1. Real Numbers. 3. The denominator of a rational number is always in the form..where m,n are nonnegative

1. Real Numbers

1. The decimal expansion of number ⁷

80 has a) terminating after two places of decimal.

b) terminating after four places of decimal.

c) terminating after three decimal places.

d) terminating after one decimal place.

2. Decimal representation of a rational number cannot be a) terminating

b) non-terminating

c) non-Terminating repeating d) non-terminating non-repeating.

3. The denominator of a rational number is always in the form……..where m,n are non- negative integers.

a. 2 ^m x 5 ⁿ b. 2 ^m x 3 ⁿ c. 3 ^m x 5 ⁿ d. 2 ^m

4. The decimal form ^𝟏𝟐𝟗

𝟐 ^𝟐 𝟓 ^𝟕 𝟕 ^𝟓 is a. terminating

b. non terminating

c. non-terminating non-repeating d nonterminating repeating

5.The decimal expansion of a Rational number is ………

a. always terminating

b. always non-terminating but repeating c. terminating or non-terminating repeating d. neither terminating nor repeating

6. 0. 57 ̅̅̅̅ in the form of P/q where q≠0 is a) ²⁶ ₄₅

b) ¹³ ₂₇

c) ⁵⁷

99

d) ¹³ ₂₉

7) The decimal expansion of _72𝑋175 ⁶³ is a. terminating

b. non terminating

c. non terminating repeating d. non terminating non repeating

8. A rational number in its decimal expansion 827.7081, what would be the prime factors of q when the number is expressed in ^𝑝

𝑞 form a. 5&7

b. 2&3 c. 3&5 d. 2&5

9) The value of 1. 34 ̅̅̅̅ +4. 12 ̅̅̅̅ is ---- a) ⁵⁴¹

99

b) ⁴⁴¹

99

c) ⁵⁵¹

9

d) ⁵⁴¹

9

10) There are 56, 32 and 40 students in class IV, V , VI respectively. Buses are to be hired to take these students to a park, then what is the maximum number of students who can sit in the bus if each bus takes equal no. of students.

a. 8 b. 10 c. 12 d. 6

11) If we express 48 as product of primes , we get a. 2 ⁴ x 5

b. 2 ⁴ x 3

c. 2 ³ x 3

d. 2 ² x 3 ²

12) If two positive integers A & B can be expressed as A = x ² y ³ and B = 𝑥 ³ 𝑦 ⁵ 𝑧 ; x,y and z being prime numbers then HCF (A,B) is...

a. x²y ⁴ b. x²y ³ c. X ² Y ³ Z d. x ³ y ³

13. If HCF (12,X) = 4 and LCM (12, X) = 9, then the value of X is a. 4

b. 3 c. 9 d. 12

14. The LCM & HCF of 72 and 56 is a. 8, 504

b. 8. 0168 c. 6, 504 d. 6, 378

15) The Fundamental Theorem of Arithmetic says that every composite number can be factorized as a…

a. Product of Natural numbers b. Product of integers

c. Product of Real Numbers d. Product of primes

16) The prime factorization of a natural number is……… except for the order of its………factors a. unique, prime

b. Prime, unique c. composite, unique d. unique, composite

17. The LCM and HCF of two numbers are 528 and 64 respectively. If other number 48, the other number is …..

a. 352 b. 604 c. 176 d. 704

18) The ratio between the LCM and HCF of 15, 10, 20 is…

a) ⁵

24

b) ¹²

5

c) ²⁴ ₁

d) ¹² ₁

19. First on a marathon race three persons step off together and their steps measure 35 cm, 40 cm, 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

a. 2520 b.1890 c. 840 d.2420

20. If HCF & LCM of two numbers are 8 and 2042, then the product of two no. is…….

a. 16336 b. 16436 c. 14336 d. 6336

21. For any integers p and q and if we represent in the form of p/q, then it is a ……

a. whole number b. rational number c. natural number d. Even number

22. The largest number that divides 70 and 125 which leaves the remainder 5 and 8 respectively is

a. 65 b. 31 c. 13 d. 19

23. The values of X & Y in the given figure are 2

Y X

4

8

a. x=32 y = 64 b. x = 64 y = 32 c. x = 12 y = 14 d. x = 2 y = 1

24. To enhance the speaking skills of grade V students, the school nominates you and two of your friends to set your up a class library. There are two sections - section A and section B of grade V. There are 40 students in section A and 34 students in section B

1) What is the minimum no. of books you will acquire for the class library, so that they can be distributed equally among students of section A & B.

a. 680 b. 860 c. 100 d. 800

2) If the product of two positive integers is equal to the product of their HCF & LCM is true then the HCF(40,34) is…

a. 8 b. 2 c. 10 d. 12

3) 40 can be expressed as a its product of primes as a. 2²x5

b. 2 ³ x5 ² c. 2 ³ 𝑋5 d. 2²x3

4) 2×3×7×11 + 11 is a a. Prime no.

b. Composite no

c. Neither prime nor composite d. Irrational

25) A puzzle competition is being conducted in school and one your friends is making a puzzle of a factor tree, He has some difficulty and asks for your help in completing quiz for the friends,

X

3 150

Y

5

50

0 P

Observe the tree diagram.

1. what the valve of X?

a. 350 b. 450 c. 153 d. 147

2. What is the value of Y ? a. 3

b. 2 c. 4 d. 1

3. What is the value of P?

a. 20 b. 45 c. 55 d. 10

4. The prime factor of 250 is a. 5 ³ x 2 ²

b. 5 ³ x 2 ² c. 5 ² x 2 d. 5 ³ x 2 Answer Key

1. B

2. D

3. A

4. D

5. C

6. C

7. A

8. D

9. A

10. A

11. B

12. B

13. B

14. A

15. D

16. A

17. D

18. D 19. A 20. A 21. B 22. C 23. A

24. Case Study Questions 1. A

2. B 3. C 4. B

25. Case study Questions 1. B

2. A

3. D

4. D

2. Polynomials

1. The degree of the polynomial is (x+1)(x ² -x-x ⁴ +1) is a. 2

b. 3 c. 4 d. 5

2. Graph of linear polynomial is a. Single line

b. Parabola c. Circle

d. Intersecting line

3. The degree of linear polynomial is a. 1

b. 2 c. 3 d. 4

4. If P(x) = ax+b, the zero of the P(x) is a. -b

b. -a/b c. -b/a d. A

5. A polynomial having degree 3 is called a. Linear polynomial

b. Quadratic polynomial c. Cubic polynomial d. Constant polynomial

6. Any quadratic polynomial in x is of the form _____

a. ax ² +bx+c, a,b,c are real numbers & 𝑎 ≠ 0 b. ax ² +bx+c, a,b,c are natural numbers & a=0 c. ax ² +bx+c, a,b,c are whole numbers & a=0 d. ax ² +bx+c, a,b,c are irrational numbers & a=0

7. If zeros of quadratic polynomial ax ² + bx + c, 𝑎 ≠ 0 are equal then a. c & a have opposite sign

b. c & b have opposite sign c. c & a have same sign d. c & b have same sign

8. The Zero of ^{𝑥 2}

2 − ^𝑥

2 − 6 is a) 4

b) -4

c) 2

d) 3

9. If 𝛼, 𝛽 are the zeroes of the x ² + 4x +1 then the value of ^𝛼+𝛽

𝛼𝛽 is …..

