Q.1
nth derivative of Sinh(x) is
  • a) 0.5(ex – e-x)
  • b) 0.5(e-x – ex)
  • c) 0.5(ex – (-1)n e-x)
  • d) 0.5((-1)-n e-x -ex)
Q.2
If y=log⁡(x⁄(x2 – 1)), then nth derivative of y is ?
  • a) (-1)(n-1) (n-1)!(x(-n) + (x-1)(-n) + (x+1)(-n))
  • b) (-1)n (n)! (x(-n-1) + (x-1)(-n-1) + (x+1)(-n-1))
  • c) (-1)(n+1) (n+1)!(x(-n) + (x-1)(-n) + (x+1)(-n))
  • d) (-1)n(n)! (x(-n-1) + (x-1)(-n+1) + (x+1)(-n+1))
Q.3
If x = a(Cos(t) + tand y = a(Sin(t) + t2 + tthen dy/dx equals to
  • a) (Cos(t) + 3t2 + 2t) / (-Sin(t) + 2t)
  • b) (Sin(t) + 3t2 + 2t) / (-Cos(t) + 2t)
  • c) (Sin(t) + 3t2 + 2t) / (Cos(t) + 2t)
  • d) (Cos(t) + 3t2 + 2t) / (Sin(t) + 2t)
Q.4
If y=tan(-1)⁡(x) , then which one is correct ?
  • a) y3 + y12 + 4xy2 y1=0
  • b) y3 + y12 + xy2 y1=0
  • c) y3 + 2y12 + xy2 y1=0
  • d) y2 + 2y12 + 4xy2 y1=0
Q.5
If y=x4⁄x2-then?
  • a) 0.5*(-1)n (n-1)! [(x-1)-n-1 + (x+1)-n-1]
  • b) 0.5*(-1)n (n-1)! [x– n-1 + (x-1)-n-1 + (x+1)-n-1]
  • c) 0.5*(-1)n (n-1)! [(x-1)-n + (x+1)-n)]
  • d) 0.5*(-1)n (n-1)! [x-n + (x-1)-n + (x+1)-n]
Q.6
If y=sin(-1)⁡(x) then select the true statement.
  • a) y2 = xy13
  • b) y3 = xy23
  • c) y2 = xy12
  • d) y3 = xy12
Q.7
nth derivative of y = sincosis
  • a) 1⁄8 cos⁡(x + nπ⁄2) –1⁄16 5n cos⁡(x + nπ⁄2) – 1⁄16 3n cos⁡(3x + nπ⁄2)
  • b) 1⁄8 sin⁡(x+nπ⁄2) –1⁄16 5n cos⁡(x + nπ⁄2) – 1⁄16 3n cos⁡(3x + nπ⁄2)
  • c) 1⁄8 cos⁡(x+nπ⁄2) –1⁄16 5n sin⁡(x + nπ⁄2) – 1⁄16 3n sin⁡(3x + nπ⁄2)
  • d) 1⁄8 sin⁡(x + nπ⁄2) –1⁄16 5n sin⁡(x + nπ⁄2) – 1⁄16 3n sin⁡(3x + nπ⁄2)
Q.8
Find nth derivative of y = Sin(x) Cos3(x)
  • a) (1/4) 2nSin(2x+nπ/2) + (1/8) 4nSin(4x+nπ/2)
  • b) (1/4) 2nCos(2x+nπ/2) + (1/8) 4nSin(4x+nπ/2)
  • c) (1/4) 2nSin(2x+nπ/2) + (1/8) 4nCos(4x+nπ/2)
  • d) (1/4) 2nCos(2x+nπ/2) + (1/8) 4nCos(4x+nπ/2)
0 h : 0 m : 1 s