J.K.SHAH CLASSES C.P.T.

- MATHEMATICS & STATISTICS

CHAPTER-3
EQUATIONS
HOME WORK
1. Solution of the equations is x – y = -2 & 2x + 3y = 36is
(a) 6, 8 (b) 8, 6 (c) 3, 5 (d) none

2. The value of x and y in x + y = 7 and 3x – 2y = 11 is

(a) 2, 5 (b) 5, 2 (c) 3, 4 (d) None

3. The value of x and y in 3x + 2y = 11 and 2x + 3y = 4 is

(a) 2, 5 (b) 5, 2 (c) 5, -2 (d) none

4. The graphs of the equation 3x + 2y = 5 and 2x – y = 11 are

(a) intersecting (b) parallel (c) coincident (d) none

5. The graphs of the equation 3x + 6y = 9 and 9x + 18y = 27 are

(a) intersecting (b) parallel (c) coincident (d) none

6. The graphs of the equation 4x – 5y = 7 and 8x – 10y = 9 are

(a) intersecting (b) parallel (c) coincident (d) none

7. The value of p for which graphs of 2x + py = 7 and 4x + 2y = 14 are coincident

(a) 1 (b) 2 (c) 7 (d) none

8. The system of equation 5x – 4y = 7 and 3x – 2y = 15 have

(a) unique solution (b) infinite solution
(c) no solution (d) none

9. The system of equation 9x – 17 y = 34 and 36x – 68y = 115 have

(a) unique Solution (b) infinite Solution
(c) no solution (d) none

10. The price of 9 pencils and 5 pens is ` 90. Whereas the price of 5 pencils and 4
pens is ` 61. The price of 6 pencils and 3 pens is
(a) ` 55 (b) ` 57 (c) ` 55 (d) none

11. If 4 is added to the numerator of a fraction the fraction becomes equal to 1. If 1 is

1
subtracted from the denominator, the fraction becomes equal to . The fraction is
2
7 3 3
(a) (b) (c) (d) none
3 8 7

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12. The income of two persons are in the ratio 9 : 7 and their expenditure are in the
ratio 4 : 3. If both of them save ` 200 per month. Find the monthly income of both.
(a) `1700, ` 1200 (b) ` 1600, ` 1200
(c) ` 1800, ` 1400 (d) none

1
13. If 4 is added to the numerator of a fraction the fraction becomes equal to . If 5 is
2
1
subtracted from the denominator. The fraction becomes equal to . The fraction
3
is
14 3 3
(a) (b) (c) (d) none
5 14 11

14. There are two numbers. If we add one to each number their ratio becomes 2 : 3. If
1 be decreased from each no. their ratio become 1 : 2. The numbers are
(a) 3, 1 (b) 1, 3 (c) 1, 5 (d) none

15. A father’s age is equal to the ages of 5 children. In fifteen years, his age will be
only half of their united age. Find his present age.
(a) 40 years (b) 45 years (c) 42 years (d) none

16. The roots of equation x2 – 6x + 8 = 0 are

(a) ±2 (b) 4, 2 (c) 3, 1 (d) none

17. The value of c for which the equation 2x2 – 9x + c = 0 have equal roots
81 8
(a) (b) (c) 9 (d) none
8 81

18. The positive value of m for 6x2 – mx + 5 = 0 have roots in the ratio 1 : 2 is
(a) 15 3 (b) 3 15 (c) 15 (d) none

19. The quadratic equation whose roots are 3 + 5 and 3 - 5 is

(a) x2 – 6x + 2 = 0 (b) x2 – 4x + 6 = 0
2
(c) x – 6x + 4 = 0 (d) none

20. The quadratic equation whose one of the roots is 6 + 11

(a) x2 – 12x + 25 = 0 (b) x2 – 25x + 12 = 0
2
(c) x – 18x + 15 = 0 (d) none

21. Factor of x2 + 4√2 x + 6 are

(a) (x + 3 2 ) (x + 2 ) (b) (x + 2 ) (x + 3 )

(c) (x + 2 2 ) (x – 2 3 ) (d) none

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22. Factor of x2 – 2x – 6 are

(a) (x + 1 + 2 ) (x + 2 + 2) (b) (x + 1 + 2 ) (x + 1 - 2)
(c) (x + 2 + 2 ) (x + 2 - 2) (d) none

23. The roots in x4 – 26x2 + 25 = 0 are

(a) ± 1, ± 5 (b) ± 1, ± 3 (c) ± 2, ± 5 (d) none

4
24. The roots of 2x + = 9 are
x
1
(a) 4, 2 (b) 4, 3 (c) 4, (d) none
2

25. Value of x in x + 2x = 1 is
1
(a) 4 (b) (c) 2 (d) none
4
1 1
26. In 6 (x2 + 2
) – 25 (x - ) + 12 = 0. The value of x are
x x
1 1 1 1
(a) 3, 4, 5, 6 (b) 3, , 2, (c) 3, - , 2 - (d) none
3 2 3 2
27. Product of Anokhi age five year ago to her age after 9 year is 51. The present
age of Anokhi is
(a) 9 year (b) 8 year (c) 7 years (d) none

28. The sides of a right triangle containing the right angle are4x and 5x – 4. If the area
of triangle is 210 m2. Find the sides of triangle
(a) 8, 15, 17 (b) 20, 21, 29 (c) 3, 4, 5 (d) None
29. The sum of squares of two consecutive natural numbers is 841. The smaller
number is
(a) 20 (b) 21 (c) 19 (d) none
30. A fast train takes 30 hour less than a slow train for a journey of 600 km. If the
speed of slow train is 10 km/h less than that of the fast train. Find the speed of
fast train.
(a) 20 (b) 30 (c) 40 (d) none

