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The property of water that enables it to

stabilize temperature in bodies of organisms

and thus makes it indispensible for life is:

1. High specific heat

2. High latent heat of fusion

3. High latent heat of vaporization

4. High cohesion and adhesion

The element that makes up the highest

percent weight of the human body is:

1. Carbon

2. Hydrogen

3. Oxygen

4. Nitrogen

The number of high energy bonds in a molecule

of ATP is:

1. 1

2. 2

3. 3

4. 4

The molecule that is never branched and is

straight is:

1. Amylose

2. Amylopectin

3. Glycogen

4. Cellulose

An amino acid that is negative charged amongst

the following will be:

1. Glutamic acid

2. Lysine

3. Arginine

4. Histidine

The correct ascending order of percent

composition of various components of a typical

cell would be:

1. Protein – Carbohydrate – Lipids – Nucleic acids

2. Protein – Nucleic acids – Carbohydrate – Lipids

3. Carbohydrates – Protein – Nucleic acids– Lipids

4. Carbohydrates – Protein – Lipids – Nucleic

acids

Type of bonds that stabilize a tertiary structure

of a protein include all the following except:

1. van der Waal’s interactions

2. Hydrophobic interactions

3. Disulfide linkage

4. Covalent bonds

Protein molecules that assist in the proper

folding of other proteins are known as:

1. Ubiquitins

2. Chaperonins

3. Prions

4. Calmodulins

A ribosome inhibiting secondary metabolite

protein found in the castor plant is:

1. Ricin

2. Abrin

3. Concanvalin A

4. Vinblastin

When an enzyme-substrate reaction tends

toward zero order, the only way to make a

reaction speed up is to:

1. Add more substrate

2. Add more enzyme

3. Increase the temperature

4. Increase the pressure in the medium

The Glucose transpoter protein present in the

baso-lateral surface of the intestinal epithelial

cells is:

1. GLUT 1

2. GLUT 2

3. GLUT 3

4. GLUT 4

The plot represents the relationship between

substrate concentration and velocity for a

single enzyme in the absence (curve x) and

presence (curve y) of a compound that binds

allosterically to the enzyme. The allosteric

compound is:

1. a competitive inhibitor.

2. a noncompetitive inhibitor.

3. an irreversible inhibitor.

4. an activator.

The metal ion that acts as a cofactor for both

alcohol dehydrogenase and carbonic anhydrase

is:

1. Magnesium

2. Iron

3. Zinc

4. Nickel

The living state can be best described as a:

1. non equilibrium steady state

2. non equilibrium non steady state

3. equilibrium non steady state

4. equilibrium steady state

The blood concentration of glucose ina normal

healthy individual is:

1. 3.5 – 4.0 mM

2. 4.0 – 4.5 mM

3. 4.5 – 5.0 mM

4. 5.0 – 5.5 mM

All the following assumptions apply to

Michaelis-Menten kinetic analyses of enzyme

action EXCEPT

1. the total enzyme concentration studied at each

substrate concentration is fixed in analysis of

enzyme kinetics.

2. formation of enzyme-substrate complex does

not appreciably decrease the concentration of

substrate.

3. Km decreases with competitive inhibition.

4. maximal velocity is reached when the enzymesubstrate complex is equal to the total concentration of enzyme present.

The conversion of glucose into lactic acid in

our muscles takes place in:

1. 9 metabolic steps

2. 10 metabolic steps

3. 11 metabolic steps

4. 12 metabolic steps

The living state is synonymous with:

1. Cellular organization

2. Metabolism

3. Consciousness

4. Reproduction

In case of incomplete dominance, the F1

progeny of a monohybrid cross resemble:

1. Either of the parents

2. The male parent

3. Neither of the parents

4. Both parents

What is applicable to both Klinefelter’s

syndrome and Turner’s syndrome?

I. They result from non-disjunction of sex

chromosomes during gamete formation

II. They can be identified by a karyotype

III. They have 44 autosomes

1. I and II only

2. I and III only

3. II and III only

4. I, II and III

An exchange of segments between nonhomologous chromosomes is called as:

1. Crossing over

2. Inversion

3. Reciprocal translocation

4. Transposing

Suppose two genes A and B are located on the

same chromosome but are 60 map units apart.

What fraction of the progeny from the cross

AB/ab x ab/ab would be Ab/ab?

1. 60%

2. 50%

3. 30%

4. 25%

If a father and son are both affected by redgreen colour blindness, then what can be said

definitely?

I. The son has received the trait from the father.

II. The mother of the affected son has to be

affected by red-green colour blindness.

III. Any sister of the affected son can never be

affected by red-green colour blindness,

1. I and II only

2. I and III only

3. II and III only

4. None

If individuals of genotype AaBbCc are

intercrossed, how many different phenotypes

can appear in their offspring?

1. 3

2. 6

3. 8

4. 9

Genes A and B are farther apart than are genes

A and C, and all three are linked. What cannot

be concluded?

1. B might be between A and C.

2. C might be between A and B.

3. A might be between B and C.

4. More crossovers will occur between A and B

than between A and C.

A man of which of the following blood groups

could not be the father of a group O child?

