VITEEE Solved Sample Paper

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VIT (formerly Vellore Institute of Technology) has been conducting an entrance examination, VITEEE (VIT Engineering Entrance Examination – 2013) for admission to B.Tech. degree programs. VIT was the first educational institution in India to get international accreditation for its programs. Based on the performance in VITEEE 2013 entrance exam candidates will be admitted in 1st year of engineering degree programs leading to the award of Bachelor of Engineering (B.E) and Bachelor of Technology (B.Tech)

VITEEE Question Bank

Instrucrion:

The question paper will contain 3 [Three] parts as indicated below. All Questions will be of OBJECTIVE TYPE

PART-I – Physics             40 questions
PART-II – Chemistry        40 questions
PART-III – Mathematics  40 questions

No Negative Marking

PHYSICS (Question 1 to 40)

Q1 .One centimeter on the main scale of venire calipers is divided into ten equal parts. If 10 divisions of venire scale coincide with 8 small divisions of the main scale, the least count of the calipers is :

1. 0.01 cm
2. 0.02 cm
3. 0.05 cm
4. 0.005 cm

Ans: 1

Q2. The relative density of the material of a body is the ratio of its weight in air and the loss of its weight in water. By using a spring balance, the weight of the body in air measured to be(5.00 0.05 N while in water it reads (4 ± 0.05)N . Then the maximum possible percentage error in relative density is :

1. 11 %
2.10 %
3. 9%
4. 7%

Ans: 4

Q3. The pairs of physical quantities that have the same dimensions are :

1. Reynolds number and coefficient of friction
2. Latent heat and gravitational potential
3. Curie and frequency of light wave
4. Planck’s constant and torque

Ans: 2

 1.The object moves with constantly increasing velocity from O to A and then it moves with constant velocity
2. Velocity of the object increases uniformly
3. Average velocity is zero
4. The graph shown is impossible

 Ans: 3

Q5.  Equation  of  displacement  for  any  particle is  s  = 3t³  + 7t²  + 14t  + 8m.  Its acceleration at time t = 1 sec is: 

1. 10 m/s²
2. 16 m/s²
3. 25 m/s²
4. 32 m/s²

Ans: 4

Q6.  A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be :

1. 100 m/s
2. 55 m/s
3. 550 m/s
4.660 m/s

Ans: 2

Q7. A satellite revolves around the earth in an elliptical orbit. Its speed:

1. Is the same at all points in the orbit
2. Is greatest when it is closest to the earth
3. Is greatest when it is farthest from the earth
4. Goes on increasing or decreasing continuously depending upon the mass
of the satellite

Ans: 2

Q8. A spherical planet has a mass M0 and diameter D0. A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity which is proportional to:

1. M_o /D_o²
2. 4mM_o /D_o²
3.  4M_o /D_o²
4. mM_o/Do²

Ans: 3

 Q9. A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The relative densities of concrete and sawdust are 2.4 and 0.3 respectively. For this sphere to float with its entire volume submerged under water, the ratio of the mass of concrete to the mass of sawdust will be

1. 8
2. 4
3. 3
4. Zero

 ^Ans: 2

 Q10. The rate of flow of a liquid through a capillary tube under a constant pressure head is Q. If the diameter of the tube is reduced to half and its length is doubled, then the new rate of flow of liquid will be

1.Q/4
2.Q/8
3.16Q
4.Q/32

Ans: 4

Q11. A Coil of inductance 300 mH and resistance 2Ω is connected to a source of voltage 2V. The current reaches half of its steady of its steady state value in

1. 0.15 s
2. 0.3 s
3. 0.5 s
4. 0.1 s

 ^Ans : 4

 Q12. In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current In primary is 4A then that in the secondary is

1. 4A
2. 2A
3. 6A
4. 10A

 ^Ans : 2

 Q13. In an LCR series ac circuit, the voltage across each of the components, L, C and R is 50V, the voltage across the LC combination will be

1.50 V
2.50√2 V
3.100 V
4. 0 V

Ans: 4

Q14. According to kinetic theory of gases the temperature of a perfect gas is

1. Independent of the kinetic energy of the molecules.
2. Inversely proportional to kinetic energy of the molecules
3. Directly proportional to both kinetic energy and potential energy of the
molecules.
4. Directly proportional to kinetic energy of the molecules.

