Solved Viteee Sample Paper

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SOLVED VITEEE 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 accreditations 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)

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

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

.No negative Marking

VITEEE by oureducation.in

CHEMISTRY (Question 1 to 40)

Q. 1. Which one of the following is the correct statement?

i. Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase.
ii. B2H6.2NH3 is known as ‘inorganic benzene’.
iii. Boric acid is a protonic acid.
iv. Beryllium exhibits coordination number of six.

Ans: i

Q. 2. Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in the presence of H2SO4 The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl

i. reduces permanganate to Mn2+ .
ii. oxidises oxalic acid to carbon dioxide and water.
iii. gets oxidised by oxalic acid to chlorine.
iv. furnishes H+ ions in addition to those from oxalic acid

Ans: i

Q. 3. Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is

i. R2SiCl2
ii. R3SiCl
iii. R4Si
iv. RSiCl3

Ans: iv

Q. 4. Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

i. Metal sulphides are less stable than the corresponding oxides.
ii. CO2 is more volatile than CS2 .
iii. Metal sulphides are thermodynamically more stable than CS2.
iv. COis thermodynamically more stable than CS2.

Ans: i

 Q.5. Four species are listed below

i.HCO3
ii.H3O
iii)HCO4
iv)HSO4F

Which one of the following is the correct sequence of their acid strength?

(A) (i) < (iii) < (ii) < (iv)
(B) (iii) < (i) < (iv) < (ii)
(C) (iv) < (ii) < (iii) < (i)
(D) (ii) < (iii) < (i) < (iv)

Ans: i

 Q. 6. Which one of the following constitutes a group of the isoelectronic species?

i) CN,N2,O2-2,C2-2
ii)N2,O2,NO+,CO
iii) C2-2, O2-2,CO,NO
iv)NO+, C2-2,CN,N2

Ans: iv

Q. 7. Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

i. p-nitrophenol
ii. nitrobenzene
iii. 2,4,6-trinitrobenzene
iv. o-nitrophenol

Ans: iv

Q.8. The ionization enthalpy of hydrogen atom is 1.312 x 106 Jmol-1. The energy required to excite the electron in the atom from n = 1 to n = 2 is

i)7.56 x105 Jmol-1         ii)9.84x 105 Jmol-1               iii)8.51x 105 Jmol-1         iv)6.56x 105 Jmol-1

Ans: ii

Q.9 The organic chloro compound, which shows complete stereochemical inversion during a SN2reaction, is

i) (CH3)2CHCl
ii)CH3Cl
iii)(C2H5)2CHCl
iv)(CH3)3CCl

Ans: ii

Q.10 Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotized and then heated with cuprous bromide. The reaction mixture so formed contains

i. mixture of o-; and p-bromoanilines
ii. mixture of o- and m-bromotoluenes
iii. mixture of o- and p-bromotoluenes
iv. mixture of o- and p-dibromobenzenes

Ans: iii

Q. 11. At 800 C, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80o C and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mmHg)

i. 48 mol percent
ii. 50 mol percent
iii. 52 mol percent
iv. 34 mol percent

Ans: ii

Q.12. Which one of the following pairs of species have the same bond order?

i)O2 and CN
ii)NO+ and CN+

iii)CN and NO+
iv)CN and CN+

Ans: iii

Q. 13. The equilibrium constants Kp1 and Kp2  for the reactions Xßà 2Y and Zßà P+Q respectively are  in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressures at these equilibria is

i. 1 : 3
ii. 1 : 9
iii. 1 : 36
iv. 1 : 1

Ans: iii

Q. 14. In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the correct statement?

i. H2 is removed through occlusion with Pd.
ii. CO is oxidised to CO2 with steam in the presence of a catalyst followed by absorption of CO2.
iii. CO and H2 are fractionally separated using differences in their densities.
iv. CO is removed by absorption in aqueous Cu2Cl2 solution

Ans: ii

Q. 15 In which of the following reactions new carbon-carbon bond is not formed :

(A) Cannizaro reaction
(B) Wurtz reaction
(C) Aldol condensation
(D) Friedel-Craft reaction

Ans : (A)

Q. 16. A compound is formed by substitution of two chlorine for two hydrogens in propane. The number of possible isomeric compounds is

(i) 4                              (ii) 3                             (iii) 5                                        (iv) 2

Ans : (iii)

Q17. Which statement is incorrect

(i)Phenol is a weak acid
(ii) Phenol is an aromatic compound
(iii) Phenol liberates CO2 from Na2CO3 soln
(iv) Phenol is soluble in NaOH

 Ans : (iii)

Q18. Which of the following statements regarding ozone is not correct ?

