arun singh rawat - maths by arun sir
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ARUN SINGH RAWAT
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Maths by Arun Singh Rawat sir ARUN SINGH RAWAT
β QUADRATIC EQUATION LIVE TEST
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a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
I. 7xΒ² β 23x + 18 = 0
II. 4yΒ² β 9y + 5 = 0
Sol.I. 7xΒ² β 23x + 18 = 0 7xΒ² β 14x β 9x + 18 = 0 (7x β 9) (x β 2) = 0
x =9
7, 2
II. 4yΒ² β 9y + 5 = 0 4yΒ² β 4y β 5y + 5 = 0 4y (y β 1) β 5(y β 1) = 0 (4y β 5) (y β 1) = 0
y =5
4, 1
β x > y
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I. 10xΒ² - 11x β 6 = 0
II. yΒ² + 5y + 6 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 10xΒ² - 11x β 6 = 0 5x (2x β 3) + 2 (2x β 3) = 0 (5x + 2) (2x β 3) = 0
x = β2
5,
3
2
II. yΒ² + 5y + 6 = 0 yΒ² + 2y + 3y + 6 = 0 y (y + 2) +3 (y + 2) = 0 (y + 3) (y + 2) = 0 y = β 2, β3
β x > y
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I. 13xΒ² β 29x + 16 = 0 II. 6yΒ² β 11y + 5 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 13xΒ² β 29x + 16 = 0 13xΒ² β 13x β 16x + 16 = 0 13x (x β 1) β16 (x β 1) = 0(13x β 16) (x β 1) = 0
x =16
13, 1
II. 6yΒ² β 11y + 5 = 0 6yΒ² β 6y β 5y + 5 = 0 6y (y β 1) β 5 (y β 1) = 0(6y β 5) (y β 1) = 0
y =5
6, 1
β x β₯ y
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I. x = πππII. π² β π π = 144
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x = 169 = 13II. (y β 1)Β² = 144y β 1 = 12 or y β 1 = β 12y = 13 or y = β 11β x β₯ y
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I. 2xΒ² - 9x + 9 = 0
II. 6yΒ² - 17y + 12 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 2xΒ² - 9x + 9 = 0
2xΒ² - 6x β 3x + 9 = 0
(2x-3)(x-3)=0
π₯ =3
2, 3
II. 6yΒ² - 17y + 12 = 0
6yΒ² - 8y β 9y + 12 = 0
(2y-3)(3y-4)=0
π¦ =3
2,4
3β΄ x β₯ y
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I. 7y + 3x = 27
II. 9y + 7x = 53
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
Multiply (i) by 7 and multiply (ii) by 3 and subtract (ii)
from (i)
y = 15
11
π₯ =64
11β΄ x > y
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I. 3xΒ² + 5x β 112 = 0
II. 2yΒ² + 19y + 42 =0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 3xΒ² + 5x β 112 = 0
3xΒ² + 21x β 16x β 112 = 0
(3x-16)(x+7)=0
π₯ = β7,16
3II. 2yΒ² + 19y + 42 = 0
2yΒ² + 12y + 7y + 42 = 0
(2y+7)(y+6)=0
y = -6, β7
2
no relation
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I. 28xΒ² + 33x + 9 = 0
II. 25yΒ² + 50y + 24 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
I. 28xΒ² + 33x +9 =0
28xΒ² + 21x + 12x + 9 = 0
(7x+3)(4x+3)=0
π₯ = β3
4, β
3
7II. 25yΒ² + 50y + 24 = 0
25yΒ² + 30y + 20y + 24 = 0
(5y+6)(5y+4)=0
π¦ = β4
5, β
6
5β΄ x > y
