MUSAT– 2019

SAMPLE TEST PAPER

INSTRUCTIONS

In each part of the paper, each section contains 30 questions. Total number of pages are

16. Please ensure that the Questions paper you have received contains ALL THE

QUESTIONS in each section and PAGES.

Duration: 2 Hours Max. Marks: 100

1. A small bar magnet ring is placed on the axis of a small conducting ring of radius r. The

ring is pushed towards the dipole at a speed v that is kept constant. When the dipole-ring

separation is x:

(A) the induced current in the loop varies as x-8

(B) the magnetic flux through the loop varies as x-8

(C) the force on the ring due to magnetic dipole varies as x-8

(D) the magnetic moment of the ring due to the magnetic dipole varies as x-4

2. A block of mass 100g slides on a rough horizontal surface. If the speed of the block

decreases from 10 m/s to 5 m/s, the thermal energy developed in the process is:

(A)3.75 J

(B)37.5 J

(C)0.375J

(D)0.75 J

3. Needles N1, N2 and N3 are made of ferromagnetic, a paramagnetic and a diamagnetic

substance respectively. A magnet when brought close to then will :

(A) Attract N1 and N2 strongly but repel N3

(B) Attract N1 strongly, N2 weakly and repel N3 weakly

(C) Attract N1 strongly but repel N2 and N3 weakly

(D) Attract all three of them

4. A thin glass (refractive index 1.5) lens has optical power of -5D in air . Its optical power

in a liquid medium with refractive index 1.6 will be :

(A) 1D

(B) -1D

(C) 25D

(D) -25D

5. An automobile travelling with a speed of 60km/h, can brake to stop within a distance of

20m. If the car is going twice as fast, i.e. 120 km/h, the stopping distance will be:

(A) 20 m

(B) 40 m

(C) 60 m

(D) 80 m

6. Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance

for 5 cm and are uniformly charged. if the spheres are connected , the ratio of the

magnitude of the electric fields at the surface of the spheres A and B is:

(A)4 :1

(B)1:2

(C)2:1

(D)1:4

Physics

7. A body is dropped and observed to bounce a height greater than the dropping height.

Then:

(A) The collision is elastic.

(B) There is additional source of energy during collision

(C) It is not possible

(D) This type of phenomenon does not occur in nature.

8. What can be the possible velocity displacement (v – s) graph of a particle moving in a

straight line under constant acceleration:

(A) straight line

(B) parabola

(C) ellipse

(D) circle

9. Pick up the correct statements:

(A) Area under a-t graph gives velocity

(B) Area under a-t graph gives change in velocity

(C) Path of projectile as seen by another projectile is a parabola,

(D) A body, whatever be its motion, is always at rest in a frame of reference fixed to the

body itself.

10. A mass m is moving with a constant velocity parallel to the x-axis. Its angular

momentum w.r.t. the origin

(A) remains constant

(B) goes on increasing

(C) goes on decreasing

(D) is zero

11. A particle executes S.H.M. in a line 4 cm long. Its velocity when passing through the

centre of line is 12 cm/s. The period will be

(A) 2.047 s

(B) 1.047 s

(C) 3.047 s

(D) 0.047 s

12. A mass M is split into two parts, m and (M–m), which are then separated by a certain

distance. What ratio of m/M maximizes the gravitational force between the two parts

(A) 1/3

(B) 1/2

(C) 1/4

(D) 1/5

13. Two spherical conductors B and C having equal radii and carrying equal charges in

them repel each other with a force F when kept apart at some distance. A third spherical

conductor having same radius as that of B but uncharged is brought in contact with B, then

brought in contact with C and finally removed away from both. The new force of repulsion

between B and C is

(A) F / 4

(B) 3F / 4

(C) F / 8

(D) 3F / 8

14. On increasing the temperature of a conductor, its resistance increases because

(A) Relaxation time decreases

(B) Mass of the electrons increases

(C) Electron density decreases

(D) None of the above

15. A plane mirror reflecting a ray of incident light is rotated through an angle Ɵ about an

axis through the point of incidence in the plane of the mirror perpendicular to the plane of

