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In the following questions pick the odd thing out :
$$\sin^2 x + \cos^2 x$$
$$\sec^2 x - \tan^2 x$$
$$\tan^2 x + \cot^2 x$$
$$\cosec^2 x - \cot^2 x$$
Eagle
Vulture
Owl
Crow
ABYZ
CDWX
EFUV
GHTS
$$x^3 - 4 = 0$$
$$x^3 - 3 = 0$$
$$x^3 - 2 = 0$$
$$x^3 - 1 = 0$$
(5, 6, 11)
(6, 7, 13)
(7, 8, 15)
(8, 9, 19)
Each of the questions follows definite pattern. Observe the same and fill in the blanks with suitable answers.
$$\frac{1}{5}, \frac{5}{10}, \frac{10}{17}, \frac{17}{26}, ..........., \frac{37}{50}$$
$$\frac{26}{37}$$
$$\frac{36}{37}$$
$$\frac{26}{50}$$
$$\frac{36}{49}$$
6, 12, 20, 30, ......, 56
50
48
44
42
The logic here is
12 - 6 = 6
20-12 = 8
30-20 = 10
The difference between the consecutive numbers is increasing by 2.
The next difference should be 12.
$$\therefore\ $$The missing number is 30+12 = 42
Hence, the correct answer is Option D
$$\frac{1}{2}, \frac{8}{5}, \frac{27}{10}, ...... \frac{125}{26}, \frac{37}{50}$$
$$\frac{36}{17}$$
$$\frac{32}{13}$$
$$\frac{64}{17}$$
$$\frac{81}{25}$$
Numerator
1^3 =1
2^3 = 8
3^3 = 27
4^3 = 64
Denominator
5-2 = 3
10-5 = 5
next difference should be 7
Hence 10 + 7 = 17
4, 1, 9, 3, 16, 6, 25, 10, 36, ............
15
20
25
30
1, 4, 27, 256, .........
625
3152
1024
3125
$$1^1=1$$
$$2^2=4$$
$$3^3=27$$
$$4^4=256$$
Similarly, the next number in the series = $$5^5=3125$$
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