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P-SAT 2014 - 15

(PIONEER’S SCHOLARSHIP/ADMISSION TEST) {+1 MEDICAL}

General Instructions:-

The question paper contains 90 objective multiple choice questions.

There are three parts in the question paper consisting of

Section-A: MATHEMATICS (1 to 30)

Section-B: CHEMISTRY (31 to 60),

Section-C: PHYSICS (61 to 90).

Each right answer carries (4 marks) and wrong (–1mark)

The paper consists of 90 questions. The maximum marks are 360.

Maximum Time 3Hrs.

Give your response in the OMR Sheet provided with the Question Paper.

Name: _______________________________Father Name:______________________________

Mobile: ______________________________School:__________________________________

Solution Visits: www.pioneermathematics.com/latest_updates.com

http://www.pioneermathematics.com/latest_updates.com



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Section –A {Biology}

1. Nicpotiana sylvestris flower only during long days and N. tabacum flowers only during short days. If

raised in the laboratory under different photoperiods, they can be induced to flower at the same time

and can be cross fertilized to produce self-fertile offspring. What is the best reason for considering N.

sylvestris and N. tabacum to be separate species?

(a) They are physiologically distinct (b) They are morphologically distinct

(c) They cannot interbreed in nature (d) They are reproductively distinct.

Ans. (c)

2. Phenetic classification of organism is based on

(a) observable characteristics of existing organisms (b) the ancestral lineage of existing organism

(c) dendrogram based on DNA characteristics (d) sexual characteristics

Ans. (a)

3. Which of the following statements regarding cilia is not correct?

(a) The organized beating of cilia is controlled by fluxed of Ca2+ across the membrane

(b) Cilia are hair-like cellular appendages

(c) Microtubules of cilia are composed of tubulin

(d) Cilia contain an outer ring of nine doublet microtubules surrounding to single microtubules

Ans. (a)

4. Which of the following is correct about heterospory?

(a) Selaginella and Salvinia are heterosporous

(b) Heterosporous, pteridophytes have macro (large) and micro (small) spores

(c) The development of zygote within female gametophyte is the precursor to the seed habit

(d) All of the above

Ans. (d)

5. Which of the following is not correctly matched ?

(a) Physalia – Portugese man of war

(b) pennatula – Sea anemone

(c) Gorgonia – Sea fan

(d) Meanderin – Brain coral

Sol : (b)

6. At retrogreesive metamorphosis, the urochordate larva

(a) loss notochord

(b) loss tail



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(c) experience reduction of nervous system to a visceral ganglion

(d) All of above

Ans. (d)

7. The correct floral formula of chilli is

Ans. (a)

8. Annual plants, which complete their life cycle within a brief or short (4-6 weeks) period, are called

ephemeral annuals or ephemerals. All of the following are ephemerals except

(a) Argemone (b) Artemisia (c) Astragalus (d) Bambusa

Ans. (d)

9. The scutellum observed in a gain of wheat or maize is comparable to, which part of the seed in other

monocotyledons.

(a) Cotyledon (b) Endosperm (c) Aleurone layer (d) Plumule

Ans. (a)

10. In dicot stem, vascular bundles are conjoint, collateral and open, whereas monocots vascular bundles

are

(a) conjoint, collateral and closed (b) radial, collateral and open

(c) radial, biocollateral and closed (d) concentric, collateral and open

Ans. (a)

11. Which of the statement is incorrect?

(a) Cartilage contains chondrin, which makes the matrix

(b) matrix of bone is formed by ossein

(c) Haversian canal system is characteristic of mammalian bone

(d) Volkman’s canal connect the lacuna present in the cartilage

Ans. (d)

12. Smooth muscle fibres are

(a) cylindrical, unbranched, striated multinucleate and voluntary

(b) spindle-shape, unbranched, non- striated, uninucleate and involuntary.

(c) Cylindrical, unbranched, non-striated, multinucleate and involuntary



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(d) spindle-shaped, striated, uninucleate and voluntary.

Ans. (b)

13. Na+/K+ pump is

(a) a passive transport

(b) an active transport

(c) an osmotic process

(d) a diffusion process

Ans. (b)

14. According to widely accepted ‘fluid mosaic model’. Cell membranes are semi-fluid, where lipids and

integral proteins can diffuse randomly. In recent years, this model has been modified in several

respects. In this regard, which of the following statements is incorrect?

