1. How many words beginning with T and ending with E can be made (with no letter repeated) out of the letters of the word ‘TRIANGLE’ ?

2. There are 10 true-false questions in a examination. Then these questions can be answered in:

3. If repetition of the digits is allowed, then the number of even natural numbers having three digits is

4. The number of squares that can be formed on a chess board is

5. Given 12 points in a plane, no three of which are collinear. Then number of line segments can be determined, are:

6. How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed

7. How many factors are 2⁵ × 3⁶ × 5² are perfect squares

8. The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is

9. How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order?

10. The total number of ways of selecting six coins out of 20 one rupee coins, 10 fifty paise coins and 7 twenty five paise coins is:

11. The probability that in a random arrangement of the letter of the word ‘UNIVERSITY’, the two I’s do not come together is:

12. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If T_n+1 – T_n = 21, then n equals

13. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

14. In how many ways in which 8 students can be sated in a line is

15. Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is