56. Match the interval(s) of x, for which fx) is real Column-4 Column-l (A) 2x + 2/(x) = 2 V1012-- 1012 1-5K 7X-7 (D) (x)-./(x2-3x-10)(In(X-3),-d) T Space for Rough Work

If x is real, tehn range of (3x -2)/(7x+5) is :

The interval for which the given function f(x)=2x^3-3x^2-36x+7 is decreasing , is

Simplify : 7x + 3x(x-4) = ? A. 10x + 12 B. 10x - 12 C. 3x^(2) + 5x D. 3x^(2) - 5x

Let f(x) = |x -1| + |x-2| + |x-3| , match the column I for the value of k column II. {:("Column - I" , " Column -II"),("(A) f(x) = k has no solution " ,"(p) 1 " ),("(B) f(x)=k has only one solution" , "(q) 2"),(" (C) f(x) = k has two solution of same sign " , "(r) 4"),("(D) f(x)= k has two solution of opposite sign" , "(s) 5"),(,"(t) 8"):}

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

Simplyfy: (3x^(2) + 5x - 7)(x -1)- (x^(2) - 2x +3)(x + 4)

(d)/(dx)((7x^(2)-22x+4)/(x^(5)))=

Divide (10 x^(4) + 17 x^(3) - 62 x^(2) + 30 x - 3) by (2x^(2) + 7x - 1)

IF f(x)=2x^3+3x^2-12x+5 , then the interval in which (l_1) increases and (l_2) decreases is