(a) Proteins in cell membranes can travel within the lipid bilayer

(b) Proteins can remain confined within certain domain of the membrane

(c) Proteins can also undergo flip-flop movements in the lipid bilayer

(d) Many proteins remain completely embedded within the lipid bilayer

Ans. (c)

15. In non-competitive inhibition, the allosteric inhibitor

(a) attaches to the substrate, preventing it from attaching to the active site

(b) change the pH of the environment, thus preventing enzyme-substrate complex formation

(c) cause the substrate to polymerize, preventing individual enzyme-substrate attachment

(d) attaches to the enzyme at a site away from the active site, altering the shape of the enzyme

Ans. (d)

16. A certain species of animal has six pairs of chromosomes. How many molecules of DNA do the nuclei of

these animals have during G2-phase?

(a) 12 (b) 48 (c) 6 (d) 24

Ans. (d)

17. The DNA content of a cell is measured in the G2-phase. After meiosis-I, the DNA content of one of the

cells produced is

(a) equal to that of the G2-cell (b) twice that of the G2cell

(c) 1/2 that of the G2 cell (d) 1/4 that of the G2 cell

Ans. (c)



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18. In a plant cell, OP is equal to

(a) TP–DPD (b) DPD –TP (c) TP–DP (d) DPD+TP

Ans. (d)

19. Farmers in a particular region were concerned that pre-mature yellowing of leaves of a pulse crop

might cause decrease in the yield. Which treatment could be most beneficial to obtain maximum seed

yield?

(a) Frequent irrigation of the crop

(b) Treatments if the plants with cytokinins along with a small dose of nitrogenous fertilizer

(c) Removal of all yellow leaves and spraying the remaining green leaves with 2, 4, 5-trichlorophenoxy

acetic acid

(d) Application of iron and magnesium to promote synthesis of chlorophyll.

Ans. (a)

20. For yielding one molecule of glucose the Calvin cycle turns

(a) Two times (b) four times (c) six times (d) eight times

Ans. (c)

21. Brunner’s gland is present in

(a) liver (b) duodenum (c) oesophagus (d) stomach

Ans. (b)

22. Teeth of most reptiles and amphibians are

(a) acrodont (b) thecodont (c) heterodont (d) diphyodont

Ans. (a)

23. If an incision had to be made in the small intestine to remove an obstruction, which tunic would be cut

first?

(a) Muscularis (b) Mucosa (c) Submucosa (d) Adventitia

Ans. (d)

24. Oxygen and carbon dioxide concentration in the alveolar air are respectively

(a) 16% and 4% (b) 19.8% and 4.6% (c) 21% and 4% (d) 13.1% and 5.3%

Ans. (d)

25. People living at sea level have around 5 million RBCs per cubic millimeter of their blood, whereas

those living at an altitude of 5400 metres have around 8 million. This is because at high altitude

(a) People get pollution-free air to breathe and more oxygen is available

(b) atmospheric O2 level is less and hence more RBCs are needed to absorb the required amount of O2

to survive



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(c) there is more UV radiation, which enhanced RBCs proportion.

(d) People eat more nutritive food, therefore more RBCs are formed

Ans. (b)

26. Increase of oxyhaemoglobin leads to increase in acidic nature. This is

(a) Bohr’s effect (b) Hamburger phenomenon

(c) Chloride shift (d) Haldane’s effect

Ans. (d)

27. Arteries are best defined as the vessels, which

(a) carry blood away from the heart to different organs

(b) break up into capillaries, which reunite to form a vein

(c) carry blood from one visceral organ to another visceral organs

(d) supply oxygenated blood to the different organs

Ans. (c)

28. A drop of each of the following is placed separately on four slides. Which of them will not coagulate?

(a) Blood plasma

(b) Blood serum

(c) Sample from the thoracic duct of lymphatic system

(d) Whole blood from pulmonary vein

Ans. (b)

29. When the atrioventricular bundle is completely interrupted the

(a) atria beat at an irregular rate

(b) ventricles typically contract at 30 to 40 beats/min

(c) PR intervals in the ECG are longer than normal but remain constant from best to beat

(d) QRS complex varies in shape from beat to beat

Ans. (b)

30. Match the blood vessels of human listed under column A with the functions given under B. Choose the

answer, which gives the combination of the alphabets of the two columns.

