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Identify the wrong statement in context of heartwood
(1) Organic compounds are deposited in it
(2) It is highly durable
(3) It conducts water and minerals efficiently
(4) It comprises dead elements with highly lignified walls

Alexander Von Humboldt described for the first time
(1) Ecological Biodiversity
(2) Laws of limiting factor
(3) Species area relationships
(4) Population Growth equation

Which of the following is made up of dead cells?
(1) Xylem Parenchyma
(2) Collenchyma
(3) Phellem
(4) Phloem

The vascular cambium normally gives rise to
(1) Phelloderm
(2) Primary phloem
(3) Secondary xylem
(4) Periderm

In the case of poriferans, the spongocoel is lined with flagellated cells called
(1) Ostia
(2) Oscula
(3) Choanocytes
(4) Mesenchymal cells

Which among these is the correct combination of aquatic mammals?
(1) Seals, Dolphins, Sharks
(2) Dolphins, Seals, Trygon
(3) Whales, Dolphins, Seals
(4) Trygon, Whales, Seals

Which of the following represents the order of 'Horse'?
(1) Equidae
(2) Perissodactyla
(3) Caballus
(4) Ferus

Select the correct route for the passage of sperms in frogs:
(1) Testes $\to$Bidder's canal$\to$Kidney$\to$Vasa efferentias$\to$Urinogenital duct$\to$Cloaca
(2) Testes$\to$Vasa efferentia$\to$Kidney$\to$Seminal Vesicle$\to$Urinogenital duct$\to$Cloaca
(3) Teste$\to$Vasa efferentia$\to$Bidder's canal$\to$Ureter$\to$Cloaca
(4) Teste$\to$Vasa efferentia$\to$Kidney$\to$Bidder's canal$\to$Urinogenital duct$\to$Cloaca

Which one of the following is related to the Ex-situ conservation of threatened animals and plants?
(1) Wildlife Safari parks
(2) Biodiversity hot spots
(3) Amazon rainforest
(4) Himalayan region

An important characteristic that Hemichordates share with Chordates is 
(1) Absence of notochord
(2) The ventral tubular nerve cord
(3) Pharynx with gill slits
(4) Pharynx without gill slits

The region of Biosphere Reserve which is legally protected and where no human activity is allowed is known as:
(1) Core zone
(2) Buffer zone
(3) Transition zone
(4) Restoration zone

Viroids differ from viruses in having:
(1) DNA molecules with a protein coat
(2) DNA molecules without a protein coat
(3) RNA molecules with a protein coat
(4) RNA molecules without a protein coat

Which of the following are found in extreme saline conditions?
(1) Archaebacteria
(2) Eubacteria
(3) Cyanobacteria
(4) Mycobacteria

Mycorrhizae are the example of:
(1) Fungistasis
(2) Amensalism
(3) Antibiosis
(4) Mutualism

An example of colonial alga is 
(1) Chlorella
(2) Volvox
(3) Ulothrix
(4) Spirogyra

Spliceosomes are not found in cells of:
(1) Plants
(2) Fungi
(3) Animals
(4) Bacteria

Life cycle of Ectocarpus and Fucus respectively are
(1) Haplontic, Diplontic
(2) Diplontic, Haplodiplontic
(3) Haplodiplontic, Diplontic
(4) Haplodiplontic, Haplontic

Which among the following are the smallest living cells, known without a definite cell wall, pathogenic to plants as well as animals and can survive without oxygen?
(1) Bacillus
(2) Pseudomonas
(3) Mycoplasma
(4) Nostoc

DNA replication in bacteria occurs
(1) During s-phase
(2) Within nucleolus
(3) Prior to fission
(4) Just before transcription

Which of the following is not polymeric?
(1) Nucleic acids
(2) proteins
(3) Polysaccharides
(4) Lipids

Which one of the following statements is correct, with reference to enzymes?
(1) Apoenzyme = Holoenzyme + Coenzyme
(2) Holoenzyme = Apoenzyme + Coenzyme
(3) Coenzyme = Apoenzyme + Holoenzyme
(4) Holoenzyme = Coenzyme + Co-factor

A gene whose expression helps to identify transformed cell is known as
(1) Selectable marker
(2) Vector
(3) Plasmid
(4) Structural gene

The association of histone H1 with a nucleosome indicates:
(1) Transcription is occurring
(2) DNA replication is occurring
(3) The DNA is condensed into a Chromatin Fibre
(4) The DNA double helix is exposed

The DNA fragments separated on an agarose gel can be visualized after staining with:
(1) Bromophenol blue
(2) Acetocarmine
(3) Aniline blue
(4) Ethidium bromide

What is the criterion for DNA fragments movement on agarose gel electrophoresis?
(1) The larger the fragment size, the farther it moves
(2) The smaller the fragment size, the farther it moves
(3) Positively charged fragments move to the farther end
(4) Negatively charged fragments do not move

DNA fragments are
(1) Positively charged
(2) Negatively charged
(3) Neutral 
(4) Either positively or negatively charged depending on their size

The process of separation and purification of expressed protein before marketing is called
(1) upstream processing
(2) Downstream processing
(3) Bioprocessing
(4) Postproduction processing

The hepatic portal vein drains blood to the liver from
(1) Heart 
(2) Stomach
(3) Kidney
(4) Intestine

Adult human RBCs are enucleate. Which of the following statement(s) is /are most appropriate explanation for this feature?
(i) They do not need to reproduce
(ii) They are somatic cells
(iii) They do not metabolize
(iv) All their internal space is available for oxygen transport
(1) Only (iv)
(2) Only (i)
(3) (i), (iii) and (iv)
(4) (ii) and (iii)

MALT constitutes about ________ percent of the lymphoid tissue in human body
(1) 50%
(2) 20%
(3) 70%
(4) 10%

Lungs are made up of air-filled sacs the alveoli. They do not collapse even after forceful expiration, because of:
(1) Residual Volume
(2) Inspiratory Reserve Volume
(3) Tidal volume
(4) Expiratory Reserve Volume

Attractants and rewards are required for:
(1) Anemophily
(2) Entomophily
(3) Hydrophily
(4) Cleistogamy

