UNIT-5 APTITUDE-I PDF
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Uploaded by TerrificComputerArt1720
City Montessori School
B. N. Tripathi
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This document is a unit on aptitude, focusing on simplification, percentage, profit, loss, average, and coding. It details examples and questions, suitable for university-level engineering mathematics students.
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Content Simplification Percentage Profit, Loss & discount Average Number & Series Coding & decoding Algebra 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 4 ...
Content Simplification Percentage Profit, Loss & discount Average Number & Series Coding & decoding Algebra 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 4 Unit Objective (CO 5) Course Objective This course aims to sensitize students with the gamut of skills which facilitate them to enhance their employability quotient and do well in the professional space. These skills are imperative for students to establish a stronger connect with the environment in which they operate. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 5 Simplification (CO 5) Basic Rules of Simplification BODMAS Rule It defines the correct sequence in which operations are to be performed in a given mathematical expression to find the correct value. This means that to simplify an expression, the following order must be followed - B = Brackets, the order - (), {} and [] - should be strictly followed. O = Order (Powers, Square Roots, etc.) D = Division M = Multiplication A = Addition S = Subtraction 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 6 Topic objective of Simplification (CO 5) Eliminate the unnecessary parts of a process. Combine and rearrange the rest of the process. Simplify the necessary part of the process. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 7 Simplification(Contd.) (CO5) Q. 1: Solve: 4 + 10 - 3 × 6 ÷ 3 + 4 Sol. 4 + 10 - 18/3 + 4 = 4 + 10 - 6 + 4 (Division and multiplication, left to right) 14 - 6 + 4 = 8 + 4 = 12 (Addition and Subtraction, left to right) Q. 2: Evaluate or simplify the following expression (a) 9 - { 7 – 24 ÷ ( 8 + 6 × 2 – 16 ) } (b) ( - 3 ) × ( - 12 ) ÷ (- 4 ) + 3 × 6 (c) 17- { 8 ÷ (2 × 3 - 4)} (d) 5 × 2 – [3 – { 5 – (7 + 2 × 4 - 19)}] 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 8 Multiple Choice Questions (CO5) Ques. 1 : 9/42 ÷ 108/63 × 328 – 5/7 + 7/5 = ? (a) 35 (b) 32 (c) 40 (d) 21 Ques. 2 :√(2809.001) ÷ 7.98 × (12.01)2 + 46.002 = ? (a) 1025 (b) 1000 (c) 2050 (d) None of these Ques. 3 :(35% of 74000) ÷ ? = (123 % of 13.02)2 × 2.01 (a) 50 (b) 60 (c) 100 (d) 55 Ques. 4 :(25)3 −(30)3 +(5)3 (a) -1125 (b) 1250 (c) -2500 (d) -11250 Ques. 5: If x = (√126 × √63 × √45) / (√147 × √243), then the value of x is (a) √5 (b) √10 (c) 10 (d) 5 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 9 Ans. Of Multiple Choice Questions (CO5) Ans: 1.c 2. b 3.a 4.d 5.b 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 10 Quiz(CO5) Evaluae(23)3 +(−15)3 +(−8)3 Simplify(3 5 + 2 7)(3 5 − 2 7) 1 1 1 1 Simplify + + + (NIET 2022-23) 3+√7 7+√5 5+√3 3+1 𝑏+𝑐 𝑥 𝑎 𝑎+𝑏 𝑥 𝑏 𝑥 𝑐 𝑐+𝑎 Simplify 𝑥𝑏 𝑥𝑐 𝑥𝑎 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 11 Percentages (CO5) The term per cent means ‘for every hundred’. It can best be defined as: “ A fraction whose denominator is 100 is called a percentage, and the numerator of the fraction is called the rate per cent.” Basic concept: X% of Y (or) X of Y% = X/100 × Y ; = X × Y/100 =XY/100 ; = XY/100 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 12 Topic objective of Percentages (CO5) Percent Describe the relationship between ratios, fractions, decimals and percents. Identify the decimal equivalent of a percent. Identify the fractional equivalent of a percent. Label percentages with the symbol %. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 13 Percentages (CO5) Q.1. Evaluate or simplify 28% of 450 + 45% of 280 Sol. = 28/100 × 450 + 45/100 × 280 = 2 × 280 × 45/100 = 252 Q.2. Evaluate or simplify the following expression (a) 50/3% of 600gm -100/3% of 180gm (b) 45 % of 750 – 25% of 480 (c) 860 % of 50 + 50 % of 860 Q.3. If 50% of 𝑥 − 𝑦 is 30% of 𝑥 + 𝑦 then what percent of 𝑥 is 𝑦? (NIET 2020-2021) 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 14 Application of percentage (CO5) Type 1: Salary based Problem Q.1. A man spends 60% of his income. His income is increased by 20% and his expenditure also increases by 10%. Find the percentage decrease in his saving? Solution : Let initially income is 100. So, expenditure = 60 and saving = 40 now income is increased by 20% i.e. 120. So, expenditure = (70/100)*120 = 84 and saving = 36 so % percent decrease in saving = (4/40)*100 = 10% 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 15 Application of percentage (CO5) Q.2. P’s income is 20% more than Q’s income. How much % Q’s income less than P’s income ? Solution : B income = 100 A income = 100 × 120/100 = 120 % = (120 − 100/120) × 100 = 16.67% Q.3. A reduction of 20% percent in the price of rice enables a housewife to buy 5 kg more for rupees 1200. Find the reduced price per kg of rice. Solution : let original price is x rupees per kg 1200/(4x/5) – 1200/x = 5 We will get x = 60, so reduced price = (4× 60)/5 = 48 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 16 Application of percentage (CO5) Type 2: Population Related Problem Concept : Let the population of a town be P now and suppose it increases at the rate of R % per annum, Then: Case 1: Population after n year = P (1+ R/100)n Case 2: Population n years ago = P/ (1+ R/100)n Q.1. The population of a town is 15000. It increases by 10 percent in the first year and 20 percent in the second year. But in the third year it decreases by 10 percent. What will be the population after 3 years. Solution : 15000 × (11/10) × (12/10) × (9/10) = 17820 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 17 Application of percentage (CO5) Type 3: Examination based problem Q.1. A got 30% of the maximum marks in an examination and failed by 10 marks. However, B who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination? Solution : (30/100) × T = P -10 (40/100) × T = P + 15 So, you will get P = 85 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 18 Application of percentage (CO5) Type 4: Concept of net change or net effect(only valid for 2-D) Case 1: If x% increases and y% also increases Then, net effect = x + y + xy/100 Case 2: If x% increases and y% decreases Then, net effect = x – y – xy/100 Q.1. Rishi salary is first increased by 20% and then decreased by 25%. How much percent the salary increased/decreased ? Solution : Net change = 20 – 25 – 500/100 Net change = -10 So percentage decrease is 10%. