Statement-1: Solution of the differential equation `tany *dy/dx =sin(x+y)+sin(x-y)` is `secy+2cosx=c`
.Statement-2: The differential equation `tany *dy/dx =sin(x+y)+sin(x-y)` is homogenous
(A) Both 1 and 2 are true and 2 is the correct explanation of 1
(B) Both 1 and 2 are true and 2 is not correct explanation of 1
(C) 1 is true but 2 is false
(D) 1 is false but 2 is true

Statement-1: Curve satisfying the differential equation dy/dx=y/(2x) and passing through the point (2,1) is a parabola having focus (1/2,0) Statement-2: The differential equation dy/dx=y/(2x) is homogeneous. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The solution of the differential equation (x^2+y^2)dx=2xydy satisfying y(1)=0 is x^2-y^2=x .Statement-2: The differential equation (x^2+y^2)dx=2xydy can be solved by putting y=vx . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The differential equation of all circles in a plane must be of order 3.Statement-2: The differential equation of family of curve y=asinx+bcos(x+c) , where a,b,c are parameters is 2. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Consider the differential equation of the family of curves y^2=2a(x+sqrt(a)) , where a is a positive parameter.Statement 1: Order of the differential equation of the family of curves is 1.Statement 2: Degree of the differential equation of the family of curves is 2. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: int_0^([x]) 4^(x-[x])dx=(3[x])/(2log2) ,Statement-2: int_0^([x]) a^(x-[x])dx=[x]int_0^1 a^(x-[x])dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement 1: The equation of the common tangent to the curves y^2 = 8x and xy= -1 is y=x+2 . Statement 2: Curves y^2 = 8x and xy=-1 intersect at (1/2, -2) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

The general solution of the differential equation (dy)/(dx)+sin((x+y)/2)=sin((x-y)/2) is

The general solution of the differential equation (dy)/(dx)+sin((x+y)/2)=sin((x-y)/2) is

Let I_1=int_0^1 e^x/(1+x)dx and I_2=int_0^1(x^2e^(x^2))/(2-x^3)dx Statement-1: I_1/I_2=3e Statement-2: int_a^b f(x)dx=int_a^b f(a+b-x)dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curves y=ln|x| , y-axis and y=1-|x| is 2 sq. units.Statement-2: Both the curves y=log|x| and y=1-|x| are symmetric about y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true