incidence, then

(A) The reflected ray does not rotate

(B) The reflected ray rotates through an angle Ɵ

(C) The reflected ray rotates through an angle 2Ɵ

(D) The incident ray is not fixed

16. Two equally charged, identical metal spheres A and B repel each other with a force 'F'.

The spheres are kept fixed with a distance 'r' between them. A third identical, but

uncharged sphere C is brought in contact with A and then placed at the mid-point of the

line joining A and B. The magnitude of the net electric force on C is

(A) F

(B) 3F/4

(C) F/2

(D) F/4

17. The force required to separate two glass plates of area 10–2 m2 with a film of water of

0.05 mm thick between them, is (surface tension of water is 70 × 10–3 N/m)

(A) 28 N

(B) 14 N

(C) 50 N

(D) 38 N

18. The only property possessed by ferromagnetic substance is

(A) hysteresis

(B) susceptibility

(C) directional property

(D) attracting magnetic substances

19. The internal resistance of a cell is measured by a potentiometer. Which of the following

statement is not true for the internal resistance of the cell?

(A) Internal resistance depends between the two electrode plates

(B) Internal resistance does not depend on the area of the plates immersed in the electrolyte

(C) Internal resistance depends on the nature of the electrolyte

(D) Internal resistance depends on the nature of the electrodes

20. 80 gm of water at 30°C is poured on a large block of ice at 0°C. The mass of ice that

melts is –

(A) 160 gm

(B) 80 gm

(C) 40 gm

(D) 30 gm

21. Two metallic spheres P and Q of the same surface area are taken. The weight of P is

twice that of Q. Both the spheres are heated to the same temperature and left in a room to

cool by radiation. The ratio of the rate of cooling of Q to P is :

(A) √2 : 1

(B) 2 : 1

(C) 1 : 2

(D) 1 : (2)1/3

22. Two electric lamps of 40 watt each are connected in parallel. The power consumed by

the combination will be –

(A) 20 watt

(B) 60 watt

(C) 80 watt

(D) 100 watt

23. In preparation for a landing on the bright side of the moon, surface temperature of

moon has to be estimated. Assume Lunar surface material is a good insulator. It is given

that solar constant is 1353 watts/m2 . Assume absorptivity and emissivity of moon is same.

Approximate surface temperature of moon is (stefan’s constant = 5.67 × 10–8 Wm–2K–4)

(A) 120ºC

(B) 300ºC

(C) 500ºC

(D) 720ºC

24. In the circuit shown in the figure, V must be:

(A) 50 V

(B) 100 V

(C) 75 V

(D) 25 V

25. In a laboratory four convex lenses L1 , L2 , L3 and L4 of focal lengths 2, 4, 6 and 8 cm,

respectively are available. Two of these lenses form a telescope of length 10 cm and

magnifying power 4. The objective and eye lenses are respectively

(A) L2 , L3

(B) L2 , L4

(C) L1 , L2

(D) L4 , L1

26. An electric kettle has two heating coils. When one of the coils is connected to an AC

source, the water in the kettle boils in 10 min. When the other coil is used the water boils in

40 min. If both the coils are connected in parallel, the time taken by the same quantity of

water to boil will be :

(A) 25 min

(B) 15 min

(C) 8 min

(D) 4 min

27. A wire suspended vertically from one of its ends is stretched by attaching a weight of

200 N to the lower end. The weight stretches the wire by 1 mm. The elastic energy stored

in the wire is :

(A) 0.2 J

(B) 10 J

(C) 20 J

(D) 0.1 J

28. A thin conducting ring of radius R is given a charge +Q. The electric field at the centre

O of the ring due to the charge on the part AKB of the ring is E. The electric field at the

centre due to the charge on the part ACDB of the ring is

(A) 3E, along KO

(B) E, along OK

(C) E, along KO

(D) 3E, along OK

29. The resistance of a wire is 10 Ω. Its length is increased by 10% by stretching. The new

resistance will now be

(A) 12 Ω

(B) 1.2 Ω

(C) 13 Ω

(D) 11 Ω

30. Half-lives of two radioactive substances A and B are respectively 20 min and 40 min.

Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of

remaining number of A and B nuclei is:

(A) 1 : 16

(B) 4 : 1

(C) 1:4

(D) 1:1

1. The four points whose co-ordinates are (2, 1), (1, 4), (4, 5), (5, 2) form

(A) A rectangle which is not a square

(B) A trapezium which is not a parallelogram

(C) A square

(D) A rhombus which is not a square

2. If a, b, c are non-zeros, then the system of equations (α + a)x + α y + α z = 0, αx+( α + b)y+ αz=0, ax + αy + (α + c)z = 0 has a non-trivial solution if

(A) α –1

= – (a–1 + b–1 + c–1)

(B) α –1

= a + b + c

(C) α + a + b + c = 1

(D) None of these

3. The straight line ax + by + c = 0 where abc ≠ 0 will pass through the first quadrant if

(A) ac > 0, bc > 0

(B) ac > 0 and bc < 0

(C) bc > 0 and/or ac > 0

(D) ac < 0 and/ or bc < 0

4. A variable circle having fixed radius ‘a’, passes through origin and meets the co-ordinate axes

in points A and B. Locus of centroid of triangle OAB, ‘O’ being the origin is -

(A) 9(x2 + y

2) = 4a

2

(B) 9(x2 + y

2) = a

2

(C) 9(x2 + y

2) = 2a

2

(D) 9(x2 + y

2) = 8a

2

5. Which one of the following is wrong ?

(A) The elements on the main diagonal of a symmetric matrix are all zero

(B) The elements on the main diagonal of a skew-symmetric matrix are all zero

(C)For any square matrix A, 1/2(A + A') is symmetric

(D) For any square matrix A, 1/2(A – A') is skew-symmetric

6. In a football championship, there were played 153 matches. Every two teams played one

match with each other. The number of teams participating in the championship is

(A) 14

(B) 22

(C) 18

(D) none of these

Mathematics

7. The equation |z – i| + |z + i| = k, k > 0, can represent an ellipse, if k2 is

(A) < 1

(B) < 2

(C) > 4

(D) none of these

8. An man and his wife appear for an interview for two posts. The probability of the man’s

selection is 1/5 and that of his wife’s selection is 1/7. The probability that at least one of them is

selected, is

(A) 9/35

(B) 12/35

(C) 2/7

(D) 11/35

9. If from any point P on the circle x2 + y

2 + 2gx + 2fy + c = 0, tangents are drawn to the circle x

2

+ y2 + 2gx + 2fy + c sin

2α + (g2 + f

2) cos

2α = 0, then angle between the tangents is

(A)α

(B) 2α

(C) α/2

(D) none of these

10. Let α and β are the roots of x2 – x + 1 = 0 , then the value of α50

+ β50

is -

(A) 0

(B)

(C) 2

(D) 1

11. For positive integer n, 10n-2

> 91n, then complete set of values of n is

(A) 1, 2, 3, 4

(B) 6, 7, 8, 9,...

(C) 5, 6, 7, 8,...

(D) 7, 8, 9, 10,...

12. In ABC, AB = AC. Let C1 denote the incircle of ABC. Circle C2 is tangent to sides

AB,AC and to circle C1. If radius of circles C1 and C2 are 2 and 1 respectively, then area of

ABC is

(A) 8

(B) 4

(C) 16

(D) 8

13. If |z – 3 –4i| = 4, Where i = then maximum possible value of |z| is,

(A) 9

(B) 7

(C) 5

(D) 6

14. The number of arrangements of the letters of the word PALANHAR in which no two vowels

are together and exactly two vowels are at odd places, is-

(A) 3600

(B) 1440

(C) 2880

(D) 720

15. Let P be the parabola in the plane determined by the equation y = x2. Suppose a circle C in

the plane intersects P at four distinct points. If three of these points are (17,289), (–2,4), (13,169),

then sum of the perpendicular distance from the directrix of P to all four of the intersection

points is-

(A) 1177

(B) 1247

(C) 1369

(D) 1421

16. Equation of a common tangent to the circle, x2 + y

2 – 6x = 0 and the parabola, y

2 = 4x, is:

(A) 2 y = 12 x + 1

(B) 2 y = – x – 12

(C) y = x + 3

(D) y = 3x + 1

17. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls

and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse

to be the members of the same team, is:

(A) 200

(B) 300

(C) 500

(D) 350

18. If a, b and c be three distinct real numbers in G. P. and a + b + c = xb, then x cannot be :

(A) 4

(B) –3

(C) –2

(D) 2

19. The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and

parallel to y-axis also passes through the point :

(A) (–3, 0, –1)

(B) (3, 3, –1)

(C) (3, 2, 1)

(D) (–3, 1, 1)

20. If 0 denotes the acute angle between the curves, y = 10 – x2 and y = 2 + x2, then |tan 0| is

equal to :

(A) 4/9

(B) 7/17

(C) 8/17

(D) 8/15

21. If the area enclosed between the curves y=kx2 and x=ky

2, (k>0), is 1 square unit. Then k is:

(A)

(B)

(C)

(D)

22. The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder

is:

(A) 1365

(B) 1256

(C) 1465

(D) 1356

23. Consider the statement : "P(n): n2 – n + 41 is prime." Then which one of the following is

true?

(A) P(5) is false but P(3) is true

(B) Both P(3) and P(5) are false

(C) P(3) is false but P(5) is true

(D) Both P(3) and P(5) are true

24. For each tϵR, let [t] be the greatest integer less than or equal to t. Then,

(A) equals –1

(B) equals 1

(C) does not exist

(D) equals 0

25. If R and R' are symmetric relations (not disjoint) on a set A, then the relation R R' is

(A) reflexive

(B) symmetric

(C) transitive

(D) none of these

26. Let

Then, f(x) is continuous on the set

(A) R

(B) R – 1

(C) R – 2

(D) R – 1, 2

27. Consider a triangular plot ABC with sides AB=7m, BC=5m and CA=6m. A vertical lamp-

post at the mid-point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is:

(A) 7

(B)

(C)

(D)

28. Let f : R→R be a function such that f(x) = x3+x

2f'(1) + xf''(2)+f'''(3), xϵR. Then f(2) equal :

(A) 8

(B) –2

(C) –4

(D) 30

29. If the system of equations

x+y+z = 5

x+2y+3z = 9

x+3y+az = b

has infinitely many solutions, then b–a equals:

(A) 5

(B) 18

(C) 21

(D) 8

30. The mean of five observations is 5 and their variance is 9.20. If three of the given five

observations are 1, 3 and 8, then a ratio of other two observations is :

(A) 4 : 9

(B) 6 : 7

(C) 5 : 8

(D) 10 : 3

1. Which of these has highest frequency?

(A) Cosmic rays

(B) X-Rays

(C) Radio waves

(D) Micro waves

2. In isotope the number of neutrons is –

(A) Same

(B) Different

(C) Both

(D) None

3. The rms velocity of molecules of a gas of density 4 kg m-3

and pressure 1.2 × 105 Nm

-2 is

(A) 900 ms-1

(B) 120 ms-1

(C) 600 ms-1

(D) 300 ms-1

4. One gram of silver gets distributed between 10 cm3 of molten zinc and 100 cm

3 of molten lead

at 800 o C. The percentage of silver in the zinc layer is approximately

(Given: Partition coefficient of Ag in Zn and Pb is 300)

(A) 89

(B) 91

(C) 97

(D) 94

5. Which of these is not radioactive?

(A) Astanine

(B) Francium

(C) Tritium

(D) Zirconium

6. The heaviest naturally occurring element is –

(A) Thorium

(B) Uranium

(C) Polonium

(D) Plutonium

7. How long (approximate) should water be electrolysed by passing through 100 A current so

that the oxygen released can completely burn 27.66 g of diborane ? (Atomic weight of B=10.8 u)

