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Symptoms of altitude sickness include all except

1. Nausea                     2.   Fatigue
2. Heart palpitation       4.   Hyperoxia

Shivering during cold is beneficial for mammals. It helps to

Many adaptations of an organism have evolved over a long duration of evolution and are______

The main reason behind building burrows in soil by burrowing animals is

Choose the odd one out with respect to structure formed in the different organisms during suspended phase.

Smaller animals tend to lose body heat very fast as compared to larger animals because they have

Select the incorrect statement

Population size in any given habitat is also known as _______

A striking difference between immigration and emigration is _____

Study the following equation in context of population growth and choose the correct option
       dN/dt=(B-D)×N
       Substituting r in place of B-D then
       dN/dt=rN
       Here, r is known as _______

What four factors define population growth?

Which of the following is true concerning exponential growth?

Read the following statements and select the correct option with respect to population attributes.
a. Population density is necessarily measured in numbers.
b. Tiger census is often based on pug marks and fecal pellets.
c. Biomass is not a meaningful measure to known population size.
d. Size of a population for any species is not a static parameter.
1. a. and b.              2. a. and d.
3. c. and d.              4. b. and d.

Select the incorrect statement regarding different population attributes.

A species whose distribution is restricted to a small geographical area because of the presence of a competitive superior species is found to expand its distributional range dramatically when the competing species is experimentally removed. This phenomenon is known as

Find out the false statements

Find out the incorrect statement

Through resource partitioning

The association between clown fish and sea anemone is the same as between

For the defense against predators, butterflies become highly distasteful due to having certain chemical in their bodies. What is the source of the chemical?

Predation, parasitism and commensalism share a common characteristic, that is

Which of the following is not correct?

Secondary productivity means

Match Column-I with Column-II and select the correct option
     Column-I                                              Column-II
a. Fragmentation                 (i) Break down of detritus into smaller particles
b. Leaching                         (ii) Precipitation of water soluble nutrients as unavailable salt
c. Catabolism                      (iii) Degradation of detritus by bacterial and fungal enzymes
1. a. — (i) ; b. — (ii) ; c. — (iii)
2. a. — (ii) ; b. — (iii) ; c. — (i)
3. a. — (iii) ; b. — (ii) ; c. — (i)
4. a. — (iii) ; b. — (i) ; c. — (ii)

Humus is degraded by some microbes and release of inorganic nutrients occur by the process known as

Following are the two main structural features of an ecosystem
a. Species composition
b. Energy flow
c. Decomposition
d. Stratification
1. a. and d.               2. b. and c.
3. Only a.                 4. b. and d.

Cycling of material in ecosystem is entirely dependent upon

The process of decomposition is in the following order

Net primary productivity

Most important climatic factors that regulate the rate of decomposition are

Gross primary productivity is

Which law is obeyed during energy flow in an ecosystem?

Find the incorrect statement

A graphical representation known as ______is required to express food or energy relationship between organisms at different trophic levels.

Find the correct statement

A food web

Orderly and sequential changes in communities, parallel with the changes in the physical environment is known as

The entire sequence of communities that successively, change in a given area are called

1. extinction.                        2. evolution.
2. succession.                      4. sere.

Find out the total number of true statements from the following:
a. Primary succession is a very slow process, taking thousands of years for the climax to be reached.
b. All succession whether taking place in water or land, proceeds to a similar climax community, the mesic.
c. As succession proceeds, the number and types of animals and decomposers also change
d. Saprophytes are not given any place in the ecological pyramids even though they play a vital
role in the ecosystem.
1. One                            2. Two
3. Three                         4. Four

Amount of nutrients present in soil at any given time is referred as

1. Standing state           2.   Standing quality
2. Standing crop            4.   Both 1. and 2.

Which of the following majorly regulates the amount of carbon in the atmosphere?

What price tag did Robert Constanza put for fundamental ecosystem services?

1. 33 trillion US $                    2. 22 trillion US $
2. 12 trillion US $                    4. 44 trillion US $

Out of the total cost of various ecosystem services, the soil account for __________%, recreation and nutrient cycling constitute less than ___________% and climate regulation and habitat for wildlife account for about __________% each.

1. 50; 6; 10                      2. 50; 10; 6
2. 50; 30; 20                    4. 20; 30; 50

The two major differences between carbon and phosphorus cycles are
a. Atmospheric inputs of phosphorus through rainfall are much smaller than carbon inputs
b. Atmospheric inputs of phosphorus through rainfall are much greater than carbon inputs
c. Gaseous exchange of phosphorus between organism and environment is not negligible
d. Gaseous exchange of phosphorus between organism and environment is negligible
1. a. and b.                    2. b. and c.
3. a. and d.                    4. a. and c.

