Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Class: 8Samacheer KalviMax Marks: 59
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 10 × 1 = 10
Choose the correct answer. (Answer all questions.)
1.Which of these rational number which have additive inverse?A. 7B. \(\frac{-5}{7}\)C. 0D. all of these[1]
2.Common prime factors of 36,60 and 72 areA. 2 × 2B. 2 × 3C. 3 × 3D. 3 × 2 × 2[1]
3.In how many ways can you answer 3 multiple choice questions, with the choices A,B,C and D?A. 4B. 3C. 12D. 64[1]
4.When I go shopping, I will buyA. something that looks attractiveB. something my friend hasC. something that I need to purchaseD. the first thing I see in the store[1]
5.By selling a flower pot for Z528, a woman gains 20%. At what price should she sell it to gain 25%?A. ₹ 500B. ₹ 550C. ₹ 553D. ₹ 573[1]
6.What is the marked price of a hat which is bought for Z210 at 16% discount?A. ₹ 243B. ₹ 176C. ₹ 230D. ₹ 250[1]
7.15% of 25% of 10000 = ________ .A. 375B. 400C. 425D. 475[1]
8.\(\frac{1}{2}-\left(\frac{3}{4}-\frac{5}{6}\right) \neq\left(\frac{1}{2}-\frac{3}{4}\right)-\frac{5}{6}\) illustrates that subtraction does not satisfy the ________ property for rational numbers.A. commutativeB. closureC. distributiveD. associative[1]
9.Which is not correct?A. \(\left(\frac{-1}{4}\right)^{2}\) = 4 -2B. \(\left(\frac{-1}{4}\right)^{2}=\left(\frac{1}{2}\right)^{4}\)C. \(\left(\frac{-1}{4}\right)^{2}\) = 16 -1D. \(-\left(\frac{1}{4}\right)^{2}\) = 16 -1[1]
10.0.0000000002020 in scientific form is __________ .A. 2.02 × 10 9B. 2.02 × 10 -9C. 2.02 × 10 -8D. 2.02 × 10 -10[1]
Part II — Fill in the Blanks 5 × 1 = 5
Fill in the blanks. (Answer all questions.)
11.Similar triangles have the same ________ but not necessarily the same size.[1]
12.The rational numbers \(\frac{-8}{3}\) and \(\frac{8}{3}\) are equidistant from _________.[1]
13.The total area of the histogram is _________ to the total frequency of the given data.[1]
14.Loss or gain percentage is always calculated on the ________ .[1]
15.A line segment which joins any two points on a circle is a _______ .[1]
Part III — True or False 5 × 1 = 5
Write True or False. (Answer all questions.)
16.A square is a parallelogram.[1]
17.The cube of 0.0012 is 0.000001728.[1]
18.(i) The cube of 24 ends with the digit 4.[1]
19.(-10,20) lies in the second quadrant.[1]
20.The cube root of 250047 is 63.[1]
Part IV — Short Answer Questions 12 × 2 = 24
Answer briefly. (Answer all questions.)
21.Verify the identity property for addition and multiplication for the rational numbers \(\frac{15}{19}\) and \(\frac{-18}{25}\).[2]
22.Subtract – 2mn from 6mn.[2]
23.A student can type 21 pages in 15 minutes. At the same rate, how long will it take student to type 84 pages?[2]
24.Peter had a Two hundred rupee note. After buying 7 copies of a book he was left with 60.[2]
25.Find the simple interest on Rs. 5a 2 b 2 for 4ab years at 7b% per annum.[2]
26.If 35 women can do a piece of work in 16 days, In how many days will 28 women do the same work?[2]
27.The data on modes of transport used by the students to come to school are given below. Draw a pie chart for the data.[2]
28.Find the standard form of (i) \(\frac{36}{-96}\) (ii) \(\frac{-56}{-72}\) (iii) \(\frac{27}{18}\)[2]
29.In how many years will ₹ 2000 become ₹ 3600 at 10% p.a simple interest?[2]
30.Write in standard form: Mass of planet Uranus is 8.68 × 10 25 kg.[2]
31.Find the square root of the following decimal numbers and fractions. (i) 2.89 (ii) 67.24 (iii) 2.0164 (iv) \(\frac{144}{225}\) (v) \(7 \frac{18}{49}\)[2]
32.Find the square of the following numbers. (i) 17 (ii) 203 (iii) 1098[2]
Part V — Long Answer Questions 3 × 5 = 15
Answer in detail. (Answer all questions.)