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 19 Application of percentage (CO5) Type 5: Election based problem Q.1. In an election a candidate who got 25% of the total votes polled was defeated by his rival by 270 votes. Assuming that there were only 2 candidates in the election, find the total number of votes polled. Solution : Let total number of votes polled = x 75% x – 25% x = 270 50% of x = 270 x = (270×100)/50 x = 540 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 20 Multiple Choice Questions (CO5) Q. 1. Ankita is 25 years old. If Rahul’s age is 25% greater than that of Ankita then how much percent Ankita’s age is less than Rahul’s age? (a) 40% (b) 35% (c) 10% (d) 20% Q. 2. In an examination, 50% of the students passed in Science and 75% passed in Social, while 20% students failed in both the subjects. If 270 students passed in both subjects, find the total number of students who appeared in the exam? (a) 400 (b) 540 (c) 600 (d) 750 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 21 Multiple Choice Questions (CO5) Q. 3. The population of a village has increased annually at the rate of 20%. If at the end of 3 years it is 21600, the population in the beginning of the first year? (a) 10000 (b) 12500 (c) 15000 (d) 17500 Q.4. A student has to get 40 percent marks to pass an examination. He got 60 marks but fails by 20 marks. Find the maximum marks of the examination. (a) 150 (b) 200 (c) 300 (d) 400 Q.5. If the price of a commodity is increased by 30%, by how much % a consumer must reduce his consumption so to keep the expenditure same ? (a) 100/13 (b) 200/13 (c) 300/13 (d) 400/13 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 22 Ans. of Multiple Choice Questions (CO5) ANS. 1. d 2. c 3. b 4.b 5. c 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 23 Quiz(CO5) Water tax is increased by 20% but its consumption is decreased by 20%.Find the increase or decrease in the expenditure of the money? (NIET 2023-24) The total population of a village is 5000. The number of male and female increase by 10% and 15% respectively and consequently the population of the village become 5600. What was the number of males in the village? (NIET 2021-22) A city has a population of 300000 , out of which 180000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate female is ? (NIET 2021-22) A person multiplied a number by 3/5 instead of 5/3 , what is the percentage error in the calculation ? (NIET 2022-23) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 24 Unit-5 Quiz(CO5) If 30% of A is added to 40% of B, the answer is 80% of B. What percentage of A is B? A student multiplies a number by 5 instead of dividing it by 5.What is the % change in the result of this mistake? If the numerator of a fraction is increased by 20% and its denominator is decreased by 10%, the fraction become 3/2.Find the original fraction? (NIET 2021-22) If a number increase from 20 to 28, what is the increasing percentage? (NIET 2022-23) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 25 Unit-5 Exercise (CO5) Q.1. A got 37.5 % marks less than B, then by what percent the marks of B is more than the marks of A? (a) 60 % (b) 37.5 % (c) 27.27 % (d) 40 % Q.2. In an election contest between A and B, A wins by the margin of 240 votes. If A gets 60% of the total votes, total votes are: (a) 1000 (b) 900 (c) 800 (d) 1200 Q.3. A's salary is 20% more than B’s; B's salary is 10% less than C's. If A's salary is Rs. 1080, find C's salary. (a) 900 (b) 1200 (c) 1000 (d) none of these Q.4. In an examination, 50% students failed in English and 40% in Math and 15% students failed in both subjects. If 200 students passed in both the subjects, find the number of students appeared in the exam. (a) 500 (b) 600 (c) 800 (d) 1000 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 26 Exercise (CO5) Q.5. The price of petrol increased by 25% and so a person reduced his consumption by 25%. What percentage is the rise or fall in the expenditure incurred by him on petrol? (a) 6.25% increasing (b) 0.625% decreasing (c) 6.25% decreasing (d) 0.625 increasing Q.6. The length of a rectangle is increased by 60%. By what percent would be width have to be decreased to maintain the same area? (a) 37.5 % (b) 60% (c) 75% (d) None of these Q.7. In an election between two candidates, the candidate who got 60% of valid votes won by a majority of 200 votes. If out of total votes polled 80% votes are valid. What is the total number of votes polled? (a) 1000 (b) 1250 (c) 1500 (d) 1300 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 27 Exercise (CO5) Q. 8. A candidate scores 25 % marks and fails by 30 marks, while another candidate who scores 50 % marks get 20 marks more than the minimum marks required to pass the examinations. Find the maximum marks for the examination. (NIET 2021-22) (a) 200 (b) 100 (c) 400 (d) 500 Q. 9. Reduction in price of sugar by 20% allows a household to buy 45 kg more for Rs.450. Find the original price of the sugar. (a) Rs 2/ kg (b) Rs 2.5/ kg (c) Rs 3/ kg (d) None Q. 10. In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of students failed in both the subjects, then the percentage of students who passed in both the subjects was: (a) 44 (b) 50 (c) 54 (d) 56 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 28 Recap (CO5) Basic concept of percentage Different type of question (1) Salary based Problem (2) Population Related Problem (3) Examination based problem (4) Concept of net change or net effect(only valid for 2-D) (5) Election based problem 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 29 Profit & Loss (CO5) Basic Concept Profit = SP – CP Profit % = (SP/CP − 1) × 100 Loss = CP − SP Loss % = (1 − SP/CP) × 100 Formulae SP = CP (1 ± x/100) Where, +x = profit % −x = loss % 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 30 Topic objective of Profit & Loss (CO5) Profit and loss account is prepared after the preparation of trading account. The main objective of preparing profit and loss account is to achieve the operating results of a company at the end of accounting period. Profit and loss account is a nominal account having debit side and credit side. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 31 Profit & Loss (CO5)(Contd.) Q. 1. The CP of an article is 5/6th of the SP. What is the percentage profit or loss? Solution : CP = 5/6 of SP SP/CP = 6/5 Profit % = (6/5 − 1) × 100 = 20 Q. 2. A man bough 18 oranges for a rupee and sold them at 12 oranges for a rupee. What is the profit percentage? Solution : CP of 18 = SP of 12 SP/CP = 18/12 = 3/2 Profit % = (3/2 −1) × 100 = 50 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 32 Profit & Loss (CO5)(Contd.) Q. 3. If a wholesaler sells a tin of coffee at ₹ 528.He faces a loss of 12%. If he decides to sell it at ₹ 636, what will be profit percentage? Solution : SP = CP (1− x/100) 528 = CP (1− 12/100) CP = ₹ 600 Profit = 636 − 600 = 36 Profit % = (36/600) ×100 = 6 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 33 Profit & Loss (CO5)(Contd.) Q. 4. If a sari is sold for ₹ 2880 the seller will face 10% loss, at what price should he sell to gain 20% profit? Solution: SP = CP(1 − x/100) 2880 = CP (1− 10/100) CP = ₹ 3200 Now, to gain 20% profit Selling price = 3200(1+ 20/100) SP = ₹ 3840 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 34 Profit & Loss (CO5)(Contd.) Q. 5. Rajesh purchased 35 kg of rice at the rate of Rs.9.50 per kg and 30 kg at the rate of Rs.10.50 per kg. He mixed the two. Approximately, at what price (in Rupees) per kg. should he sell the mixture to make 35 per cent profit in the transaction? (NIET 2022-23) Solution: CP of 65 kg of the mixture = Rs (35*9.50+30*10.50) = Rs 647.50 Therefor , required rate =(647*135)/65*100 =Rs 133.50/kg 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 35 Discount (CO5) Marked Price : the marked price or list price is the price that is indicated or marked on the product. Markup(m) = MP − CP Markup % = (MP/CP − 1) ×100 Discount : Discount is the reduction given on the marked price. Discount = MP− SP Discount % = (1− SP/MP) × 100 Successive Discount : If two successive discount of x% and y% are converted into single equivalent discount = x + y − xy/100 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 36 Topic objective of Discount (CO5) Discounts to reward customers who purchase in bulk, repeat customers and employees build customer loyalty. Promotional discounts, used sparingly, offer temporary advantages including maximizing sales, revenue and profit. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 37 Discount (CO5)(Contd.) Formulae : Selling Price = MP(1− d/100) CP(1± x/100) = SP = MP (1− d/100) Q. 1. A discount of 20% is given on the marked price of an article. The shopkeeper charges sales tax of 10% on the discounted price. If the selling price be ₹1848, what is the marked price (in rupees) of the article? Solution: Let the MP be x. Then, 1848 = MP(1 − 20/100)(110/100) MP = 2100 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 38 Discount (CO5)(Contd.) Q. 2. A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. Find his gain%. Solution: Let, CP of an article = ₹ 100 Then, marked price of an article = ₹120 Selling price = MP (1−d/100) = 120(1−15/100) = 102 Gain %= (102 − 100)/100 ×100 = 2 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 39 Discount (CO 5) (Contd.) Q. 3. (a) If two successive discount are 30% and 10%. Find single equivalent discount. Solution: Single equivalent discount = 30 + 10 − 300/100 = 37% (b) A tire is sold at three successive discount of 20%, 30% and 20%. What is the net discount? Solution : single discount = 20 + 30 − 600/100 = 44% Net discount = 44 + 20 − 880/100 = 55.2% 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 40 Discount (CO5) (Contd.) Q. 4.Arun sells an object to Benny at a profit of 15%, Benny sells that object to Chandan for ₹1012 and makes a profit of 10%. At what cost did Arun purchase the object? (NIET2022-23) Solution : Let the actual cost price at which Arun bought the object be x When Arun sells the object to Benny Profit % = 15% ∴ selling price of object = [(100 + 15)/100] × x = 1.15x Now, this cost price of the object for Benny When Benny sells the object to Chandan Selling Price = ₹1012 Profit % = 10% ∴ Selling price = [(100 + 10)/100] × 1.15x ⇒ 1012 = [(100 + 10)/100] × 1.15x X= 800 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 41 Multiple Choice Questions (CO 5) Q.1. A shopkeeper uses weight of 460 gram instead of 500 gram and the sells the articles at the cost price. What is the profit percentage? (a) 40% (b) 23% (c) 8.7 % (d) 20% Q.2. The MP of an article is 30% higher than its CP and 20% discount is allowed on this article then the profit percentage? (a) 10% (b) 14% (c) 4% (d) 25% Q.3. A single discount equivalent to three successive discounts of 5%, 10%, 20% is? (a) 68.4% (b) 35% (c) 31.6% (d) 32% 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 42 Multiple Choice Questions (CO 5) Q. 4. Trader uses a weight of 920 gram instead of 1 kg and sells the articles at the marked price which is 15% above the cost price. Find the profit percentage. (a) 25% (b) 23% (c) 20% (d) 10 % Q. 5. The marked price of a shirt and trousers are in the ratio 1 : 2. The shopkeeper gives 40% discount on the shirt. If the total discount on both is 30% , then the discount offered on the trousers is? (a) 15% (b) 25% (c) 20% (d) 30% 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 43 Ans. Of Multiple Choice Questions (CO5) ANS: 1. c 2. c 3.c 4. a 5. b 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 44 Quiz(CO5) A machine is sold for Rs5060 at a gain of 10%. What would have been the gain or loss % if it had been sold for Rs 4370? A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is Rs.800, then the cost price is? (NIET 2021-22) If a watch is sold at Rs.60, there is a loss of 15% for a profit of 2%, the watch is to be sold at what ? A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash. Find his net loss or profit ? A discount of 20% is given on the marked price of an article.The shopkeeper charges sales tax of 10% on the discounted price. If the selling price be Rs 1848,what is the marked price of the article? (NIET 2022-23) A tradesman marks his goods at 35% above its cost price and allows a discount of 17.5% for purchase in cash. What profit per cent does he make ? (NIET 2023-24) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 45 Unit-5 Exercise (CO5) Q. 1. A man sold an umbrella for Rs. 1800 and incurs a loss of 20%, and then what is the cost price of the umbrella? (a) 1440 (b) 2160 (c) 2250 (d) 2320 Q.2. The cost price of 12 pens is equal to the selling price of 10 pens. Find the gain percent. (a) 20% (b) 25% (c) 10% (d) 16.66% Q. 3. A toy is sold at 25% profit. If it had been sold at 15% loss, the selling price would have been Rs. 120 less. The toy costs (a) Rs. 240 (b) Rs. 360 (c) Rs. 300 (d) Rs. 350 Q.4. A retailer marks all his goods at 50% above the cost price and offers a discount of 25% on the marked price. What is his actual profit on the sales? (a) 25% (b) 12.5% (c) 15% (d) 20% 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 46 Exercise (CO5) Q.5. A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is Rs. 800, then the cost price is? (NIET 2021-22) (a) Rs. 600 (b) Rs. 700 (c) Rs. 800 (d) Rs. 900 Q. 6. An article is listed at Rs. 1800 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or loss, if he gives a single discount of 16% instead of two discounts? (a) Rs. 11.52 loss (b) Rs. 11.52 gain (c) Rs. 12.62 loss (d) Rs. 12.52 gain Q.7. A single discount equivalent to three successive discounts of 5%, 10%, 20% is? (a) 68.4% (b) 35% (c) 31.6% (d) 32% Q.8. Instead of selling the bicycle for Rs.2000, a shopkeeper sold it for Rs. 1500.Find the loss incurred in transaction? (NIET 2023-24) 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 47 Exercise (CO5) Q. 8. Pankaj purchased an item for Rs. 7500 and sold it at the gain of 24%. From that amount he purchased another item and sold it at the loss of 20%. What is his overall gain/loss? (NIET 2021-22) (a) Loss of Rs. 140 (b) Gain of Rs. 60 (c) Loss of Rs. 60 (d) neither gain or Loss Q. 9. A man purchases a certain number of toffees at 6 per rupee and the same number of toffees at 7 per rupee. He mixes the toffees and sells them at 6 per rupee. What is his gain or loss percent? (a) 6.692% loss (b) 7.692% gain (c) 7.692% loss (d) 7.386% gain Q. 10. The difference between the selling prices after a discount of 40% on Rs.500 and two successive discount of 36% and 4% on the same amount is : (a) 0 (b) Rs.2 (c) Rs.1.93 (d) Rs.7.20 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 48 Recap (CO5) Basic concept of Profit & Loss Profit = SP – CP Loss = CP – SP Formulae: SP = CP (1 ± x/100) Basic concept of Discount Discount = MP− SP CP (1 ± x/100) = SP = MP ( 1 – d/100) Concept of successive discount 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 49 Average (CO5) Average = Sum of observation/Number of observation Q. 1. Find the average of all prime numbers between 30 and 50. Solution : There are five prime numbers between 30 and 50. There are 31, 37, 41, 43 and 