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Physics Multiple Choice Questions and Answers, High school final essays of Physics

Physics

A collection of multiple-choice questions covering various topics in physics, including projectile motion, gravitation, wave phenomena, optics, and more. Each question is followed by a set of answer choices, allowing students to test their understanding of fundamental physics concepts. Suitable for high school students preparing for exams or seeking to reinforce their knowledge.

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SATISH SCIENCE ACADEMY
DHANORI PUNE - 411015
PCM
ENTRANCE EXAM - MHT - CET
Time Allowed: 3 hours Maximum Marks : 200
General Instructions:
• All questions are compulsory.
• There are two sections.
• Section A has 100 questions from Physics and Chemistry.
• Section B has 50 questions from Mathematics.
Section - A (Physics)
1) The projectile attains maximum height when it is projected
at an angle of [1]
a) 30ob) 120o
c) 45od) 90o
2) The gravitational force of attraction between Earth and
Venus, if the distance between them is 2.5×107km, is
[mass of Venus = 4.8 ×1024kg, mass of the Earth = 6
×1024 kg][1]
a) 4.1×1018N b) 3.1×1018N
c) 2.1×1018N d) 5.1×1018 N
3) A particle of mass m is subjected to an attractive central
force of magnitude k
r2, k being aconstant. At the instant
when the particle is at its extreme position in its closed
orbit at a distance ’a’from the centre of force, its speed
is k
2ma .If the distance of other extreme is b, finda
b.
[1]
a) 2 b) - 1
c) 4 d) 3
4) Equal masses of two liquids are filled in two identical
calorimeters. The rate of cooling will [1]
a) Be same for both the liquids.
b) Depend on the specific heat of liquids.
c) Depend on the mass of the liquids.
d) Depend on the nature of calorimeters.
5) Neon is 20 times heavier than hydrogen. The equal vol-
umes of hydrogen and neon are mixed. The ratio of
speed of sound in the mixture to that in hydrogen is [1]
a) √32
17 b) √2
17
c) √1
8d) √2
21
6) For an angle of incidenceθon an equilateral prism of
refractive index √3, the ray refracted is parallel to the
base inside the prism. The value of θis [1]
a) 75° b) 60°
c) 30° d) 45°
7) If the critical angle for the material of a prism is C
and the angle of the prism is A, then there will be no
emergent ray when [1]
a) A <C
2b) A < 2C
c) A > 2 C d) A = 2 C
8) The power of a thin convex lens (ang= 1.5) is +5.0 D.
When it is placed in liquid of refractive index anlthen it
behaves as a concave lens of focal length 100 cm. The
refractive index of liquid anlwill be [1]
a) √3b) √2
c) 1.875 d) 1.68
9) The figure shows some of the electric field lines corre-
sponding to an electric field. The figure suggests
[1]
a) EA= EC> EBb) EA= EB= EC
c) EB= EA< ECd) EA> EB> EC
10) The rate of change of angular momentum is called [1]
a) Angular velocity. b) Torque.
c) Force. d) Linear momentum.
11) The P.E. of particle of mass 0.1 kg moving along x -
axis is given by U = 5x (x - 4) J where x is in metres.
It can be concluded that the wrong option is [1]
a) The period of oscillation of particle isπ
5s
b) The particle executes SHM
c) The speed of the particle is maximum at x = 2 m
d) The particle is acted upon by a constant force
12) A simple pendulum of length l has a brass bob attached
at its lower end. Its period is T. If a steel bob of
same size having density x times that of brass replaces
the brass bob and its length is changed so that period
becomes 2T, then new length is [1]
a) 4l
xb) 2l
c) 4l d) 4l x
13) A particle is executing S.H.M. of periodic time ‘T’. The
time taken by a particle in moving from mean position
to half the maximum displacement is (sin 30°= 0.5) [1]
a) T
12 b) T
4
c) T
2d) T
8
14) In series LCR circuit R = 18Ωand impedance is 33 Ω
. An r.m.s. voltage 220 V is applied across the circuit.
The true power consumed in a.c. circuit is [1]
a) 400 W b) 800 W
c) 220 W d) 600 W
15) If n drops of a liquid, each with surface energy E, join
to form a single drop, then [1]
a) The energy released will be E(n - n2/3).
b) The energy absorbed or released will be nE (22/3 -
1).
c) Some energy will be absorbed in the process.
d) The energy released in the process will be nE (n -
n1/3).
16) For a certain organ pipe, three successive resonance fre-
quencies are observed at 425, 595 and 765 Hz, respec-
pf3
pf4
pf5
pf8