(A) 1.6 hours

(B) 6.4 hours

(C) 0.8 hours

Chemistry

(D) 3.2 hours

8. Which has highest calorific value?

(A) Fat

(B) Protein

(C) Carbohydrate

(D) Amino Acid

9. Which law of thermodynamics introduces the concept of entropy?

(A) 0

(B) 1

(C) 2

(D) 3

10. Which has the highest ionization potential?

(A) Li

(B) B

(C) Ne

(D) F

11. Reverse of swelling of gel is known as –

(A) Syneresis

(B) Thixotropy

(C) Sorption

(D) None

12. The most abundant metal in earth crust is –

(A) Fe

(B) Mg

(C) Ca

(D) Al

13. The ratio of y for inert gases is-

(A) 1.33

(B) 1.66

(C) 2.13

(D) 99

14. Which among the following is called a pseudo solid?

(A) CaF2

(B) Glass

(C) NaCl

(D) All of these

15. Pyrex glass is obtained by fusing together _______.

(A) 60 to 80% Al2O3, 10 to 25% SiO2 and remaining amount of B2O3

(B) 60 to 80% B2O3, 10 to 25% Al2O3 and remaining amount of SiO2

(C) 60 to 80% SiO2, 10 to 25% B2O3 and remaining amount of Al2O3

(D) 60 to 80% SiO2, 10 to 25% Al2O3 and remaining amount of B2O3

16. The structure of ethylene is –

(A) Linear

(B) Tetrahedral

(C) Octahedral

(D) Triangular

17. Which one has the hydrogen bonding?

(A) HCl

(B) HBr

(C) HF

(D) HI

18. Which statement about solution is correct?

(A) When vitamin D dissolves in fat, vitamin D is the solvent and fat is the solute.

(B) In a solution of NaCl in water, NaCl is the solute and water is the solvent.

(C) An aqueous solution consists of water dissolved in a solute.

(D) The concentration of a solution is the amount of solvent dissolved in 1 dm3 of solution.

19. Which is the best definition of electronegativity?

(A) Electronegativity is the energy required for a gaseous atom to gain an electron.

(B) Electronegativity is the attraction of an atom for bonding a pair of electrons.

(C) Electronegativity is the attraction between the nucleus and the valence electron of an atom.

(D) Electronegativity is the ability of an atom to attract electrons from another atom.

20. Which structure has delocalized π electrons?

(A) O3

(B) CO

(C) HCN

(D) CO2

21. Quartz is a crystalline variety of _______.

(A) silica

(B) sodium silicate

(C) silicon carbide

(D) silicon

22. The structure of sodium chloride crystal is _______.

(A) body centered cubic lattice

(B) face centered cubic lattice

(C) octahedral

(D) square planar

23. What is the best definition of rate of reaction?

(A) The time it takes to use up all the reactants

(B) The rate at which all the reactants are used up

(C) The time it takes for the one of the reactants to be used up

(D) The increase in concentration of a product per unit time

24. Transition metals, when form interstitial compounds, the non-metals (H, B, C, N) are

accommodated in _______.

(A) voids or holes in cubic-packed structure

(B) tetrahedral voids

(C) octahedral voids

(D) all of these

25. Diamond is an example of _______.

(A) solid with hydrogen bonding

(B) electrovalent solid

(C) covalent solid

(D) glass

26. What is the IUPAC name for HCOOCH2CH2CH3?

(A) Butanoic acid

(B) Butanal

(C) Methyl propanoate

(D) Propyl methanoate

27. Which conditions are required to obtain a good yield of carboxylic acid when ethanol is

oxidized using potassium dichromate (VI), K2Cr2O7 (aq)?

I. Add sulfuric acid

II. Heat the reaction mixture under reflux

III. Distil the product as the oxidizing agent is added

(A) I and II only

(B) I and III only

(C) II and III only

(D) I, II and III

28. Which statement about substitution reactions are correct?

I. The reaction between sodium hydroxide and 1-chloropentane predominantly follows an

SN2 mechanism.

II. The reaction between sodium hydroxide and 2-chloro-2-methylbutane predominantly

follows an SN2 mechanism.

III. The reaction of sodium hydroxide with 1-chloropentane occurs at a slower rate than with

1-bromopentane.

(A) I and II only

(B) I and III only

(C) II and III only

(D) I, II and III

29. Which compound can exist as stereoisomers?

(A) CH3CH2CHO

(B) CH3CH2COCH3

(C) CH3CH(CH3)2

(D) CH3CH2CHOHCH3

30. What is the order of increasing energy of the orbitals within a single energy level?

(A) d < s < f < p

(B) s < p < d < f

(C) p < s < f < d

(D) f < d < p < s