47. Required average = (31 + 37 + 41 + 43 + 47)/5 = 199/5 = 39.8 Q. 2. Find the average of first 85 natural numbers. Solution : Sum of first n natural number = n(n + 1)/2 So, sum of first 85 natural numbers = (85 × 86)/2 = 3655 Required Average = 3655/85 = 43 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 50 Average (CO5)(Contd.) Q. 3. Nine person went to a hotel for taking their meals. Eight of them spent ₹ 12 each on their meals and the ninth spent ₹ 8 more than the average expenditure of all the nine. What was the total money spent by them? Solution : let the average expenditure of all the nine be ₹ x. then, 12 × 8 + (x+8) = 9x 8x = 104 or x = 13 total money spent = 9x = 9 × 13 = ₹117 Q. 4. The average weight of 10 person in a boat is increased by 1.8 kg when one of the crew, who weight 53 kg is replaced by new man. Find the weight of the new man. Solution : Total weight increased = 1.8 × 10 = 18 kg Weight of new man = 53 + 18 = 71 kg 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 51 Average (CO5)(Contd.) Q. 5. The average of marks of 17 students in an examination was calculated as 71. But it was later found that the mark of one student had been wrongly entered as 65 instead of 56 and another as 24 instead of 50. The correct average is? (NIET 2021-22) Solution: No.of students =17 Average marks =71 Total marks as previously entered =17x71=1207 Total marks as corrected =1207–65+56–24+50=1224 Corrected average =1224/17=72 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 52 Topic objective of Average (CO5) In statistics, an average is defined as the number that measures the central tendency of a given set of numbers. The objectives of statistical Average can be: 1. To facilitate comparison. For instance, measures of central value, by reducing the mass of data to one single figure, enable comparison to be made. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 53 Multiple Choice Question (CO5) Q.1. The average age of 10 students in a class is 20. If a new student is also included, then the new average age of all the students increases by 1. The age of the new student is? (a) 21 (b) 30 (c) 31 (d) 41 Q.2. A student on her first 3 tests received an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests? (a) N + 20 (b) N + 10 (c) N + 4 (d) N + 5 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 54 Multiple Choice Question (CO5) Q.3. Average of 13 number is 68. Average of its first seven numbers is 63 and last seven number is 70.Find out the seventh number. (a) 45 (b) 47 (c) 49 (d) 52 Q.4. Average of 10 numbers is 14.8.if two numbers 5 and 23 are replaced by 13 and 26 respectively, then what is the new average? (a) 15.9 (b) 13.8 (c) 16.3 (d) 14.5 Q.5. The mean of three numbers is 21. The range of this data set is 12 and the difference between the two smallest numbers is 3. The greatest of the three numbers is. (a) 24 (b) 27 (c) 25 (d) 28 Q.6. A man had 7 children. When their average age was 12 years , a child aged 6 years died. The average of reaming 6 children is (NIET 2023-24) (a) 13 years (b) 10 years (c) 11 years (d) 14 years 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 55 Ans. of Multiple Choice Question (CO5) ANS: 1. c 2. d 3. b 4. a 5.d 6. a 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 56 Quiz(CO5) The average of 12 numbers is 9. If each number is multiplied by 2 and added to 3, then find average of the new set of numbers ? The averages of runs scored by cricket player in 11 innings is 63 and the average of his first six innings is 60 and the average of last six innings is 65. Find the runs scored by him in the sixth innings ? The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ? (NIET 2021-22) The average marks obtained by 22 candidates in an examination are 45. The average marks of the first 10 candidates are 55 and those of the last eleven are 40.The number of marks obtained by the eleventh candidate is ? (NIET 2021-22) Aman goes to park daily. His last week average speed with which he completed one round of the park was 47Km/h, for the first four days was 37Km/h, and that for the last four days was 52.5Km/h. Find out the time taken by Aman to travel 203 Km if he travels with the speed of the fourth day? (NIET 2023-24) In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then find the number of girls in the school? (NIET 2023-24) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 57 Unit-5 Exercise (CO5) Q.1. The average age of four boys, five years ago was 9 years. On including a new boy, the present average age of all the five is 15 years. The present age of the new boy is (a) 14 years (b) 6 years (c) 15 years (d) 19 years Q.2. If the average of 39, 48, 51, 63, 75, 83, x and 69 is 60, then the value of x is : (a) 52 (b) 53 (c) 50 (d) 51 Q.3. A batsman makes a score of 58 runs in the 15th innings and thus increases his average by 3 runs. What is the average after 15th inning? (a) 12 (b) 14 (c) 16 (d) 18 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 58 Exercise (CO5) Q.4. In a family of 5 members, the average age at present is 33 years. The youngest member is 9 years old. The average age of the family just before the birth of the youngest member was (a) 24 years (b) 30 years (c) 29 years (d) 25 years Q.5. The average age of 14 girls and their teacher’s age is 15 years. If the teacher’s age is excluded, the average reduces by 1. What is the teacher’s age? (a) 32 years (b) 30 years (c) 29 years (d) 35 years Q.6. If out of 10 selected students for an examination, 3 were of 20 years, age, 4 of 21 and 3 of 22 years, the average age of the group is (a) 22 years (b) 21 years (c) 21.5 years (d) 20 years 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 59 Exercise (CO5) Q.7 A man had 7 children. When their average age was 12 years, a child aged 6 years died. The average age of remaining six children is (a) 13 years (b) 10 years (c ) 11 years (d) 14 years (NIET 2021-22) Q.8. The average of 5 consecutive numbers is n. If the next two numbers are also included, the average of the 7 number will (a) Increase by 2 (b) Increase by 1 (c) Remain the same (d) Increase by 1.4 Q.9 If the mean of four observations is 20 and when a C constant is added to each observation the mean becomes 22 The value of C is?(NIET 2022-23) (a) 2 (b) -2 (c ) 4 (d) None of these 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 60 Recap (CO5) Average = Sum of observation/Number of observation 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 61 Number & Series (CO5) Tips For Number Series (1) Try to observe if there are any familiar numbers in the given series. (2) Familiar numbers are the numbers which are easy to identify like primes numbers, perfect squares, cubes. (3) If you are unable to find familiar number, Calculate the differences between the numbers and observe the pattern in the differences. (4) If the differences are growing slowly it might be an addition or subtraction series or If the differences are growing rapidly it might be a square series, cube series, or multiplicative series. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 62 Number & Series (CO5) (Contd.) (5) If the differences also are not having any pattern then observe every alternate number (i.e. every 3rd number form a series) for any pattern. (6) The possible cases may be like sum or the average of two consecutive numbers gives 3rd number. (7)If still you do not find any pattern, it signifies that the series follows a complex pattern. Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 63 Topic objective of Number & Series (CO5) Series Number Sequence: Concepts & Tricks.... A numerical series is given in which a number is wrongly placed. You are asked to identify that particular wrong number. A numerical series is given in which a specific number is missing. You are required to find out that missing number. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 64 Number & Series (CO5) (Contd.) Different type question pattern Type 1: Fibonacci Series The Fibonacci sequence is a series of numbers where a no. is found by adding up the nos. before it. Q. 1. 0,1,1,2,3,5,8,13,21,___. Solution : Q. 2. 20, 12, 32, 44, 76, 120,____. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 65 Number & Series (CO5) (Contd.) Type 2: Addition series There can be 2 types of pattern in addition series. (A) Same number Addition series In this type of series, the difference between 2 consecutive elements is same i.e. same digit is to be added to the previous element to obtain the next element. Q.3. 3, 6, 9, 15, 18,___. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 66 Number & Series (CO5) (Contd.) (B) Increasing order Addition series In the given series, the difference between 2 consecutive numbers is in increasing order. Q.4. 2, 5, 9, 14, 20, 27,____. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 67 Number & Series (CO5) (Contd.) Type 3: Subtraction series (A) Same Number Subtraction Series In this type of series, each time the same number is subtracted from the previous element to obtain the next element. Q.5. 52, 49, 46, 43, 40,____. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 68 Number & Series (CO5) (Contd.) (B) Increasing order Subtraction Series Q.6. 94, 90, 85, 79, 72, 64,___. Solution : Here the difference between 2 consecutive elements is in increasing order. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 69 Number & Series (CO5) (Contd.) Type 4: Multiplication Series (A) Same number multiplication Series In this series, the ratio between 2 consecutive elements is same. Q.7. 4, 12, 36, 108, 324,____. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 70 Number & Series (CO5) (Contd.) (B) Increasing order of Multiplication Series In this type of series, elements are multiplied in increasing order to find the next element. Q.8. 5, 5, 7.5, 15,__ Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 71 Number & Series (CO5) (Contd.) Type 5: Addition & Multiplication together Q.9. 1, 3, 7, 15, 31,____. Solution : Type 6: Decimal Fraction Q.10. 36, 18, 18, 27, 54,___. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 72 Number & Series (CO5) (Contd.) Type 7: Difference of difference series Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference. Q.11. 1, 3, 8, 19, 39, 71,_____. Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 73 Number & Series (CO5) (Contd.) Type 8: Twin series In this type of series, odd place element males one series while the even place elements make another series. Q.12. 3, 6, 6, 12, 9, 18,______. Solution : Type 9: Tri-series Q.13. 2, 9, 23, 3, 8, 25, 4,_____. (NIET 2022-23) 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 74 Number & Series (CO5) (Contd.) Type 10: Square series & Cube series Q. 14. 4, 9, 16, 25, 36, 49,____. Solution : In the given series, the following pattern is used 22, 32, 42, 52, 62, 72, 82 Type 11: Square & Cube addition Q.15. 2, 3, 7, 16,_____. Solution : In the given series, the following pattern is used 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 75 Multiple Choice Questions (CO 5) Finding the Missing terms: Q.1. 1, 6, 15,?, 45, 66, 91 (a) 25 (b) 26 (c) 27 (d) 28 Q.2. 625, 5, 125, 25, 25, ?,5 (a) 5 (b) 25 (c) 125 (d) 625 Q.3. 9, 225, 16, 196,25, 169, ?,144 (a) 56 (b) 36 (c) 26 (d) 23 Q.4. 13 : 2197 :: 16 : ? (a) 256 (b) 2704 (c) 4096 (d) 3378 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 76 Multiple Choice Questions (CO 5) Find out the wrong number. Q.5. 196 169 144 121 101 (a) 101 (b) 121 (c) 169 (d) 196 Q.6. 3 10 27 4 16 64 5 25 125 (a) 3 (b) 4 (c) 10 (d) 27 Q.7. 2 5 10 17 26 37 50 64 (a) 17 (b) 26 (c) 37 (d) 64 Q.8. 16 22 30 45 52 66 (a) 30 (b) 45 (c) 52 (d) 66 Q.9. 125 126 124 127 123 129 (a) 126 (b) 124 (c) 123 (d) 129 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 77 Ans. of Multiple Choice Questions (CO5) Ans: 1.d 2.c 3.b 4.b 5.a 6.c 7.d 8. b 9. d 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 78 Quiz(CO5) Find the missing terms: 1015, 508, 255, 129, 66.5, -, 20.875 6, 5, 7, 12.5, 27, -? 6, 24, 60, 120, 210, -? 7, 12, 20, 37, 81, 206, -? (NIET 2021-22) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 79 Unit-5 Exercise (CO5) Q. 1. 1, 2, 9, ?, 16900 (a) 19 (b) 121 (c) 100 (d) 45 Q.2. 2, 4, 16, 512, ? (a) 2048 (b) 16384 (c) 524288 (d) 131072 Q.3. 6, 9, 7, 10, 8, 11, ? (a) 14 (b) 8 (c) 9 (d) 11 Q. 4. 563, 647, 479, 815, ? (a) 672 (b) 386 (c) 279 (d) 143 Q.5. 0, 7, 26, 63, 124, ? (a) 210 (b) 215 (c) 211 (d) 224 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 80 Exercise (CO5) Q.6. 72, 9, 82, 10, 88, 16, 86, 14, 99, ? (a) 102 (b) 22 (c) 18 (d) 16 Q.7. 6, 5, 7, 12.5, 27, ? (a) 69 (b) 57.5 (c) 67.5 (d) 69.5 Q.8. 2, 11, 58, 295, 1482,? (a) 6750 (b) 4450 (c) 6459 (d) 7419 Q.9. 2,11,58,295,1482, ? (NIET 2021-22) (a) 6750 (b) 4450 (c) 6459 (d) 7459 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 81 Recap (CO5) Tips For Number Series Different type question pattern (1) Fibonacci Series (2) Addition series (3) Subtraction series (4) Multiplication Series (5) Addition & Multiplication together (6) Decimal Fraction (7) Difference of difference series (8) Twin series (9) Tri-series 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 82 Coding & Decoding (CO5) Coding means to hide the meaning of any message and decoding means to understand the actual meaning of that message. Coding-decoding is one of the most important topic in reasoning section of any competitive exams. We can expect 5-6 questions from this section. Types of Coding-Decoding: Letter Coding Number Coding Symbol Coding Deciphering Message Word Coding/Numerical Coding Substitution Coding 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 83 Topic objective of Coding & Decoding(CO5) Coding is a process used to encrypt a word, a number in a particular code or pattern based on some set of rules. Decoding is a process to decrypt the pattern into its original form from the given codes.Number Coding In this type of questions, a word is replaced by certain numbers according to some specific rule. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 84 Coding & Decoding (CO5) (Contd.) Type 1: Letter Coding Order List of Alphabets: 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 85 Coding & Decoding (CO5) (Contd.) Q. 1. If “EXAM” is coded as “FYBN”, how is “RESULT” coded in the same language? Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 86 Coding & Decoding (CO5) (Contd.) Type 2: Number Coding Number Coding are based on numbers or numerical digits, given on some special pattern which look likes some code. In this first you have to look the both letter code and notice the numeric digit coded to that alphabet, and answer the common pattern available in the option. Q.2. If “ADDA” is coded as “5885”, “PEN” is coded as "147", how is “EDEN” coded in the same language? Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 87 Coding & Decoding (CO5) (Contd.) Type 3: SYMBOL CODING: Symbol Coding are based on Symbols. In this type of coding either alphabetical code are assigned to symbols or symbols are assigned to alphabets. Q.3. If “LESD” is written as “ @ $ & # “ , “NAC” is written as “ % ? * “, how “CANDLES” is coded in the same way? Solution : 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 88 Coding & Decoding (CO5) (Contd.) Type 4: Deciphering Message Word Coding/Numerical Coding Q.4. In a certain code language, 'put tir fin' means 'delicious juicy fruit'; 'tie dip sig' means 'beautiful white lily' and 'sig lon fin' means 'lily and fruit'. What is the code for 'and' in the language? Solution : In the first and third statements, the common code word is 'fin' and the common word is 'fruit'. So, 'fin ' stands for 'fruit'. In the second and third statements, the common code word is 'sig' and the common word is 'lily'. So, 'sig' stands for 'lily'. Thus, in the third statement, 'Lon' means 'and'. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 89 Coding & Decoding (CO5) (Contd.) Type 5: Substitution Coding In this type of coding, some particular words are assigned with certain substitution and on the basis of substitution word the code is derived. Q.5. If ‘white’ is called ‘blue’, ‘blue’ is called ‘red’, ‘red’ is called ‘yellow’, ‘yellow’ is called ‘green’, ‘green’ is called ‘black’, ‘black’ is called ‘violet’ and ‘violet’ is called ‘orange’, then what would be the color of human blood? Solution : The color of human blood is ‘red’ but here ‘red’ is called ‘yellow’. So, the color of human blood will be ‘yellow’. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 90 Multiple Choice Question (CO5) Directions (1-5): Read the following information carefully and answer the questions given below. All the codes given below are only in two letters format. “Banks are digital today” is written as “Zi Li Ki Ti”, “Money transfer through banks” is written as “Di Ki Si Fi”, “Digital money easy today” is written as “Si Zi Ti Bi” and “Today we have leave” is written as “Gi Xi Vi Zi”. (1) What is the possible code for “Easy for transfer”? (a) Fi Bi Zi (b) Di Ji Bi (c) Bi Ti Ui (d) Fi Li Xi 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 91 Multiple Choice Question (CO5) (2) If “Banks have money” is coded as “Gi Si Ki”, then what will be the code for “Leave”? (a) Di (b) Li (c) Zi (d) Cannot be determined (3) What is the code for “Transfer”? (a) Di (b) Either Di or Fi (c) Fi (d) Cannot be determined (4) What is the word for the code “Si” in the given code language? (a) Today (b) Banks (c) Money (d) Digital (5) If “Money market easy” is written as “Bi Si Ci”, then what will be the code for “Market”? (a) Bi (b) Si (c) Ci (d) Either Si or Ci 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 92 Multiple Choice Question (CO5) Q.6. In a certain code, TEACHER is written as VGCEJGT. How is CHILDREN written in that code ? (a)EJKNEGTP (b)EGKNFITP (c)EJKNFGTO (d)EJKNFTGP Q.7. If MACHINE is coded as 19-7-9-14-15-20-11, how will code DANGER? (a)11-7-20-16-11-24 (b)13-7-20-9-11-25 (c)10-7-20-13-11-24 (d)13-7-20-10-11-25 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 93 Multiple Choice Question (CO5) Q.8. In certain code language, ‘617’ means ‘sweet and hot’, ‘735’ means ‘coffee is sweet’ and ‘263’ means ‘tea is hot’. Which of the following mean ‘coffee is hot’ ? (a)731 (b)536 (c)753 (d)None of these Q.9. If ‘air’ is called ‘green’, ‘green’ is called ‘red’, ‘red’ is called ‘sea’, ‘sea’ is called ‘blue’, ‘blue’ is called ‘water’ and ‘water’ is called ‘pink’, then what is the color of grass? (a) Green (b) Air (c) Red (d) Pink Q.10. If ‘blue’ means ‘green’, ‘green’ means ‘yellow’, ‘yellow’ means ‘orange’, ‘orange’ means ‘black’, ‘black’ means ‘white’, ‘white’ means ‘red’, ‘red’ means ‘pink’, ‘pink’ means ‘brown’, ‘brown’ means ‘grey’, then what is the color of human blood? (a) White (b) Red (c) Black (d) none of these Q.11. If “PROMPT” is coded as QSPLOS , then “ PLAYER” should be ? (NIET 2023-24) (a) QMBZFS (b) QMBXDQ (c) QUREXM (d) URESTI. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 94 Ans. Multiple Choice Question (CO5) Ans: 1. b. 2.d 3.b 4.c 5.c 6.d 7.c 8.b 9. c 10.a 11. b 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 95 Quiz(CO5) If 35+48=40, 23+34=24, 15+25=26, then 11+21=? 14. In a certain code language 1326 is coded as 8673 and 5470 is coded as 4529, what is the code for 0009 in language? (NIET 2021-22) Banks are digital today” is written as “Zi Li Ki Ti”, “Money transfer through banks” is written as “Di Ki Si Fi”, “Digital money easy today” is written as “Si Zi Ti Bi” and “Today we have leave” is written as “Gi Xi Vi Zi”. What is the possible code for “Easy for transfer”? (NIET 2022-23) In a certain code language, ‘po se de’ means ‘she is good’, ‘tep re po’ means ‘good are clever’ and ‘se tep flu’ means ‘boy is clever’. Which of the following means ‘are’ in that language? If in a code language, COULD is written as BNTKC and MARGIN is written as LZQFHM, how will MOULDING be written in that code? (NIET 2022-23) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 96 Unit-5 Quiz(CO5) If ‘green’ is called ‘white’, ‘white’ is called ‘yellow’, ‘yellow’ is called ‘blue’, ‘blue’ is called ‘pink’ and ‘pink’ is called ‘black’, then what is the colour of milk? (NIET 2021-22) In certain code language ‘si po re’ means ‘book is thick’, ‘ti na re’ means ‘bag is heavy’, ‘ka si’ means ‘interesting book’ and ‘de ti’ means ‘that bag’. What should stand for ‘that is interesting’ in that code language? (NIET 2021-22) In certain code language, ROCK=47 and LATE=38. Find the code for FOOL? (NIET 2021-22) In a certain code language, GOODNESS is written as HNPCODTR, then how GREATNESS will be written in the same code language? (NIET 2023-24) B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 97 Unit-5 Exercise (CO5) Q. 1. If in a certain code “RANGE” is coded as 12345 and “RANDOM” is coded as 123678. Then the code for the word “MANGO” would be? (a) 82357 (b) 84629 (c) 82347 (d) 83274 Q.2. If “PROMPT” is coded as QSPLOS, then “PLAYER” should be? (a) QMBZFS (b) QMBXDQ (c) QUREXM (d) URESTI Q.3. In a certain code language, 'no more food' is written as 'ta ka da' and 'more than that' is written as 'sa pa ka'. How is 'that' written in that code language? (a) Sa (b) ka (c) sa or pa (d) data inadequate Q.4.In a certain code GUEST is written as 53@$2 and MEAN is written as 6@4#. How is SAME written in that code? (a) 4$6@ (b) $46@ (c) $36@ (d) 5$6@ 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 98 Exercise (CO5) Q.5. In certain code, RELATION is written as ZKDQMNHS and NOSE is written as NMDR. How will MISTER be written in that code? (a) NHRQFS (b) QHLMDQ (c) RHLMDQ (d) RHLQDS Q.6. In certain code language, CHANAKYA is coded as ZBPZMZSX. How will KAUTILYA be coded in the same code language? (a) ZBMNFGZP (b) ZBORGFZP (c) ZBOMFGZP (d) ZBONGFZP Q.7. In a certain code language, 732 means ‘intelligent trained faculty’ 285 means ‘highly intelligent student’, 816 means ‘student and teacher’. Which