Column A Column B

A. Renal portal 1. Carries blood to varies body parts

B. Pulmonary vein 2. Is portal vein

C. Dorsal aorta 3. Carries oxygenated blood

D. Pulmonary artery 4. Carries dioxygenated blood

5. Absent in man



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Codes

(a) A –5, B–1, C–3, D–2

(b) A–5, B–3, C–1, D–4

(c) A–4, B–5, C–3, D–1

(d) A–5, B–1, C–2, D–3

Ans. (b)



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Section – B (Chemistry)

31. Which has maximum number of atoms?

(a) 24 g of C (12) (b) 56 g of Fe (56) (c) 27 g of Al (27) (d)108 g of Ag (108)

Sol : (a)

Number of atoms = number of moles × Avogadro’s number (NA)

Number of atoms in 24 g C = A A

24N 2N

12

Number of atoms in 56 g of Fe A A

56N N

56

Number of atoms in 27 g of Al = A A

27N N

27

Number of atoms in 108 g of Ag = A A

108N N

108

Hence, 24 g of carbon has the maximum number of atoms.

32. An element X has following isotopic composition; 200X : 90%; 199X : 8.0%; 202X : 2.0%. The average

atomic mass of naturally occurring element X is closet to

(a) 199 amu (b) 200 amu (c) 201 amu (d) 202 amu

Sol : (b)

Average at. mass = 0.9 × 200 + 0.08 × 199 + 0.02 × 202

= 180 + 15.92 + 4.04 = 199.96 200 amu

33. If uncertainty in position and momentum are equal, then uncertainty in velocity is

(a) h

(b) 1 h

2m (c)

h

2 (d)

1 h

m.

Sol: (b)

hx. p

4π

2 hp

4π

1 h 1 hp or m v

2 π 2 π

1 hv

2m π



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34. Which of the following sets of quantum numbers represents the highest energy of an atom?

(a) n = 3, l = 1, m = 1, s = +½ (b) n = 3, l = 2, m = 1, s = +½

(c) n = 4, l = 0, m = 0, s = +½ (d) n = 3, l = 0, m = 0, s = +½.

Sol : (b)

It has highest value of (n + l).

35. The wavelength of the radiation emitted, when in a hydrogen atom electron falls from infinity to

stationary state 1 would be (Rydberg constant = 1.097×107 m–1)

(a) 91 nm (b) 192 nm (c) 406 nm (d) 9.1× 10–8 nm

Sol : (a)

7 1 7 1

2

1 1 11.097 10 m 1.097 10 m

1

9

7 7

1 10m nm 91 nm.

1.097 10 1.097 10

36. Which one of the following sets of ions represents a collection of isoelectronic species ?

(a) K+, Cl–, Ca2+, Sc3+ (b) Ba2+, Sr2+, K+, Ca2+

(c) N3–, O2–, F–, S2– (d) Li+, Na+, Mg2+, Ca2+.

Sol: (a)

K+, Cl–, Ca2+ and Sc3+ contain 18 electron each.

37. Which of the following is the most basic oxide ?

(a) SeO2 (b) Al2O3 (c) Sb2O3 (d) Bi2O3.

Sol: (d)

The basic character of oxides increase on descending a group and decrease on moving across a

period from left to right. Bi occupies very low position in its group.

38. Which of the following represents isostructural pairs?

(a) [NF3, NO3] and [BF3, H3O+] (b) [NF3, HN3] and [NO 3 , BF3]

(c) [NF3, H3O+] and [NO 3 , BF3] (d) [NF3, H3O+] and [HN3, BF3]

Sol : (c)

NF3 and H3O+ are pyramidal whereas NO3– and BF3 are trigonal planar.

39. Specify the coordination geometry around and hybridization of N and B atoms in 1 : 1 complex of BF3

and NH3.

(a) N: tetrahedral, sp3; B: tetrahedral, sp3 (b) N: pyramidal, sp3 B: pyramidal, sp3



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(c) N: pyramidal, sp3 B: planar, sp3 (d) N: pyramidal, sp3 B: tetrahedral, sp3

Sol : (a)

3

F H

| |

F B N H Both 'B' and 'N' sp tetrahedral.

| |

F H

40. Which of the following contains maximum number of lone pairs on the central atom?

(a) ClO 3 (b) XeF4 (c) SF4 (d) I 3

Sol : (d)

41. The percentage of p-character in forming P–P bonds in P4 molecule is

(a) 25% (b) 33% (c) 50% (d) 75%

Sol : (d)

In forming P4 molecule, P atom uses sp3 hybrid orbitals. Thus, p-character in hybrid orbitals 75%.

