MOCK TEST for UPSEE 2016

Time : 3 Hrs.

MM : 600

GENERAL INSTRUCTIONS :

1. UPSEE consists of one paper of three subjects - Physics, Chemistry and Maths. Each subject contains 50 questions and each correct answer carries four marks. No negative marking.

2. The exam can be written in Hindi or English. After a candidate clears this exam there is another examination of objective type Hindi questions to check the basic knowledge of Hindi of candidate.

3. Read each question carefully.

4. It is mandatory to use Blue/Black Ball Point Pen to darken the appropriate circle in the answer sheet. 5. Mark should be dark and should completely fill the circle in the answer sheet.

6. Do not use white-fluid or any other rubbing material on answer sheet. No change in the answer once marked is allowed.

7. Rough work must not be done on the answer sheet.

8. Student cannot use log tables and calculators or any other material in the examination hall.

9. Before attempting the question paper, student should ensure that the test paper contains all pages and no page is missing.

Choose the correct answer :

1. The vectors a b _{, and c} are related by _{c b a}  _{ } . Which diagram below illustrates this relationship?

(1) a b c (2) (3) b c a (4) a c b Ph.: 011-47623456 Fax : 011-47623472

MOCK TEST

MOCK TEST

MOCK TEST

MOCK TEST

MOCK TEST

for

UPSEE 2016

UPSEE 2016

UPSEE 2016

UPSEE 2016

UPSEE 2016

PHYSICS

2. Acceleration versus time graphs for four objects are shown below. All axes have the same scale. Which objects have the greatest change in velocity in the interval t = 0 to t = t₀? (1) ac ce le ra tio n t0 a0 t (2) ac ce le ra tion t0 a0 t (3) ac ce le ra tio n t0 a0 t (4) ac ce le ra tio n t0 a0 t

3. A stone is released from an elevator moving up with an acceleration a₀. The acceleration of the stone after the release is

(1) a₀ upward (2) a₀ downward (3) g + a₀ downward (4) g downward

(2) 4. Acceleration-time graph of a particle moving along

X-axis as shown. Find the speed of particle at time t = 5 sec (Take initial speed of particle is zero)

5 5 a (ms )–2 t(s) 10 (1) 5 ms–1 _{(2) 10 ms}–1 (3) 15 ms–1 _{(4) 25 ms}–1

5. Light is an electromagnetic wave. Its speed in vacuum is given by the expression

(1)  _{0 0} (2) 0 0 1   (3) 0 0   (4) 00  

6. Kirchhoff’s first law i.e. _{∑ i 0}at a junction is based on the law of conservation of

(1) Charge (2) Energy

(3) Momentum (4) Angular momentum 7. The earth's radius is R and acceleration due to

gravity at its surface is g. If a stone of mass m is sent to a height h = R/5 from the earth’s surface, the potential energy increases by

(1) mgh (2) 4

5mgh

(3) 5₆mgh (4) 6

7mgh

8. If all the resistors shown have the value of 2  each, the equivalent resistance between A & B is

A B

(1) 2 (2) 4 

(3) 6  (4) 8 

9. For the myopic eye, the defect is cured by (1) Convex lens (2) Concave lens (3) Cylindrical lens (4) Toric lens

10. The work function of sodium is 2.3 eV. The threshold wavelength of sodium will be

(1) 2000 Å (2) 4000 Å

(3) 5380 Å (4) 6380 Å

11. An -particle and a proton travel with same velocity in a magnetic field perpendicular to the direction of their velocities. Find the ratio of the radii of their circular path.

(1) 4 : 1 (2) 1 : 4

(3) 2 : 1 (4) 1 : 2

12. Distance between a frog and an insect on a horizontal plane is 10 m. Frog can jump with a maximum speed of ₁₀ ms–1_{. Minimum number of}

jumps required by the frog to catch the insect is (g = 10 ms–2₎

(1) 5 (2) 10

(3) 100 (4) 50

13. A particle starts from the origin at t = 0 and moves in the XY-plane with constant acceleration a in the y direction. Its equation of motion is y = bx2_{. The}

x-component of its velocity is

(1) Variable (2) 2a b (3) 2 a b (4) 2 a b

14. A body is thrown horizontally with a velocity 2gh from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance X from the tower. The value of X is

(1) h (2)

2 h

(3) 2h (4) 2h/3

15. A man crosses the river perpendicular to river flow in time t seconds and travels an equal distance down the stream in T seconds. The ratio of man's speed in still water to the speed of river water will be (1) 2 2 2 2 t T t T   (2) 2 2 2 2 T t T t   (3) 2 2 2 2 t T t T   (4) 2 2 2 2 T t T t  