Read the given statements and choose the right option
a. The amount of living matter (biomass) present at every tropical level is called standing crop
b. Saprophytes do not form part of ecological pyramids
c. Ecological pyramid does not account the same species belonging to two or more trophic levels
d. Humus is reservoir of nutrients
1. All are correct
2. All are incorrect
3. Only d. is correct
4. a, d and c are correct

A major advantage of using YAC as a cloning vector over the plasmids is that :
1. it can replicate independently
2. it can be selected easily
3. it can accommodate larger inserts
4. it has multiple cloning sites

What is the problem in providing a bone marrow transplant to a patient of SCID as a treatment?
1. rejection of the graft by the recipient
2. graft-versus-host disease
3. cardiovascular failure
4. anaphylaxis

Genetic engineering of nitrogen fixation is made difficult by the fact that it :
1. is a complex process involving many enzymes
2. is a process that is partly anaerobic
3. involves about 15 genes (the Nif Genes)
4. All of these

Which of the following genetically modified product is used to dissolve blood clots in patients of coronary Thrombotic stroke?

The genetically engineered vaccine for the prevention of hepatitis B is made with the help of the microbe :

The advantage of using DNA polymerases from thermophilic organisms in PCR is that:

First discovered, Type II restriction endonuclease was

Which of the following genetic disease would be amenable to genetic engineering?

Using recombinant DNA technology, genes from a donor cell can be implanted into a bacterium for DNA replication and protein synthesis. The kind of cell(s) that can be used as gene donors in this technology is/are:
1. Bacteria only
2. Either yeast or bacteria only
3. Eukaryotic cells only
4. Any kind of cell

A gene carried by recombinant DNA is cloned when:
1. Its host bacterium divides by binary fission
2. It is transcribed
3. It is fragmented by restriction enzymes
4. It is hybridized

A piece of nucleic acid used to find a gene, by forming a hybrid with it, is called a
1. Probe
2. Vector
3. Restriction sequence
4. Retrovirus

In situ hybridization is used to :

Restriction enzymes are synthesized by

A bacterium adds methyl group to its DNA, by a process known as modification, in order to:

A fragment of DNA, cut by a restriction enzyme, forms bonds with other DNA molecules that have
1. Been fragmented by the same restriction enzyme
2. Sticky ends
3. Plasmid component
4. Attached methyl group

Hybridization of mRNA with DNA can reveal which segment of the DNA are introns and which segment are exons. When the magnification is high enough to see the molecule, the introns appear as
1. Single stranded loops in a double stranded molecule
2. Separate fragments
3. Triple stranded nucleic acid molecules
4. Barr bodies

Which of the following primers would allow copying of the single-stranded DNA sequence 5' ATGCCTAGGTC?

The "Southern" technique involves:

Which of the following tools of recombinant DNA technology is INCORRECTLY paired with one of its uses?

DNA from a eukaryotic organism is digested with a restriction endonuclease and the resulting fragments are cloned into a plasmid vector. Bacteria transformed by these plasmids collectively contain all of the genes of the organism. This culture of bacteria is referred to as :

Which of the following is not part of the normal process of cloning recombinant DNA in bacteria?

A key feature of insertional mutagenesis for the identification of plasmids containing recombinant DNA is:

The first drug produced using recombinant DNA technology is used to treat:

Which gene transfer technique involves the use of a fatty bubble to carry a gene into a somatic cell?
1. electroporation
2. liposome transfer
3. microinjection
4. particle bombardment

What type of probe would you use for a Western blot experiment?

Prior to the production of recombinant human insulin, diabetic patients could use insulin isolated from cattle. Which of the listed items would not be a drawback to this procedure?

Bacteria that are unable to synthesize chemicals that allow the formation of ice crystals have been engineered. Commercial fruit farmers can spray this bacterial strain on their fruit plants, with the idea that they will compete with unmodified bacteria and reduce frost damage. This is an example of:

In gene knockout technology:

Which of the following explains why production of transgenic plants is easier than production of transgenic animals?
1. Plant cells can grow in cell culture.
2. Plant cells have a lower number of potentially lethal genes.
3. Plant cells are totipotent.
4. Production of mutant plants poses less ethical dilemmas than production of mutant animals.

What process causes shortening of telomeres during cell division?
1. DNA synthesis.
2. Exonuclease removal of primers.
3. Ligation of DNA fragments.
4. Telomerase activity.

Which of these uses of transgenic technology is not directly relevant to agricultural applications?

Which of these is an accurate description of gene therapy?

