Let `n_k` be the number of real solutions lx+1l+|x-3|=K, then

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 f(x)=2x^(3)-3x^(2)+1 then number of distinct real solution (s) of the equation f(f(x))=0 is/(are) k then (7k)/(10^(2)) is equal to_______

If f(x)=2x^(3)-3x^(2)+1 then number of distinct real solution(s) of the equation f(f(x))=0 is(are) k then (7k)/(10^(2)) is equal to

If f(x)=2x^(3)-3x^(2)+1 then number of distinct real solution (s) of the equation f(f(x))=0 is/(are) k then (7k)/(10^(2)) is equal to_______

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 .

Assertion (A) : The number of positive integral solutions of x_(1)+x_(2)+x_(3)=10 is 36. Reason (R) : The number positive integral solutions of the equation x_(1)+x_(2)+x_(3)+.......+x_(k)=n is ""^(n-1)C_(k-1) , The correct answer is

Let n and k be positive such that n leq (k(k+1))/2 .The number of solutions (x_1, x_2,.....x_k), x_1 leq 1, x_2 leq 2, ........,x_k leq k , all integers, satisfying x_1 +x_2+.....+x_k = n , is .......