1. Which of the following blood cells have smallest diameter?
Red blood cells
Thrombocytes
Neutrophils
Lymphocytes
(b) Thrombocytes (platelets) are the smallest blood cells in diameter, ranging from 2-3 µm.
2. Trachoma is a disease of
Conjunctiva
Sclera
Iris
Lens
(a) Trachoma is an infectious disease that affects the conjunctiva, the membrane lining the eyelids and covering the white part of the eye.
3. Iron is absorbed from
Duodenum
Jejunum
Ileum
Ascending colon
(a) The majority of iron absorption occurs in the duodenum and the upper part of the jejunum.
4. Definite diagnosis of a cancer can be made by
Endoscopy
CT scan
Histopathology
Ultrasonography
(c) Histopathology, which involves examining tissue samples under a microscope, provides the most definite diagnosis of cancer.
5. Polymerase chain reaction is
A technique of forming copies of DNA
An asexual method of multiplication of microorganism
Cascade of chemical reactions within a cell
Process of synthesizing fibres in a textile factory
(a) Polymerase chain reaction (PCR) is a laboratory technique used to amplify single or a few copies of a piece of DNA across several orders of magnitude, generating thousands to millions of copies of a particular DNA sequence.
6. Vital capacity refers to the
Pulmonary function test
Capacity of vital centers of the brain
Power of leg muscles
Pumping power of the heart
(a) Vital capacity (VC) is a pulmonary function test that measures the total amount of air a person can exhale after a maximal inhalation. It represents the maximum amount of usable air.
7. Vitamins are needed in our body for their
[Coenzymes assist enzymes in turning substrates into products. They can be used by multiple types of enzymes and change forms. Specifically, coenzymes function by activating enzymes, or acting as carriers of electrons or molecular groups. Vitamins are a source of coenzymes]
Caloric value
Catalytic activity
Co-enzyme activity
Immunological (defense) action
(c) Vitamins are essential organic compounds that often function as co-enzymes or precursors of co-enzymes, assisting enzymes in metabolic reactions.
8. The full form of "LASER" ….. Stimulated Emission of Radiation:
Light amplified
Lately adsorbed
Locally active
Light altered
(a) The full form of LASER is Light Amplification by Stimulated Emission of Radiation.
9. The cranial nerve responsible for the sensation from the tongue are
Vagus and Facial
Hypoglossal and Vagus
Glossopharyngeal and Facial
Trigeminal and Vagus
(c) The sense of taste from the tongue is primarily carried by the Facial nerve (anterior two-thirds) and the Glossopharyngeal nerve (posterior one-third). General sensation from the tongue is carried by the Trigeminal nerve.
10. Palpitation that may be felt while facing the interview is primarily due to the activation of
Central nervous system
Peripheral nervous system
Sympathetic nervous system
Para-sympathetic nervous system
(c) Palpitation and other physiological responses to stress, like during an interview, are primarily due to the activation of the sympathetic nervous system, which prepares the body for 'fight or flight'.
11. Linear acceleration and cobalt machine equipments are treating patients are likely to be found in
[Cobalt-60 machine, Linear acceleration machine]
Tuberculosis centre
Hospital for tropical medicine
Cancer ♋ hospital
Mental hospital
(c) Cobalt-60 machines and linear accelerators are radiation therapy equipment used for cancer treatment and are therefore found in cancer hospitals.
12. Ovary is the female gonad that secretes
Glucocorticoid and mineralocorticoids
Oestrogen and Progesterone
Follicle stimulating hormone
Luitenizing hormone
(b) The ovaries are the primary female gonads and their main function is to produce eggs (ova) and secrete the female sex hormones, oestrogen and progesterone.
13. Muscle 💪 spasms may occur in the deficiency of
Thyroxine
Parathyroid hormone
Testosterone
Vasopressin
(b) Muscle spasms can occur due to hypocalcemia (low blood calcium levels), which can be a result of parathyroid hormone deficiency.
14. Neurohypophysis is
Anterior pituitary
Posterior pituitary
Intermediate pituitary
Lateral pituitary
(b) Neurohypophysis is another name for the posterior pituitary gland.