a) – 4 b) 4 c) ¼ d) -1/4

10. The value of k is, if -4 is a zero of polynomial x ² -2x-(3k+3) a) 8

b) -7 c) 7 d) 10

11. The shape of the quadratic polynomial is

a)straight line b)parabola c)Hyperbola d)ellipse 12. if the zero of quadratic polynomial 𝑥 ² + (𝑎 + 1)𝑥 + 𝑏 are 2 & -3 then

a) a=-7, b=-1 b) a=5, b=-1 c) a=2, b=-6 d) a=0, b=-6

13. The zero of the polynomials 𝑥 ² + 7𝑥 + 10 are a) 2&5

b) -2 & 5 c) -2 & -5 d) 2 5 ⁄ , 2 5 ⁄

14. A quadratic polynomial can have almost ____________ zeros a) 0

b) 1 c) 2 d) 3

15. A cubic polynomial can have at most _____________ zero a) 0

b)1 c)2 d) 3

16. Following are the zeros of p(x)= x ² -1 a)1,-1

b)-1,2

c) -2, 2

d) -3, 3

17. . If 𝛼, 𝛽 are the zeroes of the x ² + 4x +4 then the value of 𝛼 − 𝛽 is …..

a) – 4 b) 4 c) 0 d) -1

18. If p(x) =3𝑥 ³ − 2𝑥 ² + 6𝑥 − 5, then the value of p(2) is a)49

b)23 c)32 d)24

19. If one zero of the quadratic polynomial 𝑥 ² + 3𝑥 + 𝑘 is 2, the value of k is a) 10

b) -10 c) 6 d) 4

20. Which are the zero of p(x) =𝑥 ² + 7𝑥 + 12 a) 4 &-3

b) -4 & 3 c) -4 & -3 d) 4 3 ⁄ , 3 4 ⁄

21. If 9a + 3b + c > 0 and the polynomial f(x) = ax2 + bx + c has no real roots, then:

(A) c > 0 (B) c < 0

(C) c = 0 (D) Cannot be determined uniquely.

22. Graph of a polynomial p(x) is shown, where horizontal line is x-axis and vertical line is y-axis. The minimum number of real zeroes of p(x) is

(A) 4 (B) 1

(C) 2 (D) 3

23. In figure , graph of a polynomial p(x) is shown where horizontal line is x-axis and vertical line is y-axis. The minimum number of real zeroes of p(x) is/are

(A) 1 (B) 2

(C) 3 (D) 4

24. Graph of polynomial p(x) is shown where horizontal line is x-axis and vertical line is y-axis. The minimum number of zeroes of this polynomial is/are

(A) 2 (B) 1

(C) 3 (D) 4

25. The number of points the graph of the equation (x – 3) ² + (x – 4) ² + (x – 5) ² = 0 cuts the x -axis is /are

(A) 2 (B) 1

(C) 0 (D) 3

26. If polynomial p(x) = ax2 + bx + c has no real zeros and 16a + 4b + c < 0 then :

(A) c = 0 (B) c > 0

(C) c < 0 (D) Cannot be determined uniquely

27. If y-axis acts as a mirror then the graph of polynomial f(x) = x(x-1)(x-2) cuts x axis at how many points?

(A) 3 (B) 4

(C) 5 (D) 6

28. If y-axis acts as a mirror, then the graph of polynomial f(x) = (x-1)(x-2)(x-3) cuts x axis at how many points?

(A) 3 (B) 4

(C) 5 (D) 6

29. If x- axis acts as a mirror then graph of x ² + 𝑥 + 1 cuts x- axis at how many points?

(A) 0 (B) 1

(C) 2 (D) 4

30.How many roots the equation

2 2 5

2 5

 

 

 x x

x have

(A) One (B) Two

(C) Infinite (D) No real roots

31. If p  q  r  s , then the roots of the equation ( x  p )( x  r )  2 ( x  q )( x  s )  0 are (A) Real and distinct (B) Real and equal

(C)Imaginary (D)One real one Imaginary

32. If the graph of polynomial cuts the x axis at ‘N” points then the number of zeroes of the polynomial will definitely be

(A) less then ‘N’ (B) equal to ‘N’

(C) more then or equal to ‘N’ (D) less then or equal to ‘N’

33. If the polynomial is of degree ‘N” then the graph of the polynomial will definitely cut the x axis at points which are

(A) less then ‘N’ (B) equal to ‘N’

(C) more then or equal to ‘N’ (D) less then or equal to ‘N’

34. Graph of polynomial ^{f x}   ^{ ax 2  bx  c}

(A) a  0,b 0  and c  0 (B) a  0,b  0 ^and c  0 (C) a 0,b   0 and c  0 (D) a  0,b  0 and c  0

 

f x  ax  bx  c

35. The graph of the polynomial is shown below where horizontal line is x-axis and vertical line as y-axis.

The degree of the polynomial cannot be

(A) 4 (B)2

(C) 3 (D) 5

36. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomial x²+2x+1 then what is the value of ¹

𝛼 + ¹

𝛽

a) -1 b) -2 c) -3 d) -4

37. If 𝛼 & 𝛽 are the zeroes of the polynomial 2𝑥 ² − 13𝑥 + 6, then what is the value of 𝛼 + 𝛽?

a) ¹

2 b) ¹³

2 c) − ¹³

2 d) ²

13

38. If the sum and product of the zeroes of a quadratic polynomial 3 & -10 respectively find the quadratic polynomial?

a) x ² -3x-10

b) x² + 3x + 10

c) x² + 3x -10

d) x²- 3x + 10

39. If 𝛼 𝑎𝑛𝑑 𝛽 are zeroes and the quadratic polynomial (𝑥) = 𝑥 ² − 𝑥 − 4 , then the value of ¹

𝛼 +

1

𝛽 − 𝛼𝛽 is a) ¹⁵

4 b)− ¹⁵

4 c) 4 d) 15

40. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the quadratic polynomial 𝑓(𝑥) = 𝑎𝑥 ² + 𝑏𝑥 + 𝑐 then the value of 𝛼 ⁴ + 𝛽 ⁴ 𝑖𝑠

a) ^(𝑏

2 −2𝑎𝑐) ² +𝑎 ² 𝑐 ²

𝑎 ⁴ b) ^(𝑏

2 −2𝑎𝑐) ² −𝑎 ² 𝑐 ²

𝑎 ⁴

c) ^(𝑏

2 −2𝑎𝑐) ² −2𝑎 ² 𝑐 ²

𝑎 ⁴ d ) ^(𝑏

2 +2𝑎𝑐) ² +2𝑎 ² 𝑐 ² 𝑎 ⁴

41. The graph of y= p(x) is given in figure below. The graph is of y= p(x), where p(x) is a polynomial.

Find the number of zeros of p(x).

a. 1 b. 2 c. 0 d. 3

42. The graph of y= p(x) is below , for p(x) find the number of zeros of p(x)

a. 0 b. 1 c. 2 d. 3

43. The graph of x= p(y) is given below for some polynomial p(y). Find the number of zeros of p(y)

a. 1 b. 2 c. 3 d. 4

44. Graph of x= f(y) is given, find the number of zeros.

a. 0 b. 1 c. 2 d.3

45. Graph of y = f(x) is given, Find the zeros of f(x)

a. -3,0 b. -2,2 c. 1,0 d. 1,3

46. ---is the product of the zeros of -2x ² + kx+6 a. 3 b. -3 c. 4 d. -4

47. --- is the sum of zeros of the given quadratic polynomial -3x ² + k a. 0 b. 1 c. 2 d.3

48. If ax ² + bx + c be any polynomial and its 𝛼 and 𝛽 are the zeros of the polynomial then 𝛼 + 𝛽 =--- a. a b. b c. - a/b d. – b/a

