Directions:1-10) In each of the following questions, two equations(i) and (ii) are given. You have to solve them and find the correct option.

1.
a) 2x2-23x-70=0
b) 2y2-7y-72=0

Ans: 5
a)2x2-28x+5x-70=0
2x(x-14) +5(x-14) =0
x=14 and x=-5/2
x=14 and x=-2.5

b) 2y2-7y-72=0
2y2+9y-16y-72=0
2y(y-8) +9(y-8) =0
y=8 and y=-9/2
y=8 and y=-4.5
Hence x=y or cannot be determined.

2.
a) 45x2-43x+10=0
b) 17y2+48y-9=0

Ans: 1
a) 45x2-43x+10=0
45x2-25x-18x+10=0
(9x-5)(5x-2)=0
x=5/9 and 2/5
x=0.5 and 0.4

b) 17y2+48y-9=0
17y2+51y-3y-9=0
(y+3)(17y-3)=0
y=-3 and 3/17
y=-3 and 0.17
Hence x>y

3.
a) 14x+16y=10
b) 12x-10y=56

Ans: 1
14x+16y=10……… (1)
Multiply (1) with 6, then we have
84x+96y=60 ………… (2)
12x-10y=56 …………. (3)
Multiply (3) with 7, then
84x-70y=392 ………. (4)
x= 3 and y= – 2
Hence x > y

4.
a) 3x2-16x +20=0
b) 3y2-17y+24=0

Ans: 5
a)3x^2-16x +20=0
3x^2-10x-6x +20=0
3x(x-2)-10(x-2) =0
x=10/3 and 2

b) 3y^2-17y+24=0
3y^2-9y -8y+24=0
3y(y-3)-8(y-3) =0
y=8/3 and 3
Hence x=y Or cannot be determined.

5.
a) 3x^2-24x +36=0
b) 2.5y2 +5y -20=0

Ans: 4
a) 3x^2-24x +36=0
x^2-8x +12=0
x^2-2x-6x +12=0
x(x-2)-6(x-2)=0
x=2 and 6

b) 2.5y^2+5y -20=0
y^2+2y -8=0
(y-2)(y+4)=0
y=2 and -4
Hence x ≥y

6.
a) 5-52x+96=0
b) 5-22y +24=0

Ans: 4
a)5x2-52x+96=0
5x2 -12x-40x+96=0
5x(x-8)-12(x-8) = 0
x=8 and 12/5

b) 5y2 -22y +24=0
5y2 -10y-12y +24=0
5y(y-2)-12(y-2) = 0
y=2 and 12/5
Hence x ≥ y

7.
a) 6x-52√x+112=0
b) 4y-30√y+56=0

Ans: 4
a) 6x- 52√x + 112=0
6x-24√x-28√x+112=0
6√x(√x-4)-28(√x-4) = 0
√x=14/3 and 4
x=196/9 and 16

b) 4y-30√y + 56=0
4y-16√y-14√y+56=0
(4√y-14)(√y-4) = 0
√y= 7/2 and 4
y=49/4 and 16
Hence x ≥y

8.
a) 3x+23y=184
b) 4x+11y=125

Ans: 1
a) 3x+23y=184……………….(1)
b) 4x+11y=125.……………….(2)

Multiply equation (1) by 4
12x+92y=736
Multiply the equation (2) by 3
12x+33y=375
After solving these two equations, we get
y= 6.12 and x=14.41
Hence x > y

9.
a) 3x =19683
b)2x =1024

Ans: 2
a) 3x =19683
3x = 39
x=9

b)2y =1024
2y =210
y=10
Thus x<y

10.
a) x2 -5.8x + 8.41=0
b) y2 – 3.8y + 3.12=0

Ans: 1
a) x2 – 5.8x +8.41=0
x2 – 2.9x – 2.9x + 8.41=0
(x-2.9) (x-2.9) = 0
x=2.9 and 2.9

b) y2 – 3.8y + 3.12=0
y2 -1.2y-2.6y + 3.12=0
(y-1.2) (y-2.6) = 0
y= 1.2 and 2.6
Thus x>y

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