In the first gene cloning experiment:

An important limitation to the use of Agrobacterium tumefaciens is that it can not:
1. infect dicots
2. be genetically modified
3. be cultured on a nutrient medium
4. infect crop plants such as wheat and corn

A danger of genetic engineering is that the genetically modified bacterium can escape the lab and infect humans. This possibility can best be prevented by:

If you are using a vector with lacZ as a screenable marker, which of the following bacterial strains would you want to use as host cells?
1. lacO^-
2. lacI^-
3. lacZ^-
4. Any of these would work.

Which of the enzymes whose recognition sites are shown here would produce sticky ends compatible with BstAUI (5'-G|GTACC-3')?
1. Bcl I (5'-T|GATCA-3')
2. Sun I (5'-C|GTACG-3')
3. Hind III (5'-A|AGCTT-3')
4. Kpn I (5'-GGTAC|C-3')

Which of the following would NOT be a useful selectable marker?

Diseases amenable to treatment by gene therapy:
1. Must be relatively mild.
2. Must be caused by a defect in cells that are clinically accessible.
3. Must have other types of treatments available in case gene therapy fails.
4. Must lower the humoral and cell mediated immune responses

One possible use of transgenic plants is in the production of human proteins, such as vaccines. Which of the following is a possible hindrance that must be overcome?

Which of the following is one of the technical reasons why gene therapy is problematic?

The DNA profiles below represent four different individuals. Which of the following statements is consistent with the results?
 
1. B is the child of A and C.
2. C is the child of A and B.
3. D is the child of B and C.
4. A is the child of B and C.

Dideoxyribonucleotide chain-termination is a method of
1. cloning DNA.
2. sequencing DNA.
3. digesting DNA.
4. synthesizing DNA.

What is the most logical sequence of steps for splicing foreign DNA into a plasmid and inserting the plasmid into a bacterium?

1. I, II, IV, III, V
2. II, III, V, IV, I
3. III, II, IV, V, I
4. III, IV, V, I, II

How many formula units are there in the unit cell of Sodium Chloride?
1. 2
2. 4
3. 6
4. 8

The most unsymmetrical and symmetrical system are respectively
1. Tetragonal, Cubic
2. Triclinic, Cubic
3. Rhombohedral, Hexagonal
4. Orthorhombic, Cubic

In a compound atoms of element Y form CCP lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of compound will be
1. X₃Y₄
2. X₂Y₃
3. X₂Y
4. X₄Y₃

The edge of unit cell of fcc of Xe crystal is 620 pm. The radius of Xe atom is 
1. 219.23 pm
2. 235.16 pm
3. 189.37 pm
4. 319.23 pm

Schottky defect occurs mainly in electrovalent compound where
1. Positive ions have larger size
2. Negative ions have small size 
3. Positive and negative ions are of similar size
4. Positive ions are big and negative ions are small

The appearance of colour in solid alkali metal halides is generally due to 
1. Frenkel defect
2. Interstitial defect
3. F - Centres
4. Schottky Defect

The edge length of fcc unit cell of NaCl is 508 pm. If the radius of cation is 110 pm then radius of anion is
1. 114 pm
2. 249 pm
3. 288 pm
4. 398 pm

An element (Atomic mass = 50 g/mol) having fcc stucture has unit cell edge length 400 pm. The density of element is
1. 5.188 g/cc
2. 10.376 g/cc
3. 2.56 g/cc
4. 1.2 g/cc

In a crystalline solid, anion B are arranged in cubic close packing and cation A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, the formula for the solid is 
1. AB
2. AB₂
3. A₂B
4. A₂B₃

In a FCC lattice, atom A occupies the corner positions and atom B occupies the face centred positions. If one atom of B is missing from one of the face centred points, the formula of the compound is 
1. A₂B
2. AB₂
3. AB
4. A₂B₅

In HCP arrangement, the co-ordination number is
1. 6
2. 12
3. 8
4. 10
 
 

A binary solid has a structure with B^- ion constituting the lattice and A⁺ ion occupying 25% tetrahedral holes. The formula of solid is 
1. AB
2. A₂B
3. AB₂
4. AB₄

A solid has a bcc structure. If the distance of closest approach between the two atoms 1.73 $\stackrel{o}{A}$. The edge length of the cell is
1. 200 pm
2. $\frac{\sqrt{3}}{\sqrt{2}} pm$
3. 142.2 pm
4. 400 pm

A metal crystallises as body centred cubic lattice with the edge length of unit cell equal to 0.304 nm. If the molar mass of the metal is 50.3 g mol^-1, its density is
1. 5.945 g cm^-3
2. 2.9725 g cm^-3
3. 8.9175 g cm^-3
4. 4.458 g cm^-3
 

The edge length of the unit cell of NaCl crystal lattice is 5.623 $\stackrel{o}{A}$, density is 2.16 g cm^-3 and the molar mass of NaCl is 58.5 g mol^-1. The number of formula units per unit cell is
1. 4
2. 3
3. 1
4. 2

