Model Question [nET-2023]

Choose the one lettered choice that is best in each case and then fill in the corresponding circle in the answer
sheet provided.
Each question carries equal mark. Time: 2hrs
F.M. 1x100=100

MATHEMATICS
1) If A∩B = ϕ
A) A ⊂ B B) B⊂A
C) A ∩ B = ϕ D) A⊂B
2) The inequality 2 ≤ x ≤ 4 is same as
A) |x – 2|≤1 B) |x – 3|≤1
C) |x – 3|≤2 D) |x – 3|≤ 4

3) If A = (– 1, 3] and B = [0, 4), then A – B is

A) [– 1, 0) B) (– 1, 0]
C) [– 1, 0] D) (– 1, 0)

4) If f– 1(x) = 2x – 1, then f(x) is

A 2x + 1 B) 1
2x 1
C) x 1 D) x 1
2 2
5) The value of log16 64 is
A) 3 B) 2
2 3
C) 2 D) 3
6) The parabola y = ax2 is wider than y = x2 if
A) a<1 B) |a| < 1
C) a>1 D) |a| > 1
7) If the three positive numbers a, b, c are in AP, then
A) b2 = ac B) b2< ac
C) b=a+c D) b2> ac
8) If |x| < 1 and y = x + x2 + x3 + ….. …. … to ∞, then x is equal to

A) 1 B) 1
y 1 y
C) y D) 1 y
1 y y
9) If A is a square matrix, then A + AT is a

A) diagonal matrix B) scalar matrix

C) skew-symmetric matrix D) symmetric matrix
10)  3 2 
The inverse of the matrix   is
5 5 
A) 1  5 2  B) 1  5 2 
   
5  5 3  10  5 3 
C) 1  5 2 D) 1  3 2 
   
25  5 3  15  5 5 

11) 4 x4
If  0 , then the value of x is
2 x 1
A) 6 B) –6
C) 3 D) –3

12) 1  3i
If z = , then z 3 is equal to
2
A) i B) 1

C) –i D) –1

13) The multiplicative inverse of 3 – 2i is

A) 3 2 B) 2 3
 i  i
13 13 13 13
C) 3 2 D) 2 3
 i  i
13 13 13 13

14) The amplitude of the complex number – √ 3 – i is

A)  B) 2
6 3
C) 11 D) 7
6 6

15) The maximum value of sin x + cos x is

A) 1 B) 2
C) √2 D) 1/√2

16) The general solution of the equation 4 cos2 x = 1 is

A)  B) 
n  n 
6 6
C)  D) 
n  n 
3 3
17) The smallest angle of the triangle having sides 7cm, 4√3cm and √13cm is
A) 30o B) 60o
C) 45o D) 15o

18) The distance between the lines 4x – 3y = 22 and 4x – 3y = 12 is

A) 0 B) 2
C) 10 D) 5
19) The equation 3x2 + xy – y2 – 3x + 6y + k = 0 represents a pair of straight line, then k is
A) 9 B) –9
C) 0 D) 1
20) The line y = mx+ c is normal to the circle x2 + y2 = a2 if
A) c   a 1  m2 B) c=0
C) m=0 D) c=m=0
21) The equation of the tangent to the circle x2 + y2 = 13 at the point (2, 3) is
A) 2x + 3y = √13 B) 2x  3y = 13
C) 2x  3y = √13 D) 2x + 3y = 13

22) The equations ax + by + c = 0 and αx + βy + γ = 0 represents the same line if and only if
A) a b B) a = α, b = β, c = γ

 
C) a b c D) c=γ
 
  
23) The value of b for which the equations 9x + 4y = 9 and 7x + by = 5 have no solution is
A) 4 B) 7

C) 9 D) 28
28 9
24) lim  2 x  1 for x  0
f ( x) for the function f ( x)   is
x0  2 x  1 for x  0
A) 0 B) 1
C) –1 D) not exist
25) x  k, x  1
The value of k for which the function f ( x)   is continuous at x = 1 is
5  x, x  1
A) 4 B) 5
C) –3 D) 3
26) 1
The derivative of  x with respect to x is
x
A) 1 B) x2
1 ln x 
x2 2
C) ln x +1 D) 0