33.Identify the numerical co-efficient of each term in the following expressions. (i) 2x 2 – 5xy + 6y 2 + 7x – 10y + 9[5]
34.Factorise the following by taking out the common factor (i) 18xy – 12yz[5]
35.Name the quadrilaterals (a) Which have diagonals bisecting each other.[5]
🔑 Show Answer Key — Set 1
- 1. (D) all of these Hint: Additive inverse of 7 is -7 Additive inverse of \(\frac{-5}{7}\) is \(\frac{5}{7}\) Additive inverse of 0 is 0
- 2. (d) 3 × 2 × 2 Hint: Prime factors of 36 are 2 × 2 × 3 × 3 Prime factors of 60 are 2 × 2 × 3 × 5 Prime factors of 72 are 2 × 2 × 2 × 3 × 3 ∴ Common prime factors are 2 × 2 × 3
- 3. 64
- 4. (c) something that I need to purchase
- 5. (B) ₹ 550 Hint: If selling price (sp) = ₹ 528 Gain % = 20 % ∴ CP = ?
- 6. (D) ₹ 250 Hint: Let marked price be MP Discounted price = ₹ 210 Rate of discount = 16% As per formula:
- 7. (A) 375 Hint: 15% of 25% of 10000 is First let us do 25% of 10,000, which isNext 15% of the above is \(\frac{15}{100}\) × 2500 = 375
- 8. (D) associative
- 9. \(-\left(\frac{1}{4}\right)^{2}\) = 16 -1 Hint: (-2) – 3 x (- 2) – 2 = (-2) – 3 – 2 = (-2) – 5 (\(-\frac { 1 }{ 2 }\))5 = \(-\frac { 1 }{ 32 }\)
- 10. (D) 2.02 × 10 -10 Hint: 0.0000000002020
- 11. Shape
- 12. 0
- 13. proportional
- 14. Cost Price
- 15. Chord
- 16. True
- 17. False
- 18. True
- 19. True Hint: (-10, 20) x = -10, y = 20 ∴ (-10, 20) lies in second quadrant – True
- 20. True
- 21. Identify property for addition verified.Identify property for multiplication verified.
- 22. 6 mn – (-2mn) = 6mn + (+ 2mn) = (6 + 2)mn = 8mn
- 23. Direct proportion No. of minutes = x k = \(\frac{21}{15}\) \(\frac{21}{15}=\frac{84}{x}\)
- 24. Let cost of one book be ‘x’ ∴ Given that 200 – 7 × x = 60 ∴ 200 – 7x = 60
- 25. (refer textbook)
- 26. Inverse proportion No. of days = x k = 35 × 16 ∴ 28 × x = 35 × 16Try These (Text Book Page No. 145)
- 27. Converting the percentage into components parts of 360°. we haveMode of Transport by students.
- 28. (i) \(\frac{36}{-96}\) = \(\frac{-36 \div 12}{96 \div 12}=\frac{-3}{8}\) (ii) \(\frac{-56}{-72}\) = \(\frac{-56 \div(-8)}{-72 \div(-8)}=\frac{7}{9}\) (iii) \(\frac{27}{18}\) = \(1 \frac{9}{18}=1 \frac{1}{2}\)
- 29. I = 3600 – 2000 = 1600Try These (Text Book Page No. 141)
- 30. Mass of Planet Uranus = 86800000000000000000000000 kg [23 zeros after 88]
- 31. (i) 2.89√2.89 = 1.7 (ii) 67.24√67.24 = 8.2 (iii) 2.0164√2.0164 = 1.42(iv) \(\frac{144}{225}\)(v) \(7 \frac{18}{49}\)\(\sqrt{7 \frac{18}{49}}=2 \frac{5}{7}\)
- 32. (i) 17(ii) 203(iii) 1098
- 33. Numerical co efficient in 2x 2 is 2 Numerical co efficient in -5xy is -5 Numerical co efficient in 6y 2 is 6 Numerical co efficient in 7x is 7 Numerical co efficient in -10y is -10 Numerical co-efficient in 9 is 9 (ii) \(\frac{x}{3}+\frac{2 y}{5}\) – xy + 7 Numerical co efficient in \(\frac{x}{3}\) is \(\frac{1}{3}\) Numerical co efficient in \(\frac{2 y}{5}\) is \(\frac{2}{5}\) Numerical co efficient in – xy is – 1 Numerical co efficient in 7 is 7