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

 Ans: iii

Q19. What is obtained when nitrobenzene is treated sequentially with (i)NH4Cl/Zn dust and (ii) H2SO4/Na2Cr2O7?

 (i) meta-chloronitrobenzene
(ii) para-chloronitrobenzene
(iii) nitrosobenzene
(iv) benzene

Ans: iii

Q20. 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

 (i) 5 + log 2–log 3
(ii) 5 –log 2
(iii) 5 –log 3
(iv) 5 –log 6

 Ans: ii

Q21. Radioactivity of a sample (z=22) decreases 90% after 10 years. What will be the half life of the sample?

 (i) 5 years                    (ii) 2 years                   (iii) 3 years                  (iv) 10 years

Ans: iii

Q22. Upon treatment with Al(OEt)3 followed by usual reaction (work up), CH3CHO will produce

i) Only CH3COOCH2CH3
ii) a mixture of CH3COOH and EtOH
iii) only CH3COOH
iv) only EtOH

Ans: i

Q23. 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.

i) p-nitrotoluene is formed in excess
ii) equimolar amounts of p-nitrotoluene and p-nitrochlorobenzene are formed
iii) p-nitrochlorobenzene is formed in excess
iv) m-nitrochlorobenzene is formed in excess

 Ans: i

Q24. Upon treatment with Al(OEt)3 followed by usual reaction (work up), CH3CHO will produce

i) Only CH3COOCH2CH3
ii) a mixture of CH3COOH and EtOH
iii) only CH3COOH
iv) only EtOH

Ans: i

Q25.Which of the following will decrease the pH of a 50 ml solution of 0.01 M HCl?

(i) addition of 5 ml of 1 M HCl
(ii) addition of 50 ml of 0.01 M HCl
(iii) addition of 50 ml of 0.002 M HCl
(iv) addition of Mg

 Ans : (i)

Q26. In aluminium extraction by the Bayer process, alumina is extracted from bauxite by sodium hydroxide at high temperature and pressures Al2O3(s) +2OH(aq) à 2Al2O2 (aq)+H2O (l) Solid impurities such as Fe2O3 and SiO2 are removed and then Al(OH)4 is reprecipitated :

 2Al(OH)4à Al2O3.3H2O(s)+ 2OH  (aq). In the industrial world :

(i) Carbon dioxide is added to precipitate the alumina
(ii) Temperature and pressure are dropped and the supersaturated solution seeded
(iii) Both (i) and (ii) are practised
(iv) The water is evaporated

Ans : (ii)

Q. 27. At 800 C, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture solution of ‘A’ and ‘B’ boils at 80o C and 1 atm pressure, the amount of ‘A’ in the mixture is (1 atm = 760 mmHg)

i. 48 mol percent
ii. 50 mol percent
iii. 52 mol percent
iv. 34 mol percent

Ans: ii

Q. 28. In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the correct statement?

i. H2 is removed through occlusion with Pd.
ii. CO is oxidised to CO2 with steam in the presence of a catalyst followed by absorption of CO2 in alkali.
iii. CO and H2 are fractionally separated using differences in their densities.
iv. CO is removed by absorption in aqueous Cu2Cl2 solution

