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Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we require three non-collinea..

Question: Find n if P(n,4) = 20P(n,2) Answer: ..

Number of ways of filling hundred's place = 2 Number of ways of filling ten's place = 2 Number of ways of filling unit's place = 2 By the fundamental principle of counting, the total number of numbers = 2 x 2 x 2 =..

The matrices are scalar matrices of order 2 and 3 respectivel..

i) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..

Question: Convert the following into factorials: i) 5.6.7.8.9.10 ii) 4.6.8.10.12 Answer: i) ii) ..

Question: A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, and he is not permitted to attempt more than 4 from each group. In how many ways can he make his choice? Answer: ..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is given by 47.5 sq.units..

The number of permutations of n different things taken r at a time is the same as the number of ways of filling n letters and r blank spaces, supposed to be arranged in a straight line as shown above. Each blank is accommodating only one letter. We may fill the first blank with any one of the n ..

= (32.16.8.4.2)(33.31.30.18.17.15.14.13.12.11.10....3.1) = (2 5 .2 4 .2 3 .2 2 .2 1 )(33.31.30.....3.1) which is divisible by 2 1 5 . vi) (n! + 1) is not divisible by any natural number between 2 and ..