Sample Paper for COMEDK

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Sample Paper for COMEDK Entrance Examination

The COMEDK UGET 2013 sample paper contain 3 papers through this sample paper for comedk we have tried to keep focus objective questions which are asked ion comedk exams

• Physics
• Chemistry
• Mathematics

Each section have 60 questions and for each correct answer there is one mark.This question paper have the solved answers which will help the students to get ideas about the paper pattern, question distribution and the marks allocated for each section.

The students can download COMEDK UGET 2013 sample papers to refer to the previous year questions, practice them and get better scores in order to get admission in their favourite engineering institute.

Sample paper for exam of comedk

Sample Paper for COMEDK

Section A

Physics:

1. Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be:

(1.)    6
(2.)    2
(3.)    3
(4.)    5

2. A coil is suspended in a uniform magnetic field; with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminum plate is placed near to the coil, it stops. This is due to:

(1.)    Electromagnetic induction in the aluminum plate giving rise to electromagnetic damping.
(2.)    Development of air current when the plate is placed.
(3.)    Induction of electrical charge on the plate.
(4.)    Shielding of magnetic lines of force as aluminum is a paramagnetic material.

3. 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

4. Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particles are respectively rp, rd and ra. Which one of the following relation is correct?

(1.)    R_α= r_d>r_p
(2.)    R_α= r_p=r_d
(3.)    R_α= r_p<r_d
(4.)    R_α>r_d>r_p

5. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

(1.)    5.6 m
(2.)    7.2 m
(3.)    2.4 m
(4.)    3.2 m
6. This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describe the two Statements.

If two springs S₁ and S₂ of force constants k₁ and k₂, respectively, are stretched by the same force, it is found that more work is done on springs S₁ than on spring S₂.

Statement 1: If stretched by the same amount, work done on S_1, will be more than on S₂.

Statement 2: k₁<k₂

(1.)    Statement 1 is true, Statement 2 is true, and Statement 2 is not the correct explanation of statement 1.
(2.)    Statement 1 is false, Statement 2 is true.
(3.)    Statement 1 is true, Statement 2 is false.
(4.)    Statement 1 is true, Statement 2 is also true, and Statement 2 is the correct explanation of Statement 1.

7. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it, If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is:

(1.)    3%
(2.)    6%
(3.)    Zero
(4.)    1%

8. A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :

(1.)    600K
(2.)    Efficiency of Carnot engine cannot be made larger than 50%
(3.)    1200K
(4.)    750K

9. Radar has a power of 1kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance up to which it can detect object located on the surface of the earth (Radius of earth = 6.4X10⁶ m) is:

(1.)    64 km
(2.)    80 km
(3.)    16 km
(4.)    40 km

10. A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now:

(1.)    2f
(2.)    F
(3.)    f/2
(4.)    3f/4

11. The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’

And ‘R’ (radius of earth) is 10 m/s² and 6400 km respectively. The required energy for this work will be:

(1.)    6.4X10¹⁰ Joules
(2.)    6.4X10¹¹ Joules
(3.)    6.4X10⁸ Joules
(4.)    6.4X10⁹ Joules
12. A Boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be:

(1.)    20 m
(2.)    20√2 m
(3.)    10 m
(4.)    10√2 m

13. If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = πs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ‘b’ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :

(1.)    2/b
(2.)    0.693/b
(3.)    B
(4.)    1/b

14. Two cars of masses m₁ and m₂ are moving in circles of radii r₁ and r₂ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :

(1.)    1 : 1
(2.)    M₁r₁ : m₂r₂
(3.)    M₁ : M₂
(4.)    R₁ : r₂

15. Assume that a neutron breaks into a proton and an electron. The energy released during this process is :

{Mass of neutron = 1.6725X10^-27 kg

Mass of proton = 1.6725X10^-27 kg

Mass of electron = 9X10^-31 kg}

(1.)    5.4 MeV
(2.)    0.73 MeV
(3.)    7.10 MeV
(4.)    6.30 MeV

16. A wooden wheel of radius R is made of two semicircular parts. The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ∆T and it just steps over the wheel. As it cools down to surrounding parts together. If the coefficient of linear expansion of the metal is α,and its Young’s modulus is Y, the force that one part of the wheel applies on the other part is :

(1.)    2SYα∆T
(2.)    2πSYα∆T
(3.)    SYα∆T
(4.)    πSYα∆T

17. Two electric bulbs marked 25W-220V and 100W-220V are connected in series to a 440V supply. Which of the bulbs will fuse?

