25-03-2025

2701CJA101022240063 JM

PHYSICS

1) Electric field on the axis of a small electric dipole at a distance r is E; and at a distance of 2r on its
perpendicular bisector, the electric field is E2 .Then the ratio E2 : E1 is

(A) 1: 4
(B) 1:16
(C) 1: 8
(D) 1: 2

2) The displacement of a particle of mass 0.1 kg from its mean position is given by,
(where all the quantities are in S.I. unit). Period of motion is 0.1s. The
total energy of the particle is

(A)
(B) 0.05 J
(C)
(D) 5 J

3) A copper rod of 88 cm and an aluminium rod of unknown length have their increase in
length independent of increase in temperature. The length of aluminum rod is:

(A) 88 cm
(B) 68 cm
(C) 6.8 cm
(D) 113.9 cm

4) The photon of frequency is incident on a metal surface whose threshold frequency is .

The kinetic energy of the emitted photoelectrons will be

(A)
(B)
(C)
(D)

5) It is possible to recognize a person by hearing his voice even if he is hidden behind a solid
wall. This is due to the fact that his voice

(A) has definite pitch.

(B) has a definite quality.
(C) has a definite capacity.
(D) can penetrate the wall.

6) The velocity of water in river is 8 km/hr of the upper surface. The river is 12 m deep. If
the coefficient of viscosity of water is 10–2 poise then the shearing stress between horizontal layers
of water is

(A) 0.25 × 10–2 N/m2

(B) 1.85 × 10–3 N/m2
(C) 1.5 × 10–3 N/m2
(D) 0.75 × 10–3 N/m2

7) Assuming the expression for the pressure exerted by the gas on the walls of the container, it can
be shown that pressure is

(A)
kinetic energy per unit volume of a gas.

(B)
kinetic energy per unit volume of a gas.

(C)
kinetic energy per unit volume of a gas.

(D)
kinetic energy per unit volume of a gas.

8) Two identical light sources s1 and s2 emit light of same wavelength . These light rays will exhibit
interference if their

(A) phase differences remain constant.

(B) phases are distributed randomly.
(C) light intensities remain constant.
(D) light intensities change randomly.

9) An ideal choke takes a current of 10 ampere when connected to an A.C supply of 125 volt and 50
Hz. A pure resistor under the same conditions takes a current of 12.5 ampere. If the two are
connected to an A.C. supply of volt and 40 hertz, then the current in a series combination of
the above resistor and inductor is

(A) 10 ampere
(B) 12.5 ampere
(C) 20 ampere
(D) 25 ampere

10) Assertion: Corresponding to a path difference x, the phase difference is Reason : The
phase difference between displacement and velocity of a particle executing S.H.M is π.

(A) Assertion is True, Reason is true ; Reason is a correct explanation for Assertion.
(B) Assertion is True, Reason is True; Reason is not a correct explanation for Assertion.
(C) Assertion is True, Reason is False.
(D) Assertion is False, Reason is True.

11) The reactance of a circuit is zero. It is possible that the circuit contains

(A) two inductors connected in parallel with each other.

(B) an inductor and a capacitor.
(C) a capacitor but no inductor.
(D) an inductor but no capacitor.

12) 1 litre of an ideal gas at 27 °C is heated at a constant pressure to 127 °C. The final volume is
approximately

(A) 7.5 litre

(B) 1.3 litre
(C) 0.75 litre
(D) 13 litre

13) In a semiconductor diode, the barrier potential offers opposition to only

(A) majority charge carriers.

(B) minority charge carriers.
(C) free electron in n-region.
(D) hole in the p-region.

14) Two tuning forks have frequencies 380 Hz and 384 Hz respectively. When they are
sounded together, maximum sound is heard. How long will it take to hear the minimum sound?

(A)

(B)

(C)

(D)

15) Two simple pendulums of lengths 1.44 m and 1.96 m start swinging together. After how
many vibrations will they again start swinging together?