16. Two blocks A and B each of mass m are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks A and B respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is

30°m 2F B A m F (1) F (2) F/2 (3) _{F/ 3} (4) 3F

17. In the figure shown, the pulleys and strings are massless. The acceleration of the block of mass 4 m just after the system is released from rest is ( = sin–1 _(3/5)) m m m 4   (1) 2₅g downwards (2) 2 5 g upwards (3) 5 11 g upwards (4) 5 11 g downwards

18. Two points of rod move with velocities 3V and V perpendicular to the rod and in the same direction separated by a distance r. Then the angular velocity of the rod is

(1) 3V r (2) 4V r (3) 5V r (4) 2V r

19. A ring of radius R rolls without sliding with a constant velocity. The radius of curvature of the path followed by any particle of the ring at the highest point of its path will be

(1) R (2) 2R

(3) 4 R (4) None of these

20. A system is shown in the figure. The time period for small oscillations of the two blocks will be

m K 2 K m (1) 2 3m K  (2) 2 3 2 m K  (3) 2 3 4 m K  (4) 2 3 8 m K 

21. A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

(1) 4RT (2) 5RT

(3) 15RT (4) 11RT

22. Maxwell's velocity distribution curve is given for two different temperatures. For the given curves

V T1 N T2 (1) T₁ > T₂ (2) T₁ < T₂ (3) T₁ T₂ (4) T₁ T₂

23. The values of kinetic energy K and potential energy U are measured as follow K = 100.0 ± 2J, U = 200.0 ± 1.03. Then the percentage error in the measurement of mechanical energy is

(1) 2.5 % (2) 1 %

(3) 0.5 % (4) 1.5 %

24. An electric field is given by E_x = –2x3 _{K N/C.}

The potential of the point (1, –2), if potential of the point (2, 4) is taken as zero, is

(1) –7.5 × 103 _{V (2) 7.5 × 10}3 _V

(3) –15 × 103 _{V (4) 15 × 10}3 _V

25. Electrical potential 'V' in space as a function of co-ordinates is given by V 1 1 1

x y z

   . Then the electric field intensity at (1,1,1) is given by (1)   ₍ _{i j k}₎ (2) ₍ _{i j k} ₎

(3) Zero (4) 1







(4) 26. In the circuit shown, each resistance is 2. The

potential of point A is equal to

5 V 12 V

A

(1) 11 V (2) –11 V

(3) 9 V (4) –9 V

27. A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is (1) Zero (2) kpQ₃ R (3) 2kpQ₃ R (4) kpQ₃

R only if the charge is uniformly distributed

on the ring

28. Equivalent capacitance between points A and B is (capacitance of each capacitor is C)

A B

(1) 2 C (2) 3 C

(3) 4 C (4) C

29. Induced electric field is (1) Conservative in nature (2) Non-conservative in nature (3) Form closed loop

(4) Both (2) and (3) 30. Select the correct option.

(1) Time varying magnetic field produces electric field

(2) Time varying electric field produces magnetic field

(3) Both (1) and (2) (4) None of these

31. Direction of electromagnetic wave is along the vector

(1) _{E B} _ (2) _{B E} _

(3) _E (4) _B

32. Torque on magnetic dipole of dipole moment

 

M in uniform magnetic field

 

B is given by

(1) _{M B} _. (2) _{M B} _. (3) _{M B} _ (4) _{B M} _

33. If the radius of the earth were to shrink by one percent, its mass remaining the same, acceleration due to gravity on the earth's surface would

(1) Decrease (2) Remain unchanged (3) Increase (4) Zero

34. A satellite is moving with a constant speed V in a circular orbit about the earth, an object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is

(1) 1 2

2mv (2) mv2

(3) 3 2

2mv (4) 2mv2

35. If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium, then the value of q is

(1) 2 Q (2) 2 Q  (3) 4 Q (4) 4 Q 

36. If the electric flux entering and leaving an enclosed surface, respectively are ₁ and ₂, the electric charge inside the surface will be

(1) (₂ – ₁)₀ (2) (₁ + ₂)₀ (3)



2 1



0     (4)



1 2



0    

37. Two coherent point sources S₁ and S₂ are separated by a small distance d shown. The fringes obtained on the screen will be

Screen D

d S1 S2

(1) Straight lines (2) Semi-circles (3) Concentric circles (4) Points

38. A beam of unpolarized light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented such that its principal axis makes an angle of 45° relative to that of A. The intensity of the emergent light is (1) 0 2 I (2) 0 4 I (3) 0 8 I (4) I₀

