hpsc.gov.in HCS Main Exam Mathematics Question Paper : Haryana Public Service Commission

Name of the Organization : Haryana Public Service Commission
Name of the Exam : HCS (Ex.Br.) Main Exam
Subject : Mathematics
Document Type : Previous Question Paper
Year : 2014

Website : http://hpsc.gov.in/en-us/
Download Sample/Model Question Paper : https://www.pdfquestion.in/uploads/11138-Math.pdf

HCS Main Exam Mathematics Question Paper :

Mathematics :
Code : 14
Time:3 Hours
M.M.: 150

Related : HPSC HCS Main Exam Indian History Question Paper : www.pdfquestion.in/11131.html 

Note:
** Attempt five questions. All questions carry equal marks. Question number I is compulsory.
** Answer any two questions from part I and two questions from part II.

** The parts of the same questions must be answered together and must not be interposed between answers to other questions.
** In case of any discrepancy in the English and Hindi versions, English version will be taken as final.

1. Answer any four of the following :
(a) Find eigen values and eigen vectors of the matrix
(b) A river 10 m deep and 100 m wide is flowing at the rate 4.5 kmlh. Find the volume of water running into the sea per second from the river.
(c) Describe the surface whose equation in cylindrical coordinates is z : r
(d) Find the order & degree of following differential equation (D2 -D+5) = Sin X

2.(a)LetV be the vector space consisting of all functions of the form :
cosx + B et. sinx consider the followin g linear transformation : L:V – V: L(f) ft+ f Find the matrix representing L with respects the basis {et”cosx, e’- sinx}

(b) find the solution of the following system of linear equations
x1+X2+3X3 = 3
-X1+X2+X3 = -1
2×1+3X2+8x=4

(d) Classiff the following small disturbance potential equation for compressible flows
(e)pind the stationary points of y: xt-3x+2 and determine their nature.

4(a)Prove that if x>0, and n>l then
(c) A cylindri cal jar of radius I 5cm is filled with water upto a height of 25cm. 1 5 spherical balls of radius i 2cm each are immersed in the Jar. Find the new level to which water is filled in the take 3

5.(a)Find the equation in cylindrical coordinates for the ellipsoid 4x’ + 4y’ * z’ : l.
(b) Find the angle between the line x-1/2 =y=z-3/6 and the plane 10x+2y-llz = 3

Chemistry :
Q.1: In a zero-order reaction for every 10o rise of temperature, the rate is doubled. If the temperature is increased from 10?C to l00oC, the rate of the reaction will become
(A) 64 times
(B) 128 times
(C) 256 times
(D) 512 times

Q.2: Based on the first law of thermodynamics, which one of the following is correct?
(A) For an isothermal process, q: +w
(B) For an isochoric process, AU : -q
(C) For an adiabatic process, AU: -w
(D) For a cyclic process, g: -w

Q.3: The temperature of the system decreases in an
(A) Adiabatic compression
(B) Isothermal expansion
(C) Isothermal compression
(D) Adiabatic expansion

Q.4: The standard emf of galvanic cell involving 3 moles of electrons in its redox reaction is 0.59 V. The equilibrium constant for the reaction of the cell is
(A) 102s
(B) 1020
(c) 1015
(D)1030

Q.5: In which of the following process, a maximum increase in entropy is observed?
(A) dissolution of salt in water
(B) condensation of water
(C) sublimation of naphthalene
(D) melting of ice

Q.6: In a reaction, A + B —+ Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactxnts (A and B) are doubled. rate law for the reaction can be written as
(A) Rate = klAl [B]
(B) Rate = klAl2[B]
(c) Rate = klAl[B]2
(D) Rate = klAl2[B]2

Q.7: The enthalpy of fusion of water is 1.435 kcal/mol. The molar entropy change for the Melting of ice at OoC is
(A) 5.260 cal(mol K)
(B)0.526 cal(mol K)
(C) 10.52 ca(mol K)
(D)21.04 cal(mol K)

Q.8: The activation energy of a reaction at a given temperature is found to be 2.303 RT J mofr. The ratio of rate constant to the Arrhenius factor is
(A) 0.1
(B) 0.01
(c) 0.000l
(D) 0.02

Q.9: Which of the following is correct for philosophic sols?
(A) They are irreversible
(B) They are formed by inorganic substances
(C) They are readily coagulated by addition of electrolytes
(D) They are self-stabilized

Q.10: The time taken for l0o/o completion of a first order reaction is 20 min. Then, for 1000g completion, the reaction will take
(A)40 mins
(B)60 mins
(C)50 mins
(C)30 mins