एक nonlinear स्प्रिंग द्वारा लगाया गया बल Fइसकी लंबाई में वृद्धि xके साथ समीकरण F=-k_1x^2-k_2x^4...

The function 'f' is defined by f(x) = 2x - 1 , if x gt 2, f(x) = k if x = 2 and x^(2) - 1 if x lt 2 is continuous, then the value of k is equal to

5x + 2y = 2k , 2 (k + 1 ) x + ky = (3k + 4)

Find the values of k for which roots of the following equations are real and equal: (i) 12x^(2)+4kx+3=0 (ii) kx^(2)-5x+k=0 (iii) x^(2)+k(4x+k-1)+2=0 (iv) x^(2)-2(5+2k)x+3(7+10k)=0 (v) 5x^(2)-4x+2+k(4x^(2)-2x-1)=0 (vi) (k+1)x^(2)-2(k-1)x+1=0 (vii) x^(2)-(3k-1)x+2k^(2)+2k-11=0 (viii) 2(k-12)x^(2)+2(k-12)x+2=0

f(x) is a polynomial function satisfying f(x) . f(y) = f(x) + f(y) + f(xy) - 2 AA x, y in R , it is given that f(1) = 2, f(3) = 10, f(4) = 10k_(1) + k_(2) (k_(1), k_(2) in I^(+)) then k_(2) is___

For a double diferentiable function f(x) if f''(x) ge 0 then f(x) is concave upward and if f''(x) le 0 then f(x) is concave downward if f(x) is a concave upward in [a,b] and alpha , beta in [a,b] the (k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) ge f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2))) where K_(1)+K_(2) in R if f(x) is a concave downward in [a,b] " and "alpha, beta in [a,b] " then "(k_(1)(alpha)+k_(2)f(beta))/(k_(1)+k_(2)) le f((k_(1) alpha +k_(2)beta)/(k_(1)+k_(2))) where k_(1)+k_(2) in R then answer the following : Which of the following is true