39. The angle of incidence at which reflected light is totally polarised for reflection from air to glass (refractive index ) is

(1) sin–1₍) _{(2) sin}–1₍)

(3) tan–1_(1/) _{(4) tan}–1₍)

40. If the kinetic energy of a free electron doubles, its de Broglie Wavelength changes by the factor

(1) ₂ (2) 1

2

(3) 2 (4) 1

2

41. The work function of a substance is 4.0 eV. The longest wavelength of light can cause photoelectron emission from this substance is approximately

(1) 540 nm (2) 400 nm

(3) 310 nm (4) 220 nm

42. Which of the following transition in hydrogen atoms emits photons of the highest frequency? (1) n = 6 to n = 2 (2) n = 2 to n = 1 (3) n = 1 to n = 2 (4) n = 2 to n = 6 43. Backlash error present in

(1) Vernier caliper

(2) Screw gauge and vernier caliper (3) Screw gauge

(4) Vernier caliper and spherometer

44. If N₀ is the original mass of a substance of half-life period t_(1/2) 5 years, then the amount of substance left after 15 years is

(1) 0 8 N (2) 0 16 N (3) 0 2 N (4) 0 4 N

45. A 220 V, 1000 W bulb is connected across a 110 V main supply. The power consumed will be

(1) 1000 W (2) 750 W

(3) 500 W (4) 250 W

46. By increasing the temperature, the specific resistance of a conductor and a semiconductor (1) Increases for both

(2) Decreases for both (3) Increases, decreases (4) Decreases, Increases

47. When a rubber-band is stretched by a distance x, if exerts a restoring force of magnitude F = ax + bx2_{, where a and b are constant. The}

work done in stretching the unstretched rubber band by L is (1) 2 2 2 3 aL _bL (2) 2 3 1 2 2 3 aL bL ⎛ ⎞  ⎜ ⎟ ⎝ ⎠ (3) aL2 _{+ bL}3 ₍₄₎ 1



2 3



2 aL bL

48. Two particles A and B, initially at rest move towards each other by a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2V, the speed of the centre of mass of the system is

(1) 3 V (2) V

(3) 1.5 V (4) 0

49. The speed of sound in oxygen gas at a certain temperature is 460 ms–1_{. The speed in helium gas}

at the same temperature will be (assume both gases to be ideal)

(1) 1420 ms–1 _{(2) 500 ms}–1

(3) 650 ms–1 _{(4) 330 ms}–1

50. Curie temperature is the temperature above which (1) A paramagnetic material becomes

ferromagnetic

(2) A ferromagnetic material becomes paramagnetic

(3) A paramagnetic material becomes diamagnetic (4) A ferromagnetic material becomes diamagnetic

(6)

CHEMISTRY

51. Which of the following aldehydes give cannizzaro’s

reaction when heated with concentrated base? (1) (CH₃)₃C – CHO (2) (CH₃)₂CHCHO (3) CH₃CHO (4) C₆H₅CH₂CHO

52. Which of the following is not a condensation polymer? (1) Nylon-6, 6 (2) Natural rubber

(3) Terrylene (4) Bakelite

53. The mixture of equal masses of SO₃ and O₂ gases is allowed to effuse through an orifice. The relative rate of effusion 3 2 SO O r r is (1) 1 5 (2) 2 2 5 5 (3) 2 5 (4) 2 5 54. Bronze is a mixture of (1) Pb – Zn (2) Pb + Sn (3) Cu + Sn (4) Cu + Zn 55. If 2 I /I E   0.50 V and 2 3 I /I E   0.20 V then 3 I /I E  is (1) 0.30 V (2) 0.65 V (3) 1.30 V (4) –0.067 V

56. The correct order of hybridisation of the central atom in the following species NF₃, BF₃, PF₅, [SiF₆]2– _is

(1) sp2 _sp3 _sp3_d2 _sp3_d

(2) sp3 _sp2 _sp3_{d sp}3_d2

(3) sp2 _sp3 _sp3_{d sp}3_d2

(4) sp3 _sp2 _sp3_d2 _sp3_d3

57. A binary solid consisting A+ _{and B}– _{has structure with}

B– _{ions consisting the lattice and A}+ _{ions occupying}

25% tetrahedral holes. The formula of the solid is

(1) AB (2) A₂B

(3) AB₂ (4) AB₄

58. In the reaction sequence

CH₃ – C  C – H CH MgBr3 CH₄ + A _{(ii) H O/H}(i) CO₂ 2 B.