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(I) 16x2 - 16x + 3 = 0(II) 2y2 - y - 3 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(I) 16x2 - 16x + 3 = 0=> 16x2 - 12x - 4x + 3 = 0=> 4x(4x - 3) - (4x - 3) = 0=> (4x - 3)(4x - 1) = 0=> x = ΒΎ or ΒΌ=> x = 0.75 or 0.25(II) 2y2 - y - 3 = 0=> 2y2 - 3y + 2y - 3 = 0=> y(2y - 3) + (2y - 3) = 0=> (2y - 3)(y + 1) = 0=> y = 3/2, or -1=> y = 1.5 or -1When x = 0.75 and y = 1.5, so, x < yAnd, when x = 0.75 and y = -1 so, x > yAnd, when x = 0.25 and y = 1.5 so, x < yAnd, when x = 0.25 and y = -1 so, x > yHence, the relation cannot be established between x and y
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(I) 2x2 - 7x + 5 = 0
(II) y =π
π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(I) 2x2 - 7x + 5 = 0=> 2x2 - 2x - 5x + 5 = 0=> 2x(x - 1) - 5(x - 1) = 0=> (2x - 5)(x - 1) = 0=> x = 5/2 or 1=> x = 2.5 or 1
And, y = 3
8=> y = 2When x = 2.5 and y = 2 so, x > yAnd, when x = 1 and y = 2 so, x < yHence, relationship cannot be established between x and y.
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(I) x2 - 11x + 10 = 0(II) y2 - 5y + 6 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
x2 - 11x + 10 = 0=> x2 - x - 10x + 10 = 0=> (x - 10)(x - 1) = 0=> x = 10, 1(II) y2 - 5y + 6 = 0=> y2 - 2y - 3y + 6 = 0=> y(y - 2) - 3(y - 2) = 0=> (y - 2)(y - 3) = 0=> y = 2 or 3When x = 10 and y = 2, so, x > yAnd, when x = 10 and y = 3, so, x > yAnd, when x = 1 and y = 2, so, x < yAnd, when x = 1 and y = 3, so, x < yHence, relationship cannot be established between x and y.
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(I) 3x2 + 7x - 20 = 0(II) 6y2 - y - 15 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
3x2 + 7x - 20 = 0(x + 4)(3x - 5) = 0x = -4 and 5/36y2 - y - 15 = 0(2y + 3)(3y - 5) = 0y = -3/2 and 5/3Hence, relation can't be determined.
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I. 3xΒ² β 22x + 40 = 0
II. 2yΒ² β 17y + 36 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 3xΒ² β 22x + 40 = 0
3xΒ² β 12x β 10x + 40 = 0
3x(x β 4) β 10 (x β 4) = 0
(3x β 10) (x β4) = 0
π₯ =10
3, 4
II. 2yΒ² β 17y + 36 = 0
2yΒ² β 8y β 9y + 36 = 0
2y(y β 4) β9 (y β 4) = 0
(2yβ9) (y β 4) = 0
y = 9
2, 4
y β₯ x
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I. 5xΒ² + 7x β 90 = 0
II. 3yΒ² + 28y + 64 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 5xΒ² + 7x β 90 = 0
5xΒ² + 25x β 18x β 90 = 0
5x (x + 5) β 18 (x + 5)= 0
(x + 5) (5x β 18) = 0
π₯ = β5,18
5II. 3yΒ² + 28y + 64 = 0
3yΒ² + 12y + 16y + 64 = 0
3y (y + 4) + 16 (y + 4) = 0
(3y + 16) (y +4) = 0
y = β16
3. β4
No relation can be established between x & y
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I. xΒ² β 14x + 48 = 0
II. 2yΒ² β 19y + 45 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. xΒ² β 14x + 48 =0
xΒ² β 6x β 8x + 48 = 0
x(x β 6) β 8 (x β 6) = 0
(x β 8) (x β 6) = 0
x= 8, 6
II. 2yΒ² β 19y + 45 = 0
2yΒ² β 10y β 9y + 45 = 0
2y (y β 5) β 9(y β 5) = 0
(2y β 9) (y β 5) = 0
π¦ =9
2, 5
x > y
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I. 2xΒ² + 13x + 20 = 0
