Directions:1-5) In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option.
1.
i) 2x2-23x+56=0
ii) 3y2+13y+4=0
Ans:1 i) 2x2-23x+56=0
2x2-16x-7x+56=0
(2x-7)(x-8)=0
x= 7/2 or 8
ii) 3y2+13y+4=0
3y2+12y+y+4=0
(3y+1)(y+4)=0
y= -1/3 or -4
Hence x >y
2.
i) x2-22x+117=0
ii) 5y2+41y+42=0
Ans:1 i) x2-22x+117=0
x2-13x-9x+117=0
(x-13)(x-9)=0
x=13 or 9
ii) 5y2+41y+42=0
5y2+35y+6y+42=0
(y+7)(5y+6)=0
y=-7 or -6/5
Hence x >y
3.
i) 2x2-7x+5=0
ii) 2y2+y-28=0
Ans:5 i) 2x2-7x+5=0
2x2-2x-5x+5=0
(x-1)(2x-5)=0
x=1 or 5/2
ii) 2y2+y-28=0
2y2+8y-7y-28=0
(2y-7)(y+4)=0
y= -4 or 7/2
Hence the relationship cannot be determined.
4.
i) x4-[(9)9/2/√x]=0
ii) (4/√y)+ (5/√y)= √y
Ans:5 i) x4-[(9)9/2/√x]=0
x9/2-99/2=0
x9/2=99/2
x=9
ii) (4/√y)+ (5/√y)= √y
9/√y=√y
y=9
Hence, x= y
5.
i) x2+5x+4=0
ii) 3y2-13y+12=0
Ans:1 i) x2+5x+4=0
x2+4x+x+4=0
(x+1)(x+4)=0
x= -1 or -4
ii) 3y2-13y+12=0
3y2-9y-4y+12=0
(y-3)(3y-4)=0
y=4/3 or 3
Hence x< y
Directions:6-10) In the following questions, two equations numbered are given in variables p and q. You have to solve both the equations and find out the relationship between p and q. Then give answer accordingly.
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