# Sample Paper Of WBJEE 2013

State Govt. organize **WBJEE(West Bengal Joint Entrance Examination)** as a centralised test for admission of students to various private and govt. Medical and Engineering institutions in West Bengal.Students after their 12th can appear for this test for graduation courses.Two different tests are organised for all those candidates seeking admission in Medical colleges and Engineering colleges. In Medical test students will have to answer questions from biology whereas in Engineering test they will have to answer Mathematics questions..Physics and Chemistry are common to both the test.Sample Paper Of WBJEE 2013 are given for the preparation of these examination.

Exam Pattern has been changed from 2012,the question paper contains only MCQ questions having same weightage as that of 2 marks short answer questions in the previous years question paper.Each paper contains 80 questions and it has been divided in to two test-1st test contains 60 MCQ questions of 1 mark each and 2nd test 20 MCQ of 2 marks each.Negative marking is also there for every incorrect answer

**Questions:**

**SAMPLE PAPER OF WBJEE 2013**

**1.A heavy uniform chain lies on horizontal table top.If the coefficient of friction between the chain and the table surface is .25,then maximum fraction of length that can overhang on edge of the table is-**

a) 20% b)25% c)15% d)35%

**2. One Kg of copper is drawn into a wire of 1mm diameter and a wire of 2mm diameter. The resistance of the two wires will be in the ratio-**

a) 1:2 b)2:1 c)4:1 d)16:1

**3. Two identical cells each of emf E and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the values of R is-**

a)R=r/2 b)R=r/3 c)R=2r d)R=r

**4 .An alternating current of rms value 10A is passed through a 12 ohm resistor. The maximum potential difference across the resistor is –**

a) 20V b)90V c)1969.68V d)none of these

**5. Vector A and Vector B are two vectors given by A=2i+3j and B=i+j. The magnitude of the component of vector A along vector B is-**

a) 5/(2^{1/2} ) b) 3/(2)^{1/2 } c) 7/(2)^{1/2} d) 1/(2)^{1/2}

**6.In Young’s double slit experiment, the fringe width is B. If the entire arrangement is placed in a liquid of refractive index n, the fringe width becomes-**

a) nB b)B/(n+1) c) B/(n-1) d) B/n

**7. n identical droplets are charged to v volt each.If they coalesce to form a single drop then its potential will be-**

a) n^{2/3}v b)n^{1/3}v c) nv d)v/n

**8. A radioactive nucleus of mass no. A, initially at rest,emits an alpha particle with a speed v. The recoil speed of the daughter nucleus will be-**

a) 2v/(A-4) b) 4v/(A-4) c) 4v/(A+4) d)2v/(A+4)

**9. A cubical vessel of height 1 m is full of water. What is the amount of work done in pumping water out of the vessel? (g=10m/s ^{2}) .**

a) 1250J b)5000J c)1000J d)2500J

**10. A body of mass 6 kg is acted upon by a force which causes a displacement in it given by x=t ^{2}/4 m when t is time in second.The work done by force in 2 sec is-**

a) 12J b)9J c)6J d)3J

**11. When a beta+ particle is emitted from a nucleus ,then its neutron-proton ratio-**

a)increases b)decreases c)remains same d)first (a) then (b)

**12.A plane progressive wave is given by y=2cos6.284(330t-x). What is the period of the wave?**

a)(1/330)s b)(2pi*330)s c)(2pi*330)^{-1}s d)(6.284/330)s

**13. If g is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass m raised from earth’s surface to a height equal to radius R of the earth is-**

a)(mgR)/4 b)(mgR)/2 c)mgR d)2mgR

**14. A material has Poisson’s ratio .50.If a uniform rod of it suffers a longitudinal strain of 2*10 ^{-3},then the percentage change in volume is-**

a)0 .6 b)0.4 c)0.2 d)zero

**15.If the speed of light(c), acceleration due to gravity(g),and pressure(p) are taken as as fundamental units,the dimensional formula of gravitational constant(G) will be-**

a)c^{0}g^{2}p^{-3} b)c^{2}g^{-3}p^{-2} c)c^{0}g^{2}p^{-1 } d)c^{2}g^{2}p^{-2}

**16. A point initially at rest moves along x axis. Its acceleration varies with time as a=(6t+5)m/s ^{2}.If it starts from origin,the distance covered in 1^{st} second-**

a)3m b)3.5m c)4m d)4.5m

**17. When an ideal diatomic gas is heated at constant pressure ,the fraction of heat energy supplied which increases the internal energy of gas is-**

a)2/5 b)3/5 c)3/7 d)5/7

**18.A block of mass M is placed on a rough inclined plane having angle of inclination 45 ^{0}. The co-efficient of friction is 0.5.What is the acceleration of block down the inclined plane?**