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Download Physics Multiple Choice Questions and Answers and more High school final essays Physics in PDF only on Docsity!

SATISH SCIENCE ACADEMY

DHANORI PUNE - 411015

PCM

ENTRANCE EXAM - MHT - CET

Time Allowed: 3 hours Maximum Marks : 200

General Instructions:

  • All questions are compulsory.
  • There are two sections.
  • Section A has 100 questions from Physics and Chemistry.
  • Section B has 50 questions from Mathematics.

Section - A (Physics)

  1. The projectile attains maximum height when it is projected at an angle of [1] a) 30 o^ b) 120 o c) 45 o^ d) 90 o

  2. The gravitational force of attraction between Earth and Venus, if the distance between them is 2.5× 107 km, is [mass of Venus = 4.8 × 1024 kg, mass of the Earth = 6 × 1024 kg][1] a) 4.1× 1018 N b) 3.1× 1018 N c) 2.1× 1018 N d) 5.1× 1018 N

  3. A particle of mass m is subjected to an attractive central force of magnitude (^) rk 2 , k being a constant. At the instant when the particle is at its extreme position in its closed orbit at a distance ’a’ from the centre of force, its speed is 2 kma. If the distance of other extreme is b, find a b. [1] a) 2 b) - 1 c) 4 d) 3

  4. Equal masses of two liquids are filled in two identical calorimeters. The rate of cooling will [1] a) Be same for both the liquids. b) Depend on the specific heat of liquids. c) Depend on the mass of the liquids. d) Depend on the nature of calorimeters.

  5. Neon is 20 times heavier than hydrogen. The equal vol- umes of hydrogen and neon are mixed. The ratio of speed of sound in the mixture to that in hydrogen is [1] a)

32 17 b)

2 17 c)

1 8 d)

2 21

  1. For an angle of incidenceθ on an equilateral prism of refractive index

3 , the ray refracted is parallel to the base inside the prism. The value of θ is [1] a) 75° b) 60° c) 30° d) 45°

  1. If the critical angle for the material of a prism is C and the angle of the prism is A, then there will be no emergent ray when [1] a) A < C 2 b) A < 2C c) A > 2 C d) A = 2 C

  2. The power of a thin convex lens (ang= 1.5) is +5.0 D. When it is placed in liquid of refractive index anl then it behaves as a concave lens of focal length 100 cm. The refractive index of liquid anl will be [1] a)

3 b)

c) 1.875 d) 1.

  1. The figure shows some of the electric field lines corre- sponding to an electric field. The figure suggests

[1] a) EA = EC > EB b) EA = EB = EC c) EB = EA < EC d) EA > EB > EC

  1. The rate of change of angular momentum is called [1] a) Angular velocity. b) Torque. c) Force. d) Linear momentum.
  2. The P.E. of particle of mass 0.1 kg moving along x - axis is given by U = 5x (x - 4) J where x is in metres. It can be concluded that the wrong option is [1] a) The period of oscillation of particle is π 5 s b) The particle executes SHM c) The speed of the particle is maximum at x = 2 m d) The particle is acted upon by a constant force
  3. A simple pendulum of length l has a brass bob attached at its lower end. Its period is T. If a steel bob of same size having density x times that of brass replaces the brass bob and its length is changed so that period becomes 2T, then new length is [1] a) (^4) xl b) 2l c) 4l d) 4l x
  4. A particle is executing S.H.M. of periodic time ‘T’. The time taken by a particle in moving from mean position to half the maximum displacement is (sin 30°= 0.5) [1] a) 12 T b) T 4 c) T 2 d) T 8
  5. In series LCR circuit R = 18Ω and impedance is 33 Ω

