Directions: 1-5) In the following questions, two equations numbered are given in variables x and y. Solve both the equations and find out the relationship between x and y. Then give answer accordingly-
1. I. 12p2 – 5p – 3 = 0, II. 3q2 – 11q + 6 = 0
Ans:5 12p2 – 5p – 3 = 0 12p2 + 4p – 9p – 3 = 0 Gives p = -1/3, 3/4 3q2 – 11q + 6 = 0 3q2 – 9q – 2q + 6 = 0 Gives q = 2/3, 3 Put all values on number line and analyze the relationship -1/3… 2/3… 3/4… 3
2. I. 6p2 + 7p + 2 = 0, II. 15q2 – 38q – 40 = 0
Ans:5 6p2 + 7p + 2 = 0 6p2 + 4p + 3p + 2 = 0 Gives p = -2/3, -1/2 15q2 – 38q – 40 = 0 15q2 + 12q – 50q – 40 = 0 Gives q = -4/5, 10/3 Put all values on number line and analyze the relationship -4/5… -2/3… -1/2… 10/3
3. I. 3p2 – 25p + 52 = 0 II. 2q2 – 7q + 3 = 0
Ans:1 3p2 – 25p + 52 = 0 3p2 – 12p – 13p + 52 = 0 Gives p = 4, 13/3 2q2 – 7q + 3 = 0 2q2 – 6q – q + 3 = 0 So q = 1/2, 3 Put all values on number line and analyze the relationship 1/2… 3… 4… 13/3
p > q
4. I. p2 = 1156 II. q = √1156
Ans:4 p2 = 1156 So p = -34, 34 q = √1156 So q = 34 Put all values on number line and analyze the relationship -34… 34
p ≤ q
5. I. p2 – √3969 = √6561, II. q2 – √1296 = √4096
Ans:5 p2 – √3969 = √6561 p2 – 63 = 81 p2 = 144 So p = -12, 12 q2 – √1296 = √4096 q2 – 36 = 64 q2 = 100 So q = -10, 10 Put all values on number line and analyze the relationship -12… -10….10…. 12
Directions:6-10) In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give an answer
6. I. (x+3) (y+2)=12 II. 2xy+4x+5y=11
Ans:5 xy+3y+2x +6 =12
2xy+6y+4x=12—-(i)
2xy+5y+4x=11 —- (ii)
From eq. (i) — (ii)
Y = 1
From eq. (i)
x=1
x = y
7. I. (3x-2)/y = (3x+6)/(y+16) II. (x+2)/(y+4) = (x+5)/(Y+10)
Ans:2 (3x-2)/y = (3x+6)/(y+16)
48x-8y = 32 —- (i)
(x+2)/(y+4) = (x+5)/(y+10)
y = 2x —- (i)
From Equation (i) & (ii)
x=1, y=2
x<y
8. I. x2+20x+4=50-25x II. y2-10y-24=0
Ans:5 x2+20x+4=50-25x
x2+45x-46=0
x2-x+46x-46=0
x(x-1)+ 46 (x-1) =0
(x-1)(x+46)=0
X= -46 and 1
y2-10y-24=0
y2+2y -12y -24=0
y(y+2) – 12 (y+2) =0
(y-12) (y+2) =0
Y = 12 and -2
Relationship cannot be established.
9. I. (x2-10x+16)/(x2 -12x +24) = 2/3 II. y2-y-20=0
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Sir humari exam online hai to bank ki to hume waha rafh page provide kare gy jis hum numberical ki calculation kr sakhe ?
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