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1.D Explanation – I. 3x² – 24x – 15x + 120 = 0 3x(x – 8) –15(x – 8) = 0 (3x – 15) (x – 8) = 0 x = 5, 8 II. y² – 14y - 8y + 112 = 0 y(y – 14) - 8 (y – 14) = 0 (y - 8) (y – 14) = 0 y= 8 , 14 ⇒

2. B Explanation: I. x² – 28x – 39x + 1092 = 0 x(x – 28) – 39(x – 28) = 0 (x – 39) (x – 28) = 0 x = 28, 39 II. y² – 28y – 23y + 644 = 0 y(y – 28) – 23(y – 28) = 0 (y– 28) (y – 23) = 0 y = 28, 23

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⇒

3. E Explanation – I. 50x² – 20x – 40x + 16 = 0 10x(5x – 2) – 8(5x – 2) = 0 (10x – 8) (5x – 2) = 0

II. 20y² – 24y – 10y + 12 = 0 4y (5y – 6) – 2 (5y – 6) = 0 (4y – 2) (5y – 6) = 0

No relation 4. B Explanation – I. 30x² – 24x –20x + 16 = 0

6x(5x – 4) –4 (5x – 4) = 0 (5x – 4) (6x– 4) = 0

II. 24y² – 16y + 6y – 4= 0 8y (3y – 2) + 2(3y – 2) = 0 (8y + 2) (3y – 2) = 0

x ≥ y

5. C




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Explanation – I. x² + 6x + 5x + 30 = 0 x(x + 6) + 5( x+ 6) = 0 (x + 5) (x + 6) = 0 x = –5, –6 II. y² – 8y + 2y – 16 = 0 y(y – 8) + 2(y – 8) = 0 (y – 8) (y + 2) = 0 y= –2, 8 ⇒ x < y 6. E Explanation – I.

x = – 6,

II.

= 0

y =

No relation 7. C Explanation – I.

x = 27, - 53




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II.

y = 57, 53 x < y 8. A Explanation – I.

9x x =

II. 12y (y+2) – 4(y+2) = 0 y = –2,

x > y 9. C

Explanation – I. 6x =

x =

x = 3 II.

y = 5.5

x < y 10. E Explanation – I. 10x² + 663x + 198 = 0 10x² + 660x + 3x + 198 = 0 10x (x + 66) + 3 (x + 66) = 0




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(10x + 3) (x + 66) = 0

II. 3y² + 44y + 161 = 0

3y² + 21y + 23y + 161 = 0 3y(y + 7) + 23(y + 7) = 0 (y + 7) (3y + 23) = 0 y = –7, –

∴ No. relation 11. C Explanation:

12. E Explanation:

No relation can be established. 13. A Explanation:




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,

14. A Explanation: x = , y = ; x > y

15. B 16. B

∴ 17. B

∴ 18. B I. ⇒

II.

19. B I. ⇒




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II. ⇒

∴ 20. C I. ⇒ ⇒

II. ⇒ ⇒

21. A x1 = 9, x2 = 8.4 y1 = 8, y2 = 8.3 x > y 22. B

23. A Let




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After solving again

24. B

25. E 26. E

27. A

28. E

29. E

30. A




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31. B Explanation: 4x2 + 23x + 15 = 0 4x2 + 20x + 3x + 15 = 0 Gives x = -5, -3/4 4y2 – 11y + 6 = 0 4y2 – 8y – 3y + 6 = 0 Gives y= 3/4 ,2 32. D Explanation: 4x2 + 13x + 3 = 0 4x2 + 12x + x + 3 = 0 Gives x = -3, -1/4 4y2 – 7y – 2 = 0 4y2 – 8y + y – 2 = 0 Gives y = -1/4 ,2 33. A Explanation: 3x2 – 10x + 8 = 0 3x2 – 6x – 4x + 8 = 0 Gives x = 2, 4/3 3y2 + 14y + 16 = 0




