Let `n_k` be the number of real solutions `|x+1|+|x-3|=K`, then
(a) `n_K = 0` if `K lt 4`
(b) `n_K = 2` if `K gt 4`
(c) `n_K` is infinitely many if `K` = 4
(d) Minimum value of f(x) = `|x+1|+|x-3|` is 2

Let n_(k) be the number of real solution of the equation |x+1| + |x-3| = K , then

Let n_(k) be the number of real solution of the equation |x+1| + |x-3| = K , then

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N (b) n ne 3k, k in N

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

The number of values of k for which the system of the equations (k+1)x+8y=4k and k x+(k+3)y=3k-1 has infinitely many solutions is 0 b. 1 c. 2 d. infinite

The number of values of k for which the system of the equations (k+1)x+8y=4k and k x+(k+3)y=3k-1 has infinitely many solutions is 0 b. 1 c. 2 d. infinite

The number of values of k for which the system of the equations (k+1)x+8y=4k and k x+(k+3)y=3k-1 has infinitely many solutions is a. 0 b. 1 c. 2 d. infinite

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

If x^n-1 is divisible by x-k then the least positive integral value of k is(a) 1 (b) 2 (c) 3 (d) 4