27) d2y
If y = ln (sin x), then is equal to
dx 2
A) cot x B) – cosec2 x

C) sec2 x D) – cosec x cot x

28) The derivative of tan x with respect to sec x is

A) sec2 x B) cos x
C) sin x D) cosec x
29) The derivative of 5x is
A) 5xlog 5 B) 5x
C) x 5x - 1 D) 5x
log 5
30) | x |, x0
The function f ( x)   at the point x = 0 is
0, x0
A) differentiable B) continuous but not differentiable
C) not continuous D) none of these

31) The interval in which the function f(x) is increasing is

A) (2, ∞) B) [– 2, ∞)
C) (– 2, ∞) D) [2, ∞)

32) The tangent to the parabola x2 = 2y at (1, 2) makes with x-axis an angle of
A) 0o B) 45o
C) 30o D) 60o
33) The minimum value of x2 + 1/x2 is
A) 1 B) 2
C) –2 D) 3

34) If the radius of the circular plate on heating is increasing at the rate of 1.2 cm/s, then the rate of
increase of its circumference is
A) 1.2π cm/s B) 2π cm/s
C) π cm/s D) 2.4π cm/s
35) dx
 x log x
A) log(logx) +c B) x log x – x + c
C) xx + c D) (log x)/x + c

36) x
 x  3 dx is equal to

A) x + 3 ln |x + 3| + c B) x – 3 ln |x + 3| + c
C) 3 ln |x + 3| + c D) x + ln |x + 3| + c
37) e

 ln x dx is equal to
1

A) 0 B) e
C) –1 D) 1

38) ∫ xe-x dx is equal to

A) x e–x – e–x + c B) – x e–x + e–x + c
C) x e–x + e–x + c D) – x e–x – e–x + c
39) The area bounded by the curves y2 = 4x and x = 9 is
A) 12 B) 18
C) 24 D) 36
40) The area bounded by y2 = x  1, y-axis between y = 0 to y = 3 is
A) 6 B) 12
C) 9 D) 10

PHYSICS
41) What are the dimensions of Van der wall’s Constant ‘a’ in the formula: (𝑃 +
𝑎
𝑉2
) (𝑉− 𝑏) = 𝑅𝑇, Here, ‘P’ and ‘V’ and pressure and volume.
A) [M L-1 T-2] B) [M L T-2]
C) [M L5 T2] D) [M L5 T-2]

42) The maximum height (H) attained by a projectile launched with initial velocity ‘u’ and angle ‘𝜃′ is:

A) 𝑢 𝑠𝑖𝑛2 𝜃 B) 𝑢2 𝑠𝑖𝑛2𝜃
2𝑔 2𝑔
C) 𝑢2 𝑠𝑖𝑛2 𝜃 D) 𝑢2 𝑠𝑖𝑛2 𝜃
2𝑔 𝑔2

43) A body of mass 5 kg is acted upon by two perpendicular forces 8N and 6N. What is the direction of
acceleration?
A) 𝑇𝑎𝑛−1 (3/4) B) 𝑠𝑖𝑛−1 (3/4)
C) 𝐶𝑜𝑡 −1 (3/4) D) 𝑇𝑎𝑛−1 (4/3)

44) The mass of the Sun, if the mean radius of the Earth’s orbit is ‘R’ and ‘G’ is gravitational constant, is

A) 4𝜋 2 𝑅3 B) 4𝜋𝑅 2
𝐺𝑇 2 3𝐺𝑇 2
C) 4𝜋𝑅 3 D) 3𝜋 2 𝑅3
𝐺 2𝑇 4𝐺𝑇 2

45) An electron revolves round a nucleus in an orbit of radius 0.5× 10−10 𝑚. If its linear velocity in the
orbit is 2.2× 106 𝑚/𝑠, what will be its angular momentum (in SI units)?
A) 10−35 B) 10−34
C) 1035 D) 10−36

46) If two temperatures differ by 25 on Celsius scale, what is the difference on Fahrenheit scale?
A) 25 B) 45
C) 52 D) 54

47) The efficiency of a Carnot engine depends upon :

A) Nature and amount of working B) Temperature of sink only
substance
C) Temperature of source only D) Temperature of source and sink
48) Which of the following expresses the relationship between focal length (f) and radius of curvature (R)
of a curved mirror?
A) R = f/2 B) f = R/2
C) f = 2R D) R = 2f