42. The compressibility of gas is less than unity at STP. Therefore,

(a) Vm > 22.4 L (b) Vm < 22.4 L (c) Vm = 22.4 L (d) Vm > 44.8 L

Sol : (b)

Compressibility factor id

VZ 1 given

V

idV 22.4 L V (1 mol) 22.4 at STP



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43. The term that corrects for attractive forces present in real gas in van der Waal equation is :

(a) nb (b) 2

2

an

V (c) –

2

2

an

V (d) –nb.

Sol : (b)

In van der Waal equation, the correction for the attractive forces present in real gases is given by the

pressure term 2

2

an.

V

44. The maximum number of molecules is present in

(a) 15L of H2 gas at STP (0oC, 1 atm) (b) 5L of N2 gas at STP (0oC, 1 atm)

(c) 0.5 g of H2 gas (d) 10 g of O2 gas

Sol : (a)

(a) 15 L of H2 at S.T.P = 23

2315 15 6.02 10mol 4.03 10 molecules.

22.4 22.4

(b)5 L of N2 at S.T.P = 23

235 5 6.02 10mol 1.34 10 molecules.

22.4 22.4

(c) 0.5 g of H2 = 23

230.5 0.5 6.02 10mol 1.505 10 molecules.

2 2

(d) 10 g of O2 = 23

2310 10 6.02 10mol 1.88 10 molecules.

32 32

Hence (a) is correct answer.

45. A and B are ideal gases. Molar masses of A and B are in the ratio of 1: 4. The pressure of mixture A

and B are in the ratio of 1: 4. The pressure of gas mixture containing equal masses of A and B is Patm.

What is the partial pressure of B in the mixture?

(a) P/5 (b) P/2 (c) P/2.5 (d) 3P/4

Sol : (a)

Let W be the mass of each gas

A B

A A

W Wn ; n

m 4m

Total moles = A

W 1 5W1

mA 4 4m

B

A

P 4mA W Pp .

5W 4m 5

46. 0

f H of CO2(g), CO(g), N2O and NO2 (g) in kJ mol–1 are respectively –393, –110,81 and 34. The value

of H of following reaction in kJ is 2NO2(g) +3CO(g) N2O(g) + 3CO2(g)



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(a) 836 (b) 1460 (c) –836 (d) –1460.

Sol : (c)

0 0 0f product f reactant

0 0 0 0 0f 2 f 2 f f 2

H ( H ) ( H )

H 3 H (CO ) H (N O) 3 H (CO) 2 H (NO )

= 3 × (–393) + (81) – 3 × (–110) – 2 × (34) = –836

47. Which one of the following statement is false?

(a) Work is state function

(b) Temperature is a state function

(c) Change in state is completely defined when initial and final states are specified

(d) Work appears at the boundary of the system.

Sol : (a)

Work is not a state-function, it depends on path followed.

48. The standard enthalpy change and standard entropy change for oxidation of ammonia at 298 K are –

382.64 kJ mol–1 and –145.6 JK–1 mol–1 respectively. The standard Gibb’s energy change for the same

reaction at 298 K is

(a) – 221.1 kJ mol–1 (b) –339.3 kJ mol–1 (c) –439.3 kJ mol–1 (d) –523.2 kJ mol–1.

Sol: (b)

G H T S

= 382.64 – (298 × – 145.6 × 10–3)

= – 339.3 kJ mol–1

49. In the enthalpy change for the transition of liquid water to steam is 30 kJ mol–1 at 27oC, the entropy

change for the process would be

(a) 100 J mol–1 K–1 (b) 10 J mol–1 K–1 (c) 1.0 J mol–1 (d) 0.1 J mol–1 K–1.

Sol : (a)

3 1

vap 1 1vap

30 10 J molHS 100 J mol K

T 300 K

50. Equilibrium constants K1 and K2 for the following equilibria :

(a) NO(g) +1

2O2

1KNO2(g) and 2NO2(g) 2K 2NO(g) + O2(g)are related as :

(a) 2 21

1K

K (b)

22 1K K (c) 2

1

1K

K (d)

12

KK

2

Sol : (a)



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21 1/2

2

[NO ]K

[NO][O ] ..(i)

22

2 22

[NO] [O ]K

[NO ] ..(ii)

22 21 2

2

[NO ]K

[NO] [O ] ..(iii)

From equations (ii) and (iii)

2 21

1K

K

51. For the reaction,

2NO2(g) 2NO(g) + O2(g).