1. A

2. B

3. O

4. AB

Two garden pea dihybrids with round seed

shape and yellow seed color [R_{r}Y_{y}] are

intercrossed. Assuming independent

assortment, the gene for seed shape is

inherited by the progeny in a phenotypic ratio

of:

1. 3 : 1

2. 1 : 1

3. 9 : 3 : 3 : 1

4. 1 : 1 : 1 : 1

The gene for the enzyme Phenylalanine

hydroxylase is located on chromosome:

1. 7

2. 11

3. 12

4. X

A human geneticist determined the pedigree

shown in the diagram with filled symbols

showing the affected individuals. How is this

pattern of inheritance described?

1. autosomal dominant

2. autosomal recessive

3. sex-linked recessive

4. sex-linked dominant

Consider the following statements regarding

Y chromosome in humans:

I. Y chromosome is sex-determining chromosome

in humans

II. Y chromosome contains a gene, SRY, which

triggers embryonic development as a male

III. 50 % of sons of a male inherit his Y

chromosome

Of the given statements, the correct

statements are:

1. I and II only

2. I and III only

3. II and III only

4. I, II and III

Mating between black rats of identical

genotype produced offspring as follows: 14

cream colored, 47 black and 19 albino. This

ratio can be explained if the pheneomenon

exhibited here is:

1. Recessive epistasis

2. Polygenic inheritance

3. Multiple allelism

4. Incomplete penetrance

Identify the incorrect statement regarding test

cross?

1. It is used to determine the genotype of an

individual exhibiting a dominant phenotype.

2. The testcross parent is always homozygous

recessive for all of the genes under

consideration.

3. The purpose of the testcross is to discover how

many different kinds of gametes are being

produced by the individual whose genotype is

in question.

4. A homozygous dominant individual will produce

two types of progeny and a heterozygous

individual will produce only one type of progeny

Sickle cell disease is an example of:

1. Sex linked recessive disorder

2. Pleiotropy

3. Polygenic trait

4. Sex influenced trai

Unattached earlobes is dominant to attached

earlobes. Two parents, both with unattached

earlobes, had a child with attached earlobes.

What are the chances that their next child will

have attached earlobes?

1. 0 %

2. 25 %

3. 50 %

4. 100 %

What decides the frequency of an allele in a

population?

1. Dominance

2. Its location on a particular chromosome

3. Its degree of expression

4. Natural selection

What is the number of linkage groups in

humans?

1. 22

2. 23

3. 24

4. 46

Assuming complete dominance –

recessiveness and independent assortment,

the ratio of progeny with the genotypes AaBb,

AABb, Aabb and aaBb from a cross AaBb X

AABb would respectively be:

1. 4 : 4 : 2 : 0

2. 4 : 2 : 4 : 2

3. 4 : 4 : 2 : 2

4. 4 : 4: 2 : 1

A certain gene has 5 alleles. What will be the

number of possible genotypic combinations?

1. 5

2. 15

3. 32

4. 2

How many unique gametes could be produced

through independent assortment by an

individual with the genotype AaBbCCDdEE?

1. 4

2. 8

3. 16

4. 32

Three babies were mixed up in a hospital. After

consideration of the data below, which of the

following represent the correct baby and parent

combinations?

1. I-3, II-1, III-2

2. I-1, II-3, III-2

3. I-2, II-3, III-1

4. I-2, II-1, III-3

Chromosomes and genes share all of the

following characteristics except that

1. they are both present in pairs in all diploid cells.

2. they both undergo segregation during meiosis.

3. their copy numbers in the cell decrease after

meiosis, and increase during fertilization.

4. they both pair up with their homologues during

prophase of mitosis

The improvement of microscopy techniques

in the late 1800s set the stage for the

emergence of modern genetics because

1. it revealed new and unanticipated features of

Mendel’s pea plant varieties.

2. it allowed biologists to study meiosis and mitosis,

revealing the parallels between the behaviors

of genes and chromosomes.

3. it allowed scientists to see the DNA present

within chromosomes.

4. it led to the discovery of mitochondria

When Thomas Hunt Morgan crossed his

red-eyed F1 generation flies to each other, the

F2 generation included both red- and

white-eyed flies. Remarkably, all the

white-eyed flies were male. What was the

explanation for this result?

1. The involved gene was on the X chromosome.

2. The involved gene was on the Y chromosome.

3. The involved gene was on an autosome.

4. Other male-specific factors influence eye color

in flies

Males are more often affected by sex-linked

traits than females because

1. males are hemizygous for the X chromosome.

2. male hormones such as testosterone often

exacerbate the effects of mutations on the X

chromosome.

3. female hormones such as estrogen often

compensate for the effects of mutations on the

X.

4. X chromosomes in males generally have more

mutations than X chromosomes in females

It was important that Mendel examined not

just the F1 generation in his breeding

experiments, but the F2 generation as well,

because:

1. He obtained very few F1 progeny, making

statistical analysis difficult.

2. Parental traits that were not observed in the F1

reappeared in the F2, suggesting that the traits

did not truly disappear in the F1.

3. Analysis of the F1 progeny would have allowed

him to discover the law of segregation, but not

the law of independent assortment.

4. The dominant phenotypes were visible in the

F2 generation, but not in the F1.

Two true-breeding stocks of pea plants are

crossed. One parent has red, axial flowers and

the other has white, terminal flowers; all F1

individuals have red, axial flowers. If 1,000 F2

offspring resulted from the cross,

approximately how many of them would you

expect to have red, terminal flowers? (Assume

independent assortment).