(1.)    Neither
(2.)    Both
(3.)    100W
(4.)    25W

18. In a photoelectric effect experiment, the stopping potential for a wavelength of 3000Å is 2V. If the wavelength is decreased to 2000Å, the stopping potential becomes

(1.) 2 V
(2.) Less than 2V
(3.) Greater than 2 V
(4.) Zero

19. Due to an explosion under water, a gas-bubble oscillates with a period which is proportional to PapbEc, where P is static pressure, p is density of water and E is the energy released in explosion. The

1. a + b + c=1
2. a + b + c = 0
3. a-b-c = 0
4. a-b – c =1

20. A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is:

1. E/c
2. 2E/c
3. Ec
4. E/c2

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

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields and with a velocity perpendicular to both and , and comes out without any change in magnitude or direction of. Then

1. = × /B2
2. = × /B2
3. = × /E2
4. = × /E2

 22.The wavelengths involved in the spectrum of deuterium  are slightly different from that of hydrogen spectrum, because

1. sizes of the two nuclei are different
2. nuclear forces are different in the two cases
3. masses of the two nuclei are different
4. attraction between the electron and the nucleus is different in the two cases

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

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘t’ is proportional to

1. t3/4
2. t3/2
3. t1/4
4. t1/2

24. According to Newton’s law of cooling, the rate of cooling of a body is proportional to , where  is the difference of the temperature of the body and the surroundings, and ‘n’ is equal to

1. 2
2. 3
3. 4
4. 1

25. 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

 26.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

27.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

28.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

 29.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

30. 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

 31. 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

 32.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

33.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

1. –π/6
2. π/6
3. –π/3
4. π/-6

34.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

35. An 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

36.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

37.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

38. 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

39. 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
40. 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

41.  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

42. 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

43. 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

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

A ball of mass 2 kg moving with velocity 3 m/s, collides with spring of natural length 2 m and force constant 144 N/m. What will be the length of compressed spring?

1. 2 m
2. 1.5 m
3. 1 m
4.0 .5 m

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

When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

1. More frequency, less wavelength
2. More frequency, more wavelength
3. Less frequency, less wavelength
4. More frequency, constant wavelength 

46. An organ pipe open from both the ends produces 5 beats per second, when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipe produces 10 beats per second with a source of frequency 420 Hz. The frequency of source is:

1. 195 Hz
2. 205 Hz
3. 190 Hz
4. 210 Hz

47. The velocity of sound is v at 272 K. The temperature at which it is 2 v is

1. 2 x 273 K
2. 4 x 273 K
3. 8 x 273 K
4. 16 x 273 K
5. √2x 273 K

48. A body initially at 80⁰ C cools to 64⁰ C in 5 minutes and to 52⁰ C in 10 minutes. The temperature of the body after 15 minutes will be:

1. 42.0⁰ C
2. 35⁰ C
3. 47⁰ C
4. 40⁰ C 

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

Charges 4Q, q and Q are placed along x-axis at position x = 0, x = l/2 and x = l, respectively. Find the value of q, so that force on charge Q is zero

1. Q
2. 2. Q/2
3. 3. – Q/2
4. 4. – Q

50. Two point charges + 3µC and + 8µC repel each other with a force of 40 N. If a charge of – 5µC is added to each of them, the force between them will become:

1.    -10 N
2.   + 10 N
3.   20 N
4.   – 20 N

51.  The potential at a point P which is forming a corner of a square of side 93 mm with charges, Q1=33nC, Q2 = – 51 nC, Q3 = 47 nC located at the other three corners is nearly

1.   16 kV
2.   4 kV
3.   400 V
4.   160 V

52.  A six pole generator with fixed field excitation develops an emf of 100 V, when operating at 1500 rpm. At what speed must it rotate to develop 120 V?