(A) 5 oscillations of smaller pendulum

(B) 6 oscillations of smaller pendulum
(C) 4 oscillations of bigger pendulum
(D) 6 oscillations of bigger pendulum

16) Three rings, each of mass P and radius Q, are arranged as shown in the figure. The moment
of inertia of the arrangement about YY" will be

(A)

(B)

(C)

(D)

17) A dielectric is inserted between the plates of a charged and isolated parallel-plate air
capacitor. Then, the. charge on the plates and the potential difference, respectively,

(A) increases, remains the same.

(B) remains the same, increases.
(C) remains the same, decreases.
(D) decreases, remains the same.

18) Two thin converging lenses of focal lengths 0.15 m and 0.30 m are held in contact with
each other. The focal power (P) and focal length (f) of combination are

(A)

(B)

(C) P = 2D, f = 0.5 m

(D) P=10 D, f = 0.1m

19) A potentiometer wire is 10 m long and has resistance of 2 Ω/m. It is connected in series with a
battery of em.f 3 V and a resistance of 10 Ω. The potential gradient along the wire in V/m is

(A) 0.01
(B) 0.02
(C) 0.1
(D) 0.2

20) The first line of Balmer series has wavelength 6563 . What will be the wavelength of the
first member of Lyman series?

(A) 1215.4

(B) 2500

(C) 7500

(D) 600

21) In which of the following processes, heat is neither absorbed nor released by a system?

(A) isobaric
(B) isochoric
(C) isothermal
(D) adiabatic

22) A conductor in the form of a right angle ΔABC with AB =3 cm and BC =4 cm carries a current of
15 A. There is a uniform magnetic field of 8 T perpendicular to the plane of the conductor. The force
on the conductor will be

(A) 1.5 N
(B) 6.0 N
(C) 2.5 N
(D) 3.5 N

23) Relative permittivity and permeability of a material are and and , respectively. Which of the
following values of these quantities are allowed for a diamagnetic material?

(A)
(B)
(C)
(D)

24) Two different wire loops are concentric and lie in the same plane. The current in the outer loop
(I) is clockwise and increases with time. The induced current in the inner loop

(A) is clockwise.
(B) is zero.
(C) is counter clockwise.
(D) has a direction that depends on the ratio of the loop radii.

25) Same current is flowing in two a.c. circuits. First contains only inductance and second contains
only capacitance. If frequency of a.c. is increased for both, the current will

(A) increase in first circuit and decrease in second.

(B) increase in both circuits.
(C) decrease in both circuits.
(D) decreases in first circuit and increases in second.

26) The magnitudes of the gravitational potentials at distances r1 and r2 from the centre of a
uniform sphere of radius R and mass M are V1 and V2 respectively. Then

(A)
if r1 < R r2 < R

(B)
if r1 > R r2 > R

(C)
if r1 < R r2 < R

(D)
if r1 > R r2 > R

27) The current gain α of a transistor is 0.95. The change in collector current corresponding to
a change of 0.4 mA in the base current in a common emitter arrangement is

(A) 0.38 mA
(B) 2.375 mA
(C) 0.42 mA
(D) 7.6 mA

28) A sonometer wire resonates with a given tuning fork forming standing wave with 5
antinodes between two bridges when mass of 9 kg is suspended from the wire. When mass 'M'
is suspended from the wire, with same fork and same length between two bridges 3 antinodes are
formed. Mass M is

(A) 25 kg
(B) 10 kg
(C) 15 kg
(D) 20 kg

29) A rod of length 1 m and mass kg rotates at an angular speed of 6 rad s–1 about one of its
ends. The kinetic energy of the rod is

(A) 1 joule
(B) 2 joule
(C) 3 joule
(D) 4 joule

30) A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between
the plates is
(A) increased proportional to 2.

(B)
decreased proportional to .
(C) increased proportional to .

(D)
decreased proport1ona to

31) A particle of mass m is executing uniform circular motion on a path of radius r. If p is

the magnitude of its linear momentum, the radial force acting on the particle is

(A) pmr

(B)

(C)

(D)

32) When a glass prism is placed inside water, its dispersive power ________.