15. Prolonged use of alcohol in excess leads to
Eye disease
Lung disease
Liver disease
Kidney disease
(c) Chronic and excessive alcohol consumption can cause significant damage to the liver, leading to various liver diseases like cirrhosis and fatty liver.
16. Obese person is prone to develop the following disease Except
Diabetes
Heart attack
High blood pressure
Low blood pressure
(d) Obesity is a major risk factor for developing diabetes, heart attack, and high blood pressure. It is not typically associated with low blood pressure; in fact, it is more often linked to hypertension.
17. Which of the following is called cardiac glycosides?
[Digitalin obtained from Digitalis purpurea is known as Cardiac glycosides as it stimulates the Heart tone and Cardiac rhythm.]
Digitalin
Belladona
Reserpine
Colchicum
(a) Digitalin, obtained from the foxglove plant (Digitalis purpurea), is a cardiac glycoside used to increase the strength of heart contractions.
18. The following are muscles that take part in respiration EXCEPT:
Diaphragm
Intercostal muscle
Trapezius
sternocleidomastoid
(c) The diaphragm and intercostal muscles are primary muscles involved in breathing. The sternocleidomastoid is an accessory muscle of respiration, primarily used during forced breathing. The trapezius muscle is mainly involved in moving and stabilizing the shoulder blade (scapula) and extending the head at the neck.
19. The following arteries arise from the arch of the aorta except:
Lt. subclavian artery
Innominate artery
Rt. Subclavin artery
Lt. common carotid artery
(c) The arch of the aorta gives rise to three main arteries: the brachiocephalic trunk (innominate artery) which then branches into the right subclavian artery and right common carotid artery, the left common carotid artery, and the left subclavian artery. The option 'Rt. Subclavin artery' is likely a typo and meant to be 'Rt. Subclavian artery', which does arise from the innominate artery, so it's not the exception.
20. The thoracic duct drains:
Arterial blood
Venous blood
Both venous and arterial blood
Lymph
(d) The thoracic duct is the largest lymphatic vessel in the body and it drains lymph from most of the body into the bloodstream.
21. Which of the following vein carries oxygenated blood?
Hepatic vein
Pulmonary vein
Renal vein
Portal vein
(b) The pulmonary veins carry oxygenated blood from the lungs back to the left atrium of the heart.
22. The kidney develops from
Ectoderm
Endoderm
Mesoderm
Neuroectoderm
(c) The kidneys develop from the intermediate mesoderm.
23. Commonest site of elephantiasis in Bancroftian filariasis is:
Vulva
Leg
Scrotum
Arms
(b) In Bancroftian filariasis, the commonest site of elephantiasis (lymphatic filariasis) is the leg, due to the parasitic worms obstructing lymphatic vessels.
24. The wood of gymnosperms exclusively consists of:
Tracheids
Tracheae
Wood fibres
Wood parenchyma
(a) The xylem in gymnosperms lacks vessels (tracheae) and wood fibres; it mainly consists of tracheids for water conduction and mechanical support.
25. Usnea is a:
Crustose lichen
Fructicose lichen
Foliose lichen
Fungi
(b) Usnea is a genus of fruticose lichens, characterized by their shrub-like or pendant branching structures.
26. Which one shows the floral characters of Solanaceae:
⊕⚤K_(5) ⏞(C_(5) A_5 ) G _(2)
⊕<0xE2><0x99><0x90>K_(5) C_(5) A_5 G _(2)
Ebr ⊕⚤K_(5) [C_(5) ] A_(5) G _((2))
⊕⚤P_(5) A_(3+3) G _((3))
(a) The floral formula ⊕⚤K_(5) ⏞(C_(5) A_5 ) G _(2) (or sometimes written as ⊕⚤K_(5) [C_(5)] A_(5) G _((2))) correctly represents the floral characteristics of the Solanaceae family: actinomorphic (⊕), bisexual (⚤), calyx with 5 fused sepals (K_(5)), corolla with 5 fused petals (C_(5)), androecium with 5 epipetalous stamens (A_5), and gynoecium superior with 2 fused carpels (G _((2))).
