Model Practice Paper of COMEDK with solutions

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Model Practice Paper of COMEDK with solutions
Section A
Mathematics

All questions are compulsory to be attempted.

 1.  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: Option 2

2. 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: Option 2

3. 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: Option 3

4. 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: Option 1

5. 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: Option 2

6. 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: Option 3

7. 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: Option 4

8. 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: Option 3

9. 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: Option 4

10. 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: Option 4

11. 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: Option 4

12. 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: Option 4

13. P, Q, R and S are to give lectures to an audience. The organizer can arrange the order of their presentations in

1.  4 ways

2.  8 ways

3.  12 ways

4.  24 ways

5.  4C₄

Ans: Option 5

14. The number of ways of selecting 2 candidates out of 5 equally qualified candidates for a post is

1.  5P₂

2.  5!

3.  5!/2

4.  10

5.  5

Ans: Option 3

15. 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 2

16.  There are 4 letter boxes in a post office. In how many ways can a man post 8 different letters?

1.  4⁸

2.  70

3.  48

4.  None of these

Ans: Option 3

17. The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

1.  297

2.  300

3.  271

4.  none of these

Ans: Option  1

18. There are n points on a circle. The number of straight lines obtained by joining them is

1.  nC₃

2.  nC₂  – n

3.  nC₂

4.  none of these

Ans: Option 3

19. 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

20. L.C.M. of n !, (n  + 1) ! and (n + 2) ! is

1.  n !

2.  (n + 2) !

3.  n

4.  none of these

Ans: Option 3

21. There are three copies, each of four different books. The number of ways in which they can be arranged on a shelf is

1. 12!/(3!)⁴

2. 12!/(4!)³

3. 12!/3! ⁴ 4!

4.  none of these

Ans: Option 1

22. If nC₄, nC₅ and nC₆ are in A.P, then n is equal to

1.  7

2.  14

3.  7 or 14

4.  None of these

Ans: Option 2

23. The number of subsets of a set containing n distinct objects is

1.  nC₁ + nC₂ + nC₃ + …… + nC_n

2.  nC₀ + nC₁ + nC₂  +….. + nC_n

3.  2n + 1

4.  none of these

Ans: Option 1

24. Find the number of ways in which a mixed double tennis game can be arranged between 10 players consisting of 6 men and 4 women.

1.  180

2.  90

3.  48

4.  none of these

Ans: Option 3

25. The number of all possible selections which a student can make for answering one or more questions out of eight given questions in a paper, when each question has an alternative, is

1.  8C1 + 8C2 + 8C3+….. + 8C8

2.  2 × 2⁸

3.  3⁸

4.  3⁸ – 1

Ans: Option 3

26. The number of ways in which 12 balls can be divided between two friends, one receiving 8 and the other 4 is

1.   12!/8!4!

2.   12!2!/8!4!

3.   12!/8!4!2

4.  none of these

Ans: Option 1

27. The sum of all numbers greater than 1000 formed by using digits 1, 3, 5, 7, such that no digit is being repeated in any number is

1.  72,215

2.  83,911

3.  106,656

4.  114,712

Ans: Option 1

28. A box contains 2 white, 3 black and 4 red balls. The number of ways in which 3 balls can be drawn from the box, so that at least one of the balls is black is

1.  45

2.  84

3.  64

4.  none of these

Ans: Option 1

29. The number of ways in which p + q things can be divided into two groups, containing p and q things respectively is

1.  C(p + q, q)

2.  P(p + q, p)

3.  P(p + q, q)

4.  C(p + q, p – q)

Ans: Option 2

30. The number of different permutations of the letters of the word HOLIDAY is

1. 256

2. 5040

3. 2520

4. 720

Ans: Option 4

31. If n = 7 and r = 3, then the value of the expression n!/n-r+1! is

1. 24

2. 42

3. 18

4. 7

Ans: Option 4

32. If 4 flags of different colours are available. The number of possibilities of forming all possible signals, provided each signal requires the use of 2 flags one below the other is

1. 24

2. 120

3. 12

4. 48

Ans: Option 2

33. The odd numbers less than 10,000 that can be formed using the digits 0, 2, 3, 5 allowing repetition of digits are

1. 96

2. 72

3. 128

4. 256

Ans: Option 1

34. The number of three letter words that can be formed with the letters of the word ORIENTAL is

1. 256

2. 336

3. 184

4. 128

Ans: Option 1

35. The number of ways of arranging 4 letters out of all the letters of the word ‘DIRECTLY’ is

1. 1256

2. 1120

3. 5040

4. 1680

Ans: Option 1

36. The values of r and n, such that 1< n < 8 and that P (n,r) is a prime number, are

1. r = 1, n = 3, 5, 7, 11

2. r = 2, n = 2, 3, 5, 7

3. r = 1, n = 2, 3, 5, 7

4. r = 2, n = 3, 5, 7, 11

Ans: Option 1

37. Three letters are being posted in 4 letter boxes. The number of ways in which the letters can be put is

1. 81

2. 27

3. 64

4. 9

Ans: Option 1

38.  The number of outcomes for a dice tossed 6 times is

1. 6!

2. 36

3. 66

4. 66

Ans: Option 3

39. If a man and his wife enter in a bus, in which five seats are vacant, then he number of different ways in which they can be seated is

1.    2

2.    5

3.    20

4.    40

Ans: Option 3

40. There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is

1. 2¹⁰

2. 10!