49) The value of permittivity of free space (in unit Farad/meter) is:
A) 8.85 x 1012 B) 8.85 x 10-12
C) 9.1 x 109 D) 9.1 x 10-9

50) Velocity of radio wave is 3.0 × 108 m/s. A radio station broadcasts on a wavelength of 2.0 m. It’s
frequency in MHz is:
A) 1.5 x 108 B) 1.5 x 102
C) 1.5 x 106 D) 1.5

51) Truth Table:

A B C
0 0 1
1 0 1
0 1 1
1 1 0
A and B are inputs and C is the output of a logic gate. The type of such gate is:

A) NOR B) AND
C) OR D) NAND

52) A physical constant that appears in de – Broglie equation is:

A) Planck’s constant B) Faraday’s constant
C) Gravitational constant D) Boltzmann’s constant
53) Magnetic susceptibility of some materials is large and positive. Those materials are called:
A) Paramagnetic B) Ferromagnetic
C) Antiferromagnetic D) Diamagnetic

54) In which of the following materials, electrical conductivity increases with increase in temperature?
A) Cobalt B) Germanium
C) Nichrome D) Copper
55) A coil has ‘N’ turns, radius ‘a’ and carries current ‘i’.Magnetic field at it’s center is:
A) 𝜇0 𝑁𝑖 B) 𝜇0 𝑁𝑖
2𝜋𝑎 2𝑎
C) 𝜇0 𝑁𝑖 D) 𝜇0 𝑁𝑖 2
2𝜋 2𝜋𝑎

56) Which of the following phenomena is followed only by transverse waves?

A) Diffraction B) Polarization
C) Interference D) Refraction
57) The 𝛾 − ray emitted by a radioactive nucleus, actually is:
A) Photon B) Electron
C) Proton D) Neutron
58) The atomic mass unit is used for unit of:
A) Mass only B) Energy only
C) Both mass and energy D) Neither mass nor energy

59) Mass of a proton (in Kg) is equal to:

A) 9.11 × 10−31 B) 1.67 × 10−27
C) 1.68 × 10−27 D) 1.60 × 10−19
60) In a simple harmonic motion, the K.E. of the body is maximum at which position?
A) Extreme B) Between extreme and mean
C) Mean D) K.E. is constant

61) The energy stored in a capacitor is given by:

A) 1 𝑞 2 B) 1 2
𝑞 𝐶
2𝐶 2
C) 1 2 D) 1 1
𝑞𝐶
2 2 𝑞2𝐶

62) The prefix ‘ Pico’ used in a unit represents:

A) 1015 B) 10-12
C) 10-15 D) 1012
63) Which of the parameters below does not change on refraction of wave?
A) Wavelength B) Phase
C) Speed D) Frequency
64) Which of the following is correct for X – ray:
A) Deflected by electric field B) Does not possess charge
C) Deflected by magnetic field D) Possess charge
65) In parallel combination of resistors with unequal resistances, the equivalent resistance:
A) Is less than minimum of that in B) Is more than maximum of that in combination
combination

C) Remains as that of minimum one of in D) Remains as that of maximum one in combination

combination

66) A lens of power -4D is placed in contact with a lens of power +2D.The power of lens combination will
be
A) +6D B) +2D
C) -2D D) -1D
67) If the normal reaction is doubled, keeping limiting friction same, the coefficient of friction is
A) not changed B) halved

C) doubled D) tripled
68) The amount of heat required to change the state of 1kg of substance at constant temperature is called
A) Kilocal B) Calorie

C) Specific heat D) Latent heat

69) Mechanical waves can be
A) longitudinal only B) transverse only
C) both longitudinal and transverse D) neither longitudinal nor transverse

70) The bending of light waves through the corners of the obstacle is called
A) refraction B) diffraction
C) interference D) beats

ENGLISH
71) Dikendra got his servant_______ his house.
A) paint B) to paint
C) painted D) painting

72) Among the following words, _______has /æ/ sound.

A) mouth B) moon
C) sound D) add
73) The word ‘Tabulate’ has primary stress on_____ syllables.
A) 1st B) 2nd
C) 3rd D) 4th
74) The word _____has three syllables from the following.
A) absent B) academy
C) department D) beauty

75) The man has been working here______ last Monday.

A) for B) to
C) from D) since

76) If you boil the water, it____ into vapour.