 Ans: 4

Q15. At absolute zero temperature

1. The molecule of gas will have the same velocity as at 0°C
2. The molecule of gas will have the same velocity as at 100°C
3. The molecule of the gas will have zero velocity.
4. Two molecule of the gas have very high velocities

 Ans: 3

Q16.A vessel contains 1 mole of O2 gas (molar mass 32) at a temperature T. The pressure of the gas is P. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of

1. P/8
2. P
3. 2P
4. 8P

Ans: 3

Q17. An object is placed at a distance of 12 cm from a convex lens on its principal axis and a virtual image of certain size of formed. On moving the object 8 cm away from the lens, a real image of the same size as that of virtual image is formed. The focal length of the lens in cm is

1. 15
2. 16
3. 17
4. 18

Ans: 2

Q18. An object is placed at a distance (f/2) from a convex lens. The image will be

1. at one of the foci, virtual and double in size
2. at f, real and inverted
3. at 2f, virtual and erect
4. at (3/2) f, real inverted

Ans: 1

Q19. In Young’s interference experiment, the central bright fringe can be identified due to the fact that it

1. Has grater intensity than other fringes which are bright
2. Is wider than the other bright fringes
3. Is narrower than the other bright fringes
4.Can be obtained by using white light instead of monochromatic light

Ans: 4

Q20. A certain piece of silver of given mass is to be made like a wire. Which of the following combination of length (L) and the area of cross-sectional (A) will lead to the smallest resistance

1. L and A
2. 2L and A/2
3. L/2 and 2A
4. Any of the above, because volume of silver remains same

Ans: 3

Q21. The drift velocity of free electrons in a conductor is ‘v’ when a current ‘i’ is flowing in it. If both the radius and current are doubled, then drift velocity will be

1. V
2. V/2
3. V/4
4. V/8

Ans: 2

Q22.Two identical conductors of copper and aluminum are placed in an identical electric fields. The magnitude of induced charge in the aluminum will be

1. Zero
2. Greater than in copper
3. Equal to that in copper
4. Less than in copper

 Ans: 3

Q23. An inductor ‘L’ is allowed to discharge through a capacitor ‘C’. The emf induced across the inductor, when the capacitor is fully charged, is

1. maximum
2. minimum
3. zero
4. infinite

 Ans: 1

Q24. An inductor coil having some resistance is connected to an ac source. Which of the following have zero average value over a cycle:

1. induced emf in the inductor
2. current
3. both 1 and 2
4. neither 1 or 2

 Ans: 3

Q25. A proton (or charged particle) moving with velocity v is acted upon by electric field E and magnetic field B. The proton will move undeflected if

1. E is perpendicular to B
2. E is parallel to v and perpendicular to B
3. E, B and v are mutually perpendicular and n=E/B
4. E and B both are parallel to v

Ans: 3

Q26. If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is

1. 0.41
2. 0.51
3. 0.61
4. 0.71

Ans: 3

 Q27. The maximum speed of a car on a road-turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4, will be

1. 10.84 m/sec
2. 9.84 m/sec
3. 8.84 m/sec
4. 6.84 m/sec

Ans: 1

Q28. Which of the following statements is false for a particle moving in a circle with constant angular speed

1. The velocity vector is tangent to the circle
2. The acceleration vector is tangent to the circle
3. The acceleration vector points to the centre of the circle
4. The velocity and acceleration vectors are perpendicular to each other

Ans: 2

Q29. Two blocks of masses 10kg and 4 kg are connected by a spring of negligiblemass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/sec to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

1. 30 m/sec
2. 20 m/sec
3. 10 m/sec
4. 5 m/sec

Ans: 3

Q30. A p-n-p transistor in the common base mode has a dynamic input resistance of 75W. If the current gain of the amplifier is 0.98, find the voltage gain when the load resistance in the collector circuit is 7.5 kW.

