Given below are two statements:

Statement I : Sickle cell anaemia and haemophilia are autosomal dominant traits.

Statement II : Sickle cell anaemia and haemophilia are disorders of the blood.

In the light of the above statements, choose the correct answer from the options given below :

Which stage of meiosis can last for months or years in the oocytes of some vertebrates?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : When a particular restriction enzyme cuts strand of DNA, overhanging stretches or sticky ends are formed.

Reason (R) : Some restriction enzymes cut the strand of DNA a little away from the centre of palindromic site.

In the light of the above statements, choose the correct answer from the options given below :

Give the correct descending order of organisms with reference to their estimated number found in Amazon forest.

(a) Plants (b) Invertebrates (c) Fishes (d) Mammals (e) Birds

Choose the correct answer from the options given below :

In lac operon, z gene codes for

The 5-C compound formed during TCA cycle is

In meiosis, crossing over and exchange of genetic material between homologous chromosomes are catalyzed by the enzyme

All successions irrespective of the habitat proceed to which type of climax community?

When a carrier protein facilitates the movement of two molecules across the membrane in same direction, it is called

When one CO₂ molecule is fixed as one molecule of triose phosphate, which of the following photochemically made, high energy chemical intermediates are used in the reduction phase?

The ability of plants to follow different pathways in response to environment leading to formation of different kinds of structures is called

Match List-I with List-II :

Choose the correct answer from the options given below

Interfascicular cambium is present between

Which of the following growth regulators is an adenine derivative?

The chromosomal theory of inheritance was proposed by

Which of the following statement is not correct?

The Phenomenon by which the undividing parenchyma cells start to divide mitotically during plant tissue culture is called as

Match List-I with List-II

Choose the correct answer from the options given below

The residual persistent part which forms the perisperm in the seeds of beet is

The World Summit on sustainable development held in 2002 in Johannesburg, South Africa pledged for

The type of tissue commonly found in the fruit wall of nuts is :

The pioneer species in a hydrarch succession are

Given below are two statements

Statement I : DNA polymerases catalyse polymerisation only in one direction, that is 5' → 3'.

Statement II : During replication of DNA, on one strand the replication is continuous while on other strand it is discontinuous.

In the light of the above statements, choose the correct answer from the options given below:

The species that come to appear in bare area are called

Initiation of lateral roots and vascular cambium during secondary growth takes place in cells of

Match List - I with List - II.

Choose the correct answer from the options given below

To ensure that only the desired pollens fall on the stigma in artificial hybridization process

(a) the female flower buds of plant producing unisexual flowers need not be bagged.

(b) there is no need to emasculate unisexual flowers of selected female parent

(c) emasculated flowers are to be bagged immediately after cross pollination

(d) emasculated flowers are to be bagged after removal of anthers

(e) bisexual flowers, showing protogyny are never selected for cross

Choose the correct answer from the options given belows

Match List - I with List - II :

Choose the correct answer from the options given below

The number of time(s) decarboxylation of isocitrate occurs during single TCA cycle is

Match List-I with List-II

Choose the correct answer from the options given below.

Separation of DNA fragments is done by a technique known as

In general the egg apparatus of embryo sac in angiosperm consists of

The Floral Diagram represents which one of the following families?

Primary proteins are also called as polypeptides because :

Match List-I with List-II:

Choose the correct answer from the options given below:

Which type of substance would face difficulty to pass through the cell membrane?

What is the expected percentage of F₂ progeny with yellow and inflated pod in dihybrid cross experiment involving pea plants with green coloured, inflated pod and yellow coloured constricted pod?

Match List - I with List - II :

Choose the correct answer from the options given below:

If a female individual is with small round head, furrowed tongue, partially open mouth and broad palm with characteristic palm crease. Also the physical, psychomotor and mental development is retarded. The karyotype analysis of such an individual will show :

Read the following statements and identify the characters related to the alga shown in the diagram :

(a) It is a member of Chlorophyceae

(b) Food is stored in the form of starch

(c) It is monoecious plant showing oogonium and antheridium

(d) Food is stored in the form of laminarin or mannitol

(e) It shows dominance of pigments Chlorophyll a, c and Fucoxanthin

Choose the correct answer from the options given below :

Match the List-I with List-II :

Choose the correct answer from the options given below :

The enzyme (a) is needed for isolating genetic material from plant cells and enzyme (b) for isolating genetic material from fungus. Choose the correct pair of options from the following :

Identify the correct sequence of events during Prophase I of meiosis:

(a) Synapsis of homologous chromosomes

(b) Chromosomes become gradually visible under microscope

(c) Crossing over between non-sister chromatids of homologous chromosomes

(d) Terminalisation of chiasmata

(e) Dissolution of synaptonemal complex

Choose the correct answer from the options given below:

Which of the following pair represents free living nitrogen fixing aerobic bacteria?