1. 65

2. 190

3. 250

4. 565

An abnormal human of the karyotype 49,

XXXYY will form how many Barr bodies?

1. 1

2. 2

3. 3

4. 4

When the two genes in a dihybrid cross are

situated on the same chromosome:

1. The proportion of parental gene combinations

was much higher than the non-parental type.

2. The proportion of parental gene combinations

was much lesser than the non-parental type.

3. The proportion of parental gene combinations

was equal to the non-parental type.

4. Only recombinants are formed.

Match each item in COLUMN I with one in

COLUMN II and select your answer from the

codes given:

COLUMN I COLUMN II

SCIENTIST CONTRIBUTION

A. Francis Crick a. Breaking the

genetic gode

B. Nirenberg b. Established

Coenorhabditis

elegans as a model

genetics study

organism

C. Benzer c. Central dogma of

molecular biology

D. Brenner d. Bacteriophage

genetics

Codes:

A B C D

1. c a d b

2. c a b d

3. a b c d

4. a c d b

The mechanism of sex determination in

grasshoppers is:

1. XX – XY; male heterogamety

2. XX – XY; female heterogamety

3. XX – XO; male heterogamety

4. XX – XO; female heterogamety

Male pattern baldness is a ___________ trait.

1. Sex-linked

2. Sex-limited

3. Sex-influenced

4. Y-linked

Griffith co-injected the heat killed S and live

R strains of Pneumococcus bacterium into the

mice and much to his surprise the mice

developed pneumonia and died. He concluded

that:

I. Live R were transformed into Live S strain as

he was able to isolate Live S strain from the

blood of the infected mice.

II. Bacterial transformation is a stable and heritable

change as the culture of bacteria isolated from

dead mice were unable to infect other mice.

1. Both I and II are correct

2. Only I is correct

3. Only II is correct

4. Both I and II are incorrect

The radius of the double helix of B-DNA

[Watson and Crick model] is approximately:

1. 1.0 nm

2. 2.0 nm

3. 0.34 nm

4. 3.4 nm

An RNA primer is essential for DNA synthesis

carried out by DNA polymerase III. This is

because, to synthesize DNA, DNA polymerase

III requires:

1. A free 3’ – PO4 group

2. A free 5’ – PO4 group

3. A free 3’ – OH group

4. A free 5’ – OH group

On examining a sample of human DNA, it was

found that it contains approximately 24 %

thymine. Which of the following would be true

based on this finding?

1. The amount of adenine in a similar sample of

DNA from any human being will be

approximately 24 %.

2. The amount of adenine in a similar sample of

DNA from any living being will be approximately

24 %.

3. The amount of adenine in a similar sample of

DNA from any eukaryotic cell will be

approximately 24 %.

4. The amount of adenine in a similar sample of

DNA from any mammal will be approximately

24 %.

Which of the following possible modes of

replication was eliminated by Meselson and

Stahl based on the finding after one generation

of replication of the bacterium?

1. Dispersive

2. Semi-conservative

3. Conservative

4. Both 1 and 3

What would be the effect of a mutation in the

operator region of the lac operon that leads to

inability of the repressor to bind to the

operator?

1. The lac ZYA genes would be inducible by lactose

2. The lac ZYA genes will be repressed by lactose

3. The lac ZYA genes will not be expressed

4. The lac ZYA genes will be expressed constitutively

. It is possible to insert the DNA from one virus

(virus A) into the protein coat of a different

virus (virus B). If such a composite virus

infected a cell, the resultant viruses produced

in the host cell would have DNA like virus

____ and protein like ______.

1. A;B

2. A;A

3. B;B

4. B;A

The mRNA codon GUG codes for:

1. Valine

2. Glutamic acid

3. Tryptophan

4. Formylated methionine

What defines the template and coding strand

of DNA for transcription?

1. Presence of the structural gene in a transcription unit

2. The core RNA polymerase enzyme

3. Presence of the promoter in a transcription unit

4. Presence of 3’ – 5’ TAC codon on the DNA template

What radioactive isotope was used in Meselson

and Stahl experiment to prove the semiconservative mode of DNA replication?

1. ^{35}S

2. ^{32}P

3. ^{15}N

4. None

In eukaryotes RNA polymerase III

transcribes:

1. hnRNA, snRNAs and 5.8S RNA

2. tRNA, 5.8S RNA and snRNAs

3. tRNA, 5SrRNA and snRNAs

4. rRNAs – 28S, 18S and 5S

Identify the incorrect statement:

1. The DNA of the bacteriophage $\mathrm{\varphi}$ X 174 has

5386 nucleotides

2. Bacteriophage lambda DNA has 48502 base

pairs

3. The DNA of Escherechia coli has 4.6 X 10^{3}

base pairs

4. Haploid content of human DNA is 3.3 X 10^{9}

base pairs

In a DNA strand, two nucleotides are linked

through a ___________ linkage to form a

dinucleotide.

1. 3’ – 5’ phoshodiester bond

2. 5’ – 3’ phosphodiester bond

3. 1’ N-glycosidic bond

4. Two or three hydrogen bonds

A mammalian cell typically has 1.2 meters

(when completely outstretched) of double

stranded genomic DNA. The total time to

duplicate the DNA is 5 hours. How many

origins of replication are there if the rate of

duplication is 16µmeters/min?