Which of the following cell organelles is responsible for extracting energy from carbohydrates to form ATP?
(1) Lysosome
(2) Ribosome
(3) Chloroplast
(4) Mitochondrion

Which of the following components provides sticky character to the bacterial cell?
(1) Cell wall
(2) Nuclear membrane
(3) Plasma membrane
(4) Glycocalyx

Which of the following options given the correct sequence of events during mitosis?
(1) condensation$\to$nuclear membrane disassembly $\to$crossing over$\to$segregation$\to$telophase
(2) condensation$\to$nuclear membrane disassembly arrangement at equator$\to$centromere division$\to$segregation$\to$telophase
(3) condensation$\to$crossing over$\to$nuclear membrane disassembly$\to$segregation$\to$telophase
(4) condensation$\to$arrangement at equator$\to$centromere division $\to$segregation$\to$telophase

Zygotic meiosis is characteristic of 
(1) Marchantia
(2) Fucus
(3) Funaria
(4) Chlamydomonas

Anaphase promoting complex(APC) is a protein degradation machinery necessary for proper mitosis of animal cells. If APC is defective in a human cell, which of the following is expected to occur?
(1) Chromosomes will not condense
(2) Chromosomes will be fragmented
(3) Chromosomes will not segregate
(4) Recombination of chromosome arms will occur

A decrease in blood pressure / volume will not cause the release of 
(1) Renin
(2) Atrial Natriuretic Factor
(3) Aldosterone
(4) ADH

GnRH, a hypothalamic hormone, needed in reproduction, acts on
(1) The anterior pituitary gland and stimulates the secretion of LH and oxytocin
(2) Anterior pituitary gland and stimulates secretion of LH and FSH
(3) posterior pituitary gland and stimulates secretion of oxytocin and FSH
(4) Posterior pituitary gland and stimulates secretion of LH and relaxin

Hypersecretion of Growth hormone in adults does not cause further increase in height, because
(1) Growth Hormone becomes inactive in adults
(2) Epiphyseal plates close after adolescence
(3) Bones loose their sensitivity to Growth Hormone in adults
(4) Muscle fibres do not grow in size after birth

A temporary endocrine gland in the human body is
(1) Pineal gland
(2) Corpus cardiacum
(3) Corpus luteum
(4) Corpus allatum

Good vision depends on adequate intake of carotene rich food 
Select the best option from the following statements
(i) Vitamin A derivatives are formed from carotene
(ii) The photopigments are embedded in the membrane discs of the inner segment
(iii) Retinal is a derivative of vitamin A
(iv) Retinal is a light absorbing part of all the visual photopigments
(1) (i) and (ii)
(2) (i), (iii) and (iv)
(3) (i) and (iii)
(4) (ii), (iii) and (iv)

Which cells of 'Crypts of lieberkuhn' secrete antibacterial lysozyme?
(1) Argentaffin cells
(2) Paneth cells
(3) Zymogen cells
(4) Kupffer cells

A baby boy aged two years is admitted to play school and passes through a dental check-up. The dentist observed that the boy had twenty teeth. Which teeth were absent?
(1) Incisors
(2) Canines
(3) Pre-molars
(4) Molars

Which of the following options best represents the enzyme composition of pancreatic juice?
(1) Amylase, peptidase, trypsinogen, rennin
(2) Amylase, pepsin, trypsinogen, maltase
(3) Peptidase, amylase, pepsin, rennin
(4) Lipase, amylase, trypsinogen, procarboxypeptidase

Which ecosystem has the maximum biomass?
1. Forest ecosystem
2. Grassland ecosystem
3. Pond ecosystem
4. Lake ecosystem

Presence of plants arranged into well- defined vertical layers depending on their height can be seen best in:
1. Tropical Savannah
2. Tropical Rain Forest
3. Grassland
4. Temperate Forest

Which of the following in sewage treatment removes suspended solids?
1. Tertiary treatment
2. Secondary treatment
3. Primary treatment
4. Sludge treatment

Which one the following statement is not valid for aerosols?
1. They are harmful to human health
2. They alter rainfall and monsoon patterns
3. They cause increased agricultural productivity
4. They have negative impact on agricultural land

Which of the following statement is correct?
1. The ascending limb of loop of Henle is impermeable to water
2. The descending  limb of loop of Henle is impermeable to water
3. The ascending limb of loop of Henle is permeable to water
4. the descending limb of loop of Henle is immpermeable to electrolytes

Transplantation of tissues/organs fails often due to non-acceptance by the patient's body. Which type of immune-response is responsible for such rejections?
1. Autoimmune response
2. Cell-mediated immune response
3. Hormonal immune response
4. Physiological immune response

Root hairs develop from the region of 
1. Maturation
2. Elongation
3. Root cap
4. Meristematic activity

Which of the following facilitates the opening of the stomatal aperture?
1. Contraction of the outer wall of guard cells
2. Decrease in turgidity in guard cells
3. Radial orientation of cellulose microfibrils in the cell wall of guard cells
4. Longitudinal orientation of cellulose microfibrils in the cell wall of guard cells

Capacitation occurs in
1. Rete testis 
2. Epidymysis
3. Vas deferens
4. Female reproductive tract

The net filtration pressure is the interaction of the hydrostatic and osmotic pressures, driving fluid out of the capillary and is:
1. about equal to the pulse pressure at 40 mmHg
2. favored by colloid osmotic pressure of the plasma
3. opposed by the hydrostatic pressure in afferent arteriole
4. estimated to be approximately 10 mmHg in human kidneys

Out of 'X' pairs of ribs in humans only 'Y' pairs are true ribs. Select the option that correctly represents values of X and Y and provides their explanation

Which of the following is correctly matched for the product produced by them?
1. Acetobacter aceti: Antibiotics
2. Methanobacterium: Lactic acid
3. Penicillium notatum: Acetic acid
4. Scchaeomyces cerevisiae: Ethanol

If there are 999 bases in an RNA that codes for a protein with 333 amino acids. and the bases at position 901 is deleted such that the length of the RNA becomes 998 bases . how many codons will altered?
1. 1
2. 11
3. 33
4. 333