27. The vascular bundle having phloem in the centre and surrounded by xylem is termed as
Amphicribal
Amphivasal
Radial
Collateral
(b) A vascular bundle with phloem in the center and xylem surrounding it is called amphivasal (also known as leptocentric).
28. Primary endosperm nucleus is usually
Haploid
Diploid
Triploid
Pentaploid
(c) The primary endosperm nucleus (PEN) in angiosperms is formed by the fusion of one male gamete with the central cell, which contains two polar nuclei (each haploid). Thus, the PEN is typically triploid (3n).
29. When the ovule is straight or erect (so that the funicle, chalaza and micropyle) lie on one and the same verticle line), the form is called
Orthotropous
Anatropous
Amphitropous
Campylotrophous
(a) An orthotropous ovule is upright with the micropyle, chalaza, and funiculus arranged in a straight vertical line.
30. Which hormone is primarily concerned with cell division in plants?
IAA
Gibberelin
ABA
Cytokinin
(d) Cytokinins are plant hormones that primarily promote cell division (cytokinesis) and differentiation.
31. The mutation theory of evolution was proposed by
Darwin
Lamarck
Hugo de Vries
Hutchingson
(c) The mutation theory of evolution was proposed by Hugo de Vries, who suggested that new species arise suddenly from pre-existing ones through large mutations.
32. Which of the following is a biological sequence?
Consumer - Producer - Consumer
Producer - Consumer - Reducer
Producer - Consumer - Consumer
Reducer - Producer - Consumer
(b) A typical biological sequence in a food chain or food web starts with a producer (an organism that produces its own food, like a plant), followed by a consumer (an organism that feeds on other organisms), and finally, decomposers or reducers (organisms that break down dead organic matter).
33. The two daughter cells produced at the end of meiosis when compared to the parent diploid cells will have
[During Mitosis: Same amount of DNA and same no. of chromosome as those of parent cells, At the end of meiosis-I: Same amount of DNA and half number of chromosome.]
Same amount of DNA and same number of chromosomes
Same amount of DNA and half number of chromosomes
Half amount of DNA and half number of chromosomes
Half amount of DNA and same number of chromosomes
(c) Meiosis is a reductional division that results in four haploid daughter cells from a diploid parent cell. Each daughter cell has half the number of chromosomes and half the amount of DNA compared to the parent cell (at the G1 phase).
34. Carpels of Angiosperms are equivalent to
Sporophyll
Sporangia
Spores
Zygospores
(a) Carpels are megasporophylls, which are specialized leaves that bear megasporangia (ovules).
35. Which of the following monocotyledon family consists of distichous sheathing with a distinct ligule in the leaves?
Musaceae
Zinigiberceae
Cannaceae
Morantaceae
(d) Morantaceae (Arrowgrass family) in monocots typically exhibits distichous (two-ranked) sheathing leaves with a distinct ligule.
36. During anaerobic respiration yeast converts glucose into
Ethanol and CO2
Lactic acid and CO2
Pyruvic acid and CO2
Ethanol and water
(a) During anaerobic respiration (fermentation), yeast converts glucose into ethanol (alcohol) and carbon dioxide (CO2).
37. A thin membrane that envelops the structure of chromosome is known as
Matrix
Pellicle
Chromonemata
Chromomere
(b) A thin membrane that envelops the structure of a chromosome is known as the pellicle (though the existence of a distinct pellicle is debated and the term is not in common modern use).
38. Protozoan class that does not carry its name after locomotory organ is
Flagella
Rhizopoda
Sporozoa
Ciliata
(c) The class Sporozoa (now known as Apicomplexa) does not have a primary locomotory organ in its mature stage. Its members are typically parasitic and form spores. Flagella, Rhizopoda (using pseudopods), and Ciliata use flagella, pseudopods, and cilia, respectively, for locomotion.
39. Tapeworm using pig as an intermediate host is
Taenia solium
Taenia saginata
Hymenolepsis nana
Wuchereria bancrofti
(a) Taenia solium (pork tapeworm) uses pigs as its primary intermediate host.
