arun singh rawat - maths by arun sir

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.

Complete course on Quant ( A – Z Batch ) for all

Banking Exam 2021

Use Code :

AVP10

For 10%

Discount

Live Class = 5 : 00 PM

Exclusive Batch For All Banking Mains Exam

Use Code :

AVP10

For 10%

Discount

Live = 8 : 00 PM Live = 6 : 30 PM

AVP10

ENTRY CODE

Free Class on Unacademy ( Mon – Fri ) – 12 : 00 pm

Daily – 12 : 00 pm

Free Class On Unacademy

Daily Free Special Class on Unacademy With Arun Singh Rawat

Maximum Discount,

use code = AVP10

After Getting Subscriptions How to download Pdf

Give me your valuable Feedback on Unacademy

Give me your valuable Feedback on Unacademy

Maths by Arun Singh Rawat sir ARUN SINGH RAWAT

❑ QUADRATIC EQUATION LIVE TEST

Use code AVP10 For 10% discount on Unacademy any course

a) x > yb) x ≥ yc) x < yd) x ≤ ye) x = y or relationship between x and y cannot be established.

I. 7x² – 23x + 18 = 0

II. 4y² – 9y + 5 = 0

Sol.I. 7x² – 23x + 18 = 0 7x² – 14x – 9x + 18 = 0 (7x – 9) (x – 2) = 0

x =9

7, 2

II. 4y² – 9y + 5 = 0 4y² – 4y – 5y + 5 = 0 4y (y – 1) – 5(y – 1) = 0 (4y – 5) (y – 1) = 0

y =5

4, 1

⇒ x > y



I. 10x² - 11x – 6 = 0

II. y² + 5y + 6 = 0


Sol.I. 10x² - 11x – 6 = 0 5x (2x – 3) + 2 (2x – 3) = 0 (5x + 2) (2x – 3) = 0

x = –2

5,

3

2

II. y² + 5y + 6 = 0 y² + 2y + 3y + 6 = 0 y (y + 2) +3 (y + 2) = 0 (y + 3) (y + 2) = 0 y = – 2, –3

⇒ x > y



I. 13x² – 29x + 16 = 0 II. 6y² – 11y + 5 = 0


Sol.I. 13x² – 29x + 16 = 0 13x² – 13x – 16x + 16 = 0 13x (x – 1) –16 (x – 1) = 0(13x – 16) (x – 1) = 0

x =16

13, 1

II. 6y² – 11y + 5 = 0 6y² – 6y – 5y + 5 = 0 6y (y – 1) – 5 (y – 1) = 0(6y – 5) (y – 1) = 0

y =5

6, 1

⇒ x ≥ y



I. x = 𝟏𝟔𝟗II. 𝐲 – 𝟏 𝟐 = 144


Sol.

I. x = 169 = 13II. (y – 1)² = 144y – 1 = 12 or y – 1 = – 12y = 13 or y = – 11⇒ x ≥ y



I. 2x² - 9x + 9 = 0

II. 6y² - 17y + 12 = 0


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



I. 7y + 3x = 27

II. 9y + 7x = 53


Sol.

Multiply (i) by 7 and multiply (ii) by 3 and subtract (ii)

from (i)

y = 15

11

𝑥 =64

11∴ x > y



I. 3x² + 5x – 112 = 0

II. 2y² + 19y + 42 =0


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



I. 28x² + 33x + 9 = 0

II. 25y² + 50y + 24 = 0


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



(I) 16x2 - 16x + 3 = 0(II) 2y2 - y - 3 = 0


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



(I) 2x2 - 7x + 5 = 0

(II) y =𝟑

𝟖


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.



(I) x2 - 11x + 10 = 0(II) y2 - 5y + 6 = 0


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.



(I) 3x2 + 7x - 20 = 0(II) 6y2 - y - 15 = 0


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.