Frugivorous birds are found in large numbers in tropical forests mainly because of :

Identify the correct statements regarding chemiosmotic hypothesis:

(a) Splitting of the water molecule takes place on the inner side of the membrane.

(b) Protons accumulate within the lumen of the thylakoids.

(c) Primary acceptor of electron transfers the electrons to an electron carrier.

(d) NADP reductase enzyme is located on the stroma side of the membrane.

(e) Protons increase in number in stroma.

Choose the correct answer from the options given below:

Match List-I with List-II :

Choose the correct answer from the options given below:

Which of the following animals has three chambered heart?

Which of the following types of epithelium is present in the bronchioles and Fallopian tubes?

Which of the following is not an Intra Uterine Device?

Match List-I with List-II

Choose the correct answer from the options given below :

Which of the following reasons is mainly responsible for graft rejection in transplantation of organs?

Bivalent or Tetrad formation is a characteristic feature observed during

Give below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): FSH which interacts with membrane bound receptors does not enter the target cell.

Reason (R): Binding of FSH to its receptors generates second messenger (cyclic AMP) for its biochemical and physiological responses.

In the light of the above statements, choose the most appropriate answer from the options given below

Choose the correct statement about a muscular tissue

Identify the region of human brain which has pneumotaxic centre that alters respiratory rate by reducing the duration of inspiration.

The amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis is called

Select the incorrect match regarding the symbols used in the Pedigree analysis:

If the pH in lysosomes is increased to alkaline, what will be the outcome?

According to the sliding filament theory:

Pathogenic bacteria gain resistance to antibiotics due to changes in their :

Panspermia, an idea that is still a favourite for some astronomers, means:

Why CNG is considered better fuel than diesel?

(a) It can not be adulterated.

(b) It takes less time to fill the fuel tank

(c) It burns more efficiently.

(d) It is cheaper.

(e) It is less inflammable.

Choose the most appropriate answer from the options given below :

Which of the following statements are correct with respect to vital capacity?

(a) It includes ERV, TV and IRV

(b) Total volume of air a person can inspire after a normal expiration.

(c) The maximum volume of air a person can breathe in after forced expiration.

(d) It includes ERV, RV and IRV.

(e) The maximum volume of air a person can breath out after a forced inspiration.

Choose the most appropriate answer from the options given below :

How many secondary spermatocytes are required to form 400 million spermatozoa?

Mad cow disease in cattle and Cr Jacob disease in humans are due to infection by ______.

Arrange the components of mammary gland. (from proximal to distal).

(a) Mammary duct

(b) Lactiferous duct

(c) Alveoli

(d) Mammary ampulla

(e) Mammary tubules

Choose the most appropriate answer from the options given below :

Western Ghats have a large number of plants and animal species that are not found anywhere else. Which of the following term is used to notify such species?

Match List-I with List-II regarding the organs of Cockroach:

Choose the correct answer from the options given below :

Two butterfly species are competing for the same nectar of a flower in a garden. To survive and coexist together, they may avoid competition in the same garden by :

Choose the incorrect enzymatic rection:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): During pregnancy the level of thyroxine is increased in the maternal blood.

Reason (R): Pregnancy is characterised by metabolic changes in the mother.

In the light of the above statements, choose the most appropriate answer from the options given below:

Choose the correct statements:

(a) Bones support and protect softer tissues and organs

(b) Weight bearing function is served by limb bones

(c) Ligament is the site of production of blood cells.

(d) Adipose tissue is specialised to store fats.

(e) Tendons attach one bone to another.

Choose the most appropriate answer from the options given below:

If DNA contained sulfur instead of phosphorus and proteins contained phosphorus instead of sulfur, what would have been the outcome of Hershey and Chase experiment?