1.  1200 rpm
2.  1800 rpm
3.  1500 rpm
4.  400 rpm

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

In a potentiometer the null point is received at 7th wire. If now we have to change the null point at 9th wire, what should we do?

1. Attach resistance in series with battery
2. Increase resistance in main circuit
3. Decrease resistance in main circuit
4. Decrease applied emf

54.  Fleming’s left and right hand rule are used in

1.  DC motor and AC generator
2.  DC generator and AC motor
3.  DC motor and DC generator
4.  both rules are same, anyone can be used

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

For EM wave propagating along x-axis, E_max = 30 V/m, what is maximum value of magnetic field ?

1. 10^-7 T
2. 10^-8 T
3. 10^-9 T
4. 10^-6 T

56.  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

57. 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
58. 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

59.  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

60. Carbon, silicon and germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by (Eg)_C, (Eg)_Si and (Eg)_Ge respectively. Which one of the following relationships is true in their case?

1.  (Eg)_C > (Eg)_Si
2.  (Eg)_C = (Eg)_Si
3.  (Eg)_C < (Eg)_Ge
4.  (Eg)_C < (Eg)_Si

ANSWERS

Mathematics

1.  An ellipse is drawn by taking a diameter of the circle (x-1)² + y² = 1 as its semi-minor axis and a diameter of the circle x² + (y-2)² = 4 as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :

(1.)    X² + 4y² = 16

(2.)    4x² + y² = 4

(3.)    X² + 4y² = 8

(4.)    4x² + y² = 8

Ans: Option 1

2.  The length of the diameter of the circle which touches the x-axis at the point (1,0) and passes through the point (2,3) is:

1.  5/3

2.  10/3

3.  3/5

4.  6/5

Ans: Option 4

3. Let P and Q be 3X3 matrices with P≠Q. If P³ = Q³ and P²Q = Q²P, then determinant of (P²+Q²) is equal to:

1. -1

2. -2

3.  1

4. 0

Ans: Option 4

4.  If n is a positive integer, then (√3+1)²ⁿ – (√3-1)²ⁿ is:

1. a rational number other than positive integers

2. an irrational number

3. an odd positive integer

4. an even positive integer

Ans: Option 4

5. Three numbers are chosen at random without replacement from {1,2,3,….,8}. The probability that their minium is 3, given that their maximum is 6 is:

1. 2/5

2. 3/8

3. 1/5

4. ¼

Ans: Option 4

6. Assuming the balls to be identical except for difference in colors, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black ball is:

1. 879

2. 880

3. 629

4. 630

Ans: Option 1

7. If the 100 times the 100^th term of an AP with non-zero common difference equals the 50 times term, then the 150^th term of this AP is:

1. zero

2. -150

3. 150 times ots 50^th term

4. 150

Ans: Option 3

8. The area bounded between the parabolas x² = y/4 and x² = 9y, and the straight line y = 2 is :

1.  10√2

2.  20√2

3.  10√2/3

4.  20√2/3

Ans: Option 2

9. An equation of a plane parallel to the x-2y+5=0 and at a unit distance from the origin is :

1. x-2y+2z+5=0

2. x-2y+2z-3=0

3. x-2y+2z+1=0

4. x-2y+2z-1=0

Ans: Option 4

10. The equation e^sinx-e^-sinx-4=0 has:

1.  exactly four real roots

2.  infinite number of real roots

3. no real roots

4. exactly one real root

Ans: Option 1

11. The negation of the statement :

“If I become a teacher, then I will open a school”, is:

1.  I will not become a teacher or I will not open a school.

2. I will become a teacher and I will not open a school.

3. either I will not become a teacher or I will not open a school.

