| no. 1 app for banking & ssc preparation …. 18x² + 18x + 4 = 0 18x² + 12x + 6x + 4 = 0 6x...
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Solutions
S1. Ans.(e)
Sol.
I. 6x2 + 77x + 121 = 0
or, 6x2 + 66x + 11x + 121 = 0
or, 6x(x + 11) + 11(x + 11) = 0
or, (6x + 11)(x + 11) = 0
or, x = −11
6, −11
II. y2 + 9y − 22 = 0
or, y2 + 11y − 2y − 22 = 0
or, y(y + 11) − 2(y + 11)
or, (y − 2)(y + 11) = 0
or, y = 2, −11
Hence, no relationship can be established between x and y.
S2. Ans.(a)
Sol.
I. x = √625 = +25
II. y = √676 = +26
So, y > x
S3. Ans.(a)
Sol.
I. x2 + 4x + 4 = 0
(x + 2)2 = 0 ⇒ x = −2
II. y2 − 8y + 16 = 0
⇒ (y − 4)2 = 0 ⇒ y = 4
∴ y > x
S4. Ans.(d)
Sol.
I. x2 − (16)2 = (23)2 − 56
or x2 − 256 = 529 − 56
∴ x = √729 = ±27
II. y1/3 − 55 + 376 = (18)2
or y1/3 = 324 + 55 − 376
∴ y = (3)3 = 27
∴ y ≥ x
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S5. Ans.(d)
Sol.
I. x2 − 19x + 84 = 0
x2 − 7x − 12x + 84 = 0 (x − 7)(x − 12) = 0 ∴ x = 7, 12
II. y2 − 25y + 156 = 0
y2 − 13y − 12y + 156 = 0 (y − 13)(y − 12) = 0 ⇒ y = 13, 12
∴ x ≤ y
S6. Ans.(a)
Sol.
I. 12x² + 17x + 6 = 0
⇒12x² + 8x+ 9x + 6 = 0
⇒4x(3x+2)+3 (3x+2)=0
⇒ (4x+ 3) (3x+2) = 0
⇒x = −3
4 or −
2
3
II. 6y² + 5y+ 1= 0
⇒6y² + 3y + 2y+ 1=0
⇒3y(2y+ 1)+1(2y+ 1)=0
⇒ (3y+ 1) (2y+ 1) = 0
⇒y = −1
3 or −
1
2
∴ x < y
S7. Ans.(b)
Sol.
I. x3 = (216)1
3×3 = 216
⇒x = √2163
= 6 II. 6y² = 150
⇒ y² =150
6= 25
⇒y = ±5
∴ x > y
S8. Ans.(b)
Sol.
I. x² – 6x – 7 = 0
⇒x² – 7x +x– 7 = 0
⇒x(x – 7)+1(x – 7)=0
⇒ (x + 1) (x – 7) = 0
⇒ x = –1 or 7
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II. 2y² + 13y + 15 = 0
⇒ 2y² + 3y + 10y + 15 = 0
⇒y(2y + 3)+5 (2y + 3) = 0
⇒ (y + 5) (2y + 3) = 0
⇒ y = –5 or −3
2
∴ x > y
S9. Ans.(e)
Sol.
I. x² - x −√2x + √2 = 0
⇒x(x - 1) – √2(x − 1) = 0
⇒(x − √2)(x − 1) = 0
⇒x = √2 or 1
II. y² – 3y +2 = 0
⇒ y² - 2y – y+ 2 = 0
⇒y (y – 2) – 1 (y - 2) = 0
⇒ (y - 1) (y - 2) = 0
⇒ y= 1 or 2
∴ Relation cannot be established between x and y.
S10. Ans.(e)
Sol.
I. x² = 463 + 321 = 784
∴ x = ±28
II. y2 = 308 + 421 = 729
∴ y = ±27
Relation cannot be established between x and y.
S11. Ans.(b)
Sol.