numerical symbol in that code language stands for ‘highly’? (a) 5 (b) 8 (c) 7 (d) 2 Q.8.In certain code language SERIES is coded as 5625 and PIPE is coded as 2116. How will WAP be coded in the same code language? (a) 1331 (b) 1600 (c) 1728 (d) 4096 (NIET 2021-22) 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 99 Recap (CO5) Types of Coding-Decoding: Letter Coding Number Coding Symbol Coding Deciphering Message Word Coding/Numerical Coding Substitution Coding 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 100 Algebra Algebra (CO5) Remainder Theorem: When a polynomial is p(x) is divided by another polynomial ( x-a ), then the remainder of the end result that is obtained is p ( a ). Example 1: Using the Remainder Theorem, find the remainder when x6 – 5x4 + 3x2 + 10 is divided by x – 2. Solution: Let p(x) = x6 – 5x4 + 3x2 + 10 Substitute x = 2 in p(x). Remainder= p(2) = (2)6 – 5(2)4 + 3(2)2 + 10 =6 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 101 Unit-5 Algebra Algebra (CO5) Example2: The polynomial 4x2 – kx + 7 leaves a remainder of –2 when divided by x – 3. Find the value of k. Solution: Let p(x) = 4x2 – kx + 7 Put x=3 in p(x) Remainder =p(3)= -2 4(3)2 – k(3) + 7 = -2 k = 15 Therefore, the value of k is 15. B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 102 Unit-5 Algebra Algebra (CO5) Example 3: If two polynomials 2x3 + kx2 + 4x – 12 and x3 + x2 – 2x + k leave the same remainder when divided by (x – 3), find the value of k and the remainder. Solution: Let p(x) = 2x3 + kx2 + 4x – 12 and f(x) = x3 + x2 – 2x + k Thus, p(3) = f(3) 2(3)3 + k(3)2 + 4(3) – 12 = (3)3 + (3)2 – 2(3) 54 + 9k + 12 – 12 = 27 + 9 – 6 + k 8k = -24 k = -3 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 103 Unit-5 Algebra Algebra (CO5) Substituting k = -3 in p(x), we get; p(x) = 2x3 + (-3)x2 + 4x – 12 = 2x3 – 3x2 + 4x – 12 Now, p(3) = 2(3)3 – 3(3)2 + 4(3) – 12 = 54 – 27 + 12 – 12 = 27 Therefore, k = -3 and the remainder = 27. B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 104 Unit-5 Algebra Algebra (CO5) Quadratic Equation: Usually, the quadratic equation is represented in the form of ax2+bx+c=0, where x is the variable and a,b,c are the real numbers & a ≠ 0. Here, a and b are the coefficients of x2 and x, respectively. So, basically, a quadratic equation is a polynomial whose highest degree is 2. Let us see some examples: 3x2+x+1, where a=3, b=1, c=1 9x2-11x+5, where a=9, b=-11, c=5 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 105 Unit-5 Algebra Algebra (CO5) Quadratic Equation Formula: −𝑏± 𝑏2 −4𝑎𝑐 The quadratic formula to find the roots of the quadratic equation is given by 𝑥 = 2𝑎 Where b2-4ac is called the discriminant of the equation. Based on the discriminant value, there are three possible conditions, which defines the nature of roots as follows: two distinct real roots, if b2 – 4ac > 0 two equal real roots, if b2 – 4ac = 0 no real roots, if b2 – 4ac < 0 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 106 Unit-5 Algebra Algebra (CO5) Example1: Solve the equation x2+4x-5=0. Solution: x2 + 4x – 5 = 0 (x-1)(x+5) =0 x = 1 and x =-5. Example2: Solve the quadratic equation 2x2 + x – 528 = 0, using quadratic formula. Solution: −𝑏± 𝑏2 −4𝑎𝑐 By using the quadratic formula:𝑥 = 2𝑎 −1± 4225 −1±65 𝑥= = 4 4 x=16 or x=-33/2 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 107 Unit-5 Algebra Algebra (CO5) Example 3: Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with. Solution: The number of marbles Rahul had be x. Then the number of marbles Rohan had = 45 – x. The number of marbles left with Rahul after losing 5 marbles = x – 5 The number of marbles left with Rohan after losing 5 marbles = 45 – x – 5 = 40 – x B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 108 Unit-5 Algebra Algebra (CO5) The product of number of marbles = 124 (x – 5) (40 – x) = 124 x2 – 45x + 324 = 0 This represents the quadratic equation. Hence by solving the given equation for x, we get; x = 36 and x = 9 So, the number of marbles Rahul had is 36 and Rohan had is 9 or vice versa. B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 109 Unit-5 Algebra Algebra (CO5) Example 4: Find the value of 6 + 6 + 6 + ………….∞ Solution: let 𝑥 = 6+ 6+ 6+ ………….∞ 𝑥 = 6+𝑥 Squaring on both sides, we get 𝑥 2 = 6 + 𝑥 Solving we get 𝑥 = 3, −2 but the given quantity is positive. Hence x = 3 B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 110 Unit-5 Algebra (CO5) Arithmetic progression : If a is the first term and d is the common difference of an A.P. then that A.P is a + (a+d) + (a+2d)+...... If the same quantity is added (multiplied) to each term of an A.P. then the resulting series is also an A.P. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 111 Algebra (CO5) n th term of an A.P. 𝑎𝑛 = 𝑎 + 𝑛 − 1 𝑑 𝑛 Sum to first n terms of an A.P. =𝑠𝑛 = 2𝑎 + 𝑛 − 1 𝑑 2 If we know the last term of a series then 𝑠𝑛 =(a + l) where l is the last term. A series in which each term (except first term) is obtained by multiplying the preceeding term by a fixed quantity is called a Geometric progression (G.P) and the fixed quantity is called the common ratio. If a is the first term and r is the common ratio of a G.P. then that G.P is 𝑎 + 𝑎𝑟 + 𝑎𝑟 2 + 𝑎𝑟 3 + ⋯ … … … … …If every term of a G.P. is multiplied by a fixed real number, then the resulting series is also a G.P. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 112 Algebra (CO5) If every term of a G.P is raised to the same power, then the resulting series is also a G.P. The reciprocals of the terms of a G.P. is also a G.P. nth term of a G.P is 𝑎𝑛 = 𝑎𝑟 𝑛−1 The sum of first n terms of a G.P 𝑟 𝑛 −1 1−𝑟 𝑛 𝑆𝑛 = 𝑎 if 𝑟 > 1; 𝑎 if r < 1 𝑟−1 1−𝑟 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 113 Algebra (CO5) Harmonic progression If the reciprocals of the terms of a series form An A.P., then the series is called a Harmonic progression (H.P.). Example1: Find the15th term of given A.P.3+5+7+......... Solution: We know that n th term of an A.P 𝑎𝑛 = 𝑎 + 𝑛 − 1 𝑑 a = 3; d = 2, 15th term = a + 14d = 3 + 14(2) = 31 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 114 Algebra (CO5) Examlpe 2: How many terms are added in 24+20+16+ …….. 10 make the sum 72. Solution: Sum to first n terms of an A.P. is 𝑛 𝑠𝑛 = 2𝑎 + 𝑛 − 1 𝑑 2 𝑛 2𝑎 + 𝑛 − 1 𝑑 =72 2 𝑛 48 − 𝑛 − 1 4 = 144 𝑛 = 4&9 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 115 Algebra (CO 5) Example3: Which term of the series 1+2+4+8+...................... is 256 Solution: nth term of a G.P is 𝑎𝑛 = 𝑎𝑟 𝑛−1 256= 𝑎𝑟 𝑛−1 256= 1 × 2𝑛−1 28 = 2𝑛−1 n=9 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 116 Algebra (CO 5) Example 4: If 6th term of a G.P is −132 and 9th term is 1256 then find the 11th term ? Solution: 6th term = 𝑎𝑟 5 = −132 9th term = 𝑎𝑟 8 = 1256 Dividing 9th term with 6th term, 1 𝑟3 =− 8 1 𝑟=− 2 1 1 11thterm=𝑎𝑟10 = (− )8 = 2 1024 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 117 Algebra (CO5) Example 5: If the 3rd and 7th terms of a H.P. are 1/7,1/15 then find nth term? 1 Solution: General term in H.P.