1. 49
2. 98
3. 980
4. 9800

Ans: 2

Q31. The mass defect per nucleon is called:

1. binding energy
2. packing fraction
3. ionization energy
4. excitation energy

Ans: 2

Q32. Mass defect of an atom refers to:

1. inaccurate measurement of mass of nucleons
2. mass annihiliated to produce energy to bind the nucleons
3. packing fraction
4. difference in the number of neutron and protons in the nucleus

Ans: 2

Q33. Heavy water is used as a moderator in a nuclear reactor. The function of the moderator is

1. to control the energy released in the reactor
2. to absorb neutrons and stop the chain reaction
3. to cool the reactor
4. to slow down the neutron to thermal energies

Ans: 4

Q34. Two wires A and B of same material and mass have their lengths in the ratio 1 : 2. On connecting them in parallel to the same source, the rate of heat dissipation in B is found to be 5W. The rate of heat dissipation in A is

1. 10W
2. 5W
3. 20W
4. None of these

Ans: 3

Q35. Three electric bulbs of rating 60W each are joined in series and then connected to electric mains. The power consumed by these three bulbs will be

1. 180 W
2. 60 W
3. 20 W
4.20/3 W

Ans: 3

Q36. The negative Zn pole of a Daniel cell, sending a constant current through acircuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemical equivalent of Zn and Cu are 32.5 and 31.5 respectively, the increase in the mass of the positive Cu pole in this time is

1. 0.242 g
2. 0.190 g
3. 0.141 g
4. 0.126 g

Ans: 4

Q37. If Young’s interference experiment is performed using two separate identical sources of light instead of using two slits and one bulb, then

1. Interference fringes will be brighter
2. Interference fringes will be coloured
3. Interference fringes will be darker
4. No fringes will be obtained

Ans: 4

Q38. There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is C1, while the centre of mass of the ‘compartment plus passengers’ system is C2. If the passengers move about inside the compartment.

1. Both C1 and C2 will move with respect to the ground
2. Neither C1 nor C2 will move with respect to the ground
3. C1 will move but C2 will be stationary with respect to the ground
4. C2 will move but C1 will be stationary with respect to the ground.

Ans: 4

 Q39. A satellite revolves around the earth in an elliptical orbit. Its speed: 

1. Is the same at all points in the orbit
2. Is greatest when it is closest to the earth
3. Is greatest when it is farthest from the earth
4. Goes on increasing or decreasing continuously depending upon the mass of the satellite

Ans: 2

Q40. A rigid cubical block A of mass M and side L is fixed rigidly on to another cubical block of the same dimensions and of modulus of rigidity n such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is 

1. 2 π √MnL
2. 2 π √(Mn/L)
3. 2 π √(ML/n)
4. 2 π √(M/nL)

Ans: 4

                                      Chemistry (Question 1 to 40)

 Q1.At identical temperature and pressure, the rate of diffusion of hydrogen gas is 3√3 times that of a hydrocarbon having molecular formula C_nH_2n-2 . What is the value of ‘n’ ?

 (A) 1                (B) 4               (C) 3               (D) 8

Ans: B

Q2. In the hydrolysis of an organic chloride in presence of large excess of water; RCI + H2O –> ROH + HCl

(A) Molecularity and order of reaction both are 2
(B) Molecularity is 2 but order of reaction is 1
(C) Molecularity is 1 but order of reaction is 1
(D) Molecularity is 1 and order of reaction is also 1

Ans: B

Q3. The potential of a hydrogen electrode at pH = 10 is

(A) 0.59 V        (B) 0.00 V        (C) –0.59 V      (D) –0.059

Ans: C

Q4. In the reaction of sodium thiosulphate with I₂ in aqueous medium the equivalent weight of sodium thiosulphate is equal to

(A) molar mass of sodium thiosulphate
(B) the average of molr masses of Na₂S₂O₃ and I₂
(C) half the molar mass of sodium thiosulphate
(D) molar mass of sodium thiosulphate × 2

Ans: A

Q5. 0.1 (M) HCI and 0.1 (M) H2SO4 each of volume 2ml are mixed and the volume is made up to 6 ml by adding 2ml of 0.01 (N) NaCl solution. The pH of the resulting mixture is 

(A) 1.17           (B) 1.0             (C) 0.3             (D) log 2 – log 3

Ans: B

Q6. The molarity of a NaOH solution by dissolving 4 g of it in 250 ml water is 

(A) 0.4 M         (B) 0.8 M         (C) 0.2 M         (D) 0.1 M

Ans: A

Q7. Which one of the following characteristics belongs to an electrophile?

(A) It is any species having electron deficiency which reacts at an electron rich C-centre
(B.) It is any species having electron enrichment, that reacts at an electron deficient C-centre
(C) It is cationic in nature
(D). It is anionic in nature

Ans: A

Q8. Which one of the following methods is used to prepare Me₃COEt with a good yield?