Analysis shows that an oxide ore of nickel has formula $N{i}_{0.98}{O}_{1.00}.$ The percentage of nickel as $N{i}^{3+}$ ions is nearly
1. 2
2. 96
3. 4
4. 98

Perovskite is mineral containing Calcium, Oxygen and Titanium, in which oxygen atoms are at the face centres, calcium atoms are at the corners and titanium atoms are at the centre of the cube. Oxidation number of titanium in the mineral is 
1. +2
2. +3
3. +4
4. +3/4

If the distance between Na⁺ and Cl^- ions in sodium chloride crystal is X pm, the length of the edge of the unit cell is
1. 4X pm
2. X/4 pm
3. X/2 pm
4. 2X pm

In a crystal A atoms are present at all the corners and face centres while B atoms at all the edge centres and body centre of cubic unit cell. If the atoms from one of the body diagonals are removed then what will be the simplest composition of unit cell?
$$\begin{gathered} 1. A_5{B}_4 \\ 2. A_{15}{B}_{12} \\ 3. A_4{B}_5 \\ 4. A_2{B}_3 \end{gathered}$$

The number of cationic vacancies per mole in NaCl crystal, If it is doped with 10^-3 mole % GaCl₃ (ionic salt), are 
$1. 6.02\times {10}^{20}$
$2. 6.02\times {10}^{18}$
$3. 1.204\times {10}^{21}$
$4. 1.204\times {10}^{19}$

Which has highest freezing point?
1. 0.01 M NaCl
2. 0.05 M Urea
3. 0.01 M MgCl₂
4. 0.02 M NaCl

$K_f$ for $H_{2}O$ is 1.86 k/m. Therefore, the freezing point of 0.1 M NaCl solution in water is expected to be
$$\begin{gathered} 1. -1.86 °C \\ 2. -0.186 °C \\ 3. +0.372 °C \\ 4. -0.372 °C \end{gathered}$$
 

When mercuric iodide is added to the aqueous solution of potassium iodide is
1. Freezing point is raised
2. Feezing point is lowered
3. Freezing point does not change
4. Boiling point does not change
 

A 5% solution of cane sugar (molar mass = 342) is isotonic with 1% of a solution of an unknown solute. The molar mass of unknown solute is 
1. 136.2
2. 171.2
3. 68.4
4. 34.2

What is the freezing point of a solution contains 8.1 gm HBr in 100 gm water assuming the acid to be 90% ionized? (K_f for H₂O = 1.86 k/m)
$$\begin{gathered} 1. -1.86 °C \\ 2. -0.353 °C \\ 3. -3.53 °C \\ 4. 0°C \end{gathered}$$

Which of the following solution has the highest equivalent conductance?
1. 0.01 M NaCl
2. 0.05 M NaCl
3. 0.005 M NaCl
4. 0.02 M NaCl

The resistance of 0.01 N solution of an electrolyte AB at 328K is 100 ohm. The specific conductance of solution is (cell constant = 1 cm^-1)
1. 100 ohm
2. 10^-2 ohm
3. 10^-2 ohm^-1cm^-1
4. 10² ohm-cm

The increase in the molar conductivity of HCl with dilution is due to
1. Increase in the self ionisation of water
2. Hydrolysis of HCl
3. Decrease in the self ionisation of water
4. Decrease in the interionic forces

A solution of $N{a}_{2}S{O}_4$ in water is electrolysed using pt electrodes. The products at the cathode and anode are respectively 
$1. H_2, S{O}_2$
$2. O_2, NaOH$
$3. H_2, O_2$
$4. O_2, S{O}_2$

Given that
$$\begin{gathered} A{g}^{+}/Ag \to +0.80V C{o}^{2+}/Co \to -0.28V \\ C{u}^{2+}/Cu \to +0.34V Z{n}^{2+}/Zn \to -0.76V \end{gathered}$$
The most reactive metal which displaces other metals from their salts in solution is 
1. Ag
2. Cu
3. Co
4. Zn
 

The emf of the cell $Tl | T{l}^{+} (0.001 M) || C{u}^{2+} (1M) | Cu$ is 0.83V. The emf of this cell could be increased by
1. increasing the concentration of Tl⁺ ions 
2. increasing the concentration of Cu²⁺ ions 
3. increasing the concentration of both
4. None of the above 
 

For a reaction $A\left(s\right) + 2B^{+} \to A^{2+} +\hspace{0.17em}2B\left(s\right) K_c$ has been found to be ${10}^{12}$. The $E_{cell}^o$ is
1. 0.354 V
2. 0.708 V
3. 0.0098 V
4. 1.36 V

