This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find out the synonym of the underlined word in each of the following sentences.1. But because the best manner of making it is the subject of violent disputes. (a) agreements (b) applauses (c) conflicts (d) discussions2. ________ tea is one of the mainstays of civilization in the country. (a) a society in an advanced state of social development (b) a society that has slow progress (c) a society that has no progress (d) a society in an average state of social development3 ________ that they only drink it in order to be warmed and stimulated. (a) motivated (b) discouraged (c) passive (d) admired4 ________ under the spout to catch the stray leaves.(a) fresh (b) loose (c) gathered (d) harmful5. One is liable to put in too much milk.(a) likely (b) certain (c) eager (d) responsible |
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Answer» 1. (c) conflicts 2. (a) a society in an advanced state of social development 3. (a) motivated 4. (b) loose 5. (d) responsible |
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| 2. |
Which of the following factors does not adversely affect the business?(A) Strikes(B) Riots(C) Public holidays(D) Accidents |
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Answer» Correct option is (C) Public holidays |
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| 3. |
Non-verbal Representations. Look at the following non-verbal representation. Based on your understanding and inference, write a paragraph on career trends in the next decade. |
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Answer» Fastest growing occupations: It is true that most of us were not aware of the current demands in the job market 10 years ago. As the emerging jobs and the required skill sets change all the professional qualifications become irrelevant. In addition to the basic degree, it is necessary to foresee the emerging trends in the job market. This paragraph shows that the topmost opportunity to grow is in the field of wind and solar energy. Technicians are needed in this sector. There is 100% chances of placement for those who qualify themselves in operating wind mills, designing, installing and maintenance of solar panels. Paramedical profession is likely to grow exponentially. It means that those who pursue nursing, lab technician courses would get placed soon. Strikingly, Mathematicians and Statisticians wall be next in huge demand as 70% growth is for them only. As there is a boom in media services, T.V., radio, newspapers and periodicals, there is a rising demand for media persons and journalists. Against the common beleif, only 50% growth opportunity is there for professionals qualified in software development. It is heartening to note that cycle repairers and two wheeler mechanics will get opportunities next to software engineers. Though lakhs of graduates do B.Ed. course the growth opportunity in teaching jobs in colleges and schools is only 30%. The dismal picture for sportsmen and coaches is discouraging. Only 20% growth is predicted in placements for coaches and sportsmen. Finally only 10% growth is possible for those who specialise in food analysis and working in hotels. |
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| 4. |
Read the following article on the emerging career options in the modern era and answer the questions that follow.The students at the higher secondary level in schools start thinking of suitable courses to take up at the university level based on their aptitude, ability and interests. While considering the higher education options, they should also plan the career path they wish to take. In today’s complex job scenario, there is a mismatch between demand and supply on one hand we have qualified professionals desperately trying to find a job, while on the other hand, there are many professions that need suitable talented employees. But such skilled employees are unavailable.Therefore, the need of the hour is that students have an understanding of the emerging career options.Schools should take the initiative to organise career guidance and counselling sessions for students. However, students need to remember that to build a strong career, they must understand the prospective field and their primary interest. It is also important for students to focus on overall personality development and hone their communication skills as these are important for the success of their career. Students are also advised that in order to build a solid career foundation, they need to qualify suitably by pursuing a degree course in the chosen area of interest and also consider post graduate education. Diploma/Short-term courses may help one find a job in the short run but may not promise career progression. Rapid advancement in science and technology and globalisation has widened the scope of career options in the twenty-first century. Let us consider some popular careers.Fashion Designing: The current cosmopolitan and fashion-conscious wave that has taken over our country has .opened up a huge arena for careers in fashion. These careers encompass designing clothes, costumes, jewellery, footwear, wardrobe, costumes, accessories and the like.Culinary Arts: With food and cookery shows being a major trend across the world, culinary arts, a sub-domain of the hospitality sector, has now become the most sought after career.Paramedical sciences: In recent times, there has been a great demand in the health care industry. Paramedical professionals who