- 34. 18xy – 12yz = (2 × 3 × 3 × y × x) – (2 × 2 × 3 × y × z) Taking out the common factors 2, 3, y, we get = 2 × 3 × y(3x – 2z) = 6y(3x – 2z)(ii) 9x 5 y 3 + 6x 3 y 2 – 18x 2 y 9x 5 + 6x 3 y 2 – 18x 2 y = (3 × 3 × x 2 × x 3 × y × y) + (2 × 3 × x 2 × x × y × y) – (2 × 3 × 3 × x 2 × y) Taking out the common factors 3, x 2 , y, we get = 3 × x 2 × y (3x 3 y 2 + 2xy – 6) = 3x 2 y (3x 3 y 2 + 2xy – 6) (iii) x(b – 2c) + y(b – 2c) Taking out the binomial factor (b – 2c) from each term, we have = (b – 2c)(x + y) (iv)(ax + ay) + (bx + by) Taking at ‘a’ from the first term and ‘b’ from the second term we have (ax + ay )+ (bx + by) = a(x + y) + b(x + y) Now taking out the binomial factor (x + y) from each…
- 35. Square, rectangle, parallelogram, rhombus. (b) In which the diagonals are perpendicular bisectors of each other. Rhombus and square. (c) Which have diagonals of different lengths. Parallelogram and Rhombus (d) Which have equal diagonals. Rectangle, square. (e) Which have parallel opposite sides. Square, Rectangle. Rhombus, parallelogram. (f) In which opposite angles are equal. Square, rectangle. rhombus, parallelogram
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 8Samacheer KalviMax Marks: 59
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 10 × 1 = 10
Choose the correct answer. (Answer all questions.)
1.By what number should (-4) -1 be multiplied so that the product becomes 10 -1 ?A. \(\frac{2}{3}\)B. \(\frac{-2}{5}\)C. \(\frac{5}{2}\)D. \(\frac{-5}{2}\)[1]
2.Which of the following pairs represents equivalent rational numbers? (i) \(\frac{-6}{4}, \frac{18}{-12}\) (ii) \(\frac{-4}{-20}, \frac{1}{-5}\) (iii) \(\frac{-12}{-17}, \frac{60}{85}\)[1]
3.Online or television advertisements influence people on spending decisions byA. using special musicB. making them think that they need the itemC. using attractive picturesD. all the above[1]
4.The missing terms in the product -3m 3 n × 9(_) = _______ m 4 n 3 areA. mn 2 , 27B. m 2 n, 27C. m 2 n 2 , – 27D. mn 2 , – 27[1]
5.If 48% of 48 = 64% of x, then x =A. 64B. 56C. 42D. 36[1]
6.Which of the following illustrates the inverse property for addition?A. \(\frac{1}{8}-\frac{1}{8}=0\)B. \(\frac{1}{8}+\frac{1}{8}=\frac{1}{4}\)C. \(\frac{1}{8}+0=\frac{1}{8}\)D. \(\frac{1}{8}-0=\frac{1}{8}\)[1]
7.The best shopping choice is toA. shop at brand name stores always buyB. compare the choices before buyingC. the same thing my friends boughtD. buy at a regular shop always[1]
8.The sum which amounts to ₹ 2662 at 10% p.a in 3 years, compounded yearly is _________ .A. ₹ 2000B. ₹ 1800C. ₹ 1500D. ₹ 2500[1]
9.Common prime factors of 30 and 250 areA. 2 × 5B. 3 × 5C. 2 × 3 × 5D. 5 × 5[1]
10.In a class there are 26 boys and 15 girls. The teacher wants to select a boy or a girl to represent a quiz competition. In how many ways can the teacher make this selection?A. 41B. 26C. 15D. 390[1]
Part II — Fill in the Blanks 5 × 1 = 5
Fill in the blanks. (Answer all questions.)
11.The value of \(\left(\frac{-15}{23}\right) \div\left(\frac{30}{-46}\right)\) is ________ .[1]
12.The coordinates of the point in third quadrant are always _________ .[1]
13.The exterior angle of a triangle is equal to the sum of the _______ angles to it.[1]
14.The x- coordinate is always ______ on the y-axis.[1]
15.Data has already been collected by some other person is ________ data.[1]
Part III — True or False 5 × 1 = 5
Write True or False. (Answer all questions.)