(A) Mixing EtONa with Me₃CCl
(B) Mixing Me₃CONa with EtCl
(C) Heating a mixture of (1:1) EtOH and Me₃COH in presence of conc. H₂SO₄
(D) Treatment of Me₃COH with EtMgI

Ans: B

Q9. 58.5 gm of NaCl and 180gm of glucose were separately dissolved in 1000ml of water. Identify the correct statement regarding the elevation of boiling point (b.p.) of the resulting solutions.

A) NaCl solution will show higher elevation of b.p.
B) Glucose solution will show higher elevation of b.p.
C) Both the solution will show equal elevation of b.p.
D) The b.p. elevation will be shown by neither of the solutions

Ans: A

Q10. Which of the following will show a negative deviation from Raoult’s law?

A)Acetone-benzene
B)Acetone-ethanol
C)Benzene-methanol
D)Acetone-chloroform

Ans: D

Q11. In a reversible chemical reaction at equilibrium, if the concentration of any one of the reactants is doubled, then the equilibrium constant will

A). also be doubled
B.) be halved
C.) remains the same
D). becomes one-fourth

Ans:  C

Q12. Identify the correct statement from the following in a chemical reaction.

A). The entropy always increases
B) The change in entropy along with suitable change in enthalpy decides the fate of a reaction
C) The enthalpy always decreases
D) Both the enthalpy and the entropy remain constant

Ans: B

Q13. Which one of the following is wrong about molecularity of a reaction?

A) It may be whole number or fractional
B) It is calculated from reaction mechanism
C) It is the number of molecules of the reactants taking part in a single step chemical reaction
D)It is always equal to the order of elementary reaction.

Ans: A

Q14. Upon treatment with I₂ and aqueous NaOH, which of the following compounds will from iodoform?

A) CH₃CH₂CH₂CHO
B) CH₃CH₂COCH₂CH₃
C) CH₃CH₂CH₂CH₂CH₂OH
D) CH₃CH₂CH₂CH(OH)CH₃

Ans: D

Q15. Upon treatment with Al(OEt)₃ followed by usual reaction (work up), CH₃CHO will produce

A) Only CH₃COOCH₂CH₃
B) a mixture of CH₃COOH and EtOH
C) only CH₃COOH
D) only EtOH

Ans: A

Q16. Friedel-Craft’s reaction using MeCl and anhydrous AlCl₃ will take place most efficiently with

A) Benzene      B) Nitrobenzene          C) Acetophenone        D) Toluene

Ans: D

Q17. If a species has 16 protons, 18 electrons and 16 neutrons, find the species and its charge

(A) S^1-              (B) Si^2-                    (C) P^3-                  (D) S^2-

Ans: D

Q18. 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

Ans: C

Q19. Which one of the following contains P – O – P bond  

(A) Hypophosphorus acid
(B) Phosphorus acid
(C) Pyrophosphoric acid
(D) Orthophosphoric acid

Ans: C

Q20. Which of the following statements regarding ozone is not correct ?

(A) The Ozone molecule is angular in shape
(B) The Ozone is a resonance hybrid of two structures
(C) The Oxygen– Oxygen bond length in ozone is identical with that of molecular oxygen
(D) Ozone is used as germicide and disinfectant for the purification of air.

Ans: C

Q21. When a manganous salt is fused with a mixture of KNO₃ and solid NaOH the oxidation number of Mn changes from +2 to

(A) +4              (B) +3              (C) +6              (D) +7

Ans: C

Q22. Ortho-and para-hydrogens have 

(A) Identical chemical properties but different physical properties
(B) Identical physical and chemical properties
(C) Identical physical properties but different chemical properties
(D) Different physical and chemical properties

Ans: A

Q23. On mixing an alkane with chlorine and irradiating with ultra-violet light, it forms only one mono-chloro-alkane. The alkane is

(A) Propane                 (B) Pentane                 (C) Isopentane                        (D) Neopentane

Ans: D

Q24. What is obtained when nitrobenzene is treated sequentially with (i)NH₄Cl/Zn dust and (ii) H₂SO₄/Na₂Cr₂O₇?

(A) meta-chloronitrobenzene
(B) para-chloronitrobenzene
(C) nitrosobenzene
(D) benzene

Ans: C

Q25. Which of the following compounds shows evidence of the strongest hydrogen bonding?