(A) decreases
(B) remains the same
(C) increases
(D) may increase or decrease depending on refracting angle of prism

33) Surface tension of a liquid is numerically equal to

(A) surface energy

(B) surface energy per unit length.
(C) surface energy per unit area
(D) surface energy per unit volume.

34) Consider a process shown in the figure. During this process, the work done by the system

(A) continuously increases.

(B) continuously decreases.
(C) first increases, then decreases.
(D) first decreases, then increases.
35) The angular spread of central maximum, in diffraction pattern, does not depend on _______.

(A) the distance between the slit and source

(B) width of slit
(C) wavelength of light
(D) frequency of light

36) A particle with charge q moves with a velocity in a direction perpendicular to the directions
of uniform electric and magnetic fields, E and B respectively, which are mutually perpendicular to
each other. Which one of the following gives the condition for which the particle moves undeflected

in its original trajectory?

(A)

(B)

(C)

(D)

37) rectangular loop of area 0.4 m2 is lying in a magnetic field of 4 × 10–2 tesla at an angle of 60°
with the magnetic field. The magnetic flux passing through this loop will be

(A) 8 × 10–4 weber

(B) 8 × 10–3 weber
(C) 8 × 10–2 weber
(D) zero

38) The magnetic field energy in an inductor changes from maximum value to minimum value in 10
ms, when connected to an a.c. source. The frequency of the source is

(A) 25 Hz
(B) 50 Hz
(C) 200 Hz
(D) 500 Hz

39) In negotiating curve on a flat road, a cyclist Ieans inwards by an angle θ with the vertical in
order to
(A) counteract the torque of the frictional force that tends to topple him outwards.
(B) counteract the centrifugal force.
(C) generate a centripetal force.
(D) counteract the centripetal force with an equal centrifugal force.

40) The radius and mass of earth are increased by 0.5%. Which of the following statements are true
at the surface of the earth?

(A) g will increase

(B) g will decrease
(C) Escape velocity will remain same
(D) Potential energy will remain same.

41) In case of npn transistors, the collector current is always less than the emitter current because

(A) collector side is reverse biased and emitter side is forward biased.
(B) after electrons are lost in the base, only remaining ones reach the collector.
(C) collector side is forward biased and emitter side is reverse biased.
(D) collector being reverse biased attracts less electrons.

42) The equation of a plane progressive wave is When it is reflected at

a rigid support, its amplitude becomes of its Previous value. The equation of the reflected wave
is

(A)

(B)

(C)

(D)

43) The pointer reading v/s load graph for a spring balance is as given in the figure. The

spring constant is

(A) 0.1kg/cm
(B) 0.04 kg/cm
(C) 40kg/cm
(D) 15kg/cm
44) Polarised dielectric is equivalent to_______.

(A) Gaussian surface

(B) charged surface
(C) induced charged surface
(D) two charged surfaces with induced charges

45) In following figure, a current of 1.4 A flows towards the bridge circuit. The current in 2

Ω resistor is

(A) 1.4A
(B) 1.2 A
(C) 1.0 A
(D) 0.6 A

46) 'Half-life’ of a radioactive substance accounts for

(A) time required for complete disintegration complete disintegration of radioactive substance.
(B) time required for two-third disintegration of radioactive substance.
(C) time required for the disintegration of half the radioactive substance.
(D) time required for one-third disintegration of radioactive substance.

47) When the kinetic energy of an electron is increased, the wavelength of the associated wave
will________.

(A) increase
(B) decrease
(C) remain same
(D) become twice

48) A force of acts on a particle. If x is in metre, calculate the work done by the
force during the displacement of the particle from x = 0 to x = 4 m

(A) 128 J
(B) 80 J
(C) 64 J
(D) 52 J

49) A soap bubble of diameter 4 mm is formed in air. The surface tension of liquid is 15
dyne/cm. The excess pressure inside the soap bubble is
(A) 150 dyne/cm2
(B) 300 dyne/cm2
(C) 400 dyne/cm2
(D) 3 × 10–3 dyne/cm2

50) Absorption coefficient of totally blackbody is

(A) zero
(B) one
(C) more than one
(D) infinity

CHEMISTRY

1) The reagent used in Gatterman reaction is:

(A) KI
(B) H3PO2/H2O
(C) Cu powder/HCl
(D) CuCl/HCI

2) Which of the following is recycled to prepare foam packaging and light switchplates?