B will be

(1) CH₃ – C  C – CH₃ (2) CH₃ – C  C – MgBr (3) CH₃ – CH = CH – COOH (4) CH₃ – C  C – COOH

59. In the first order reaction the concentration of reactants decrease from 2 M to 0.5 M in 20 minutes. The value of specific rate constant is

(1) 69.32 min–1 _{(2) 6.932 min}–1

(3) 0.6932 min–1 _{(4) 0.06932 min}–1

60. The most stable carbocation among the following is

(1) CH3 CH2 + (2) CH CH2 + CH3 CH3 (3) OCH3 CH2 + (4) NO2 CH2 +

61. Which of the following inert gas has the highest value of electron gain enthalpy?

(1) Ne (2) Kr (3) Xe (4) He 62. The compound COOH OCOCH₃ is used as (1) Antiseptic (2) Antibiotic (3) Analgesic (4) Pesticide

63. The K_sp of Ag₂CrO₄ is 1.1 × 10–12 _{at 258 K. The}

solubility (in mol/L) of Ag₂CrO₄ in a 0.1 M AgNO₃ solution is

(1) 1.1 × 10–11 _{(2) 1.1 × 10}–10

(3) 1.1 × 10–12 _{(4) 1.1 × 10}–9

64. The correct sequence of reagents used for conversion of aniline into benzylamine (Ph – CH₂ – NH₂) is (1) NaNO₂/HCl, Cu₂(CN)₂/HCN, Sn/HCl (2) NaNO₂/HCl, CuCN/H₃O+

(3) NaNO₂/HCl, Cu+_/H

3PO3, CH3NH2

65. Compound having the lowest melting point is

(1) LiCl (2) CsCl

(3) RbCl (4) KCl

66. How many monochlorinated products are possible for 2, 3-dimethyl butane?

(1) 2 (2) 3

(3) 4 (4) 5

67. Which one is the correct IUPAC name of the following?

OH Br (1) 1-Bromo-5-hydroxycyclohexane (2) 2-Bromo-4-hydroxycyclohexane (3) 4-hydroxycyclohexene chlorine (4) 3-bromocyclohex-3-en-1-ol

68. An acid HA ionises as HA_HA. The pH of 1 M solution is 4. Its dissociation constant would be

(1) 5 (2) 5 × 10–8

(3) 1 × 10–4 _{(4) 1 × 10}–8

69. One mole of magnesium nitride on the reaction with an excess of water gives

(1) Two moles of ammonia (2) One mole of nitric acid (3) One mole of ammonia (4) Two moles of nitric acid

70. Which halide will not react with benzene in presence of anhydrous AlCl₃?

(1) CH₃CHClCH₃ (2) C₆H₅CH₂Cl (3) C₆H₅Cl (4) CH₃CH₂CH₂Cl 71. Which of the following has highest value of Ka?

(1) CH₃COOH (2) CF₃COOH (3) CI₃COOH (4) CBr₃COOH 72. Strongest base is (1) H | N (2) N (3) H | N (4) O

73. Which of the following species is diamagnetic in nature?

(1) H₂– _{(2) H}

2+

(3) H₂ (4) He₂2+

74. Which of the following on thermal decomposition yields a basic as well as acidic oxide?

(1) NaNO₃ (2) KClO₃

(3) CaCO₃ (4) NH₄NO₃

75. Which of the following will form tribromoderivatives of phenol? (1) OH Br H O 2 2 (2) CH₃ OH Br H O₂ 2 (3) OH Br CS 2 2 (4) OH Br H 2 2O CH3

76. What mass of non-volatile solute (molecular mass 40 g/mol) should be dissolved in 114 g octane to reduce its vapour pressure to 80%?

(1) 8 g (2) 4 g

(3) 2 g (4) 16 g

77. A hydrocarbon C₅H₈ consumes two moles of hydrogen and on ozonolysis it produces 2-oxopropanal and methanal. Then the hydrocarbon is

(1) CH₂ = CH – CH = CH₂ (2) CH – C = CH – CH = CH_{3 2} CH3 (3) CH₃ – CH = CH₂ (4) _{CH = C – CH = CH2 2} CH3

78. 2Cu₂O(s) + Cu₂S (s)  6Cu(s) + SO₂(g)

The species which acts as a reductant in the above reaction is

(1) Cu₂O (2) Cu₂S

(8) 79. The heat of neutralization of four acids A, B, C and D

are –13.7, –9.4, –11.2 and –12.4 kcal respectively. When they are neutralized by a common base. The acidic character obeys the order