Select the incorrect statements with respect to Cyclostomes:

(a) They lack scales and paired fins.

(b) They have circular mouth with jaws.

(c) They bear 6-15 pairs of gills.

(d) They migrate to deep sea for spawning.

Choose the most appropriate answer from the options given below:

A unique vascular connection between the digestive tract and liver is called______.

Milk of transgenic ‘Cow Rosie’ was nutritionally more balanced product for human babies than natural cow milk because it contained:

Gout is a type of disorder which leads to:

Which of the following methods is not commonly used for introducing foreign DNA into the plant cell?

Given below are two statements:

Statement I : Amino acids have a property of ionizable nature of $$-$$NH₂ and $$-$$COOH groups, hence have different structures at different pH.

Statement-II : Amino acids can exist as Zwitterionic form at acidic and basic pH.

In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Spirulina is a microbe that can be used for reducing environmental pollution.

Reason (R) : Spirulina is a rich source of protein, carbohydrates, fats, minerals and vitamins.

In the light of the above statements, choose the most appropriate answer from the options given below:

With respect to metaphase, which of the following statements is incorrect?

Against the codon 5' UAC 3', what would be the sequence of anticodon on tRNA?

Arrange the following formed elements in the decreasing order of their abundance in blood in humans:

(a) Platelets

(b) Neutrophils

(c) Erythrocytes

(d) Eosinophils

(e) Monocytes

Choose the most appropriate answer from the options given below:

Which of the following are true about the taxonomical aid 'key'?

(a) Keys are based on the similarities and dissimilarities.

(b) Key is analytical in nature.

(c) Keys are based on the contrasting characters in pair called couplet.

(d) Same key can be used for all taxonomic categories.

(e) Each statement in the key is called Lead.

Choose the most appropriate answer from the options given below:

A normal girl, whose mother is haemophilic marries a male with no ancestral history of haemophilia. What will be the possible phenotypes of the offspring?

(a) Haemophilic son and haemophilic daughter.

(b) Haemophilic son and carrier daughter.

(c) Normal daughter and normal son.

(d) Normal son and haemophilic daughter.

Choose the most appropriate answer from the options given below:

In the enzyme which catalyses the breakdown of:

H₂O₂ $$\to$$ H₂O + O₂

the prosthetic group is :

IUDs are small objects made up of plastic or copper that are inserted in the uterine cavity. Which of the following statements are correct about IUDs ?

(a) IUDs decrease phagocytosis of sperm within the uterus.

(b) The released copper ions suppress the sperm motility.

(c) IUDs do not make the cervix hostile to the sperm.

(d) IUDs suppress the fertilization capacity of sperm.

(e) The IUDs require surgical intervention for their insertion in the uterine cavity.

Choose the most appropriate answer from the options given below:

Select the correct statement regarding mutation theory of evolution.

Excretion in cockroach is performed by all, EXCEPT:

Select the correct statements.

(a) Angiotensin II activates the cortex of adrenal gland to release aldosterone.

(b) Aldosterone leads to increase in blood pressure.

(c) ANF acts as a check on renin-angiotensin mechanism.

(d) ADH causes vasodilation.

(e) Vasopressin is released from adenohypophysis.

Choose the most appropriate answer from the options given below :

If A and C make 30% and 20% of DNA, respectively, what will be the percentage composition of T and G?

Refer to the following statements for agarose-gel electrophoresis:

(a) Agarose is a natural polymer obtained from sea-weed.

(b) The separation of DNA molecules in agarose-gel electrophoresis depends on the size of DNA.

(c) The DNA migrates from negatively-charged electrode to the positively-charged electrode

(d) The DNA migrates from positively-charged electrode to the negatively-charged electrode.

Choose the most appropriate answer from the options given below :

Match List-I with List - II :

Choose the correct answer from the options given below :

Match List - I with List - II :

Choose the correct answer from the options given below :

Match List-I with List-II :

Choose the correct answer from the options given below :

The density of the solution is 2.15 g mL^$$-$$1, then mass of 2.5 mL solution in correct significant figures is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Chlorine is an electron withdrawing group but it is ortho, para directing in electrophilic aromatic substitution.

Reason (R) : Inductive effect of chlorine destabilises the intermediate carbocation formed during the electrophilic substitution, however due to the more pronounced resonance effect, the halogen stabilises the carbocation at ortho and para positioins.