16.The square of 75 is 4925.[1]
17.The multiplicative inverse exists for all rational numbers.[1]
18.(i) The points (1,1) (2,2) (3,3) lie on a same straight line.[1]
19.The simplified form of \((256)^{\frac{-1}{4}} \times 4^{2}\) is \(\frac{1}{4}\).[1]
20.If 8 x = \(\frac { 1 }{ 64 }\), the value of x is -2.[1]
Part IV — Short Answer Questions 12 × 2 = 24
Answer briefly. (Answer all questions.)
21.Ramya wants to paint a pattern in her living room wall with minimum budget. Help her to colour the pattern with 2 colours but make sure that no two q adjacent boxes are the same colour. The pattern is shown in the picture.[2]
22.Represent \(\left(\frac{1}{2}+\frac{1}{4}\right)\) by a diagram.[2]
23.Consider that you are going to a store with your total budget of ₹ 220 to buy things without changing the quantity of the items given in the list below with the following conditions. Conditions: (i) First you have to complete the price list given. (ii) You have to buy three items as per the given price list but within your budget ₹ 220. (iii) You wont carry exceeding 5kg because you have to walk home carrying them, so they cannot be bulky. Now, answer the following questions: 1. In how many ways can you buy your items? Complete the price lists given below. One is done for you. 2. Which one is the best purchase price list and why?[2]
24.Simplify \(\frac{1}{2}+\left(\frac{3}{2}-\frac{2}{5}\right) \div \frac{3}{10} \times 3\) and show that it is a rational number between 11 and 12.[2]
25.Represent the following data in ungrouped frequency table which gives the number of children in 25 families. 1, 3, 0, 2, 5, 2, 3, 4, 1, 0, 5, 4, 3, 1, 3, 2, 5, 2, 1, 1, 2, 6, 2, 1, 4[2]
26.\(\frac{486}{1000}\)[2]
27.Statement A: If 24p 2 q is divided by 3pq, then the quotient is 8p. Statement B: Simplification of \(\frac{(5 x+5)}{5}\) is 5x. (i) Both A and B are true (ii) A is true but B is false (iii) A is false but B is true (iv) Both A and B are false[2]
28.Is the number -7 a rational number? Why?[2]
29.Which among 256, 576, 960, 1025,4096 are perfect square numbers? (Hint: Try to extend the table of squares already seen).[2]
30.Try These (Text Book Page No. 122) Find the indicated percentage value of the given numbers.[2]
31.Draw the graph of the following equations: (i) x = – 7 (ii) y = 6[2]
32.Where are the even Fibonacci Numbers? Colour both the term n and where F(n) is even in yellow. Do you find any pattern? Every Third Fibonacci number is a multiple of 2(even).[2]
Part V — Long Answer Questions 3 × 5 = 15
Answer in detail. (Answer all questions.)
33.An examination paper has 3 sections, each with five questions and students are instructed to answer one question from each section. In how many different ways of can the questions be answered?[5]
34.By selling a speaker for ₹ 768, a man loses 20%. In order to gain 20%, how much should he sell the speaker?[5]
35.Find the principal if the difference between C.I and S.l on it at 15% p.a for 3 years is ₹ 1134.[5]
🔑 Show Answer Key — Set 2
- 1. (B) \(\frac{-2}{5}\) Hint: (-4) -1 = \(\left(-\frac{1}{4}\right)^{1}=\frac{-1}{4}\)
- 2. (i) \(\frac{-6}{4}, \frac{18}{-12}\) \(\frac{-6}{4}=\frac{-6 \times 3}{4 \times 3}=\frac{-18}{12}\) ∴ \(\frac{-6}{4}\) equivalent to \(\frac{-18}{12}\) (ii) \(\frac{-4}{-20}, \frac{1}{-5}\) \(\frac{-4}{-20}=\frac{-4 \div(-4)}{-20 \div(-4)}=\frac{1}{5} \neq-\frac{1}{5}\) ∴ \(\frac{-4}{-20}\) equivalent to \(\frac{1}{-5}\) (iii) \(\frac{-12}{-17}, \frac{60}{85}\) \(\frac{-12}{-17}=\frac{-12 x-5}{-17 x-5}=\frac{60}{85}\) ∴ \(\frac{-12}{-17}\) equivalent to \(\frac{60}{85}\)
- 3. (d) all the above
- 4. (A) mn 2 , 27
- 5. (D) 36 Hint: Given that 48% of 48 = 64% of xx = 36
- 6. (A) \(\frac{1}{8}-\frac{1}{8}=0\)
- 7. (b) compare the choices before buying
- 8. (A) ₹ 2000 Hint: Amount = ₹ 2662 rate of interest = 10 % p.a Time period = 3 yrs. Compounded yearly Principal (P) → required to find?