Ans: ii

Q. 29. For a first order reaction, (A)=Products, the concentration of A changes from 0.1M to 0.025M in 40 minutes. The rate of reaction when the concentration of A is 0.01M is:

i) 1.73X10-4 M/min
ii) 1.73X10-5 M/min
iii) 3.47X10-4 M/min
iv) 3.47X10-5 M/min

Ans: 2

Q30. The electrochemical equivalent of metal is 3.3 x 10-7 kg per coulomb. The mass of the metal liberated at the cathode when a 3A current is passed for 2 seconds, will be

i.  19.8 x 10-7 kg
ii.  9.9 x 10-7 kg
iii.  6.6 x 10-7 kg
iv.  1.1 x 10-7 kg

Ans: iv

Q31. Kf for water is 1.86 kg mol-1. If your automobile radiator holds 1.0 kg of water, how many grams of ethylene glycol (C2H6O2) must you add to get the freezing point of the solution lowered to -2.80C?

i. 27g
ii. 72g
iii. 93g
iv. 39g

Ans: ii

Q32. . In which of the following pairs the two species are not isostructural?

i.  AlF63- and SF6
ii. CO32- and NO3
iii. PCl4+ and SiCl4
iv. PF5 and BrF5

Ans: iii

Q33. The standard reduction potentials for Zn2+/Zn, Ni2+/Ni and Fe2+/Fe are -0.76, -0.23 and -0.44 V respectively. The reaction X+Y2+=X2+ + Y will be spontaneous when:

i. X = Zn, Y = Ni
ii. X = Ni, Y = Fe
iii. X = Ni, Y = Zn
iv. X = Fe, Y = Zn

Ans: i

Q34.The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of this acid is:

i. 1X10-7
ii. 3X10-1
iii. 1X10-3
iv. 1X10-5

Ans: iii

Q35. In which of the following pairs the two species are not isostructural?

i.  AlF63- and SF6
ii. CO32- and NO3
iii. PCl4+ and SiCl4
iv. PF5 and BrF5

Ans: iii

Q36.Which among the following will be named as dibromidobisethylene diamine chrominum (III) bromide?

i. [Cr (en) Br2] Br
ii. [Cr (en)3] Br3
iii. [Cr (en)2 Br2] Br
iv. [Cr (en) Br4]

Ans: iv

Q37. The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is:

i. – CHO, – COOH, – SO3H, – CONH2
ii. CONH2, – CHO, – SO3H, – COOH
iii– COOH, -SO3H, – CONH2, -CHO
iv. – SO3H, – COOH, – CONH2, – CHO

Ans: iii

Q. 39. Which one of the following constitutes a group of the isoelectronic species?

i) CN,N2,O2-2,C2-2
ii)N2,O2,NO+,CO
iii) C2-2, O2-2,CO,NO
iv)NO+, C2-2,CN,N2

Ans: iv

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

i. CH3CH = CHCH3
ii. CH3CH2C = CCH2CH3
iii. CH3CH2C = CCH2CH2CH3
iv. CH3CH2C = CH

Ans: iv

PHYSICS (Question 1 to 40)

Q1. 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

Q2. 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

Q3.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

Q4. 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

Q5. 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

Q6. A proton (or charged particle) moving with velocity 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 and perpendicular to B
3. E, B and are mutually perpendicular and n=E/B
4. E and B both are parallel to v

Ans: 3

Q7. 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

 Q8. 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

Q9. 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

Q10. Two blocks of masses 10kg and 4 kg are connected by a spring of negligible mass 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

Q11. 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

Q12.When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?

1.  200 Hz
2.  202 Hz
3.  196 Hz
4.  204 Hz

Ans: 1

Q13.Two concentric coils each of radius equal to 2 cm are placed at right angles to each other, 3A and 4A are the currents flowing in each coil respectively. The magnetic induction in Wb/m2 at the centre of the coils will be

 1.  12 x 10-5
2.  10-5
3.  5 x 10-5
4.  7 x 10-3

Ans: 1

Q14.The following question has four choices out of which ONLY ONE is correct. A charged particle q is shot towards another charged particle Q, which is moving with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance it will approach now will be

1.  r
2.  2r
3.  r/2
4.  r/4

Ans: 2

Q15.To demonstrate the phenomenon of interference we require two sources which emit radiations of:

1.  nearly the same frequency
2.  the same frequency
3.  different wavelength
4.  the same frequency and having a definite phase relationship