1. 250 2. 15000

3. 100 4. 500

The bacterial promotor sequence usually found

at the -10 position (ten base pairs upstream of

the transcription start site) is:

1. TTGACA

2. TAGACA

3. TATAAT

4. TATTAT

Under conditions where methionine must be

the first amino acid, what protein would be

coded for by the following mRNA?

5'-CCUCAUAUGCGCCAUUAUAAGUGACACACA-3'

1. pro his met arg his tyr lys cys his thr

2. met arg his tyr lys cys his thr

3. met arg his tyr lys

4. met pro his met arg his tyr lys cys his thr

Replication in prokaryotes differs from

replication in eukaryotes for which of the

following reasons?

1. Prokaryotic chromosomes have histones,

whereas eukaryotic chromosomes do not.

2. Prokaryotic chromosomes have a single origin

of replication, whereas eukaryotic

chromosomes have many.

3. The rate of elongation during DNA replication

is slower in prokaryotes than in eukaryotes.

4. Prokaryotes produce Okazaki fragments during

DNA replication, but eukaryotes do not.

A molecule of tRNA with anticodon AAA will

transport the amino acid:

1. Lysine

2. Methionine

3. Arginine

4. Phenylalanine

A nonsense mutation typically involves

1. Confusion of which amino acids go where in

the polypeptide chain.

2. Expansions of the ends of chromosomes due to

repeated nucleotides.

3. Inappropriate termination of translation early in

the “reading frame”.

4. A mistake that causes a portion of a

chromosome to “flip” in orientation.

Regarding gene expression, which of these

accurately distinguish prokaryotes from

eukaryotes?

1. Nucleotides in the promoter are different in

prokaryotes and eukaryotes.

2. Genes are more widely-spaced apart in

eukaryotes than prokaryotes.

3. Prokaryotic ribosomes look different than

eukaryotic ones.

4. Prokaryotic ribosomes translate mRNA

transcripts that are still being synthesized by

RNA polymerase.

The region of a gene which “tells” RNA

polymerase where the genetic message is

located is called the:

1. Start codon.

2. Promoter.

3. Transcription factor.

4. Initiator.

Which is responsible for the production of a

peptide bond between adjacent amino acids

during translation?

1. Peptidyl transferase activity of the large subunit.

2. Proteins in the large and small subunit of the

ribosome.

3. Ribozyme activity of tRNA.

4. The charging effect of aminoacyl tRNA

synthetase.

Which of the following is likely if there is a

mutation in the lacY gene of the lac operon in

E.coli?

1. The lac genes would be expressed efficiently

only in the absence of lactose.

2. The lac genes would be expressed efficiently

until the lactose supply in the cell is exhausted.

3. The lac genes would be expressed continuously.

4. Expression of the lac genes would cease

immediately.

Consider the following two statements:

I. During transcription, the template strand is read

in a 3'-to-5' direction.

II. During transcription, an RNA is transcribed in

the 5'-to-3' direction.

The correct statements is/are:

1. I only

2. II. Only

3. I and II

4. None

Identify the correct statements from the given

statements and choose the correct option:

I. Both prokaryotic and eukaryotic mRNAs have

a 5' cap.

II. Only prokaryotic mRNAs are polyadenylated

at the 3' end.

III. In prokaryotes, transcription is coupled to

translation.

IV. In eukaryotes, RNA splicing occurs after the

mRNA is transported into the cytoplasm.

V. RNA splicing requires the formation of a

spliceosome.

VI. Both prokaryotic and eukaryotic mRNAs are

synthesized by RNA polymerase.

1. III, V and VI only

2. II, III, V and VI only

3. I, III, V and VI only

4. I, III, IV, V and VI only

A molecule that can act as a genetic material

must fulfill all the following criteria except:

1. It should be able to generate its replica.

2. It should chemically and structurally be stable.

3. It should be able to express itself in the form of

Medelian characters.

4. It should provide scope for rapid changes

required for evolution.

Histones are rich in:

1. Basic amino acids lysine and arginine

2. Acidic amino acids lysine and arginine

3. Basic amino acids glutamate and aspartate

4. Acidic amino acids glutamate and aspartate

The difference between ATP and the

nucleoside triphosphates used during DNA

synthesis is that

1. The nucleoside triphosphates have the sugar

deoxyribose; ATP has the sugar ribose.

2. The nucleoside triphosphates have two

phosphate groups; ATP has three phosphate

groups.

3. ATP contains three high-energy bonds; the

nucleoside triphosphates have two.

4. ATP is found only in human cells; the nucleoside

triphosphates are found in all animal and plant

cells.

In E. coli, there is a mutation in a gene called

dnaB that alters the helicase that normally acts

at the origin. Which of the following would you

expect as a result of this mutation?

1. No proofreading will occur.

2. No replication fork will be formed.

3. The DNA will supercoil.

4. Replication will occur via RNA polymerase

alone.

If pre-mRNA is hybridized with mature mRNA,

regions loop out and can be viewed with an

electron microscope. What do the looped out

regions represent?

1. Excised exons.

2. Introns to be excised later.

3. Exons in the pre-mRNA.

4. Exons that are in the process of being fused

together.

The first genetic code of life was most likely

based on:

1. RNA

2. Single stranded DNA

3. Double stranded DNA

4. Proteins

The lac repressor protein binds to the operator

region...