The final proof for DNA as the genetic came from the experiment of
1. Griffith
2. Hershey and Chase
3. Avery, Mcleod and McCarty
4. Hargobinf Khorana

Which of the following RNAs should be most abundant in animal cell?
1. r-RNA
2. t-RNA
3. m-RNA
4. mi-RNA

During DNA replication, Okazaki fragments are used to enlongate
1. The leading strand towards replication fork
2. The lagging strand towards replication fork 
3. The leading strand away from replication fork
4. The lagging strand away from the replication fork

In Bougainvillea thorns are the modification of 
1. Stipules
2. Adventitious root
3. Stem
4. Leaf

The morphological nature of the edible part of coconut is 
1. Perisperm
2. Cotyledon
3. Endosperm
4. Pericarp

Functional megaspore is an angiosperm develops into:
1. Ovule
2. Endosperm
3. Embryo Sac
4. Embryo

Coconut fruit is a 
1. Drupe
2. Berry
3. Nut
4. Capsule

Frog's heart when taken out of the body continues to beat for sometime
Select the best option from the following statements
i. Frog is a poikilothermic
ii. Frog does not have any coronary circulation
iii. Heart is "myogenic" in nature
iv. Heart is autoexcitable 
1. Only iii
2. Only iv
3. i and ii
4. iii and iv

Myelin sheath is produced by
1. Schwann cells and Oligodendrocytes
2. Astrocytes and Schwann cells
3. Oligodendrocytes and Osteoclasts
4. Osteoclasts and Astrocytes

Receptor sites for neurotransmitters  are present on 
1. Membranes of synaptic vesicles
2. Pre-synaptic membrane
3. Tips and axons
4. Post-synaptic membrane

Asymptote in a logistic growth curve in obtained when 
1. The value of 'r' approaches zero
2. K=N
3. K>N
4. K<N

Phosphoenolpyruvate (PEP) is the primary${\mathrm{CO}}_2$ acceptor in:
1. ${\mathrm{C}}_{3 }\mathrm{plants}$
2. ${\mathrm{C}}_4 \mathrm{plants}$
3. ${\mathrm{C}}_2 \mathrm{plants}$
4. ${\mathrm{C}}_3 \mathrm{and} {\mathrm{C}}_4 \mathrm{plants}$

Which statement is wrong for Krebs' Cycle?
1. There are three points in the cycle where ${\mathrm{NAD}}^{+}$ is reduced to NADH+$H^{+}$
2. There is one point on the cycle where ${\mathrm{FAD}}^{+}$ is reduced to ${\mathrm{FADH}}_2$
3. During conversion of succinyl CoA to succinic acid, a molecule to GTP is synthesised 
4. The cycle starts with condensation of acetyl group (acetyl CoA) with pyruvic acid to yield citric acid 

With reference to factors affecting the rate of photosynthesis, which of the following statements is not correct?

Fruit and leaf drop at early stages can be prevented by the application of 
1. Cytokinins 
2. Ethylene
3. Auxins
4. Gibberellic acids 

Select the mismatch :
1. Pinus-Dioecious
2. Cycas - Dioecious 
3. Salvinia - Heterosporus
4. Equisetum - Homosporous

Plants which produce characteristics pneumatophores and show vivipary belong to 
1. Mesophytes
2. Halophytes
3. Psammophytes
4. Hydrophytes

Select the mismatch:
1. Frankia - Alnus
2. Rhodospirillum - Mychorriza
3. Anabaena - Nitrogen fixer
4. Rhizobium - Alfalfa

A disease caused by an autosomal primary non-disjunction is
1. Down's syndrome
2. Klinefelter's syndrome
3. Turner's syndrome
4. Sickle cell anemia

Thalassemia and sickle cell anemia are caused due to a problem in globin molecule synthesis. Select the correct statement
1. Both are due to a qualitative defect in globin chain synthesis
2. Both are due to quantative defect in globin chain synthesis
3. Thalamessia is due to less synthesis of globin molecules
4. Sickle cell anemia is due to a quantative problem of globin molecules

Which one from those given below is the period for Mendel's hybridization experiments?
1. 1856-1863
2. 1840-1850
3. 1857-1869
4. 1870-1877

The genotypes of a Husband and Wife are ${\mathrm{I}}^{\mathrm{A}}{\mathrm{I}}^{\mathrm{B}} \mathrm{and} {\mathrm{I}}^{\mathrm{A}}\mathrm{i}$. Among the blood types of their children, how many different genotypes and phenotypes are possible?
1. 3 genotypes : 3 phenotypes
2. 3 genotypes : 4 phenotypes
3. 4 genotypes : 3 phenotypes
4. 4 genotypes : 4 phenotypes

Among the following characters, which one was not considered by Mendel in his experiments on pea?
1. Stem - Tall or Dwarf
2. Trichomes - Glandular or non-Glandular
3. Seed - Green or Yellow
4. Pod - Inflated or Constricted

Match the following sexually transmitted diseases (Cloumn - I) with their causative agent (Column - II) and select the correct option.

1. a-ii, b-iii, c-iv, d-i
2. a-iii, b-iv, c-i, d-ii
3. a-iv, b-ii, c-iii, d-i
4. a-iv, b-iii, c-ii, d-i

The function of copper ions in copper releasing IUD's is:
1. They suppress sperm motility and fertilizing capacity of sperms
2. They inhibit gametogenesis
3. They make uterus unsuitable for implantation
4. They inhibit ovulation

In case of a couple where the male is having a very low sperm count, which technique will be suitable for fertilisation?
1. Intrauterine transfer
2. Gamete intracytoplasmic fallopian transfer
3. Artificial insemination
4. Intracytoplasmic sperm injection

A dioecious flowering plants prevent both:
1. Autogamy and xenogamy
2. Autogamy and geitonogamy
3. Geitonogamy and xenogamy
4. Cleistogamy and xenogamy

Flowers which have single ovule in the ovary and are packed into inflorescence are usually pollinated by
1. Water
2. Bee
3. Wind 
4. Bat

Double fertilization is exhibited by:
1. Gymnosperms
2. Algae
3. Fungi
4. Angiosperms