In the light of the above statements, choose the most appropriate answer from the options given below :

Two half cell reactions are given below.

$$C{o^{3 + }} + {e^ - } \to C{o^{2 + }},\,\,\,\,\,\,\,\,\,E_{C{o^{2 + }}/C{o^{3 + }}}^0 = - 1.81\,V$$

$$2A{l^{3 + }} + 6{e^ - } \to 2Al(s),\,\,\,E_{Al/A{l^{3 + }}}^0 = + 1.66\,V$$

The standard EMF of a cell with feasible redox reaction will be :

Match List-I with List-II :

Choose the correct answer from the options given below :

The correct order of first ionization enthalpy for the given four elements is :

Predict the order of reactivity of the following four isomers towards S_N2 reaction.

(I) CH₃CH₂CH₂CH₂Cl

(II) CH₃CH₂CH(Cl)CH₃

(III) (CH₃)₂CHCH₂Cl

(IV) (CH₃)₃CCl

Match List-I with List-II :

Choose the correct answer from the options given below :

Which of the following reactions is a part of the large scale industrial preparation of nitric acid?

Na₂B₄O₇ $$\buildrel {heat} \over \longrightarrow $$ X + NaBO₂

in the above reaction the product "X" is :

One mole of an ideal gas at 300 K is expanded isothermally from 1 L to 10 L volume. $$\Delta$$U for this process is :

(Use R = 8.314 J k^$$-$$1 mol^$$-$$1)

Match List-I with List-II :

Choose the correct answer from the options given below :

0.01 M acetic acid solution is 1% ionised, then pH of this acetic acid solution is :

The half life of a first order reaction is 2000 years. If the concentration after 8000 years is 0.02 M, then the initial concentration was :

The product formed from the following reaction sequence is :

The decreasing order of boiling points of the following alkanes is :

(a) heptane

(b) butane

(c) 2-methylbutane

(d) 2-methylpropane

(e) hexane

Choose the correct answer from the options given below :

Decrease in size from left to right in actinoid series is greater and gradual than that in lanthanoid series due to

Which of the following reactions is not an example for nucleophilic addition-elimination reaction?

The product formed from the following reaction sequence is

Fluorine is a stronger oxidising agent than chlorine because :

(a) F-F bond has a low enthalpy of dissociation.

(b) Fluoride ion (F^$$-$$) has high hydration enthalpy.

(c) Electron gain enthalpy of fluorine is less negative than chlorine.

(d) Fluorine has a very small size.

Choose the most appropriate answer from the options given :

K_H value for some gases at the same temperature 'T' are given :

where K_H is Henry's Law constant in water. The order of their solubility in water is :

Which of the following reactions is a decomposition redox reaction?

What is the hybridization shown by C₁ and C₂ carbons, respectively in the given compound?

OHC $$-$$ CH = CH $$-$$ CH₂COOCH₃

Match the reagents (List-I) with the product (List-II) obtained from phenol.

Choose the correct answer from the options given below :

The correct order of bond angles in the following compounds/species is :

Match List-I with List-II :

Choose the correct answer from the options given below :

If first ionization enthalpies of elements X and Y are 419 kJ mol^$$-$$1 and 590 kJ mol^$$-$$1, respectively and second ionization enthalpies of X and Y are 3069 kJ mol^$$-$$1 and 1145 kJ mol^$$-$$1, respectively. Then correct statement is :

The incorrect statement about denaturation of proteins is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The metal carbon bond in metal carbonyls possesses both $$\sigma$$ and $$\pi$$ character.

Reason (R) : The ligand to metal bond is a $$\pi$$ bond and metal to ligand bond is a $$\sigma$$ bond.

In the light of the above statements, choose the most appropriate answer from the options given below.

Which of the following is the most stable carbocation?

Given below are two statements :

Statement I : Cr²⁺ is oxidising and Mn³⁺ is reducing in nature.

Statement II : Sc³⁺ compounds are repelled by the applied magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below :

K_p for the following reaction is 3.0 at 1000 K.

CO₂(g) + C(s) $$\rightleftharpoons$$ 2CO(g)

What will be the value of K_c for the reaction at the same temperature?