(Kc =1.8×10–6 at 184oC)

(R = 0.0831 kJ/mol. K)

When Kp and Kc are compared at 184oC it is found that

(a) Whether Kp is greater than, less than or liquid to Kc depends upon the total gas pressure

(b) Kp = Kc (c) Kp is less than Kc (d) Kp is greater than Kc.

Sol : (d)

n

p cK K RT

np

c

KRT n 1 in this case

K

P

c

KRT

K

Since the value of RT is greater than 1, Kp is greater than Kc.

52. Phosphorous pentachloride dissociates as shows, in a closed reaction vessel,

PCl5(g) PCl3(g) + Cl2 (g). If total pressure at equilibrium of the reaction mixture is P and degree

of dissociation of PCl5 is x, the partial pressure of PCl3 will be

(a) x

P1 x

(b) 2x

P1 x

(c) x

Px 1

(d) x

P1 x

Sol : (a)



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5 3 2

total

PCl PCl Cl

n 1 x nx nx; n n 1 x

3PCl

nx xP P P

n 1 x 1 x

53. The following equilibrium constants are given :

I. N2 +3H2 2NH3; K1

II. N2 + O2 2NO; K2

III. H2 + 1

2O2H2O; K3

The equilibrium constant for reaction 2NH3 + 2 2

5O 2NO 3H O

2

(a) 2

1

3

KK

K (b)

33

1

2

KK

K (c)

33

2

1

KK

K (d)

2 32

1

KK

K

Sol : (c)

From given equations,

We have, 2

3 21 23

2 22 2

[NH ] [NO]K , K

[N ][O ][N ][H ],

23 1/2

2 2

[H O]K

[H ][O ]

For the given reaction,

2 32

2 5/23 2

[NO] [H O]K

[NH ] [O ]

3 2 32 3 2

2 5/21 3 2

K K [NO] [H O]

K [NH ] [O ] 3

2 3

1

K KK

K

54. The rapid change of pH near the stoichio-metric point of an acid-base titration is the basic of

indicator detection. pH of the solution is related to ratio of the concentrations of the conjugate acid

(HIn) and base (In–) forms of the indicator by the expression.

(a) log HIn

In = pKIn –pH (b) log

HIn

In = pH – pKIn

(c) logIn

HIn = pH – pKIn (d) log

In

HIn = pKIn – pH.

Sol : (c)



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a ln

[Salt] [In ]pH pK log pK log

[Acid] [HIn]

In

[In ]log pH pK .

[HIn]

55. The standard reduction potentials of three metallic ions X, Y, Z are respectively 0.52, – 3.03 and –1.18

V. The order of reducing power of the corresponding metals is

(a) Y > Z > X (b) X > Y > Z (c) Z > Y > X (d) Z > X > Y.

Sol: (a)

Lower the value of Eo, stronger the reducing agent. Reducing power : Y (Eo = – 3.03 V)

> Z (Eo = – 1.18 V) > X (Eo = 0.52 V).

56. The standard reduction potentials of four elements are given below: I = – 3.04 V,

II = – 1.90, III = 0.0 V; IV = 1.90 V which of the following will be most suitable reducing agent ?

(a) I (b) II (c) III (d) IV.

Sol: (a)

57. H2 molecule has two electrons and two nuclei. In which form of hydrogen the spin of electrons and also

the spin of nuclei are in opposite directions.

(a) Ortho hydrogen (b) Para hydrogen (c) Meta hydrogen (d) -hydrogen.

Sol: (b)

58. The compound is known by which of the following names ?

(a) Bicyclo-[2.2.1] octane (b) Bicyclo-[2.2.2] octane

(c) Bicyclo-[1.2.1] octane (d) Bicyclo-[1.1.1] octane.

Sol: (b)



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59. The IUPAC name of the compound

(a) 1, 1-dimenthyl-3-cyclohexanol (b) 1, 1-dimethyl-3-hdroxycylohexane

(c) 3, 3-dimethyl-1-cyclohexanol (d) 3, 3-dimethyl-1-hydroxyclohexane.

Sol : (c)

60. The general molecular formula, which represents the homologous series of alkanols is

(a) n 2n 2C H O (b) n 2n 2C H O (c) n 2nC H O (d) n 2n 1C H O.

Sol: (a)

Alcohols are represented by the general formula ;

2 2n 2C H O.