II. 3yΒ² + 26y + 56 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 2xΒ² + 13x + 20 = 0
2xΒ² + 8x + 5x + 20 = 0
2x(x + 4) + 5 (x + 4) = 0
(2x + 5) (x + 4) = 0
π₯ =β5
2, β4
II. 3yΒ² + 26y +56 = 0
3yΒ² + 12y + 14y + 56 = 0
3y (y + 4) + 14 (y + 4) = 0
(3y + 14) (y + 4) =0
π¦ = β14
3, β4
x β₯ y
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I. 15xΒ² + 11x + 2 = 0
II. 24yΒ² + 11y + 1 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 15xΒ² + 5x + 6x + 2 = 0
5x (3x + 1) + 2 (3x + 1) = 0
(5x + 2) (3x + 1) = 0
π₯ =β2
5, β
1
3II. 24yΒ² + 8y + 3y + 1 = 0
8y (3y +1) + 1 (3y + 1) = 0
(8y + 1) (3y + 1) = 0
π¦ = β1
3,β1
8β x β€ y
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I. xΒ² β 30x + 221 = 0
II. yΒ² β 17y + 60 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. xΒ² β 13x β 17x + 221 = 0
x (x β 13) β 17 (x β 13) = 0
(x β 17) (x β 13) = 0
x = 13, 17
II. yΒ² β 12y β 5y + 60 = 0
y (y β 12) β 5 (y β 12) = 0
(y β 5) (y β 12) = 0
y = 5, 12
β x > y
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I. xΒ² + 6x + 8 = 0
II. 8yΒ² + 22y + 15 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. xΒ² + 6x + 8 = 0
xΒ² + 2x + 4x + 8 = 0
x (x + 2) + 4 (x + 2) = 0
(x + 4) (x + 2) = 0
x = β2, β4
II. 8yΒ² + 22y + 15 = 0
8yΒ² + 10y + 12y + 15 = 0
2y (4y + 5) +3(4y + 5) = 0
(2y + 3) (4y + 5) = 0
π¦ =β3
2, β
5
4β x < y
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I. xΒ² β 20x + 96 = 0
II. yΒ² β 15y + 56 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. xΒ² β 20x + 96 = 0
xΒ² β 8x β 12x + 96 = 0
x (x β 8) β 12 (x β 8) = 0
(x β 12) (x β 8) = 0
x = 12, 8
II. yΒ² β 15y + 56 = 0
yΒ² β 7y β 8y + 56 = 0
(y β 7) (y β 8) = 0
y = 7, 8
β x β₯ y
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(i) xΒ² = (33)Β² β 62 Γ 4
(ii) yΒ² + 62y + 957 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) xΒ² = 1089 β 248
xΒ² = 841
x = Β± 29
(ii) yΒ² + 33y + 29y + 957 = 0
y (y + 33) + 29 (y + 33) = 0
(y + 29) (y + 33) = 0
y = β 29, β 33
x β₯ y
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(i) 3xΒ² β 45x + 168= 0
(ii) 3yΒ² β 39y + 126 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) 3xΒ² β 24x β 21x + 168 = 0
3x (x β 8) β 21 (x β 8) = 0
(3x β 21) (x β 8) = 0
x = 7, 8
(ii) 3yΒ² β 21y β 18y + 126= 0
3y (y β 7) β 18 (y β 7) = 0
(y β 7) (3y β 18) = 0
y = 7, 6
x β₯ y
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(i) 36xΒ² + 12x - 8= 0
(ii) 45yΒ² + 51y + 12 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
(i) 36xΒ² + 24x β 12x β 8 = 0
12x (3x + 2) β 4 (3x + 2) = 0
(3x + 2) (12x β 4) = 0
π₯ =β2
3,
1
3
(ii) 45yΒ² + 36y + 15y + 12 = 0
9y (5y + 4) + 3 (5y + 4) = 0
(5y + 4) (9y + 3) = 0
y = β4
5,
β1
3
No relation
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(i) xΒ² β 40x + 336= 0
(ii) yΒ²β 60y + 896 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i)xΒ² β 28x β 12x + 336 = 0
x (x β 28) β 12 (x β 28) = 0
(x β 12) (x β 28) = 0
x = 12, 28
(ii) yΒ² β 32y β 28y + 896 = 0