1. in the absence of lactose

2. in the presence of lactose

3. in the presence of cAMP

4. in the presence of glucose

tRNA molecules are linked to their respective

amino acids by enzymes called:

1. Phenylalanine hydroxylases

2. Beta-galactosidases

3. Ornithine decarboxylases

4. Aminoacyl-tRNA synthetases

Which of the following pairs of codons encode

the same amino acid?

1. AUG and AUC

2. UAA and UAC

3. GUA and GUG

4. UAG and UAC

Which of the following most accurately restates

Mendel’s law of segregation?

1. Genes are inherited in discrete units from one

generation to the next.

2. Genes can exist in different forms, known as

alleles.

3. Homologous chromosomes separate during

gamete formation.

4. Genes on different chromosomes are inherited

independently.

What key characteristic of T2 bacteriophage

allowed Hershey and Chase to use it in their

studies of the genetic material?

1. Its genes encode proteins that assemble to

produce the viral coat.

2. It injects its genetic material into a bacterial cell.

3. It can undergo either the lytic or lysogenic life

cycle.

4. It enters the bacterial cell to cause infection.

Which of the following is a description of

chromatin?

1. All the genetic sequences contained by

members of a particular species.

2. The DNA-protein complex which comprises

eukaryotic chromosomes.

3. Repetitive sequences contained within the

genome of an organism.

4. The protein coding sequences and their

regulatory elements.

What is a key difference between DNA pol III

and DNA ligase?

1. Only DNA pol III synthesizes phosphoester bonds.

2. Only DNA ligase synthesizes phosphoester bonds.

3. DNA pol III can synthesize DNA from 3'-5'.

4. DNA ligase can use energy from ATP rather

than nucleotides.

A recessive pair in garden pea plant will be

1. Round pea shape

2. Yellow seed colour

3. Yello pods

4. Axial flowers

A mixture of carbon monoxide and carbon dioxide is found to have a density of 1.7 g/L at S.T.P. The mole fraction of carbon monoxide is-

1. 0.37

2. 0.40

3. 0.30

4. 0.50

At constant temperature, if pressure increases by 1%, the percentage decrease of volume is-

1. 1%

2. 100/101%

3. 1/101%

4. 1/100%

A flask containing air (open to atmosphere) is heated from 300 *K* to 500 *K*. The percentage of air escaped to the atmosphere is nearly-** **

1. 16.6

2. 40

3. 66

4. 20

The correct order of solubility in an aqueous medium is:

1. CuS > ZnS > Na_{2}S

2. ZnS > Na_{2}S > CuS

3. Na_{2}S > CuS > ZnS

4. Na_{2}S > ZnS > CuS

25.3 g of Sodium carbonate Na_{2}CO_{3} is dissolved in enough water to make 250 mL of

solution. If sodium carbonate dissociates completely, molar concentration of sodium ion,

Na^{+} and carbonate ion ${\mathrm{CO}}_{3}^{2-}$ are respectively (Molar mass of Na_{2}CO_{3} = 106 g mol^{-1})

1. 0.955 M and 1.910 M

2. 1.910 M and 0.955 M

3. 1.90 M and 1.910 M

4. 0.477 M and 0.477 M

The correct order of decreasing second ionisation enthalpy of Ti (22), V (23), Cr (24) and Mn (25) is

(1) Cr > Mn > V > Ti

(2) V > Mn > Cr > Ti

(3) Mn > Cr > Ti > V

(4) Ti > V > Cr > Mn

The correct order of increasing thermal stability of K_{2}CO_{3}, MgCO_{3}, CaCO_{3} and BeCO_{3 }is:

(1) BeCO_{3} < MgCO_{3} < K_{2}CO_{3 }< CaCO_{3}

(2) BeCO_{3} < MgCO_{3} < CaCO_{3} < K_{2}CO_{3}

(3) MgCO_{3} < BeCO_{3} < CaCO_{3} < K_{2}CO_{3}

(4) K_{2}CO_{3} < MgCO_{3} < CaCO_{3} < BeCO_{3}

Concentrated aqueous sulphuric acid is 98% ${\mathrm{H}}_{2}{\mathrm{SO}}_{4}$ by mass and has a density of 1.80 g mL^{-1}. Volume of acid required to make one litre of 0.1 M H_{2}S0_{4} solution is :

(1) 11.10 mL

(2) 16.65 mL

(3) 22.20 mL

(4) 5.55 mL

The electronegativity difference between N and F is greater than that between N and H yet the dipole moment of NH_{3} (1.5 D) is larger than that of NF_{3} (0.2 D). This is because:

(1) in NH_{3} as well as in NF_{3} the atomic dipole and bond dipole are in the same direction

(2) in NH_{3} the atomic dipole and bond dipole are in the same direction whereas in NF_{3 }these are in opposite directions

(3) in NH_{3} as well as NF_{3} the atomic dipole and bond dipole are in opposite directions

(4) in NH_{3} the atomic dipole and bond dipole are in the opposite directions whereas in NF_{3} these are in the same directions

If the IUPAC name of an element is "unununium", then the correct statement regarding the element is:

1. It is an inner transition element .

2. It belongs to the 8th period in the periodic table .

3. It is a transition element .

4. It is a non-transition element.

The radius of which ion is closest to that of $L{i}^{+}$ ion ?