49. If ax ² + bx+ c be any polynomial and its 𝛼 and 𝛽 are the zeros of the polynomial then 𝛼 𝛽 =---- a. a/b b. –b/a c. c/a d. –a/b

50. p(x) = ax ² + bx+ c . If a+ b+ c = 0 then one of its zero is--- a. 1 b. 2 c. 3 d.0

51. P(x) = ax ² + bx+ c . If a+c =b, then one of its zero is--- a. 0 b. 2 c. -1 d. 3

52. --- and --- are the zeros of the quadratic polynomial P(x) = x ² -7x +12 a. 4 & 5 b. 2 & 3 c. 3 &4 d. 1 & 2

53. ---and --- are the zeros of the quadratic polynomial 4x ² + 24x +36

a. 3,3 b. -3,-3 c. 4,3 d. 2,3

54. For quadratic polynomial 100x ² -81 --- and --- are zeros of the polynomial a. 10/9, -10/9 b. 9/10, -9/10 c. 10/7, -10/7 d. ½ , 3/2

55. The sum and product of the zeros of the polynomial x ² -6x +8 are respectively a. – 3/2 and 1 b. 3/2 and 1 c. 6 and 8 d. -3/2 and -1

56. If one of the cubic polynomial x3- 7x +6 is Z then the product of the other two zeros is--- a. 3 b. -3 c. 2 d. -2

57. Polynomial 4x ³ -kx ² -8x -12 is -3/4 then the value of K is --- a. -3 b. 3 c. 1/3 d. -1/3

58. If 2 is the zero of the both the polynomials 3x ² +mx-14 and 2x ³ + nx ² + x-2 then the value of m-2n is---

a. 9 b. -9 c. -1 d. 5

59. A quadratic polynomial whose product and sum of the zeros are 1/3 and √2 respectively is--- a. 3x ² + 3√2x +1

b. 3x ² + x - 3√2x c. 3x ² –x+ 3√2x d. 3x ² - 3√2x+1

60. If 𝛼 and 𝛽 are the zeros of the polynomial ax2 + 1bx +c then the value of 𝛼 / 𝛽 + 𝛽 / 𝛼 is --- a. b ² / ab b. a ² /bc c. c ² /ab d. b ² -2ac/ ac

61. If 2, -7 and -14 are the sum, sum of the product of its zeros taken two at a time and the product of its zeros of a cubic polynomial then the cubic polynomial is

a. x ³ - 2x ² – 7x +14 b. x ³ - 2x ² +7x -14 c. x ³ - 2x ² – 7x -14 d. x ³ + 2x ² + 7x +14

62. If 𝛼 and 𝛽 are the zeros of the polynomial 3x ² + 11x -4 then the value of 𝛼 ² + 𝛽 ² is --- a. 145/9 b. 144/9 c. 150/9 d. 152/9

63. If 𝛼 and 𝛽 are the zeros of the polynomial 3x ² + 11x -4 then the value of 1/ 𝛼 +1/ 𝛽 is --- a. 11/4 b. 13/4 c. 12/4 d. 15/4

64. If 𝛼 and 𝛽 are the zeros of the polynomial x ² - 6x +8 then the value of 𝛼 ³ + 𝛽 ³ is --- a. 72 b. 76 c. 80 d. 74

65. If 𝛼 and 𝛽 are the zeros of the polynomial x ² - 6x +8 then the value of 𝛼 ² / 𝛽 + 𝛽 ² / 𝛼 is --- a. 9 b. 8 c. 12 d. 6

66. If 𝛼 and 𝛽 are the zeros of the cubic polynomial ax ³ +bx ² + cx +d then 𝛼 + 𝛽 + 𝛾 =---- a. c/a b. – c/a c. –b/a d. b/a

67. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial x ² +5x-5 then a. 𝛼 + 𝛽 > 𝛼𝛽

b. 𝛼 − 𝛽 = 𝛼𝛽 c. 𝛼 + 𝛽 < 𝛼𝛽 d. 𝛼 + 𝛽 = 𝛼𝛽

68. If 𝛼𝛼 and 𝛽𝛽 are the zeros of a quadratic polynomial X2-5x+b and 𝛼 − 𝛽 = 1 then the value of b is

a. -5 b. 5 c. -6 d. 6 69. A quadratic polynomial whose zeroes are -3 and 6 is

a. x ² + 3x + 18 b. x ² -3x + 18 c. ^𝑥

2 6 - ^𝑥

2 -3 d. x ² -3x +18

70. The sum of two zeros of the polynomial f(x) = 2x ² + (p+3)x + 5 is zero , then the value of P is a. 3 b. -3 c. -4 d. 4

71. A polynomial whose sum & product of zeroes are -4 and 3 is

a. x ² + 4x + 3 b. x ³ -4x -3 c. x ² -4x+3 d. x ² -4x-3 72. A quadratic polynomial with zeros ¼ and 1 is

a. 4x ² -3x+1 b. 4x ² -3x-1 c. 4x ² + 3x+1 d. 4x ² + 3x -1

73. Find the sum and the product of zeroes of the polynomial x2+ 7x +10 a. -7, 10 b. 7,10 c. -7, -10 d. 7, -10

Case Study

1. A barrel manufactures can produce up to 300 barrels per day the profit made from the of sale of these barrels can be modelled by the function P(x) = -10x²+3500x-66000 where P(x) is the profit in rupees and x is the number of barrels made and sold, based on this model answer the following questions.

i) when no barrels are produced what is a profit loss?

a) Rs. 22000 b) Rs. 66000 c) Rs. 11000 d) Rs. 33000 ii) what is the break even point ? (zero profit point is called break even)

a) 10 barrels. b) 30 barrels c) 20 barrels d) 100 barrels iii) what is the profit / loss if 175 barrels are produced

a) profit 266200 b) a loss 266200 c) profit 240250. d) loss 240250 iv) what is the profit /loss if 400 barrels are produced.

a) Profit RS 466200 b) loss RS 266000 c) profit RS 342000 d) loss 342000 v) what is the maximum profit which can manufactured earn?

(a) Rs 240250 b) Rs.480500 (c) Rs 680250 d) Rs 250250

2. Lavanya throws a ball upwards, from ground. It will reach a maximum height and then fall back to the ground the height of the ball from the ground

at time t is h, which is given by h = -4t² +16t +20 i) what is the height reached by. the ball after 1 second

a) 64m b)32 m c) 128 m d)20m

ii) what is the maximum height reached by the ball?

a) 54m b) 44m c) 36m d) 18m

iii) How long will the ball take to hit the ground?

a) 5 See b) 3 sec c)4 sec d) 6 sec

iv) what are the two possible times to reach the ball at the same height of 32 m?

a) 1 & 3 sec b) 1 & 4 Sec c) 1 and 2 sec d) 1 & 5 sec v) where is the ball after 5 seconds?

a) at the ground. b) rebounds c) at highest point d) fall back

3) The Prime Minister's citizen Assistance and Relief in emergency situations Fund was created on

28 march 2020, following the COVID-19 pandemic in India. The fund will be used for combating,

and containment and relief efforts against the corona virus outbreak and similar pandemic like situations. in the future.

