If `a_1,a_2,...,a_(10)` are in G.P, where `a_igt0` and `S` is a set of ordered pairs `(r,k)` such that `[[lna_1^ra_2^k,lna_2^ra_3^k,lna_3^ra_4^k],[lna_4^ra_5^k,lna_5^ra_6^k,lna_6^ra_7^k],[lna_7^ra_8^k,lna_8^ra_9^k,lna_9^ra_(10)^k]]=0`, then number of pairs `(r,k)` is (a) infinitely many (b) 1 (c) 5 (d) 3

Let a_(1),a_(2),a_(3), …, a_(10) be in G.P. with a_(i) gt 0 for i=1, 2, …, 10 and S be te set of pairs (r, k), r, k in N (the set of natural numbers) for which |(log_(e)a_(1)^(r)a_(2)^(k),log_(e)a_(2)^(r)a_(3)^(k),log_(e)a_(3)^(r)a_(4)^(k)),(log_(e)a_(4)^(r)a_(5)^(k),log_(e)a_(5)^(r)a_(6)^(k),log_(e)a_(6)^(r)a_(7)^(k)),(log_(e)a_(7)^(r)a_(8)^(k),log_(e)a_(8)^(r)a_(9)^(k),log_(e)a_(9)^(r)a_(10)^(k))| = 0. Then the number of elements in S is

If .^36C_(r+1) xx (k^2-3) = 6 xx .^35C_r , then number of ordered pairs (r, k) are (where kinI ).

If k+3, 5k-1 and 3k+2 are in A.P., find the value of k.

Four distinct points (k, 2k), (2, 0), (0, 2) and (0,0) lie on a circle for : (A) k = 0 (B) k = 6/5 (C) k = 1 (D) k = -1

Find the value of k so that 8k +4, 6k-2, and 2k + 7 will form an A.P.

The value of k for which the system of equations 2x+3y=5,\ \ \ \ 4x+k y=10 has infinite number of solutions, is (a) 1 (b) 3 (c) 6 (d) 0

Find the value of k for which following system of equations have infinitely many solution: k x+3y=2k+1,\ \ \ \ 2(k+1)x+9y=7k+1

If the centroid of the triangle formed by the points (3,\ -5),\ (-7,\ 4),\ (10 ,\ -k) is at the point (k ,\ -1) , then k= 3 (b) 1 (c) 2 (d) 4

If the function f(x)=x^3-9k\ x^2+27 x+30 is increasing on R , then (a) -1lt=k 1 (c) 0

If the point P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.