Consider two curves `C_1: y=1/x a n dC_2: y=logx` on the `x y` plane. Let `D_1` denotes the region surrounded by `C_1,C_2,` and the line `x=1a n dD_2` denotes the region surrounded by `C_1,C_2` and the line `x=adot` If `D_1=D_2,` then the sum of logarithm of possible value of `a` is _____________

Consider the two curves C_1:y^2=4x,C^2:x^2-y^2-6x+1=0. Then.

Consider the curves C_1 : x=0,C_2 :y =0, C_3 y =x^(2) +1, C_4 :y=2 ,C_5 : x =1 The area bounded by the curves C_1 ,C_3 and C_4 and which lies to the right of C_1 is ( in square units )-

Consider the curves C_1 : x=0,C_2 :y =0, C_3 y =x^(2) +1, C_4 :y=2 ,C_5 : x =1 the area enclosed between the curves C_1 ,C_2 ,C_3 and c_5 is ( in square units ) -

Consider the curves C_1 : x=0,C_2 :y =0, C_3 y =x^(2) +1, C_4 :y=2 ,C_5 : x =1 The area bounded by the curves C_3 and C_4 (in square units )

Find the area of the region bounded by the curves y=sqrt(x+2) and y=(1)/(x+1) between the lines x=0 and x=2.

If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find the value of adot

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is (a) 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

In a triangle A B C , the bisectors of angles Ba n dC lies along the lines x=y a n d y=0. If A is (1,2) , then the equation of line B C is

Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0 . Then, (a) C1 and C2 touch each other at one point (b) C1 and C2 touch each other exactly at two point (c) C1 and C2 intersect(but do not touch) at exactly two point (d) C1 and C2 neither intersect nor touch each other

The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the curve passes through the point (1,2) then the area of the region bounded by the curve, the x-axis and the line x=1 is (A) 5/6 (B) 6/5 (C) 1/6 (D) 1