The allotment officer is trying come up with a method to calculate fair division of funds across various affected families so that the fund amount and amount revised per family can be easily adjusted based on daily revised numbers. The total fund revised for village is 𝑥 ² + 6𝑥 ² + 20𝑥 + 9 the officer has divided the fund equally among families on the village and each family receives an amount of x²+2x+2. After distribution, some amount is left

i) How many families are there in the village?

a) 𝑥 + 𝑦 b)𝑥 − 3 c) 𝑥 − 4 d) 𝑥 + 3

ii) If an amount of Rs.1911 is left after distribution, what is value of x?

a) 190 b)290 c) 191 (d) 291 iii) How much amount does each family receive?

a)24490 b)34860 c)22540 d) 36865 (iv) what is the amount of fund allocated

74. RS 7272759 b) Rs. 7572681 75. Rs 6972846 d) RS 8274 888

v) How many families are there in the village?

a) 191 b) 98 c) 187 d) 195

4)

A ROLLER COASTER RIDE

A polynomial function graph consists of smooth lines with a series of hills and valleys. The

hills and valleys are called turning points. The maximum possible number of turning points is one less than

the degree of the polynomial. The graph of some polynomials can be seen as a roller coaster ride as shown

below.

1.The polynomial (x-1)(x-3)(x-5) has how many turning points.

(A) 1 (B)2

(C) 3 (D) 4

2. The biquadratic polynomial haing leading coefficient unity,will have at least how many turning points.

(A) 1 (B)2

(C) 3 (D) 4

3. Soham rides a kind of above roller coaster and he counted 3 valleys and 4 hills along a polynomial curve, then the degree of polynomial cannot be

(A) 10 (B)8

(C) 9 (D) 6

4. The polynomial (𝑥 − 2) ² (𝑥 − 3) ⁴ will have how many turning points.

(A) 2 (B)4

(C) 3 (D) 6

5. The polynomial (𝑥 − 2) ² (𝑥 − 3) ⁴ will have how many valley points.

(A) 1 (B)2

(C) 3 (D) 4

5) Any polynomial can be plotted in the form of the curve which cuts x -axis at certain point called

zeroes of the polynomials. Now assuming that x -axis is a ‘still’ pond of water, which acts as a

mirror to reflect the polynomial shape . The portion of the curve which is below is not visible and the

portion above x axis (water) is reflected back in the water and making a kind of circle as shown

above.

Example : A polynomial (x-4)(x-6)(x-8) can be drawn as

Which on reflection in water will make one circular form as shown below( part of graph which is below water is not visible)

Please answer the question that follow based on above observations.

1. The polynomial –(x-2)(x-3) will make how many circles.

(A) 0 (B)1

(C) 2 (D) 3

2.The graph of polynomial (x-5)(x-6)(x-7)(x-8) will make how many circles

(A) 1 (B)2

(C) 3 (D) 4

3.The graph of polynomial -(x-5)(x-6)(x-7)(x-8) will make how many circles

(A) 1 (B)2

(C) 3 (D) 4

4 . If the polynomial curve makes 3 circles then the degree of the polynomial can be

(A) 7 (B)4

(C) 5 (D) 6

5. A ten degree polynomial can make at the maximum how many circles?

(A) 3 (B)4

(C) 6 (D) 5

--- 6) Linear Polynomial, cubic polynomial quadratic Polynomial.

On 15 July 2021, there is heavy rain fall in Kolhapur city. The street Light wiring damaged due to same problems Rahul took picture from some areas are by his mobile, he found that some are situation in mathematical shapes

1. let we assume that in fig. 1. the wire is hanging in what mathematical shape a. Spinal

b. Circle c. Parabola d. Straight line

2. The Genra form for parabolic i.e. Polynomial a. ax + b

b. ax + by + c c. ax ² + bx + c , a= 0 d. ax ² + bx + c, a≠ 0

3. How many solutions will be there if equation is in the form ax ² + bx + c, a≠ 0.

a. 1 b. 2 c. 0 d. 3

4. Let assure the tig. 2. the wire allotted with grow as straight line the wire represent by equation.

Ax+b=0, What is the degree d_eq ⁿ a. 1

b. 2

c. 0

d. 3

5. For fig. 2 eq ⁿ ax+b=0 has how many solutions?

a. 0 b. 1 c. 2 d. 3

7. In kagal taluka, Dist. Kolhaper. Ram Visited an old Palace. Its main Gate is in the parabolic Shape.

1. if the main gate is representing by Parabolic shape, eq ⁿ reprert x²+ 4x+4 then what is the degree of equation?

a. 1 b. 2 c. 0 d. 3

2. What are the Zerses of quadratic Polynomial X²+4x+4 a. 2,2

b. -2,-2 c. 2,-2 d. -2,2

3. what is the shape of main door gate Palace.

a. quadrilateral shape b. Triangle shape c. parabolic shapes d. spririal shape

4. The numbers of zeroes to polynomials are.

a. 1 b. 3 c. 2 d. 0

5. The number of Zeroes for polynomial of p(x)=(x-2) ² +4 can have is a. 1

b. 2

c. 0

d. 3

Key Answers 1. d

2. a 3. a 4. c 5. c 6. a 7. c 8. a 9. a 10. c 11. b 12. d 13. c 14. c 15. d 16. a 17. c 18. b 19. b 20. c 21. a 22. b 23. c 24. b 25. c 26. c 27. c 28. d 29. a 30. d 31. a 32. c 33. d.

34. a

35. b

36. b

37. b

38. a

39. a

40. c

41. a

42. c

43. d

44. b

45. b

46. b

47. a

48. d

49. c 50. a 51. c 52. c 53. c 54. b 55. c 56. c 57. b 58. a 59. a 60. d 61. a 62. a 63. a 64. a 65. a 66. a 67. c 68. d 69. c 70. b 71. a 72. a 73. d

Answer Keys of Case Study

1. i) b ii c iii. c iv. b v. a

2. i) b … ii) c ……… iii) a ……. iv) a ……….. v) d 3. i) a ii) c iii) d iv) c v) d

4. i. b ii. a iii. d iv. c v. b

5. i. b ii. a iii. b iv. d v. d

6. i. a ii. d iii. b iv. a v. b

7. i. b ii. b iii. c iv. c v. c

3. Pair of linear equations in two variables

1. The general form of lineas eq ⁿ in two variables is a. ax ² +bx+c = 0

b. ax²+by+c= 0 c. ax+by+c= 0 d. ax ² +by+c = 0

2. A pair of linear equations a,x + b,y + c 1 =0 & a 2 x + b₂ y+c 2 =0 is said to be inconsistent if

a. ^𝑎1

𝑎2 ≠ ^𝑏1

𝑏2

b. ^𝑎1

𝑎2 ≠ ^𝑏1

𝑏2 ≠ ^𝑐1

𝑐2

c. ^𝑎1 _𝑎2 = ^𝑏1 _𝑏2 = ^𝑐1 _𝑐2 d. ^𝑎1

𝑎2 ≠ ^𝑐1

𝑐2

3. The pair of equations 3x-51=7 & - 6x+10y = 7 have a. unique solution

b. infinitely many solutions c. no solution

d. two solution

4. The pair of equations x=0 & x=5 has a. no solution

b. unique / one solution c. two solutions

d. infinitely many solutions

5. For what value of k do the equation 2x-3y +10=0 & 3x = ky = 15=0 represents coincident a. ⁻⁹

2

b. -11

c. ⁹

2

d. -7

6. One equation of a pair of dependent linear equations 13 equation will be 2x+5y=3. The second equations will be

a. 2x + 5y =6 b. 3x + 5y =3 c. 10x-25y+15 =0 d. 10x-25y=15

7. If x=a , y= b is the solution of the equation x+y=5 & 2x-3y =4 then the values of a & b are respectively.

a. 6,-1 b. 2,3 c. 1,4

d. ¹⁹

5 , ⁶

5

8. Two equations in two variables taken together are called a. linear equations

b. quadratic equations c. simultaneous equations d. none of these.