. An r.m.s. voltage 220 V is applied across the circuit. The true power consumed in a.c. circuit is [1] a) 400 W b) 800 W c) 220 W d) 600 W

  1. If n drops of a liquid, each with surface energy E, join to form a single drop, then [1] a) The energy released will be E(n - n2/3). b) The energy absorbed or released will be nE (22/3^ - 1). c) Some energy will be absorbed in the process. d) The energy released in the process will be nE (n - n1/3).
  2. For a certain organ pipe, three successive resonance fre- quencies are observed at 425, 595 and 765 Hz, respec-

tively. The length of the pipe is (speed of sound in air = 340 ms -^1 ) [1] a) 1.5 m b) 1 m c) 0.5 m d) 2 m

  1. A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (take g = 10 ms -^2 ) [1] a) 2

2 s b)

2 s c) 2 π

2 s d) 2 s

  1. The vibrations of a string of length 60 cm fixed at both ends are represented by displacement y = 4 sin

( (^) πx 15

cos (96π t) where x and y are in cm and t in second. The particle velocity at x = 22.5 cm and t = 0.25 s is [1] a) 100 cm s -^1 b) 4 × 96 cm s -^1 c) 96 cm s -^1 d) Zero

  1. At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given: Mass of oxygen molecule (m) = 2.76 × 10 -^26 kg, Boltzmann’s constant kB = 1.38 × 10 -^23 JK -^1 ) [1] a) 2.508× 104 K b) 8.360× 104 K c) 5.016× 104 K d) 1.254× 104 K

  2. Two beams, A and B, of plane polarised light with mutu- ally perpendicular planes of polarisation are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through 30 o^ makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then I IAB equals [1] a) 1 b) (^32) c) 13 d) 3

  3. In practice, the range of strain gauge resistance is from

. [1] a) 30 to 3000 ohms b) 30 to 300 ohms c) 3 to 3000 ohms d) 3 to 30 ohms

  1. A wire of length 100 cm is connected to a cell of e.m.f. 2 V and negligible internal resistance. The resistance of the wire is 3 Ω. The additional resistance required to produce a potential drop of 1 millivolt per cm is [1] a) 47 Ω b) 60 Ω c) 35 Ω d) 57 Ω

  2. A potentiometer has uniform potential gradient across it. Two cells connected in series (i) to support each other and (ii) to oppose each other are balanced over 6 m and 2 m respectively on the potentiometer wire. The e.m.f.s of the cells are in the ratio of [1] a) 1 : 2 b) 3 : 1 c) 1 : 1 d) 2 : 1

  3. A galvanometer of resistance G, is shunted by a resis- tance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is [1]

a) (^) (S+GG) b) (^) (SSG+G) c) S

2 (S+G) d) G

2 ( S+G)

  1. In the figure, what is the magnetic field at the point O?

[1]

a) μ 40 rI − μ 40 πIr b) μ 4 π^0 Ir + μ 2 π^0 Ir c) μ 4 π^0 Ir d) μ 40 rI + μ 40 πIr

  1. A circular coil of radius r carries a current I. The mag- netic field at its centre is B. At what distance from the centre, on the axis of the coil the magnetic field will be B 8? [1] a)

3 r b)

2 r c) 3 r d) 2 r

  1. The maximum kinetic energy of protons in a cyclotron of radius 0.4 m in a magnetic field of 0.5 T is (mass of proton = 1.67× 10 -^27 kg, charge of proton = 1.6 × 10 -^19 C) [1] a) 4 MeV b) 5 MeV c) 1.9 MeV d) 3 MeV
  2. Magnetic induction due to a toroid does not depend upon [1]

a) Permeability of a free space. b) Current flowing through a toroid. c) Radius of a toroid. d) Number of turns per unit length.

