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: 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 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: 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

Let the area bounded by the curve y=f(x) , x-axis and the ordinates x=1 and x=a be (a-1)sin(3a+4) .Statement-1: f(x)=sin(3x+4)+3(x-1)cos(3x+4) .Statement-2: If y=int_(g(x))^(h(x)) f(t)dt , then dy/dx=f(h(x)) h\'(x)-f(g(x)) 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 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 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 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: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (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 of the region R={(x,y) : |x| le |y| and x^2+y^2 le 1} is pi/4 sq. units.Statement-2: Curves |y|=|x| and x^2+y^2=1 symmetric about both x and 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

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