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1. Both lipids and proteins can flip-flop
2. While lipids can rarely flip-flop, proteins cannot
3. While proteins can flip-flop, lipids cannot
4. Neither lipids nor proteins can flip-flop

A lake near a village suffered heavy mortality of fish within a few days. Consider the following reasons for this:

Which two of the above were the main causes of fish mortality in the lake?
1. 2, 3
2. 3, 4
3. 1, 3
4. 1, 2

Given below is a diagrammatic cross-section of a single loop of human cochlea. 

 
Which one of the following options correctly represents the names of three different parts?

1.	B: Tectorial membrane   C: Perilymph   D: Secretory cells
2.	C: Endolymph   D: Sensory hair cells   A: Serum
3.	D: Sensory hair cells   A: Endolymph   B: Tectorial membrane
4.	A: Perilymph   B: Tectorial membrane   C: Endolymph

   
   
   

1. Bacterial leaf blight of rice
2. Downy mildew of grapes
3. Loose smut of wheat
4. Black rust of wheat

Which one of the following is the correct difference between rod cells and cone cells of our retina?

1. a
2. b
3. c
4. d

Match the disease in column-I with the appropriate items (pathogen/prevention/treatment) in column-II.

Which one of the following is the correct statement regarding the particular psychotropic drug specified?

Which one of the following pairs of nitrogenous bases of nucleic acids is wrongly matched with the category mentioned against it?
1. Thymine, Uracil - Pyrimidines
2. Uracil, Cytosine - Pyrimidines
3. Guanine, Adenine - Purines
4. Adenine, Thymine - Purines

The table below gives the populations(in thousands) of ten species(A--J) in four areas (a-d) consisting of the number of habitats given within brackets against each. Study the table and answer the question as follows: 
which area out of a to d shows maximum species diversity? 

1. b
2. c
3. a
4. d

To which type of barriers under innate immunity, do the saliva in the mouth and the tears from the eyes, belong?
1. Cytokine barriers
2. Cellular barriers
3. Physiological barriers
4. Physical barriers

Cornea transplant in humans is almost never rejected. This is because:
1. its cells are least penetrable by bacteria
2. it has no blood supply
3. it is composed of enucleated cells
4. it is a non-living layer

A competitive inhibitor of succinic dehydrogenase is:

Which one of the following items gives its correct total number?
1. Floating ribs in humans - 4
2. Amino acids found in proteins - 16
3. Types of diabetes - 3
4. Cervical vertebrae in humans - 8

In humans, blood passes from the post caval to the diastolic right atrium of heart due to:
1. pushing open of the venous valves
2. suction pull
3. stimulation of the sino auricular node
4. pressure difference between the caval and atrium

Consider the following four statements (A-D) about certain desert animals such as kangaroo rats: 

Which two of the above statements for such animals are true?

Which one of the following groups of three animals each is correctly matched with their one characteristic morphological feature? 

1. a
2. b
3. c
4. d

Which one of the following is the true description of an animal concerned?

If the lattice parameter for a crystalline structure is 3.6 Å, then the atomic radius in fcc crystal is: 
1. 1.81 Å
2. 2.10 Å
3. 2.92 Å
4. 1.27 Å

Equal volumes of three acid solutions of pH 3, 4 and 5 are mixed in a vessel. What will be the H⁺ ion concentration in the mixture?
1. $1.11\times {10}^{-4}$ $\mathrm{M}$
2. $3.7\times {10}^{-4}$ $\mathrm{M}$
3. $3.7\times {10}^{-3}$ $\mathrm{M}$
4. $1.11\times {10}^{-3}$ $\mathrm{M}$

In a basic medium, acetophenone yields a stable compound A with C₂H₅ONa.
The structure of A is:

1.		2.
3.		4.

 ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}\to {\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}+{\mathrm{e}}^{-};$ ${\mathrm{E}}^{\mathrm{o}}=-0.35$ $\mathrm{V}$
${\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-};$ ${\mathrm{E}}^{\mathrm{o}}=-0.77$ $\mathrm{V}$
The strongest oxidizing agent in the above equation is:
1. ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$
2. ${\mathrm{Fe}}^{2+}$
3. ${\mathrm{Fe}}^{3+}$
4. ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$

Green chemistry means such reactions that:

If uncertainty in position and momentum are equal, then the uncertainty in velocity is:
1. $\frac{1}{2\mathrm{m}}\sqrt{\frac{\mathrm{h}}{\mathrm{\pi }}}$
2. $\sqrt{\frac{\mathrm{h}}{2\mathrm{\pi }}}$
3. $\frac{1}{\mathrm{m}}\sqrt{\frac{\mathrm{h}}{\mathrm{\pi }}}$
4. $\sqrt{\frac{\mathrm{h}}{\mathrm{\pi }}}$

Kohlrausch's law states that at:

Which one of the following is most reactive towards electrophilic attack?
 

1.		2.
3.		4.

The volume occupied by one water molecule (density = 1 g cm^-3) is:
1. $9.0\times {10}^{-23}$ $$ ${\mathrm{cm}}^3$
2. $6.023\times {10}^{-23}$ $$ ${\mathrm{cm}}^3$
3. $3.0\times {10}^{-23}$ $$ ${\mathrm{cm}}^3$
4. $5.5\times {10}^{-23}$ $$ ${\mathrm{cm}}^3$

Which of the following complexes has the highest paramagnetic behaviour?
(where gly = glycine, en = ethylenediamine, ox = oxalate ion and bpy = bipyridyl moieties )
(At no : Ti= 22, V = 23, Fe = 26, Co = 27)
1. [V(gly)₂(OH)₂(NH₃)₂]⁺
2. [Fe(en)(bpy)(NH₃)₂]²⁺
3.  [Co(ox)₂(OH)₂]^-
4. [Ti(NH₃)₆]³⁺

If a gas expands at a constant temperature, it indicates that:
1. Kinetic energy of the molecules decreases
2. The pressure of the gas increases
3. The kinetic energy of the molecules remains the same
4. The number of molecules of gas increases

In a S_N2 substitution reaction of the type 
\(\mathrm{R}-\mathrm{Br}+\mathrm{Cl}^{-} \xrightarrow{\mathrm{DMF}} \mathrm{R}-\mathrm{Cl}+\mathrm{Br}^{-}\)
one of the following that has the highest relative rate is:
 

1.	\(\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2 \mathrm{Br}\)	2.
3.		4.	\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\)

Number of moles of \(MnO^-_4\) required to oxidise one mole of ferrous oxalate completely in an acidic medium will be:

If the concentration of OH ' ions in the reaction 

For the above-given reaction, A (Predominantly) is:

1.		2.
3.		4.

The following compounds are given for reference
(1) CH₃-CH₂^–
(2) H₂C=CH^–
(3) HC≡C^– 
The increasing order of basic strength is:
1. (2)>(1)>(3)
2. (3) >(2) >(1)
3. (1) >(3) >(2)
4. (1) >(2)>(3)

If 'a’ stands for the edge length of the cubic systems: simple cubic, body-centered cubic, and face-centered cubic, then the ratio of radii of the spheres in these systems will be respectively: 
1. $\frac{1}{2}\mathrm{a\; :}$ $\frac{\sqrt{3}}{4}\mathrm{a}$ $:$ $\frac{1}{{\displaystyle 2}\sqrt{2}}\mathrm{a}$
2. $\frac{1}{2}\mathrm{a\; :}$ $\sqrt{3}\mathrm{a}$ $:$ $\frac{1}{\sqrt{2}}\mathrm{a}$
3. $\frac{1}{2}\mathrm{a\; :}$ $\frac{\sqrt{3}}{2}\mathrm{a}$ $:$ $\frac{\sqrt{2}}{{\displaystyle 2}}\mathrm{a}$
4. $1\mathrm{a\; :}$ $\sqrt{3}\mathrm{a}$ $:$ $\sqrt{2}\mathrm{a}$

