UPSC Forest Apprentice Maths question paper

Can you please provide the Maths question paper of UPSC Forest Apprentice exam?

UPSC Forest Apprentice Exam details are given below:

Eligibility:
A candidate must have attained the age of 21 years and must not have attained the age of 30 years .
The candidate must hold a bachelor’s degree with at least one of following subjects namely Animal Husbandry and Veterinary Science, Botany, Chemistry, Geology, Mathematics, Physics, Statistics and Zoology or a Bachelor’s degree in Agriculture, Forestry.

Few questions of Maths paper of UPSC Forest Apprentice exam are given below:
Answer any four parts from the following :
(a) Find complete and singular integrals of (p2 +qzly = @-

(b) Obtain the iterative scheme for finding pth root of a function of single variable using Newton—Raphson method. Hence, find 7#2772311 correct
to four decimal places.

(C) Convert the following binary-numbers to the base indicated :
(i) 110111011001-10111012 w octal
(ii) [1011101 1001 - 101 1 100012 to hexa-
decimal
(iii) (0-101)2 to decimal

(d) A cannon of mass M, resting on a rough horizontal plane of coefficient of friction
ii, is fired with such a charge that the relative velocity of the ball and cannon at the moment when it leaves the cannon is u. Show that the cannon will
recoil a distance '
( mu ]2__1__
M+m 2pg
along the plane, m being the mass of
the ball.

(a) A rod of length lwith insulated sides, is initially at a uniform temperature . Its
ends are suddenly cooled to 0 °C and are kept at that temperature. Find the
temperature distribution in the rod at any time t. 14
(1 Convert the following to the base indicated against each : 7
(i) (266-375)10 to base 8
(ii) (341-24)5 to base 10
(iii) (43-3125jlo to base 2

(c) Draw the circuit diagram for 1? = AIS-0+ EB using NAND to NAND logic long.

(d) Using Runge-Kutta method, solve y” = xy’2 —y2 for x :02. Initial condi-
tions are at x=0, y=1 and y'=0. Use four decimal places for computations.