(1) A > B > C > D (2) A > D > C > B (3) D > C > B > A (4) D > B > C > A

80. Which of the following is not a condensation polymer?

(1) Glyptal (2) Dacron (3) Nylon-66 (4) PTFE 81. CHO (CH CO) O3 2 CH COONa Pyridine3 P. The product P is (1) CH – CH COOH_{2 2} (2) CH – COOH₂ (3) CH = CH – COOH (4) CH = CH – CHO

82. Given Eº_Cr3_/Cr  0.72 V, E_{Fe /Fe}º 3  0.42 V. The

potential for the cell Cr|Cr3+_{(0.1 M)|Fe}3+_{(0.01 M)|Fe is}

(1) 0.026 V (2) 0.336 V (3) –0.339 V (4) 0.26 V

83. Ease of oxidation in the following compounds will be

I. NO2 II. CH3 III. (1) I > II > III (2) III > II > I (3) I > III > II (4) II > III > I 84. Consider the following reaction sequence

2 2

H HNO

3 2

Ni

A B CH CH OH The starting component A is

(1) CH₃CN (2) CH₃NC (3) C₂H₅CN (4) CH₃NO₂

85. The equilibrium 2SO₂(g) + O₂(g) _ 2SO₃(g) shifts in forward direction if

(1) Catalyst is added

(2) More amount of reactants are used (3) Small amount of reactants are used

(4) An adsorbent is used to remove SO₃ as soon as it is formed

86. K₂Cr₂O₇ will act as an oxidising agent in (1) Acidic medium only

(2) Basic medium only (3) Neutral medium only (4) In all above three medium 87. Strength of H₂O₂ is (1) V 11.6 M (2) V 5.6 N (3) V 11.6 N (4) Both (1) & (2)

88. Which of the following is not characteristic of KMnO₄ (1) It acts as an oxidising agent only

(2) It acts as self indicator

(3) KMnO₄ is purple colour due to d–d transition (4) KMnO₄ shows the n-factor of 5 in acidic medium 89. How many sp3 _{hybrid orbitals are present in borax?}

(1) 1 (2) 2 (3) 3 (4) 4 90. B₂H₆ contains (1) 2 centre 2e– _bond (2) 3 centre 2e– _bond (3) 3 centre 4e– _bond (4) (1) & (2) only

91. In blue vitriol the number of water of crystalisation is

(1) 1 (2) 2

(3) 3 (4) 4

92. The formula of plaster of paris is (1) CaSO₄.1

2H2O (2) CaSO4.2H2O

(3) CaSO₄.3

2H2O (4) CaSO4.5H2O

93. Bleaching action of bleaching powder is due to

(1) Cl (2) O

94. Amphoteric oxide combinations are in

(1) ZnO, K₂O, SO₃ (2) ZnO, P₂O₅, Cl₂O₇ (3) ZnO, Al₂O₃, SnO₂ (4) PbO₂, SnO₂, SO₃ 95. The heat of formation for CO₂(g), H₂O(g) and CH₄(g)

are –400 kJ mol–1_{, –280 kJ mol}–1 _{and –70 kJ mol}–1_.

The heat of combustion of CH₄ in kJ mol–1 _is

(1) 890 (2) –160

(3) –890 (4) –90

96. Which of the following element has highest electron affinity?

(1) F (2) Cl

(3) Br (4) I

97. Number of peaks in curve of radial probability function with distance r from nucleus is

(1) n – l (2) n – l + 1

(3) l (4) n – 1

98. Number of H atom directly linked with P atom in H₄P₂O₅ is/are

(1) 1 (2) 2

(3) 3 (4) 4

99. Which of the following sets of ions represent a collection of isoelectronic species?

(1) C₂2–_{, O} 2 –_{, CO and NO} (2) NO+_{, C} 22–, CN– and N2 (3) Li+_{, Na}+_{, Mg}2+ _{and Ca}2+ (4) N3–_{, O}2–_{, F}– _{and S}2– 100. Structure of IF₇ is a (1) Square pyramidal (2) Trigonal bipyramidal (3) Octahedral (4) Pentagonal bipyramidal

MATHEMATICS

101. The perimeter of a right triangle is _{12 8 3} units. The sum of squares of the 3 sides is 294 sq. units. Then the value of ⎡ ⎤_{⎢ ⎥3}

⎣ ⎦ where  denotes the area of

the given triangle and [.] denotes the greatest integer function.