a)0.20g b)0.25g c)0.30g d)0.35g

**19.Two bodies of masses 1Kg and 5Kg are dropped gently from top of a tower.At a point 20cm from the ground both the bodies will have same-**

a)momentum b)kinetic energy c)velocity d)total energy

**20.The K.E of a satellite in its orbit around the earth is E.What should be the K.E of the satellite so as to enable it to escape from gravitational pull of the earth-**

a)4E b)2E c) (2)^{1/2}E d)E

**21.The average energy for molecules in one degree of freedom is-**

a)( 3kT)/2 b)( kT)/2 c)(3kT)/4 d)kT

**22.According to newton’s law of cooling thr rate of cooling of a body is proportional to the-**

a)fourth power of the temperature of the body

b) temperature of the surroundings

c) temperature of the body

d)difference in temperature of the body and the surroundings

**23.What will be the displacement of a particle from the mean position in S.H.M when its velocity is half the maximum velocity?(A=amplitude)**

a)3A/(2)^{1/2} b) (2)^{1/2}A c)3A/4 d){ (3)^{1/2}A}/2

**24.Two bodies with moment of inertia I1 and I2 (I1>I2) have equal angular momentum. If the K.E of rotation is E1 and E2 ,then**

a)E1>E2 b)E1<E2 c)E1=E2 d)none of these

**25.At a certain place, the horizontal component of earth’s magnetic field is (3) ^{1/2} times the vertical component.The angle of dip at that place is –**

a)30^{0} b)60^{0} c)45^{0} d)90^{0}

**26.Two rods of equal length and diameter have thermal conductivity 3 and 4 respectively.If they are joined in series ,the thermal conductivity of the combination would be-**

a)3.43 b)3.5 c)3.4 d)3.34

**27.A particle projected at 60 ^{0} to the horizontal with kinetic energy K.The K.E at the highest point is-**

a)K b)0 c)k/4 d)k/2

**28.If K.E of a body changes by 20% ,then its momentum would change by-**

a)20% b)24% c)44% d)none of these

**29.A wire of resistance 9 ohm is drawn out so that its new length is 3 times its original length.What is the resistance of the new wire?**

a)45 ohm b)15 ohm c)5 ohm d)none of these

**30.An electric cable having a resistance of 0.2 ohm delivers 10Kw at 200V D.C to a factory.What is the efficiency of the transmission?**

a)65% b)75% c)85% d)95%

**CHEMISTRY:**

**1.A SN2 reaction at an asymmetric carbon of a compound always gives-**

a) an enantiomer of the substance

b) a product with opposite optical rotation

c)a mixture of diastereoisomers

d)a single stereoisomer

**2.The correct order of rate of SN1 reaction for alkyl halides-**

a)3^{0}>2^{0>}1^{0 } b)3^{0}<2^{0}<1^{0} c)1^{0}<2^{0}>3^{0 } d)3^{0}=2^{0}>1^{0}

**3.With rise in temperature ,viscosity of a liquid –**

a)increases b)decreases c)remains same d)may increase or decrease

**4.The heat of formation of CO and CO _{2} are -26.4Kcal and -94.6Kcal respectively.Heat of combination of carbon monoxide will be-**

a)+26.4Kcal b)-68.2Kcal c)-120.6kcal d)+52.8Kcal

**5.Which of the following is not correct:**

a)Boric acid is a very weak monobasic acid.

b)Boric acid contains planar BO_{3} units,which are bonded together through

hydrogen bonds forming a layer structure.

c)Boric acid is used as a food preservative.

d) Boric acid is atribasic acid.

**6.The compound which will give precipitate with AgNO _{3 } solution is-**

a)CCl_{4 } b)CH_{3}-CH_{2}-Cl c)(CH_{3})CCl_{4 }d)CHCl_{3}

**7.C _{2}H_{5}OH+HX—–à C_{2}H_{5}X+H_{2}O,the order of reactivity-**

a)HCl>HBr>HI b)HI>HBr>HCl c)HBr>HCl>HI d)HI>HCl>HBr

**8.On boiling with conc. Hydrobromic acid,ethyl phenyl ether will yield-**

a)phenol and ethyl bromide

b)bromobenzene and ethanol

c)phenol and ethane

d)bromobenzene and ethane

**9.Formic acid and Acetic acid may be distinguished by the reaction with –**

a)Sodium

b) 2,4-Dinitrophenyl hydrazine

c) Sodium ethoxide

d) dilute acetic permanganate

**10.The equation of state for n moles of an ideal gas is PV=nRT,where R is contant.SI unit of R is-**

a)JK^{-1 } per molecule b)JK^{-1}mol^{-1} c)JKg^{-1}K^{-1} d)JK^{-1}g^{-1}

**11. Which is incorrect:**

a)Phenol is weak acid

b)Phenol is an aromatic compound

c) Phenol liberates CO_{2} from Na_{2}CO_{3 }solution.

d)Phenol is soluble in NaOH.

