to blame. Consumers feel helpless in t...
Read More →How do biotic and abiotic factors affect crop production?
[question] Question. How do biotic and abiotic factors affect crop production? [/question] [solution] Solution: A variety of biotic factors such as pests, nematodes, diseases, etc. can reduce the net crop production. A pest causes damage to agriculture by feeding on crops. For example, boll weevil is a pest on cotton. It attacks the cotton crop, thereby reducing its yield. Weeds also reduce crop productivity by competing with the main crop for nutrients, light, and space. Similarly, abiotic fact...
Read More →Explain the need for consumer consciousness by giving two examples.
[question] Question. Explain the need for consumer consciousness by giving two examples. [question] [solution] Solution: There is a need for consumer consciousness so that the buyers themselves can take action against cheating traders. The ISI and Agmark logos are certifications of good quality. Consumers must look for such certifications while buying goods and services. Secondly, to be able to discriminate and make informed choices, a consumer needs to have an adequate knowledge of the goods or...
Read More →What do we get from cereals, pulses, fruits and vegetables?
[question] Question. What do we get from cereals, pulses, fruits and vegetables? [/question] [solution] Solution: We get carbohydrates from cereals, proteins from pulses. fruits and vegetables provide vitamins and minerals in addition to small amount of proteins, carbohydrates & fats [/solution]...
Read More →What factors gave birth to the consumer movement in India?
[question] Question. What factors gave birth to the consumer movement in India? Trace its evolution. [/question] [solution] Solution: The factors that gave birth to the consumer movement in India are manifold. It started as a “social force” with the need to protect and promote consumer interests against unfair and unethical trade practices. Extreme food shortages, hoarding, black marketing and adulteration of food led to the consumer movement becoming an organised arena in the 1960s. Till the 19...
Read More →Write a note on how forests influence the quality of our air,
[question] Question. Write a note on how forests influence the quality of our air, soil and water resources. [/question] [solution] Solution: Forests influence the quality of our air, soil, and water resources in various ways. Some of the are: (i) Forests balance the percentages of carbon dioxide and oxygen in the atmosphere. The increasing amount of carbon dioxide caused by human activities is balanced by a larger intake of carbon dioxide by plants during the process of photosynthesis. Simultan...
Read More →We know that many human activities lead to increasing levels of pollution of the air,
[question] Question. We know that many human activities lead to increasing levels of pollution of the air, water-bodies and soil. Do you think that isolating these activities to specific and limited areas would help in reducing pollution? [/question] [solution] Solution: Yes. isolating human activities to specific areas would help in reducing levels of pollution. For example, setting up of industries in isolated regions will control pollution to some extent. The pollution caused by these industr...
Read More →Why are rules and regulations required in the marketplace?
[question] Question. Why are rules and regulations required in the marketplace? Illustrate with a few examples. [/question] [solution] Solution: Rules and regulations are required in the marketplace to protect consumers. Sellers often abdicate responsibility for a low-quality product, cheat in weighing out goods, add extra charges over the retail price, and sell adulterated/ defective goods. Hence, rules and regulations are needed to protect the scattered buyers from powerful and fewer producers...
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