support medical practitioners in areas such as optometry, pathology, nursing, physiotherapy, and dentistry are much sought after.Media, Journalism and Advertising: In this information era, print and entertainment media have become a force to reckon with. This arena has become a huge career playground because youngsters are attracted to it as the exposure and reach is greater through such mass media. We notice that radio and TV channels, internet companies and advertising agencies are increasingly recruiting qualified professionals.Hotel Management: The hotel industry is the fastest growing industry in India. The number of international travellers (both for business and leisure) is increasing. The hospitality and service industry offers career options such as house keeping, front-desk executives, tourism management, etc. 76 English-12Sports Management: With multinational companies supporting sports, careers in sports offer enormous scope. One need not be a player or an athlete to shine in a sports career because the field of sports offers various career options such as technical trainers, commentators, sports journalists, dieticians, referees, etc. Conducting sports events successfully, organizing the event laudably, preparing the ground for the event are all part of sports management.(a) When do students start thinking about their career path?(b) How can students build a strong career?(c) What are the integral aspects of a successful career?(d) What is meant by ‘culinary art’?(e) Why is media a popular career option?(f) Name some paramedical courses mentioned in the passage.(g) Why is the hotel industry seen as the fastest growing in India?(h) Does one have to be a player to opt for a career in the field of sports? Answer giving reasons.(i) Pick one word from the passage which is the opposite of ‘modern’.(j) Which word in the passage means ‘composed of people from many parts of the country’? |
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Answer» (a) At the end of plus two exams students start thinking about their career path. (b) To build a strong career, students must understand the prospective field and their primary interest. They need to qualify suitably by pursuing a degree course in their chosen area of interest. (c) Personality development, communicative competence, required skill sets, keeping abreast of technological advancements in addition to qualification in the respective field are the integral aspects of a successful career. (d) Cooking is called culinary art. (e) Media is a popular carrer option because print and entertainment media have become a force to reckon with. Radio, TV channels, internet companies and advertisement companies are increasingly recruiting qualified professionals. (f) Optometry, pathology, nursing, physiotherapy and dentistry are some popular paramedical courses. (g) The number of international travellers visiting India is rapidly growing. This has resulted in the exponential growth of hospitality and service industry. A lot of career options such as house keeping, front-desk executives, tourism management etc. are now open. (h) No. Sports journalists, dieticians, technical trainers and commentators need not be sports persons. (i) Traditional (j) International travellers |
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| 5. |
Find out the synonym of the underlined word in each of the following sentences.1. At least four others are controversial. (a) harmonious (b) disputable (c) agreeable (d) comprehensive2. One does not feel more optimistic after drinking it. (a) dejected (b) despaired(c) positive (d) disdainful3. China tea has virtues. (a) vices (b) admirable qualities (c) despicable traits (d) alarming wickedness4. They are not to be despised. (a) loved (b) yearned (c) hated (d) doted5. Army tea is made in cauldron. (a) stove (b) mini cooker (c) boiler (d) cup6. It is not to be done with the usual method of swilling it with hot water. (a) rinsing (b) drenching (c) chirping (d) cutting7. In a time of rationing, this is not an idea. (a) liberal supply(b) confiscating(c) blocking (d) restricting supply8. In some countries teapots are fitted with little dangling baskets. (a) dancing freely (b) hanging freely (c) severed (d) tied tightly9. No, strainers, muslin bags or other devices to imprison the tea. (a) discharge (b) release (c) acquit (d) detain10. One should stir it well. (a) mix thoroughly (b) drain fully (c) soak completely (d) dried fully |
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Answer» 1. (b) disputable 2. (c) positive 3. (b) admirable qualities 4. (c) hated 5. (c) boiler 6. (a) rinsing 7. (d) restricting supply 8. (b) hanging freely 9. (d) detain 10. (a) mix thoroughly |
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| 6. |
Find out the antonym of the underlined word in each of the following sentences.1. which are not to be despised. (a) hated (b) liked (c) respected (d) defeated2. One does not feel wise, braver or more optimistic.(a) opportunistic (b) cheerful (c) realistic (d) pessimistic3. Not the flat, shallow type… (a) narrow (b) wide (c) deep (d) direct4. Predicting the arrival of visitors… (a) journey (b) departure (c) migration (d) perusal5. but they are sufficient to show how subtilized the whole business has become, (a) enough (b) suffocative (c) inadequate (d) submissive |
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Answer» 1. (b) liked 2. (d) pessimistic 3. (c) deep 4. (b) departure 5. (c) inadequate |
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| 7. |