I. 3x² – 22x + 40 = 0

II. 2y² – 17y + 36 = 0


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



I. 5x² + 7x – 90 = 0

II. 3y² + 28y + 64 = 0


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



I. x² – 14x + 48 = 0

II. 2y² – 19y + 45 = 0


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



I. 2x² + 13x + 20 = 0

II. 3y² + 26y + 56 = 0


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



I. 15x² + 11x + 2 = 0

II. 24y² + 11y + 1 = 0


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



I. x² – 30x + 221 = 0

II. y² – 17y + 60 = 0


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



I. x² + 6x + 8 = 0

II. 8y² + 22y + 15 = 0


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



I. x² – 20x + 96 = 0

II. y² – 15y + 56 = 0


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



(i) x² = (33)² – 62 × 4

(ii) y² + 62y + 957 = 0


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



(i) 3x² – 45x + 168= 0

(ii) 3y² – 39y + 126 = 0


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



(i) 36x² + 12x - 8= 0

(ii) 45y² + 51y + 12 = 0


(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



(i) x² – 40x + 336= 0

(ii) y²– 60y + 896 = 0


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



(i) x² – 721 = 800

(ii) y = 𝟏𝟓𝟐𝟏


Sol.

x² = 800 + 721

x = ±39

y = 1521

y = 39

x ≤ y



I. 16x – 15y = 22II. 2x – 5y = 4


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



I. 4x² – 7x – 15 = 0II. 33y = –(9y² + 18)


Sol.I. 4x2–7x–15=0⇒ 4x2–12x+5x-15=0⇒ 4x (x-3)+5(x-3)=0⇒ (4x+5)(x-3)=0

x=-5

4; x=3

II. 33y =–(9y2+18)⇒9y2+18+33y=0⇒ 9y2+27y+6y+18=0⇒ (y+3)(9y+6)=0

Y=–3 ; y=−6

9=

−2

3

Relationship can’t be established



I. 𝒙 +𝟑

𝟐𝒙=

𝟓

𝟐

II. 𝒚𝟐 = 𝟗


Sol.

I. x+3

2𝑥=

5

2

⇒2𝑥2+3

2𝑥=

5

2

⇒ 4x2+6=10x

⇒ 4x2–10x+6=0

⇒ 4x2–4x–6x+6=0

⇒ (4x-6) (x-1)=0

⇓ ⇓

x=+3

2x=1

II. 𝑦2 = 9y = – 3, + 3

no relation



I. 𝒙 = 𝟐𝟖𝟗II. 𝒚𝟐– 𝟑𝟒𝒚 + 𝟗𝟕 =– 𝟏𝟗𝟐


Sol.

I. x = 289⇒ x = 17

II. y2 – 34y + 97 = –192⇒ y2 – 34y + 289 = 0⇒ (y – 17)2 ⇒ y = 17

i.e. x = y



I. 2𝒙𝟐 + 𝟐𝟎𝒙 =– 𝟓𝟎II. 𝒚𝟐 = 𝟐𝟓


Sol.I. 2x2 + 20x + 50 = 0

⇒ x2 + 10x + 25 = 0 ⇒ (x + 5)2 = 0⇒ x = -5II. y2 = 25y = + 5

i. e. x < y



I. x2 + 25x + 156 = 0

II. y2 + 28y + 195 = 0


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 ≤ x.



I. x2 + 7x – 198 = 0

II. y2 + 38y + 361 = 0


sol.From I:x2 + 7x – 198 = 0x2 – 11x + 18x – 198 = 0x(x – 11) + 18(x – 11) = 0(x + 18)(x – 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.



I. x2 – 31x + 228 = 0

II. y2 – 30y + 224 = 0


From I:x2– 31x + 228 = 0x2 – 12x – 19x + 228 = 0x(x – 12) – 19(x – 12) = 0(x – 12)(x – 19) = 0x = 12, 19From II:y2 – 30y + 224 = 0y2 – 14y – 16y + 224 = 0y(y – 14) – 16(y – 14) = 0(y – 14)(y – 16) = 0y = 14, 16So, no relation can be established between x and y.