The solution of nickel sulphate in which nickel rod dipped is diluted to 10 times. The potential of nickel 
1. Decreases by 60 mV
2. Increases by 30 mV
3. Decreases by 30 mV
4. Decreases by 60 mV

Two electrodes are fitted in conductance cell 1.5 cm apart while the area of cross section of each electrode is 0.75 cm². The cell constant is
1. 1.0125 cm
2. 0.5 cm
3. 2.0 cm^-1
4. 0.2 cm^-1

Pick out the incorrect statement
1. Equivalent conductance increases with dilution
2. Molar conductance increases with dilution
3. Specific conductance increases with dilution
4. Specific resistance increases with dilution

Aluminium phosphate is 100% ionized in 0.01m aqueous solution. Hence, $△T_b/k_b$ is
1. 0.01                      2. 0.015
3. 0.0175                  4. 0.02

60 gm of urea is dissolved in 1100 gm solution. To keep $△T_f/k_f$ as 1 mol/kg, amount of water separated in the form of ice will be
1. 40 gm                   2. 60 gm
3. 100 gm                 4. 200 gm

Which solution has the highest osmotic pressure?
1. 0.1 M NaCl                2. 0.5 M Urea
3. 0.1 M MgCl₂              4. 0.2 M NaCl   

An ideal solution is made by mixing 2 moles of benzene (P^o = 266 mm) and 3 moles of another liquid  (P^o = 236 mm). The total vapour pressure of the solution at the same temperature would be
1. 502 mm                2. 248 mm
3. 600 mm                4. 258 mm

A binary solution of ethanol and n-heptane is an example of 
1. Ideal solution
2. Non-ideal solution with +ve deviation
3. Non-ideal solution with -ve deviation
4. Unpredictable behaviour

0.5 M solution of urea is isotonic with
1. 0.5 M NaCl solution
2. 0.5 M sugar solution
3. 0.5 M BaCl₂ solution
4. 0.5 M solution benzoic acid in benzene

The value of ${\wedge }_{eq}^{\infty }$ for NH₄Cl , NaOH and NaCl are respectively 149.74, 248.1 and
126.4 ohm^-1cm²equiv^-1. The value of ${\wedge }_{eq}^{\infty }$ for NH₄OH is 
1. 317.44
2. 271.44
3. 71.44
4. It cannot be calculated from the data given 

In passing 3 faraday of electricity through the three electrolytic cells connected in series containing Ag⁺, Cu²⁺ and Al³⁺ respectively. The molar ratio in which the three metal ions are liberated at the electrode is 
1. 1:2:3                      2. 3:2:1
3. 6:3:2                      4. 3:4:2

Given that
$$\begin{gathered} I_{2 } + 2e^{-} \to 2I^{-} ; E^o = 0.54V \\ B{r}_2 + 2e^{-} \to 2B{r}^{-} ; E^o = 1.09V \end{gathered}$$
Predict which of the following is true
1. I^- ions will be able to reduce bromine
2. Br^- ions will be able to reduce iodine
3. Iodine will be able to reduce bromide ions
4. Bromine will be able to reduce iodide ions

What is the EMF of the cell?
Zn(s) | Zn⁺² (0.1M) || Sn⁺² (0.001M) | Sn(s)
Given $E_{Z{n}^{2+}/Zn}^o =-0.76V, E_{S{n}^{2+}/Sn}^o= -0.14V$
1. 0.62V            2. 0.56V
3. 1.12V            4. .31V

At what altitude, will the acceleration due to gravity be 25% of that at the earth's surface (given radius of the earth is R)?
1. R/4
2. R
3. 3R/8
4. R/2

At what distance from the centre of the moon is the point at which strength of the resultant of earth's and moon's gravitational field is equal to zero. The earth's mass is 81 times that of the moon and the distance between centres of the earth and that of the moon is 60R where R is the radius of the earth.
1. 6 R
2. 4 R
3. 3 R
4. 5 R

Two masses m₁ and m₂ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of d is :
1. $\frac{2\mathrm{Gd}}{({\mathrm{m}}_1 + {\mathrm{m}}_2)}$
2. $\frac{({\mathrm{m}}_{1 }+ {\mathrm{m}}_2)\mathrm{G}}{2\mathrm{d}}$
3. ${\left[({\mathrm{m}}_1 + {\mathrm{m}}_2) \frac{2\mathrm{G}}{\mathrm{d}}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
4. $({\mathrm{m}}_{1 }+ {\mathrm{m}}_2{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} 2 \mathrm{Gd}$ 

A spherical hole of radius R/2 is excavated from the asteroid of mass M as shown in fig. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is :
                                           