Section-C {Physics}

61. The vander Waal’s equation for a gas is 2

aP

V(V – b) = RT, when P, V, T, R are pressure, volume,

temperature and universal gas constant respectively with a and b as constant. The ratio b/a has the

dimensions of :

(a) [M–1L–2T2] (b) [M–1L–1T–1] (c) [ML2T2] (d) [MLT–2]

Sol : (a)

Dimensions of [a] = dimensions of PV2

Dimensions of [b] = dimensions of volume V

Dimensions of 1 2 2

2 2 2

b V 1 1[M L T ]

a PV PV [ML T ]

62. A body thrown vertically upwards with an initial velocity reaches maximum height in 6 second. The

ratio of the distances traversed by the body in the first second and the seventh second is :

(a) 1 : 1 (b) 11 : 1 (c) 1 : 2 (d) 1 : 11

Sol:(b)

Time taken by the body to move a distance upward = time taken by the body to move the same

distance downward.



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Distance traversed during ascent in first second = distance traversed during descent in 6th second.

Using the formula n

1s n a 2n 1

2during descent (u = 0)

1

1 1s g 2 6 1 11. g

2 2

2

1 1s g 2 1 1 1. g

2 2

1 2s : s 11:1

63. A car starting from rest, accelerates at the rate ‘f’ through a distance s, then continues at constant

speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is

15 s, then

(a) 21s ft

2 (b) 21

s ft4

(c) 21s ft

6 (d) 21

s ft72

Sol : (d)

the velocity time graph for the given situation canbe drawn as below. Magnitude of

slope of OA = f

fand slope of BC

2

1 2

fv ft t

2

2 1t 2t

In graph area of AOD gives distance,

21

1s ft

2 …(i)

Area of rectangle ABED gives distance travelled in time t.

2 1s ft t



18

Distance travelled in time t2,

2

3 1

1 fs 2t

2 2

Thus, 1 2 3s s s 15s

21 1s ft t ft 15s

or 21 1

1s ft t 2s 15s s ft

2

or 1ft t 12s ..(ii)

From Eqs. (i) and (ii), we have

1

1 1

ft t12s

1s ft t2

or 1

tt

6

From Eq. (i), we get

2

1

1s f t

2

2

21 t 1s f ft

2 6 72

64. Two forces of magnitudes P and 3 P act at right angles to each other. Their resultant makes angle

with P; which of the following gives the correct value of ?

(a) 300 (b) 450 (c) 600 (d) none of these

Sol: (c)

0Q 3Ptan θ 3 θ 60

P P



19

65. A projectile can have the same range R for the angles of projections. It t1 and t2 be the times of flight in

the two cases, then the product of the two times of flights is proportional to

(a)

1

R (b) R (c) R2 (d)

–

1

R

Sol : (b)

2 2 u sin u cosu sin 2R

g g

For same range 0

1 2 90

1 2

2u sin 902u sin 2u cost , t

g g g

1 2 2

4 u sin u cos 2 u sin u cos2 2Rt t .

g g g g

1 2t t R

66. A particle is undergoing uniform circular motion. Its instantaneous velocity and acceleration vectors

are

(a) in the same direction (b) perpendicular to each other

(c) opposite to each other (d) inclined at 450 to each other.

Sol : (b)

Angle between centripetal force and instantaneous displacement along circumference of circle is

always 900

0W Fs cos F 2 R cos 90 0

67. Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their

speeds are such that they each make a complete circle in the same length of time t. The ratio of

angular speed of the first to the second car is

(a) m1 : m2 (b) r1 : r2 (c) 1 : 1 (d) 1 1 2 2m r m r

Sol: (c)

2πω

T

(independent of mass m of particle and radius r of circular path).

At T is same for both particles

1

2

ω1

ω



20

68. The roadway bridge over a canal is in the form of an arc of a circle of radius 20 m. What is the

minimum speed with which a car can cross the bridge without leaving contact with the surface at the

highest point ? (g = 9.8 m/s2)

(a) 10

m / s7

(b) 14 m/s (c) 14 2 m/s (d) 14 5 m/s

Sol : (b)

cV rg 20 9.8 14 m / s

69. N bullets each of mass m kg are fired with a velocity of v m/s at the rate of n bullets per second upon

a wall. The reaction offered by the wall to the bullets is :

(a) Nmv

n (b) n N mv (c)

n Nv

m (d) nmv

Sol:(d)

pF

t

If bullets do not rebound

1p mv, t

n

mvF nmv

1/ n

70. Two masses M1 and M2 (M1 > M2) are tied to two strings passing over a frictionless pulley. If lift

accelerates downward with acceleration g

a4

, then the tension (N) in cable supporting the pulley is

(a) zero (b) 1 2

1 2

M M3g

2 M M (c) 1 2

1 2

3M Mg

M M (d) 1 2

1 2

5M Mg

M M

Sol : (c)