I. 𝟔𝟐𝟓𝒙𝟐 – 𝟑𝟕𝟓 = 𝟎

II. 𝟐𝟏𝟏𝟔𝐲 – 𝟕𝟑𝟔 = 𝟎


Sol.

I. 625𝑥2– 375 = 0⇒ 625𝑥2 = 3752

⇒ x = ±15

II. 2116𝑦– 736 = 0⇒ 46y = 736 ⇒ y = 16 y > x



I. 3x² + 5x + 2 = 0 II. 12y² + 11y + 2 = 0


Sol.I. 3x² + 5x + 2 = 0

⇒ 3x² + 3x + 2x + 2 = 0 ⇒ 3x ( x + 1) + 2 (x + 1) = 0⇒ (3x + 2) (x + 1) = 0

𝑥 =–2

3, –1

II. 12y² + 11y + 2 = 0 ⇒ 12y² + 8y + 3y + 2 = 0 ⇒ 4y (3y + 2) + 1 (3y + 2) = 0⇒ (4y + 1) (3y + 2) = 0

𝑦 =–1

4,

–2

3

y ≥ x



I. 16x + 11y = 154II. 11x + 16y = 89


Sol.16x + 11y = 15411x + 16y = 89 On solving these two equationsx =11 and y = – 2 x > y



I. 3x² + 14x – 5 = 0 II. 3y² – 19y + 6 = 0


Sol.I. 3x² + 14x – 5 = 0

⇒ 3x² + 15x – x – 5 = 0 ⇒ 3x (x + 5) – 1 (x + 5) = 0 ⇒ (3x – 1) (x + 5) = 0

x = 1

3, –5

II. 3y² – 19y + 6 = 0 ⇒ 3y² – 18y – y + 6 = 0 ⇒ 3y ( y – 6) – 1 (y – 6) = 0⇒ (3y – 1) (y – 6) = 0

𝑦 =1

3, 6

𝑦 ≥ 𝑥



I. 7x² – 11x – 6 = 0 II. 7y² – 10y + 3 = 0


Sol.I. 7x² – 11x – 6 = 0

⇒ 7x² – 14x + 3x − 6 = 0 ⇒ 7x (x – 2) + 3 (x – 2) = 0 ⇒ (7y + 3) (x – 2) = 0

𝑥 =–3

7, 2

II. 7y² – 10y + 3 = 0 ⇒ 7y² – 7y – 3y + 3 = 0 ⇒ 7y (y – 1) – 3 (y – 1) = 0 ⇒ (7y – 3) (y – 1) = 0

y =3

7, 1

No relation can be established between x and y



(i) x² – 12x + 32 = 0

(ii) y² – 20y + 96 = 0


Sol.

(i) x² – 12x + 32 = 0

x² – 8x – 4x + 32 = 0

x (x – 8) – 4 (x – 8) = 0

(x – 8) (x – 4) = 0

x = 8, 4

(ii) y² – 20y + 96 = 0

y² – 12 y – 8y + 96 = 0

y(y – 12) – 8 (y – 12) = 0

(y – 8) (y – 12) = 0

y = 8, 12

y ≥ x



(i) 2x² – 3x – 20 = 0

(ii) 2y² + 11y + 15 = 0


Sol.

(i) 2x² – 3x – 20 = 0

2x² – 8x + 5x – 20 = 0

2x (x – 4) + 5(x – 4) = 0

(x – 4) (2x + 5) = 0

x = 4, –5

2

(ii) 2y² + 11y + 15 = 0

2y² + 6y + 5y + 15 = 0

2y (y + 3) + 5 (y + 3) =0

(2y + 5) (y + 3) =0

y = –5

2, –3

x ≥ y



(i) x² – x – 6 = 0

(ii) y² – 6y + 8 = 0


Sol.

