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11.

If $\frac{1}{{}^{5}\mathrm{C}_{\mathrm{r}}}+\frac{{\displaystyle 1}}{{\displaystyle {}^{6}\mathrm{C}_{\mathrm{r}}}}=\frac{{\displaystyle 1}}{{\displaystyle {}^{4}\mathrm{C}_{\mathrm{r}}}}$, then the value of r is

4

2

5

3

12.

If A = $\left\{{5}^{\mathrm{n}}-4\mathrm{n}-1:\mathrm{n}\in \mathrm{N}\right\}$ and $\mathrm{B}=\left\{16\left(\mathrm{n}-1:\mathrm{n}\in \mathrm{N}\right)\right\}$, then

A = B

$\mathrm{A}\cap \mathrm{B}=\mathrm{\phi}$

$\mathrm{A}\subseteq \mathrm{B}$

$\mathrm{B}\subseteq \hspace{0.17em}\mathrm{A}$

13.

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

96

48

183

267

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The letters of the word 'COCHIN' are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word 'COCHIN', is

360

192

96

48

C.

96

The number of words starting with CC = 4!

The number of words starting with CH = 4!

The number of words starting with CI = 4!

The number of words starting with CN = 4!

COCHIN is the first word in the list of words beginning with CO.

Number of words that appear before the word COCHIN = 4 x 4! = 96

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15.

The number of digits in 20^{301 }$\left(\mathrm{given},{\mathrm{log}}_{10}\left(2\right)=0.3010\right)$ is

602

301

392

391

16.

The number of solutions of the equation x + y + z = 10 where x, y and z are positive integers

36

55

72

45

17.

Let n be a positive even integer. If the ratio of the largest coefficient and the 2nd largest coefficient in the expansion of (1 + x)^{n} is 11 : 10. Then, the number of terms in the expansion of (1 + x)^{n} is

20

21

10

11

18.

There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects

is 12

is 4

is 2

cannot be determined from the given information

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19.

Four speakers will address a meeting where speaker Q will always speak P. Then, the number of ways in which the order of speakers can be prepared is

256

128

24

12

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