21

1 2

1 2

2M MN 2T 2 (g a)

M M

1 2 1 2 1 2

1 2 1 2 1 2

2M M 2M M 3M Mg 3g2 g 2 g

M M 4 M M 4 M M

71. A jet of water with a cross-sectional area ‘a’ strikers a wall at angle to the normal and rebounds

elastically. If the velocity of water in the jet is , the normal force acting on the wall is :

(a) 22av cos (b) 2av cos (c) 2av cos (d) av cos

Sol: (a)

mv cos θ mv cos θpF

t t

m2v cos θ

t

ρ

mV where V volume of flowing / second.

t

= avp where v is velocity.

72. Rolling friction is

(a) Equal to static friction

(b) Greater than static friction

(c) Less than static friction

(d) May be equal to, less than or greater than depending on the situation.

Sol: (c)

73. A passenger is travelling in a train moving at 72 km/h. His suitcase is kept on the berth. The driver of

the train applies brakes such that the speed of the train decreases at a constant rate to 36 km/h in 5s.

For the suitcase not to slide during retardation of the train, the minimum coefficient of friction

between the suitcase and the berth, required is (g = 9.8 m/s2)

(a) 10

49 (b)

20

49 (c)

10

98 (d)

30

98

Sol : (a)

Retardation

21 2

1572 36

v v 18a 2 m / st 5



22

Pseudo force on suitcase = ma in forward direction.

a 2 10ma mg .

g 9.8 49

74. A body is moved along a straight line by a machine delivering constant power. The distance moved

by the body in time t is proportional to :

(a) t1/2 (b) t3/4 (c) t3/2 (d) t2

Sol : (c)

P = Fv = constant

or dp d

v constant or mv . v P(constant)dt dt

dv Pv

dt m

Integrating,

v2t 1/20

0

v P 2P[t] v t

2 m m

As 1/2 1/2dx 2P 2Pv t dx t dt

dt m m

Integrating again x = 3/2

3/22P tx t

m 3/ 2

75. A mass m accelerates uniformly from rest to a speed V in time T. The instantaneous power delivered

to body as a function of time t is given by

(a) 2

2

2

mVt

T (b)

2

2

mV.t

T (c)

22

2

1 mVt

2 T (d)

22

2

1 mV.t

2 T

Sol : (b)

Acceleration a = V 0 V

T T

Velocity attained in time t, v = u + at = V

tT

Instantaneous power

P F.v

= ma.v

=v v

m . tT T

= 2

2

mV.t

T



23

76. A particle of mass 100g is thrown vertically upwards with a speed of 5 m/s. The work done by the

force of gravity during the time the particle goes up is

(a) – 0.5 J (b) – 1.25 J (c) 1.25 J (d) 0.5 J

Sol : (b)

Work done by gravity

W F. s

= mg h cos mgh

= 2

2v 1mg mv

2g 2

= 21

0.1 5 1.25 J2

77. A shell is fired from cannon with a velocity v (m/s) at an angle with the horizontal direction. At the

highest points in its path it explodes into two pieces of equal mass. One of the pieces retraces its path

to the cannon and the speed (in m/s) of the other piece, immediately after the explosion is

(a) 3v cos (b) 2v cos (c) 3

v cos2

(d) 3

v cos2

Sol : (a)

At highest point, the shell has only horizontal component of velocity v cos . Conservation of

momentum implies

2

m mmv cos v cos v

2 2

2v 3v cos

78. The space craft of mass M moves with velocity V in free space at first ; then it explodes breaking into

two pieces. If after explosion a piece of mass m comes to rest, the velocity of other piece of space craft

will be

(a) MV

M m (b)

MV

M m (c)

mV

M m (d)

mV

M m

Sol : (a)

2Mv m 0 M m v

2

Mvv

M m



24

79. Consider a two particle system with particles having masses m1 and m2. If the first particle is pushed

towards the centre of mass through a distance ‘d’, by what distance should the second particle be

moved, so as to keep the centre of mass at the same position ?