(A) Propan–1–ol          (B) Propan–2–ol          (C) Propan–1,2–diol    (D) Propan–1,2,3–triol

Ans: D

Q26. When AgCl is treated with KCN

(A) Ag is precipitated
(B) a complex ion is formed
(C) double decomposition takes place
(D) no reaction takes place

Ans: B

Q27. A weak acid of dissociation constant 10^-5 is being titrated with aqueous NaOH solution. The pH at the point of one-third neutralisation of the acid will be

(A) 5 + log 2–log 3
(B) 5 –log 2
(C) 5 –log 3
(D) 5 –log 6

Ans: B

Q28. The equivalent weight of K₂Cr₂O₇ in acidic medium is expressed in terms of its molecular weight (M) as

A) M/3
B) M/4
C) M/6
D) M/7

Ans: C

Q29. Which of the following is correct?

A) radius of Ca²⁺ < Cl^– < S^2-
B) radius of Cl^– < S^2-< Ca²⁺
C) radius of S^2-= Cl^– = Ca²⁺
D) radius of S^2- < Cl^– < Ca²⁺

Ans: A

Q30. Radioactivity of a sample (z=22) decreases 90% after 10 years. What will be the half life of the sample?

(A) 5 years                   (B) 2 years                   (C) 3 years                   (D) 10 years

Ans: C

Q31. Upon treatment with Al(OEt)₃ followed by usual reaction (work up), CH₃CHO will produce

A) Only CH₃COOCH₂CH₃
B) a mixture of CH₃COOH and EtOH
C) only CH₃COOH
D) only EtOH

Ans: A

Q32. Boiling water reacts with C₆H₅N₂⁺Cl^– to give

(A) aniline                   (B) benzylamine                      (C) phenol                   (D) benzaldehyde

Ans: C

Q33. Aspirin is

(A) Acetyl salicylic acid
(B) Benzoyl salicylic acid
(C) Chloro benzoic acid
(D) Anthranilic acid

Ans: A

Q34. Which one of the following methods is used to prepare Me₃COEt with a good yield?

(A) Mixing EtONa with Me₃CCl
(B) Mixing Me₃CONa with EtCl
(C)Heating a mixture of (1:1) EtOH and Me₃COH in presence of conc. H₂SO₄
(D) Treatment of Me₃COH with EtMgI

Ans: D

Q35. When AgCl is treated with KCN

(A) Ag is precipitated
(B) a complex ion is formed
(C) double decomposition takes place
(D) no reaction takes place

Ans: B

Q36. Under identical conditions, the S_N1 reaction will occur most efficiently with

A) tert-butyl chloride
B) 1-chlorobutane
C) 2-methyl-1-chloropropane
D) 2-chlorobutane

Ans: A

Q37. Which one of the following is an example of co-polymer?

(A) Buna–S                  (B) Teflon                    (C) PVC            (D) Polypropylene

Ans: A

Q38. An equimolar mixture of toluene and chlorobenzene is treated with a mixture of conc. H₂SO₂ and conc HNO₃. Indicate the correct statement from the following.

A) p-nitrotoluene is formed in excess
B) equimolar amounts of p-nitrotoluene and p-nitrochlorobenzene are formed
C) p-nitrochlorobenzene is formed in excess
D) m-nitrochlorobenzene is formed in excess

Ans: A

Q39. The pK_a of a weak acid, HA is 4.80. The pK_b of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

A)7.01              B)9.22              C)9.58              D)4.79

Ans: A

Q40. The hydrocarbon which can react with sodium in liquid ammonia is

A)     CH₃CH=CHCH₃
B)     CH₃CH₂C=CCH₂CH₃
C)     CH₃CH₂C=CCH₂CH₂CH₃
D)     CH₃CH₂C=CH

Ans: D

Mathematics (Question 1 to 40)

Q1       Which of the following is incorrect?

a.         Volume of a rectangular solid = length x width x length
b.         Volume of a cube = (length of any face of the cube)³
c.         Volume of a right circular cylinder = (radius )². height
d.         Volume of a right prism = (Area of base). Height
e.         All are correct

Ans:  e

Q2       Find the solution set of   x + y = 5,     2 x – y = 7

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

Ans:  c

Q3       A square matrix A is symmetric if A = ?

a.   A^t               b.   A                c.   – A             d.   A^-1

Ans: d

Q4       How many numbers consisting of two digits can be formed from 2, 3 5,7. Each integer is to be used only once.