9. If in the equation X + 2 Y =10 the value of Y is 6 then the value of x will be a. -2

b. 2 c. 4 d. 5

10. The value of k for which equation 3x-5y =0 and kx + 10y=0 has a non-zero solution is a. 6

b. 0

c. 2

d. 5

11. If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is … (a) ⁻⁵ ₄ (b) ² ₅ (c) ¹⁵ ₄ (d) ³ ₂

12. For what values of k, do the equations 3x – y + 8 = 0 and 6x – ky = −16 represent coincident lines?

(a) ¹ ₂ (b) ⁻¹ ₂ (c) 2 (d) – 2

13. what will be the solution of the equations x - y = 2 & x +y =4 is a. 3 and 1

b. 4 and 3 c. 5 and 1 d. -1 and 3

14. The father's age is six times his sons age four years hence the age father will be four times his sons’ age. The present ages in years of the son and father are respectively a. 4 and 24

b. 4 and 3 c. 6 and 36 d. 3 and 24

15. In a competitive examination one mark is awarded for each correct answer while ¹

2

mark is deducted for every wrong answer. Jayanti answered 120 questions and got go marks. How many questions did she answer correctly ?

a. 100 b. 95 c. 90 d. 60

16. If in the equation X +3Y+10 the value of y is 4 then the value of X will be a. -2

b. 2 c. 4 d. 5

17. If 29x+ 37y = 103, 37x +29y = 95 then a. x=1, y=2

b. x=2, y=1

c. x=2, y=3

d. x=3, y=2

18. The Sum of the digits of a two-digit number is 9. If 27 is added to it the digits of the number get reversed the number is

a. 27 b. 72 c. 45 d. 36

19. A boat rowed at downstream at 15.5km/hr and upstream at 8.5 km / hr then the speed of stream is

a. 3.5 km/hr b. 5.75 km/hr c. 6.5 km/hr d. 7 km/hr

20. Two lines are given to be parallel. The equation of one of the lines is 3x + 4y = 14 , then find the equation of

other line can be …..

(a) 3x + 4y – 14 = 0 (b) 3x – 4y = 14 (c) 3x – 4y + 14 = 0 (d) 3x + 4y + 14 = 0 21. If 2x – 3y = 7 and (a+b) x – (a+b – 3 )y = 4a + b represent coincident lines, then a and b satisfy the

equation

(a) a + 5b = 0 (b) 5a + b = 0 (c) a – 5b = 0 (d) 5a – b = 0

22. The solution of the equations. X - Y = 2 & X+Y=4 is a. 3 and 5

b. 5 and 3 c. 3 and 1 d. -1 and -3

23. A pair of linear equations which has a unique solution x=2 , y=-3 is a. x+y=-1, 2-3y=-5

b. 2x+5y = -11, 4x+10y = 12 c. 2x-y = 1, 3x + 2y=0 c. x-4Y-14 =0, 5x - y -13 = 0

24. The angles of a triangle are x, y & 40° The difference between the two angles x & y is 30°.

The values of x and y are a. 45°,75°

b. 5.0°, 80°

c) 55° 85°

d) 55°, 95°

25. 10 Students of class I0 took part in Mathematics quiz. If the number of girls is 4 more than the number of boys find the number of boys took part in the quiz.

a. 3 b. 7 c. 2 d. 8

26. 5 pencils & 7 pens together cast Rs 50 whereas 7 pencils & 5 pens costs Rg 46 find the cost of 2 pencils and 3 pens

a. Rs. 42 b. Rs. 39 c. Rs. 21 d. Rs. 16

27. A linear equation in two variables has a. 1 solution

b. solutions c. no solution

d. infinitely many solutions

28. An equation ax + by + c =o is linear equation in 2 variables where a,b,c are a. natural numbers

b. whole numbers c. integers

d. oral number.

29. The pair of equations y=9 & y=-7 a. One solution

b. two solution c. infinitely many d. no Solution

30. Given is the system of inconsistent equations 2x+7y=11 & 5x+ ky-25=0 find k a. ⁻³⁵ ₂

b. 4

c. ³⁵

2

d. -4

31. A pair of linear equations to not consistent if a. if has solutions

b. it has many solutions c. graph intersects d. graph is parallel

32. In ABC, A = x ⁰ B= (39-2) &

C = y ^o , also C- B=9 ^o find the value of B a. 73°

b. 82°

c. 25°

d. 49°

33. In a triangle the sum of two angle to equal to the third angle. If the difference between two angles is_30° find the angles

a. 15°, 45°, 15°

b. 20°, 50°, 80°

c. 30°, 60°, 90°

d. 45°, 45°, 90°

34. 8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days find the time taken by the one girl alone that by one boy alone to finish the work

a. 120, 130 b. 140, 280 c. 240, 280 d. 100,120

35. find the value of a for which the system of equations ax+2y-4= 0 & x-y-3=0 will represent intersecting lines?

a. a≠-2 b. a=-2 c. a=2 d. a≠ 2

36. the pair of equations 3x+4y=k, gx+12y= 6 has infinitely many solutions if

a. k=2 b. k=6 c. k≠ 6 d. k=3

37. which of the following is not a solution of 3a+b=12 ?

a. (3,3) b. (5, -3) c. (4,10) d. (2,4)

38. how many solutions of the equation 15x-14y+11=0 are possible?

a. 2 b. No solution c. a d. infinite

39. the value of K for which equations 3x+5y=0 & kx+10y= 0 has a non-zero solutions is

a. 6 b. 0 c. 2 d. 5

40. Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. If each ride costs Rs 3, and a game of Hoopla costs Rs 4, provided she spent Rs 20.Find the correct option to represent the above situation graphically.(by taking number of times played Hoopla as y and number of rides as x)

(a) x – 2y = 0 and 4x +3y = 20 (b) x +2y = 0 and 4x +3y = 20 (c) x – 2y = 0 and 3x + 4y = 20 (d) x – 2y = 0 and 3x -4y = 20

41. find the solutions to the following system of linear equations 2pq+3q =9, p-q=2

a. (4,2) b. (3, 1) c. (2,-3) d. (-4,1)

42. A pair of equations x=03, x=5 has

a. no solution’s b. unique one solution c. two solutions d. infinitely many solutions

43. Which of the following pair of linear equations represents the graph

(a) x+y = 6 and –x + y = 2

(b) 4x – y = 4 and 3x + 2y = 14

(c) x – 4y = 4 and 2x + 3y = 14

(d) 4x + y = 4 and 3x – 2y = 14

44. the sum of a two-digit number is a 8 the number obtained by the reversing the digits exceeds the number by 18 then the given number is

a. 53 b. 35 c. 26 d. 62

45. The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution, is ..

(a) 0 (b) 0 (c) 6 (d) 8

46. find x & y in the given rectangle

A _--- x+ 3y B

3x +y 7

D C

a. x=1 and y=4 b. x=4 and y=1 c. x=2 and y=2 d. x=3 and y=1

47. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes ¼ when 8 is added to its denominator. The fractions obatained is

a. 3/12 b. 4/12 c. 5/12 d. 7/12

48. If (p, p) is the solution of equations ax + by+(t−s)=0 and bx+ay+(s−r)=(0≠b) then, which of the following must be true?