4. Neither I will become a teacher nor I will open a school.

Ans: Option 3

12. The population p(t) at time t of a certain mouse species satisfies the differential equation dp(t)/dt = 0.5p(t) + 450. If p(0) = 850, then the time at which the population becomes zero is:

1.  ln 18

2. 2 ln 18

3. ln 9

4. ½ ln 18

Ans: Option 2

13.  Let a and b be two unit vectors. If the vectors c = a+2b and d = 5a-4b are perpendicular to each other, then the angle between a and b is:

1. π/4

2. π/6

3. π/2

4. π/3

Ans: Option 2

14. A line is drawn through the point (1,2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is:

1.  -1/2

2. -1/4

3. -4

4. -2

Ans: Option 1

15. 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: Option 1}

16. 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: Option 2

17. 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: Option 1

18. 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: Option 4

19. 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: Option 2

20.  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: Option 4

21. 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: Option 3

22.  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: Option 3

23. 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: Option 4

24. 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: Option 1

25. 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: Option 1

26. 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: Option 4

27. The total number of different combinations of names which can be made from the letters of the word MISSISSIPPI, using all the letters at a time, in which no letter is repeated are

1. 150

2. 148

3. 149

4. none of these

Ans: Option 3

28. The number of ways of painting the faces of a cube with six different colours is

1.   1

2.   6

3.   6!

4.   none of these

Ans: Option 3

29. The number solution of log2(x – 1) = 2log2(x – 3) is of

1.     2

2.     1

3.     6

4.     7

Ans: Option 2

30. The value of sin 36⁰ sin 108⁰ sin 144⁰ is equal to

1. 1/4

2. 1/16

3. 3/4

4. 5/16

Ans: Option 4

31. If the period of the function

f(x) = sin(x/n) is 4p, then n is equal to

1. 1

2. 4

3. 8

4. 2

Ans: Option 4

32. A box contains 6 white and 3 black balls. Another box contains 5 white and 4 black balls. A ball is drawn from the first box and placed in the second box. A ball is now drawn at random from the first box. What is the probability that the ball drawn is white?

1. 2/3

2. 5/12

3. 3/12

4. ¾

Ans: Option 1

33. A bag contains 7 white and 9 blue balls. If two balls are drawn at random, what is the chance that one ball is white and the other is blue?

1. 16/63

2. 1/8

3. 7/20

4. 21/40

Ans: Option 4

34. The average marks of boys in a class is 52 and that of girls is 42. The combined average marks of boys and girls is 50. The percentage of boys in the class is

1. 40

2. 20

3. 80

4. 60

Ans: Option 3

35. A train of length 200 m travelling at 30 m/s overtakes another train of length 300 m travelling at 20 m/s. The time taken by the first train to pass the second train is

1. 30 s

2. 50 s

3. 10 s

4. 40 s

Ans: Option 2

36. You are collecting data from newspapers and magazines about price fluctuations of a branded product. What type of data are you referring to?

1. Primary data

2. Secondary data

3. Frequency distribution

4. None of above

Ans: Option 2

37. Consider the following statements:

(i) Mode can be computed from histogram

(ii) Median is not independent of change of scale

(iii)Variance is independent of change of origin and scale

Which of these is/are correct?

1. only (i)

2. only (ii)

3. only (i) and (ii)

4.  (i), (ii) and (iii)

Ans: Option 3

38. The class marks of a distribution are 6, 10, 14, 18, 22, 26, 30 then the class size is

1. 4

2. 2

3. 5

4. 8

Ans: Option 1

39. The digit at the unit place in the number 19²⁰⁰⁵ + 11²⁰⁰⁵ – 9²⁰⁰⁵ is

1.  2

2.  1

3.  0

4.  8

5.  9

Ans: Option 2

40. A person travelling on a straight line moves with uniform velocity v1 for some time and with uniform velocity v2 for the next equal time. The average velocity ‘v’ is given by:

1. v= v1+v2/2

2. v= √v1v2

3. 2/v= 1/v1+1/v2

4. 1/v=1/v1+1/v2

Ans: Option 1

41. A bullet of mass 0.05 kg travelling at 120 metres/sec penetrates deeply into a fixed target and is brought to rest in 0.01 sec. The distance through which it penetrates the target is:

1. 3 cm

2. 6 cm

3. 30 cm

4. 60 cm

Ans: Option 4

42. If a straight line through C (√–8,√8) making an angle of 135⁰ with the x-axis cuts the circle x = 5 cos0 , y = 5 sin0 at point A and B, then the length of AB is

1. 3

2. 7

3. 10

4. None of these

Ans: Option 3

43. The curve x³ + y³ = 3axy is symmetric along

1. x-axis

2. y-axis

3. line y = x

4. opposite quadrants

Ans: Option 3

44. H.C.F of n !, (n + 1) ! and (n + 2) ! is

1. n !