a.   10              b.   12              c.  14               d.  16

Ans: d

Q5    Find the angle of elevation of the sun when a  6m high pole makes shadow of length 2Ö3m on the horizontal plane.

a.         30⁰                   b.         45⁰                   c.         60⁰                   d.         90⁰

Ans: b

Q6       For any positive rational number k, and any real number c,  which of the following is incorrect

a.          c = k/4                   b.          c = c                  c.  c= 0         d.   c = k/2         e.    All are correct

Ans:  e

Q7       ln x dx = ?

a.   ln x – x + C         b.   ln x + C        c.   x. ln + C (*)        d.   x ln x + C       e.   None of these

Ans: d

Q8       The curve described parametrically by x = t² + t + 2 and y = t² – t + 2 represents

1. A pair of straight lines      b. an ellipse    c. a parabola     d. a hyperbola

Ans: c

Q9       A value of c for which the conclusion of mean value theorem holds for the            Function f(x) = log_e x  on [1,3] is 

1. 2 log₃ e       b. ½ log_e 3       c. log₃ e        d. log_e 3

Ans: a

Q10    The area bounded by the curve  y = f (x),the x-axis and the ordinate x = 1 and           x = b is (b – 1) sin (3b + 4). Then f ( x ) is

1. ( x – 1 )cos(3x + 4
2.  b. sin (3x + 4)
3. c. sin (3x + 4) + 3 (x – 1)cos (3x + 4)  4.
4.  cos (3x + 4)   + 3 (x – 1) sin(3x +4)

Ans: b

Q11    In a binary communication channel, the probability that a transmitted zero is 0.95 and the probability that a transmitted one is received as one is 0.90. If the  probability  that a zero is transmitted is 0.4, then the probability that a one was transmitted , given that a one was received is

1. 17/28           b.27/37           c.29/37            d.27/28

Ans: c

Q12   Let p,q,r be the sides opposite to the angles P,Q,R respectively in a triangle PQR.          If r² sinPsinQ = pq, then the triangle is

1. Equilateral                           b. acute angled but not equilateral
2. Obtuse angled                    d. right angled

Ans: d

Q13   Let P (2,-3), Q (-2,1) be the vertices of the triangle PQR. If the centroid of traingle PQR lies on the line 2x + 3y = 1, then the locus  of R is

1. 2x + 3y = 9            b. 2x – 3y = 9                 c. 3x + 2y = 5                   d. 3x – 2y = 2

Ans: c

Q14   If f is a real-valued differentiable function such that f(x)f’(x) < 0 for all real x, Then      

1. f(x) must be an increasing function
2. f(x) must be a decreasing function
3. |f(x)| must be an increasing function
4. |f(x)| must be a decreasing function

Ans: b

Q15   Rolle’s theorem is applicable in the interval [-2,2] for the function

f(x) = x³                   b. f(x) = 4x⁴                      c. f(x) =2x³ + 3                 d. f(x) = π|x|

Ans: c

Q16   Let p be the midpoint of a chord joining the vertex of the parabola y² = 8x to          another point on it. Then the locus of P is

1. y² = 2x             b. y² = 4x               c. x²/4  + y² = 1                  d. x² + y²/4 = 1

Ans: d

Q17   An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then the probability that balls of both colors are drawn is 

1. 40/143               b. 70/143              c. 3/13                d. 10/13

Ans: d

Q18   Two coins are available, one fair and the other two-headed. Choose a sign and       toss it once; assume that the unbiased coin is chosen with probability ¾. Given            that the outcome is head, the probability that the two-headed coin was chosen is 

1. 3/5                 b. 2/5                c. 1/5                d. 2/7

Ans: b

Q19   If a, b, c are in arithmetic progression, then the roots of the equation           ax²-2bx+c=0 are

1. 1 and c/a           b. -1/a and –c                c. -1 and –c/a               d. -2 and  –c/2a

  Ans: c

Q20   The points representing the complex number z for which arg [(z-2)/(z+2)] = π/3  lie  on

1. A circle           b. a straight line          c. an ellipse          d. a parabola

Ans: d

Q21   Let a, b, c, p, q, r be positive real numbers such that a, b, c are in G.P. and  a^p = b^q  = c^r. Then

1. p, q, r are in G.P.
2. b. p, q, r are in A.P.
3. c. p, q, r are in H.P.
4. p², q², r² are in A.P

Ans: b

Q22 If f is a real-valued differentiable function such that f(x)f’(x) < 0 for all real x, Then      

1. f(x) must be an increasing function
2. f(x) must be a decreasing function
3. |f(x)| must be an increasing function
4. |f(x)| must be a decreasing function

Ans: A

Q23 . x% of x is same as 10% of

            A)        x/10      B)    x²/10      C)   x³/10             D)  None.

