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`

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

Let E=(1,2,3,4) and F-(1,2) . Then the number of onto functions from E to F is:

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

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>>

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

The value of lim_(x->0)((1+2x)/(1+3x))^(1/x^2)e^(1/x) is e^(5/2) b. e^2 c. e^(-2) d. 1

The value of int_1^e((x/e)^(2x)+(e/x)^x)log_ex dx is equal to (A) e-1/(2e^2)-1/2 (B) e-1/(2e^2)+1/2 (C) e^3-1/(2e^2)-1/2 (D) none of these

L e tI_1=int_0^1(e^xdx)/(1+x) a n dI_2=int_0^1(x^2dx)/(e^(x^3)(2-x^3))dot tehn (I_1)/(I_2) is equal to (a)3/e (b) e/3 (c) 3e (d) 1/(3e)

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

The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let lambda_1 be the de-Broglie wavelength of the proton and lambda_2 be the wavelength of the photon. The ratio (lambda_1)/(lambda_2) is proportional to (a) E^0 (b) E^(1//2) (c ) E^(-1) (d) E^(-2)