2. (n + 2) !

3. (n + 1) !

4. none of these

Ans: Option 1

45. Six identical coins are arranged in a row. The number of ways, in which the number of tails is equal to the number of heads is

1. 20

2. 120

3. 36

4. none of these

Ans: Option 1

46. Let A be the non-void set of the children in a family. The relation ‘x is a brother of y’ on A is:

1. Reflexive

2. Symmetric

3. Transitive

4. Both (2) & (3)

Ans: Option 4

47. Directions:The following question has four choices out of which ONLY ONE is correct.

If f(x) = (a – xⁿ)^1/n, where a > 0 and n belong to N, then, fof(x) is equal to

1. a

2. x

3. xⁿ

4. aⁿ

^{Ans: Option 2}

48. tan x is periodic with period

1. p/2

2. p

3. 2p

4. 3p/2

Ans: Option 2

49. A has three shares in a lottery containing 3 prizes and 9 blanks, B has two shares in a lottery containing 2 prizes and 6 blanks. Compare their chances of success.

1. 13/28

2. 34/55

3. 34/715

4. None of these

Ans: Option 4

50. In the month of December, it is known that clouds or fog on an average of two days out of every three hides the sun. Find the probability that at least four out of five days the sun will be shining.

1. 15/248

2. 11/243

3. 2/81

4. 2/27

Ans: Option 2

51. (√3 + 1)⁴ + (√3 – 1)⁴ is

1. a rational number

2. an irrational number

3. a negative integer

4. None of these

Ans: Option 1

52. If a² + b² +c²= 1, then ab + bc + ca lies in the interval

1. [1/2, 2]

2. [–1, 2]

3. [–1/2, 1]

4. [–1, 1/2]

Ans: Option 3

53. The value of, integrate 1to a [x]f'(x)dx, a > 1, where [x] denotes the greatest integer not exceeding x, is

1. a f([a]) – {f(1) + f(2) +…….+f(a)}

2. a f(a) – {f(1) + f(2) +…….+f[a]}

3. [a] f(a) – {f(1) + f(2) +…..+ f([a])}

4. [a] f([a] – {f(1) + f(2) +……+ f(a)}

Ans: Option 3

54. How many words can be formed by taking four different letters of the word MATHEMATICS?

1.  7920

2.  1680

3.  70

4.  None of these

Ans: Option 2

55. A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is

1.  5!

2.  240

3.  216

4.  none of these

Ans: Option 3

56. Everybody in a room shakes hand with every other person. The total number of handshakes is 66. Find the total number of persons in the room.

1.  11

2.  12

3.  13

4.  None of these

Ans: Option 2

57. In how many ways a garland can be made from exactly 10 flowers?

1.  10!/2

2.  9!

3.  2(9!)

4.  9!/2

Ans: Option 4 

58. If nCr -1 = 36, nCr = 84 and nCr+1 = 126, then r is equal to

1.  1

2.  2

3.  3

4.  None of these

Ans: Option 3

59. The number of three digit numbers lying between 100 and 999 (inclusive) and having only two consecutive digits identical is

1.  90

2.  162

3.  153

4.  none of these

Ans: Option 2

60. The number of diagonals of a hexagon is

1.  15

2.  6

3.  9

4.  none of these

Ans: Option 3

Chemistry:

1. Ortho-Nitrophenol is less soluble in water than p- and m- Nitro phenols because :

1. Melting point of o- Nitrophenol is lower than those of m- and p- isomers

2. o- Nitrophenol is more volatile in steam than those of m- and p-isomers.

