If `y` is a function of `xa n dlog(x+y)-2x y=0,` then the value of `y^(prime)(0)` is (a)1 (b) `-1` (c) 2 (d) 0

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

If y=int1/(1+x^2)^(3/2)dx and y=0 when x=0 , then value of y when x=1 is

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

A function y=f(x) satisfies the differential equation (d y)/(d x)+x^2 y=-2 x, f(1)=1 . The value of |f^( prime prime)(1)| is

The extremities of the base of an isosceles triangle are (2,0)a n d(0,2) . If the equation of one of the equal side is x=2, then the equation of other equal side is (a) x+y=2 (b) x-y+2=0 (c) y=2 (d) 2x+y=2

If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

The equation of the line AB is y = x . If A and B lie on the same side of the line mirror 2x-y = 1 , then the equation of the image of AB is (a) x+y-2=0 (b) 8x+y-9=0 (c) 7x-y-6=0 (d) None of these

If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function of y and ac is negative, then a. a c^(prime)+c^(prime)c=0 b. a//a '=c//c ' c. a^2+c^2=a^('2)+c^('2) d. a a^(prime)+c c^(prime)=1