(Given : R = 0.083 L bar K^$$-$$1 mol^$$-$$1)

A vessel contains 3.2 g of dioxygen gas at STP (273.15 K and 1 atm pressure). The gas is now transferred to another vessel at constant temperature, where pressure becomes one third of the original pressure. The volume of new vessel in L is : (Given : molar volume at STP is 22.4 L)

Which one of the following reaction sequence is incorrect method to prepare phenol?

For a chemical reaction

4A + 3B $$\to$$ 6C + 9D

Rate of formation of C is 6 $$\times$$ 10^$$-$$2 mol L^$$-$$1 s^$$-$$1 and rate of disappearance of A is 4 $$\times$$ 10^$$-$$2 mol L^$$-$$1 s^$$-$$1. The rate of reaction and amount of B consumed in interval of 10 seconds, respectively will be :

Standard electrode potential for the cell with cell reaction

Zn(s) + Cu²⁺(aq) $$\to$$ Zn²⁺(aq) + Cu(s)

is 1.1 V. Calculate the standard Gibbs energy change for the cell reaction. (Given F = 96487 C mol^$$-$$1)

The products A and B in the following reaction sequence are :

The incorrect method for the synthesis of alkenes is

When electromagnetic radiation of wavelength 300 nm falls on the surface of a metal, electrons are emitted with the kinetic energy of 1.68 $$\times$$ 10⁵ J mol^$$-$$1. What is the minimum energy needed to remove an electron from the metal?

(h = 6.626 $$\times$$ 10^$$-$$34 Js, c = 3 $$\times$$ 10⁸ ms^$$-$$1, N_A = 6.022 $$\times$$ 10²³ mol^$$-$$1)

What fraction of Fe exists as Fe(III) in Fe_0.96O ?

(Consider Fe_0.96O to be made up of Fe(II) and Fe(III) only)

The incorrect method to synthesize benzaldehyde is

An energy of 484 J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. The moment of inertia of the flywheel is :

Let R₁ be the radius of the second stationary orbit and R₂ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $${{{R_1}} \over {{R_2}}}$$ is :

During a cloudy day, a primary and a secondary rainbow may be created, then the :

The reciprocal of resistance is :

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

Match List-I with List-II

	List-I (x-y graphs)		List-II (Situations)
(a)		(i)	Total mechanical energy is conserved
(b)		(ii)	Bob of a pendulum is oscillating under negligible air friction
(c)		(iii)	Restoring force of a spring
(d)		(iv)	Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below

The distance covered by a body of mass 5 g having linear momentum 0.3 kg m/s in 5 s is :

The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to

A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by the wire of the coil is 1 A, the value of magnetic field produced at the centre of the coil will be (permeability of free space $$ = 4\pi \times {10^{ - 7}}$$ H/m) nearly

The magnetic field of a plane electromagnetic wave is given by $$\overrightarrow B = 3 \times {10^{ - 8}}\cos (1.6 \times {10^3}x + 48 \times {10^{10}}t)\widehat j$$, then the associated electric field will be :

The restoring force of a spring with a block attached to the free end of the spring is represented by

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they continue moving in the same path, which the fire cracker would have followed, had it not exploded.

Reason (R) : Explosion of cracker (rocket) occurs due to internal force only and no external force acts for this explosion.

In the light of the above statements, choose the most appropriate answer from the option given below

A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30$$^\circ$$ above the horizontal. The maximum height attained by the ball during its motion is

(g = 10 m/s²)

Given below are two statements

Statement I : In an a.c circuit, the current through a capacitor leads the voltage across it.

Statement II : In a.c circuit containing pure capacitance only, the phase difference between the current and voltage is $$\pi$$.

In the light of the above statements, choose the most appropriate answer from the options given below

A cell of emf 4 V and internal resistance 0.5 $$\Omega$$ is connected to a 7.5 $$\Omega$$ external resistance. The terminal potential difference of the cell is

An ideal gas follows a process described by the equation $$P{V^2} = C$$ from the initial $$({P_1},\,{V_1},\,{T_1})$$ to final $$({P_2},\,{V_2},\,{T_2})$$ thermodynamic states, where C is a constant. Then

The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is

Identify the equivalent logic gate represented by the given circuit

The light rays having photons of energy 4.2 eV are falling on a metal surface having a work function of 2.2 eV. The stopping potential of the surface is

Identify the function which represents a non-periodic motion.