(a) 2r=s+t b) 2t=r+s c) 2s=r+t d) r+s+t=0

49. 5 pencils and 7 pens together cost Rs. 50 where as 7 pencils and 5 pens together cost rs. 46. The cost of 1 pen is

a. Rs. 5 b. Rs. 6 c. Rs. 3 d. Rs. 4

50. the solution of px+qy =p-q & qx-py =p+q is

a. x=-1 and y=1 b. x=1 and y=1 c. x=0 and y=0 d. x=1 and y=-1

51. The area of triangle formed by the lines x = 6 , y =0 and x = y is ..

(a) 36 sq.unit (b) 18 sq. unit (c) 9 sq. unit (d) 72 sq.unit

52) For which value(s) of 𝜆 do the pair of linear equations 𝜆x + y = 𝜆 ² and x + 𝜆y = 1 have infinitely many solutions…

(a) 𝜆 = −1,1 (b) 𝜆 ≠ 1,−1 (c) 𝜆 = −2,2 (d) 𝜆 ≠ 2, −2

53) Anil scored 55 marks in Maths test receiving marks for each correct answer and losing I mark for each wrong answer Had 4. marks been awarded for each correct answer and 2 marks deducted for wrong answer, the Anil would have got to marks. The number of the questions in the Maths test are

a) 10 b) 15 c) 20 d) 25

54) The addition of numerator and denominator of a fraction is three less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator find the fraction will be

a) ³ ₇

b) ⁴ ₇

c) ⁵ ₇

d) ⁷

4

55) Asha has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are respectively

(a) 15 and 35

c) 35 and 15 b) 25 and 25 d) 35 and 20

56) The father's age is six times his son's age. Four year hence, the age of the father will be four times his son's age. The present ages of the son and the father, in years are

a) 3 and 24 b) 4 and 24 c) 5 and 30 d) 6 and 36

57) The coach of cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. The cost of each bat and ball is

a) 50 and 500 b) 400 and 45 c) 500 and 50 d) 400 and 50

58) A fraction becomes 9/11 if 2 is added to both the numerator and the denominator If, 3 is added to both the numerator and the denominator it becomes 5/6, then the fraction is..

a) 5/9 b) 6/9 c) 7/9 d) 8/9

59) Five years ago, Nuri was thrice as old as sonu. Ten years later, Nuri will be twice as old as Sonu. The present ages of Nuri and Sonu are

a) 20 yrs and 50 yrs

b) 30 yrs and 40 yrs

c) 50 yrs and 20 yrs

d) 60 yrs and 30 yrs

60) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. The fixed charge and charge and the "charge for each extra day is…

a) Rs. 15 and Rs. 3 b) Rs 20 and Rs. 5 c) Rs 22 and Rs. 7 d) Rs. 25 and Rs. 10

61) The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference between the two digits of the number?

a) 3 b) 6 c) 9 d) 12

62) The larger of two supplementary angles exceeds the smaller by 20 degrees. The angles are.

a) 90°, 90°

b) 95⁰ 85⁰°

C) 100⁰, 80°

d) 120°, 60°

63) The difference between two numbers is 20 and one number is three times the other then the numbers are

a) 15 and 35 b) 20 and 40 c) 25 and 45 d) 30 and 10

64) Three are two positive numbers such that Sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is..

a) x > y

b) x ≥ y

b) x < y

b) x ≤ y

65) The sum of two digits of a number is 12. If the digits are reversed, then the number so formed exceeds the original number by 18. The original number is

a) 56 b) 57 c) 64 d) 79

66). In a competitive examination, one mark is awarded for each correct answer. While ½ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

(a). 60 (b). 90 (c). 95

(d). 100

67). The ratio of the areas of the two triangles formed by the lines representing the equation 2x + y = 6 and 2x – y +2=0 with the X-axis and the lines with the Y-axis is …

(a) 1:2 (b) 2:1 (c) 4:1 (d) 1:4 68).

COLUMN -1 COLUMN -2

1. 3x + 2y = 5 and 2x – 3y – 7 = 0 (i) parallel 2. ⁴ ₃ x + 2y = 8 and 2x + 3y = 12 (ii) intersecting 3. 2x – 3y = 8 and 4x – 6y = 9 (iii) coincident Choose the correct option from the following

(a) 1 – (i) , 2 – (ii) , 3- (iii) (b) 1 – (ii) , 2- (iii) , 3 – (i) (c) 1 – (iii) , 2 – (i) , 3 – (ii) (d) 1 – (ii) , 2 – (i) , 3 - (iii)

69). The perimeter of a rectangle is 44 Cm. Its length exceeds twice its breadth by 4cm. the area of the rectangle is?

(a). 46cm ² (b). 49cm ² (c). 69 cm ²

(d). 96cm ²

70). The sum of a two digit number is 8. The number obtained by reversing the digits exceeds the number by 18. Then given number is :

(a). 53 (b). 26 (c). 35

(d). 62

71). The pair of equations, x= 0 and x = - 4 has

(a) unique solution (b) no solution (c) infinitely many solution (d) exactly two solutions

72). The cost of a pencil is thrice the cost of rubber. The equivalent linear equation in two variables of above statement is :

(a). P = 3r (b). P = 3 – r (c). P = 1/3 + X

(d). P = 3 + r

73). Sum of two numbers is 35 and their difference is 13, then the numbers are

(a). 24 and 12 (b). 24 and 11 (c). 12 and 11

(d). 25 and 11

74). If 1 is added in numerator and denominator then a fraction changes to 4. If 1 is subtracted from numerator and denominator, fraction changes to 7. Numerator of the fraction is

(a). 2 (b). 3 (c). 7

(d). 15

75). Five years ago, Ram was thrice as old as Shyam and ten years later Ram shall be twice as old as shyam, then the present age of Ram is

(a). 20 Yrs (b). 30 Yrs (c). 40 Yrs

(d). 50 Yrs

76). The difference between two numbers is 14 and the difference between their square is 448, then the numbers are

(a). 25 and 9 (b). 22 and 9 (c). 23 and 9

(d). 23 and 10

77). Rs. 4900 were divided among 150 children. If each girl gets Rs. 50 and a boy gets Rs. 25 then the number of boys is:

(a). 100 (b). 102 (c). 104

(d). 105

78). Two numbers are in the ratio 1: 3. If 5 is added to both the numbers, the ratio becomes 1:2. The numbers are

(a). 5 and 15 (b). 6 and 18 (c). 7 and 21

(d). 9 and 27

79). From a bus stand in Bangalore, if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur,

the total cost is Rs. 46; but if we buy 3 tickets to Malleswaram and 5 tickets to yeshwanthpur the total

cost is Rs.74. The fares from the bus stand to Malleswaram and to Yeshwanthpur are

(a). 4 and 6 (b). 6 and 8 (c). 8 and 10 (d). 10 and 12

80). Places A and B are 100Km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at f=different direction and different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. The speeds of the two cars are

(a). 20Km/h and 30 Km/h (b). 40Km/h and 50Km/h

(c). 40Km/h and 60Km/h (d). 50Km/h and 70Km/h

81). Solve the following system of equations.

2

𝑥 + _3𝑦 ² = 6; ³ _𝑥 + ² _𝑦 = 0; x, y ≠ 0

(a). x = - 6, y = 4 (b). x = 2, y = - 3 (c). x = 6, y = - 4 (d). x = 1, y = 1 82). Ramesh travels 760km to his home parthy by train and parthy by car. He takes 8Hrs, if he travels 160 km by train and rest by car. He takes 12 Mins more, if he travels 240km by train and rest by car. Find the correct option to represent the above situation algebraically.