Ans: 3

 Q16.The following question has four choices out of which ONLY ONE is correct. Alternating current cannot be measured by D.C. ammeter because:

1.  A.C. cannot pass through D.C. ammeter
2.  A.C. changes direction
3.  average value of current for complete cycle is zero
4.  D.C. ammeter will get damaged

Ans: 2

Q17.An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

1.  Zero
2.  0.5%
3.  5%
4.  None of these

Ans:  1

Q18.A tuning fork of known frequency 256 Hz makes 5 beats with the vibrating string of a piano. The beat frequency decreases to 2 beat per sec when increased. The frequency of the piano string before increasing the tension was:

1.  (250 + 2) Hz
2.  (256 – 2) Hz
3.  (256 – 5) Hz
4.  (256 + 5) Hz

Ans: 3

Q19.The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The band gap in (eV) for the semiconductor is:

1.  1.1 eV
2.  2.5 eV
3.  0.5 eV
4.  0.7 eV

Ans: 3

Q20.The following question has four choices out of which ONLY ONE is correct.Two simple harmonic motions are represented by the equations y1 = 0.1and y2 = 0.1 cos t. The phase difference of the velocity of particle 1, with respect to the velocity of particle 2 is

 

  • –π/6
  • π/6
  • –π/3
  • π/-6

Ans: 4

Q21.The following question has four choices out of which ONLY ONE is correct. A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement x. Which of the following statements is true?

1.  KE is maximum when x = 0
2.  TE is zero when x = 0
3.  KE is maximum when x is maximum
4.  PE is maximum when x = 0

Ans: 3

Q22An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity e=4.0, then

1.  wavelength is doubled and frequency remains unchanged
2.  wavelength is doubled and frequency becomes half
3.  wavelength is halved and frequency remains unchanged
4.  wavelength and frequency both remain unchanged

Ans: 1

Q23. The following question has four choices out of which ONLY ONE is correct. A coil of inductance 300 mH and resistance 2 is connected to a source of voltage 2V. The current reaches half of its steady state value in :

1.  0.05 s
2.  0.1 s
3.  0.15 s
4.  0.3 s

Ans: 3

Q24. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then:

1.  its velocity will decrease
2.  its velocity will increase
3.  it will turn towards right of direction of motion
4.  it will turn towards left of direction of motion

Ans: 3

Q25.  A spring of spring constant 5 x 103 N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

1.  12.50 Nm
2.  18.75 Nm
3.  25.00 Nm
4.  6.25 Nm

Ans: 3

Q26. A spectrometer gives the following reading when used to measure the angle of a prism,

Main scale reading: 58.5 degree
Vernier scale reading: 09 divisions

Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the Vernier scale are 30 and match with 29 divisions of the main scale. The angle of the prism from the above data:

1. 59 degree
2. 58.59 degree
3. 58.77 degree
4. 58.65 degree

Ans: 3

Q27. The electrochemical equivalent of metal is 3.3 x 10-7 kg per coulomb. The mass of the metal liberated at the cathode when a 3A current is passed for 2 seconds, will be

1.  19.8 x 10-7 kg
2.  9.9 x 10-7 kg
3.  6.6 x 10-7 kg
4.  1.1 x 10-7 kg

Ans: 4

Q28.The change in the value of ‘g’ at a height ‘h’ above the surface of Earth is the same as at a depth ‘d’ below the surface of Earth. When both ‘d’ and ‘h’ are much smaller than the radius of Earth, then which one of the following expressions is correct?

1. d=h/2
2.   d=3h/2
3.  d = 2h
4.  d = h

Ans: 3

Q29.  If the mass of moon is  of Earth’s mass, its radius is  of Earth’s radius and if ‘g’ is acceleration due to gravity on Earth, what is the acceleration due to gravity on moon?

1. g/3
2. g/90
3. g/10
4. g/9

Ans: 3

Q30. A spring (spring constant = k) is cut into 4 equal parts and two parts are connected in parallel. What is the effective spring constant?

1. 4k
2. 16k
3. 8k
4. 6k

Ans: 4

Q31. The following question has four choices out of which ONLY ONE is correct.

