The term independent of x in the expansions of${\left(\sqrt{\mathrm{x}} - \frac{2}{\sqrt{\mathrm{x}}}\right)}^{18} \mathrm{is}$

• $- {}^{18}\mathrm{C}_9{2}^9$

• ${}^{18}\mathrm{C}_9{2}^{12}$

• ${}^{18}\mathrm{C}_9{2}^6$

• ${}^{18}\mathrm{C}_6{2}^8$

T_m denotes the number of triangles that canbe formed with the vertices of a regular polygon of m sides. If T_{m + 3} - T_m = 15, then m is equal to

• 3

• 6

• 9

• 12

The sum of all 4-digit numbers that can be formed using the digits 2, 3, 4, 5, 6 without repetition, is

• 533820

• 532280

• 533280

• 532380

${}^{37}\mathrm{C}_4 + \sum _{\mathrm{r} = 1}^5{}^{\left(42 - \mathrm{r}\right)}\mathrm{C}_{\mathrm{r}} = ?$

• ${}^{41}\mathrm{C}_4$

• ${}^{39}\mathrm{C}_4$

• ${}^{38}\mathrm{C}_4$

• ${}^{42}\mathrm{C}_4$

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ...

For a positive integer $\mathrm{n}, {\left(1 + \frac{1}{\mathrm{x}}\right)}^{\mathrm{n}}$ is expanded in increasing powers of x. If three consecutive coefficients in this expansion are in the ratio, 2 : 5 : 12 , then n is equal to _____

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ......

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :

• 36

• 63

• 38

• 54

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are a like, is _________.

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :

• 3000

• 2250

• 2255

• 1500