40. Pharyngeal nephridia in earthworm are present in
3rd, 4th and 5th segments
4th, 5th and 6th segments
5th, 6th and 7th segments
Behind the 15th segments
(b) In earthworms, tufts of pharyngeal nephridia are typically found in segments 4th, 5th, and 6th.
41. Dentition in frog is
Homodont
Heterodont
Thecodont
Biodont
(a) Frogs have homodont dentition, meaning their teeth are all similar in shape and size.
42. The hind brain of frog 🐸 consists of
Optic lobe
Medulla oblongata and cerebellum
Optic lobes and medulla oblongata
Diencephalon and medulla oblongata
(b) The hindbrain of a frog consists of the medulla oblongata and the cerebellum.
43. The part of ear that distinguish different pitches is the
Organ of Corti
Tympanic membrane
Semi-circular canals
Auditory nerve
(a) The organ of Corti, located within the cochlea of the inner ear, contains hair cells that vibrate at different frequencies in response to sound waves, allowing us to distinguish different pitches.
44. Which one is a parasite and also a vector?
Plasmodium
Flea
Housefly
Silkworm
(a) Plasmodium, the parasite that causes malaria, is transmitted to humans by the bite of infected female Anopheles mosquitoes, making the mosquito a vector. Plasmodium itself is a parasite.
45. The eggs of cockroach is
Isolecithal
Telolecithal
Microlecithal
Centrolecithal
(b) Cockroach eggs are telolecithal, meaning they have a large amount of yolk concentrated at one pole (the vegetal pole).
46. The greek word from which the word 'ecological' is derived is
Oikos
Iokos
Ioku
Siokus
(a) The word 'ecology' is derived from the Greek word 'oikos', meaning 'house' or 'household'.
47. Which of the following is a living fossil?
Limulus
Ginkgo
Archaeopteryx
Peripatus
(a) Limulus (horseshoe crab) is considered a living fossil because it has remained relatively unchanged in morphology for millions of years and resembles fossils from the Paleozoic era.
48. Codon is contained in
[A series of codons in part of a messenger RNA (mRNA) molecule. Each codon consists of three nucleotides, usually corresponding to a single amino acid. The nucleotides are abbreviated with the letters A, U, G and C. This is mRNA, which uses U (uracil).]
DNA
tRNA
mRNA
rRNA
(c) A codon is a sequence of three nucleotides that forms a unit of genetic code in a messenger RNA (mRNA) molecule.
49. In a given atom no two electrons can have the same value of all the quantum numbers. This is called
Hund's rule
Aufbau principle
Uncertainty principle
Pauli's exclusive principle
(d) The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers.
50. Which of the following is the correct electons configuration of Fe3+ ion?
1s^2 2s^2 2p^6 3s^2 3p^6 3d^4 4s^1
1s^2 2s^2 2p^6 3s^2 3p^6 3d^3 4s^2
1s^2 2s^2 2p^6 3s^2 3p^6 3d^5
1s^2 2s^2 2p^6 3s^2 4s^2 4p^3
(c) The electron configuration of a neutral iron atom (Fe) with atomic number 26 is 1s2 2s2 2p6 3s2 3p6 3d6 4s2. When iron forms a 3+ ion (Fe3+), it loses three electrons. These electrons are removed from the outermost shells first. So, the two 4s electrons and one 3d electron are removed, resulting in the configuration 1s2 2s2 2p6 3s2 3p6 3d5.
51. The number of ions produced form a molecule of Potassium Ferricyanide in aqueous solution are
2
3
4
5
(c) Potassium ferricyanide has the formula K3[Fe(CN)6]. When dissolved in water, it dissociates into ions as follows: K3[Fe(CN)6] → 3K+ + [Fe(CN)6]3-. This produces a total of 3 potassium ions and 1 ferricyanide ion, making a total of 4 ions.
52. The equilibrium constant is expressed as either Kc or Kp. In which of the following reaction Kp and Kc will have the same numberical value.