1. GM/R²
2. GM/2R²
3. GM/8R²
4. 7GM/8R²

If the radius of the earth be increased by a factor of 5, by what factor its density be changed to keep the value of g the same?
1. 1/25
2. 1/5
3. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{5}$}\right.$
4. 5

Two springs of force constant k and 2k are connected to a mass as shown below. The frequency of oscillation of the mass is :

$1. \frac{1}{2\mathrm{\pi }}\sqrt{\frac{k}{m}}$
$2. \frac{1}{2\mathrm{\pi }}\sqrt{\frac{2k}{m}}$
$3. \frac{1}{2\mathrm{\pi }}\sqrt{\frac{3k}{m}}$
$4. \frac{1}{2\mathrm{\pi }}\sqrt{\frac{m}{k}}$

An infinite number of masses, each of one kg are placed on the +ve X-axis at 1m, 2m, 4m............from the origin. The magnitude of the gravitational field at origin due to this distribution of masses is:
1. 2G
2. $\frac{4\mathrm{G}}{3}$
3. $\frac{3\mathrm{G}}{4}$
4. $\infty$

A satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing about a point on the equator is :
1. 48 hrs
2. 24 hrs
3. 12 hrs
4. never

A satellite of the earth is revolving in a circular orbit with a uniform velocity v. If the gravitational force suddenly disappears, the satellite will
1. Continue to move the same velocity in the same orbit.
2. move tangentially to the original orbit with velocity v.
3. fall down with increasing velocity.
4. come to a stop somewhere in its original orbit.

At what height above the earth's surface does the acceleration due to gravity fall to 1% of its value at the earth's surface?
1. 9R
2. 10R
3. 99R
4. 100R

Two concentric shells of uniform density of mass M₁ and M₂ are situated as shown in the figure. The forces experienced by a particle of mass m when placed at position A, B, C respectively are (given OA = p, OB = q and OC = r)
                       
1.  $\mathrm{Zero}, \mathrm{G}\frac{{\mathrm{M}}_1\mathrm{m}}{{\mathrm{q}}^2} \mathrm{and} \mathrm{G}\frac{({\mathrm{M}}_{1 }+ {\mathrm{M}}_2)\mathrm{m}}{{\mathrm{p}}^2}$
2.  $\mathrm{G}\frac{({\mathrm{M}}_{1 }+ {\mathrm{M}}_2)\mathrm{m}}{{\mathrm{p}}^2}, \mathrm{G}\frac{({\mathrm{M}}_{1 }+ {\mathrm{M}}_2)\mathrm{m}}{{\mathrm{q}}^2} \mathrm{and} \mathrm{G}\frac{{\mathrm{M}}_1\mathrm{m}}{{\mathrm{r}}^2}$
3. $\mathrm{G}\frac{{\mathrm{M}}_1\mathrm{m}}{{\mathrm{q}}^2}, \mathrm{G}\frac{({\mathrm{M}}_1 + {\mathrm{M}}_2)\mathrm{m}}{{\mathrm{p}}^2} \mathrm{and} \mathrm{Zero}$
4. $\mathrm{G}\frac{({\mathrm{M}}_1 + {\mathrm{M}}_2)\mathrm{m}}{{\mathrm{p}}^2}, \mathrm{G}\frac{{\mathrm{M}}_1\mathrm{m}}{{\mathrm{q}}^2} \mathrm{and} \mathrm{Zero}$

A newly discovered planet has a density eight times the density of the earth and a radius twice the radius of the earth. The time taken by 2 kg mass to fall freely through a distance S near the surface of the earth is 1 second. Then the time taken for a 4 kg mass to fall freely through the same distance S near the surface of the new planet is :
1. 0.25 sec.
2. 0.5 sec.
3. 1 sec.
4. 4 sec.

The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity ${\omega }_o$. The acceleration due to the gravity on the planet's surface is :
1. $\frac{{\mathrm{r}}^3{\mathrm{\omega }}_0}{\mathrm{R}}$
2. $\frac{{\mathrm{r}}^3{{\mathrm{\omega }}_0}^3}{{\mathrm{R}}^2}$
3. $\frac{{\mathrm{r}}^3{{\mathrm{\omega }}_0}^2}{\mathrm{R}}$
4. $\frac{{\mathrm{r}}^3{{\mathrm{\omega }}_0}^2}{{\mathrm{R}}^2}$

The mass and diameter of a planet are twice those of earth. What will be the period of oscillation of pendulum on this planet if it is a seconds pendulum on earth?
1. $\sqrt{2 } \mathrm{second}$
2. $2\sqrt{2 } \mathrm{second}$
3. $\frac{1}{\sqrt{2}} \mathrm{second}$
4. $\frac{1}{2\sqrt{2}} \mathrm{second}$