(A) Polyethylene terephthalate

(B) High density polyethylene
(C) Polypropylene
(D) Polystyrene

3) Mist is a colloidal solution of__________.

(A) solid in gas

(B) gas in gas
(C) liquid in gas
(D) gas in liquid

4) Molecular formula of the functional isomer of methyl formate is_________.

(A) C2H4O2
(B) C3H6O2
(C) C4H8O2
(D) C5H10O2

5) Identify the INCORRECT statement regarding glucose.

(A) Naturally occurring glucose is known as dextrose.

(B) It has five hydroxyl groups.
(C) It is highly soluble in alcohol.
(D) It is an aldohexose

6) Which of the following is INCORRECT for aromatic hydrocarbons?

(A) They burn with sooty flame.

(B) They do not undergo addition reactions easily.
(C) They are not attacked by normal oxidizing and reducing agents.
(D) They decolourise dilute alkaline aqueous KMnO4 and Br2 in CCl4.

7) The molar solubility of calcium oxalate, CaC2O4 at 25 °C is 4.8 × 10–5 mol/dm3. The value of Ksp
is____________.

(A) 2.3 × 10–9

(B) 2.3 × 10–10
(C) 4.4 × 10–9
(D) 4.4 × 10–10

8) Calculate rate of appearance of B in following reaction 3A →2B + C, if rate of disappearance of A

is 0.050 mol dm–3 s–1

(A) 0.025 mol dm–3 s–1

(B) 0.033 mol dm–3 s–1
(C) 0.075 mol dm–3 s–1
(D) 0.050 mol dm–3 s–1

9) Identify the CORRECT statement.

In lanthanoids, the d-orbitals are filled gradually while in actinoids, f-orbitals are filled
(A)
gradually.
(B) Lanthanoids form complexes easily as compared to actinoids.
(C) Lanthanoids do not form oxocations, but actinoids form oxocations.
(D) Actinoids are more reactive than lanthanoids.

10) Which of the following is NOT a chiral molecule?

(A)
(B)

(C)

(D)

11) The CORRECT decreasing order of solubility in water will be_______.

(A) C2H5NH2>(C2H5)2NH>(C2H5)3N
(B) (C2H5)2NH>C2H5NH2>(C2H5)3N
(C) C2H5NH2>(C2H5)3N > (C2H5)2NH
(D) (C2H5)3N > C2H5NH2 > (C2H5)2NH

12) Which of the following is CORRECT about melamine-formaldehyde resin?

(A) Itis a thermosetting plastic

(B) Itis an elastomer.
(C) Itis prepared by addition polymerisation.
(D) Itis a biodegradable polymer.

13) Amongst the following, HBr reacts fastest with_______.

(A) propan-1-ol
(B) propan-2-ol
(C) 2-methylpropan-1-ol
(D) 2-methylpropan-2-ol

14) ___________show highest melting points in their respective series.

(A) Cr, Mo and Ta

(B) V, Nb and W
(C) Ti, Zr and Hf
(D) Cr, Mo and W

15) For the reaction, CH4(g) + H2(g) → C2H6(g), Kp = 3.356 × 1017 . Calculate ΔG° for the reaction at 298
K.
(A) +100kJ mol–1
(B) +50 kJ mol–1
(C) –50 kJ mol–1
(D) –100 kJ mol–1

16) The solubility of the following salts in water increases with increase in
temperature, EXCEPT_______.

(A) Na2SO4
(B) KNO3
(C) KCl
(D) NaNO3

17) Calculate radius of second orbit of He+.

(A) 52.9 pm
(B) 105.8 pm
(C) 238.1 pm
(D) 211.6 pm

18) ‘What mass of an oxygen gas will occupy 8.21 L of volume at 1 atm pressure and 400
K temperature?

