Directions (Q. 1 – 5): In each of these questions a number series is given. What value will come in place of the question mark (?) in the following series?
1. 0.5, ?, 1.5, 4.5, 13, 38.75
1) 0.5
2) 0.75
3) 1
4) 1.5
5) None of these
2. 13, 18, 22, 25, 27, 28, ?
1) 30
2) 28
3) 32
4) 33
5) None of these
3. 2, 10, 30, 68, 130, 222, ?
1) 280
2) 290
3) 320
4) 350
5) None of these
4. 11, 24, 16, 38, 27, 64, ?
1) 34
2) 38
3) 44
4) 36
5) None of these
5. 821, 460, 749, 580, 701, 652, ?
1) 668
2) 677
3) 766
4) 686
5) None of these
Direction (Q. 6-10): In the following questions, there are two equations (I) and (II) solve the equations and answer according to following codes:
1) if x < y
2) if x > y
3) if x = y
4) if x >= y
5) if x <= y
6.
I. 2x^2 – 13x + 21 = 0
II. 2y^2 – 7y + 3 = 0
7.
I. x^2 – 12x + 35 = 0
II. 6y^2 + 11y +3 = 0
8.
I. 2x^2 – 17 x +21 = 0
II. y^2 – 15y + 56 = 0
9.
I. x^2 + 2x – 8 = 0
II. 2y^2 – 15y + 28 = 0
10.
I. x = √(1/9)
II. 9y^2 – 6y + 1 = 0
Answers:
1. 1
(.5 + .5) × .5 = .5
(0.5 + 1) × 1 = 1.5
(1.5 + 1.5) × 1.5 = 4.5
(4.5 + 2) × 2 = 13
(13 + 2.5 ) × 2.5 = 38.75
2. 2
2 × 6.5 = 13
3 × 6 = 18
4 × 5.5 = 22
5 × 5 = 25
6 × 4.5 = 27
7 × 4 = 28
8 × 3.5 = 28
3. 4
1 + 1^3 = 2
2 + 2^3 = 10
3 + 3^3 = 30
4 + 4^3 = 68
5 + 5^3 = 130
6 + 63 = 222
7 + 73 = 350
4. 3
11 × 2 + 2 = 24
24 ÷ 2 + 4 = 16
16 × 2+ 6 = 38
38 ÷ 2 + 8 = 27
27 × 2 + 10 = 64
64 ÷ 2 + 12 = 44
5. 2
821 – 19^2 = 460
460 + 17^2 = 749
749 – 13^2 = 580
580 + 11^2 = 701
701 – 7^2 = 652
652 + 52 = 677
6. 4
I. 12 x^2 – 6x – 7x + 21 = 0
x = 3, 7/2
II. 2y^2 – 7y + 3 = 0
y = 3, 1/2
7. 2
I. x^2 – 12x + 35 = 0
x = 7 or 5
II. 6y^2 + 11y + 3 = 0
y = -1/3, -3/2
x > y
8. 5
I. 2x^2 – 17 x + 21= 0
or, 2x^2 – 14 x – 3 x + 21 = 0
x = 7 or 3/2
II. y^2 – 15 y + 56 = 0
y^2 – 8y – 7y + 56 = 0
y(y – 8) – 7 (y – 8) = 0
(y – 8) (y – 7)
y = 8, 7
x <= y
9. 1
I. x^2 + 2x – 8 = 0
x^2 + 4 x – 2 – 8 = 0
x = – 4 or +2
II. 2 y^2 – 15 y + 28 = 0
y = 7/2, 4
x < y
100. 3
I. x = 1/3
II. 9y^2 – 6y + 1 = 0
(3y – 1)^2 = 0
y = 1/3
x = y
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