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3y2 + 6y + 8y + 16 = 0 Gives y = -8/3, -2 34. D Explanation: 3x2 + 16x + 20 = 0 3x2 + 6x + 10x + 20 = 0 Gives x = -10/3, -2 3y2 + 8y + 4 = 0 3y2 + 6y + 2y + 4 = 0 Gives y = -2, -2/3 35. E x = 5/2, 4 y = -4/3, 4 36. C x = 3/2, 3 y = -4, 3/2 37. C x = 3, 8/3 y = -5/2, 3 38. B x = -2, -10/3 y = -1/3, 5 39. C x = 4, 9/2 y = 2/3, 4 40. D




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x = -5, 1/3 y = 1/3, 6 41. C Explanation: x2 – 25x + 114 = 0 x2 – 19x – 6x + 114 = 0 (x – 6)(x – 19) = 0 x = 19 or x = 6 y2 – 10y + 24 = 0 y2 – 6y – 4y + 24 = 0 (y – 4)(y – 6) = 0 y = 6 or y = 4 42. A 43. B Explanation: x2 – 7 √3 x + 36 = 0 ⇒ x2 – 4 √3 x – 3 √3 x + 36 = 0 ⇒ x (x – 4 √3) – 3√3 (x – 4√3) = 0 ⇒ (x – 3√3) (x – 4√3) = 0




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∴ x = 3√3, 4√3 y2 – 11√3 y + 84 = 0 ⇒ y2 – 4√3 y – 7√3 y + 84 = 0 ⇒ y (y – 4√3)– 7√3 (y – 4√3) = 0 ⇒ (y – 7 √3) (y – 4√3) = 0 ∴ y = 7 √3, 4√3 44. E Explanation: 2x2 – 21x + 34 = 0 2x2 – 4x – 17x + 34 = 0 (x – 2)(2x – 17) = 0 x = 2 or x = 17/2 2y2 – 19y + 44 = 0 2y2 – 8y – 11y + 44 = 0




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(y – 4)(2y – 11) = 0 ∴ y = 4 or y = 11/2 45. D Explanation: (48 – 12) / x4/7 = x10/7 36 = x(10/7 + 4/7) 36 = x2 x = ± 6 y3 + 783 = 999 y3 = 999 – 783 y3 = 216 y = 6 46. B Explanation: 6x2 – 5x – 6 = 0 6x2 – 9x + 4x – 6 = 0 x = -2/3, 3/2 2y2 – 13y + 20 = 0 2y2 – 8y – 5y +20 = 0 y = 4, 5/2 47. C Explanation: 5x2 – 7x – 6 = 0 5x2 – 10x + 3x – 6 = 0




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x = -3/5, 2 5y2 + 23y + 12 = 0 5y2 + 20y + 3y + 12 = 0 y = -4, -3/5 48. B Explanation: 5/7 – 5/21 = √x/42 10/21 = √x/42 √x = 20 x = 400 √y/4 + √y/16 = 250/√y 5√y/16 = 250/√y y = 800 49. A Explanation: x2 – 13√2 x + 60 = 0 x2 – 10√2x – 3√2 x + 60 = 0 x(x – 10√2) – 3√2 (x – 10√2) = 0 (x – 3√2) (x – 10√2) = 0 x = 3√2, 10√2




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y2 + 3√5 y – 20 = 0 y2 + 4√5 y – √5 y – 20 = 0 y(y + 4√5) – √5 (y + 4√5) = 0 (y – √5)(y + 4√5) = 0 ⇒ y = – 4√5,√5 50. E Explanation: 6x2 + 25x + 21 = 0 6x2 + 18x + 7x + 21 = 0 6x(x + 3) + 7 (x + 3) = 0 (x + 3) (6x + 7) = 0

x = – 7

, – 3 6

5y2 – 176y – 333 = 0 5y2 – 185y + 9y – 333 = 0




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5y(y – 37) + 9 (y – 37) = 0 (y – 37) (5y + 9) = 0

⇒ y = 37, – 9 5

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