The last digit of `(1!+2!++2005 !)^(500)` is

(A) 9

(B) 2

(C) 7

(D) 1

The last two digits of the number 3^(400) are: (A) 81 (B) 43 (C) 29 (D) 01

If matrix A is given by A=|[6, 11], [2, 4]| , then the determinant of A^(2005)-6A^(2004) is a. 2^(2006) b. (-11)2^(2005) c. -2^(2005) d. (-9)2^(2004)

If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+bsqrt((1-b^2))+csqrt((1-c^2)) will be (A) 2a b c (B) a b c (C) 1/2a b c (D) 1/3a b c

For a real number a with 0 lt a lt (1)/(2) , if b = 1 - a + a^(2) - a^(3) + …, c = 1 - b + b^(2) - b^(3)+… and d = 1 + c + c^(2) +… , find the value of (d-a)

A seven-digit number without repetition and divisible by 9 is to be formed by using seven digits out of 1, 2, 3, 4, 5, 6, 7, 8, 9. The number of ways in which this can be done is (a) 9! (b) 2(7!) (c) 4(7!) (d) non of these

An n-digit number is a positive number with exactly n Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is (a) 6 (b) 7 (c) 8 (d) 9

Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7),(7,3,7)]=[0,0,0] Let b=6, with a and c satisfying (E). If alpha and beta are the roots of the quadratic equation ax^2+bx+c=0 then sum_(n=0)^oo (1/alpha+1/beta)^n is (A) 6 (B) 7 (C) 6/7 (D) oo

If n integers taken at random are multiplied together , then the probability that the last digit of the product is 1, 3, 7, or 9 is a. 2^n//5^n b. 4^n-2^n//5^n c. 4^n//5^n d. none of these

Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 } . Find (B – C)′

If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9 , then the probability that the digit is even, is (a) 4/9 (b) 5/9 (c) 1/9 (d) 2/3