Find out the synonym of the underlined word in each of the following sentences.1. You can prepare a very similar drink. (a) unidentical (b) almost the same (c) unique (d) distinct2. You could make a drink by dissolving sugar in hot water. (a) segregating(b) filter (c) strain(d) making a solution3. Shallow type cup doesn’t hold much. (a) deep (b) profound (c) cylindrical (d) of little depth4. Milk that is too creamy always gives tea a sickly taste. (a) rich (b) flavoured (c) unpleasant (d) un healthy5. There is also a mysterious social etiquette. (a) clear (b) comprehensible (c) lucid (d) incompressible6. A social etiquette surrounds teapot. (a) evils (b) goods and services (c) vices (d) socially accepted behaviour7. There are some subidiarv. (a) major(b) crucial (c) vital (d) supplementary8. Such as telling fortune… (a) evil (b) wisdom (c) luck (d) omen9. predicting the arrival of visitors. (a) cautioning (b) addressing (c) foretelling (d) doubting10. Be quite sure of wringing out of one’s ration the twenty good, strong cups of tea. (a) smothering (b) squeezing out (c) making out (d) breathing out |
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Answer» 1. (b) almost the same 2. (d) making a solution 3. (d) of little depth 4. (c) unpleasant 5. (d) incompressible 6. (d) socially accepted behaviour 7. (d) supplementary 8. (c) luck 9. (c) foretelling 10. (b) squeezing out |
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| 8. |
A farmer while working on his farm was bitten by a poisonous snake. The workers in the farm immediately rushed him to the nearby health centre. The doctor right away gave him an injection to save his life. What did the doctor inject and why? Explain. |
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Answer» The doctor injected an antivenom. The antivenom contains preformed antibodies which when injected act on the pathogen immediately provide protection by providing passive immunity |
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| 9. |
a. Why is there a fear amongst the guardians that their adolescent wards may get trapped in drug/alcohol abuse? b. Explain ‘addiction’ and ‘dependence’ in respect of drugs/alcohol abuse in youth. |
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Answer» a. Adolescents are easily affected by (or are vulnerable to) peer pressure. Curiosity, need for adventure and excitement, and experimentation constitute common causes for motivation. A child’s natural curiosity motivates him/her to experiment. Television, movies, newspapers, internet also promote drug use. b. Addiction is the psychological attachment to certain effects such as euphoria or temporary feeling of well-being. Dependence is the tendency of the body to show withdrawal syndrome or symptoms if regular doses of drug/alcohol is abruptly discontinued. |
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| 10. |
Give four characteristics of d-block elements. |
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Answer» 1. They show variable oxidation state 2. They form coloured ions 3. They are used as catalyst. 4. They form alloys. |
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| 11. |
Give the general characteristics of the long form of Modern periodic table? |
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Answer» General characteristics of the long form of Periodic table :- (i) There are in all 18 vertical columns i.e. 18 groups in the long form periodic table. (ii) There are groups numbered from 1 to 18 from the left. (iii) There are seven horizontal rows called periods. (iv) The elements of groups 1, 2 and 13 to 17 are called main group elements. (v) The elements of group 3 to 12 are called transition elements. |
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| 12. |
Give the main features of s-block elements. |
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Answer» S – block elements :- The elements in which the last electron enters the s – orbital of their outer most energy level are called s – block elements. It has elements of groups 1 and 2. The general electronic configuration of s – block elements is ns1-2. |
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| 13. |
Likely bond angles of SF4 molecule area. 89° , 117°b. 120° , 180° c. 45° , 118°d. 117° , 92° |
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Answer» Correct option is a. 89° , 117° |
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| 14. |
Calculate the number of atoms present in 1.4 g of N2 molecule. |
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Answer» 28 g of N2 molecule contain 2 × 6.023 × 1023 atoms. Hence, 1.4 g of N2 molecules contain \(\frac{2\times6.023\times10^{23}}{28}\) = 1.04 = 6.023 x 1022 atoms. |
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| 15. |
How many electrons are present in 16 g of CH4? |
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Answer» 1 molecule of CH4 = 6 + 4 = 10 electrons, 16 g of CH4 contains 10 × 6.022 × 1023 = 6.022 × 1024 |
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| 16. |
Calculate the mass of 112 cm3 of hydrogen gas at STP. |
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Answer» Since 22400 cm3 of hydrogen at STP weight = 2g Therefore, 112 cm3 of hydrogen at STP weight = \(\frac{2}{22400}\) x 112 = 0.01 g |
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| 17. |
Born occurs in nature in the form of two isotopes 115B and 105B in ratio of 81% and 19% respectively. Calculate its average atomic mass. |
