Directions (Q. 1–4): In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer

1) if x > y
2) if x >= y
3) if x < y
4) if x <= y
5) if x = y or relationship between x and y cannot be determined.

1.
I. x^2 + x – 20 = 0
II. y^2 + 13y + 40 = 0

2.
I. x^2 – 11x + 30 = 0
II. y^2 – 13y + 40 = 0

3.
I. x^2 + 10x + 25 = 0
II. 5y^2 – 2 15 y + 9 = 0

4.
I. 10x^2 – 29x – 21 = 0
II. y^2 + 13y – 68 = 0

Directions (Q. 5–7): What value should come in the place of question mark (?) in the following number series?

5. 362, 452, 550, 656, ?
1) 770
2) 772
3) 670
4) 870
5) 790

6. 25, 28, 26, ?, 27, 30
1) 28
2) 32
3) 34
4) 29
5) 36

7. 9, 12, 30, 99, ?
1) 406
2) 418
3) 408
4) 416
5) 424

Directions (Q. 8–10): What value should come in the place of question mark (?) in the following questions?

8. 168.781 – 112.412 – 8.409 – 1.150 = ?
1) 44.81
2) 46.81
3) 40.81
4) 47.81
5) 46.61

9. [(3√27) + 2√27) * (27√27 + 26√27)] – 159√27 = ?
1) 1431
2) 1331
3) 1421
4) 1441
5) 1231

10. 8.5% of 160 – 0.42% of 750 = ?
1) 11.45
2) 12.45
3) 13.45
4) 9.45
5) 10.45

1.2
I. x^2 + 5x – 4x – 20 = 0
(x – 4) (x + 5) = 0
x = 4, – 5

II. y^2 + 8y + 5y + 40 = 0
(y + 8) (y + 5) = 0
y = –8, – 5
x >= y

2.5
I. x^2 – 6x – 5x + 30 = 0
(x – 5) (x – 6) = 0
x = 5, 6

II. y^2 – 8y – 5y + 40 = 0
(y – 8) (y – 5) = 0
y = 8, 5
No relationship between ‘x’ and ‘y’ exits.

3. 3;
I. (x + 5)^2 = 0
x = –5

II. (√5y – √3)^2 = 0
x = √3/√5

4. 5
I. 10x^2 – 35x + 6x – 21 = 0
(5x + 3) (2x – 7) = 0
x = -3/5, 7/2

II. y^2 + 17y – 4y – 68 = 0
(y – 4) (y + 17) = 0
y = 4, –17
No relationship between x and y exists.

5. 1;

6. 4

7. 3

8. 2
? = 46.81

9. 1
? = (3 + √27)(53√27) - 159√27
= 159√27 + 53 * 27 - 159√27 = 1431

10. 5
? = 8.5/100 * 160 - 0.42/100 * 750
= 13.6 - 3.15 = 10.45