ARUN SINGH RAWAT Unacademy Top Banking Quantitative Aptitude Educator ✓ More than 7 Year Teaching Experience in Banking Exams. ✓ Taught in All Top Online Educations Platform Mahendras, Adda247 & WiFiStudy. ✓ Currently Teaching in Unacademy & Bankers way YouTube Channel. ✓ More than 200 times in you tube Trending videos. ✓ Best Faculty Award in 2017 & Most Engaging Educator Award 2020. ✓ Given Highest Number of selections through YouTube & All My Paid course ✓ Qualified IBPS PO, RRB PO, in 2014, SSC CGL, SSC CHSL Qualified in 2015. ✓ More than 200+ videos on YouTube. Approx. 100 Million views on YouTube.
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ARUN SINGH RAWAT
Unacademy Top Banking Quantitative Aptitude Educator
✓ More than 7 Year Teaching Experience in Banking Exams.
✓ Taught in All Top Online Educations Platform Mahendras, Adda247 & WiFiStudy.
✓ Currently Teaching in Unacademy & Bankers way YouTube Channel.
✓ More than 200 times in you tube Trending videos.
✓ Best Faculty Award in 2017 & Most Engaging Educator Award 2020.
✓ Given Highest Number of selections through YouTube & All My Paid course
✓ Qualified IBPS PO, RRB PO, in 2014, SSC CGL, SSC CHSL Qualified in 2015.
✓ More than 200+ videos on YouTube. Approx. 100 Million views on YouTube.
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Maths by Arun Singh Rawat sir ARUN SINGH RAWAT
❑ QUADRATIC EQUATION LIVE TEST
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a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
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I. x = 𝟏𝟔𝟗II. 𝐲 – 𝟏 𝟐 = 144
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x = 169 = 13II. (y – 1)² = 144y – 1 = 12 or y – 1 = – 12y = 13 or y = – 11⇒ x ≥ y
❑ QUADRATIC EQUATION LIVE TEST
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I. 2x² - 9x + 9 = 0
II. 6y² - 17y + 12 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 2x² - 9x + 9 = 0
2x² - 6x – 3x + 9 = 0
(2x-3)(x-3)=0
𝑥 =3
2, 3
II. 6y² - 17y + 12 = 0
6y² - 8y – 9y + 12 = 0
(2y-3)(3y-4)=0
𝑦 =3
2,4
3∴ x ≥ y
❑ QUADRATIC EQUATION LIVE TEST
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I. 7y + 3x = 27
II. 9y + 7x = 53
a) x > yb) x ≥ yc) x < yd) x ≤ 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
𝑥 =64
11∴ x > y
❑ QUADRATIC EQUATION LIVE TEST
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I. 3x² + 5x – 112 = 0
II. 2y² + 19y + 42 =0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 3x² + 5x – 112 = 0
3x² + 21x – 16x – 112 = 0
(3x-16)(x+7)=0
𝑥 = −7,16
3II. 2y² + 19y + 42 = 0
2y² + 12y + 7y + 42 = 0
(2y+7)(y+6)=0
y = -6, −7
2
no relation
❑ QUADRATIC EQUATION LIVE TEST
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I. 28x² + 33x + 9 = 0
II. 25y² + 50y + 24 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
I. 28x² + 33x +9 =0
28x² + 21x + 12x + 9 = 0
(7x+3)(4x+3)=0
𝑥 = −3
4, −
3
7II. 25y² + 50y + 24 = 0
25y² + 30y + 20y + 24 = 0
(5y+6)(5y+4)=0
𝑦 = −4
5, −
6
5∴ x > y
❑ QUADRATIC EQUATION LIVE TEST
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(I) 16x2 - 16x + 3 = 0(II) 2y2 - y - 3 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ 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 = ¾ or ¼=> 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
❑ QUADRATIC EQUATION LIVE TEST
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(I) 2x2 - 7x + 5 = 0
(II) y =𝟑
𝟖
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
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.
