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In each of these questions, one term in the given number series is wrong. Find out the wrong term.
5, 15, 81, 479, 3360, 26897
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5 x 4 – 5 = 15
15 x 5 + 6 = 81
81 x 6 – 7 = 479
479 x 7 – 8 = 3361 (not 3360)
3361 x 8 + 9 = 26897
23, 46, 76, 110, 152, 192
4 x 6 – 1 = 23
6 x 8 – 2 = 46
8 x 10 – 4 = 76
10 x 12 – 8 = 112 (Not 110)
12 x 14 – 16 = 152
14 x 16 – 32 = 192
What value should come at the place of question mark in the following number series?
10, 15, 30, 65, 155 ?
10 x 0.5 + 10 = 15
15 x 1 + 15 = 30
30 x 1.5 + 20 = 65
65 x 2 + 25 = 155
155 x 2.5 + 30 = 417.5
215, 335, 485, 665, 875, ?
63 – 13 = 215
73 – 23 = 335
83 – 33 = 485
93 – 43 = 665
103 – 53 = 875
113 – 63 = 1115
44, 72, 104, 140, 180, ?
4 x 11 = 44
6 x 12 = 72
8 x 13 = 104
10 x 14 = 140
12 x 15 = 180
14 x 16 = 224
In each of the following questions, two equations are given. You have to solve these equations to find the relation between x and y.
1. 8x2 – 15x + 7 = 0
2. 2y2 – 15y + 28 = 0
I.8x2 – 15x + 7 = 0
=> 8x2 – 8x – 7x + 7 = 0
=> 8x(x – 1) – 7(x – 1) = 0
=> (8x – 7)(x – 1) = 0
=> x = 7/8, 1
II.2y2 – 15y + 28 = 0
=> 2y2 – 8y – 7y + 28 = 0
=> 2y(y – 4) – 7(y – 4) = 0
=> (2y – 7)(y – 4) = 0
=> y = 7/2, 4
Hence, x < y
1. 2x2 – 7x + 6 = 0
2. y2 + 13y + 42 = 0
I.2x2 – 7x + 6 = 0
=> 2x2 – 4x – 3x + 6 = 0
=> 2x(x – 2) – 3(x – 2) = 0
=> (2x – 3)(x – 2) = 0
=> x = 3/2, 2
II.y2 + 13y + 42 = 0
=> y2 + 6y + 7y + 42 = 0
=> y(y + 6) + 7(y + 6) = 0
=> (y + 7)(y + 6) = 0
=> y = -7, -6
Hence, x > y
1. 2x2– 9x + 9 = 0
2. 8y2+ 34y + 21 = 0
I.2x2– 9x + 9 = 0
=> 2x2 – 6x – 3x + 9 = 0
=> 2x(x – 3) – 3(x – 3) = 0
=> (2x – 3)(x – 3) = 0
=> x = 3/2, 3
II.8y2+ 34y + 21 = 0
=> 8y2 + 28y + 6y + 21 = 0
=> 4y(2y + 7) + 3(2y + 7) = 0
=> (4y + 3)(2y + 7) = 0
=> y = -3/4, -7/2
1. 2x2 – 13x + 15 = 0
2. 3y2 + 28y + 65 = 0
I.2x2 – 13x + 15 = 0
=> 2x2 – 10x – 3x + 15 = 0
=> 2x(x – 5) – 3(x – 5) = 0
=> (2x – 3)(x – 5) = 0
=> x = 3/2, 5
II.3y2 + 28y + 65 = 0
=> 3y2 + 15y + 13y + 65 = 0
=> 3y(y + 5) + 13(y + 5) = 0
=> (3y + 13)(y + 5) = 0
=> y = -13/3, -5
1. x2 = 2401
2. y3 = 117649
I.x2 = 2401
=> x = ± √2401
=> x = ± 49
II.y3 = 117649
=> y = 3√117649
=> y = 49
Hence, x ≤ y
Correct (-)
Wrong (-)
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