  1. Which of the following are uses of electromagnets? [1]

a) To lift ferromagnetic substances such as iron. b) All of these c) In circuit brakers, braking system of train. d) Used in charged particles accelerators (cyclotrons).

  1. A ferromagnetic material is heated above its Curie tem- perature. Which one is a correct statement? [1]

a) Ferromagnetic domains are not influenced. b) Ferromagnetic domains are perfectly arranged. c) Ferromagnetic domains become random. d) Ferromagnetic material changes itself into diamag- netic material.

  1. Permeability of diamagnetic materials are [1] a) Zero b) Greater than unity c) Less than unity d) Equal to unity
  2. The use of study of hysteresis curve for a given material is to estimate the [1] a) Voltage loss b) Current loss c) Power loss d) Hysteresis loss
  3. A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The reading of A.C. voltmeter is 220 V, if the copper ring has a cut such as not to form a complete loop, then the acceleration of the falling magnet is

[1] a) Equal to ’g’ b) Greater than ’g’ c) Less than ’g’ d) Zero

a) 8.1 mA b) 1.0 mA c) 8.0 mA d) 0.1 mA

Section - A (Chemistry)

  1. Which of the following statements is INCORRECT? [1]

a) Composition of a mixture can be varied to any extent. b) Pure substances have a definite chemical composi- tion. c) Water and table salt are examples of a compound. d) The constituents of a compound can be easily sep- arated by physical methods.

  1. The number of unpaired electrons in chromium (Z = 24) is. [1] a) 6 b) 3 c) 8 d) 5

  2. What is the oxidation number of gold in the complex [AuCl 4 ] -^? [1] a) +1 b) + c) +3 d) +

  3. Chloride of metal Y was found to be deliquescent and on crystallisation formed a hydrate. The metal Y is. [1] a) Li b) M c) Na d) K

  4. At constant T and P, Avogadro law is represented as

. [1] a) V∝ n b) V∝ (^) n^1 c) V∝ (^1) NA d) V∝ NA

  1. The colloidal system of a liquid dispersed in a liquid medium is called a/an. [1] a) Gel b) Aerosol c) Emulsion d) Foam

  2. X 60 %H 2 SO 4 −−−−−−→ 373 K Alkene

Y −^75 −%H−−^2 −SO−→^4 413 K

Alkene X and Y are respectively. [1] a) X = n - Propyl alcohol, Y = tert - Butyl alcohol b) X = Isopropyl alcohol, Y = n - Propyl alcohol c) X = Isopropyl alcohol, Y = tert - Butyl alcohol d) X = n - Propyl alcohol; Y = Isopropyl alcohol

  1. An alkeneA on reaction with O 3 and Zn - H 2 O gives propanone and ethanal in an equimolar ratio. The addition of HCl to alkene A gives B as the major product. The structure of product B is. [1]

a) H 3 C −

CH 2 Cl | CH 2 −CH − CH 3

b) H 3 C − C | Cl

H −

CH 3 | C |

H

CH 3

c) Cl − CH 2 − CH 2 −

CH 3 | C |

H

CH 3

d) H 3 C − CH 2 −

CH 3 | C | Cl

− CH 3

  1. IUPAC name of the compoundCH 3 − C | CH 2 | CH 3

H − CH 2 −

CH(OH) − CH 3 is. [1] a) 2 - ethylpentan - 2 - ol

b) 3 - methylhexan - 2 - ol c) 4 - methylhexan - 2 - ol

d) 4 - ethylpentan - 2 - ol

  1. defect arises when foreign atoms, that is, atoms different from the host atoms, are present in the crystal lattice. [1] a) Frenkel b) Metal excess c) Impurity d) Schottky
  2. In a close - packed arrangement of N particles, the number of tetrahedral holes is. [1] a) 2N b) N 2 c) N d) 4N
  3. The boiling point of chloroform was raised by 0.323 K when 0.5143 g of anthracene, was dissolved in 35 g of chloroform. The molecular mass of anthracene is. (Kb of CHCI 3 = 3.9 K kg mol -^1 ) [1] a) 177.42 g/mol b) 242.32 g/mol c) 132.32 g/mol d) 79.42 g/mol
  4. Which among the following is TRUE for the value of Henry’s law constant KH? [1]