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Answer» Average atomic mass = \(\frac{11\times81+10\times19}{100}\) = 10.81 |
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| 18. |
Soap works in which of the following? (a) Soft water (b) Hard water (c) Both soft and hard water (d) None of these |
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Answer» (a) Soft water |
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| 19. |
Hydrocarbon tail is towards which side in a micelle? (a) Towards centre (b) On surface (c) Keeps changing (d) In any direction |
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Answer» (a) Towards centre |
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| 20. |
What does SBR stand for? |
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Answer» SBR stand for styrene(S)butadiene (B) rubber (R). |
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| 21. |
(1) From the cis-polyisoprene structure of natural rubber explain the low strength of van der Waals forces in it. (2) Explain how the vulcanization of natural rubber improves its elasticity. |
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Answer» (1) (i) Natural rubber is cis-polyisoprene. It is obtained by polymerization of isoprene units at 1, 4 positions. In rubber molecule, double bonds are located between C2 and C3 of each isoprene unit. These cis-double bonds do not allow the polymer chain to come closer. Therefore, only weak vander Waals’ forces are present. Since the chains are not linear, they can be stretched just like springs and exhibit elastic properties. (ii) Cis-1, 4 polyisoprene (Natural rubber), due to this cis configuration about the double bonds, has the adjacent chain that do not fit together well (there is no close packing of adjacent chains). The only force that interact is the weak or low strength of van der Waals’ forces. (iii) Cis-polyisoprene has a coiled structure in which the various polymer chains are held together by weak van der Waals’ forces. (2) (i) Vulcanization of rubber is a process of improvement of the rubber elasticity and strength by heating it in the presence of sulphur, which results in three dimensional cross-linking of the chain rubber molecules (polyisoprene) bonded to each other by sulphur atoms. (ii) Vulcanisation makes rubber more elastic and more stiffer. On vulcanisation, sulphur forms cross links at the reactive sites of double bonds and thus rubber get stiffened. (iii) The improved properties of vulcanised rubber are (i) high elasticity (ii) low water absorption tendency, (iii) resistance to oxidation. |
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| 22. |
Who was the first scientist to classify elements according to their properties? |
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Answer» The German Chemist, Johann Dobereiner in early 1829 was the first to consider the idea of trends among properties of element. |
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| 23. |
What is the basis of triad formation of elements? |
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Answer» The middle element of each of the triads had an atomic weight about half way between the atomic weights of the other two. Also the properties of the middle element were in between those of the other two members. Dobereiner’s relationship is known as the haw of triads. |
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| 24. |
Difference between Electron gain enthalpy and Electronegativity. |
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Answer»
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| 25. |
Bond Formation. |
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Answer» Bonds formed between electropositive atoms are metallic, whereas those formed between electronegative atoms are covalent. If there is a difference in electronegativity values of two bonded atoms a polar covalent bond is formed where percent ionic character increases with the increase in the difference in electronegativity. When ∆EN > 1.7, the bond is said to have an ionic character greater than or equal to 50% and is referred to as an ionic bond (a bond between an electropositive and an electronegative atom). • Polarisation of the anion by the cation in an ionic compound leads to the development of a covalent character in ionic bonds. Fajan's rules for estimating covalent character states that small cations, large anions, large charge on either ion and cations with non-noble gas configuration give rise to the covalent character of ionic bonds. |
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| 26. |
Name two pairs showing diagonal relationship. |
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Answer» Li and Mg; Be and Al. |
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| 27. |
Name two trans-uranic elements. |
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Answer» Answer is Np and Pu. |
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| 28. |
i. What are trans-uranic elements?ii. Write their names. |
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Answer» i. Transuranic elements are the man-made elements with atomic number higher than 92 (the atomic number of uranium). These elements are prepared by nuclear reactions which involve transformation of naturally occuring elements. ii. The elements from atomic numbers 104 (Rf) to 112 (Uub) are identified. Elements upto atomic number 118 (Uuo) are synthesized. They are listed in the following table.