The rate constants k₁ and k₂ for two different reactions are 10¹⁶. e^-2000/T and 10¹⁵. e^-1000/T, respectively. The temperature at which k₁= k₂ is:
1. $1000$ $\mathrm{K}$
2. $\frac{2000}{2.303}$ $\mathrm{K}$
3. $2000$ $\mathrm{K}$
4. $\frac{1000}{2.303}$ $\mathrm{K}$

The volume of oxygen gas (O₂) needed to completely burn 1 L of propane gas (C₃H₈)  (both O₂ & propane measured at 0°C and 1 atm) will be:
1. 7 L
2. 6 L
3. 5 L
4. 10 L

The correct order of increasing bond angles in the following triatomic species is:
1. ${\mathrm{NO}}_2^{-}$ $<$ ${\mathrm{NO}}_2^{+}$ $<$ ${\mathrm{NO}}_2$
2. ${\mathrm{NO}}_2^{-}$ $<$ ${\mathrm{NO}}_2$ $<$ ${\mathrm{NO}}_2^{+}$
3. ${\mathrm{NO}}_2^{+}$ $<$ ${\mathrm{NO}}_2$ $<$ ${\mathrm{NO}}_2^{-}$
4. ${\mathrm{NO}}_2^{+}$ $<$ ${\mathrm{NO}}_2^{-}$ $<$ ${\mathrm{NO}}_2$

How many stereoisomers does this molecule have? 

The correct order of increasing bond order among the given is -
1. ${\mathrm{O}}_2^{-}$ $<$ $\mathrm{NO}$ $<$ ${\mathrm{C}}_2^{2-}$ $<$ ${\mathrm{He}}_2^{+}$
2. $\mathrm{NO}$ $<$ ${\mathrm{C}}_2^{2-}$ $<$ ${\mathrm{O}}_2^{-}$ $<$ ${\mathrm{He}}_2^{+}$
3. ${\mathrm{C}}_2^{2-}$ $<$ ${\mathrm{He}}_2^{+}$ $<$ $\mathrm{NO}$ $<$ ${\mathrm{O}}_2^{-}$
4. ${\mathrm{He}}_2^{+}$ $<$ ${\mathrm{O}}_2^{-}$ $<$ $\mathrm{NO}$ $<$ ${\mathrm{C}}_2^{2-}$

An organic compound contains carbon, hydrogen, and oxygen. Its elemental analysis gave C, 38.71%, and H, 9.67%. The empirical formula of the compound would be:

The moles of lead (II) chloride that will be formed from a reaction
between 6.5 g of PbO and 3.2 g of HCl are:
1. 0.044
2. 0.333
3. 0.011
4. 0.029

 The structure of C in the below-mentioned reaction is: 

1.
2.
3.
4.

The stability of carbanions in the following:
 
is in the order of:

The dissociation equilibrium of a gas AB₂ can be represented as 
 $2A{B}_2\left(g\right)$ $\leftrightharpoons$ $2AB\left(g\right)$ $+$ $B_2\left(g\right)$ $$
The degree of dissociation is ‘x’ and is small compared to 1. The expression relating the degree of dissociation (x) with equilibrium constant K_P and total pressure p is:
1. (2KP/p)
2. (2Kp /p)^1/3
3. (2KP/p)^1/2
4. (KP/P)

Which one of the following statements is not true?

In the given hydrocarbon, 
 
The state of hybridization of carbons 1, 3, and 5 are:
1. sp², sp, sp³
2. sp, sp³, sp²
3. sp, sp², sp³
4. sp³, sp², sp

The value of K_P1 and K_p2 for the reactions
 $X$ $\leftrightharpoons$ $Y$ $+Z$ $......\left(i\right)$
$and$ $A$ $\leftrightharpoons 2B$ $......\left(ii\right)\hspace{0.17em}$
are in the ratio of 9 : 1. If the degree of dissociation of X and A is equal, then the total pressure at equilibrium(i) and (ii) are in the ratio:

In DNA, the complementary bases are:
1. Adenine and thymine; guanine and cytosine
2. Adenine and thymine; guanine and uracil
3. Adenine and guanine, thymine and cytosine
4. Uracil and adenine; cytosine and guanine

The bromination of acetone occurring in an acid solution is represented by the equation. 
CH₃COCH₃(aq)+ Br₂(aq) → 
CH₃COCH₂Br(aq) + H⁺(aq) + Br^-(aq) 
The kinetic energy data were obtained for given reaction concentrations. 
Initial concentrations, M 
 $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$   $\left[{\mathrm{Br}}_2\right]$    $\left[{\mathrm{H}}^{+}\right]$
   0.30             0.05      0.05
   0.30             0.10      0.05
   0.30             0.10      0.10
   0.40             0.05      0.20
Initial rate, the disappearance of Br₂, Ms^-1 
5.7 $\times$ 10^-5
5.7 $\times$  10^-5
1.2 $\times$ 10^-4
3.1 $\times$ 10^-4
Based on the above data, the rate of the equation is:
1. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{H}}^{+}\right]$
2. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[\mathrm{CH}={\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$
3. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$ ${\left[{\mathrm{H}}^{+}\right]}^2$
4. $\mathrm{Rate}$ $=$ $\mathrm{k}$ $\left[{\mathrm{CH}}_3{\mathrm{COCH}}_3\right]$ $\left[{\mathrm{Br}}_2\right]$ $\left[{\mathrm{H}}^{+}\right]$

The value of the equilibrium constant of the reaction 
 $\mathrm{HI}\left(\mathrm{g}\right)$ $\leftrightharpoons$ $\frac{1}{2}{\mathrm{H}}_2\left(\mathrm{g}\right)$ $+$ $\frac{1}{2}{\mathrm{I}}_2$ is 8.0.
The equilibrium constant of the reaction
 ${\mathrm{H}}_2\left(\mathrm{g}\right)$ $+$ ${\mathrm{I}}_2\left(\mathrm{g}\right)$ $\leftrightharpoons$ $2\mathrm{HI}\left(\mathrm{g}\right)\hspace{0.17em}$ will be-

CFSE (in the octahedral field) will be maximum in:
(Atomic number Co = 27)
1. ${\left[\mathrm{Co}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$
2. ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$
3. ${\left[\mathrm{Co}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$
4. ${\left[\mathrm{Co}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3\right]}^{3-}$

If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:
1. 4%
2. 6%
3. 8%
4. 2%

The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

The voltage gain of an amplifier with 9% negative feedback is 10. The voltage gain without feedback will be:
1. 90
2. 10
3. 1.25
4. 100

The energy required to charge a parallel plate condenser of plate separation, \(d\) and plate area of cross-section, \(A\) such that the uniform electric field between the plates is \(E,\) is:
1. $\frac{1}{2}$ ${\mathrm{\epsilon }}_0{\mathrm{E}}^2/\mathrm{Ad}$
2. ${\mathrm{\epsilon }}_0{\mathrm{E}}^2/\mathrm{Ad}$
3. ${\mathrm{\epsilon }}_0{\mathrm{E}}^2\mathrm{Ad}$
4. $\frac{1}{2}$ ${\mathrm{\epsilon }}_0{\mathrm{E}}^2\mathrm{Ad}$

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

A current of \(3~\text{A}\) flows through the \(2~\Omega\) resistor shown in the circuit. The power dissipated in the \(5~\Omega\) resistor is:
    

A p-n photodiode is made of a material with a bandgap of 2.0 eV. The minimum frequency of the radiation that can be absorbed by the material is nearly:
1. $10\times {10}^{14}$ $\mathrm{Hz}$
2. $5\times {10}^{14}$ $\mathrm{Hz}$
3. $1\times {10}^{14}$ $\mathrm{Hz}$
4. $20\times {10}^{14}$ $\mathrm{Hz}$