3. o- Nitrophenol shows Intramolecular H- bonding

4. o- Nitrophenol shows Intermolecular H- bonding

Ans: Option 3

2. How many chiral compounds are possible on monochlorination of 2- methyl butane?

1. 6

2. 8

3. 2

4. 4

Ans: Option 3

3. Iron exhibits +2 and +3 oxidation states. Which of the following statements about iron is incorrect?

1. Ferrous compounds are more easily hydrolyzed than the corresponding ferric compounds.

2. Ferrous oxide is more basic in nature than the ferric oxide.

3. Ferrous compounds are relatively more ionic than the corresponding ferric compounds.

4. Ferrous compounds are less volatile than the corresponding ferric compounds.

Ans: Option 2

4. What is DDT among the following:

1. Non-biodegradable pollutant

2. Greenhouse gas

3. A fertilizer

4. Biodegradable pollutant

Ans: Option 1

5. K_f 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?

1. 27g

2. 72g

3. 93g

4. 39g

Ans: Option 2

6. Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of mono substituted alkyl halide?

1. Neohexane

2. Tertiary butyl chloride

3. Neopentane

4. Isohexane

Ans: Option 1

7. The equilibrium constant (K_c) for the reaction, N₂(g) + O₂(g) = 2NO(g) at temperature T is 4X10^-4. The value of K_c for the reaction, NO(g)= ½ N2(g) + ½ O₂(g) at the same temperature is:

1. 50.0

2. 0.02

3. 2.5X10²

4. 4X10^-4

Ans: Option 1

8. 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:

1. 1.73X10^-4 M/min

2. 1.73X10^-5 M/min

3. 3.47X10^-4 M/min

4. 3.47X10^-5 M/min

Ans: Option 2

9. Aspirin is known as:

1. Methyl salicylic acid

2. Acetyl salicylic acid

3. Phenyl salicylic acid

4. Acetyl salicylate

Ans: Option 2

10. The molecule having smallest bond angle is:

1. PCl₃

2. NCl₃

3. AsCl₃

4. SbCl₃

Ans: Option 4

11. The compressibility factor for a real gas at high pressure is:

1. 1- pb/RT

2. 1+RT/pb

3. 1

4. 1+pb/RT

Ans: Option 4

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

1. NH₄NO₃

2. NaNO₃

3. KClO₃

4. CaCo3

Ans: Option 4

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

1.  AlF₆^3- and SF₆

2. CO₃^2- and NO₃^–

3. PCl₄⁺ and SiCl₄

4. PF₅ and BrF5

Ans: Option 3

14. Which of the following compounds can be detected by Molisch’s test?

1. Primary alcohols

2. Nitro Compounds

3. Sugars

4. Amines

Ans: Option 2

15. The increasing order of the ionic radii of the given isoelectronic species is:

1. K⁺, S^2-, Ca²⁺, Cl^–

2. Cl^–, Ca²⁺, K⁺, S^2-

3. S^2-, Cl^–, Ca²⁺, K⁺

4. Ca²⁺, K⁺, Cl^–, S^2-

Ans: Option 4

16. Which one of the following statements is correct?

1. All amino acids except glutamic acid are optically active.

2. All amino acids except lysine are optically active.

3. All amino acids are optically active

4. All amino acids except glycine are optically active.

Ans: Option 1

17. 2- Heyne gives trans – 2 – Hexane on treatment with:

1. LiAlH₄

2. Pt/H₂

3. Li/NH₃

4. Pd/BaSO₄

Ans: Option 4

18. The species which can best serve as initiator for the cationic polymerization is:

1. BuLi

2. LiAlH₄

3. HNO₃

4. AlCl₃

Ans: Option 2

19. 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:

1. X = Zn, Y = Ni

2. X = Ni, Y = Fe

3. X = Ni, Y = Zn

4. X = Fe, Y = Zn

Ans: Option 1

20. Lithium forms body centered cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be:

1. 152 pm

2. 75 pm

3. 300 pm

4. 240 pm

Ans: Option 4

21. The electrons identified by quantum numbers n and 1 :

(a) n = 4, l = 1

(b) n = 4, l = 0

(c) n = 3, l = 2

(d) n = 3, l = 1

Can be placed in order of increasing energy as:

