Directions (Qs. 1 - 25): In the following questions, two equations are given. You have to solve both and establish the relation between given variables.

1. I. x2 - 9x + 20 = 0       II. y2 - 7y + 12 = 0
1) x > y           2) x y             3) x < y           4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 9x + 20 = 0
⇒ x2 - 5x - 4x + 20 = 0
⇒ x (x - 5) - 4 (x - 5) = 0
⇒ (x - 5) (x - 4) = 0
⇒ x = 5 or 4 y2 - 7y + 12 = 0
⇒ y2 - 4y - 3y + 12 = 0
⇒ y (y - 4) - 3 (y - 4) = 0
⇒ (y - 4) (y - 3) = 0
⇒ y = 4 or 3
∴ x y
Ans: 2

2. I. x3 = 64        II. 2y2 - 17y + 36 = 0
1) x > y         2) x y            3) x < y             4) x y
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x3 = 64
⇒ x = 3√64 = 4
2y2 - 17y + 36 = 0
⇒ 2y2 - 8y - 9y + 36 = 0
⇒ 2y (y - 4) - 9 (y - 4) = 0
⇒ y = 4 or 4.5
∴ x y
Ans: 4

3. I. x2 - x - 56 = 0       II. y2 - 20y + 99 = 0
1) x > y          2) x y              3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: x2 - x - 56 = 0
By solving, x = -7 and 8
y2 - 20y + 99 = 0
By solving, y = 9 and 11
∴ x < y
Ans: 3

4. I. 2x2 + 19x + 42 = 0        II. 4y2 + 43y + 30 = 0
1) x > y            2) x y              3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2018)
Sol: 2x2 + 19x + 42 = 0
By solving, x values are -6 & -3.5
4y2 + 43y + 30 = 0
By solving, y values are -10 & -0.75
∴ Relation can’t be established
Ans: 5

5. I. 2x2 + 48 = 20x          II. y2 - 6 = y
1) x > y          2) x y             3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 + 48 = 20x
By solving, x values are 6 & 4
y2 - 6 = y
By solving, y values are 3 & -2
∴ x > y
Ans: 1

6. I. 2x2 - x - 6 = 0       II. 6y2 + 17y + 5 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2020)
Sol: 2x2 - x - 6 = 0
By solving, x values are 2 & -1.5
6y2 + 17y + 5 = 0
By solving, y values are -2.5 & -0.33
∴ Relation can’t be established
Ans: 5

7. I. x2 - 6x + 8 = 0       II. y2 + y - 6 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 6x + 8 = 0
by solving we get x values as 2 and 4
y2 + y - 6 = 0
by solving we get y values as 2 and -3
∴ x y
Ans: 2

8. I. x2 + 17x + 66 = 0          II. y2 + 10y + 24 = 0
1) x > y          2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 17x + 66 = 0
By solving, x = -6 and -11 y2 + 10y + 24 = 0
By solving, y = -4 and -6
∴ x y
Ans: 4

9. I. x2 + x - 20 = 0       II. y2 - 4y - 21 = 0
1) x > y        2) x y        3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 + x - 20 = 0
By solving, x values are 4 & -5 y2 - 4y - 21 = 0
By solving, y values are 7 & -3
∴ Relation can’t be established
Ans: 5
Shortcut: When in both equations, if constant values are negative (in this question, -20 & -21) then the answer is always no relation.

10. I. 5x2 + 3x - 2 = 0      II. 4y2 - 7y + 3 = 0
1) x > y          2) x y              3) x < y                  4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2020)
Sol: 5x2 + 3x - 2 = 0
By solving, x values are 0.4 & -1
4y2 - 7y + 3 = 0
By solving, y values are 1 & 0.75
∴ x < y
Ans: 3

11. I. x2 + 10x + 9 = 0       II. 2y2 + 14y + 24 = 0
1) x > y           2) x y              3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 10x + 9 = 0
by solving we get x values as - 9 and -1
2y2 + 14y + 24 = 0
by solving we get y values as -3 and -4
∴ Relation can’t be established
Ans: 5

12. I. x2 - 16x + 63 = 0      II. y2 - 18y + 81 = 0
1) x > y            2) x y              3) x < y            4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 16x + 63 = 0
By solving x values are 7 & 9
y2 - 18y + 81 = 0
By solving y values are 9 & 9
∴ x y
Ans: 4