N2+3H2 O⇌2NH3
PCl5⇌PCl3+Cl3
2SO2+O2⇌2SO3
N2+O2⇌2NO
(d) The relationship between Kp and Kc is given by Kp = Kc(RT)Δn, where Δn is the change in the number of moles of gaseous species (products - reactants). Kp and Kc have the same numerical value when Δn = 0. In the reaction N2(g) + O2(g) ⇌ 2NO(g), Δn = (2) - (1+1) = 0. Therefore, for this reaction, Kp = Kc.
53. The rate constant of a zero order reaction is k and the initial concentration is a, the half life of the reaction will be
1/ak
k/2
ak/2
a/2k
(d) For a zero-order reaction, the rate law is given by Rate = k[A]0 = k. The integrated rate law is [A]t = [A]0 - kt. The half-life (t1/2) is the time it takes for the concentration of the reactant to decrease to half of its initial value, i.e., [A]t = [A]0/2 = a/2. So, a/2 = a - kt1/2 => kt1/2 = a - a/2 = a/2 => t1/2 = a/2k.
54. Atomic hydrogen produces formaldehyde when it reacts with
Water
Carbon dioxide
Carbon monoxide
Formic acid
(c) Atomic hydrogen reacts with carbon monoxide to produce formaldehyde (HCHO).
55. Calgon, used as a water softener is
Na2 [Na4 (PO3 )6 ]
Na3 [Na3 (PO3 )6 ]
Na4 [Na2 (PO3 )6 ]
Na4 [Na2 (PO4 )6 ]
(c) Calgon is the trade name for sodium hexametaphosphate, which has the formula Na4[Na2(PO3)6]. It is used as a water softener by complexing with calcium and magnesium ions.
56. Purification of aluminium by electroytic process is known as
Hoope's process
Serpeck's process
Hall's process
Bayer's process
(a) Hoope's process is an electrolytic method used for the purification of aluminium.
57. When SO2 reacts with iron
Fe2 O3 is formed
FeS is formed
Fe is oxidised
Fe is reduced
(b) When sulfur dioxide (SO2) reacts with iron (Fe) at high temperatures, iron sulfide (FeS) and iron(III) oxide (Fe2O3) can be formed. However, under certain conditions, FeS is a likely product.
58. Which one of the following is the Mohr's salt?
CuSO4.5H2 O
(NH4 )2 SO4.FeSO4.6H2 O
Al2 (SO4 )3.K2 SO4.24H2 O
FeSO4.7H2 O
(b) Mohr's salt is a double salt with the chemical formula (NH4)2SO4.FeSO4.6H2O, also known as ammonium ferrous sulfate hexahydrate.
59. An alkyl halide can be converted to alcohol by
Addition
Eliminationo
Substitution
Dehydrogenation
(c) Alkyl halides undergo nucleophilic substitution reactions with aqueous hydroxide (OH-) ions to form alcohols.
60. An organic compound 'A' on treatment with silver nitrate followed by acid hydrolysis gave acetic acid. The compound 'A' is
C2 H5 OH
CH3 Cl
C2 H5 Cl
CH3 COCl
(d) Compound 'A' reacts with silver nitrate (AgNO3) followed by acid hydrolysis to give acetic acid (CH3COOH). This suggests that 'A' is likely an acid halide. Acetyl chloride (CH3COCl) reacts with AgNO3 to form silver chloride and acetyl nitrate, which upon hydrolysis yields acetic acid and nitric acid.
61. Identify Z in the following reactions: C2 H5 Cl (→Alcoh?l KOH)┬ X→(Br2 ) Y→(KCN Z
CH3 CH2 CN
CN−CH2 CH2−CN
BrCH2 CH2 CN
BrCH=CHCN
(a) The reaction sequence is as follows: Ethyl chloride (C2H5Cl) reacts with alcoholic KOH to undergo dehydrohalogenation, forming ethene (X: CH2=CH2). Ethene reacts with Br2 to undergo addition, forming 1,2-dibromoethane (Y: BrCH2CH2Br). 1,2-dibromoethane reacts with KCN (alcoholic) to undergo nucleophilic substitution, forming propanenitrile (Z: CH3CH2CN).