a) Increases with increase in temperature. b) Is same for all gases. c) First increases and then drcreases with incrase in temperature. d) Is greater for gases with higher solubilities.

  1. A system is said to be in thermodynamic equilibrium when,. i. The temperature of the system is non - uniform and different from the temperature of the surroundings ii. The mechanical properties are non - uniform through- out the system iii. The state functions of the system do not change with time iv. Only pressure of the reaction is at equilibrium [1] a) Option (c) b) Option (a) c) Option (d) d) Option (b)
  2. For the reaction, C 3 H8(g) + 5O2(g)→ 3CO2(g) + 4H 2 O(l)at constant temperature and pressure, ∆ H is equal to. [1] a) ∆ U - 5RT b) ∆ U - 3RT c) ∆ U - 2RT d) ∆ U - RT
  3. Eo^ values of Mg2+/Mg is - 2.37 V, of Zn2+/Zn is - 0.76 V and Fe2+/Fe is - 0.44 V. Which of the following statements is CORRECT? [1] a) Zn oxidises Fe b) Zn Reduces Fe2+ c) Mg| oxidises Fe d) Zn reduces Mg2+
  4. Which of the following is NOT a secondary voltaic cell? [1] a) Mercury cell b) Dry cell c) Nickel - cadmium cell d) Lead storage battery
  5. The unit of rate constant for a certain reactions is time -^1. The order of the reaction is. [1] a) 2 b) 0 c) 1 d) 3

  1. In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is. [1] a) 60 minutes b) 30 minutes c) 15 minutes d) 7.5 minutes

  2. The solubility of AgCl(S) with solubility product 1.6 × 10 -^10 in 0.1 M NaCl solution would be. [1] a) 1.6× 10 -^9 M b) 1.26× 10 -^5 M c) 1.6× 10 -^9 M d) Zero

  3. The pH of 10^5 M KOH solution will be. [1] a) 9 b) 5 c) 10 d) 11

  4. The H+^ ion concentration of a solution is 0.1 M. Its pH is. [1] a) 1.0 b) 0. c) 10 d) 0.

  5. Which of the following is NOT formed when HBr reacts with H 2 SO 4? [1] a) H 2 O b) H 2 S c) Br 2 d) SO 2

  6. Which of the following oxoacid contains a peroxide link- age? [1] a) H 2 S 2 O 8 b) H 2 SO 3 c) H 2 S 2 O 3 d) H 2 S 2 O 7

  7. The stability of hexahalides (EX 6 type) of group 16 ele- ments follows the order. [1]

a) Iodides > bromides > fluorides > chlorides b) Iodides > bromides > chlorides > fluorides c) Chlorides > fluorides > bromides > iodides d) Fluorides > chlorides > bromides > iodides

  1. Which of the following pairs has both the ions coloured in aqueous solution? (Atomic numbers of Sc = 21, Ti = 22, Ni = 28, Cu = 29, Mn = 25) [1] a) Mn2+, Ti3+^ b) Ti3+, Cu+ c) Ni2+, Ti4+^ d) Sc3+, Mn2+

  2. The number of d - electrons in cobalt (Z = 27) is. [1] a) 7 b) 5 c) 6 d) 8

  3. Which among the following complexes is heteroleptic and cationic in nature? [1] a) [Ni(CO) 4 ] b) [Co(NH 3 ) 4 Cl 2 ]Cl c) [Pt(NH 3 ) 2 Cl 2 ] d) K 4 Fe(CN) 6 ]