A particle executes linear simple harmonic motion with amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

 

  1. 1/2π√3
  2. 2π√3
  3. 2π/√3
  4. √3/2π

Ans: 4

Q32. 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

Q33. The negative Zn pole of a Daniel cell, sending a constant current through a circuit, decreases in mass by 0.13 g in 30 minutes. If the electrochemicalequivalent 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

Q34. 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

 Q35. 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

Q36.  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

Q37.  If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature?

1.   1.4 times
2.   4 times
3.   2 times
4.   1/4 times

Ans: 2

Q38. The electrochemical equivalent of a metal is 3.3 x 10-7 kg/C. The mass of metal liberated at cathode by 3 A current in 2s will be

1.   19.8 x 10-7 kg
2.   9.9 x 10-7 kg
3.   6.6 x 10-7 kg
4.   1.1 x 10-7 kg

Ans: 2

Q39. The interference phenomenon can take place

1.   in all waves
2.   in transverse waves only
3.   in longitudinal waves only
4.   in standing waves only

Ans: 1

Q40.  As the electron in bohr orbit of hydrogen atom passes from state n = 2 to n = 1, the kinetic energy K and potential energy U change as

1.  K two-fold, U four-fold
2.  K four-fold, U two-fold
3.  K four-fold, U also four-fold
4.  K two-fold, U also two-fold
5.  no change in K and U

Ans: 2

MATHEMATICS (Question 1 to 40)

Q1. Let X = {1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can be formed such that YC=X, ZC=X and Y∩Z is empty, is:

1.  53
2.  52
3.  35
4.  25

Ans: 1

 Q2. If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k equals:

1. 11/5
2. 29/5
3. 5
4. 6

Ans: 2

Q3. In a ∆PQR, if 3 sin P+4 cos Q =6 and 4 sin Q+3 cos P = 1, then the angle R is equal to:

1. 3π/4
2. 5π/6
3. π/6
4. π/4

Ans: 1

Q4. A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:

1. 9/2
2. 9/7
3. 7/9
4. 2/9

Ans:  4

Q5. If z ≠ 1 and z2/z-1 is real, then the point represented by the complex number lies:

1.  on the imaginary axis.
2. either on the real axis or on a circle passing through the origin.
3. on a circle with centre at the origin.
4. either on the real axis or on a circle not passing through the origin.

Ans: 2

 Q6.  If the lines x-1/2 = y+1/3 = z-1/4 and x-3/1 = y-k/2 = z/1 intersects, then k is equal to:

1. 0
2. -1
3. 2/9
4. 9/2

Ans:  4

Q7. If f(x) = logx, then f(x) – f(xy)  + f(y) is equal to

1. logx + logy + logxy
2. logx + logy
3. 0
4. logy

Ans: 3

Q8.  A tower is 61.25 m high. A rigid body is dropped from its top and at the same instant another body is thrown upwards from the bottom of the tower with such a velocity that they meet in the middle of the tower. The velocity of the projection of the second body is:

1. 20 m/sec
2. 25 m/sec
3. 24.5 m/sec
4. none of these

Ans: 3

Q9. If a body is projected vertically upwards with velocity u and t seconds afterwards another body is similarly projected with the same velocity, then the two  bodies will meet after T seconds of the projection of the second body, where T =

1. u-gt/2g
2. u-2gt/2g
3. 2u-gt/g
4. 2u-gt/2g

Ans: 4

Q10. A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C(-1, 1, 2). Then the angle between the faces OAB and ABC will be

1. Cos(19/35)
2. Cos(17/31)
3. 30 Degree
4. 90 Degree

Ans:  1

Q11. The points A (2a, 4a), B (2a, 6a) and C (2a + √3a, 5a) (a > 0) are the vertices of

1. an acute angled triangle
2. a right angled triangle
3. an isosceles triangle
4. none of these

