Total number less than `3xx10^8` and can be formed using the digits 1, 2, 3 is equal to a. `1/2(3^9+4xx368)` b. `1/2(3^9-3)` c. `1/2(7xx3^8-3)` d. `1/2(3^9-3+3^8)`

The number of n digit number formed by using digits {1,2,3} such that if 1 appears, it appears even number of times, is

Total number of six-digit numbers that can be formed having the property that every succeeding digit is greater than the preceding digit is equal to a. ^9C_3 b. ^10 C_3 c. ^9p_3 d. ^10 p_3

The number of five-digit numbers which are divisible by 3 that can be formed by using the digits 1,2,3,4,5,6,7,8 and 9 , when repetition of digits is allowed, is

Find the values of the following and check for equality: (-3) xx [2 + (-8)] and [(-3) xx 2] + [(-3) xx 8]

The number of four-digit numbers that can be formed by using the digits 1,2,3,4,5,6,7,8 and 9 such that the least digit used is 4 , when repetition of digits is allowed is

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

If sum of an infinite G.P. p ,1,1//p ,1//p^2,.... .i s9//2 then value of p is a. 3 b. 3/2 c. 3 d. 9/2

Twelve balls are distribute among three boxes. The probability that the first box contains three balls is a. (110)/9(2/3)^(10) b. (9)/110(2/3)^(10) c. ((12)C_3)/(12^3)xx2^9 d. ((12)C_3)/(3^(12))

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0 . If its diagonals intersect at (-1,-2) , then which one of the following is a vertex of this rhombus ? (1) (-3,-9) (2) (-3,-8) (3) (1/3,-8/3) (4) (-(10)/3,-7/3)