  4. The color of the coordination compound is due to transition of electrons. [1] a) P - p b) P - d c) D - d d) S - p

  5. In the complex K 3 [Fe(CN) 6 ],. [1]

a) Charge on the complex ion is 0 b) Coordination sphere is K+ c) Coordination number of Fe is 6 d) Oxidation number of Fe is +

  1. Identify the product (X).

[1]

a) CHCl = CH - CH 3 b) CH≡ C - CH 2 Cl c) CH 2 = CCl - CH 3 d) CH 2 = CH - CH 2 Cl

  1. Which one is most reactive towards SN1 reaction? [1] a) PhCH 2 Cl b) PhCH(Ph)Cl c) PhCH(CH 3 )Cl d) PhC(CH 3 )(Ph)Cl
  2. Chlorobenzene on treatment with concentrated sulphuric acid yields. [1]

a)

b) Both

and

c)

d) Neither

nor

  1. What are a, b, c and d in the following reaction? a(CH 3 ) 3 C - OH + b Al −→ c[(CH 3 ) 3 C - O] 3 Al + d H 2 [1] a) A : 6, b : 2, c : 2, d : 3 b) A : 3, b : 1, c : 1, d : 2 c) A : 4, b : 1, c : 1, d : 2 d) A : 4, b : 2, c : 1, d : 2
  2. Name the catalyst used in commercial method of prepa- ration of phenol. [1]

a) Cobalt naphthenate b) Anhydrous aluminium chloride c) Calcium phosphate d) Silica

  1. The common name of C 6 H 5 - O - CH 3 is. [1] a) Ethyl phenyl ether b) Methyl phenyl ether c) Hexyl methyl ether d) Benzyl ethyl ether
  2. Acetaldehyde on warming with Fehling solution gives a red precipitate of. [1] a) Cuprous oxide b) Cupric oxide c) Elemental copper d) Cu(OH) 2

on reductive ozonolysis yields. [1] a) 6 - oxoheptanoic acid b) 6 - hydroxyheptanal c) 3 - hydroxypentanal d) 6 - oxoheptanal

  1. Which of the following will give the addition product with NaHSO 3? [1] a) CH 3 COOH b) CH 3 OH c) CH 3 COCH 3 d) CH 3 CH 2 Cl
  1. If

x y z

 (^) , then

x y z

 (^) is

equal to [2]

a)

b)

c)

d)

  1. Let A and B be two matrices of order n× n. Let A be non - singular and B be singular. Consider the following: i. AB is singular. ii. AB is non - singular. iii. A -^1 B is singular. iv. A -^1 B is non - singular. Which of the above is/are correct? [2] a) I and iii b) I only c) Iii only d) Ii and iv

  2. The value ofλ for which the matrix

2 λ 3 − 1 0 3

will not be invertible, is [2] a) 92 b) − 29 c) 9 d) - 9

  1. The value of cos -^1 (cos 12) - sin -^1 (sin 14) is [2] a) π 2 b) - 2 c) 4 π + 2 d) 8 π - 26

  2. Cos

[

tan−1 1 3 + tan−1 1 2

]

= [2]

a) √^12 b) π 4 c) 12 d)

√ 3 2

  1. The solution of the equation cos^2 x - 2 cos x = 4 sin x - sin 2x, 0 ≤ x ≤ π , is [2] a) π - tan -^1 (2) b) π - cot -^1

2

c) π + tan -^1

d) π + cot -^1

2

  1. The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60o. If the third side is 3, the remaining fourth side is [2] a) 2 b) 4 c) 5 d) 3

  2. The value of x which satisfies the equation tan -^1 x =

sin -^1

√^3 10

is [2] a) 13 b) − (^13) c) 3 d) - 3

∫ (^) e 1

1+log x x dx =^ [2] a) 32 b) (^1) e c) 23 d) (^12)

