Statement-1: Solution of the differential equation `dy/dx tany=sin(x+y)+sin(x-y)` is `secy+2cosx=c`.Statement-2: The differential equation `dy/dx tany=sin(x+y)+sin(x-y)` is (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: y(x)=sin(x+pi/4) Statement-2: Integrating factor of the given differential equation is secx . (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: 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 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

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: Order of the differential equation of the family of curves y=asinx+bcos(x+c) is 3.Statement 2: Order of the differential equation of a family of curves is equal to the number of independent arbitrary constants in the equation of family of curves. . (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 differential equation (1+x^2) dy/dx+2xy=4x^2 is 3y(1+x^2)=4x^3+c .Statement-2: The solution of a linear differential equation can be obtained by multiplying it by its integrating factor. (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 curve y= - x^2/2 + x + 1 is symmetric with respect to the line x=1 . Statement 2: A parabola is symmetric about its 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 a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true