(a). ¹⁶⁰ _𝑥 + ⁶⁰⁰ _𝑦 = 8; ²⁴⁰ _𝑥 + ⁵²⁰ _𝑦 = ⁴¹ ₅ (b). ₁₆₀ ^𝑥 + ₆₀₀ ^𝑦 = 8; ₂₄₀ ^𝑥 + ₅₂₀ ^𝑦 = ₄₁ ⁵ (a). ¹⁶⁰

𝑥 + ⁶⁰⁰

𝑦 = ¹

8 ; ²⁴⁰

𝑥 + ⁵²⁰

𝑦 = ⁵

41 (b). ⁸

𝑥 + ⁸

𝑦 = ¹⁶⁰

600 ; ^5𝑥

41 + ^41𝑦

5 = ²⁴⁰

520

83). Solve for x and y.

𝑥−𝑦

𝑥𝑦 = 9; ^𝑥+𝑦

𝑥𝑦 = 5

(a). x = -1/2, y = 1/7 (b). x = -1/5 , y = ½ (c). x = -1/5 , y = 1/7 (d). x= =1/7 , y = 1/5

84). Find two numbers such that the sum of twice the first and thrice the second is 89 and four times the first exceeds five times the second by 13.

(a). 50 & 47 (b). 37 & 40 (c). 22 & 15 (d). 20 & 17

85). A boat 60km upstream and 88 km downstream in 20 hrs. In another trip, it went 80km upstream and 110 km downstream in 26hrs. Find out the speed of the stream.

(a). 8km/hr (b). 5 km/hr (c). 10 km/hr

(d). 3 km/hr

86). Shilpa’s age is rtwice her son’s age, four years ago, her son’s age was 20 years less than her mother.

Find shilpa’s current age.

(a). 20 yrs (b). 30yrs (c). 50yrs

(d). 25yrs

87). There are 2 friends, kavita and Manisha, they both decided to buy some books for library, they both together spent Rs. 200 on buying items, but Manisha spent 4 more than half the amount Kavita spent.

Calculate the amount spent by kavita.

(a). 120/- (b). 132/- (c). 70/-

(d). 170/-

88). If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is … (b) ⁻⁵ ₄ (b) ² ₅ (c) ¹⁵ ₄ (d) ³ ₂

89). Distance between two cities is 300km. A person has to travel from one to another using bus and train both. It takes 4 hours to travel. If he go 60 km by train and remaining distance is covered by bus. If 100km is travelled by train and remaining by bus. It takes 10min longer. Find the speed of the train.

(a). 80km/hr (b). 60 km/hr (c). 100km/hr

(d). 140 km/hr

90). A shopkeeper sells a saree at 8% profit and a sweater at 10% discount; there by getting a sum of rs.

1008. If she has sold the saree at 10% profit and the sweater of 8% discount. She would have get Rs.

1028. Then find the cost price of the saree.

(a). 400/- (b). 600/- (c). 800/-

(d). 500/-

91). A motor boat can travel 30km upstream & 28 km downstream in 7hrs. It can travel 21 km upstream and return in 5hrs. Find the speed of boat in still water.

(a). 110 km/hr (b). 40 km/hr (c). 10km/hr

(d). 4 km/hr

92). 8 men and 12 boys can finish a piece of work in 10days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one boy alone to finish the work.

(a). 140 days (b). 160 days (c). 180 days

(d). 280 days

93). Solve the following pair of linear equations to find the value of x & y

5

𝑥+1 - _𝑦−1 ² = ¹ ₂ ; _𝑥+1 ¹⁰ - _𝑦−1 ² = ⁵ ₂

(a). x = - 2, Y = 3 (b). x = - 4, Y = - 5 (c). x = 5, Y = 4 (d). x = 4, Y = 5

(94). Solve: for x and y

5

𝑥+𝑦 + _𝑥−𝑦 ² = 3 ; _𝑥−𝑦 ¹⁵ - _𝑥−𝑦 ⁴ = - 1

(a). x = 2, Y = 3 (b). x = 3, Y = -2 (

c). x = 0, Y = 1 (d). x =1, Y = 1 (95). Solve for x and y

2

√𝑥 + ³

√𝑦 = 2 ; ⁴⁰

√𝑥 - ⁹⁰

√𝑦 = - 10

(a). x = 4, Y = 9 (b). x = 9, Y = 4 (c). x = 10, Y = - 1 (d). x =0, Y = -1

(96). A piece of work is done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. How many days will it take for 9 men and 15 women to finish that work?

(a). 10 days (b). 9 days (c). 3 days

(d). 15 days

(97). From the following, identify the graph of the pair of linear equations which represents inconsistent …

(a) (b)

(c) (d)

(98). It can take 12 hrs to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hrs and the pipe of smaller diameter for 9hrs, only half of the pool can be filled. How long would it take for larger diameter pipe to fill the pool.

(a). 30hrs (b). 20hrs (c). 40hrs (d). 10hrs

Case Study Based Questions.

1. Deepak bought 3 notebooks and 2 pens for Rs. 80. his friend Ram said that price of each notebook could be Rs. 25. Then three notebooks would cost Rs. 75, The two pens would cost Rs. 5 and Each pen could be for Rs. 2.50. Another friend Ajay felt That Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of each notebook would also be Rs. 16.

Lohit Also bought the same type of notebooks and pens as Deepak. He paid 110 for 4 notebooks and 3 pens. Later Deepak guess the cost of one pen is Rs. 10 and Lohit guess the cost of one notebook is Rs. 30.

(i). Form the pair pf linear equations in two variables from this situation by taking cost of one notebook as Rs. X and cost of one pen as y:

(a). 3x + 2y = 80 and 4x + 3y = 110 (b). 2x + 3y = 80 and 3x + 4y = 110 (c). x + y = 80 and x + y = 110 (d). 3x + 2y = 110 and 4x + 3y = 80 (ii). Find the cost of one notebook?

(a). 5/- (b). 10/- (c). 15/- (d). 20/- (iii). Find the cost of one pen?

(a). 5/- (b). 10/- (c). 15/- (d). 20/-

(iv). Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.

(a). 350/- (b). 400/- (c). 420/- (d). 450/- (v). Find whose estimation is correct in the given statement.

(a). Deepak (b). Lohit (c). Ram (d). Ajay

2. Riya decides to use public transport to cover a distance of 300 km. She travels this distance partially by train and remaining by bus. She takes 4 hrs. if she travels 60km by bus & the remaining by train. If she travels 100km by bus and remaining by train, she takes 10 minutes more.

(i). Find the speed of train

(a). 80km/hr (b). 100km/hr (c). 60km/hr (d). 50km/hr

(ii). Find the speed of the bus

(a). 45km/hr (b). 60km/hr (c). 55km/hr (d). 80km/hr

(iii). Which concept has been used to solve the above problem?

(a). Trigonometry (b). Arithmetic Progression

(c). A pair of Linear equations in two variables. (d). Quadratic equations.

(iv). Which values of Riya have been depicted here?

(a)Benefit of public transport (b)Spending more time in traveling

(c)Spending more money (d)Controlling the pollution of environment (v). If am ≠bl, then the system of equations ax + by = c and lx + my = n has …..

(a) has unique solution (b) has no solution (c) has infinitely many solutions (d) exactly two solutions

3. During Diwali vacation, Kesari tours and travels arranged a trip for college students to Dandeli Hills which is famous for fresh river rafting. They started their journey at early morning on decided day and reached there at evening. The journey was smooth . Next day morning the group decided to go for boating. As they reached to river they started to set the boat. They started boating from one place to another place which is at a distance of 42km and then again returns to the starting place. They took 20 hrs in all. The time taken by them riding downstream in going km is equal to the time taken by them riding upstream in going 6Km. For calculating they took speed of the boat as ‘X’ km/hr and the speed of the river as ‘y’ km/hr. Based on the above situation, Answer the following questions.