I. 9x2 − 27x + 20 = 0
9x2 − 12x − 15x + 20 = 0
3x(3x − 4) − 5(3x − 4) = 0 (3x − 4)(3x − 5) = 0
x =5
3or
4
3
II. 6y2 − 5y + 1 = 0
6y2 − 2y − 3y + 1 = 0
2y(3y − 1) − 1(3y − 1) = 0
y =1
3or
1
2
x > y
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S12. Ans.(d)
Sol.
I. 3x2 − 22x + 40 = 0
3x2 − 12x − 10x + 40 = 0
3x(x − 4) − 10(x − 4) = 0
(x − 4)(3x − 10) = 0
x = 4 or 10
3
II. 2y2 − 19y + 44 = 0
2y2 − 11y − 8y + 44 = 0
y(2y − 11) − 4(2y − 11) = 0
(2y − 11)(y − 4) = 0
y =11
2or 4
y ≥ x
S13. Ans.(c)
Sol.
I. 2x2 − 11x + 14 = 0
2x2 − 7x − 4x + 14 = 0
x(2x − 7) − 2(2x − 7) = 0
(2x − 7)(x − 2) = 0
x =7
2or 2.
II. 2y2 − 7y + 6 = 0
2y2 − 4y − 3y + 6 = 0
2y(y − 2) − 3(y − 2) = 0
(y − 2)(2y − 3) = 0
y = 2 or3
2
x ≥ y
S14. Ans.(e)
Sol.
I. x2 = 49
x = ±7
II. y2 − 4y − 21 = 0
y2 − 7y + 3y − 21 = 0
y(y − 7) + 3(y − 7) = 0
(y − 7)(y + 3) = 0
y = 7 or − 3
No relation
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S15. Ans.(e)
Sol.
I. 3x2 − 13x − 10 = 0
3x2 − 15x + 2x − 10 = 0
3x(x − 5) + 2(x − 5) = 0 (x − 5)(3x + 2) = 0
x = 5 or−2
3
II. 3y2 + 10y − 8 = 0
3y2 + 12y − 2y − 8 = 0 3y(y + 4) − 2(y + 4) = 0 (y + 4)(3y − 2) = 0
y = −4 or2
3
No relation
S16. Ans.(b)
Sol.
I. y² + 2y – 3 = 0
y² +3y – y - 3 = 0
(y + 3) (y- 1) = 0
y = -3 or 1
II. 2x² -7x + 6 = 0
2x² - 4x -3x + 6= 0
2x(x - 2) – 3 (x- 2) = 0
(x - 2) (2x - 3) = 0
x = 2 or 3
2
x > y
S17. Ans.(d)
Sol.
I. x² = 961
x = ± 31
II. y =√961 = 31
y ≥ x
S18. Ans.(c)
Sol.
I. 15x² - 19x +6 = 0
15x² - 9x – 10x + 6 = 0
3x (5x - 3) -2 (5x - 3) = 0
(5x- 3) (3x- 2) = 0
x =3
5 or
2
3
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II. 45y² - 47y + 12= 0
45y² - 20y – 27y + 12= 0
5y (9y - 4) – 3 (9y - 4) = 0
(9y - 4) (5y - 3) = 0
y =4
9 or
3
5
x ≥ y
S19. Ans.(a)
Sol.
I. 2x² + 5x + 2 = 0
2x² + 4x + x + 2 = 0
2x (x + 2) +1 (x+ 2) = 0
x = -2 or −1
2
II. 12 y² + 7y + 1 = 0
12y² + 4y+ 3y+ 1 = 0
4y(3y + 1) + 1 (3y+ 1) = 0
(3y + 1) (4y+ 1) = 0
y = −1
3 or −
1
4
y > x
S20. Ans.(c)
Sol.