Homozygous purelines in cattle can obtained by:
1. mating of related individuals of same breed
2. mation of unrelated individuals of same breed
3. mating of individual of different breed
4. mating of individuals of different species
 

Artificial selection to obtain cows yielding higher milk output represents
1. Stabilizing selection as it stabilizes this character in the population
2. Directional as it pushes the mean of the character in one direction
3. Disruptive as it splits the population into two one yielding higher output and the other lower output
4. Stabilizing followed by disruptive as it stabilizes the population to produce higher yielding cows
 

The water potential of pure water is
1. Zero
2. Less than zero
3. More than zero but less than one
4. More than one

In BrF₃ molecule, the lone pairs occupy equatorial positions to minimize:

KO₂ is used in oxygen cylinder in space air craft and submarines because it:
1. absorbs CO₂ and increase O₂ content
2. eliminate moisture
3. absorbs CO₂
4. produces O₂

The heating of phenyl-methyl ethers with HI producers.
(1) Ethyl chlorides
(2) Iodobenzene
(3) Phenol
(4) Benzene

Identify A and predict the type of reaction

(1) 
  and elimination addition
(2)
and cine substitution reaction
(3)
 and cine substitution reaction
(4) 
and substitution reaction
 

Which of the following reaction is appropriate for converting acetamide to methanamine?
(1) Carbylamine reaction
(2) Hoffmann hypobromamide reaction
(3) Stephens reaction
(4) Gabriels phthalimide synthesis

Predict the correct intermediate and product in the following reaction
$H_{3}C-C\equiv CH\underset{HgS{O}_4}{\overset{H_{2}O, H_{2}S{O}_4}{\to }}intermdiate\to Product$
$\left(A\right) \left(B\right)$
1. 
2. 
3. 
4. 
 
 
 

Which among the following depicts the correct order of acidity?
(1) $C{H}_2=C{H}_2>C{H}_3-CH=C{H}_2>C{H}_3-C\equiv CH>CH\equiv CH$
(2) $CH\equiv CH>C{H}_3-C\equiv CH>C{H}_2=C{H}_2>C{H}_3-C{H}_3$
(3) $CH\equiv CH>C{H}_2=C{H}_2>C{H}_3-C\equiv CH>C{H}_3-C{H}_3$
(4) $C{H}_3-C{H}_3>C{H}_2=C{H}_2>C{H}_3-C\equiv CH>CH\equiv CH$

An example of a sigma bonded organometallic compound is:
(1) Ruthenocene
(2) Grignard's reagent
(3) Ferrocene
(4) Cobaltocene

Consider the reactions:

Identify  A, X, Y and Z
1. 
2. 
3. 
4. 

The correct increasing order of basic strength for the following compounds is:

(1) II < III < I
(2) III < I < II
(3) III < II < I
(4) II < I < III

Which of the following statements is not correct?
(1) Insulin maintains sugar level in the blood of a human body
(2) Ovalbumin is a simple food reserve in egg-white
(3) Blood proteins thrombin and fibrinogen are involved in blood clotting
(4) Denaturation makes the proteins more active

Of the following, which is the product formed when cyclohexanone undergoes aldol condensation followed by heating?
(1) 

(2)

(3)

(4)

The species, having bond angles of $120°$ is
(1) $P{H}_3$
(2) $Cl{F}_3$
(3) $NC{l}_3$
(4) $BC{l}_3$

Which one of the following pairs of species have to same bond order?
(1) CO, NO
(2) $O_2, N{O}^{+}$
(3) $C{N}^{-}, CO$
(4) $N_2, {O_2}^{-}$

Match the interhalogen compounds of column I with the geometry in column II and assign the correct code.

(1) a (iii), b (iv), c (i), d (ii)
(2) a (iii), b (i), c (iv), d (ii)
(3) a (v), b (iv), c (iii), d (ii)
(4) a (iv), b (iii), c (ii), d (i)

A first order reaction has a specific reaction rate ${10}^{-2} se{c}^{-1}$. How much time will it take for 20 g the reactant to reduce to 5 g?
(1) 238.6 second
(2) 138.6 second
(3) 346.5 second
(4) 693.0 second

The equilibrium constants of the following are:
$N_2+3H_2\rightleftharpoons 2N{H}_3 K_1$
$N_2+O_2\rightleftharpoons 2NO K_2$
$H_2+\frac{1}{2}{O}_2\to H_{2}O K_3$
The equilibrium constant (K) of the reaction:
$K$
$2 N{H}_3+\frac{5}{2}{O}_2\rightleftharpoons 2NO+3H_{2}O, will be$
1. $\frac{K_1{K}_3^2}{K_2}$
2. $\frac{K_2{K}_3^3}{K_1}$
3. $\frac{K_2{K}_3^{}}{K_1}$
4. $\frac{K_2^3{K}_3^{}}{K_1}$

Mechanism of a hypothetical reaction $X_2+Y_2\to 2XY$ is given below:
(i) $X_2\to X+X\left(fast\right)$
(ii) $X+Y_2\rightleftharpoons XY+Y\left(slow\right)$
(iii) $X+Y\to XY\left(fast\right)$
The overall order of the reaction will be:
(1) 1
(2) 2
(3) 0
(4) 1.5

A gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 atm from an initial volume of 2.50 L to a final volume of 4.50 L. The change in internal energy $∆U$ of the gas in joules will be:
(1) 1136.25 J
(2) - 500 J
(3)  - 505 J
(4)  + 505 J

For a given reaction, $∆H=35.5 kJ mo{l}^{-1} and ∆S=83.6 J{K}^{-1}mo{l}^{-1}$. The reaction is spontaneous at: (Assume that $∆H and ∆S$ do not vary with temperature)
(1) T > 275 K
(2) T > 425 K
(3) All temperature
(4) T > 298 K

Mixture of chloroxylenol and terpineol acts as
(1) Analgestic
(2) Antiseptic
(3) Antipyretic
(4) Antibiotic

The IUPAC name of the compound

(1) 3-keto-2-methylhex-4-enal
(2) 5-formylhex-2-en-3-one
(3) 5-methyl-4-oxohex-2-en-5-al
(4) 3-keto-2-methylhex-5-enal