1. $N{a}^{+}$

2. $B{e}^{2+}$

3. $M{g}^{2+}$

4. $A{l}^{3+}$

The correct order of ${\mathrm{IE}}_{2}$ is:

(1) Ne>F>O>N

(2) O>F>Ne>N

(3) Ne>O>F>N

(4) O>Ne>F>N

Which of the following compound is most acidic?

1. $C{l}_{2}{O}_{7}$ 2. ${P}_{4}{O}_{10}$

3. $S{O}_{3}$ 4. ${B}_{2}{O}_{3}$

If *P* and *T* are second period p-block elements then which of the following graph show correct relation between valence electrons in ${P}_{2}$ to ${T}_{2}$ (corresponding molecules) and their bond order is :

(a)

(b)

(c)

(d)

Consider the following changes:

$M\left(s\right)\to M\left(g\right).....\left(i\right)\phantom{\rule{0ex}{0ex}}M\left(s\right)\to {M}^{2+}\left(g\right)+2{e}^{-}.....\left(ii\right)\phantom{\rule{0ex}{0ex}}M\left(g\right)\to {M}^{+}\left(g\right)+{e}^{-}.....\left(iiii\right)\phantom{\rule{0ex}{0ex}}{M}^{+}\left(g\right)\to {M}^{2+}\left(g\right)+{e}^{-}......\left(iv\right)\phantom{\rule{0ex}{0ex}}M\left(g\right)\to {M}^{2+}\left(g\right)+2{e}^{-}......\left(v\right)$

The second ionization energy of M could be calculated from the energy values associated with :

(a) 1+3+4 (b) 2-1+3

(c) 1+5 (d) 5-3

Incorrect statement among the following is -

1. Van der Waals' radius of iodine is more than its covalent radius

2. All isoelectronic ions belong to the same period of the periodic table

3. $\mathrm{I}.{\mathrm{E}}_{1}$ of N is higher than that of O while $\mathrm{I}.{\mathrm{E}}_{2}$ of O is higher than that of N

4. The electron affinity N is almost zero while that of P is 74.3 kJ $mo{l}^{-1}$

First three ionisation energies (in kJ/mol) of three representative elements are given below:

Element $I{E}_{1}$ $I{E}_{2}$ $I{E}_{3}$

P 495.8 4562 6910

Q 737.7 1451 7733

R 577.5 1817 2745

Then incorrect option is :

1. Q: Alkaline earth metal.

2. P: Alkali metal.

3. R: s-block element.

4. All three: P,Q & R belong to the same period.

The incorrect statement is:

(1) The second ionisation energy of Se is greater than that of second ionisation energy of As

(2) The first ionisation energy of ${C}^{2+}$ ion is greater than that of first ionisation energy of ${N}^{2+}$ ion

(3) The third ionisation energy of F is greater than that of third ionisation energy of O

(4) Helogens have highest I.E. in respective period

The process requiring the absorption of energy is :

1. $F\to {F}^{-}$

2. $H\to {H}^{-}$

3. $Cl\to C{l}^{-}$

4. $O\to {O}^{2-}$

Given below are four orders for the size of the species. Choose the correct ones :

(a) ${\mathrm{Al}}^{3+}<{\mathrm{Mg}}^{2+}<{\mathrm{Na}}^{+}<{\mathrm{F}}^{-}$

(b) ${\mathrm{Al}}^{3+}<{\mathrm{Mg}}^{2+}<{\mathrm{Li}}^{+}{\mathrm{K}}^{+}$

(c) ${\mathrm{Fe}}^{4+}<{\mathrm{Fe}}^{3+}<{\mathrm{Fe}}^{2+}<\mathrm{Fe}$

(d) $\mathrm{Mg}>\mathrm{Al}>\mathrm{Si}>\mathrm{P}$

1. (a), (b) & (c)

2. (b), (c) & (d)

3. (a), (c)

4. (a), (b), (c) & (d)

The van der waals' constants for a gas are : $\mathrm{a}=4{\mathrm{lit}}^{2}\mathrm{atm}{\mathrm{mol}}^{\u20132},\mathrm{b}=0.04\mathrm{lit}{\mathrm{mol}}^{\u20131}$. lts Boyle temperature is roughly

(1) ${100}^{0}\mathrm{C}$

(2) $1220\mathrm{K}$

(3) ${1220}^{0}\mathrm{C}$

(4) $1600\mathrm{K}$

${\mathrm{SO}}_{3}$(g) decomposes according to the equation

$2{\mathrm{SO}}_{3}\left(\mathrm{g}\right)\stackrel{}{\to}2{\mathrm{SO}}_{2}\left(\mathrm{g}\right)+{\mathrm{O}}_{2}\left(\mathrm{g}\right)$

A sealed container contains 0.5 mol of ${\mathrm{SO}}_{3}$ gas at 100°C and 2 atm pressure. What would be the pressure in the container if the ${\mathrm{SO}}_{3}$ gas is decomposed completely according to the above equation and the temperature were maintained at 100°C –

(A) 0.5 atm

(B) 1.0 atm

(C) 2.0 atm

(D) 3.0 atm

Two flasks A and B of equal volume containing ${\mathrm{NH}}_{3}$ and HCl gases, are connected by a narrow tube of negligible volume. The two gases were prevented from mixing by stopper fitted in connecting tube. For further detail of experiment refer to the given figure. What will be final pressure in each flask when passage connecting two tubes are opened. Assume ideal gas behaviour of ${\mathrm{NH}}_{3}$ and $\mathrm{HCl}$ gas and the reaction.