On a new scale of temperature, which is linear and called the \(\mathrm{W}\) scale, the freezing and boiling points of water are \(39^\circ ~\mathrm{W}\)$$and \(239^\circ ~\mathrm{W}\) respectively. What will be the temperature on the new scale corresponding to a temperature of \(39^\circ ~\mathrm{C}\) on the Celsius scale?
1. \(78^\circ ~\mathrm{C}\)
2. \(117^\circ ~\mathrm{W}\)
3. \(200^\circ ~\mathrm{W}\)
4. \(139^\circ ~\mathrm{W}\)

If \(Q\), \(E\), and \(W\) denote respectively the heat added, the change in internal energy, and the work done in a closed cycle process, then:
1. \(W=0\)
2. \(Q=W=0\)
3. \(E=0\)
4. \(Q=0\)

A closed-loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR, and RQ are F₁, F_2, and F₃ respectively, and are in the plane of the paper and along the directions shown, then which of the following forces acts on the segment QP?
      
1. ${\mathrm{F}}_3-{\mathrm{F}}_1-{\mathrm{F}}_2$
2. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2+{\mathrm{F}}_2^2}$
3. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2-{\mathrm{F}}_2^2}$
4. ${\mathrm{F}}_3-{\mathrm{F}}_1+{\mathrm{F}}_2$

The decay constants of two radioactive materials X₁ and X₂ are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei.  The ratio of the number of nuclei of X₁ to that of X₂  will be \(1/e\) after a time:
1. \(\lambda\)
2. \(\frac{1}{2\lambda }\)
3. \(\frac{1}{4\lambda }\)
4. \(\frac{e}{\lambda }\)

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is:
1. $\sqrt{\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}}$
2. $\sqrt{\frac{{\mathrm{f}}_2}{{\mathrm{f}}_1}}$
3. $\frac{{\mathrm{f}}_1+{\mathrm{f}}_2}{{\mathrm{f}}_1{\mathrm{f}}_2}$
4. None of the above

The distance travelled by a particle starting from rest and moving with an acceleration \(\frac{4}{3}\) ms^-2, in the third second is:
1. \(6\) m
2. \(4\) m
3. \(\frac{10}{3}\) m
4. \(\frac{19}{3}\) m

The circuit is equivalent to: 
 
1. AND gate
2. NAND gate
3. NOR gate
4. OR gate

A particle of mass \(m\), charge \(Q\), and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B\). What will be the kinetic energy of the particle after seconds?

A particle of mass \(1\) mg has the same wavelength as an electron moving with a velocity of  \(3\times 10^{6}\) ms^-1. The velocity of the particle is:
(Mass of electron = \(9.1 \times 10^{-31}\) kg)
1. \(2.7 \times 10^{-18}~\text{ms}^{-1}\)
2. \(9 \times 10^{-2}~\text{ms}^{-1}\)
3. \(3 \times 10^{-31}~\text{ms}^{-1}\)
4. \(2.7 \times 10^{-21}~\text{ms}^{-1}\)

A particle shows the distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point:

         

1. B
2. C
3. D
4. A

A cell can be balanced against 100 cm and 110 cm of potentiometer wire, respectively with and without being short-circuited through a resistance of 10 Ω. Its internal resistance is:
1.  1.0 Ω
2.  0.5 Ω
3.  2.0 Ω
4.  zero

If \(M(A,~Z)\), \(M_p\)${}_{}$, and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) (\(1~u=931.5~\text{MeV/c}^2\)) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is:
                 
1.  $0.5$ $\mathrm{N}$
2.  $1.5$ $\mathrm{N}$
3.  $\frac{\sqrt{3}}{4}$ $\mathrm{N}$
4.  $\sqrt{3}$ $\mathrm{N}$

Two periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:
1.  $2\left({\mathrm{l}}_1+{\mathrm{l}}_2\right)$
2.  ${\left({\sqrt{\mathrm{I}}}_1+{\sqrt{\mathrm{l}}}_2\right)}^2$
3.  ${\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)}^2$
4.  $2\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)$

A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:
1.  100 ms^-1
2.  80 ms^-1
3.  40 ms^-1
4.  120 ms^-1