(A) 8 g
(B) 4 g
(C) 2 g
(D) 12 g

19) When a non-electrolyte, non-volatile solute is dissolved in water, the observed depression
in freezing point of water is 0.186 K. What is the molality of the solution if molal depression constant
for water is 1.86 K kg mol–1?

(A) 0.001 m
(B) 0.01 m
(C) 0.1m
(D) 1.0 m

20) Consider the reactions

The average C–H bond enthalpy is __________.

(A) y kcal
(B) x1 kcal
(C) x/4 kcal
(D) x1/4 kcal

21) Find the rate constant of a first order reaction if it is 25% completed in 20 minutes.

(A) 1.43 × 10–2 minute–1

(B) 4.44 × 10–2 minute–1
(C) 9.78 × 10–2 minute–1
(D) 1.20 × 10–3 minute–1

22) The product of the reaction between dialkyl cadmium and acy] chloride is a/an_______.

(A) aldehyde
(B) ketone
(C) carboxylic acid
(D) ester

23) The side chain R in cysteine is_______.

(A) –CH2Ph
(B) –CH2PH
(C) –CH2SH
(D) –CH2NH2

24) The formula of potassium amminetrichloroplatinate(II) is, _______.

(A) K[Pt(NH3)Cl3]
(B) K[Pt(NH3)Cl5]
(C) K2[Pt(NH3)Cl3]
(D) K3[Pt(NH3)Cl3]

25) Identify the strongest oxidising agent.

(A) Na
(B) Pt2+
(C) I2
(D) Sn2+

26) Which of the following are examples of weak bases?

(A) Fe(OH)3 and Cu(OH)2

(B) Fe(OH)3 and NaOH
(C) KOH and Cu(OH)2
(D) NH4OH and NaOH

27) The rate law for a reaction between the substances A and B is given by, rate = k[A]n [B]m. On
halving the concentration of A and doubling the concentration of B, the ratio of the new rate to the
earlier rate of the reaction will be as__________.

(A)

(B) (m + n)
(C) (n – m)
(D) 2(m – n)

28) Which of the following statements is INCORRECT?

(A) For given alkyl group (here – CH3), boiling point decreases as, RI> RBr > RCl > RF.
(B) The C-X bond length increases from fluorine to iodine.
(C) For isomeric alkyl halides, boiling point decreases with increased branching.
(D) The C-X bond strength increases with an increase in size of halogen atom.

29) Identify the functional group in the product formed.

(A) Tertiary amine

(B) Ketone
(C) Ester
(D) Amide

30) Identify secondary alcohol from the following.

(A) ethanol
(B) isopropyl alcohol
(C) methyl alcohol
(D) n-propyl alcohol

31) Match the following

Column I Column II

i. Limestone a. Cao

ii. Quicklime b. Ca(OH)2

iii. Slaked lime c. CaCO3

iv Caustic soda d. NaOH

(A) i - c; ii - a; iii - b; iv - d
(B) i - d; ii - a; iii - b; iv - c
(C) i - c; ii - b; iii - a; iv - d
(D) i - b; ii - c; iii - d; iv - a

32) In an experiment, I g of a non-volatile solute was dissolved in 100 g of acetone (molar mass = 58
g mol–1) at 298 K. The vapour pressure of the solution was found to be 192.5 mm Hg. The molecular
weight of solute is (vapour pressure of acetone = 195 mm Hg)__________g mol–1.

(A) 25.24
(B) 35.24
(C) 45.24
(D) 55.24

33) Identify the INCORRECT statement regarding canonical forms.

The average of all canonical forms contributes to overall bonding characteristic features of the
(A)
molecule.
(B) Only the lowest energy canonical form is adequate to explain all the properties of the molecule.
(C) Energy of the resonance hybrid structure is less than the energy of any single canonical form
(D) Each canonical form differs from the other only in the position of electrons.

34) A system releases 700 J of heat and does work. The change in internal energy (ΔU) for
the process is -460 J. The work done is_____.