y (y β 32) β 28 (y β 32) = 0
(y β 32) (y β 28)
y = 28, 32
x β€ y
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(i) xΒ² β 721 = 800
(ii) y = ππππ
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
xΒ² = 800 + 721
x = Β±39
y = 1521
y = 39
x β€ y
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I. 16x β 15y = 22II. 2x β 5y = 4
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
16x β 15y = 22(2x β 5y = 4)Γ3 (make y terms equal in both the equations and on subtracbarrelg the II eqn from the I )β 16xβ15y = 22
6xβ15y = 12β10x = 10
β x = 1Put x = 1 in eqn 2xβ5y = 4β 2Γ1β5y = 4β 5y = 2β4 = β2
β y = β2
5
π. π. x > y
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I. 4xΒ² β 7x β 15 = 0II. 33y = β(9yΒ² + 18)
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 4x2β7xβ15=0β 4x2β12x+5x-15=0β 4x (x-3)+5(x-3)=0β (4x+5)(x-3)=0
x=-5
4; x=3
II. 33y =β(9y2+18)β9y2+18+33y=0β 9y2+27y+6y+18=0β (y+3)(9y+6)=0
Y=β3 ; y=β6
9=
β2
3
Relationship canβt be established
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I. π +π
ππ=
π
π
II. ππ = π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x+3
2π₯=
5
2
β2π₯2+3
2π₯=
5
2
β 4x2+6=10x
β 4x2β10x+6=0
β 4x2β4xβ6x+6=0
β (4x-6) (x-1)=0
β β
x=+3
2x=1
II. π¦2 = 9y = β 3, + 3
no relation
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I. π = πππII. ππβ πππ + ππ =β πππ
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x = 289β x = 17
II. y2 β 34y + 97 = β192β y2 β 34y + 289 = 0β (y β 17)2 β y = 17
i.e. x = y
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I. 2ππ + πππ =β ππII. ππ = ππ
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 2x2 + 20x + 50 = 0
β x2 + 10x + 25 = 0 β (x + 5)2 = 0β x = -5II. y2 = 25y = + 5
i. e. x < y
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I. x2 + 25x + 156 = 0
II. y2 + 28y + 195 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
sol.From I:x2 + 25x + 156 = 0x2 + 13x + 12x + 156 = 0x(x + 13) + 12(x + 13) = 0(x + 13)(x + 12) = 0x = -13, -12From II:y2 + 28y + 195 = 0y2 + 15y + 13y + 195 = 0y(y + 15) + 13(y + 15) = 0(y + 15)(y + 13) = 0y = -15, -13So, y β€ x.
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I. x2 + 7x β 198 = 0
II. y2 + 38y + 361 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
sol.From I:x2 + 7x β 198 = 0x2 β 11x + 18x β 198 = 0x(x β 11) + 18(x β 11) = 0(x + 18)(x β 11) = 0x = -18, 11From II:y2 + 38y + 361 = 0y2 + 19y + 19y + 361 = 0y(y + 19) + 19(y + 19) = 0(y + 19)(y + 19) = 0y = -19, -19So, x > y.
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I. x2 β 31x + 228 = 0
II. y2 β 30y + 224 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
From I:x2β 31x + 228 = 0x2 β 12x β 19x + 228 = 0x(x β 12) β 19(x β 12) = 0(x β 12)(x β 19) = 0x = 12, 19From II:y2 β 30y + 224 = 0y2 β 14y β 16y + 224 = 0y(y β 14) β 16(y β 14) = 0(y β 14)(y β 16) = 0y = 14, 16So, no relation can be established between x and y.