62. The r.m.s. velocity of gas molecules is given by:
√(3PV/M)
√(2RV/M)
√(2E/3)
√(PV/RT)
(a) The root mean square (r.m.s.) velocity of gas molecules is given by the formula vrms = √(3RT/M), where R is the ideal gas constant, T is the absolute temperature, and M is the molar mass. Using the ideal gas law, PV = RT for one mole of gas, so we can substitute RT with PV, giving vrms = √(3PV/M).
63. A circular disc of mass 'm' and radius 'r' is rotating about its axis with uniform speed of v. What is its kinetic energy?
mv2
1/2 mv2
1/4 mv2
1/8 mv2
(c) The kinetic energy of a rotating object is given by K.E. = (1/2)Iω2, where I is the moment of inertia and ω is the angular velocity. For a circular disc rotating about its axis, the moment of inertia is I = (1/2)mr2. The angular velocity ω is related to the linear velocity v by ω = v/r. Substituting these values, we get K.E. = (1/2) * (1/2)mr2 * (v/r)2 = (1/4)mr2 * (v2/r2) = (1/4)mv2.
64. The common mercury thermometer can be used to measure temperatures between….
-30 °C to 100 °C
0 °C to 200 °C
-30 °C to 200 °C
-30 °C to 357 °C
(d) A common mercury thermometer typically has a range from about -30 °C (the freezing point of mercury) to 357 °C (the boiling point of mercury).
65. A metallic bar is heated from 0 °C to 100 °C. The coefficient of linear expansion is 10-5 k-1. What will be the percentage increase in length?
0.01%
0.1%
1%
10%
(b) The change in length ΔL is given by ΔL = αL0ΔT, where α is the coefficient of linear expansion, L0 is the original length, and ΔT is the change in temperature. Percentage increase in length = (ΔL/L0) * 100 = (αL0ΔT / L0) * 100 = αΔT * 100. Given α = 10-5 K-1 and ΔT = 100 °C - 0 °C = 100 K. Percentage increase = (10-5 * 100) * 100 = 10-3 * 100 = 0.1%.
66. The velocity of sound in air at NTP is 300 m/s. If the pressure is increased to 4 times the atmospheric pressure, then the velocity of sound will be
150 ms-1
300 ms-1
600 ms-1
1200 ms-1
(b) The velocity of sound in an ideal gas is given by v = √(γP/ρ), where γ is the adiabatic index, P is the pressure, and ρ is the density. For an ideal gas at a constant temperature, if the pressure is increased n times, the density also increases n times (from the ideal gas law PV = nRT or P = ρRT/M). Therefore, the ratio P/ρ remains constant at a constant temperature. Thus, the velocity of sound in air is independent of pressure changes at constant temperature. So, the velocity will remain 300 ms-1.
67. A capacitor of capacitance 50 μF is charged to 10 volts. Its energy is equal to
2.5×10(−3) joules
2.5×104 joules
5×10(−2) joules
1.2×108 joules
(a) The energy stored in a capacitor is given by E = (1/2)CV2, where C is the capacitance and V is the voltage. Given C = 50 μF = 50 × 10-6 F and V = 10 volts. So, E = (1/2) * (50 × 10-6) * (10)2 = (1/2) * 50 × 10-6 * 100 = 25 × 10-6 * 100 = 25 × 10-4 = 2.5 × 10-3 joules.
68. A piece of wire of resistance 4 ohm is bent through 180 ° at the midpoint and the two halves are twisted together. Their resistance is
8 ohm
1 ohm
2 ohm
5 ohm
(b) A wire of resistance 4 ohm has two halves each with a resistance of 2 ohm when bent at the midpoint. When these two halves are twisted together, they form a parallel combination. The equivalent resistance of two resistors in parallel is given by 1/Req = 1/R1 + 1/R2. Here, R1 = 2 ohm and R2 = 2 ohm. So, 1/Req = 1/2 + 1/2 = 2/2 = 1. Therefore, Req = 1 ohm.
