Directions (Q. 1-5): In each of the following questions two equations I and II are given. You have to solve both the equations and give answer:
1) if x > y
2) if x < y
3) if x <= y
4) if x >= y
5) if x = y or no relationship can be established between x and y.
1.
I. 14 x^2 – 43x + 20 = 0
II. 33y^2 + 72y + 12 = 0
2.
I. x^2 - 8 x + 15 = 0
II. y^2 - 5 y + 6 = 0
3.
I. 4y^2 + 3 y - 1 = 0
II. x^2 - 6x + 5 = 0
4.
I. 8x + 3y = 15
II. 6x + 2y = 12
5.
I. 15x^2 - 13x2 + 2 = 0
II. 35y^2 - 12y + 1 = 0
Directions (Q. 6-10): What should come in place of the question mark (?) in the following series?
6. 680, 655, 704, 623, 744, ?
1) 575
2) 675
3) 600
4) 913
5) None of these
7. 10, 10, 20, ?, 110, 300, 930
1) 40
2) 35
3) 45
4) 50
5) 60
8. 1, ?, 22, 188, 2052, 28748
1) 2
2) 3
3) 6
4) 16
5) 10
9. 50327, 7169, 1215, 223, 76, ?
1) 1
2) 2
3) 3
4) 4
5) 8
10. 14, 34, 62, ?, 142, 194
1) 94
2) 98
3) 108
4) 112
5) None of these
Answers:
1. 1
14x^2 - 43x + 20 = 0
x = 4/7 or 5/2
33y^2 + 6y + 66y + 12 = 0
y = -2 or -2/11
x > y
2. 4
x = 3 or, 5
y = 2 or, 3
3. 1
y = 1/4 or -1
x = 1 or 5
x > y
4. 2
x = 3, y = –3
x > y
5. 4
x = 1/5, 2/3
y = 1/7, 1/5
x >= y
6. 1
680 - 5^2 = 655
655 + 7^2 = 704
704 - 9^2 = 623
623 + 11^2 = 744
744 - 13^2 = 575
7. 3
10 × 1/2 + 5 = 10
10 × 1 + 10 = 20
20 × 1 1/2 + 15 = 45
45 × 2 + 20 = 110
110 × 2 1/2 + 25 = 300
300 × 3 + 30 = 930
8. 3
1 × 2 + 4 = 6
6 × 5 - 8 = 22
22 × 8 + 12 = 188
188 × 11 - 16 = 2052
2052 × 14 + 20 = 28748
9. 4
50327 - 12^2 ÷ 7 = 7169
7169 + 11^2 ÷ 6 = 1215
1215 - 10^2 ÷ 5 = 223
223 + 9^2 ÷ 4 = 76
76 - 8^2 ÷ 3 = 4
10. 2
2 + 3 × 4 = 14
4 + 5 × 6 = 34
6 + 7 × 8 = 62
8 + 9 × 10 = 98
10 + 11 × 12 = 142
12 + 13 × 14 = 194