Which of the following is dependent on temperature?
(1) Molality
(2) Molarity
(3) Mole fraction
(4) Weight percentage

The element Z = 114 has been discovered recently. It will belong to which of the following family / group and electronic configuration?
(1) Halogen family, [Rn] $5f^{14}6d^{10}7s^{2}7p^5$
(2) Carbon family, [Rn] $5f^{14}6d^{10}7s^{2}7p^2$
(3) Oxygen family, [Rn] $5f^{14}6d^{10}7s^{2}7p^4$
(4) Nitrogen family, [Rn] $5f^{14}6d^{10}7s^{2}7p^6$

Correct increasing order for the wavelengths of absorption in the visible region for the complexes of $C{o}^{3+}$ is:
1. ${\left[Co{\left(en\right)}_3\right]}^{3+}, {\left[Co{\left(N{H}_3\right)}_6\right]}^{3+},{\left[Co{\left(H_{2}O\right)}_6\right]}^{3+}$
2. ${\left[Co{\left(H_{2}O\right)}_6\right]}^{3+}, {\left[Co{\left(en\right)}_3\right]}^{3+},{ \left[Co{\left(N{H}_3\right)}_6\right]}^{3+}$
3. ${\left[Co{\left(H_{2}O\right)}_6\right]}^{3+}, {\left[Co{\left(N{H}_3\right)}_6\right]}^{3+},{ \left[Co{\left(en\right)}_3\right]}^{3+}$
4. ${\left[Co{\left(N{H}_3\right)}_6\right]}^{3+}, {\left[Co{\left(en\right)}_3\right]}^{3+},{ \left[Co{\left(H_{2}O\right)}_6\right]}^{3+}$

Pick out the correct statement with respect to ${\left[Mn{\left(CN\right)}_6\right]}^{3-}$:
(1) It is $s{p}^3{d}^2$ hybridised and octahedral
(2) It is $s{p}^3{d}^2$ hybridised and tetrahedral
(3) It is $d^{2}s{p}^3$ hybridised and octahedral
(4) It is $ds{p}^2$ hybridised and square planar

The correct order of the stoichiometries of AgCl formed when $AgN{O}_3$ in excess is treated with the complexes: $CoC{l}_3.6N{H}_3, CoC{l}_3.5N{H}_3, CoC{l}_3.4N{H}_3$ respectively is:
(1) 1 AgCl, 3 AgCl, 2 AgCl
(2) 3 AgCl, 1 AgCl, 2 AgCl
(3) 3 AgCl, 2 AgCl, 1 AgCl
(4) 2 AgCl, 3 AgCl, 1 AgCl

It is because of inability of $n{s}^2$ electrons of the valence shell to participate in bonding that:
(1) $S{n}^{2+}$ is reducing while $P{b}^{4+}$ is oxidizing
(2) $S{n}^{2+}$ is oxidizing while $P{b}^{4+}$ is reducing
(3) $S{n}^{2+}$ and $P{b}^{2+}$ are both oxidizing and reducing
(4) $n^{4+}$ is reducing while $P{b}^{4+}$ is oxidizing

The reason for greater range of oxidation states in actinoids is attributed to:
(1) The radioactive nature of actinoids
(2) Actinoid contraction
(3) 5f, 6d and 7s levels having comparable energies
(4) 4f and 5d levels being close in energies

In the electrochemical cell:
$Zn\left|ZnS{O}_4(0.01 M)\right|\left|CuS{O}_4(1.0 M)\right|Cu,$ the emf of this Daniel cell is $E_1$. When the concentration $ZnS{O}_4$ is changed to 1.0 M and that of CuSO changed to 0.01 M, the emf changes to $E_2$. From the following, which one is the relationship between $E_1 and E_2$? (Given, $\frac{RT}{F}$ = 0.059)
(1) $E_1=E_2$
(2) $E_1<E_2$
(3) $E_1>E_2$
(4) $E_2=0\ne E_1$

The correct statement regarding electrophile is
(1) Electrophile is a negatively charged species and can form a bond by accepting a pair of electrons from a nucleophile
(2) Electrophile is a negatively charged species and can form a bond by accepting a pair of electrons from another electrophile
(3) Electrophiles are generally neutral species and can form a bond by accepting a pair of electrons from a nucleophile
(4) Electrophile can be either neutral or positively charged species and can form a  bond by accepting a pair of electrons from a nucleophile

With respect to the conformers of ethane, which of the following statements is true?
(1) Bond angle remains same but bond length changes
(2) Bond angle changes but bond length remains same
(3) Both bond angle and bond length change
(4) Both bond angles and bond length remains same

Extraction of gold and silver involves leaching with $C{N}^{-}$ ion. Silver is later recovered by:
(1) Liquation
(2) Distillation
(3) Zone refining
(4) Displacement with Zn

Which one is the most acidic compound?
(1)

(2)

(3)

(4)

The most suitable method of separation of 1 : 1 mixture of ortho and para-nitrophenols is:
(1) Sublimation
(2) Chromatography
(3) Crystallization
(4) Steam distillation

Concentration of the $A{g}^{+}$ ions in a saturated solution of $A{g}_2{C}_2{O}_4 is 2.2\times {10}^{-4} mol L^{-1}$. Solubility product of $A{g}_2{C}_2{O}_4$ is:
(1) $2.42\times {10}^{-8}$
(2) $2.66\times {10}^{-12}$
(3) $4.5\times {10}^{-11}$
(4) $5.3\times {10}^{-12}$

Which one of the following statements is not correct?
(1) Catalyst does not initiate any reaction
(2) The value of the equilibrium constant is changed in the presence of a catalyst in the reaction at equilibrium
(3) Enzymes catalyze mainly biochemical reactions
(4) Coenzymes increase the catalytic activity of enzyme

Which of the following is a sink for CO?
(1) Haemoglobin
(2) Micro-organisms present in the soil
(3) Oceans
(4) Plants

In which pair of ions both the species contain S-S bond?
(1) $S_2{O}_7^{2-}, S_2{O}_3^{2-}$
(2) $S_4{O}_6^{2-}, S_2{O}_3^{2-}$
(3) $S_2{O}_7^{2-}, S_2{O}_8^{2-}$
(4) $S_4{O}_6^{2-}, S_2{O}_7^{2-}$