69. A man of 1 kg is suspended by a thread. It is lifted up with acceleration of 5 ms-2 and lowered down with an acceleration 5 ms-2, the ratio of the tension in the thread is:
1:2
2:1
3:1
3:2
(d) When lifted up with acceleration a, the tension Tup - mg = ma => Tup = m(g+a). When lowered down with acceleration a, mg - Tdown = ma => Tdown = m(g-a). Given m = 1 kg, a = 5 ms-2. Assuming g = 10 ms-2, Tup = 1(10+5) = 15 N. Tdown = 1(10-5) = 5 N. The ratio Tup/Tdown = 15/5 = 3/1. If we assume g = 9.8 ms-2, Tup = 1(9.8+5) = 14.8 N. Tdown = 1(9.8-5) = 4.8 N. The ratio Tup/Tdown = 14.8/4.8 ≈ 3.08/1 which is close to 3:1. There might be an error in the options provided if g=10 is assumed. Let's re-examine with option 3:2. If Tup = 3x and Tdown = 2x. 3x = 1(g+5), 2x = 1(g-5). Dividing, 3/2 = (g+5)/(g-5) => 3g - 15 = 2g + 10 => g = 25 ms-2 which is not realistic. Let me stick with 3:1 based on g=10. The option 3:1 is closest to my calculation with standard g value as well.
70. A body of mass 'm' is suspended from a string of length l. Minimum horizontal velocity that should be given to the body in its lowest position so that it may complete full revolution in vertical plane with the point of suspension as the centre of circle is
√2lg
√3lg
√4lg
√5lg
(d) For a body to complete a full vertical circle, the minimum velocity at the lowest point is given by v = √(5gl), where g is the acceleration due to gravity and l is the length of the string.
71. A body is projected with a velocity equal to twice the escape velocity from the earth. The velocity of the body in free space will be
Ve
1.5ve
√2 v_e
√3 v_e
(d) Let the escape velocity be ve. The projection velocity is v = 2ve. Using conservation of energy, the initial kinetic energy is (1/2)m(2ve)2 = 2mve2. The gravitational potential energy at the surface of the earth is -GMm/R. So, the total initial energy is Ei = 2mve2 - GMm/R. We know that escape velocity ve = √(2GM/R), so ve2 = 2GM/R or GMm/R = (1/2)mve2. Therefore, Ei = 2mve2 - (1/2)mve2 = (3/2)mve2. In free space, the potential energy will be zero. Let the velocity of the body in free space be v'. Then the final energy is Ef = (1/2)mv'2. By conservation of energy, Ei = Ef => (3/2)mve2 = (1/2)mv'2 => v'2 = 3ve2 => v' = √3 ve.
72. A boat 🛥 having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is
60 kg
72 kg
48 kg
90 kg
(a) The volume of water displaced by the boat when the man gets on it is equal to the volume of the submerged part due to the man's weight. The area of the bottom of the boat is A = length × breadth = 3m × 2m = 6 m2. The boat sinks by a height of h = 1 cm = 0.01 m. The volume of water displaced due to the man's weight is V = A × h = 6 m2 × 0.01 m = 0.06 m3. The mass of water displaced is equal to the mass of the man (Archimedes' principle). Mass of water = Volume × density of water = 0.06 m3 × 1000 kg/m3 = 60 kg. Therefore, the mass of the man is 60 kg.
73. A diver in water at a depth 1 m sees the whole outside world 🌎 horizontal circle of radius…… when the refractive index is μ.
1/(μ−1)
1/√(μ^2−1)
μ/√(μ^2−1)
1/μ
(b) The diver sees the outside world through a cone of light emerging from the water surface. The angle of this cone is the critical angle (C), where sin C = 1/μ. The radius (r) of the horizontal circle seen by the diver at a depth (h) is given by r = h tan C. We know sin C = 1/μ, so we can find tan C. Consider a right-angled triangle where the opposite side is 1 and the hypotenuse is μ. The adjacent side will be √(μ2 - 1). Therefore, tan C = opposite/adjacent = 1/√(μ2 - 1). Given the depth h = 1 m, the radius r = 1 * (1/√(μ2 - 1)) = 1/√(μ2 - 1).