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31. In a cricket match Anil took one wicket more than the thrice the number of wicket
taken by Sachin. If the product of the number of wickets taken by both is 14. Find
the number of wickets taken by Sachin.
(a) 3 (b) 7 (c) 2 (d) none
32. If α and β are the roots of the quadratic equation ax2 + bx + c = 0. The value of
α 3 + β 3 is
3abc − b3 3abc − a 3 3abc − c3
(a) (b) (c) (d) none
a3 c3 a3
33. If α and β are the roots of the equal square. ax2+ bx + c = 0. Then the value of
α 2 + β 2 is
b 2 − ac b 2 − 2ac b2 − a 2
(a) (b) (c) (d) none
a2 a2 a2
34. x = 4 is a solution of the equation 3x2 + (k – 1) x + 16 = 0if k has value :
(a) 17 (b) –17 (c) 15 (d) –15

35. The quadratic polynomial in x whose zeros are a, 2a is :

(a) (x + a) (x – 2a) (b) (x – 2a) (x + 2a)
(c) (x + a) (x + 2a) (d) (x – a) (x – 2a)

x−2
36. The solution of 2 – x = would include :
x
(a) –2, -1 (b) 2, -1 (c) –4, 2 (d) 4, -2

37. The common root of the equations x2 - 7x + 10 = 0 and x2 -10x + 16 = 0 is :

(a) –2 (b) 3 (c) 5 (d) 2

38. If the product of the roots of x2 - 3x + k = 10 is –2 the value of k is :

(a) –2 (b) 8 (c) 12 (d) –8

39. If one root of the equation 2x2 - ax + 6 = 0 is 2 then a equals :

7 7
(a) 7 (b) (c) – 7 (d) -
2 2

40. The ratio of the sum and the product of the roots of 7x2 - 12x + 18 = 0 is :
(a) 7 : 12 (b) 2:3 (c) 3 : 2 (d) 7 : 18

41. The roots of 2x2 - 6x + 3 = 0 are :

(a) real, unequal and rational (b) real, unequal and irrational
(c) real and equal (d) imaginary

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42. The equation x2 + 4x + k = 0 has real roots. Then :

(a) k ≥ 4. (b) k ≤4 (c) k ≤0 (d) k ≥0

43. Roots of ax2 + b = 0 are real and distinct if

(a) ab> 0 (b) ab< 0 (c) a, b> 0 (d) a, b< 0

44. If log10(x2 – 6x + 45) = 2, then the values of x are :

(a) 6, 9 (b) –7, 2 (c) 10, 5 (d) 11, -5

x + 4 x − 4 10
45. The roots of + = are :
x−4 x+4 3
(a) ± 4 (b) ± 6 (c) ± 8 (d) 2 ± 3

46. If the ratio between the roots of the equations lx2 + nx + n = 0 is p : q, then the
p q n
value of + + is :
q p l
(a) 1 (b) 3 (c) 0 (d) –1

x 1− x 1
47. The value of in the equation + = 2 is :
1− x x 6
5 7 9
(a) (b) (c) (d) None
13 13 13
 1   1
48. The value of x in the equation 8  x 2 + 2  − 42  x −  + 29 = 0 is :
 x   x
1 1
(a) 4 (b) –2 (c) (d)
2 4
49. The value of x in the equation 4 x − 3 + 2 x + 3 = 6 is :
(a) 3 (b) 1 (c) 100 (d) 111

50. The roots of the equation 4x – 3(2x + 2)+ 32 = 0 would include :

(a) 1, 2 & 3 (b) 1&2 (c) 1&3 (d) 2&3

51. The solution set of the equation 5 x +1 + 52 − x = 126 is :

(a) {1, 2} (b) {−1, 2} (c) { 1, − 2} (d) { −1, − 2}
1
52. The sum of a number and its reciprocal is 2 . The number is :
20
5 3 4 1
(a) (b) (c) (d)
4 4 3 6

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53. Solving equation z2 -6z + 9 = 4√2 − 6 + 6 following following roots are

obtained
(a) 3 + 2√3, 3 - 2√3 (b) 5, 1
(c) all the above (d) None

54. Solving equation (2x+1) (2x+3) (x-1) (x-2) =150 the roots available are

± √
 D D
(a) (b) –3 (c) − ,3 (d) None
  

55. Solving equation (2x+3) (2x+5) (x-1) (x-2) = 30 the roots available are


±√
G
(a) 0,152. -1154, 954 (b) 0,− ,
 




(c) 0,− ,− , (d) None
  

56. Solving equation Hy  + 4y − 21 +HA  − y − 6 = H6y  − 5y − 39 following roots

are obtained
(a) 2, 3, 5/3 (b) 2, 3, -5/3 (c) -2, -3, 5/3 (d) -2, -3, -5/3

ANSWERS

1. (a) 2. (b) 3. (c) 4. (a) 5. (c) 6. (b) 7. (a)

8. (a) 9. (c) 10. (b) 11. (c) 12. (c) 13. (b) 14. (d)

15. (b) 16. (b) 17. (a) 18. (b) 19. (c) 20. (a) 21. (a)

22. (d) 23. (a) 24. (c) 25. (b) 26. (c) 27. (b) 28. (b)

29. (a) 30. (a) 31. (c) 32. (a) 33. (b) 34. (d) 35. (d)

36. (b) 37. (d) 38. (b) 39. (a) 40. (b) 41. (b) 42. (b)

43. (b) 44. (d) 45. (c) 46. (c) 47. (c) 48. (a) 49. (a)

50. (d) 51. (b) 52. (a) 53. (c) 54. (a) 55. (b) 56. (b)

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