(1) 40 mm Hg

(2) 60 mm Hg

(3) 20 mm Hg

(4) 10 mm Hg

The valves X and Y are opened simultaneously. The white fumes of ${\mathrm{NH}}_{4}\mathrm{Cl}$ will first form at :

(1) A

(2) B

(3) C

(4) A, B and C simultaneously

Two flasks of equal volume are connected by a narrow tube (of negligible volume) at 27ºC and contain 0.70 mole of ${\mathrm{H}}_{2}$ at 0.5 atm. One of the flasks is then immersed in a hot bath, kept at 127 ºC, while the other remains at 27 ºC. The final pressure is -

1. 5.714 atm

2. 0.5714 atm

3. 2.5214 atm

4. 5.5114 atm

Calculate number of electrons present in 9.5 g of ${\mathrm{PO}}_{4}^{3-}$:

1. $6$

2. $5{\mathrm{N}}_{\mathrm{A}}$

3. $0.1{\mathrm{N}}_{\mathrm{A}}$

4. $4.7{\mathrm{N}}_{\mathrm{A}}$

Equivalent weight of ${\mathrm{H}}_{3}{\mathrm{PO}}_{2}$ when it disproportionate into ${\mathrm{PH}}_{3}$ and ${\mathrm{H}}_{3}{\mathrm{PO}}_{3}$ is:

1. M

2. M/2

3. M/4

4. 3M/4

Density of dry air containing only ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$ is 1.15 g/L at 740 mm and 300 K. What is % composition of ${\mathrm{N}}_{2}$ by weight in the air?

1. 78%

2. 75.5%

3. 70.02%

4. 72.75%

In preparation of iron from haematite $\left(F{e}_{2}{O}_{3}\right)$by the reaction with carbon

$F{e}_{2}{O}_{3}+C\to Fe+C{O}_{2}$

How much 80% pure iron could be produced from 120 kg of 90% pure $F{e}_{2}{O}_{3}$ ?

1. 94.5 kg

2. 60.48 kg

3. 116.66 kg

4. 120 kg

A mixture of $N{H}_{4}N{O}_{3}and(N{H}_{4}{)}_{2}HP{O}_{4}$ contain 30.40% mass per cent of nitrogen. What is the mass ratio of the two components in the mixture?

1. 2 : 1

2. 1 : 2

3. 3 : 4

4. 4 : 1

0.607 g of a silver salt of tribasic organic acid was quantitatively reduced to 0.37 g of pure Ag.What is the mol. wt. of the acid?

1. 207 g

2. 210 g

3. 531 g

4. 324g

2.0 g sample contain mixture of ${\mathrm{SiO}}_{2}$ and ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$, on very strong heating leave a residue weighing 1.96 g. The reaction responsible for loss of weight is ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}\left(\mathrm{s}\right)\stackrel{}{\to}{\mathrm{Fe}}_{3}{\mathrm{O}}_{4}\left(\mathrm{s}\right)+{\mathrm{O}}_{2}\left(\mathrm{g}\right)$ (unbalance equation)

What is the percentage by mass of ${\mathrm{SiO}}_{2}$ in original sample?

1. 10%

2. 20%

3. 40%

4. 60%

0.8 mole of a mixture of CO and CO_{2} requires exactly 40 gram of NaOH in solution for complete conversion of all the CO_{2} into Na_{2}CO_{3}. How many moles more of NaOH would it require for conversion into Na_{2}CO_{3}, if mixture (0.8 mole) is completely oxidised to CO_{2}?

1. 0.2

2. 0.6

3. 1

4. 1.5

25.4 g of ${\mathrm{I}}_{2}$ and 14.2 g of ${\mathrm{Cl}}_{2}$ are made to react completely to yield a mixture of ICI and ICI_{3}. The mole of ICI and ICI_{3} formed, is respectively -

1. 0.5, 0.2

2. 0.1, 0.1

3. 0.1, 0.3

4. 0.3, 0.4

60 mL of a mixture of nitrous oxide and nitric oxide was exploded with excess of hydrogen. If 38 mL of ${\mathrm{N}}_{2}$ was formed, calculate the volume of each gas in the mixture. All measurements are made at constant P and T.

1.20 ml +30 ml

2. 44 ml + 16 ml

3. 10 ml+40 ml

4 .25 ml +25 ml

The angular momentum of an electron in d orbital is equal to

1. $\sqrt{6}\overline{)\mathrm{h}}$

2. $\sqrt{2}\mathrm{h}$

3. $2\sqrt{3}\mathrm{h}$

4. 0 h

The haemoglobin from the red blood corpuscles contains approximately 0.33% iron by mass. The molar mass of haemoglobin is 67,200. The number of iron atoms in each molecule of haemoglobin is -

(atomic mass of iron=56):

1. 2

2. 3

3. 4

4. 5

Which mixture is lighter than humid air?

1. ${\mathrm{N}}_{2}+{\mathrm{O}}_{2}+{\mathrm{SO}}_{2}$

2. ${\mathrm{N}}_{2}+{\mathrm{O}}_{2}+{\mathrm{CO}}_{2}$

3. ${\mathrm{N}}_{2}+{\mathrm{O}}_{2}+{\mathrm{C}}_{2}{\mathrm{H}}_{6}$

4. ${\mathrm{N}}_{2}+{\mathrm{O}}_{2}+\mathrm{He}$

Which is not correct curve for gay-lusacc's law?

