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) x3 – 39304 = 0
b) y2 – 1296=0

Ans: 5
a) x3 – 39304 = 0
x3 = 39304
x=34

b) 2y2 – 5184=0
y2 =1296
y=±36
Thus, the relationship cannot be determined.

2.
a) 624-342-120+88x =784+248+516+22
b) (21y-504)(18y-576)=0

Ans: 2
a) 624-342-120+88x =784+248+516+22
624+88x= 2032
88x=1408
x=16

b) (21y-504)(18y-576)=0
21y- 504=0, 18y-576=0
21y=504, 18y=576
y=24 and 32
Thus x<y

3.
a) 26x^2-64x+24=0
b) 2y^2-28y+96=0

Ans: 2
a) 26x^2-64x+24=0
13x^2-32x+12=0
(X-2)(13x-6)=0
x=2 and 6/13

b) 2^2-28y+96=0
y^2-14y+48=0
(y-6)(y-8)=0
y=6 and 8
Thus x<y

4.
a) 16y + 10x=48
b) 8y+7x=32

Ans: 1
10x+16y=48……(1)
7x+8y=32………(2)
Multiplying (2) by 2 and solving equations, we get
x=4   and    y=0.5
Thus x>y

5.
a) 2x^2+11x+9=0
b)2y^2-7y+6=0

Ans: 2
a) 2x^2+11x+9=0
2x(x+1) +9(x+1) =0
(x+1)(2x+9)=0
x=-4.5 and -1

b) 2y^2-7y+6=0
2y^2-4y-3y+6=0
2y(y-2)-3(y-2) =0
y=1.5 and 2
Thus x<y

Direction (6-10): In the following questions, two equations I and II are given. You have to solve both the equations.
Give Answer

6.
I. p2 – 18p + 72= 0
II. 5q2 – 18q + 9 = 0

Ans: 1
p2 – 18p + 72= 0
(p-12)(p-6) = 0
Gives p = 6, 12
5q2 – 18q + 9 = 0
5q2 – 15q – 3q + 9 = 0
5q (q-3) – 3(q-3) =0
(5q-3) (q-3) =0
Gives q = 3/5, 3
Put on number line
3/5   3    6  12
P > q

7.
I. p2 = 4
II. 3q2 – 4q – 4 = 0

Ans: 5
p2 = 4
Gives p = 2 , -2
3q2 – 4q – 4 = 0
3q2 – 6q + 2q – 4 = 0
Gives q = -2/3, 2
Put on number line
-2      -2/3        2
So no relation

8.
I. 6p2 – 5p – 6 = 0
II. 2q2 – 13q + 20 = 0

Ans: 2
6p2 – 5p – 6 = 0
6p2 – 9p + 4p – 6 = 0
Gives p = -2/3, 3/2
2q2 – 13q + 20 = 0
2q2 – 8q – 5q +20 = 0
Gives q = 4, 5/2
Put on number line
-2/3   3/2    5/2    4
P < q

9.
I. 2p2 – 5p = 0
II. 3q2 – 7q – 6 = 0

Ans: 5
2p2 – 5p = 0
p(2p-5) = 0
Gives p = 0, 5/2
3q2 – 7q – 6 = 0
3q2 – 9q + 2q – 6 = 0
Gives q = -2/3, 3
Put on number line
-2/3    0   5/2         3
There is no relation

10.
I. 2p2 + 5p + 2= 0
II. 2q2 + 19q + 45 = 0

Ans: 1
2p2 + 5p + 2= 0
2p2 + 4p + p + 2= 0
Gives p = -1/2, -2
2q2 + 19q + 45 = 0
2q2 + 10q + 9q + 45 = 0
Gives q= -10/2, -9/2
Put on number line
-10/2     -9/2    -2     -1/2
P > q

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