qqqq

Find the radius of curvature at any point in the curve y + ln cos x = 0.

• 1.5707

• cos x

• sec x

• 1

A periodic function has zero average value over a cycle and its Fourier series consists of only odd cosine terms. What is the symmetry possessed by this function?

• odd

• even

• odd quarter wave

• even quarter wave

Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation x^2 + 4y^2 = 4.

• 2

• 3

• 4

• 5

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?

• dy/dx – x = 0

• x dy + y dx = 0

• 2x dy – y dx = 0

• 2y dx – x dy = 0

Find all values of z for which e4z = i. 

• [(- π/6) + (kπ/2)] i

• [(- π/8) + (kπ/2)] i

• [(π/6) + (kπ/2)] i

• (π/8) + (kπ/2)] i

The axis of the hyperbola through its foci is known as:

• minor axis

• major axis

• conjugate axis

• transverse axis

When a metallic ball bearing is placed inside a cylindrical container of radius 2 cm, the height of the water inside the container increases by 0.6 cm. What is the radius of the ball bearing ?

• 1.2 cm

• 1.8 cm

• 0.6 cm

• 2.2 cm

Find the general solution of y’ = y sec x

• y = C (sec x + tan x)

• y = C (sec2 x + tan x)

• y = C (sec x tan x)

• y = C (sec x – tan x)

Determine the differential equation of the family of lines passing through (h, k).

• (x + h)dx – (y – k)dy = 0

• (x – h)dx – (y – k)dy = 0

• (y – k)dx – (x – h)dy = 0

• (y – k)dx – (x – h)dy = 0

 

Evaluate    lim   x --> 0      ( 1 + 2x )^( 1 + 2x ) / x

  

• e2

• e

• 1

• 0