- 9. (a) 2 × 5 Prime factors of 30 are 2 × 3 × 5 Prime factors of 250 are 5 × 5 × 5 × 2 ∴ Common prime factors are 2 × 5
- 10. 41
- 11. 1
- 12. negative
- 13. interior
- 14. Zero
- 15. Secondary
- 16. False
- 17. False
- 18. True Hint: The points (1, 1), (2, 2), (3, 3) all satisfy the equation y = x which is straight line. Hence, it is true
- 19. True
- 20. True
- 21. (refer textbook)
- 22. Try These (Text Book Page No. 3)
- 23. (refer textbook)
- 24. (refer textbook)
- 25. The data given is raw data. Ascending order : 0, 1, 2, 3, 4, 5, 6∴ Tabulating in frequency distribution table we get
- 26. \(\frac{486}{1000}\) = 0.486
- 27. (ii) A is true but B is false Hint:
- 28. A rational number, Because – 7 = \(\frac{-14}{2}=\frac{p}{q}\)
- 29. 256 = 16 2 576 = 24 2 4096 = 64 2 ∴ 256, 576, and 4096 are perfect squares
- 30. Try These (Text Book Page No. 124)
- 31. (refer textbook)
- 32. i.e., a multiple of F(3) or 2 = F(3)
- 33. The tree diagram for this may be∴ Number of possible ways to select one questions from each of 3 sections is 3 × 5 = 15 ways
- 34. Selling price (SP) of speaker = ₹ 768 Loss % = 20 % as per formula∴ CP = \(\frac{768 \times 100}{80}\) = 960 For gain of 20%, we should now calculate the selling price= 96 × 12 = ₹ 1152
- 35. Rate of interest (r) = 15% p.a time period (n) = 3 years Difference between CI & SI is given as 1134 Principal = ? → required to find Using formula for difference Simple Interest SI = \(\frac{P n r}{100}\) Compound Interest CI = p(1 + i) n – p1134 = P[(1.15) 3 – 1 – 0.45] = P(1.52 – 1.45) = P (0.07) ∴ p = \(\frac{1134 \times 100}{0.07 \times 100}=\frac{113400}{7}\) P = ₹ 16200Objective Type Questions
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 8Samacheer KalviMax Marks: 59
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 10 × 1 = 10
Choose the correct answer. (Answer all questions.)
1.The exterior angle of a triangle is 1200 and one of its interior opposite angle 58°, then the other opposite interior angle is _________A. 62°B. 72°C. 78°D. 68°[1]
2.When 60 is subtracted from 60% of a number to give 60, the number isA. 60B. 100C. 150D. 200[1]
3.Closure property is not true for division of rational numbers because of the numberA. 1B. 1C. 0D. \(\frac { 1 }{ 2 }\)[1]
4.Sum of a number and its half is 30 then the number is ______A. 15B. 20C. 25D. 40[1]
5.Which of the following data can be represented in a histogram? (i) The number of mountain climbers in the age group 20 to 60 in TamilNadu.[1]
6.\(\frac{3}{4} \times\left(\frac{1}{2}-\frac{1}{4}\right)=\frac{3}{4} \times \frac{1}{2}-\frac{3}{4} \times \frac{1}{4}\) illustrates that multiplication is distributive overA. additionB. subtractionC. multiplicationD. division[1]
7.Every _____ number of the Fibonacci sequence is a multiple of 8A. 2 thB. 4 thC. 6 thD. 8 th[1]
8.The number of digits in the square root of 123454321 is ______.A. 4B. 5C. 6D. 7[1]
9.(a – b) = 3 and ab = 5 then a 3 – b 3 = __________A. 15B. 18C. 62D. 72[1]
10.Every 3 rd number of the Fibonacci sequence is a multiple of_______A. 2B. 3C. 5D. 8[1]
Part II — Fill in the Blanks 5 × 1 = 5
Fill in the blanks. (Answer all questions.)
