Let `E=1/(1^2)+1/(2^2)+1/(3^2)+` Then, a.`E<3` b. `E >3//2` c. `E >2` d. `E<2`

Let E=1/(1^2)+1/(2^2)+1/(3^2)+ Then, a. E 3//2 c. E >2 d. E<2

Let E=(1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+ Then,a.E 3/2c.E>2d.E<2

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

Show that 1+(1+3)/(2!)+(1+3+3^2)/(3!)+...=1/2(e^3-e)

Let a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx , then 4e^a =

Let a=int_0^(log2) (2e^(3x)+e^(2x)-1)/(e^(3x)+e^(2x)-e^x+1)dx , then 4e^a =

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ f(0)=0 , then a. f((1)/(2))lt(1)/(2) and f((1)/(3)) gt (1)/(3) b. f((1)/(2))gt(1)/(2) and f((1)/(3)) gt (1)/(3) c. f((1)/(2)) lt (1)/(2) and f((1)/(3)) lt (1)/(3) d. f((1)/(2)) gt (1)/(2) and f((1)/(3)) lt (1)/(3)

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

e_(1),e_(2),e_(3),e_(4) are eccentricities of the conics xy=c^(2),x^(2)-y^(2)=c^(2),(x^(2))/(a^(2))-(y^(2))/(b^(2))=1,(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 and sqrt((1)/(e_(1)^(2))+(1)/(e_(2)^(2))+(1)/(e_(3)^(2))+(1)/(e_(4)^(2)))=sec theta then 2 theta is

The direction ratios of a normal to the plane through (1,0,0)a n d(0,1,0) , which makes and angle of pi/4 with the plane x+y=3, are a. <<1,sqrt(2),1 >> b. <<1,1,sqrt(2)>> c. <<1,1,2>> d. << sqrt(2),1,1>>