25. The integer k for which the inequality `x^2 -2(4k 1)x 15k 2k-7 0 is valid for any real x is (2) 3 (3) 4 (4) 5

The integer k for which the inequality x^(2) - 2(4k-1)x + 15k^(2) - 2k - 7 gt 0 is valid for any x is :

The integer k ,for which the inequality x^(2)-2(3k-1)x+8k^(2)-7>0 is valid for every x in R is

For what values of k is the inequality x^(2)-(k-3)x-k+6>0 valid for all real x?

The number of integral values of k for which the inequality x^(2)-2(4k-1)x+15k^(2)-2k-7 ge0 hold for x in R are _____________

Find all values of k for which the inequality, 2x^(2)-4k^(2)x-k^(2)+1gt0 is valid for all real x which do not exceed unity in the absolute value.

If the inequality cot^(2)x + (k +1) cot x - (k-3) < 0 is true for at least one x in (0, pi//2) , then k in .

Number of values of k for which the lines k x+y+1=0 x+k y+2=0 x+y+k=0 are concurrent is 3 (2) 2 (3) 1 (4) 0

Find the value of k for which x^(2) + k(4x + k - 1) + 2 = 0 has real and equal roots.