= 𝑎+ 𝑛−1 𝑑 1 1 3rd term = = ⇒ 𝑎 + 2𝑑 = 7 … (1) 𝑎+2𝑑 7 1 1 7rd term = = ⇒ 𝑎 + 6𝑑 = 15 … 2 𝑎+6𝑑 15 Solving (1) and (2) we get, a=3 and d=2 1 1 General term = = 3+ 𝑛−1 2 2𝑛+1 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 118 Multiple Choice Question (CO5) 1.If x4 - 3x + 5 is divided by 2x - 1, then the remainder is (a) 35⁄16 (b) −35⁄16 (c) 57/16 (d) 3 2. If x² - 7x + a has a remainder 1 when divided by x + 1, then a is (a) a = -7 (b) a = 7 (c) a = 0 (d) a = 1 3. If x³ + 9x +5 is divided by x, then the remainder is (a) 9 (b) 0 (c) −9 (d) 5 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 119 Multiple Choice Question (CO 5) 4. Rohini could have gotten 10 additional marks out of a possible 30 on her math test, which would have been the square of her actual score 9 times. How many marks did she receive on the exam? (a)16 (b) 18 ( c) 15 ( d) 14 5. The equation 2x² + kx + 3 = 0 has two equal roots, then the value of k is (a) ±√6 (b) ± 4 (c) ±3√2 (d) ±2√6 6. The equation 12x² + 4kx + 3 = 0 has real and equal roots, if (a) k = ±3 (b) k = ±9 (c) k = 4 (d) k = ±2 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 120 Multiple Choice Question (CO5) 7. If the common difference of an arithmetic progression is 4 and the first term is 3, what is the 10th term? (a) 39 (b) 43 (c) 47 (d) 53 8. What is the sum of the first 20 terms of an arithmetic progression whose first term is 5 and common difference is 3? (a) 670 (b) 620 (c) 610 ( d) 600 9. The 6th term of an arithmetic progression is equal to twice the 2nd term. What is the ratio of the 5th term to the 3th term? (a) 7/5 (b) 7/3 (c ) 9/5 (d) None of these 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 121 Multiple Choice Question (CO5) 10. If a,4,b are in AP and a,2,b are in GP, then a,1,b are in (a) AP (b) GP (c) HP (d) None of these 11. The 6th term of a GP is 32 and its 8th term is 128, then the common ratio of the GP is (a) -1 (b) 2 ( c) 4 (d) -4 12. The first term of a GP is 27 and its 8th term is 1/81. Find the sum of its first 10 terms 27 1 81 1 27 1 81 1 (a) 1− (b) 1+ (c) 1− (d) 1− 2 310 2 310 2 39 2 310 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 122 Ans. Of Multiple Choice Question (CO5) Ans. 1.c 2. a 3.d 4. c 5. c 6. a 7. a 8. a 9. a 10.c 11. b 12. d 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 123 Exercise (CO5) Q.1. If x = (√126 × √63 × √45) / (√147 × √243), then the value of x is (a) √5 (b) √10 (c) 10 (d) 5 Q.2. A reduction of 20% percent in the price of rice enables a housewife to buy 5 kg more for rupees 1200. Find the reduced price per kg of rice. Q.3. A student has to get 40 percent marks to pass an examination. He got 60 marks but fails by 20 marks. Find the maximum marks of the examination. Q.4. If the price of a commodity is increased by 30%, by how much % a consumer must reduce his consumption so to keep the expenditure same ? Q.5. If a sari is sold for ₹ 2880 the seller will face 10% loss, at what price should he sell to gain 20% profit? 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 124 Exercise (CO5) Q.6. A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. Find his gain%. Q.7. The average weight of 10 person in a boat is increased by 1.8 kg when one of the crew, who weight 53 kg is replaced by new man. Find the weight of the new man. Q.8. The mean of three numbers is 21. The range of this data set is 12 and the difference between the two smallest numbers is 3. Find the greatest of the three numbers. Q.9. 13 : 2197 :: 16 : ? (a) 256 (b) 2744 (c) 4096 (d) 3378 Q.10. 1015, 508, 255, 129, 66.5, ?, 20.875 (a) 34.50 (b) 35 (c) 35.30 (d) 35.75 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 125 Exercise (CO5) Q.11. Find out the wrong number of : 125 126 124 127 123 129 Q.12. If “Money market easy” is written as “Bi Si Ci”, then what will be the code for “Market”? Q.13. If MACHINE is coded as 19-7-9-14-15-20-11, how will code DANGER? Q.14. If ‘grass is green’ is coded as ‘$#@’, ‘grass in pink’ is coded as ‘%@&’ and ‘ green colour park’ is coded as ‘$&*’ , then what is the code for ‘colour is green’ ? Q.15. A Shopkeeper buys two bicycles for Rs. 750. He sells first bicycle at a profit of 22% and the second bicycle at a loss of 8%. What is the SP of first bicycle if in the whole transaction there is no profit no loss? 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 126 Exercise (CO5) Q.11. If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first 𝑛 terms of the A.P. Q.12. The 14𝑡ℎ term of an AP is twice its 8 𝑡ℎ term. If its 6𝑡ℎ term is −8, then find the sum of its first 20 terms. Q.13. The equation kx² + kx + 3 = 0 has two equal roots, then find the value of k ? Q.14. The polynomial 5x2 – kx + 3 leaves a remainder of 3 when divided by x – 1. Find the value of k. Q.15. In a G.P, the 6th term is 24 and the 13th term is 3/16 then find the 20th term of the sequence. 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 127 Summary (CO5) We discussed the following points with students: Course Objective COs and POs of subject Mapping of COs and Pos Prerequisite and Recap Simplification Percentage Profit, Loss & discount Average Number & Series Coding & decoding Algebra MCQs 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 128 Faculty Video Links, Youtube Links and Online Courses Details Suggested Links: Simplification https://youtu.be/gh4igD4fAqM Percentage https://youtu.be/gbR_m1byDns Profit ,Loss &Discount https://youtu.be/58BWZL8f2qQ B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 129 Unit-5 Faculty Video Links, Youtube Links and Online Courses Details Suggested Links: Average https://youtu.be/mzGZfv63oD4 Number &Series https://youtu.be/Wgg34HnJDv4 Coding &Decoding https://youtu.be/0qTnewnVRLo B. N. Tripathi Engineering Mathematics-I(BAS0103) 12/5/2024 130 Unit-5 Reference Website - https://www.GovernmentAdda.com Books references – R.S. Agrawal 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 131 Reference Website - https://www.GovernmentAdda.com Books references – R.S. Agrawal 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 132 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2023-24 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 133 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2023-24 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 134 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2023-24 12/5/2024 B. N. 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QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 143 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 144 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 145 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 146 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 147 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2022-23 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 148 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2021-22 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 149 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2021-22 12/5/2024 B. N. 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QUESTION PAPER PATTERN FOR OFFLINE MODE 2020-21 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 158 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2020-21 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 159 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2020-21 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 160 END SEM. QUESTION PAPER PATTERN FOR OFFLINE MODE 2023-24 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5 161 162 12/5/2024 B. N. Tripathi Engineering Mathematics-I(BAS0103) Unit-5