A thin conducting ring of radius \(R\) is given a charge \(+Q.\) The electric field at the centre O of the ring due to the charge on the part AKB of the ring is \(E.\) The electric field at the centre due to the charge on the part ACDB of the ring is:

                   

1. \(3E\) along KO
2. \(E\) along OK
3. \(E\) along KO
4. \(3E\) along OK

The velocity of electromagnetic radiation in a medium of permittivity ${\epsilon }_0$ and permeability ${\mu }_0$ is given by:
1.  $\sqrt{\frac{{\mathrm{\epsilon }}_{\mathrm{o}}}{{\mathrm{\mu }}_{\mathrm{o}}}}$
2.  $\sqrt{{\mathrm{\mu }}_{\mathrm{o}}{\mathrm{\epsilon }}_{\mathrm{o}}}$
3.  $\frac{1}{\sqrt{{\mathrm{\mu }}_{\mathrm{o}}{\mathrm{\epsilon }}_{\mathrm{o}}}}$
4.  $\sqrt{\frac{{\mathrm{\mu }}_{\mathrm{o}}}{{\mathrm{\epsilon }}_{\mathrm{o}}}}$

A point performs simple harmonic oscillation of period \(\mathrm{T}\) and the equation of motion is given by; \(x=a \sin (\omega t+\pi / 6)\). After the elapse of what fraction of the time period, the velocity of the point will be equal to half of its maximum velocity?
1. \( \frac{T}{8} \)
2. \( \frac{T}{6} \)
3. \(\frac{T}{3} \)
4. \( \frac{T}{12}\)

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of a focal length of \(10\) cm. The diameter of the sun is \(1.39\times10^9\) m and its mean distance from the earth is \(1.5\times10^{11}\) m. What is the diameter of the sun's image on the paper?
 

In an AC circuit, the emf (e) and the current (I) at any instant are given respectively by 
e = E₀sin$\mathrm{\omega }$t 
I = I₀sin$\left(\mathrm{\omega t}-\mathrm{\varphi }\right)$ 
The average power in the circuit over one cycle of AC is:
1.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$
2.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$ $\sin$ $\mathrm{\varphi }$
3.  $\frac{{\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}}{2}$ $\cos$ $\mathrm{\varphi }$
4.  ${\mathrm{E}}_{\mathrm{o}}{\mathrm{I}}_{\mathrm{o}}$

A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms^-1 to \(20\) ms^-1 while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:

A thin rod of length \(L\) and mass \(M\) is bent at its midpoint into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:
1.  \(\frac{ML^2}{24}\)
2.  \(\frac{ML^2}{12}\)
3.  \(\frac{ML^2}{6}\)
4.  \(\frac{\sqrt{2}ML^2}{24}\)

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
1.  $2\mathrm{mv}$
2.  $\mathrm{mv}/\sqrt{2}$
3.  $\mathrm{mv}\sqrt{2}$
4.  zero

Two points are located at a distance of \(10\) m and \(15\) m from the source of oscillation. The period of oscillation is \(0.05\) s and the velocity of the wave is \(300\) m/s. What is the phase difference between the oscillations of two points?
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\pi\)
4. \(\frac{\pi}{6}\)

Two nuclei have their mass numbers in the ratio of \(1:3.\) The ratio of their nuclear densities would be:
1. \(1:3\)
2. \(3:1\)
3. \((3)^{1/3}:1\)
4. \(1:1\)

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:
1.  Mv Newton
2.  2Mv Newton
3.  $\frac{\mathrm{Mv}}{2}$ Newton
4.  zero

The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:

At \(10^{\circ}\mathrm{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x\). At \(110^{\circ}\mathrm{C}\) this ratio is:
1. \(x\)
2. \(\frac{383}{283}x\)
3. \(\frac{10}{110}x\)
4. \(\frac{283}{383}x\)

Silicon gives p-type of semiconductor on doping with:
1. Germanium.
2. Arsenic.
3. Selenium.
4. Boron.