$HgC{l}_2 and I_2$ both when dissolved in water containing $I^{-}$ ions the pair of species formed is:
(1) $Hg{I}_2, {I_3}^{-}$
(2) $Hg{I_4}^{2-}, I^{-}$
(3) $Hg{I_4}^{2-}, {I_3}^{-}$
(4) $H{g}_2{I}_2, I^{-}$

Name the gas that can readily decolourise acidifine $KMN{O}_4$ solution.
(1) $C{O}_2$
(2) $S{O}_2$
(3) $N{O}_2$
(4) $P_2{O}_5$

A 20 litre container at 400 K contains $C{O}_2\left(g\right)$ at pressure 0.4 atm and an excess of SrO (neglect the volume of solide SrO). The volume of the container is now decreased by moving the movable piston fitted in the container. The maximum volume of the container, when pressure of $C{O}_2$ attains its maximum value, will be:
(Given that: $SrC{O}_3\left(s\right)\rightleftharpoons SrO\left(s\right)+C{O}_2\left(g\right), K_P=1.6 atm)$
(1) 5 litre
(2) 10 litre
(3) 4 litre
(4) 2 litre

Which one is the wrong statement?
(1) de-Broglie's wavelength is given by $\lambda =\frac{h}{mv}$ , where m = mass of the particle, $\nu$ = group velocity of the particle
(2) The uncertainty principle is $∆E\times ∆t\ge \frac{h}{4\pi }$
(3) Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement
(4) The energy of 2s orbitals is less than the energy of 2p orbital in case of Hydrogen like atoms

Ionic mobility of which of the following alkali metal ions is lowest when aqueous solution of their salt are put under an electric field?
(1) Na
(2) K
(3) Rb
(4) Li

Which is the incorrect statement?
(1) $Fe{O}_{0.98}$ has non stoichiometric metal deficiency defect
(2) Density decreases in case of crystals with schottky's  defect
(3) NaCl(s) is insulator, silicon is semiconductor, silver is conductor, quartz is piezo electric crystal
(4) Frenkel defect is favoured in those ionic compounds in which sizes of cation and anions are almost equal

The de-broglie wavelength of a neutron in thermal equilibirum with heavy water at a temperature T (kelvin) and mass m, is :
1. $\frac{\mathrm{h}}{\sqrt{\mathrm{mkT}}}$
2. $\frac{\mathrm{h}}{\sqrt{3\mathrm{mkT}}}$
3. $\frac{2\mathrm{h}}{\sqrt{3\mathrm{mkT}}}$
4. $\frac{2\mathrm{h}}{\sqrt{\mathrm{mkT}}}$

The photoelectric threshold wavelength of silver is $3250\times {10}^{-10} \mathrm{m}$. The velocity of the electron ejected from a silver surface by the ultraviolet light of wavelength 25.3 $\stackrel{\mathrm{o}}{\mathrm{A}}$ is : 
$\left(\mathrm{Given} \mathrm{h}=4.14\times {10}^{-15} \mathrm{eV} \mathrm{and} \mathrm{c}=3\times {10}^8 {\mathrm{ms}}^{-1}\right)$
1. $\approx 60\times {10}^5 {\mathrm{ms}}^{-1}$
2. $\approx 0.6\times {10}^6 {\mathrm{ms}}^{-1}$
3. $\approx 61\times {10}^3 {\mathrm{ms}}^{-1}$
4. $\approx 0.3\times {10}^6 {\mathrm{ms}}^{-1}$

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is 
1. 2
2. 1
3. 4
4. 0.5

One end of string length l is connected to a particle of mass 'm' and the other end is connected to small peg on a smooth horizontal table. If the particle moves speed 'v', the net force on the particle (directed towards center) will be (T represents the tension in the string)
1. T
2. $\mathrm{T}+\frac{{\mathrm{mv}}^2}{\mathrm{l}}$
3. $\mathrm{T}=\frac{{\mathrm{mv}}^2}{\mathrm{l}}$
4. zero

The resistance of a wire 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be 
1. nR
2. $\frac{\mathrm{R}}{\mathrm{n}}$
3. ${\mathrm{n}}^2\mathrm{R}$
4. $\frac{\mathrm{R}}{{\mathrm{n}}^2}$ 

A potentiometer is an accurate and versatile device to make electrical measurements of E.M.F, because the method involves :
1. Cells
2. Potential gradients
3. A condition of no current flow through the galvanometer
4. A combination of cells, galvanometer and resistances

Figure shows a circuit three identical resistors with Resistance R = 9.0 $\mathrm{\Omega }$ each, two identical inductors with inductance L = 2.0 mH, and an ideal battery $\mathrm{\epsilon }=18 \mathrm{V}$. The current 'i' through the battery just after the switch closes is 

1. 2 mA
2. 0.2 A
3. 2 A
4. 0 ampere

In an electromagnetic wave in free space the root mean square value of the electric field is ${\mathrm{E}}_{\mathrm{rms}}=6\mathrm{V}/\mathrm{m}$. The peak value of the magnetic field is 
1. $1.41\times {10}^{-8} \mathrm{T}$
2. $2.83\times {10}^{-8} \mathrm{T}$
3. $0.70\times {10}^{-8} \mathrm{T}$
4. $4.23\times {10}^{-8} \mathrm{T}$

The diagrams below show regions of equipotentials

A positive charge is moved from A to B in each diagram 
1. Maximum work is required to move q in figure (c)
2. In all the four cases the work done is the same
3. Minimum work is required to move q in figure (a)
4. Maximum work is required to move q in figure (b)

A capacitor is charged by battery . The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system 
1. Increases by a factor of 4
2. Decreases by a factor of 2
3. Remains the same
4. Increases by a factor of 2

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will :
1. keep floating at the same distance between them
2. Move towards each other
3. Move away from each other
4. Will become stationary