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| 29. |
What are actinoids? |
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Answer» The series of elements from Thorium (Z = 90) to Lawrencium (Z = 103) in which 5f orbitals are progressively filled are called actinoids. The elements are called actinoid because many physical and chemical properties are similar to actinium which is the prototype of the actinoids. |
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| 30. |
What are alloys? Name an important alloy which contains some of the lanthanoid metals. Mention its uses. |
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Answer» An alloy is a solid or solution of two or more elements in a metallic matrix. It can either be a partial solid solution or a complete solid solution. Alloys are usually found to posses different physical properties than those of the component elements. An important alloy of lanthanoids is Mischmetal It contains lanthanoids (4 - 95%), iron (5%) and traces of S, C, Si, Ca and Al. Uses:
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| 31. |
The approximate percentage of iron in misch metal is____ |
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Answer» The approximate percentage of iron in misch metal is 5 |
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| 32. |
What is Misch metal? Give its one use |
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Answer» Misch metal is an alloy of lanthanum metal and iron and traces of S, Ca, C or Al. It is used in making bullets and lighter flint. |
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| 33. |
Draw the structure and name the product formed if the following alcohols are oxidized' Assume that an excess of oxidizing agent is used.2-butanol |
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Answer» CH3-CH=CH-COOH But-2-en-1-oic acid or 2-butenoic acid |
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| 34. |
How many alcohols with molecular formula C4H10O are chiral in nature?(i) 1(ii) 2(iii) 3(iv) 4 |
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Answer» 1 alcohols with molecular formula C4H10O are chiral in nature. |
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| 35. |
Draw the structure and name the product formed if the following alcohols are oxidized' Assume that an excess of oxidizing agent is used.CH3 CH2 CH2 CH2 OH |
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Answer» CH3CH2 CH2 COOH Butanoic acid |
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| 36. |
A floweriest buys 100 dozen roses at Rs 2 a dozen. By the time the flowers are delivered, 20 dozen roses are mutilated and are thrown away. At what price should he sell the rest if he needs to make a 20% profit on his purchase? |
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Answer» Given cost of 1 dozen roses = Rs. 2 Number of roses bought by the florist = 100 dozens Thus, cost price of 100 dozen roses = 2 x 100 = Rs. 200 Roses left after discarding the mutilated ones = 80 dozens Calculating the price at which the florist should sell the 80 dozen roses in order to make a profit of 20%, we have Profit % = ((SP-CP)/CP) x100 = ((SP-200)/200) x 100 40 = SP – 200 SP = Rs. 240 Therefore, the SP of the roses should be Rs. 240/80 = Rs. 3 per dozen. |
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| 37. |
Find the gain or loss percent when CP = ₹620 and SP = ₹713. |
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Answer» We know that SP is more than CP so it’s a gain.As the formula states Gain = SP – CP 713 – 620 = 93 Gain% = (Gain × 100) / CP = (93 × 100) / 620 = 15% |
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| 38. |
The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent. |
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Answer» Cost price of 10 article = selling price of 9 article Let CP of 1 article = Rs. x Selling price of 9 article = 10x Selling price of 1 article = \(\frac{10x}{9}\) Hence, Profit = \(\frac{10x}{9}\) - x = \(\frac{x}{9}\) = Gain% = \(\frac{gain}{cost\,price}\)x 100 = \(\frac{\cfrac{x}{9}}{x}\)x 100 = \(11\frac{1}{9}\)% |
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| 39. |
Find the selling price when CP = ₹645 and Loss = 13 1/3 %. |
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Answer» As the formula states SP = ((100 – Loss %) /100) × CP= ((100-(40/3))/100) × 645 = ((260/3)/100) × 645 = (260/300) × 645 =559 ∴ The selling price is 559 |
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| 40. |
By selling an article for Rs 240, a man makes a profit of 20%.What is his C.P.? What would his profit percent be if he sold the article for Rs 275? |
