Question 1 :
<font>If the letters of the word ‘KRISNA’ are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word ‘KRISNA’ is</font></p>

Question 2 :
Six points in a plane be joined in all possible ways by indefinite straight lines and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points or intersection is equal to

Question 3 :
If ⁿC_{n − r} + 3 • ⁿC_{n − r + 1} + 3 • ⁿC_{n − r + 2} + ⁿC_{n − r + 3} = ^xC_r, then x=

Question 4 :
The total number of natural numbers of six digits that can be made with digits 1, 2, 3, 4, if all digits are to appear in the same number at least once, is

Question 5 :
The number of all four digit numbers which are divisible by 4 that can be formed from the digits 1, 2, 3, 4 and 5 is

Question 6 :
Let A be the set of 4 digit number a₁a₂a₃a₄, where a₁ &lt; a₂ &lt; a₃ &lt; a₄,then n(A) is equal to

Question 7 :
If ⁸C_r − ⁷C₃ = ⁷C₂, then r is equal to

Question 8 :
At an election there are five candidates and three members to be elected, and an elector may vote for any number of candidates not greater than the number to be elected. Then the number of ways in which an elector may vote is

Question 9 :
S₁, S₂, …, S₁₀ are the speakers in a conference. If S₁ addresses only after S₂, then the number of ways the speakers address is

Question 10 :
<font>In a plane there are 37 straight lines of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Then the number of intersection points the lines have is equal to</font></p>

Question 11 :
<font>In a plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both points A and B, and no two are parallel. Then the number of intersection points the lines have is equal to -</font></p>

Question 12 :
<font>By using the digits 1, 3, 5, 7, the sum of all the 4 digits numbers formed in which repetitions of digits is not allowed , is -</font></p>

Question 13 :
In how many ways n books can be arranged in a row so that two specified books are not together?

Question 14 :
<font>The number of all possible words that can be formed using the all letters at a time of the word 'MATHEMATICS' is</font></p>

Question 15 :
Five digited numbers with distinct digits are formed by using the digits, 5, 4, 3, 2, 1, 0. The number of those numbers which are multiples of 3, is

Question 16 :
If ⁿC_r denotes the number of combinations of n things takes r at a time, then the expression ⁿC_{r + 1} + ⁿC_{r − 1} + 2 × ⁿC_r, equals

Question 17 :
In a football championship, there were played 153 matches. Every team played one match with each other. The number of teams participating in the championship is

Question 18 :
The straight lines I₁, I₂, I₃ are parallel and lie in the same plane. A total numbers of m points are taken on I₁, n points on I₂, k points on I₃. The maximum number of triangles formed with vertices at these points is

Question 19 :
<font>Number of words that can be made by arranging the letters of the word ARRANGE so that the word begin with A but do not end with E is</font></p>

Question 20 :
<font>The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is</font></p>