RPSC Senior Scientific Officer Ballistic Paper 2019 – Part B Mathematics
Total Questions – 100 Duration – Two hours
No. of questions from Mathematics – 60 Nos.
A circular board of mass ‘m’ and radius ‘a’ is placed on smooth horizontal plane, and a boy of mass ‘M’ runs round of edge of it at a uniform rate, then true statement is
(a) The plane will remain stable
(b) The plane will turn in the direction of boy about its centre.
(c) The plane will turn opposite to the direction of boy about an axis perpendicular to plane of board at a distance of Ma/(m+M) from centre
(d) The plane will turn in the direction of boy about an axis perpendicular to plane of board at a distan ma/(m+M)
The resolved part of the effective force of a body in any direction is equal to the whole mass multiplied by the ______. Choose the correct option to fill the blank.
(a) moment about centre of gravity
(b) moment of mementum about centre of gravity
(c) reversed acceleration of centre of gravity
(d) acceleration of centre of gravity
The momental ellipse at the centre of an elliptic area is
(a) a similar and similarly situated ellipse
(b) a similar but not similarly situated ellipse
(c) not similar but similarly situated ellipse
(d) neither similar nor similarly situated ellipse
Let a circular plate of radius r turns about an axis which is a horizontal tangent to plate, then the position of the centre of percussion from axis is
(a) 5r/4
(b) 4r/5
(c) 4r/3
(d) r/4
A cylinder of mass ‘m’ rolls down a smooth plane whose inclination to the horizon is ‘a’ unwrapping as it goes a fine string fixed to the highest point of the plane; then true statement is
(a) Tension of string = (2/3)mg sin a
(b) Tension of string = (2/3) g sin a
(c) Acceleration of cylinder = (2/3) g sin a
(d) Acceleration of cylinder = g sin a
A uniform circular plate is turning in its own plane about a point A on its circumference. Suddenly A is freed and a point B also on the circumference, is fixed. If the plate is reduced to rest then arc AB will be nth part of the circumference; then n is
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/6
A rigid body moves under the action of no forces so that resolved part of its angular velocity about one of the principal axes at the centre of gravity is constant, then the angular velocity of body _____
Choose the correct option.
(a) must be proportional to reciprocal of angular momentum
(b) can never be constant
(c) must be constant
(d) will have an oscillatory behaviour
A uniform rod AB of mass M and length 2a is lying on a smooth table and is truck at A by a horizontal blow J perpendicular to rod, then the true statement is
(a) Linear velocity of centre of gravity will be = J/aM
(b) Angular velocity of rod will be 3J/aM
(c) Angular velocity = 2 (linear velocity in magnitude)
(d) Linear velocity of centre of gravity after impact = JM
Daily wages of 10 workers in a factory are given below. Compute the variance. Wages in dollars are
15, 18, 13, 20, 17, 10, 16, 19, 22, 20
(a) 11.7
(b) 11.8
(c) 17
(d) 12.8
A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are done without replacement. The probability that the first drawing will give 3 white balls and the second 3 red balls is
(a) 7/429
(b) 7/15
(c) 5/143
(d) 1076/2145
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