(1) 2 (2) 3

(3) 4 (4) 1

102. The number of solutions of



sinxcosx



tan2x 1in the interval



0,4



is

(1) 3 (2) 5

(3) 7 (4) 9

103. The number of integral values of x satisfying the equation



log₇x

 

2 log₇x



2 is

(1) 3 (2) 5

(3) 6 (4) 7

104. The number of integers satisfying the inequality 1 6 x x  x is (1) 3 (2) 7 (3) 8 (4) 9 105. If the value of 4 4 1 ₁₁₉ x x

  , then the value of

3 3 1 – x x ⎡ ⎤ ⎢ ⎥

⎣ ⎦ is equal to (where [.] denotes the greatest

integer function)

(1) 12 (2) 18

(3) 24 (4) 36

106. The domain of f(x) is (0, 1), let the domain of y = f(ex_{) + f(ln|x|) be (a, b), then [a + b – 0.7] is}

equal to (where [.] denotes the greatest integer function)

(1) – 5 (2) – 4

(3) 0 (4) 3

107. In a triangle ABC, if A = 30° and 2 3 2 – 1

2 3 – 2 1 b c     

then angle B is equal to

(1) 97.5° (2) 52.5°

(3) 15° (4) 75°

108. The number of 6-digits numbers that can be made with the digits 0, 1, 2, 3, 4 and 5 so that even digits occupy odd places, without repetition, is

(1) 24 (2) 36

(10) 109. The sum of the series ₂9 ₃13 ₄17

5 .2.1 5 .3.2 5 .4.3  ... to   is equal to (1) 1 (2) 9 5 (3) 1 5 (4) 2 5 110. If





18 1 – 8 9 i i x  

∑

and





18 ₂ 1 – 8 45 i i x  

∑

, then the

standard deviation of variables x₁, x₂ - - - - -, x₁₈ is (1) 4 9 (2) 9 4 (3) 3 2 (4) 3 8

111. If (2a, 3b) is the mid-point of a chord passing through the vertex of parabola y2 _{= 4x, then}

(1) 9b2 _{= 8a (2) 9b}2 _{= 4a} (3) 9b2 _{= 16a (4) 3b}2 _{= 8a} 112. The negation of (p  r)  (q  p) is (1) (p  ~ r)  (q  ~ p) (2) (p  ~ r)  (q  ~ p) (3) (p  ~ r)  (q  ~ p) (4) (p  ~ r)  (q  ~ p)

113. The circles x2 _{+ y}2 _{+ 4x + c = 0 and x}2 _{+ y}2 _{+ 4y}

+ c = 0 touch when the value of C is

(1) 0 (2) 1

(3) 2 (4) 4

114. The length of the latus rectum of the parabola x = ay2 _{+ by + c is} (1) 4 a (2) 3 a (3) 1_a (4) _{4 a}1 115. The equation 2 2 1 2 5 x _ y _     represents an ellipse for (1)  > 5 (2)  < 2 (3) 2 <  < 5 (4)   

116. General equation of a plane which is parallel to x-axis is

(1) ax + d = 0 (2) ax + by + d = 0 (3) by + cz + d = 0 (4) ax + cz + d = 0

117. The locus of the mid-point of a chord of the circle x2 _{+ y}2 _{= 4 which subtends a right angle at the}

origin is

(1) x + y = 2 (2) x2 _{+ y}2 _{= 1}

(3) x2 _{+ y}2 _{= 2 (4) x + y = 1}

118. If cot 1 cot 1 cot 1

2  _x  _y  _z , then x + y + z equals (1) xyz (2) xy + yz + zx (3) 2xyz (4) 0 119. If x = ylnxy, then dx dy equals (1) ( ) ( ) y x y x x y   (2) (( )) x x y y x y   (3) ( ) ( ) y x y x x y   (4) (( )) x x y y x y   120. The value of 1 ln 0 lim (cosec ) x x  x is (1) 1 (2) –1 (3) e (4) 1 e

121. If the system of equations a3_{x + (a + 1)}3_{y + (a + 2)}3_{z = 0,}

ax + (a + 1)y + (a + 2)z = 0, x + y + z = 0 has a non-zero solution, then value of a is