∫ π 4 0 x^ sec

(^2) x dx = [2]

a) π 4 + log

b) 1 - 12 log

c) 1 + log

d) π 4 - log

∫ π 2 0

2 sin^ x 2 sin^ x+2cos^ x^ dx =^ [2] a) π b) 2 π c) 2 d) π 4

1

1 x^2 e^

− x (^1) dx = [2]

a)

√e− 1 e b)

e - 1 c)

√e+ e d)

e + 1

∫ (^) π 0

x tan x sec x+cos x dx =^ [2] a) π

2 4 b)^

π^2 2 c) 3 π

2 2 d)^

π^2 3

  1. Let the position vectors of two points A and B bea⃗ +⃗ b+c⃗ and a⃗ − 2 ⃗b + 3c⃗ respectively. If the points P and Q di- vide AB in the ratio 1 : 3 internally and externally respectively, then 3 |AB⃗ | = [2] a) 3 | PQ⃗ | b) 4 | PQ⃗ | c) 2 | PQ⃗ | d) 12 | PQ⃗ |

  2. Ifx⃗ · ⃗a = 0 ,x⃗ · ⃗b = 0 andx⃗ · ⃗c = 0 for some non - zero vector x⃗ , then the true statement is [2] a) [⃗ a⃗b⃗ c] = 1 b) [⃗ a⃗b⃗ c] ̸= 1 c) [⃗ a⃗b⃗ c] ̸= 0 d) [⃗ a⃗b⃗ c] = 0

  3. Position vector of a point which divides line joining points A and B whose position vectors are2ˆi+ˆj −kˆ and ˆi−ˆj +2ˆk externally in the ratio 5 : 2 is [2] a) ˆi + 7ˆj − 12 ˆk b) ˆi − 7 ˆj + 12ˆk c) 13 (ˆi − 7ˆj + 12kˆ) d) 13 (ˆi + 7ˆj − 12 ˆk)

  4. The number of straight lines that are equally inclined to the three dimensional co - ordinate axes, is [2] a) 8 b) 4 c) 6 d) 2

  5. If lines a^2 x^2 + bcy^2 = a (b + c) xy are mutually per- pendicular, then [2] a) A^2 + b^2 + c^2 = 0 b) B^2 + ca = 0 c) A^2 + bc = 0 d) C^2 + ab = 0

  6. A line from the origin meets the lines x− 2 1 =^

y− 1 − 2 =^

z+ 1 and^

x− (^83) 2 =^

y+ − 1 =^

z− 1 1 at P and Q respectively. If length PQ = d, then d^2 is equal to [2] a) 4 b) 6 c) 3 d) 5

  1. Foot of perpendicular of point (2, 2, 2) in the plan x + y + z = 9 is [2] a) (9, 0, 0) b) (1, 1, 1) c) (3, 3, 3) d) (2, 6, 1)
  2. D.c.s of a line segment AB are √− 172 , √^317 , √− 172. If AB = √ 17 and A ≡ (3, - 6, 10), then co - ordinates of B will be [2] a) (1, - 3, 8) b) (2, 5, 8) c) (1, - 2, 4) d) ( - 1, 3, - 8)

  1. The derivative of sin x w.r.t. cos x is [2] a) Cot x b) - tan x c) - cot x d) Tan x

  2. The derivative of sin -^1

2 x

1 − x^2

with respect to sin -^1

3 x − 4 x^3

is [2] a) 12 b) (^23) c) 1 d) (^32)

  1. A stone is falling freely and describes a distance s in t seconds given by equation s = 12 gt^2. The acceleration of the stone is [2] a) Non - uniform b) Zero c) Uniform d) Indeterminate