13. I. x2 - 11x + 28 = 0      II. y2 - 12y + 36 = 0
1) x > y           2) x y             3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2018)
Sol: x2 - 11x + 28 = 0
By solving, x values are 7 & 4
y2 - 12y + 36 = 0
By solving, y values are 6 & 6
∴ Relation can’t be established
Ans: 5

14. I. 6x2 + 31x + 33 = 0      II. y2 - 32y + 247 = 0
1) x > y        2) x y           3) x < y             4) x y
5) x = y or the relationship cannot be established  (SBI JA - 2016)
Sol: 6x2 + 31x + 33 = 0
By solving, x values are -3 2/3 & -1 1/2
y2 - 32y + 247 = 0
By solving, y values are 13 & 19
∴ x < y
Ans: 3

15. I. x2 + 7x + 10 = 0         II. y2 + y = 2
1) x > y            2) x y             3) x < y              4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 7x + 10 = 0
by solving we get x values as -2 and -5
y2 + y = 2
by solving we get y values as 1 and -2
∴ x y
Ans: 4

16. I. x2 - 8x + 15 = 0         II. y2 - 12y + 36 = 0
1) x > y         2) x y          3) x < y             4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 8x + 15 = 0
By solving x = 3 & 5
y2 - 12y + 36 = 0
By solving y = 6 & 6
∴ x < y
Ans: 3

17. I. 2x2 + 13x + 21 = 0          II. 2y2 + 27y + 88 = 0
1) x > y          2) x y             3) x < y                  4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 + 13x + 21 = 0
x values are -3 & -3.5
2y2 + 27y + 88 = 0
y values are -8 & -5.5
∴ x > y
Ans: 1

18. I. x2 - 13x + 40 = 0          II. y2 - 6y + 5 = 0
1) x > y             2) x y            3) x < y           4) x y
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x2 - 13x + 40 = 0
By solving, x values are 8 & 5
y2 - 6y + 5 = 0
By solving, y values are 5 & 1
∴ x y
\Ans: 2

19. I. x2 - 11x + 28 = 0   II. y2 - 9y + 18 = 0
1) x > y          2) x y           3) x < y           4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 11x + 28 = 0
By solving, x = 7 and 4
y2 - 9y + 18 = 0
By solving, y = 6 and 3
∴ Relation can’t be established
Ans: 5

20. I. x2 + 36 = 12x           II. 11y - 42 = 4y
1) x > y          2) x y            3) x < y            4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 36 = 12x
by solving we get x values as 6 and 6
11y - 42 = 4y
by solving we get y values as 6
∴ x = y
Ans: 5

21. I. x2 - 15x + 44 = 0        II. y2 - 23y + 132 = 0
1) x > y        2) x y         3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 - 15x + 44 = 0
By solving, x values are 11 & 4
y2 - 23y + 132 = 0
By solving, y values are 11 & 12
∴ x y
Ans: 4

22. I. x2 - 4 = 0        II. y2 - 6y + 9 = 0
1) x > y         2) x y           3) x < y             4) x y
5) x = y or the relationship cannot be established (SBI JA - 2020)
Sol: x2 - 4 = 0
⇒ x = √4 = ± 2
x values are +2 & -2
y2 - 6y + 9 = 0
y values are 3 & 3
∴ x < y
Ans: 3

23. I. 2x2 - 17x + 33 = 0    II. y2 - 8y + 15 = 0
1) x > y          2) x y           3) x < y         4) x y
5) x = y or the relationship cannot be established
Sol: 2x2 - 17x + 33 = 0
x values are 3 & 5.5
y2 - 8y + 15 = 0
y values are 3 & 5
∴ x y
Ans: 2

24. I. x2 + 11x + 30 = 0       II. y2 - 23y + 76 = 0
1) x > y          2) x y          3) x < y          4) x y
5) x = y or the relationship cannot be established
Sol: x2 + 11x + 30 = 0
By solving, x values are -5 & -6
y2 - 23y + 76 = 0
By solving, y values are 19 & 4
∴ x < y
Ans: 3

25. I. 3x2 - 14x + 16 = 0      II. 5y2 - 16y + 12 = 0
1) x > y           2) x y        3) x < y       4) x y
5) x = y or the relationship cannot be established (SBI JA - 2018)
Sol: 3x2 - 14x + 16 = 0
By solving, x values are 2 & 2. 2/3
5y2 - 16y + 12 = 0
By solving, y values are 2 & 1. 1/5
∴ x y
Ans: 2

Posted Date : 24-05-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.