Ans: 1

 Q12. The smallest positive integer n for which is (1+i/1-i) power n = 1 is

1. 8
2. 12
3. 16
4. None of these

Ans: 4

Q13.  A value of c for which the conclusion of mean value theorem holds for the            Function f(x) = logx  on [1,3] is 

a.2 loge       b. ½ log3       c. log3 e        d. log3

Ans: a

Q14    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

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

Ans: b

Q15    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

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

Ans: c

Q16   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

a.Equilateral                           b. acute angled but not equilateral

c.Obtuse angled                    d. right angled

Ans: d

Q17   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

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

Ans: c

Q18   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: 2

Q19   Rolle’s theorem is applicable in the interval [-2,2] for the function

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

Ans: c

Q20   Let p be the midpoint of a chord joining the vertex of the parabola y= 8x to          another point on it. Then the locus of P is

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

Ans: d

Q21   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 

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

Ans: d

Q22   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 

a.3/5    b. 2/5    c. 1/5    d. 2/7

Ans: b

Q23. 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

Q24   If a, b, c are in arithmetic progression, then the roots of the equation           ax2-2bx+c=0 are

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

  Ans: c

Q25     A sequence is defined by the recurrence relation Un+1= 4un-9 What is the value of u2

a . 11
b  .7
c .35
d .-16

Ans: a

Q26 .  Let a, b, c, p, q, r be positive real numbers such that a, b, c are in G.P. and  ap = bq  = cr. Then

a.p, q, r are in G.P.
b. p, q, r are in A.P.
c. p, q, r are in H.P.
d.p2, q2, r2 are in A.P

Ans: b

Q27.   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

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

Ans: c

Q28.  AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is

1. (7√3/2)1/√3-1 m
2.  (7√3/2) √3+1 m
3.  (7√3/2) √3-1 m
4. (7√3/2)1/√3+1 m

Ans: 2

Q29. It is given that the events A and B are such that P (A) = ¼, P. A/B = ½ and P. B/A = 2/3 then P (B) is

1. 1/6
2. 1/3
3. 2/3
4. ½

Ans: 2

Q30. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A  B) is

1. 3/5
2. 0
3. 1
4. 2/5

Ans: 3

Q31. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is

1. 8/3
2. 2/3
3. 4/3
4. 5/3

Ans: 1

Q32. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

1. (0, 2)
2. (1, 0)
3. (0, 1)
4. (2, 0)

Ans: 2

Q33. The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y − 3 = 0 is

1. (3, −4)
2. (− 3, 4)
3. (− 3, −4)
4. (3, 4)

Ans: 3

Q34. Let f : N → Y be a function defined as f (x) = 4x + 3, where Y = {y  N : y = 4x + 3 for some x  N}. Show that f is invertible and its inverse is

1.  g (y) =(3y + 4)/3
2. g (y) = (4 +y + 3)/4
3. g (y) =(y + 3)/4
4. g (y) =(y – 3)/4

Ans: 4

Q35. The conjugate of a complex number is 1/(i −1) . Then the complex number is

1. -1/ (i-1)
2. 1/(i+1)
3. -1/(i+1)
4. 1/(i-1)

Ans: 3

Q36. Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x − y is an integer}. Which one of the following is true?

1. neither S nor T is an equivalence relation on R
2. both S and T are equivalence relations on R
3. S is an equivalence relation on R but T is not
4. T is an equivalence relation on R but S is not

Ans: 4

Q37. The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

1.  1
2. 2
3. -2
4. -4

Ans: 4

Q38. The solution of the differential equation dy/dx = (x + y)/x satisfying the condition y (1) = 1 is

1. y = ln x + x
2. y = x ln x + x2
3.  y = xe(x−1)
4. y = x ln x + x

Ans: 4

Q39. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

1. a = 0, b = 7
2. a = 5, b = 2
3. a = 1, b = 6
4. a = 3, b = 4

Ans: 4

Q40.A sequence is defined by the recurrence relation Un+1=1/2 un+12 ,u2=20 . What is the value of uo

1. 8
2.14
3.44
4.152

Ans: 3

 

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3 Responses to Solved Viteee Sample Paper

  1. Aryaman says:

    Engineering

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    VIT is a very reputated university . Students preparing for VITEEE must go through this paper

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