If `n` is a natural number and `n=p1x_1\ p2x_2\ p3x_3` , where `p_1,\ p_2,\ p_3` are distinct prime factors, then the number of prime factors for `n` is `x_1+x_2+x_3` (b) `x_1+x_2+x_3` (c) `(x_1+1)(x_2+1)(x_3+1)` (d) None of the above

If n is a natural and n=p_1^(x_1)p_2^(x_2)p_3^(x_3)," where "p_1,p_2,p_3 are distinct prime factors, then the number of prime factors for his

If n is a natural number and n=p1x_(1)backslash p2x_(2)backslash p3x_(3), where p_(1),backslash p_(2),backslash p_(3) are distinct prime factors,then the number of prime factors for n is x_(1)+x_(2)+x_(3)(b)x_(1)+x_(2)+x_(3)(c)(x_(1)+1)(x_(2)+1)(x_(3)+1) (d) None of the above

If P_(1),P_(2),.......P_(m+1) are distinct prime numbers.The the number of factors of P_(1)^(n)P_(2)P_(3)...P_(m+1) is :

If x^(2)-2x-1 is a factor of px^(3)+qx^(2)+1 , (where p , q are integers) then find the value of p +q.

If Y={x|x is a positive factor of the number 2^(p-1)(2^(p)-1) where 2^(p)-1 is a prime ~ number}~ Write~ Y~ in~ roaster~ form.~

IF x,2y,3z are in A.P. where x,y,z are unequal number in a G.P., then the common ratio of this G.P. is (a) 3 (b) 1/3 (c) 2 (d) 1/2

Let X_k=(p_1*p_2*...*p_k)+ 1,where p_1, p_2, ...,p_k are the first k primes. Consider the following : 1. X_k is a prime number. 2. X_k is a composite number . 3. X_k+1 is always an even number. Which of the above is/are correct? (a) 1 only (b) 2 only (c) 3 only (d) 1 and 3

If x_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

Thenumber of distinct terms in the expansion of (x_1+x_2+……..+x_p)^n is (A) ^(n+p)C_n (B) n+p+1 (C) n+1 (D) ^(n+p-1)C_(p-1)