Ans:    (B) x²/10.

Q24. If the side of a square is increased by 25%, then its area is increased by:

            A)        25%                B)   40.5%         C)  55%            D)  56.25%.

Ans:    (D) 56.25%.

Q.25. The maximum value of sin A + cos A = ?.

            A)        1          B)        2          C)        2.5      D)        0.666

Ans:    (B)

Q26. Here are two statements about the circle with equation (x-2)²+(y-3)²=25 and the line with equation 4x-3y+1=0

(1)  The line intersects the circle at (6, 6)
(2)  The line is a diameter of the circle

A        Only statement (2) is correct
B       Only statement (1) is correct
C       Both statements are correct
D       Neither statement is correct

 Ans: C

Q28   If a, b, c are in arithmetic progression, then the roots of the equation           ax²-2bx+c=0 are

1. 1 and c/a    b. -1/a and –c    c. -1 and –c/a    d. -2 and  –c/2a

  Ans: c

Q29     A sequence is defined by the recurrence relation U_n+1= 4u_n-9 What is the value of u₂

A . 11
B  .23
C .35
D .-16

Ans: A

Q30 .  Let a, b, c, p, q, r be positive real numbers such that a, b, c are in G.P. and  a^p = b^q  = c^r. Then

1. p, q, r are in G.P.
2. b. p, q, r are in A.P.
3. c. p, q, r are in H.P.
4. p², q², r² are in A.P

Ans: b

Q31.   Let P (2,-3), Q (-2,1) be the vertices of the triangle PQR. If the centroid of traingle PQR lies on the line 2x + 3y = 1, then the locus  of R is

1. 2x + 3y = 9    b. 2x – 3y = 9    c. 3x + 2y = 5    d. 3x – 2y = 2

Ans: c

Q32.A sequence is defined by the recurrence relation U_n+1=1/2 u_n+12 ,u₂=20 . What is the value of u_o

1. 8
2.14
3.44
4.152

Ans: 3

Q33   Let p be the midpoint of a chord joining the vertex of the parabola y² = 8x to          another point on it. Then the locus of P is

1. y² = 2x        b. y² = 4x         c. x²/4  + y² = 1       d. x² + y²/4 = 1

Ans: d

Q34 The length of the diameter of the circle x²+y²+4x-6y-3=0 is

1. 4
2. 8
3. 16
4. 3

Ans: 3

Q35.The curve described parametrically by x = t² + t + 2 and y = t² – t + 2 represents

1. A pair of straight lines      b. an ellipse    c. a parabola     d. a hyperbola

Ans: c

Q36. The curve descibed parametrically by x=t²+t+2 and  y=t²-t+2 represents

1. a pair of straight lines
2. ellipse
3. hyperbola
4. parabola

Ans : 4

Q37. If f is a real-valued differentiable function such that f(x)f’(x) < 0 for all real x, Then      

1. f(x) must be an increasing function
2. f(x) must be a decreasing function
3. |f(x)| must be an increasing function
4. |f(x)| must be a decreasing function

Ans: A

Q38. A value of c for which the conclusion of mean value theorem holds for the function F(x)=log_ex on [1,3] is 

1. 2log₃e
2.1/2 log_e3
3.4log₃e
4.log_e3

Ans: 2

Q39.   Two coins are available, one fair and the other two-headed. Choose a sign and       toss it once; assume that the unbiased coin is chosen with probability ¾. Given            that the outcome is head, the probability that the two-headed coin was chosen is 

1. 3/5                b. 2/5                 c. 1/5                   d. 2/7

Ans: b

Q40.In a binary communication channel, the probability that a transmitted zero is received as zero is 0.95 and the probability that a transmitted one is received as one is 0.90. If the probability that a zero is transmitted is 0.4, then the probability that a one was transmitted, given that a one was received is

1.17/28
2.27/37
3.29/37
4.27/28

Ans: 4