An inductor of inductance 2 mH is connected to a 220 V, 50 Hz ac source. Let the inductive reactance in the circuit is X₁. If a 220 V dc source replace the ac source in the circuit, then the inductive reactance in the circuit is X₂. X₁ and X₂ respectively are :

The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability $${\mu _0}$$ and permittivity $${\varepsilon _0}$$ is (Given that c - velocity) of light in free space

The threshold frequency of a photoelectric metal is v₀. If light of frequency 4v₀ is incident on this metal, then the maximum kinetic energy of emitted electrons will be :

The equivalent resistance of the infinite network given below is :

If the screen is moved away from the plane of the slits in a Young's double slit experiment, then the :

If $$\overrightarrow F = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow r = 3\widehat i + 2\widehat j - 2\widehat k$$, then the scalar and vector products of $$\overrightarrow F $$ and $$\overrightarrow r $$ have the magnitudes respectively as

The physical quantity that has the same dimensional formula as pressure is

The effective capacitances of two capacitors are 3 $$\mu$$F and 16 $$\mu$$F, when they are connected in series and parallel respectively. The capacitance of two capacitors are :

After passing through a polariser a linearly polarised light of intensity I is incident on an analyser making an angle of 30$$^\circ$$ with that of the polariser. The intensity of light emitted from the analyser will be

In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth) :

(Given g = 10 ms^$$-$$2)

The incorrect statement about the property of a Zener diode is :

A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If W₁, W₂ and W₃ represent the work done by the gravitational force along the respective paths, then :

A standard filament lamp consumes 100 W when connected to 200 V ac mains supply. The peak current through the bulb will be :

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s^$$-$$1. If the viscosity of oil at room temperature is 0.9 kg m^$$-$$1 s^$$-$$1, the viscous drag force is :

In a gravitational field, the gravitational potential is given by, $$V = - {K \over x}$$ (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

The percentage error in the measurement of g is : (Given that $$g = {{4{\pi ^2}L} \over {{T^2}}}$$, $$L = (10\, \pm \,0.1)$$ cm, $$T = (100\, \pm \,1)$$ s)

Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is : ($$\mu$$₀ = 4$$\pi$$ $$\times$$ 10^$$-$$7 SI unit)

The magnetic field on the axis of a circular loop of radius 100 cm carrying current $$I = \sqrt 2 \,A$$, at point 1 m away from the centre of the loop is given by :

Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s^$$-$$1 K^$$-$$1 m^$$-$$1 and 50 J s^$$-$$1 K^$$-$$1 m^$$-$$1 respectively. The free ends of copper and steel are held at 100$$^\circ$$C and 0$$^\circ$$C respectively. The temperature at the junction is, nearly :

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 $$\times$$ 10³⁹. The ratio of the proportionality constant, $$K = {1 \over {4\pi {\varepsilon _0}}}$$ to the gravitational constant G is nearly (Given that the charge of the proton and electron each = 1.6 $$\times$$ 10^$$-$$19 C, the mass of the electron = 9.11 $$\times$$ 10^$$-$$31 kg, the mass of the proton = 1.67 $$\times$$ 10^$$-$$27 kg) :

The position-time (x - t) graph for positive acceleration is

Six charges +q, $$-$$q, +q, $$-$$q, +q, and $$-$$q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q₀ to the centre of the hexagon from infinity is

($${\varepsilon _0}$$ - permittivity of free space)

An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eye piece used in the construction of the telescope are 20 m and 2 cm respectively. Consider the following statements about the telescope :

(a) The distance between the objective and eye piece is 20.02 m

(b) The magnification of the telescope is ($$-$$) 1000

(c) The image of the planet is erect and diminished

(d) The aperture of eye piece is smaller than that of objective

The correct statements are :

The magnetic flux linked to a circular coil of radius R is

$$\phi = 2{t^3} + 4{t^2} + 2t + 5$$ Wb

The magnitude of induced emf in the coil at t = 5 s is

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :

An organ pipe filled with a gas at 27$$^\circ$$C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90$$^\circ$$C, the resonance frequency at the same mode will be

The sliding contact C is at one fourth of the length of the potentiometer wire (AB) from A as shown in the circuit diagram. If the resistance of the wire AB is R₀, then the potential drop (V) across the resistor R is