Q21. Option D

1. I. 2x2 + 2x – x – 1 = 0

or, 2x(x + 1) – 1(x + 1) = 0

or, (x + 1) (2x – 1) = 0

x = -1, ½

1. 6y
2 – 3y – 10y + 5 = 0

or, 3y(2y – 1) – 5(2y – 1) = 0

or, (3y – 5)(2y – 1) = 0

y = -3, 11/3

x  y

Q22. Option E
I. 21x
2 – 45x – 77x + 165 = 0

or, 3x(7x – 15) – 11 (7x – 15) = 0

or, (3x – 11) (7x – 15) = 0
x = 11/3, 15/7

II. 3y2 + 9y – 11y – 33 = 0

or,3y(y + 3) – 11(y + 3) = 0

or,(3y – 11) (y + 3) = 0

y = -3, 11/3

Q23. Option C

1. 5x2 – 20x – 9x + 36 = 0

or, 5x(x – 4) – 9(x – 4) = 0

or,(x – 4) (5x – 9) = 0
x = 4, 9/5

1. 10y2 + 15y – 18y – 27 = 0

or, 5y(2y + 3) – 9(2y + 3) = 0

or, (2y + 3) (5y – 9) = 0

y = 9/5, -3/2
x
y

Q24. Option B

eqn (I) × 3 – eqn (II) × 4

21x + 12y = 9

20x + 12y = 12

–       –             –
x          = -3
and y = 6
x <y

Q25. Option A
I. 7x
2 – 21x – 33x + 99 = 0

or, 7x(x – 3) – 33(x – 3) = 0

or, (x – 3) (7x – 33) = 0

x = 3, 33/7

1. 4y2 – 6y – 10y + 15 = 0

or, 2y(2y – 3) – 5(2y – 3) = 0

or, (2y – 3)(2y – 5) = 0

y = 3/2, 5/2

Q26. Option A
I. 5x
2 – 45x – 42x + 378 = 0

or, 5x(x – 9) – 42(x – 9) = 0

or, (5x – 42) (x – 9) = 0

x = 9, 42/5

II. 3y2 – 24y – 25y + 200 = 0

or, 3y(y – 8) – 25(y – 8) = 0

or, (y – 8) (3y – 25) = 0

y = 8, 25/3
x>y

Q27. Option E

1. 10x2 – 16x + 15x – 24 = 0

or, 2x(5x – 8) + 3(5x – 8) = 0

or, (2x + 3) (5x – 8) = 0

x = -3/8, 8/5

1. y2 – 2y = 0

or, y(y – 2) = 0

y = 0, 2

Q28. Option D

1. x2 – 2x – 3x + 6 = 0

or, x(x – 2) – 3(x – 2) = 0

or, (x – 2) (x – 3) = 0

x = 2,3
II. 2y
2 – 6y – 9y + 27 = 0

or, 2y(y – 3) – 9(y – 3) = 0

or, (y – 3) (2y – 9) = 0

y= 3, 9/2         x  y

Q29. Option B

eqn (I) × 5 + eqn (II) × 2

15x + 10y = 1505

14x – 10y = 148

29x = 1653

x =1653/29 = 57

and y = 65
x < y

Q30. Option C
I. 14x2 – 37x + 24 = 0

or, 14x2 – 21x – 16x + 24 = 0

or, 7x(2x – 3) – 8(2x – 3) = 0

or, (2x – 3) (7x – 8) = 0

x=3/2, 8/7

1. 28y2 – 53y + 24 = 0

or, 28y2 – 21y – 32y + 24 = 0

or, 7y(4y – 3) – 8(4y – 3) = 0

or, (7y – 8) (4y – 3) = 0

y= 8/7 , ¾
x
y