3. 10²³

4. 10²

Ans: Option 1

41. The circle x2   + y2   = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

1. –35 < m < 15

2. 15 < m < 65

3. 35 < m < 85

4. –85 < m < –35

Ans: Option 3

42. For two data sets, each of size 5, the variances are given to be 4 and 5 and the  corresponding

means are given to be 2 and 4, respectively. The variance of the combined data set is

1. 11/2

2. 6

3. 13/2

4. 5/2

Ans: Option 1

43. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

1. 2/7

2. 1/21

3. 2/23

4. 1/3

Ans: Option 1

44. Consider the system of linear equations:

x1   + 2×2   + x3   = 3

2x1   + 3×2   + x3   = 3

3x1   + 5×2   + 2×3   = 1

The system has

1. exactly 3 solutions

2. a unique solution

3. no solution

4. infinite number of solutions

Ans: Option 3

45. There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

1. 36

2. 66

3. 108

4. 3

Ans: Option 3

46. Let f: (–1, 1) − R be a differentiable function with f(0) = –1 and f’(0) = 1. Let g(x) = [f(2f(x) + 2)]2. Then g’(0) =

1. -4

2. 0

3. 2

4. 4

Ans: Option 1

47.  Let p(x) be a function defined on R such that p(x) = p(1 – x), for all x  [0, 1], p(0) = 1 and p(1) = 41.

Then p(x) dx equals

1. 21

2. 41

3. 42

4. √41

Ans: Option 1

48. A person is to count 4500 currency notes. Let an   denote the number of notes he counts in the n

minute. If a1   = a2   = …… = a10 = 150 and a10, a11, …… are in A.P. with common difference –2, then the time taken by him to count all notes is

1. 34 minutess

2. 125 minutes

3. 135 minutes

4. 24 minutes

Ans: Option 1

49. The line L given by x/5+y/b= 1 passes through the point (13, 32). The line K is parallel to L and has the equation x/c +y/3= 1. Then the distance between L and K is:

1. √17

2. 17/√15

3. 23/√17

4. 23/√15

Ans: Option 3

50. A line AB in three-dimensional space makes angles 45⁰ and 120⁰ with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle0 with the positive z-axis, then 0 equals

1. 45 degree

2. 60 degree

3. 75 degree

4. 30 degree

Ans: Option 2

51. The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

1. 1

2. 2

3. 3

4. 4

Ans: Option 1

52. If a and b are the roots of the equation x2   – x + 1 = 0, then a2009 + b2009 =

1. -1

2. 1

3. 2

4. -2

Ans: Option 2

53. Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x – y + z = 5.

Statement-2: The plane x – y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).

1. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

2. Statement-1 is true, Statement-2 is false

3. Statement-1 is false, Statement-2 is true

4. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement

Ans: Option 1

54. The number of 3 X 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

1. 5

2. 6

3. at least 7

4. less than 4

Ans: Option 3

55. If two tangents drawn from a point P to the parabola y2   = 4x are at right angles, then the locus of P is

1. 2x+1 = 0

2. x = -1

3. 2x-1 = 0

4. x = 1

Ans: Option 2

56. The vectors a=i-j+2k and c=xi+j+yk are mutually orthogonal, then (x,y) =

1. (2, -3)

2. (-2. 3)

3. (3, -2)

4. (-3, 2)

Ans: Option 4

57. The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is

1. 4√2+2

2. 4√2-1

3. 4√2+1

4. 4√2-2

Ans: Option 4

58. Let a = ˆj – kˆ and c = ˆi – ˆj – kˆ . Then vector b satisfying a ´ b + c = 0 and a × b = 3 is

1. 2i-j+2k

2. i-j-2k

3. i+j-2k

4. –i+j-2k

Ans: Option 4

59. 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: Option 4

60. 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: Option 4

Section B

Physics

1.  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: Option 2

2.  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: Option 2

3. 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: Option 2

4. 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

Ans: Option 3

5. 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

Ans: Option 4

6. 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

Ans: Option 3

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

1. 2 x 273 K

2.  2.4 x 273 K

3. 8 x 273 K

4.16 x 273 K

5. √2x 273 K

Ans: Option 4

8. 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. 42.7⁰ C

2. 35⁰ C

3. 47⁰ C

4. 40⁰ C

Ans: Option 2

9. 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. Q/2

3. – Q/2

4. – Q

Ans: Option 3

10. 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

Ans: Option 4

11. 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

Ans: Option 1

12. 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

Ans: Option 4

13. 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

Ans: Option 3

14. 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

Ans: Option 2

15. For EM wave propagating along x-axis, Emax = 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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 3

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. Then

1. a + b + c=1

2. a + b + c = 0

3. a-b-c = 0

4. a-b – c =1

Ans: Option 3

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. 4.  E/c2

Ans: Option 4

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

Ans: Option 4

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

Ans: Option 4

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

Ans: Option 3

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

Ans: Option 3

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

Ans: Option 1

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

Ans: Option 1

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

Ans: Option 2

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

Ans: Option 3

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

Ans: Option 2

29. 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: Option 1

30. 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: Option 3

31. 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: Option 3

32. 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

Ans: Option 4

33. 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: Option 3

34. 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

Ans: Option 1

35. 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. 3.  0.15 s
4. 0.3 s

Ans: Option 3

36. 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: Option 3

37.  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: Option 3

38. 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: Option 3

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

Ans: Option 4

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

Ans: Option 3

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

Ans: Option 3

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

Ans: Option 4

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

Ans: Option 4

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

Ans: Option 4

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

Ans: Option 3

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 2

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. Q/2

3. – Q/2

4. – Q

Ans: Option 2

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

Ans: Option 4

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

Ans: Option 4

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

Ans: Option 3

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 2

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

Ans: Option 1

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

5.  no change in K and U

Ans: Option 2

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

Ans: Option 1

Section C

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 3

 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)₂CHC

4. (CH₃)₃CC

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-bromoanilin

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

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 CH

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

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