PIEAS MS Fellowship Past paper 2012 Mathematics portion

PIEAS MS Fellowship Past paper 2012 Mathematics Portion

1) Two dice are thrown. What is the probability that the sum of dots shown is 4 or 6?
d) 5/18

a) 1/4

b) 1/6

c) 2/9

2) A poll is 20 m apart from a man. The man is making an angle of elevation of 45 degree with the pole head. What is the height of poll?

a) 15m

b) 25m

c) 20m

d) 17.707m

3) If -2, 4, 10 are in A.P then which term of the A.P is 148?

a) 25

b) 26

c) 32

d) 33

4) If f(x+1/x) = x- 1/x then f(x) =?

5) If a cylindrical bar has a radius 2 m and height 9 cm and if it is melted and become a sphere. What is the radius of sphere?

a. 3

b. 6

c. 9

d. None

 6) Find dy/dt if x=sqrot7/8 and x^2+ y^3=1 and dx/dt=2.

a) -4/3 √14

b) -3/4 √14

c) -4/3 √15

d) -3/4 √14


7) ‎[(1-underoot 3 i) /(1+underoot 3 i)]^5 is equivalent to

a) (1-undroot 3 i)/2

b)  (1+undroot 3i)/2

c) (1+3i)/2

d) none

8) 7x^2=9y is

a) parabola

b) cycloid

c) hyperbola

d) ellipse

9) integral from -1 to 2 of x + modulus (x)

a) 0

b) 3

c) -1

d) 2

10) A cuboid has length y, width 3y and depth y then what is its surface area??

a) 14y^2

b) 15y^2

c) 3y^3

d) 5y^2

11) A sphere has radius 6cm. if it is changing at rate 2cm/sec then what will be the rate of change of volume?

a) 288 pi

b) 300 pi

c) 36 pi

d) 8 pi


12) A car starts at 10.00 am at speed of 60km/h and 2^nd starts one hour later at 80km/h. at what time will the 2^nd car overtake the 1^st?

a) 1 pm

b) 2 pm

c) 3 pm

d) will never cross

13) 3x-4y+11=0
       3x-4y+5=0
find the minimum distance between the lines.


14) Equation of circle is x^2 + y^2 +2gx + 6fy = 0.
What is the equation of tangent passing through the point (-1, 1)

15) The length of chord of circle represented by x^2+4x+4+y^2+6y+9=9 passing through centre is??

16) Length of diameter of circle represented by equation 2x^2+2y^2-8=0 ??