11.The value of \(\frac{-5}{12}+\frac{7}{15}\) = ________ .[1]
12.If in a ∆ PQR, PR 2 = PQ 2 + QR 2 , then the right angle of ∆ PQR is at the vertex _______ .[1]
13.Histogram is a graphical representation of_________ data.[1]
14.\(\frac{-19}{5}\) lies between the integers _________ and _________ .[1]
15.The total bill amount of a shirt costing ₹ 575 and a T-shirt costing ₹ 325 with GST of 5% is ________ .[1]
Part III — True or False 5 × 1 = 5
Write True or False. (Answer all questions.)
16.79570 is not a perfect cube.[1]
17.The standard form of 2 × 10 -4 is 0.0002.[1]
18.In a right angled triangle, the hypotenuse is the greatest side.[1]
19.There are an unlimited number of rational numbers between 10 and 11.[1]
20.Say True or False (i) 8x 3 y ÷ 4x 2 = 2xy[1]
Part IV — Short Answer Questions 12 × 2 = 24
Answer briefly. (Answer all questions.)
21.Observe that, \(\frac{1}{1.2}+\frac{1}{2.3}=\frac{2}{3}\) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}=\frac{3}{4}\) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}=\frac{4}{5}\) Use your reasoning skills, to find the sum of the first 7 numbers in the pattern given above.[2]
22.Using the given picture find the total special offer price of fresh sweets and bakery products to buy \(\frac { 1 }{ 2 }\) kg laddu, 1 kg cake, 6 pockets of bread.[2]
23.Add the fractions : \(\frac{3}{5}+\frac{5}{8}+\frac{7}{10}\).[2]
24.“An equation is multiplied or divided by a non zero number on either side:’ Will there be any change in the solution?[2]
25.Simplify: (3.769 × 10 5 ) + (4.21 × 10 5 )[2]
26.Find the cube root 24 × 36 × 80 × 25.[2]
27.A number when increased by 18% gives 236. Find the number.[2]
28.Shanthi has 5 chudithar sets and 4 frocks. In how many possible ways, can she wear either a chudithar or a frock?[2]
29.A rupee spent in a cloth manufacturing company is distributed as follows. Represent this in a pie chart. Particulars Paise Farmer 20 Spinner 35 Dyer 15 Weaver 15 Printer 05 Salary 10[2]
30.What is 25% of 30% of 400?[2]
31.If selling an article for ₹ 820 causes 10% loss on the selling price, then find its cost price.[2]
32.Find the sum (i) \(\frac{7}{5}+\frac{3}{5}\) (ii) \(\frac{7}{5}+\frac{5}{7}\) (iii) \(\frac{6}{5}+\left(\frac{-14}{15}\right)\) (iv) \(-4 \frac{2}{3}+7 \frac{5}{12}\)[2]
Part V — Long Answer Questions 3 × 5 = 15
Answer in detail. (Answer all questions.)