(A) –460 J
(B) + 240 J
(C) –250 J
(D) +460 J

35) The mass of sulphur dioxide produced by burning 32 g of sulphur in excess of oxygen in contact
process is _______g. (Average atomic mass : S = 32 u, O = 16 u).

(A) 32
(B) 64
(C) 128
(D) 160

36) What is the concentration of silver nitrate solution which has the molar conductivity of
and the conductivity of at 298 k ?

(A) 0.02 M
(B) 0.05 M
(C) 0.1 M
(D) 0.08 M

37) Which of the following statements are TRUE?

(A) In SeCl2, there are two lone pairs of electrons on the central atom.
(B) SeO2 is amphoteric in nature.
(C) HBr is a liquid at room temperature.
(D) SbCl3 is more covalent than SbCl5.

38) Which of the following matches are CORRECT

(I) Frenkel defect: Electrical neutrality of the compound is preserved .
(II) Schottky defect: Density of the substance decreases.
(III) Schottky defect: Combination of vacancy defect and interstitial defect.
(IV) Frenkel defect: Small difference between size of cation and anion.

(A) I, II
(B) I, III
(C) I, IV
(D) I, II, IV

39) Match the following

Oxidation no. of underlined

Compound
element

i. a. +2.5

ii. N3H b. +1.5

iii. Mg2P2O7 c. +5

iv. Na2S4O6 d. –1/3

(A) i-c, ii-b, iii-d, iv-a
(B) i-b, ii-d, iii-c, iv-a
(C) i-d, ii-c, iii-a, iv-b
(D) i-a, ii-d, iii-b, iv-c

40) Which of the following reaction is NOT involved in contact process used for manufacturing
sulfuric acid?

(A)

(B)

(C)
(D)

41) Hydrides of transition metals are used as powerful _____agents.

(A) bleaching
(B) dehydrating
(C) oxidising
(D) reducing

42) Which of the following alcohol contains –OH group attached to a sp2 hybridised carbon atom ?

(A) Eth-l-en-l-ol
(B) 2-Phenylpropan-2-ol
(C) Prop-2-en-l-ol
(D) 2-Methylpropanol

43) When a solution of Grignard reagent is added to ___________, a magnesium salt of carboxylic acid
is obtained which on acidification gives carboxylic acid.

(A) ice
(B) dry ice
(C) water
(D) sulphur dioxide

44) Which of the following statements is INCORRECT?

(A) Dihydrogen in used in the manufacture of vanaspati ghee.

(B) A mixture of liquid hydrogen and liquid oxygen is used as rocket fuel.
(C) Dihydrogen is used in the manufacture of ammonia by Haber’s process.
(D) Liquid hydrogen is used for cutting and welding purposes.

45) The number of geometrical isomers of [CrCl2(en)2]+ is_______.

(A) 2
(B) 3
(C) 4
(D) 6

46) Which of the following statements is INCORRECT about hyperconjugation?

(A) Hyperconjugation is also known as no bond resonance.

(B) Hyperconjugation is a permanent effect which stabilizes cation.
Greater the number of alkyl groups attached to the positively charged carbon atom, greater is
(C)
the effect of hyperconjugation.
Hyperconjugation arises due to the partial overlap of sp2–s with the empty p-orbital of adjacent
(D)
positively charged carbon atom.

47) A weak monobasic acid is 2% dissociated in its 0.01 M solution. Calculate its dissociation
constant.

(A) 4.0 × 10–6

(B) 5.0 × 10–5
(C) 2.0 × 10–6
(D) 2.0 × 10–5

48) An aldehyde or ketone reacts with hydrogen cyanide to form corresponding

cyanohydrin derivatives. This reaction is an example of ______.

(A) nucleophilic addition

(B) nucleophilic substitution
(C) electrophilic addition
(D) electrophilic substitution

49) What is the purpose of the graphite rod in the dry cell?