(i) x² – x – 6 = 0

x² – 3x + 2x – 6 = 0

x (x – 3) +2 (x – 3) = 0

(x – 3) (x + 2) = 0

x = 3, –2

(ii) y² – 6y + 8 = 0

y² – 2y – 4y + 8 = 0

y (y – 2) – 4 (y – 2) = 0

(y – 2) (y – 4) = 0

y = 2, 4




(i) x² + 14x - 32 = 0

(ii) y² – y – 12 = 0


Sol.

(i) x² + 14x - 32 = 0

x² + 16x -2x - 32 = 0

x (x +16) -2 (x +16) = 0

(x -2) (x + 16) = 0

x = –16, 2

(ii) y² – y – 12 = 0

y² – 4y + 3y – 12 = 0

y(y – 4) + 3(y – 4) = 0

(y + 3) ( y – 4) = 0

y = – 3, 4




(i) x² – 9x + 20 = 0

(ii) 2y² – 12y + 18 = 0


Sol.

(i) x² – 9y + 20 = 0

x² – 5y – 4y + 20 = 0

x (x – 5) –4 (y – 5) = 0

(x – 4) (x – 5) = 0

x = 4, 5

(ii) 2y² – 12y + 18 = 0

2y² – 6y – 6y + 18 = 0

2y (y – 3) –6 (y – 3) =0

(2y – 6) (y – 3) = 0

y = 3, 3

x > y



I. 𝟏𝟒𝒙 − 𝟐𝟓 = 𝟓𝟗 − 𝟕𝒙

II. 𝒚 + 𝟐𝟐𝟐 − 𝟑𝟔 = 𝟖𝟏


Sol. 𝑥 = 4𝑦 = 3

∴ 𝑥 > 𝑦

S52. Ans.(e)

Sol. 𝑥 = 4, 1.8

𝑦 = −1.5, 1.8

∴ 𝑥 ≥ 𝑦



I. 5x2 – 29x + 36 = 0

II. 10y2 – 3y – 27 =0


Sol. 𝑥 = 4, 1.8

𝑦 = −1.5, 1.8

∴ 𝑥 ≥ 𝑦



I. 𝐱 −𝟔

𝐱= 𝟎

II. 𝐲𝟑 − 𝟔 𝟑⁄𝟐 = 𝟎


Sol. I. 𝑥 2 = 6

or, 𝑥 = 6

II. 𝑦3 = 63

2

or, 𝑦 = 6∴ x=y



I. 3x2+5x−𝟖=0II. y2−𝟒y+3=0


Sol. 3𝑥2 + 8𝑥 − 3𝑥 − 8 = 0𝑥 3𝑥 + 8 − 1 3𝑥 + 8 = 0

𝑥 = 1,−8

3

𝑦2 − 𝑦 − 3𝑦 + 3 = 0𝑦 𝑦 − 1 − 3 𝑦 − 1 = 0𝑦 = 1, 3𝑥 ≤ 𝑦



𝐈. 𝐱𝟐 + 𝐲𝟐 = 𝟑𝟑𝟒𝟏II. 𝐱𝟐−𝐲𝟐 = 𝟖𝟗𝟏


Sol. On adding, 2𝑥2 = 4232Or, x = 46,-46On subtracting, 2𝑦2 = 2450Or, y = 35,-35No relation



I. 𝐱𝟐 − 𝟕𝐱 + 𝟏𝟐 = 𝟎𝐈𝐈. 𝐲𝟐 − 𝟖𝐲 + 𝟏𝟐 = 𝟎




𝐈. 𝟐𝐱𝟐 + 𝐱 − 𝟐𝟖 = 𝟎𝐈𝐈. 𝟐𝐲𝟐 − 𝟐𝟑𝐲 + 𝟓𝟔 = 𝟎


arun singh rawat - maths by arun sir

Documents