The acceleration due to gravity at a height 1 km above the earth is the same as at depth of d below the surface of earth. Then 
1. $\mathrm{d}=\frac{1}{2} \mathrm{km}$
2. d = 1 km 
3. $\mathrm{d}=\frac{3}{2} \mathrm{km}$
4. d = 2 km

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are ${\mathrm{K}}_1 \mathrm{and} {\mathrm{K}}_2$. The thermal conductivity of the composite rod will be 

1. $\frac{{\mathrm{K}}_1+{\mathrm{K}}_2}{2}$
2. $\frac{3\left({\mathrm{K}}_1+{\mathrm{K}}_2\right)}{2}$
3. ${\mathrm{K}}_1+{\mathrm{K}}_2$
4. $2\left({\mathrm{K}}_1+{\mathrm{K}}_2\right)$

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be 
1. 225
2. 450
3. 1000
4. 1800

Thermodynamic processes are indicated in the following diagram 

Match the following 

1. P$\to$a, Q$\to$c, R$\to$d, S$\to$b
2. P$\to$c, Q$\to$a, R$\to$d, S$\to$b
3. P$\to$c, Q$\to$d, R$\to$b, S$\to$a
4. P$\to$d, Q$\to$b, R$\to$a, S$\to$c

A gas mixture consists of 2 moles of ${\mathrm{O}}_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is 
1. 4 RT
2. 15 RT
3. 9 RT
4. 11 RT

A carnot engine having an efficiency of $\frac{1}{10}$ as heat engine is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is 
1. 1 J
2. 90 J
3. 99 J
4. 100 J

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction is shown in figure. Magnitude of force per unit length on the middle wire 'B' is given by 

1. $\frac{{\mathrm{\mu }}_0{\mathrm{I}}^2}{2\mathrm{\pi d}}$
2. $\frac{2{\mathrm{\mu }}_0{\mathrm{I}}^2}{\mathrm{\pi d}}$
3. $\frac{\sqrt{2}{\mathrm{\mu }}_0{\mathrm{I}}^2}{\mathrm{\pi d}}$
4. $\frac{{\mathrm{\mu }}_0{\mathrm{I}}^2}{\sqrt{2}\mathrm{\pi d}}$

A 250 turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $\mathrm{\mu A}$ and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180$°$ against the torque is :
1. 9.1 $\mathrm{\mu J}$
2. 4.55 $\mathrm{\mu J}$
3. 2.3 $\mathrm{\mu J}$
4. 1.15 $\mathrm{\mu J}$

A long solenoid of diameter 0.1 m has $2\times {10}^4$ turns per meter. At the centre of the solenoid , a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is $10{\mathrm{\pi }}^2\mathrm{\Omega }$, the total charge flowing through the coil during this time is 
1. 32 $\mathrm{\pi } \mathrm{\mu C}$
2. 16 $\mathrm{\mu C}$
3. 32 $\mathrm{\mu C}$
4. 16 $\mathrm{\pi } \mathrm{\mu C}$

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time ${\mathrm{t}}_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time ${\mathrm{t}}_2$. The time taken by her to walk up on the moving escalator will be 
1. $\frac{{\mathrm{t}}_1+{\mathrm{t}}_2}{2}$
2. $\frac{{\mathrm{t}}_1{\mathrm{t}}_2}{{\mathrm{t}}_2-{\mathrm{t}}_1}$
3. $\frac{{\mathrm{t}}_1{\mathrm{t}}_2}{{\mathrm{t}}_2+{\mathrm{t}}_1}$
4. $t_1-t_2$

Consider a drop of rain water having mass 1 g falling from a height of 1 Km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 $\mathrm{m}/{\mathrm{s}}^2$. The work done by the (i) gravitational force and the (ii) resistive force of air is 
1. (i) -10 J (ii) -8.25 J
2. (i) 1.25 J (ii) -8.25 J
3. (i) 100 J (ii) 8.75 J
4. (i) 10 J (ii) -8.75 J

The x and y coordinates of the particle at any time are $\mathrm{x}=5\mathrm{t}-2{\mathrm{t}}^2$ and y = 10 t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2 s is
1. 0
2. 5 $\mathrm{m}/{\mathrm{s}}^2$
3. -4 $\mathrm{m}/{\mathrm{s}}^2$
4. -8 $\mathrm{m}/{\mathrm{s}}^2$

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively 

1. $\mathrm{g},\frac{\mathrm{g}}{3}$
2. $\frac{\mathrm{g}}{3},g$
3. g,g
4. $\frac{\mathrm{g}}{3},\frac{\mathrm{g}}{3}$

Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is $\left(\mathrm{e}+∆\mathrm{e}\right)$. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size ) apart is zero, then $∆\mathrm{e}$ is the order of [Given mass of hydrogen ${\mathrm{m}}_{\mathrm{b}}=1.67\times {10}^{-27} \mathrm{kg}$]
1. ${10}^{-20}$ C
2. ${10}^{-23}$ C
3. ${10}^{-37}$C
4. ${10}^{-47}$C
 

Radioactive material 'A' has decay constant $\text{'}8\mathrm{\lambda }\text{'}$ and material 'B' has decay constant $\text{'}\mathrm{\lambda }\text{'}$. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'A' to that 'B' will be $\frac{1}{e}$ ?
1. $\frac{1}{\mathrm{\lambda }}$
2. $\frac{1}{7\mathrm{\lambda }}$
3. $\frac{1}{8\mathrm{\lambda }}$
4. $\frac{1}{9\mathrm{\lambda }}$

A spring of force constant k is cut into lengths of ratio 1:2:3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k':k'' is 
1. 1:6
2. 1:9
3. 1:11
4. 1:14

A particle executes linear simple harmonic motion with an amplitude of 3 cm, When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is 
1. $\frac{\sqrt{5}}{\mathrm{\pi }}$
2. $\frac{\sqrt{5}}{2\mathrm{\pi }}$
3. $\frac{4\mathrm{\pi }}{\sqrt{5}}$
4. $\frac{2\mathrm{\pi }}{\sqrt{3}}$

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decreases in radius is 
1. $\frac{\mathrm{p}}{\mathrm{B}}$
2. $\frac{\mathrm{B}}{3\mathrm{p}}$
3. $\frac{3\mathrm{p}}{\mathrm{B}}$
4. $\frac{\mathrm{p}}{3\mathrm{B}}$

