A function is defined as `f:[a_1, a_2, a_3, a_4, a_5, a_6]vec{b_1, b_2, b_3}dot` Column I, Column II Number of subjective functions, p. is divisible by 9 Number of functions in which `f(a i)!=b i` , q. is divisible by 5 Number of invertible functions, r. is divisible by 4 Number of many be functions, s. is divisible by 3 , t. not possible

(a) How many numbers of two digits are divisible by 3 ? (b) How many numbers of three digits are divisible by 9 ?

{:("Column A", "Column B"),("The number of prime number divisible by 2","The number of prime numbers divisible by 3"):}

Let f:A->A be an invertible function where A= {1,2,3,4,5,6} The number of these functions in which at least three elements have self image is

If A={1,2,3}, B={1,3,5,7,9}, the ratio of number of one-one functions to the number of strictly monotonic functions is ………. .

If function f(x) is defined from set A to B, such that n(A)=3 and n(B)=5 . Then find the number of one-one functions and number of onto functions that can be formed.

The greatest integer by which 1+sum_(r=1)^(30)rxxr ! is divisible is a. composite number b. odd number c. divisible by 3 d. none of these

Column I Column II Total number of function f:{1,2,3,4,5}vec{1,2,3,4,5} than are on to and f(i)!= is equal to p. divisible by 11 If x_1, x_2x_3=2xx5xx7^2, then the number of solution set for (x_1, x_2, x_3)w h e r ex_1 in N ,x_1>1 is q. divisible by 7 Number of factors of 3780 are divisible b; either 3 or 2 both is r. divisible by 3 Total number of divisor of n=2^5xx3^4xx5^(10) that are of the form 4lambda+2,lambdageq1 is s. divisible by 4

Consider the number N= 7 7 4 9 5 8 P 9 6 Q (i) If P=2 and the number N is divisible by 3, then number of possible values of Q islare (ii) If N is divisible by 4, then values of P and Q is/are (iii) If N is divisible by 8 and 9 both, then number of possible ordered pair (P, Q)

Let f:A->B be a function defined by f(x) =sqrt3sin x +cos x+4. If f is invertible, then

Let X={a_1, a_2, ,a_6}a n dY={b_1, b_2,b_3}dot The number of functions f from xtoy such that it is onto and there are exactly three elements x in X such that f(x)=b_1 is 75 (b) 90 (c) 100 (d) 120