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I. πππππ β πππ = π
II. πππππ² β πππ = π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 625π₯2β 375 = 0β 625π₯2 = 3752
β x = Β±15
II. 2116π¦β 736 = 0β 46y = 736 β y = 16 y > x
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I. 3xΒ² + 5x + 2 = 0 II. 12yΒ² + 11y + 2 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 3xΒ² + 5x + 2 = 0
β 3xΒ² + 3x + 2x + 2 = 0 β 3x ( x + 1) + 2 (x + 1) = 0β (3x + 2) (x + 1) = 0
π₯ =β2
3, β1
II. 12yΒ² + 11y + 2 = 0 β 12yΒ² + 8y + 3y + 2 = 0 β 4y (3y + 2) + 1 (3y + 2) = 0β (4y + 1) (3y + 2) = 0
π¦ =β1
4,
β2
3
y β₯ x
β QUADRATIC EQUATION LIVE TEST
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I. 16x + 11y = 154II. 11x + 16y = 89
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.16x + 11y = 15411x + 16y = 89 On solving these two equationsx =11 and y = β 2 x > y
β QUADRATIC EQUATION LIVE TEST
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I. 3xΒ² + 14x β 5 = 0 II. 3yΒ² β 19y + 6 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 3xΒ² + 14x β 5 = 0
β 3xΒ² + 15x β x β 5 = 0 β 3x (x + 5) β 1 (x + 5) = 0 β (3x β 1) (x + 5) = 0
x = 1
3, β5
II. 3yΒ² β 19y + 6 = 0 β 3yΒ² β 18y β y + 6 = 0 β 3y ( y β 6) β 1 (y β 6) = 0β (3y β 1) (y β 6) = 0
π¦ =1
3, 6
π¦ β₯ π₯
β QUADRATIC EQUATION LIVE TEST
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I. 7xΒ² β 11x β 6 = 0 II. 7yΒ² β 10y + 3 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.I. 7xΒ² β 11x β 6 = 0
β 7xΒ² β 14x + 3x β 6 = 0 β 7x (x β 2) + 3 (x β 2) = 0 β (7y + 3) (x β 2) = 0
π₯ =β3
7, 2
II. 7yΒ² β 10y + 3 = 0 β 7yΒ² β 7y β 3y + 3 = 0 β 7y (y β 1) β 3 (y β 1) = 0 β (7y β 3) (y β 1) = 0
y =3
7, 1
No relation can be established between x and y
β QUADRATIC EQUATION LIVE TEST
Use code AVP10 For 10% discount on Unacademy any course
(i) xΒ² β 12x + 32 = 0
(ii) yΒ² β 20y + 96 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) xΒ² β 12x + 32 = 0
xΒ² β 8x β 4x + 32 = 0
x (x β 8) β 4 (x β 8) = 0
(x β 8) (x β 4) = 0
x = 8, 4
(ii) yΒ² β 20y + 96 = 0
yΒ² β 12 y β 8y + 96 = 0
y(y β 12) β 8 (y β 12) = 0
(y β 8) (y β 12) = 0
y = 8, 12
y β₯ x
β QUADRATIC EQUATION LIVE TEST
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(i) 2xΒ² β 3x β 20 = 0
(ii) 2yΒ² + 11y + 15 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) 2xΒ² β 3x β 20 = 0
2xΒ² β 8x + 5x β 20 = 0
2x (x β 4) + 5(x β 4) = 0
(x β 4) (2x + 5) = 0
x = 4, β5
2
(ii) 2yΒ² + 11y + 15 = 0
2yΒ² + 6y + 5y + 15 = 0
2y (y + 3) + 5 (y + 3) =0
(2y + 5) (y + 3) =0
y = β5
2, β3
x β₯ y
β QUADRATIC EQUATION LIVE TEST
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(i) xΒ² β x β 6 = 0
(ii) yΒ² β 6y + 8 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) xΒ² β x β 6 = 0
