Evaluate :

`3r - 2k^3 + 3r + 2k^3`

Find the value of k if x-3 is a factor of k^(2)x^(3)-kx^(2)+3kx-k

Find the value of k, if (x-3) is a factor of k^(3)x^(3)-x^(2)+3x-1

If r = 3 is a root of quadratic equation kr^(2) - kr - 3 = 0 then find the value of k

If a_1,a_2,a_3 are in G.P. having common ratio r such that sum_(k=1)^n a_(2k-1)= sum_(k=1)^na_(2k+2)!=0 then number of possible value of r is (A) 1 (B) 2 (C) 3 (D) none of these

If line vec r=( hat i-2 hat j- hat k)+lambda(2 hat i+ hat j+2 hat k) is parallel to the plane vec r.(3 hat i-m hat k)=14 , then the value of m is (1). 2 (2) -2 (3) 0 (4) 3

Let S _(K) = sum _(r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2r +1))) . Then lim _( k to oo) S _(k) is equal to :

Find the values of k for which f(x)=kx^(3)-9kx^(2)+9x+3 is increasing on R .

A man can row 9 1/3 kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is : a. 3 1/3 k m//h r b. 3 1/9k m//h r c. 4 2/3k m//h r d. 4 1/2k m//h r

If k=1,l=2,m=0,p=3,q=4,r=5 then find the values of (3k^2)/p^2 and (kr^k)/q^l

Find the value of k if 3^(k+8) = 27^(2k+1)