Using properties of determinants, evaluate `|[18, 40 ,89],[ 40 ,89, 198 ],[89 ,198, 440]|dot`

If f(x)=|[a,-1, 0],[a x, a,-1],[a x^2,a x, a]|,using properties of determinants find the value of f(2x) − f(x).

The following marks are obtained by students in a test : 82,72,91,90,86,85,92,70,71,83,89,94,85,79,62 .Find the range of the marks

Find the geometric mean of the following number : 18,40,25 and 45.

The coordinates of the points A,B,C and D are (-2,3), (8,9), (0,4) and (3,0) respectively . Find the ratio in which the line -segment overline(AB) is divided by the line -segment overline(CD) .

To obtain grade A^+ is an examination a student must score an average of 90 marks or moe in five papers each of 100 marks. IF his marks in first four papers be 87, 89, 95,90, then find the minimum marks the should score in fifth paper is he wants to achieve grade A^+ .

Find the sum of n terms 1+4+13+40+121+....dot

If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant 'K' where A, B, C are integers lying between 0 and 9, then determinant |(A,3,6),(8,9,C),(2,B,2)| is always divisible by

Find two negative integers whose difference is 3 and sum of their squares is 89.

A point on the parabola y^2=18 x at which the ordinate increases at twice the rate of the abscissa is (a)(2,6) (b) (2,-6) (c) (9/8,-9/2) (d) (9/8,9/2)

The integers x and y are chosen at random with replacement from nine natural numbers 1,2,3,….8,9 find the probability that (x^2-y^2) is divisible by 2