xΒ² β 3x + 2x β 6 = 0
x (x β 3) +2 (x β 3) = 0
(x β 3) (x + 2) = 0
x = 3, β2
(ii) yΒ² β 6y + 8 = 0
yΒ² β 2y β 4y + 8 = 0
y (y β 2) β 4 (y β 2) = 0
(y β 2) (y β 4) = 0
y = 2, 4
No relation can be established between x and y
β QUADRATIC EQUATION LIVE TEST
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(i) xΒ² + 14x - 32 = 0
(ii) yΒ² β y β 12 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) xΒ² + 14x - 32 = 0
xΒ² + 16x -2x - 32 = 0
x (x +16) -2 (x +16) = 0
(x -2) (x + 16) = 0
x = β16, 2
(ii) yΒ² β y β 12 = 0
yΒ² β 4y + 3y β 12 = 0
y(y β 4) + 3(y β 4) = 0
(y + 3) ( y β 4) = 0
y = β 3, 4
No relation can be established between x and y
β QUADRATIC EQUATION LIVE TEST
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(i) xΒ² β 9x + 20 = 0
(ii) 2yΒ² β 12y + 18 = 0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) xΒ² β 9y + 20 = 0
xΒ² β 5y β 4y + 20 = 0
x (x β 5) β4 (y β 5) = 0
(x β 4) (x β 5) = 0
x = 4, 5
(ii) 2yΒ² β 12y + 18 = 0
2yΒ² β 6y β 6y + 18 = 0
2y (y β 3) β6 (y β 3) =0
(2y β 6) (y β 3) = 0
y = 3, 3
x > y
β QUADRATIC EQUATION LIVE TEST
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I. πππ β ππ = ππ β ππ
II. π + πππ β ππ = ππ
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol. π₯ = 4π¦ = 3
β΄ π₯ > π¦
S52. Ans.(e)
Sol. π₯ = 4, 1.8
π¦ = β1.5, 1.8
β΄ π₯ β₯ π¦
β QUADRATIC EQUATION LIVE TEST
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I. 5x2 β 29x + 36 = 0
II. 10y2 β 3y β 27 =0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol. π₯ = 4, 1.8
π¦ = β1.5, 1.8
β΄ π₯ β₯ π¦
β QUADRATIC EQUATION LIVE TEST
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I. π± βπ
π±= π
II. π²π β π πβπ = π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol. I. π₯ 2 = 6
or, π₯ = 6
II. π¦3 = 63
2
or, π¦ = 6β΄ x=y
β QUADRATIC EQUATION LIVE TEST
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I. 3x2+5xβπ=0II. y2βπy+3=0
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol. 3π₯2 + 8π₯ β 3π₯ β 8 = 0π₯ 3π₯ + 8 β 1 3π₯ + 8 = 0
π₯ = 1,β8
3
π¦2 β π¦ β 3π¦ + 3 = 0π¦ π¦ β 1 β 3 π¦ β 1 = 0π¦ = 1, 3π₯ β€ π¦
β QUADRATIC EQUATION LIVE TEST
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π. π±π + π²π = ππππII. π±πβπ²π = πππ
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
Sol. On adding, 2π₯2 = 4232Or, x = 46,-46On subtracting, 2π¦2 = 2450Or, y = 35,-35No relation
β QUADRATIC EQUATION LIVE TEST
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I. π±π β ππ± + ππ = πππ. π²π β ππ² + ππ = π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.
β QUADRATIC EQUATION LIVE TEST
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π. ππ±π + π± β ππ = πππ. ππ²π β πππ² + ππ = π
a) x > yb) x β₯ yc) x < yd) x β€ ye) x = y or relationship between x and y cannot be established.