(1) –1 (2) 0

(3) 1 (4) 2

122. If A is square matrix of order n, then adj(adj. (A)) is equal to

(1) |A|n–1 _{A (2) |A|}n–2 _A

(3) |A|n–2 _{I (4) |A|}n _A

123. If cos tan



1



sin cot



1 3







y , then

(1) 4 5 y  (2) 2 5 y  (3) 2 5 y  (4) 2 10 11 y 

124. The angle at which the curve y = kekx _{intersects the}

y-axis is

(1) tan–1 _(k2_{) (2) cot}–1 _(k2₎

(3) _sec1



_{1 k} 4



₍₄₎ 2 

125. 7 7 1 (1 ) x dx x x  

∫

equals (1) ln 2ln(1 7) 7 x x C (2) ln 2ln(1 7) 7 x x C (3) ln 2ln(1 7) 7 x x C (4) ln 2ln(1 7) 7 x x C 126. Let y = {x}[x] _{where {x} denotes the fractional part of}

x and [x] denotes greatest integer  x, then

3 0 

∫

ydx (1) 5 6 (2) 2 3 (3) 1 (4) 11 6 127. 2 cos 1 x x I dx a    

∫

equals (1) 4  (2)  (3) 3  (4) 2 

128. For all a, b  R, the function f(x) = 3x4 _{– 4x}3 _{+ 6x}2

+ ax + b has (1) No extremum

(2) Exactly one extremum (3) Exactly two extremum (4) Exactly three extremum 129. 2 ln(6 )x dx x

∫

is equal to (1) 1 ln(6 )₈⎡_⎣ x2 ⎤ _⎦3 C (2) 1 ln (6 )2 2 4⎡⎣ x ⎤ ⎦ C (3) 1 ln(6 )2 2⎡⎣ x ⎤ ⎦ C (4) 4 2 1 ln(6 ) 16⎡⎣ x ⎤ ⎦ C 130. ₃ 1 1 dx x  x

∫

equals (1) ln



3x 1 x 1



C (2) 1/2 1/3 1/6 (1 ) (1 ) 6 log(( 1) 1 3 2 x x _{x C} ⎛  _  _{   }⎞ ⎜ ⎟ ⎝ ⎠ (3) 1/2 1/6 (1 ) 6 log(( 1) 1 3 x _{x C} ⎛  _{   }⎞ ⎜ ⎟ ⎝ ⎠ (4) 1/2 1/3 1/6 1/6 (1 ) (1 ) 6 (1 ) log(( 1) 1) 3 2 x x _{x x C} ⎛  _  _{    } ⎞_ ⎜ ⎟ ⎝ ⎠ 131. lim 1 1 1 ... 1 1 2 n na na na nb ⎡ _{   } ⎤ ⎢ _{ } ⎥ ⎣ ⎦ is equal to (1) ln b⎛ ⎞⎜ ⎟_a ⎝ ⎠ (2) ln a⎛ ⎞⎜ ⎟⎝ ⎠b (3) ln a (4) ln b

132. The area of the region under the graph of y = xe–ax

as x varies from 0 to , where a is a positive constant, is (1) 1 a (2) 2 1 1 a a (3) 2 1 1 a a (4) 2 1 a

133. The solution of the differential equation

2 1 2 [ sin 1] dy dx  xy x y  is (1) _x2_(cosy2_siny2_2cey2_{) 2} (2) _y2_(cosx2_siny2_2cey2_{) 2} (3) _x2_(cosy2_siny2_ey2_{) 4 c} (4) x2(cosy2siny22 ) 2c  134. If _a_2b_3c_0, then _{a b b c c a}         ( ), k a b where k is equal to (1) 0 (2) 1 (3) 2 (4) 3

135. The unit vector perpendicular to the lines

1 x₃1 y₁2 z₂1 L       and 2 2 2 3 1 2 3 x y z L       is (1) ˆ ₇ˆ ₇ˆ 99 i j k    (2) ˆ ₇ˆ ₅ˆ 5 3 i j k    (3) ˆ 7ˆ 5ˆ 5 3  i j k (4) 7ˆ 7ˆ ˆ 99   i j k

136. A pair of dice is thrown five times. The probability that doubles appear at least 3 times is

(1) 23 324 (2) 23 162 (3) 23 648 (4) 17 162

(12)

  

137. A and B are events such that A  B , P(A | B) = P(B | A) then

(1) A = B (2) P(A) = P(B)

(3) A and B are independent (4) All of these

138. If the vector _{a b c}_{, ,}  form the sides BC, CA, AB respectively of ABC, then

(1) _{a b b c c a}_. _{ .}  _{ . 0} (2) _{a b b c c a}          ₀ (3) _{a b b c c a}_. _{ .}  _{ .}

(4) _{a b b c c a}_{     }     ₀

139. Number of divisors of the forms (4n + 2), n W (set of whole numbers) of the integer 240 is

(1) 4 (2) 8

(3) 10 (4) 3

140. The area bounded by the curves y 



x1 ,









2 1 y  x and 1 4 y  is (1) 1 3 (2) 2 3 (3) 1 4 (4) 1 5

141. A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then mean of the remaining item is

(1) 6.5 (2) 5.5

(3) 4.5 (4) 5.0

142. If tan2 2tan2 1, then cos2 sin2 is equal to (1) 1 (2) 2 (3) –1 (4) 0 143. If x1, y1, z1 are in G.P., then 1 , 1 ln x 1 _, 1 1 ln 1 ln y  z are in (1) A.P. (2) H.P. (3) G.P.