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a, and time period T. The speed of pendulum at x = a/2 will be :
$1. \frac{\mathrm{\pi a}\sqrt{3}}{T}$
$2. \frac{\mathrm{\pi a}\sqrt{3}}{2T}$
$3. \frac{3{\pi }^{2}a}{T}$
$4. \frac{\mathrm{\pi a}}{T}$

A particle starts from rest at a distance R from the centre and along the axis of a fixed ring of radius R & mass M. Its velocity at the centre of ring is :
                                         
1. $\sqrt{\frac{\sqrt{2}\mathrm{GM}}{\mathrm{R}}}$
2. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{R}}}$
3. $\sqrt{\left(1-\frac{1}{\sqrt{2}}\right)\frac{\mathrm{GM}}{\mathrm{R}}}$
4. $\sqrt{\left(2 - \sqrt{2}\right)\frac{\mathrm{GM}}{\mathrm{R}}}$

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V. Due to the rotation of the planet about its axis, the acceleration due to gravity g at equator is 1/2 of g at poles. The escape velocity of a particle on the planet in terms of V.
1. V_e = 2V
2. V_e = V
3. V_e = V/2
4. V_e = $\sqrt{3}$V

Two point masses of mass 4m and m respectively separated by d distance are revolving under mutual force of attraction. Ratio of their kinetic energies will be :
1. 1 : 4
2. 1 : 5
3. 1 : 1
4. 1 : 2

Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity  $\frac{{\mathrm{V}}_{\mathrm{A}}}{{\mathrm{V}}_{\mathrm{B}}}$ is -
1. 2
2. $\sqrt{2}$
3. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.$
4. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

A simple harmonic motion having an amplitude A and time period T is represented by the equation: 
$\mathrm{y}=5\sin \pi (\mathrm{t} + 4) \mathrm{m}$
Then the values of A (in m ) and T (in sec ) are:
1. A = 5; T = 2
2. A = 10; T = 1
3. A = 5; T = 1
4. A = 10; T = 2

The displacement of a body executing SHM is given by x= A sin (2$\mathrm{\pi }$t + $\mathrm{\pi }$/3). The first time from t = 0 when the velocity is maximum is :
1. 0.33 sec
2. 0.16 sec
3. 0.25 sec
4. 0.5 sec

The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant. It is possible when :
1. amplitude of oscillation is double while the frequency remains constant
2. amplitude is doubled while frequency is halved 
3. frequency is doubled while the amplitude is halved
4. frequency is doubled while amplitude remains constant

The potential energy of a simple harmonic oscillator of mass 2 kg in its mean position is 5J. If its total energy is 9J and its amplitude is 0.01 m, its time period would be :
1. $\frac{\mathrm{\pi }}{10} \sec$
2. $\frac{\mathrm{\pi }}{20} \sec$
3. $\frac{\mathrm{\pi }}{50} \sec$
4. $\frac{\mathrm{\pi }}{100} \sec$

A plank with a small block on top of it is undergoing vertical SHM. Its period is 2 sec. The minimum amplitude at which the block will separate from plank is :
1.$\frac{10}{{\mathrm{\pi }}^2}$
2. $\frac{{\mathrm{\pi }}^2}{10}$
3. $\frac{20}{{\mathrm{\pi }}^2}$
4. $\frac{\mathrm{\pi }}{10}$

The time period of a particle executing SHM is 8 sec. At t = 0 it is at the mean position. The ratio of the distance covered by the particle in the 1st second to the 2nd second is :
1. $\frac{1}{\sqrt{2} + 1}$
2. $\sqrt{2}$
3. $\frac{1}{\sqrt{2} }$
4. $\sqrt{2} + 1$

The angular velocity of motion whose equation is $4\frac{d^2\mathrm{y}}{d{\mathrm{t}}^2} + 9\mathrm{y} = 0$ is : (y = displacement and t = time) -
1. $\frac{9}{4}$
2. $\frac{4}{9}$
3. $\frac{3}{2}$
4. $\frac{2}{3}$

Two particles are in SHM in a straight line. Amplitude A and time period T of both the particles are equal. At time t = 0, one particle is at displacement Y₁ = + A and the other at Y₂ = -A/2, and they are approaching towards each other. After what time they cross each other?
1. T/3
2. T/4
3. 5T/6
4. T/6

Two particles execute SHM of the same amplitude of \(20\) cm with the same time period along the same line about the same equilibrium position. The maximum distance between the two is \(20\) cm. Their phase difference in radians is:
1. \(\frac{2\pi}{3}\)
2. \(\frac{\pi}{2}\)
3. \(\frac{\pi}{3}\)
4. \(\frac{\pi}{4}\)