1. a<c<b<d

2. c<d<b<a

3. d<b<c<a

4. b<d<a<c

Ans: Option 4

22. According to Freundlich adsorption isotherm, which of the following is correct?

1. x/m∞p⁰

2. x/m∞p¹

3. x/m∞p^1/n

4. All the above are correct for different ranges of pressure

Ans: Option 1

23. The density of a solution prepared by dissolving 120 g of urea (mol. Mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is:

1. 2.005 M

2. 0.50 M

3. 1.78 M

4. 1.02 M

Ans: Option 2

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

1. 1X10^-7

2. 3X10^-1

3. 1X10^-3

4. 1X10^-5

Ans: Option 3

25. Iodoform can be prepared from all except:

1. Isobutyl alcohol

2. Ethyl methyl ketone

3. Isopropyl alcohol

4. 3 – Methyl – 2 – butanone

Ans: Option 3

26. Very pure hydrogen (99.9%) can be made by which of the following processes?

1. Reaction of salt like hydrides with water

2. Reaction of methane with steam

3. Mixing natural hydrocarbons of high molecular weight

4. Electrolysis of water

Ans: Option 3

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

1. [Cr (en) Br₂] Br

2. [Cr (en)₃] Br₃

3. [Cr (en)₂ Br2] Br

4. [Cr (en) Br₄]^–

Ans: Option 4

28. Which one of the following is the correct statement?

1. Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase.

2. B₂H₆2NH₃ is known as ‘inorganic benzene’.

3. Boric acid is a protonic acid.

4. Beryllium exhibits coordination number of six.

Ans: Option 1

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

1. – CHO, – COOH, – SO₃H, – CONH₂

2. CONH₂, – CHO, – SO₃H, – COOH

3. – COOH, -SO₃H, – CONH₂, -CHO

4. – SO₃H, – COOH, – CONH₂, – CHO

Ans: Option 3

30. 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

    1. 7.01

2. 9.22

3. 9.58

4. 4.79

Ans: Option 1

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

1. CH₃CH = CHCH₃

2. CH₃CH₂C = CCH₂CH₃

3. CH₃CH₂C = CCH₂CH₂CH₃

4. CH₃CH₂C = CH

Ans: Option 4

32. 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

1. reduces permanganate to Mn²⁺

2. oxidises oxalic acid to CO₂ and water

3. gets oxidized by oxalic acid to chlorine.

4. furnishes H⁺ ions in addition to those from oxalic acid.

Ans: Option 1

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

1. R₂SiCl₂

2. R₃SiCl

3. R₄Si

4. RSiCl₃

Ans: Option 4

 34. Which of the following factors is of no significance for roasting sulphide ores to the oxide and not subjecting the sulphides ores to carbon reduction directly?

1. Metal sulphides are less stable than the corresponding oxides

2. CO₂ is more volatile than CS₂.

3. Metal sulphides are thermodynamically more stable than CS₂

4. CO₂ is thermodynamically more stable than CS₂.

Ans: Option 1

35. The organic chloro compound, which shows complete stereochemical inversion during a S_N2 reaction, is 

1.  (CH₃)₂CHCl

2.  CH₃Cl

3.  (C₂H₅)₂CHCl

4. (CH₃)₃CCl

Ans: Option 2

36. 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

1. mixture of o-; and p-bromoanilines

2. mixture of o- and m-bromotoluenes

3. mixture of o- and p-bromotoluenes

4. mixture of o- and p-dibromobenzenes

Ans: Option 3

37. At 800 C, the vapor pressure of pure liquid “A” is 520 mm Hg and that o pure liquid “B” is 1000 mm Hg. If a mixture solution of “A” and “B” boils at 800 C and 1 atm pressure, the amount of “A” in the mixture is (1 atm = 760 mm Hg)

1. 48 mol %

2. 50 mol %

3. 52 mol %

4. 34 mol %

Ans: Option 2

38. The equilibrium constants K₁ and K₂ for the reactions X=2Y and Z=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 pressure at these equilibrium is:

1. 1:3

2. 1:9

3. 1:36

4. 1:1

Ans: Option 1

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

1. H₂ is removed through occlusion with Pd.

2. CO is oxidized to CO₂ with steam in the presence of a catalyst followed by absorption of CO₂ in alkali.

3. CO and H₂ are fractionally separated using differences in their densities.

4. CO is removed by absorption in aqueous Cu₂Cl₂ solution.

Ans: Option 2

40. Which of the following property helps the substance to absorb moisture when, exposed to air?

1. Dehydration

2. Deliquescence

3. Decantation

4. Distillation

Ans: Option 2

41. What is the S.I. unit of the molar conductivity?

1. S^{m- 1} mol²

2. m² mol S^-1

3. S² m mol^-1

4. S m² mol^{– 1}

Ans: Option 4

42. Which of the following lattices has the most symmetrical arrangement of the lattice points?

1. Parallelogram lattice

2. Square lattice

3. Rectangular lattice

4. Hexagonal lattice

Ans: Option 1

43. In case of which of the following ionic solids, the radius ratio is minimum?

1. NaCl

2. CsCl

3. B₂O₃

4. ZnS

Ans: Option 3

44. Aqua regia is

1. HCl + HNO₃

2. 3HCl + HNO₃

3. HCl + H₂SO₄

4. HCl + H₂SO₄

Ans: Option 2

45. Which of the following has the lowest fusion temperature?

1. Naphthalene

2. NaCl

3. Diamond

4. Cr

Ans: Option 1

46. Which of the following processes is not a spontaneous process?

1. Expansion of gas into vacuum

2. Passage of gas from lower to higher pressure

3. Dissolution of salt in water

4. Evaporation of ether

Ans: Option 2

47. A thermodynamic process in which the volume of the system remains constant is known as

1. adiabatic process

2. isobaric process

3. isochoric process

4. isothermal process

Ans: Option 3

48. Ionisation depends upon

1. pressure

2. volume

3. dilution

4. None of these

Ans: Option 3

49. Which of the following reactions is an irreversible reaction?

1. 2NH₃ = N₂ + 3H₂

2. PCl₅=  PCl₃ + Cl₂

3. KClO₃ = KCl + O₂

4. SO₃ = SO₂ + O₂

Ans: Option 3

50.  A mixture of sand and iodine can be separated by

1. Distillation

2. Fractionation

3. Sublimation

4. Filtration

Ans: Option 3

51.  Formation of silver mirror is the test for

1. aldehydes

2. acids

3. thioalcohols

4. ethers

Ans: Option 1

52. The compound which gives violet colouration with neutral ferric chloride is

1. phenol

2. salicylic acid

3. salicylaldehyde

4. all of the above

Ans: Option 4

53. Which of the following nitro compounds behaves as an acid in the presence of a strong alkali?

1. Primary

2. Secondary

3. Tertiary

4. Both 1 and 2

Ans: Option 4

54.  Which of the following molecules has the highest boiling point, if the molecular weights are nearly the same?

1. CH₃CH₂CH₂CH₂OH

2. CH₃CH₂COOH

3. CH₃ CH₂O CH₂ CH₃

4. CH₃CH₂COCH₃

Ans: Option 2

55. An example for chromophore is

1. – N = N-

2. – OH

3. – CN

4. – C₆H₅ 

Ans: Option 1

56. Which of the following compounds is not soluble in NaOH?

1. Fe(OH)₃

2. Zn(OH)₂

3. Al(OH)₃

4. Sn(OH)₂

Ans: Option 3

57.  A simple salt is formed by the neutralization of

1. an acid by a base

2. an oxididsing agent by a reducing agent

3.a complex salt by a double salt

4. all of them

Ans: Option 2

58. For which of the following compounds, the hydration energy is greater than the lattice energy?

1. CaF₂

2. PbSO₄

3. AgCl

4. NaCl

Ans: Option 1

59.  The reaction, Zn + 2 HCl = ZnCl2 + H2,  is an example of

1. simple decomposition

2. simple combination

3. single displacement

4. double decomposition

Ans: Option 3

60. The stability of the complex is minimum in which of the following central metal ions?

1.  Fe2+

2.  Co2+

3.  Mn2+

  4.  Ni2+

Ans: Option 4

ANSWERS

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