(4) None of A.P., G.P. and H.P.

144. If A and B are two sets consisting of 5 and 3 elements respectively such that

((  ) (  )) 2

n A B B A , then number of elements in the power set of (A B ) ( B A )are

(1) 219 _{(2) 2}21

(3) 220 _{(4) 2}22

145. Lines OA and OB are drawn from origin O with direction cosines proportional to (1, 2, –1) and (3, –2, 3) respectively. The direction ratios of the normal to the plane OAB are

(1) (2, –3, –4) (2) (–4, 3, –2) (3) (4, –3, –2) (4) (4, 3, 2) 146. Solution of the differential equation

ln dy 4x 2y 2, (1) 1,y dx ⎛ _{⎞    } ⎜ ⎟ ⎝ ⎠ is (1) 2e2(y1) e4xe4 (2) 2e2(y1) e4( 1)x (3) 2e2(y1) 2e4x (4) 2e2(y1) 4e4x

147. A ball is thrown straight up from the top of 64 feet tall building with initial speed of 48 feet per second. The height of the ball as a function of time can be modelled by the function h t

 

 16t248t64. How long will it take for the ball to hit the ground?

(1) 2 s (2) 4 s

(3) 6 s (4) 1 s

148. A train of length 150m, travelling at 20m/s overtakes another train of length 350 m, travelling at 10m/s in the same direction. The time taken by first train to pass the second train is

(1) 50 s (2) 40 s

(3) 30 s (4) 35 s

149. If the resultant of two forces of magnitude P and

3

P acting on a particle is of magnitude 2P, then the angle between their line of action is

(1) 60° (2) 75° (3) 90° (4) 120° 150. If – – – y y y y y y a be b ce c de a be b ce c de  _  _  , then a, b, c, d are (1) in A.P. (2) in G.P.

1. (4) 2. (4) 3. (4) 4. (4) 5. (2) 6. (1) 7. (3) 8. (1) 9. (2) 10. (3) 11. (3) 12. (2) 13. (4) 14. (3) 15. (3) 16. (4) 17. (4) 18. (4) 19. (3) 20. (3) 21. (4) 22. (2) 23. (2) 24. (1) 25. (2) 26. (4) 27. (2) 28. (4) 29. (4) 30. (3) 31. (1) 32. (3) 33. (3) 34. (2) 35. (4) 36. (1) 37. (3) 38. (2) 39. (4) 40. (2) 41. (3) 42. (2) 43. (3) 44. (1) 45. (4) 46. (3) 47. (1) 48. (4) 49. (1) 50. (2) 51. (1) 52. (2) 53. (2) 54. (3) 55. (2) 56. (2) 57. (3) 58. (4) 59. (4) 60. (3) Ph.: 011-47623456 Fax : 011-47623472

MOCK TEST

for

UPSEE-2016

ANSWERS

Time : 3 Hrs.

MM : 600

61. (1) 62. (3) 63. (2) 64. (1) 65. (1) 66. (1) 67. (4) 68. (4) 69. (1) 70. (3) 71. (2) 72. (1) 73. (3) 74. (3) 75. (1) 76. (1) 77. (4) 78. (2) 79. (2) 80. (2) 81. (3) 82. (4) 83. (4) 84. (1) 85. (4) 86. (1) 87. (4) 88. (3) 89. (2) 90. (4) 91. (1) 92. (1) 93. (1) 94. (3) 95. (3) 96. (2) 97. (1) 98. (2) 99. (2) 100. (4) 101. (2) 102. (2) 103. (3) 104. (2) 105. (4) 106. (1) 107. (1) 108. (1) 109. (3) 110. (3) 111. (2) 112. (1) 113. (3) 114. (3) 115. (4) 116. (3) 117. (3) 118. (1) 119. (2) 120. (4) 121. (1) 122. (2) 123. (2) 124. (2) 125. (3) 126. (4) 127. (4) 128. (2) 129. (2) 130. (4) 131. (1) 132. (4) 133. (1) 134. (3) 135. (2) 136. (3) 137. (2) 138. (2) 139. (1) 140. (1) 141. (4) 142. (4) 143. (2) 144. (2) 145. (1) 146. (1) 147. (2) 148. (1) 149. (3) 150. (2)