(a) 2

1

md

m (b) 1

1

md

m m (c) 1

2

md

m (d) d

Sol : (c)

1 1 2 2cm

1 2

m x m xx

m m

1 2 2

1 2

m d m x0

m m

12

2

m dx

m

80. A body A of mass M while falling vertically downwards under gravity breaks into two parts, a body B

of mass M

3 and body C of mass

2

3M. The centre of mass of the bodies B and C taken together shifts

compared to that of body A

(a) does not shift (b) depends on height of breaking

(c) towards body B (d) towards body C

Sol : (a)

In the absence of external force, the centre of mass of component bodies is same as centre of mass of

parent body.

81. The amount of work required to send a body of mass m from earth’s surface to a height R

2, where R

is radius of earth is

(a) mgR

2 (b)

mgR

3 (c)

mgR

4 (d)

5

3mgR

Sol : (b)

2 1W U U

= GMm GMm

R RR2



25

= GMm 2 GMm

1R 3 3R

=

2R g m1 1mg R

3 R 3

82. Suppose the gravitational force varies inversely on the nth power of distance. The time period of

revolution of a planet in a circular orbit of radius r around the sun will be proportional to

(a) rn+1 (b) r(n + 1)/2 (c) rn + 2 (d) r(n + 2)/2

Sol : (b)

n

1F

R

n

KF

R

2

n

KmR

R

n 1

K

mR

n 1

2 K

T mR

n 1 /2m

T 2 . RK

83. In a planetary motion, the areal velocity of the position vector of planet depends an angular velocity

and distance (r) of the planet form the sun. The correct relation for areal velocity dA

dtis

(a) dA

rdt

(b) 2dAr

dt (c) 2dA

rdt

(d) dA

rdt

Sol: (c)

22dA L mr ω

r ωdr 2m 2m

84. A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm.

Find the work to be done to take the particle far away from the sphere (G = 6.67 × 10–11 N-m2/kg2)

(a) 3.33 × 10–10 J (b) 13.34 × 10–10 J (c) 6.67 × 10–10 J (d) 6.67 × 10–9 J

Sol : (c)



26

2 1

GMm GMmW U U 0

R R

= 11 3

10

2

6.67 10 100 10 106.67 10 J

10 10

85. A child is standing with folded hands at the centre of platform rotating about its central axis. The

kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of

the system doubles. The kinetic energy of the system now is

(a) 2K (b) K

2 (c)

K

4 (d) 4K

Sol : (b)

Kinetic energy 2L 1

K2I I

for constant angular momentum (L).

When I is doubled, kinetic energy in halved.

86. A thin wire of length L and uniform linear mass density is bent into a circular loop with centre O as

shown. The moment of inertia of the loop about the axis AB is

(a) 3

2

L

8 (b)

3

2

L

16 (c)

3

2

5 L

16 (d)

3

2

3 L

8

Moment of inertia of loop about tangent AB is

2gI I MR

2 2 21 3MR MR MR

2 2

M Lρ 2π Rρ

23 L

I L ρ2 2π

3

2

3ρ L

8 π

87. Let F

be the force acting on a particle, having position vector r,

be the torque of this force about

the origin, then



27

(a) r . 0 and F . 0

(b) r . 0 and F . 0

(c) r . 0 and F . 0

(d) r . 0 and F . 0

Sol: (d)

τ r F

τ . r r F . r 0

τ . F r F . F 0

88. A soap film is slowly blown under isothermal conditions in air at NTP to a radius R. How much work

is done ? Surface tension of film is T.

(a) 24 R T (b) 28 R T (c) 218 R T (d) zero

Sol : (b)

Work done = 2×(24 R )×T =

28 R T

89. Two spherical soap bubbles of radii r1 and r2 in vaccum coaslesce under isothermal conditions. The

resulting bubble has radius R such that

(a) 1 2r rR

2 (b) 2 2

1 2R r r (c) 1 2r rR

2 (d) 1 2

1 2

r rR

r r

Sol: (b)

1 1 2 2p V p V pV

3 3 31 2

1 2

4 4T 4 4T 4 4Tπr . πr . πR .

3 F 3 r 3 R

2 21 2R r r

90. Water flows in a streamline manner through a capillary tube of radius ‘a’. The pressure difference is

p and rate of flow is Q. If the radius is reduced to 'a '

2 and the pressure is increased to 2p, then the

rate of flow becomes

(a) 4Q (b) Q (c) Q

2 (d)

Q

8 Sol : (d)

4

4

aπ 2p

πpa 2Q , Q'

8ηl 8ηl

Q' 1 QDividing Q'

Q 8 8

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