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Answer» Let CP = Rs. x SP = Rs. 240 Let profit be Rs. P. Now, profit % = 20% Since Profit % = (Profit/CP) x 100 20 = (P/x) x 100 P = 20x/100 = x/5 Profit = SP – CP = 240 – x P = 240 – x x /5 = 240 – x 240 = x + x/5 240 = 6×15 x = 1200/6 x = 200 So, CP = Rs. 200 New SP = Rs. 275 and CP = Rs. 200 Profit % = {(SP – CP)/CP} x 100 {(275 – 200)1200} x 100 = (75/200) x 100 = 7500/200 = 37.5% |
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| 41. |
Factorize the following expressions: 27x2 – 12y2 |
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Answer» We have, 27x2 – 12y2 = 3 [(3x)2 – (2y)2] (By using the formula (a2 – b2) = (a-b) (a+b)) = 3 (3x + 2y) (3x – 2y) |
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| 42. |
Factorize the following expressions:16x2 – 25y2 |
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Answer» We have, 16x2 – 25y2 = (4x)2 – (5y)2 (By using the formula (a2 – b2) = (a + b) (a – b) we get,) = (4x + 5y) (4x – 5y) |
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| 43. |
Factorize the following expressions:144a2 – 289b2 |
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Answer» We have, 144a2 – 289b2 = (12a)2 – (17b)2 (By using the formula (a2 – b2) = (a-b) (a+b)) = (12a + 17b) (12a – 17b) |
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| 44. |
Factorize the following expressions: (x + 2y)2 – 4 (2x – y)2 |
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Answer» We have, (x + 2y)2 – 4 (2x – y)2 = (x + 2y)2 – [2 (2x – y)]2 = [(x + 2y) + 2 (2x – y)] [x + 2y – 2 (2x – y)] = (x + 4x + 2y – 2y) (x – 4x + 2y + 2y) = (5x) (4y – 3x) |
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| 45. |
Factorize the following expressions:(2a – b)2 – 16c2 |
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Answer» We have, (2a – b)2 – 16c2 = (2a – b)2 – (4c)2 (By using the formula (a2 – b2) = (a-b) (a+b)) = (2a – b + 4c) (2a – b – 4c) |
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| 46. |
Factorize the following expressions:125x2 – 45y2 |
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Answer» We have, 125x2 – 45y2 = 5 (25x2 – 9y2) = 5 [(5x)2 – (3y)2] (By using the formula (a2 – b2) = (a-b) (a+b)) = 5 (5x + 3y) (5x – 3y) |
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| 47. |
Define Arithmetic mean. |
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Answer» The Arithmetic Mean between two numbers is the number which when placed between them forms an arithmetic progression with them. Thus if x is the arithmetic mean of two given numbers a and b, then a, x, b form an A.P. ∴ x – a = b – x ⇒ x = \(\frac{a+b}{2}\) Ex. The arithmetic mean between – 4 and 6 is \(\frac{6+(-4)}{2}\) = 1. |
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| 48. |
Find the sum of n terms of an A.P. |
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Answer» Let the A.P. be a, a + d, a + 2d, ... Let l be the last term and S the required sum. Then, S = \(\frac{n}{2}\) (a + l ) = \(\frac{ Number\, of\, terms}{2}\) (First term + Last term) = \(\frac{n}{2}\) (a + a + (n – 1) d) = \(\frac{n}{2}\) (2a + (n-1)d), where n is the number of terms, a is first term and d is common difference. Also, nth term = Sum of n terms – Sum of (n – 1) terms i.e., Tn = Sn – Sn–1. Ex. The sum of 20 terms of the the A.P. 1, 3, 5, 7, 9.... is S20 = \(\frac{20}{2}\) (2 ×1 + (20 - 1)× 2) (∵ a = 1, d = 2, n = 20) = 10 × 40 = 400 |
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| 49. |
How to get nth term of an A.P. |
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Answer» nth term of an A.P.: The nth term of an A.P. a, a + d, a + 2d, a + 3d, ... is Tn = a + (n – 1)d where Tn denotes nth term, a the first term, n the number of terms and d the common difference. Also, common difference d = Tn – Tn–1. Ex. The 9th term of the A.P.: 2, 5, 8.... is T9 = 2 + (9 – 1) × 3 = 2 + 24 = 26. Note : Here a = 2, d = 3. |
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| 50. |
If the continued product of three numbers in G.P. is 216 and the sum of their products in pair is 156, find numbers. |
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Answer» Let three numbers in G.P. be \(\frac{a}{r}\), a, ar … (i) Given, \(\frac{a}{r}\). a. ar = 216 ⇒ a3 = 216 = 63 ⇒ a = 6 Therefore sum of their product in pair are: \(\frac{a}{r}\) × a + a × ar × \(\frac{a}{r}\) = 156 ⇒ \(\frac{36}{r}\) + 36r + 36 = 156 (∴ a = 6) ⇒ \(\frac{36}{r}\) + 36r = 120 ⇒ \(\frac{3}{r}\) + 3r = 10 ⇒ 3r2 − 10r + 3 = 3 ⇒ (3r − 1)(r − 3) = 0 ⇒ r = \(\frac{1}{3}\), 3 Substituting value of a and r in eq (i), we get 18, 6, 2 when r = \(\frac{1}{3}\) and 2, 6,18 when when r = 3 |
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