(A) To serve as the cathode of the cell

(B) To prevent leakage of the electrolyte paste
(C) To provide a porous barrier between the anode and cathode
(D) To serve as the electrolyte

50) Copper crystallizes into fee structure and the unit cell has length of edge 3.61 x 10–8 cm.
Calculate the density of copper if the molar mass of Cu is 63.5 g mol–1 [a3.NA = 28.3 cm3 mol–1]

(A) 11.2 g cm–3

(B) 5.24 g cm–3
(C) 14.9 g cm–3
(D) 8.93 g cm–3

MATHEMATICS

1) A random variable X has the following probability distribution :

X=x –1 0 1 2 3 4

P(X = x) 0.25 2k 0.1 k 0.15 2k

Then, the expected value of X is
(A) 0.5
(B) 1.5
(C) 0.7
(D) 1.3

2) The two parts of 120 for which the sum of double of first and square of second part is minimum,
are

(A) 60, 60
(B) 119, 1
(C) 118,2
(D) None of these
3) If , then

(A)

(B)

(C)

(D)

4) If
is continuous in [0, 3], then the value of k is

(A) –1
(B) 0
(C) –3
(D) –2

5) Negation of (~p → q) is

(A)

(B)

(C)

(D)

6) The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is

(A)

(B)

(C)

(D) None of these

7) Let f: R→R be defined as f(x) = |x| + |x2 – 1|. The total number of points at which f attains either a
local maximum or a local minimum is
(A) 2
(B) 4
(C) 5
(D) 6

8) Let be the p.d.f of a r.v. X. If C1 = {x : 1 < x < 2} and C2 = {x : 4 <

x < 5}, then

(A)

(B)

(C)

(D)

9) Find out which of the following statements have the same meaning:
i. If Meena makes a software then she happy.
ii. If Meena does not make a software then she is not happy.
iii. If Meena is not happy then she hasn't made a software
iv. If Meena is happy then she has made a software.

(A) (i, ii) and (iii, iv)

(B) i, ii, iii
(C) (i, iii) and (ii, iv)
(D) ii, iii, iv

10) The value of c in (0, 2) satisfying the mean value theorem for the function
is equal to

(A)

(B)

(C)

(D)

11) The vector equation of the line passing through the points (3,2, 1) and (1, 3, 1) is

(A)

(B)
(C)

(D)

12) is equal to

(A)

(B)

(C)

(D)

13) The inverse of the matrix is

(A)

(B)
(C)

(D)

14) If z1 = 3 – 2i and z2 =–1 + 3i, then Im(z1z2) =

(A) –3
(B) –11
(C) 3
(D) 11

15) The equation of the plane passing through the points (1,–2, 1), (2,–1,–3) and (0 , 1, 5) is

(A)

(B)

(C)

(D)

16) The combined equation of the lines which pass through the origin and each of which makes
an angle of 30° with the line 3x + 2y – 11 = 01 is

(A) 23x2 + 48xy + 3y2 = 0

(B) 23x2 + 48xy – 3y2 = 0
(C) 23x2 – 48xy + 3y2 = 0
(D) 23x2 – 48xy – 3y2 = 0

17) Let and be two unit vectors. If the

vectors and are perpendicular to each other, then the angle between and is
(A)

(B)

(C)

(D)

18) If , then cot × cot y is equal to

(A)

(B)

(C) ab
(D) a – b

19) The coordinates of the foot of perpendicular from (2, –1, 5) to the line are

(A) (0,2,3)
(B) (1,2,3)
(C) (2,1,3)
(D) (1,3, 2)

20)

(A)

(B)

(C)

(D)

21) The number of solutions of sin x + sin 3x + sin 5x = 0 in the interval is

(A) 2
(B) 3
(C) 4
(D) 5

22) If the vectors are coplanar, then c is

(A) A.M.of a and b
(B) G.M.of a and b
(C) Sum of a and b
(D) HM.of a and b

23) The equation of the plane passing through a point having position vector and
parallel to the vectors and is

(A)

(B)

(C)

(D)

24) In a , then a2, b2, c2 are in

(A) A.P
(B) G.P
(C) H.P
(D) None of these

25) Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x),

X-axis and the ordinates and is . Then is

(A)

(B)

(C)

(D)

