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

If int_0^ooe^(-ax)dx=1/a , then int_0^oo(x^n)e^(-ax)dx is

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

Assetion: a_1,a_2,a_3,…………. an are not in G.P. Reason: a_(n+1)=a_n (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: a^2,b^2,c^2 are in A.P., Reason: 1/(b+c), 1/(c+a), 1/(a+b) are in A.P. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: sum_(r=0)^n(r+1).^nC_r=(n+2)2^(n-1) , Reason: sum_(r=0)^n(r+1).^nC_rx^r=(1+x)^n+nx(1+x)^(n-1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: sum_(r=0)^n(r+1).^nC_r=(n+2)2^(n-1) , Reason: sum_(r=0)^n(r+1).^nC_rx^r=(1+x)^n+nx(1+x)^(n-1) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R 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 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: 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