  2. The function f(x) = 1 - x^3 - x^5 is decreasing for [2] a) 1≤ x ≤ 5 b) X≤ 1 c) All values of x d) X≥ 1

  3. The equation of the tangent to the curve

x +

( y^ = a at a^2 4 ,^

a^2 4

is [2] a) Xy = a 2 2 b)^ X -^ y =^

a^2 2 c) X + y = a

2 2 d)^ Xy = a

2

  1. The tangent to the curve x^2 + y^2 - 2x - 3 = 0 is parallel to X - axis at the points [2] a) (± 3, 0) b) (± 1, 2) c) (1,± 2) d) (2,±
  1. If

∫ (^) f (x) log cos x dx = -^ log (log cos x) + c, then f(x) is equal to [2] a) - sin x b) - cos x c) - tan x d) Tan x

∫ (^) x sin x x cos x−sin x− 1 dx =^ + c^ [2] a) - log |x sin x - cos x - 1| b) Log |x cos x - sin x - 1| c) Log |x sin x - cos x - 1| d) - log |x cos x - sin x - 1|

∫ (^) x− 1 (x+1)^2 dx^ =^ [2] a) 2 log |x + 1| - (^) x+1^1 + c b) Log |x + 1| - (^) x+1^2 + c c) (^) x+1^2 - log |x + 1| + c d) Log |x + 1| + (^) x+1^2 + c

(e^2 x+e−^2 x)^2 dx^ =^ [2] a) (^) 2(e− 4 x^1 +1) + c b) (^) 4(e− 4 x^1 +1) + c c) (^) 2(e 41 x+1) + c d) (^) 4(e 41 x+1) + c

  1. The area bounded by the curve y = |sin x|, X axis and the lines x =−π and x = π is [2] a) 3 sq. units b) 2 sq. units c) 1 sq. unit d) 4 sq. units

  2. The area of the region above X - axis included between the parabola y^2 = x and the circle x^2 + y^2 = 2x in square units is [2] a) 32 − π 4 b) π 4 − (^32) c) π 4 − (^23) d) 23 − π 4

  3. The solution of the equation d dyx +

1 −y^2 1 −x^2 = 0^ is^ [2] a) x

1 − y^2 + y

1 − x^2 = c b) None of these

c) x

1 + y^2 + y

1 + x^2 = c d) x

1 − y^2 − y

1 − x^2 = c

  1. The order of the differential equationy

dy dx

= (^) dyx dx

dy dx

is [2] a) 3 b) 4 c) 1 d) 2

  1. The solution of the differential equation d dyx + 3 x

2 1+x^3 y^ = sin^2 x 1+x^3 is^ [2] a) Y(1 + x^3 ) = x + 12 sin 2x + c b) Y(1 + x^3 ) = cx + 12 sin 2x + c c) Y(1 + x^3 ) = cx - 12 sin 2x + c d) Y(1 + x^3 ) = x 2 − 14 sin 2 x + c

  1. If y = f(x), passes through the point (1, - 1) and satisfies the equation y(1 + xy)dx = x dy, thenf

2

is equal to [2] a) − 45 b) (^45) c) 25 d) − (^25)

  1. A bag contains 4 red and 6 black balls. Three balls are drawn at random. Then the probability distribution of the number of red balls is [2]

a)

X 0 1 2 3

P(X) 15235969

b)

X 0 1 2 3

P(X) 19295646

c)

X 0 1 2 3

P(X) 16 12 103 301

d)

X 0 1 2 3

P(X) 16 23 104 103

  1. Which of the following distribution of probabilities of a random variable X is the probability distribution? [2]

a)

X 0 1 2

P(X) 0.1 0.7 0.

b)

X 2 3 4 5

P(X) 0.2 0.2 0.2 0.

c)

X 0 1 2 3

P(X) 0.3 0.2 0.4 0.

d)

X 1 2 3 4

P(X) 0.5 0.5 0.2 0.

  1. If X follows a binomial distribution with parameters n = 6 and p. If 9P(X = 4) = P(X = 2), then p = [2] a) 14 b) (^12) c) 13 d) 1
  2. If X B (n, p) with n = 10, p = 0.4, then E(X^2 ) = [2] a) 4 b) 2. c) 3.6 d) 18.