Two particles P and Q describe simple harmonic motions of the same period, the same amplitude, along the same line about the same equilibrium position O. When P and Q are on opposite sides of O at the same distance from O, they have the same speed of 1.2 m/s in the same direction. When their displacements are the same, they have the same speed of 1.6 m/s in opposite directions. The maximum velocity in m/s of either particle is 
1. 2.8
2. 2.5
3. 2.4
4. 2

A particle performs SHM with a period T and amplitude a. The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is :
1. a/T
2. 2a/T
3. 3a/T
4. a/2T

If a spring has a time period T and is cut into n equal parts, then the time period of each part will be :
$1. T\sqrt{n}$
$2. \frac{T}{\sqrt{n}}$
$3. nT$
$4. T$

A graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is -

A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will :
1. Remain unchanged 
2. Increase
3. Decrease
4. Become erratic

If a hole is bored along the diameter of the earth and a stone is dropped into the hole :
1. The stone reaches the centre of the earth and stops there
2. The stone reaches the other side of the earth and stops there 
3. The stone executes simple harmonic motion about the centre of the earth 
4. The stone reaches the other side of the earth and escapes into space.

Choose the incorrect answer.
When the point of suspension of the pendulum is moved its period of oscillation -
1. Decreases when it moves vertically upwards with acceleration a 
2. Decreases when it moves vertically downwards with acceleation less than g
3. Increases when it moves horizontally with acceleration a 
4. Decreases when it moves horizontally with acceleration a

A pendulum suspended from the ceiling of a train has period T when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation will 
1. Increase
2. Decrease
3. Remained unaffected
4. Become infinite 

The work done by a string of simple pendulum during one complete oscillation is equal to :
1. Total energy of pendulum
2. Kinetic energy of pendulum
3. Potential energy of pendulum
4. Zero

A particle of mass m is hanging vertically by an ideal spring of force constant K. If the mass is made to oscillate vertically, its total energy is :
1. Maximum at extreme position 
2. Maximum at mean position 
3. Minimum at mean position 
4. Same at all position 

Length of the second's pendulum is decreased by 1%, then the gain or loss in time per day will be : 
1. 432 sec
2. 4.40 sec
3. 44 sec
4. 0.44 sec

A body of mass m is suspended from a rubber cord with force constant K. The maximum distance over which the body can be pulled down for the body's oscillation to remain harmonic is :
1. $\frac{2\mathrm{mg}}{\mathrm{K}}$
2. $\frac{\mathrm{mg}}{\mathrm{K}}$
3. $\frac{2\mathrm{K}}{\mathrm{mg}}$
4. $\frac{\mathrm{mg}}{2\mathrm{K}}$

A particle executes simple harmonic motion along a straight line with an amplitude A. The potential energy is maximum when the displacement is 
1. $\pm \mathrm{A}$
2. Zero
3. $\pm \raisebox{1ex}{$\mathrm{A}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
4. $\pm \raisebox{1ex}{$\mathrm{A}$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.$

The earth moves around the sun in an elliptical orbit as shown in the figure. The ratio $\frac{OA}{OB} = x$. The ratio of the speeds of the earth at B and at A is :

$1. \sqrt{x}$
$2. x$
$3. x^2$
$4. x\sqrt{x}$

A body is released from a point at a distance r from the centre of the earth. If R is the radius of earth and r > R, then the velocity of the body at the time of striking the earth will be:
$1. \sqrt{gR}$
$2. \sqrt{2gR}$
$3. \sqrt{\frac{2gR}{r-R}}$
$4. \sqrt{\frac{2gR(r-R)}{r}}$

A straight rod of length L extends from x = a to x = L+a. The gravitational force, it exerts on a point mass m at x = 0, if mass per unit length is $\mathrm{A}+{\mathrm{Bx}}^2$ is :
(a) $\mathrm{Gm}\left[\mathrm{A}\left(\frac{1}{\mathrm{a}+\mathrm{L}}-\frac{1}{\mathrm{a}}\right)+\mathrm{BL}\right]$
(b) $\mathrm{Gm}\left[\mathrm{A}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{a}+\mathrm{L}}\right)+\mathrm{BL}\right]$
(c) $\mathrm{Gm}\left[\mathrm{A}\left(\frac{1}{\left(\mathrm{a}+\mathrm{L}\right)}-\frac{1}{\mathrm{a}}\right)-\mathrm{BL}\right]$
(d) $\mathrm{Gm}\left[\mathrm{A}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{a}+\mathrm{L}}\right)-\mathrm{BL}\right]$

A body performs SHM. Its kinetic energy K varies with time T as indicated in the graph :

Tobacco plant has been made resistant to the tobacco mosaic virus by :