" 15."(3x+1)/(2x^(2)-x+3)" (UP "2007,08,12

Solve the equation (1)/(2)log_(2007)(x^(2)+5x)=log_(2007)sqrt(x-3)

In DeltaABC, if BC is unity, sin(A/2)=x_1,sin(B/2)=x_2, cos(A/2)=x_3,cos(B/2)=x_4 with ((x_1)/x_2)^2007-((x_3)/x_4)^2007=0, then the length of ACis .......

Find the HCF of 15x^(2) + 8 x - 12, 3x^(2) + x - 2,3x^(2) - 2x , 9x^(2) - 12 x + 4

The coefficient of x^(70) in the product (x-1)(x^(2)-2)(x^(3)-3)dots(x^(12)-12) is

If x = 4 +sqrt(15) . Find the value of x^(2) +(1)/(x^(2)) and x^(3) + ( 1)/(x^(3))

If (x+1)(x+3) is the HCF of (x^(2)+3x+2)(x^(2)+2x+a) and (x^(2)+7x+12)(x^(2)+7x+b) ,then the value of 6a+3b=

Find the values of x for which the following functions are maximum or minimum: (i) x^(3)- 3x^(2) - 9x (ii) 4x^(3)-15x^(2)+12x+1

lim _ ( x to 2 ) ( 3 ^(x) + 3 ^( 3 - x ) - 12 ) /( 3 ^( - x//2) - 3 ^( 1 -x)) is equal to __________