26) If z1 = 5+ 3i and z2 = 2 – 4i, then z1 + z2 =

(A) 7 – i
(B) 7 + i
(C) 5 + i
(D) 5 – i

27) In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is

(A) 49
(B) 8
(C) 16
(D) 25

28) The feasible region of an LPP is shown in the figure. If z = 3x + 9y, then the minimum value of z

occurs at

(A) (5, 5)
(B) (0, 10)
(C) (0, 20)
(D) (15, 15)

29) If , then k =

(A)

(B)

(C)

(D)

30) If m and n are the order and degree of the differential equation

, then

(A) m = 4 and n = 5
(B) m = 4 and n = 1
(C) m = 4 and n = 3
(D) m = 4 and n = 2

31) If f(x) = logx (logx), then f'(x) at x = e is

(A) e

(B)

(C) 1
(D) None of these
32) If the p.d.f. of a continuous random variable X is then the value of
k is

(A) 6
(B) 10
(C) 12
(D) 16

33) Let f(x) = (1 + b2) x2 + 2bx + 1 and let m(b) be the minimum value of f(x). As b varies, the range
of m(b) is

(A) [0, 1]

(B)

(C)

(D) (0, 1]

34) The total number of points on the curve x2 – 4y2 = 1 at which the tangents to the curve are
parallel to the line x = 2y is

(A) 0
(B) 1
(C) 2
(D) 4

35) If , then equals

(A)

(B)

(C)

(D)

36) Which of the following statements is a tautology?

(A)

(B)
(C)

(D)

37) If function is continuous at x = 3, then the value of k will be

(A) –1
(B) 6
(C) –3
(D) –2

38) The p.m.f. of ar.v. X is

Then, EX) =

(A)

(B)

(C)

(D)

39) The angle of intersection of curves x = y2, 3y = 5 – 2x3 at (1, 1) is

(A)

(B)

(C)

(D) π

40) How many words can be formed with the letters of the word MANAGEMENT by
rearranging them

(A)

(B)

(C)
(D) 10!

41) and are any three vectors such that and ,

then and are

(A)
inclined at angle of between them

(B)
inclined at angle of between them
(C) perpendicular
(D) parallel

42)

(A) x sec (log x) + c

(B) tan (log x) + c
(C) sec (log x) + c
(D) x tan (log x) + c

43) If is perpendicular , then is equal to

(A) 3
(B) –5
(C) 7
(D) –8

44) If , then the values of a and b respectively

are

(A)

(B)

(C)

(D) None of these

45) If the line is perpendicular to the line , then the value of k is

(A) –5
(B) 7
(C) –7

(D)
46)

(A)

(B) does not exist

(C)

(D)

47)

(A)

(B)

(C)

(D)

48) The function f(x) = x3 – 3x2 – 24x + 5 is an increasing function in the interval

(A)
(B)
(C)
(D)

49) The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 =0 and
4x + 3y + 2z + 1 = 0 and the origin is

(A) 3x + 2y+ z + 1 = 0
(B) 3x + 2y + z = 0
(C) 2x + 3y + 2 = 0
(D) x + y + z = 0

50) For what value of k, the points (0, 0), (1, 3), (2,4) and (k, 3) are concyclic?

(A) 4
(B) 9
(C) 6
(D) 8
 ANSWER KEYS

PHYSICS

Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A. B A B D A B B A A C B B A C D A C D D A
Q. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
A. D B A C D A D A C B D A C A A A B A A B
Q. 41 42 43 44 45 46 47 48 49 50
A. B D B C C C B C B B

CHEMISTRY

Q. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
A. C D C A C D A B C C A A D D D A B A C D
Q. 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
A. A B C A B A D D D B A C B B B A A A B C
Q. 91 92 93 94 95 96 97 98 99 100
A. D A B D A D A A A D

MATHEMATICS

Q. 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
A. D B A B B C C C C B C A B D B A C B B B
Q. 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
A. B B C A A A D A B D B A D A A C B B C D
Q. 141 142 143 144 145 146 147 148 149 150
A. D D D A D C A A B B
 SOLUTIONS

PHYSICS

CHEMISTRY

MATHEMATICS