I. 2x² –13x + 21 = 0
2x² - 7x - 6x + 21 = 0
x(2x - 7) – 3 (2x - 7) = 0
(2x - 7) (x - 3) = 0
x =7
2 or 3
II. 5y² - 22y + 21 = 0
5y² - 15y – 7y + 21 = 0
5y(y- 3) – 7 (y- 3) = 0
(y - 3) (5y - 7) = 0
y = 3 or7
5
x ≥ y
S21. Ans.(c)
Sol.
I. 8x2 + 26x + 15 = 0
⇒ 8x2 + 20x + 6x + 15 = 0 ⇒ (2x + 5)(4x + 3) = 0
⇒ x =−5
2,
−3
4
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II. 4y2 + 24y + 35 = 0
4y2 + 10y + 14y + 35 = 0
(2y + 5)(2y + 7) = 0
y =−5
2,−7
2
⇒x ≥ y
S22. Ans.(e)
Sol.
I. x2 − 5x − 24 = 0
⇒ (x − 8)(x + 3) = 0
⇒ x = 8, −3
II. y2 − 7y − 18 = 0
(y − 9)(y + 2) = 0
y = 9, −2
No relation
S23. Ans.(a)
Sol.
I. 6x2 + 19x + 15 = 0
⇒ (2x + 3)(3x + 5)
⇒ x =−3
2,
−5
3
II. 24y2 + 11y + 1 = 0
(3y + 1)(8y + 1) = 0
y =−1
8,−1
3
⇒ x < y
S24. Ans.(b)
Sol.
I. 9x2 − 27 + 20 = 0
⇒ 9x2 − 15x − 12x + 20 = 0
⇒ (3x − 5)(3x − 4) = 0
⇒ x =5
3,
4
3
II. 6y2 − 5y + 1 = 0
6y2 − 3y − 2y + 1 = 0
(2y − 1)(3y − 1) = 0
y =1
2,1
3
⇒ x > y
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S25. Ans.(d)
Sol.
I. x2 − 6x + 9 = 0
⇒ x = 3, 3
II. y2 − 11y + 24 = 0
⇒ y = 8, 3
⇒y ≥ x
S26 Ans.(d)
Sol.
I. 8x² + 6x – 5 = 0
8x² + 10x – 4x -5 = 0
2x(4x + 5) – 1(4x + 5) = 0
(4x + 5) (2x - 1) = 0
x = −5
4, or
1
2
II. 12y² - 22y + 8 = 0
12y² – 16y – 6y + 8 = 0
4y(3y – 4) –2 (3y – 4) = 0
(3y – 4) (4y – 2) = 0
y =4
3 or
2
4
y ≥ x
S27. Ans.(c)
Sol.
I. 18x² + 18x + 4 = 0
18x² + 12x + 6x + 4 = 0
6x (3x + 2) +2 (3x + 2) = 0
(3x + 2) (6x + 2) = 0
x =−2
3 or
−2
3=
−1
3
II. 12y² + 29y + 14 = 0
12y² + 21y + 8y + 14 = 0
3y(4y + 7) +2 (4y + 7) = 0
(4y+ 7) (3y +2) = 0
y = −7
4 or
−2
3
x ≥ y
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S28. Ans.(d)
Sol.
I. x2 – 16 = 0
x = ± 4
II.y²– 9y + 20 = 0
y² – 5y – 4y + 20 = 0
y(y – 5) –4 (y– 5) = 0
(y– 5) (y– 4) = 0
y = 5 or 4
y ≥ x
S29. Ans.(a)
Sol.
I. x² = 144
x = ± 12
II. y= √169
y = 13
y > x
S30. Ans.(a)
Sol.
I. 2x² + 11x + 14 = 0
2x² + 7x + 4x + 14 = 0
x(2x + 7) +2 (2x+ 7) = 0
x = −7
2 or − 2
II. 4y² + 12y + 9 = 0
4y² + 6y +6y + 9 = 0
2y (2y+ 3) + 3 (2y+ 3) = 0
(2y + 3) (2y + 3) = 0
y = −3
2 or
−3
2
y > x
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