A) changes B) will change
C) would change D) will be changed
77) The passive form of the sentence, ‘Everybody speaks English all over the world’ is________.
A) English was spoken all over the world B) English is spoken all over the world

C) English is being spoken all over the D) English has been spoken all over the world
world
78) Question tag of the sentence, ‘Let’s prepare the minute’, ______________?
A) shall we B) will you
C) do you D) don’t we

79) I explained that I was ____artist, but that I was sometimes _______ plumber as well.
A) an, the B) a, a
C) an, a D) an, an
80)
The indirect speech of He says “I will meet you at the station” is_____________.
A) he says that he would meet him at the B) he said that he would meet him at the station
station
C) he said that he will meet him at the D) he says that he will meet him at the station
station
CHEMISTRY
81) Minimum energy required for the molecules to enter into the reaction is called
A) Potential energy B) Kinetic energy
C) Activation energy D) Nuclear energy

82) Le -Chatelier’s principle is not applicable to

A) Homogenous reaction B) Not homogenous reaction
C) System that is in equilibrium D) System that is not in equilibrium

83) Why liquid ammonia is used in refrigerator? Because of its

A) High basicity B) High heat of vaporization
C) High dipole moment D) All the above

84) Tick the necessary conditions for Geometrical isomerism

A) There should be carbon - carbon B) First carbon must contain two different groups
double bond compound attached
C) Second carbon must contain same D) All the above
group as the first carbon

85) Which test is useful to distinguish formaldehyde with acetaldehyde?

A) Schiff’s test B) Fehling’s test
C) Test with Iodine in basic condition D) Tollen’s test

86) Bromomethane can be converted into methanol in suitable chemical environment, the reaction involved
is
A) Nucleophilic substitution B) Electrophilic substitution
C) Elimination D) Addition

87) Markovnikoff’s rule is applicable to

A) Free radical addition reaction B) Electrophilic addition reaction
C) Substitution reaction D) Elimination reaction

88) In which type of reaction, the number of pi bonds in the product increases?
A) Elimination reaction B) Addition reaction
C) Substitution reaction D) Electrophilic addition reaction

89) A sample of drinking water was found to be severely contaminated with chloroform (CHCl3) supposed
to be a carcinogen. The level of contamination was 20 ppm (by mass), express this in % by mass.
A) 20x 10 5x100 B) 20/10 6 x100
C) 20/10 5x100 D) 20x106 x100
90) Which of the following is optically active compound?
A) Formic acid B) Acetic acid
C) Phenol D) Lactic acid
91) Transition metal compounds are colorful because
A) it has unpaired electrons in d orbitals B) it has completely filled d orbitals
C) it has filled p orbitals D) All the above

92) Tick the correct order according to the size of ionic/atomic radii
A) Cu++ > Ca > Cl-> Al+3 B) Ca> Cu++ > Cl-> Al+3
C) Ca> Cl-> Cu++ > Al+3 D) Ca> Cl-> Al+3>Cu++

93) Which of the following metals are used for manufacturing batteries of mobile phone
A) Cobalt and Zn B) Cobalt and Lithium
C) Nickel and Lithium D) Cadmium and lithium

94) The consequences of global warming is

A) Precipitation pattern changes B) Rise of temperature
C) Drought D) All the above

95) In the galvanic cell

A) Oxidation occurs at anode and B) Oxidation occurs at cathode and reduction occurs
reduction occurs at cathode at anode
C) Only oxidation occurs at cathode D) Only reduction occurs at anode

96) If you titrate 1M H2SO4 solution against 50ml of 1M NaOH solution, what volume of H2SO4, in
milliliters,
A) 25 will be needed for neutralization? B) 10
C) 75 D) 2

97) Which of the following pair of compounds can be used to illustrate the law of Multiple Proportions?
A) NO &NO2 B) ZnO2&ZnCl2
C) H2O&HCl D) CH4&CO2

98) 4grams of hydrogen are ignited with 4 grams of oxygen. How many grams of water can be formed
A) 0.5 B) 4.5
C) 2.5 D) 36

99) Which of the following atom normally forms monoatomic molecule?

A) Oxygen B) Hydrogen
C) Nitrogen D) Helium

100) What is the approximate pH of a 0.005M solution of H2SO4 ?

A) 5 B) 1
C) 2 D) 13