AOD and electricity | nda test

Question no. 1

If a positive charge is shifted from a low potential region to a high potential region , the electric potential energy
decreases
  increases
  remains the same
  may decrease / increase

Question no. 2

Work done in moving a unit positive charge through a distance of x metre on an equipotential surface is
  x joule
  1/x joule
  0
x²

Question no. 3

f(x) = cos x is monotonic decreasing under which one of the following condition ?
(0 , π/2) only
  (π/2 , π) only
  (0 , π)
  (0 , 2π)

Question no. 4

A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90 degree. What is the maximum area which can be enclosed inside the quadrilateral ?
68 cm²
  70 cm²
  71.25 cm²
  72.25 cm²

Question no. 5

What are the points on the curve x² + y² -2x - 3 = 0 where the tangents area parallel to x-axis ?
  ( 1 ,2) and(1 ,-2)
  (0, √3) and ( 0 , -√3)
  (3 , 0) and ( -3 , 0)
  (2 , 1) and ( 2 , -1 )

Question no. 6

How many tangents are parallel to x-axis for the curve y = x² -4x+3 ?
  1
  2
  3
  No tangent is parallel to x-axis

Question no. 7

The maximum value of (lnx)/x is
  e
  1/e
  2/e
  1

Question no. 8

What is the maximum value of 16sinx - 12sin²x ?
  3/4
  4/3
  16/3
  4

Question no. 9

At an extreme point of a function f(x) , the tangent to the curve is
parallel to the x-axis
  prependicular to the x-axis
inclined at an angle 45^o to the x-axis
  inclined at an angle 60^o to the x-axis

Question no. 10

What is the minimum value of |x| ?
1
-1
  0
  2

Question no. 11

A charged spherical shell does not produce an electric field at any
  interior
  outer point
  beyond 2 metres
  beyond 10 metres

Question no. 12

Assertion : Force between two charges is quadrupled when distance between them is halved.
Reason : F ∝ 1/r² as per coulomb's law
  Both assertion and reason is true and reason is correct explanantion of assertion
  Both assertion and reason is true and reason is not correct explanantion of assertion
  Assertion is true but reason i false
  Both assertion and reason are false

Question no. 13

The realtion between joule and volt is
  1 joule = 1 coulomb / 1 volt
  1 joule = 1 volt / 1 coulomb
  1 volt = 1 joule / 1 coulomb
  1 volt = 1 coulomb / 1 joule

Question no. 14

The potential difference applied to an x-ray tube is 5 kv and current through it is 3.2 mA, then the number of electrons striking the target per second is
2 × 10¹⁶
5 × 10⁶
1 × 10¹⁷
4 × 10¹⁵

Question no. 15

A soap bubble is charged to a potential of 16 V. Its radius is the doubled. The potential of the bubble now will be
  16 V
  8 V
  4 V
  2 V

Question no. 16

The unit of permittivity of free space ε_o is
coulomb² / newton- metre²
  coulomb² / (newton- metre)²
  coulomb / newton- metre
  newton- metre² / coulomb²

Question no. 17

Capacity of a conductor depends upon
  Size of conductor
  thickness of conductor
  material of conductor
  All of these

Question no. 18

Three different capacitors are connected in series , then :
  they will have equal charges
  they will have same potential
  both 1 and 2
  none of these

Question no. 19

A cylinder is inscribed in a sphere of radius r. What is the height of the cylinder of maximum volume ?
  2r/√3
  r/√3
  2r
  r√3

Question no. 20

What is the maximum value of the function f(x) = 4sin²x + 1 ?
  5
  3
  2
  1