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is 

1. 650 $\mathrm{kg} {\mathrm{m}}^{-3}$
2. 425 $\mathrm{kg} {\mathrm{m}}^{-3}$
3. 800 $\mathrm{kg} {\mathrm{m}}^{-3}$
4. 928 $\mathrm{kg} {\mathrm{m}}^{-3}$

If ${\mathrm{\theta }}_1$ and ${\mathrm{\theta }}_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\mathrm{\theta }$ is given by 
1. ${\cot }^2\mathrm{\theta }={\cot }^2{\mathrm{\theta }}_1+{\cot }^2{\mathrm{\theta }}_2$
2. ${\tan }^2\theta ={\tan }^2{\theta }_{\mathit{1}}\mathit{+}{\tan }^{\mathit{2}}{\theta }_{\mathit{2}}$
3. ${\cot }^2\mathrm{\theta }={\cot }^2{\mathrm{\theta }}_1-{\cot }^2{\mathrm{\theta }}_2$
4. ${\tan }^2\theta ={\tan }^2{\theta }_{\mathit{1}}\mathit{-}{\tan }^{\mathit{2}}{\theta }_{\mathit{2}}$

The ratio of resolving powers of an optical microscope for two wavelengths ${\mathrm{\lambda }}_1=4000 \stackrel{\mathrm{o}}{\mathrm{A}}$ and ${\mathrm{\lambda }}_2=6000 \stackrel{\mathrm{o}}{\mathrm{A}}$ is 
1. 8:27
2. 9:4
3. 3:2
4. 16:81

A thin prism having refracting angle $10°$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be 
1. 4$°$
2. 6$°$
3. 8$°$
4. 10$°$

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $\mathrm{\theta }$, the spot of the light is found to move through a distance y on the scale. The angle $\mathrm{\theta }$ is given by 
1. $\frac{\mathrm{y}}{2\mathrm{x}}$
2. $\frac{\mathrm{y}}{\mathrm{x}}$
3. $\frac{\mathrm{x}}{2\mathrm{y}}$
4. $\frac{\mathrm{x}}{\mathrm{y}}$

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ?
1. 25 $\mathrm{m}/{\mathrm{s}}^2$
2. 0.25 $\mathrm{rad}/{\mathrm{s}}^2$
3. 25 $\mathrm{rad}/{\mathrm{s}}^2$
4. 5 $\mathrm{m}/{\mathrm{s}}^2$

Which of the following statements are correct ?
(i) Centre of mass of a body always coincides with the centre of gravity of the body
(ii) Centre of mass of a body is the point at which the total gravitational torque on the body is zero
(iii) A couple on a body produce both translational and rotational motion in a body
(iv) Mechanical advantage greater than one means that small effort can be used to a lift a large load
1. (ii) and (iv)
2. (i) and (ii)
3. (ii) and (iii)
4. (iii) and (iv)

In a common emitter transistor amplifier the audio signal voltage across the collector is 3V. The resistance of collector is 3 $\mathrm{k\Omega }$. If current gain is 100 and the base resistance is  2 $\mathrm{k\Omega }$, the voltage and power gain of the amplifier is 
1. 200 and 1000
2. 15 and 200
3. 150 and 15000
4. 20 and 2000

The given electrical network is equivalent to 

1. AND gate
2. OR gate
3. NOR gate
4. NOT gate

Which one of the following represents forward bias diode ?
1. 
2. 
3. 
4. 

A physical quantity of the dimensions of length that can be formed out of c,G and $\frac{{\mathrm{e}}^2}{4{\mathrm{\pi \epsilon }}_0}$ is [ c is velocity, G is universal constant of gravitation and e is the charge ] :
1. $\frac{1}{c^2}{\left[G\frac{{\mathrm{e}}^2}{4{\mathrm{\pi \epsilon }}_0}\right]}^{1/2}$
2. $c^2{\left[G\frac{{\mathrm{e}}^2}{4{\mathrm{\pi \epsilon }}_0}\right]}^{1/2}$
3. $\frac{1}{c^2}{\left[\frac{{\mathrm{e}}^2}{\mathrm{G}4{\mathrm{\pi \epsilon }}_0}\right]}^{1/2}$
4. $\frac{1}{c}G\frac{{\mathrm{e}}^2}{4{\mathrm{\pi \epsilon }}_0}$

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8^th bright fringe in the medium lies where 5^th dark fringe lies in air. The refractive index of the medium is nearly
1. 1.25
2. 1.59
3. 1.69
4. 1.78

Two cars moving in opposite directions approach each other  with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [ velocity of sound 340 m/s]
1. 250 Hz
2. 361 Hz
3. 411 Hz
4. 448 Hz

Two polaroids ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are placed with their axis perpendicular to each other. Unpolarised light ${\mathrm{I}}_0$ is incident on ${\mathrm{P}}_1$. A third polarised ${\mathrm{P}}_3$ is kept in between ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ such that its axis makes an angle 45$°$ with that of ${\mathrm{P}}_1$. The intensity of transmitted light through ${\mathrm{P}}_2$ is 
1. $\frac{{\mathrm{I}}_0}{2}$
2. $\frac{{\mathrm{I}}_0}{4}$
3. $\frac{{\mathrm{I}}_0}{8}$
4. $\frac{{\mathrm{I}}_0}{16}$

The two nearest harmonics of a tube closed at one end and open at other end are 220 hz and 260 Hz. What is the fundamental frequency of the system ?
1. 10 Hz
2. 20 Hz
3. 30 Hz
4. 40 Hz

Two discs of same amount of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ${\mathrm{\omega }}_1 \mathrm{and} {\mathrm{\omega }}_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is 
1. $\frac{1}{2}I{\left({\omega }_1+{\omega }_2\right)}^2$
2. $\frac{1}{4}I{\left({\omega }_1\mathit{-}{\omega }_2\right)}^2$
3. $I{\left({\omega }_1\mathit{-}{\omega }_2\right)}^2$
4. $\frac{1}{8}I{\left({\omega }_1\mathit{-}{\omega }_2\right)}^2$