The sum of series `1/2!+1/4!+16!+……….` is (A) `(e^2-1)/2` (B) `(e^2-2)/e` (C) `(e^2-1)/(2e)` (D) `)(e-1)^2)/(2e)`

The sum of the series 1+1/4.2!1/16.4!+1/64.6!+………to oo is (A) (e+1)/(2sqrt(e)) (B) (e-1)/sqrt(e) (C) (e-1)/(2sqrt(e)) (D) (e+1)/2sqrt(e)

The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1) e^(-2) (2) e^(-1) (3) e^(-1//2) (4) e^(1//2)

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

The value of int_(0)^((pi)/(4))(e^((1)/(cos^(2)x))*sin x)/(cos^(3)x)dx equals (A) (e^(2)-e)/(2)(B)(e^(4)-1)/(4)(C)(e^(2)+e)/(4) (D) (e^(4)-1)/(2)

The area bounded by y=|e^|x|-e^(-x)| , the x-axis and x=1 is (A) int_0^1 (e^x-e^(-x))dx (B) e+e^(-1)-2 (C) e+e^(-1)+2 (D) (sqrt(e)-1/sqrt(e))^2

A variable point P on the ellipse of eccentricity e is joined to the foci S and S'. The eccentricity of the locus of incentre of the triangle PSS' is (A) sqrt((2e)/(1+e)) (B) sqrt((e)/(1+e)) (C) sqrt((1-e)/(1+e))(D)(e)/(2(1+e))

The sum of the series (1^(2))/(2!)+(2^(2))/(3!)+(3^(2))/(4!)+ is e+1 b.e-1 c.2e+1 d.2e-1

The value of int_(-1)^(1)e^(|x|)dxis : (a) 2(e+1)^(-1), (b) 2(e-1) (c) 2(e-2), (d) 3(e-1)

When the tangent to the curve y=xlogx is parallel to the chord joining the points (1, 0) and (e ,\ e) , the value of x is e^(1//1-e) (b) e^((e-1)(2e-1)) (c) e^((2e-1)/(e-1)) (d) (e-1)/e

(e^(2x)+2e^(x)+1)/(e^(x))