❑ QUADRATIC EQUATION LIVE TEST
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(I) x2 - 11x + 10 = 0(II) y2 - 5y + 6 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ 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 ≥ yc) x < yd) x ≤ 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. 3x² – 22x + 40 = 0
II. 2y² – 17y + 36 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 3x² – 22x + 40 = 0
3x² – 12x – 10x + 40 = 0
3x(x – 4) – 10 (x – 4) = 0
(3x – 10) (x –4) = 0
𝑥 =10
3, 4
II. 2y² – 17y + 36 = 0
2y² – 8y – 9y + 36 = 0
2y(y – 4) –9 (y – 4) = 0
(2y–9) (y – 4) = 0
y = 9
2, 4
y ≥ x
❑ QUADRATIC EQUATION LIVE TEST
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I. 5x² + 7x – 90 = 0
II. 3y² + 28y + 64 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 5x² + 7x – 90 = 0
5x² + 25x – 18x – 90 = 0
5x (x + 5) – 18 (x + 5)= 0
(x + 5) (5x – 18) = 0
𝑥 = −5,18
5II. 3y² + 28y + 64 = 0
3y² + 12y + 16y + 64 = 0
3y (y + 4) + 16 (y + 4) = 0
(3y + 16) (y +4) = 0
y = −16
3. −4
No relation can be established between x & y
❑ QUADRATIC EQUATION LIVE TEST
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I. x² – 14x + 48 = 0
II. 2y² – 19y + 45 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x² – 14x + 48 =0
x² – 6x – 8x + 48 = 0
x(x – 6) – 8 (x – 6) = 0
(x – 8) (x – 6) = 0
x= 8, 6
II. 2y² – 19y + 45 = 0
2y² – 10y – 9y + 45 = 0
2y (y – 5) – 9(y – 5) = 0
(2y – 9) (y – 5) = 0
𝑦 =9
2, 5
x > y
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I. 2x² + 13x + 20 = 0
II. 3y² + 26y + 56 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 2x² + 13x + 20 = 0
2x² + 8x + 5x + 20 = 0
2x(x + 4) + 5 (x + 4) = 0
(2x + 5) (x + 4) = 0
𝑥 =−5
2, −4
II. 3y² + 26y +56 = 0
3y² + 12y + 14y + 56 = 0
3y (y + 4) + 14 (y + 4) = 0
(3y + 14) (y + 4) =0
𝑦 = −14
3, −4
x ≥ y
❑ QUADRATIC EQUATION LIVE TEST
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I. 15x² + 11x + 2 = 0
II. 24y² + 11y + 1 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. 15x² + 5x + 6x + 2 = 0
5x (3x + 1) + 2 (3x + 1) = 0
(5x + 2) (3x + 1) = 0
𝑥 =−2
5, −
1
3II. 24y² + 8y + 3y + 1 = 0
8y (3y +1) + 1 (3y + 1) = 0
(8y + 1) (3y + 1) = 0
𝑦 = −1
3,−1
8⇒ x ≤ y
❑ QUADRATIC EQUATION LIVE TEST
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I. x² – 30x + 221 = 0
II. y² – 17y + 60 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x² – 13x – 17x + 221 = 0
x (x – 13) – 17 (x – 13) = 0
(x – 17) (x – 13) = 0
x = 13, 17
II. y² – 12y – 5y + 60 = 0
y (y – 12) – 5 (y – 12) = 0
(y – 5) (y – 12) = 0
y = 5, 12
⇒ x > y
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I. x² + 6x + 8 = 0
II. 8y² + 22y + 15 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x² + 6x + 8 = 0
x² + 2x + 4x + 8 = 0
x (x + 2) + 4 (x + 2) = 0
(x + 4) (x + 2) = 0
x = –2, –4
II. 8y² + 22y + 15 = 0
8y² + 10y + 12y + 15 = 0
2y (4y + 5) +3(4y + 5) = 0
(2y + 3) (4y + 5) = 0
𝑦 =−3
2, −
5
4⇒ x < y
❑ QUADRATIC EQUATION LIVE TEST
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I. x² – 20x + 96 = 0
II. y² – 15y + 56 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
I. x² – 20x + 96 = 0
x² – 8x – 12x + 96 = 0
x (x – 8) – 12 (x – 8) = 0
(x – 12) (x – 8) = 0
x = 12, 8
II. y² – 15y + 56 = 0
y² – 7y – 8y + 56 = 0
(y – 7) (y – 8) = 0
y = 7, 8
⇒ x ≥ y
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(i) x² = (33)² – 62 × 4
(ii) y² + 62y + 957 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) x² = 1089 – 248
x² = 841
x = ± 29
(ii) y² + 33y + 29y + 957 = 0
y (y + 33) + 29 (y + 33) = 0
(y + 29) (y + 33) = 0
y = – 29, – 33
x ≥ y
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(i) 3x² – 45x + 168= 0
(ii) 3y² – 39y + 126 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
(i) 3x² – 24x – 21x + 168 = 0
3x (x – 8) – 21 (x – 8) = 0
(3x – 21) (x – 8) = 0
x = 7, 8
(ii) 3y² – 21y – 18y + 126= 0
3y (y – 7) – 18 (y – 7) = 0
(y – 7) (3y – 18) = 0
y = 7, 6
x ≥ y
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(i) 36x² + 12x - 8= 0
(ii) 45y² + 51y + 12 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
(i) 36x² + 24x – 12x – 8 = 0
12x (3x + 2) – 4 (3x + 2) = 0
(3x + 2) (12x – 4) = 0
𝑥 =–2
3,
1
3
(ii) 45y² + 36y + 15y + 12 = 0
9y (5y + 4) + 3 (5y + 4) = 0
(5y + 4) (9y + 3) = 0
y = –4
5,
–1
3
No relation
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(i) x² – 40x + 336= 0
(ii) y²– 60y + 896 = 0
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
(i)x² – 28x – 12x + 336 = 0
x (x – 28) – 12 (x – 28) = 0
(x – 12) (x – 28) = 0
x = 12, 28
(ii) y² – 32y – 28y + 896 = 0
y (y – 32) – 28 (y – 32) = 0
(y – 32) (y – 28)
y = 28, 32
x ≤ y
❑ QUADRATIC EQUATION LIVE TEST
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(i) x² – 721 = 800
(ii) y = 𝟏𝟓𝟐𝟏
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
x² = 800 + 721
x = ±39
y = 1521
y = 39
x ≤ y
❑ QUADRATIC EQUATION LIVE TEST
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I. 16x – 15y = 22II. 2x – 5y = 4
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.
Sol.
16x – 15y = 22(2x – 5y = 4)×3 (make y terms equal in both the equations and on subtracbarrelg the II eqn from the I )⇒ 16x–15y = 22
6x–15y = 12⇒10x = 10
⇒ x = 1Put x = 1 in eqn 2x–5y = 4⇒ 2×1–5y = 4⇒ 5y = 2–4 = –2
⇒ y = −2
5
𝑖. 𝑒. x > y
❑ QUADRATIC EQUATION LIVE TEST
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I. 4x² – 7x – 15 = 0II. 33y = –(9y² + 18)
a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.