**12.In which of the following,carbon-carbon bond is not formed:**

a)Cannizaro reaction b)wurtz reaction c)Aldol condensation d)Friedal-Crafts reaction.

**13.Half life of a radioactive substance is 20 min.The time between 20% and 80% decay is-**

a)20 min b)30 min c)40 min d)25 min

**14.The potential of a hydrogen electrode at pH=10 is-**

a)0.59 V b).00 V c)-.59 V d)-.059 V

**15.In a periodic table the basic character of oxides-**

a) increases from left to right and decreases from top to bottom

b) decreases from right to left and increases from top to bottom

c) decreases from left to right and increases from top to bottom

d) decreases from left to right and increases from bottom to top

**16.Which of the following substance gives a positively charged sol?**

a)Gold b)Arsenius sulphite c)Starch d)Ferric hydroxide

**17.N-Bromoacetamide on heating with KOH gives-**

a)1^{0} amine^{ }b)2^{0} amine c)3^{0 }amine d)quaternary ammonium salt

**18.Among the following hydroxide ,which has the lowest value of Ksp at ordinary temperature-**

a)Mg(OH)_{2} b)Ca(OH)_{2} c)Ba(OH)_{2} d)Be(OH)_{2}

**19.The correct order of basic strength among the following compounds:**

a)Li_{2}O<Na_{2}O<K_{2}O<Rb_{2}O

b)Rb_{2}O>Na_{2}O=K_{2}O>Li_{2}O

c) Li_{2}O>Na_{2}O>K_{2}O>Rb_{2}O

d) Na_{2}O>Li_{2}O>K_{2}O>Rb_{2}O

**20. Which of the following is non-ionisable-**

a)[Co(NH_{3})_{5}Cl]Cl

_{ }b) [Co(NH_{3})_{4}Cl_{2}]Cl

c) [Co(NH_{3})_{6}]Cl_{3}

d)[Co(NH_{3})_{3}Cl_{3}]

**21.Which of the following ions has the highest reduction potential?**

a)Li^{+} b)Na^{+} c)K^{+} d)Rb^{+}

**22. Oxidation of Cr ^{3+} in acid solution gives-**

a)CrO_{2}^{–} b)CrO_{4}^{2-} c)Cr_{2}O_{7}^{2-} d) Cr^{2+}

**23.Correct set of four quantum number for the valence electrons of rubidium-**

a) 5,0,0,+1/2 b)5,1,0,+1/2 c)5,1,1,+1/2 d)6,0,0,+1/2

**24.Which one is the colligative property??**

a) boiling point b)vapour pressure c)osmotic pressure d)freezing point

**25.A dehydrating agent commonly used in laboratory is-**

a)MgCO_{3} b)CaF_{2} c)CaCl_{2} d)MgF_{2}

**26.Alkaline hydrolysis of an ester is called-**

a) neutralization b)esterification c)polymerization d)saponification

**27.The halide, which will not react with benzene in presence of anhydrous AlCl _{3} is-**

a)CH_{3}CHClCH_{3} b)C_{6}H_{5}CH_{2}Cl c)C_{6}H_{5}Cl d)CH_{3}CH_{2}CH_{2}Cl

**28.When electrons are trapped in the crystal lattice in place of anion vacancy, the defect in the crystal is called-**

a)F-centre b)G-centre c)dislocation d)electronic defect

29.The conjugate acid of NH_{2}^{–} is-

a)NH_{3} b)NH_{4}^{+} c)N_{2}H_{4} d)NH_{2}OH

30.Which of the following has P-O-P bond?

a)Hypophosphorous acid b)Pyrophosphoric acid c)Phosphorous d)Orthophosphoric acid

**MATHEMATICS:**

**1.Let R be the set of real number and the mapping f:R—–>R and g:R—->R be defined by f(x)=5-x ^{2} and g(x)=3x-4,then the values of (fog)(-1) is-**

a) -44 b) -54 c)-32 d)-64

**2.If sum of an infinite geometric series is 4/5 and its 1 ^{st} term is 3/4, then common ratio is-**

a)7/16 b)9/16 c)1/9 d)7/9

**3.The number of permutation by taking all letters and keeping the value of the words COMBINE in odd places is-**

a)96 b)244 c)512 d)576

**4.If in the expansion of (a-2b) ^{n}, the sum of 5^{th} and 6^{th} term is zero, then value of a/b is-**

a)(n-4)/5 b){2(n-4)}/5 c)5/(n-4) d)5/{2(n-4)}

**5.If C is the reflection of A(2,4) in x-axis and B is the reflection of C in y-axis, then |AB| is-**

a)20 b)2*(5)^{1/2} c)4*(5)^{1/2} d)4

**6.The line y=2t ^{2} intersects the ellipse x^{2}/9 +y^{2}/4 =1 in real points if-**

a)|t|<=1 b)|t|<1 c)|t|>1 d|t|>=1

**7.If A and B are square matrices of the same order and AB=3I, then A ^{-1} is equal to-**

a)3B b)B/3 c)3B^{-1} d)B^{-1}/3

**8.The co-ordinates of the focus of the parabola described parametrically by x=5t ^{2}+2, y=10t+4 are –**

a)(7,4) b)(3,4) c)(3,-4) d)(-7,4)

