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

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: If int_0^oo e^(-ax)dx=1/a , then int_0^oo x^me^(-ax)dx=(lfloorm)/a^(m+1) ,Statement-2: d^n/dx^n(e^(kx))=k^n e^(kx) and d^n/dx^n(1/x)=((-1)^nlfloorn)/x^(n+1) (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 curve y=xsinx , x-axis and ordinates x=0 and x=2pi is 4pi .Statement-2: The area bounded by the curve y=f(x) , x-axis and two ordinates x=a and x=b is int_a^b |y|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: int_-3^3 x^8{x^9}dx=2xx3^7 , where {x} denotes the fractional part of x .Statement-2: [x]+[-x]=-1 , if x is not an integer, where [x] denotes the integral part of x . (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=x^2 and y=2/(1+x^2) is 2pi-2/3 Statement-2: The area bounded by the curves y=f(x), y=g(x) and two ordinates x=a and x=b is int_a^b[f(x)-g(x)]dx , if f(x) gt g(x) . (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

Statement-1: The area bounded by the curve y=2x^2 and y=x^2+4 is 32/3 sq. units.Statement-2: The area bounded by the curves x=f(y), x=g(y) and two abscissae y=c and y=d is int_c^d|f(y)-g(y)|dy . (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: 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