33.The sum of three numbers is 58. The second number is three times of two-fifth of the first number and the third number is 6 less than the first number. Find the three numbers.[5]
34.From the measures given below, find the area of the sectors. (i) Length of the arc = 48 m, r = 10 m[5]
35.What percentage ola day is 10 hours?[5]
🔑 Show Answer Key — Set 3
- 1. (a) 62° As per property of A. exterior angle is equals to sum of interior opposite angles Let the other interior angle to be found be ‘x’ ∴ x + 58 = 120° ∴ x = 120 – 58 = 62°
- 2. (D) 200 Hint: Let the number be ‘X’ 60% of the number is \(\frac{60}{100}\) × x = \(\frac{60x}{100}\) Given that when 60 is subtracted from 60%, we get 60 i.e \(\frac{60}{100}\) x – 60 = 60 ∴ \(\frac{60}{100}\) x 60 + 60 = 120 ∴ x = \(\frac{120 \times 100}{60}\) = 200
- 3. (C) 0
- 4. (b) 20 Hint: Let number be ‘x’ ∴ half of number is \(\frac{x}{2}\) Sum of number and it’s half is given by x + \(\frac{x}{2}\) = 30 [Multiplying by 2 on both sides] 2x + x = 30 × 2 3x = 60 x = \(\frac{60}{3}\) = 20
- 5. Yes (ii) Production of cycles in different years. No(iii) The number of students in each class of a school. No (iv) The number votes polled from 7 am to 6 pm in an election. Yes (v) The wickets fallen from 1 over to 50th over in a one day cricket match. Yes
- 6. (B) subtraction
- 7. (c) 6 th
- 8. (B) 5 Hint: \(\frac{n+1}{2}=\frac{10}{2}=5\)
- 9. (D) 72 Hint: (a – b) = 3 (a – b) 2 = 3 2 a 2 + b 2 – 2ab = 9 a 2 + b 2 – 2(5) = 9 a 2 + b 2 = 9 + 10 a 2 + b 2 = 19 a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) = 3(19 + 5) = 3(24) = 72
- 10. (a) 2 Hint: Every 3 rd number in Fibonacci sequence is a multiple of 2
- 11. \(\frac{1}{20}\)
- 12. Q Hint:
- 13. grouped
- 14. -4 and -3
- 15. Cost of price shirt = ₹ 575 (CP) GST = 5%Cost of price shirt = ₹ 325 (CP) GST = 5%∴ Total bill amount = ₹ 603.75 + ₹ 341.25 = ₹ 945
- 16. True
- 17. False
- 18. True Hint:
- 19. True
- 20. True(ii) 7ab 3 ÷ 14 ab = 2b 2 False
- 21. Think (Text Book Page No. 26)
- 22. (refer textbook)
- 23. LCM of 5, 8, 10 = 5 × 2 × 4 = 40
- 24. Not be any change in the solution
- 25. (3.769 × 10 5 ) + (4.21 × 10 5 ) = 3,76,900 + 4,21,000 = 7,97,000 = 7.979 × 10 5
- 26. (refer textbook)
- 27. Let the number be x. Given that when it is increased by 18%, we get 236.
- 28. Shanthi her 5 chudidhar sets and 4 frocks. She wear either chudidhar or a frock. ∴ Total possible ways = 5 + 4 = 9 ways
- 29. 1 Rupee = 100 paise.Expenditure of a cloth manufacturing company.
- 30. Required to find 25% of 30% of 400The percentage decrease calculator determines the change from one amount to a lesser amount in terms of percent decrease.
- 31. Given that selling price (SP) = ₹ 820 Loss % = 10 %
- 32. (i) \(\frac{7}{5}+\frac{3}{5}\)(ii) \(\frac{7}{5}+\frac{5}{7}\)(iii) \(\frac{6}{5}+\left(\frac{-14}{15}\right)\)(iv) \(-4 \frac{2}{3}+7 \frac{5}{12}\)
- 33. Here what we know a + b + c = 58 (sum of three numbers is 58) Let the first number be b ‘x’ b = a + 3 (the second number is three times of of the first \(\frac{2}{5}\) number) b = 3 × \(\frac{2}{5}\)x \(\frac{6}{5}\)x Third number = x – 6 Sum of the numbers is given as 58. ∴ x + \(\frac{6}{5}\)x + (x – 6) = 58 Multiplying by 5 throughout, we get 5 × x + 6x + 5 × (x – 6) = 58 × 5 5x + 6x + 5x – 30 = 290 ∴ 16x = 290 + 30 ∴ 16x = 320 ∴ x = \(\frac{320}{16}\) x = 20 1 st number = 203 rd number = 24 – 16 = 14
- 34. Area of the sector A = \(\frac{l r}{2}\) sq. units l = 48m r = 10m = \(\frac{48 \times 10}{2}\) m 2 = 24 × 10m 2 = 240 m 2 Area of the sector = 240 m 2 (ii) length of the arc = 50 cm, r = 13.5 cm Length of the arc l = 12.5 cm Radius r = 6 cm Area of the sector A = \(\frac{l r}{2}\) sq. units A = \(\frac{12.5 \times 6}{2}\) A = 12.5 × 3cm 2 A = 37.5 cm 2 Area of the sector A = 37.5 cm 2
- 35. In a day, there are 24 hours . ∴ 10 hrs out of 24 hrs is \(\frac{10}{24}\) As a percentage, we need to multiply by 100 ∴ Percentage = \(\frac{10}{24}\) × 100 = 41.67%