**9.In a triangle ABC if sinAsinB=(ab)/c ^{2} ,then triangle is-**

a) equilateral b)isosceles c)right angled d)obtuse angled

**10.The eccentricity of hyperbola 4x ^{2}-9y^{2}=36 is-**

a)(11)^{1/2}/3 b)(15)^{1/2}/3 c)(13)^{1/2}/3 d)(14)^{1/2}/3

**11.If in a triangle sinA, sinB, sinC are in A.P, then its –**

a) altitudes are in A.P b) altitudes are in H.P c)angles are in A.P d)angles are in H.P

**12.The total number of real roots of the equation 2x ^{4}+5x^{2}+3=0 are-**

a)4 b)0 c)2 d)3

**13.The number of committee of 3 members can be formed from 6 girls and 4 ladies-**

a) 6C_{5 } b)10P_{5} c) 252 d)120

**14.The number of all possible selections of one or more questions from 8 given questions, each question having an alternative is-**

a)2^{8}-1 b)3^{8}-1 c)4^{8}-1 d) none of these

**15. If one end of a diameter of circle 2x ^{2}+2y^{2}-4x-4y+2=0 is (3,2) ,then other end is-**

a) (2,3) b)(4,-2) c)(2,-1) d) (-1,2)

**16 .The equation x ^{2}+y^{2}+4x+6y+13=0 represents-**

a) a circle b)a pair of two distinct straight lines c)a point d) none of these

**17 .If the quadratic equation ax ^{2}+2cx+b=0 and ax^{2}+2bx+c=0 and a not equal to c, and both these equations have a common root, then a+4b+4c is equal to-**

a)-2 b)-1 c)0 d)1

**18.The equation of directrix of the parabola y ^{2}+4y+4x+2=0 is-**

a)x=-1 b)x=1 c)x=-3/2 d)x=3/2

**19.The straight line x+y=k touches the parabola y=(x-x ^{2}) if k is equal to-**

a)0 b)1 c)-1 d) none of these

**20.The straight line passing through the point of intersection of the straight lines x-3y+1=0 and 2x+5y-9=0 and having infinite slope and at a distance 2 units from the origin has the euation –**

a)x=2 b)3x+4y-1=0 c)y=1 d)none of these

**21.If a,b,c are in A.P, then the straight line ax+by+c=0 ,will always pass through the point-**

a) (-1,-2) b)(1,-2) c)(-1,2) d)(1,2)

**22.If |x ^{2}-x-6|=x+2,then the values of x are-**

a) -2,2,-4 b) -2,2,4 c)3,2,-2 d)4,4,3

**23.The solution of equation 2x ^{2}+3x-9<=0 is given by-**

a)3/2<=x<=3 b)-3<=x<=3/2 c)-3<=x<=3 d)3/2<=x<=2

**24.The tangent to the circle x ^{2}+y^{2}=5 at the point (1,-2) also touches the circle x^{2}+y^{2}-8x+6y+20=0.Then its point of contact is-**

a) (-2,1) b) (-1,1) c)(-3,0) d(3,-1)

**25.The distance between the pair of parallel lines x ^{2}+4xy+4y^{2}+3x+6y-4=0 is-**

a) (5)^{1/2} b)2/(5)^{1/2} c)1/(5)^{1/2} d)(5)^{1/2}/2

**26.If n arithmetic means are inserted between 2 and 38 and the sum of resulting series is obtained as 200,then the values of n is-**

a)6 b)8 c)9 d)10

**27.If x ^{2}+6x-27>0 and x^{2}-3x-4<0, then**

a)x>3 b) x<4 c)3<x<4 d)x=7/2

**28.Let the circles x ^{2}+y^{2}+8y-20=0 and x^{2}+y^{2}+6x+k=0, touching each other internally ,then value of k is-**

a)6 b)8 c)9 d) none of these

**29.Equation of tangent to the parabola y ^{2}=4ax parallel to y=2x+3 is-**

a)y=2x+a b)2y=4x-a c)2y=4x+a ^{ }d) none of these

**30.A bag contains 5 brown socks and 4 white socks. A man selects two socks from the bag without replacement.The probability that the selected socks will be of the same colour is-**

a)5/108 b)1/6 c)5/18 d)4/9

**Mathmatics Sample Paper of WBJEE**

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