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

If log_e(1/(2)(a+b))=1/2(log_e a+log_e b), then a/(3b) =

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>>

Let E=[(1)/(3)+(1)/(50)]+[(1)/(3)+(2)/(50)]+... upto 50 terms,then exponent of 2 in (E)! is

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1 and f(0)=0 , then (A) f(1/2)lt1/2 and f(1/3)gt1/3 (B) f(1/2)gt1/2 and f(1/3)gt1/3 (C) f(1/2)lt1/2 and f(1/3)lt1/3 (D) f(1/2)gt1/2 and f(1/3)lt1/3

(2d^(2)e^(-1))^(3)xx(d^(3)/e)^(-2)=

Let f (x)= {{:(((1)/(e ^(x-2))-3))/((1)/(3 ^(x-2))+1), x gt 2), ((b sin{-x})/({-x}), x lt 2),(c, x=2):}, whre {.} denotes fraction part function, is continous at x=2, then b+c=

L e tI_1=thetaint_0^1(e^xdx)/(1+x)a n dI_2thetaint_0^1(x^2dx)/(e^x^3(2-x^3))dott e h n(I_1)/(I_2)i se q u a lto 3/e (b) e/3 (c) 3e (d) 1/(3e)