(i). The speed of the boat in downstream is

(a). x + y km/hr b). x – y km/hr (c). x.y km/hr (d). x/y km/hr (ii). The speed of the boat in upstream is

(a). x + y km/hr b). x – y km/hr (c). x.y km/hr (d). x/y km/hr (iii). The speed of the boat in still water is

(a). 5km/hr (b). 2km/hr (c). 7km/hr (d). 10km/hr

(iv). The speed of river is

(a). 5km/hr (b). 2km/hr (c). 7km/hr (d). 10km/hr

(v) The general form of the pair of linear equations in two variables is …….. ( )

(a) a 1 x +b 1 y + c 1 = 0, a 2 x +b 2 y + c 2 = 0 where a 12 +b 12 = 0 and a 22 +b 22 = 0

(b) a 1 x +b 1 y + c 1 = 0, a 2 x +b 2 y + c 2 = 0 where a 12 +b 12 = 0 and a 22 +b 22 ≠0

(c) a 1 x +b 1 y + c 1 = 0, a 2 x +b 2 y + c 2 = 0 where a 12 +b 12 ≠ 0 and a 22 +b 22 = 0

(d) a 1 x +b 1 y + c 1 = 0, a 2 x +b 2 y + c 2 = 0 where a 12 +b 12 ≠ 0 and a 22 +b 22 ≠ 0

4. A construction company started constructing a building. In the beginning they started construction with 8 men and 12 boys, They took 10 days to complete the work while 6 men and 8 boys can finish it in 14 days. For calculating the time taken by one man as ‘x’ and one boy as ‘y’ to finish the work.

Based on the above situation, answer the following questions.

(i). Time taken by man to finish the work in 1 day

(a). x (b). 1/x (c). 8/y (d). 6x

(ii). Time taken by boy to finish the work in 1 day.

(a). 8x (b). 12/x (c). 1/y (d). 12/y

(iii). Number of days taken by man to complete work.

(a). 120 days (b). 100 days (c). 140 days (d). 200 days

(iv). Number of days required by boys to complete work.

(a). 280 days (b). 300 days (c). 260 days (d). 100 days

(v) If a pair of linear equations is consistent, then the lines will be …( )

(a) parallel (b) always coincident

(c) intersecting or coincident (d) always intersecting

Answer key

1. b

2. b

3. c

4. c

5. a

6. c

7. d

8. c

9. a

10. a

11. c

12. c

13. a

14. c

15. a

16. a

17. a

18. d

19. a

20. d

21. c

22. c

23. c

24. c

25. a

26. c

27. d

28. d

29. d

30. c

31. d

32. c

33. c

34. b

35. a

36. a

37. d

38. d

39. a.

40. c

41. b

42. a

43. b

44. b

45. c

46. a

47. c

48. c

49. a

50. d

51 b

52 b

53 b

54 c

55 b

56 d

57 c

58 c

59 c

60 a

61 a

62 c

63 d

64 b

65 b

66 d

67 c

68 b

69 d

70 a

71 b

72 a

73 b

74 d

75 d

76 c

77 c

78 a

79 c

80 c

81 b 82 a 83 a 84 c 85 d 86 b 87 b 88 c 89 b 90 b 91 c 92 d 93 d 94 b 95 a 96 c 97 c 98 b

Case study Answer Key 1. …

i. a

ii. d iii. b iv. c

v. a

2. ….

i. a

ii. b iii. c iv. d

v. a

3. …

i. a

ii. b iii. a iv. b

v. d

4. …

i. b

ii. c

iii. c

iv. a

v. c

4. Triangles

1. If in two triangles ABC and POR,

𝐴𝐵 𝑄𝑅 = ^𝐵𝐶

𝑃𝑅 = ^𝐶𝐴

𝑃𝑄 then a. P Q R ~ C A B b. P Q R ~ A B C c. C B A ~ P Q R d. B C A ~ P Q R

2. If ABC ~ EDF and ABC is not similar to DEF, then which of the following is not true?

a. BC X EF = AC X FD b. AB X E F = AC X DE c. BC X DE = AB X EF d. BC X DE = AB X FD

3. In the fig given below, two line segments AC and BD intersect each other at the points P Such that PA = 6cm, PB = 3cm, pc = 2.5 cm PD=5cm, LAPB = 50° and CDP = 30°. Then PBA is equal to.

a. 50⁰ b. 30°

c. 60°

d. 100°

4. A square and rhombus are always.

a. Similar

b. Congruent

c. Similar but not congruent d. neither similar nor congruent

5. It is given that ABC ~ DFE

A = 30° C = 50° AB = 5cm AC=8cm and DF = 7.5cm.

Then the following true a. DE = 12cm, F =50⁰ b. DE = 12 cm, F = 100⁰ c. EF = 12cm, D = 100⁰ d. GF = 12cm, CD = 30⁰

6. In triangle ABC and DEF, B= LE

F=LC and AB = 3DE. Then the two triangles are a. congruent but not similar

b. Similar but not congruent c. neither congruent not Similar d. congruent as well as similar

7. If in triangles ABC and DEF

^𝐴𝐵 _𝐸𝐹 = ^𝐴𝐶 _𝐷𝐸 , then they will be similar when a. A = LD

b. A = LE c. B = LE d. C = LF

8. In ABC, AB = 3 and AC= 4 cm and AD is the bisector of A, Then BD: DC is a. 9:16

b. 4:3

c. 3:4

d. 16:9

9. ABCD is Parallelogram with diagonal AC. If a line XY is drawn such that XY ll AB then BX / XC = ?

a. (AY/AC) b (DZ/AZ) c (AZ/ZD) d (AC/AY)

10. In ABC. Given that DE || BC, D IS the mid point of AB and E is a midpoint of AC Then the ratio AE : EC is

a. 1:3 b. 1:1 c. 2:1 d. 1:2

11. In ABC, AC =15 cm and DE I I BC If AB/AD=3 Find EC

a. 5cm b. 10cm c. 2.5cm.

d. 9cm.

12. D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3cm, BD=5cm BC = 12.8 cm and DE // BC. Then length of DE is

a. 4.8cm

b. 7.6cm

C. 19.2 cm d. 2.5 m

13. If in two triangles ABC and POR

𝐴𝐵

𝑄𝑅 = ^𝐵𝐶 _𝑃𝑅 = _𝑃𝑄 ^𝐶𝐴 then

a. P Q R ~ C A B b. P Q R ~ A B C c. C B A ~ P Q R d. B C A ~ P Q R

adjoining figure, PQ∥BC then what 14. In the

could be the values of AQ and QC respectively

1CM

3CM

a. 3 cm and 6cm b. 2cm and 6cm

c. 3cm and 4 cm d. 1cm and 6 cm

15. In the given figure, DE∥BC if AB= 7.6 cm and AD = 1.9cm then AE: EC is

a. 1: 4 b. 4:1 c. 1: 3 d. 3:1

16. Triangle ABC ~triangle PQR, angle B=50°, angle C=70° then angle P is

a. 50° b. 60° c. 40° d. 70°

17. which geometry figures are always similar

a. quadrilaterals b. circles

c. triangles d. polygons

18. In figure, DE∥BC then then x equal to

a. 1.4 cm b. 2cm c. 4c m d. 2.5 cm

19. two congruent triangles are actually similar triangles with the ratios of corresponding slides as

a. 1:2 b. 1:1 c. 1: 3 d. 2:1