1 .

2.

3.

4.

Four particles have speed 2, 3, 4 and 5 cm/s respectively. Their rms speed is:

1. $3.5\mathrm{cm}/\mathrm{s}$

2. $\left(27/2\right)\mathrm{cm}/\mathrm{s}$

3. $\sqrt{54}\mathrm{cm}/\mathrm{s}$

4. $\left(\sqrt{54}/2\right)\mathrm{cm}/\mathrm{s}$

The compressibility factor for nitrogen at 330 K and 800 atm is 1.90 and at 570 K and 200 atm is 1.10. A certain mass of ${\mathrm{N}}_{2}$ occupies a volume of $1{\mathrm{dm}}^{3}$ at 330 K and 800 atm. Calculate volume occupied by same quantity of ${\mathrm{N}}_{2}$ gas at 570 K and 200 atm:

1. 1 L

2. 2 L

3. 3 L

4. 4 L

The van der Waals parameters for gases W, X, Y and Z are

Gas |
a (atm L |
b(L mol |

W |
4.0 |
0.027 |

X |
8.0 |
0.030 |

Y |
6.0 |
0.032 |

Z |
12.0 |
0.027 |

Which one of these gases has the highest critical temperature?

1. W

2. X

3. Y

4. Z

The temperature at which the second virial coefficient of real gas is zero is called:

1. Critical temperature

2. Triple point

3. Boiling point

4. Boyle's temperature

What will happen to gas if it is adiabatically expanded at 600 K if its Boyle's temperature is 290 K?

1. Heating

2. Cooling

3. Constant

4. None

The van der Waal's equation of law of corresponding states for 1 mole of gas is:

1. $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^{2}}\right)\left(3{\mathrm{V}}_{\mathrm{r}}-1\right)=8{\mathrm{T}}_{\mathrm{r}}$

2. $\left({\mathrm{P}}_{\mathrm{r}}-\frac{3}{{\mathrm{V}}_{\mathrm{r}}^{2}}\right)\left(3{\mathrm{V}}_{\mathrm{r}}-1\right)=8{\mathrm{T}}_{\mathrm{r}}$

3. $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^{2}}\right)\left(3{\mathrm{V}}_{\mathrm{r}}+1\right)=8{\mathrm{\pi T}}_{\mathrm{r}}$

4. $\left({\mathrm{P}}_{\mathrm{r}}+\frac{3}{{\mathrm{V}}_{\mathrm{r}}^{2}}\right)\left(3{\mathrm{V}}_{\mathrm{r}}+1\right)=8$

Energy due to position of a particle is given by, $\mathrm{U}=\frac{\mathrm{\alpha}\sqrt{\mathrm{y}}}{\mathrm{y}+\mathrm{\beta}}$, where $\mathrm{\alpha}$ and $\mathrm{\beta}$ are constants, y is distance. The dimensions of ($\mathrm{\alpha}$ × $\mathrm{\beta}$) are

1. $\left[{\mathrm{M}}^{0}{\mathrm{LT}}^{0}\right]$

2. $\left[{\mathrm{M}}^{1/2}{\mathrm{L}}^{3/2}{\mathrm{T}}^{-2}\right]$

3. $\left[{\mathrm{M}}^{0}{\mathrm{L}}^{-7/2}{\mathrm{T}}^{0}\right]$

4. $\left[{\mathrm{ML}}^{7/2}{\mathrm{T}}^{-2}\right]$

A physical quantity x depends on qualities y and z as follows: x = Ay + B tanCz , where A, B and C are constants. Which of the following do not have the same dimensions?

1. x and B

2. C and ${\mathrm{z}}^{-1}$

3. y and B/A

4. x and A

A dust particle oscillates in air with a time period which depends on atmospheric pressure P, density of air d and energy of the particle E, then time period is proportional to

1. ${\mathrm{p}}^{5/6}{\mathrm{d}}^{1/2}{\mathrm{E}}^{1/3}$

2. ${\mathrm{p}}^{1/2}{\mathrm{d}}^{3}{\mathrm{E}}^{1/3}$

3. ${\mathrm{p}}^{1/3}{\mathrm{d}}^{1/2}{\mathrm{E}}^{2}$

4. ${\mathrm{p}}^{-2}{\mathrm{d}}^{-1/2}{\mathrm{E}}^{-3}$

Which of the following group have different dimension?

1. Potential difference, EMF, voltage

2. Pressure, stress, Young’s modulus

3. Heat, energy, work-done

4. Dipole moment, electric-flux, electric field

If a copper wire is stretched to make its radius decrease by 0.1%, then the percentage increase in resistance is approximately

1. 0.1 %

2. 0.2 %

3. 0.4%

4. 0.8%

Two resistances of 400 $\mathrm{\Omega}$ and 800 $\mathrm{\Omega}$ connected in series with a 6 volt battery of negligible internal resistance. A voltmeter of resistance 10,000$\mathrm{\Omega}$ is used to measure the potential difference across 400 $\mathrm{\Omega}$. The error in the measurement of potential

difference in volts approximately is

1. 0.01

2. 0.02

3. 0.08

4. 0.05

If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is

1. 25 %

2. 50 %

3. 100 %

4. 125

The diameter of a wire is measured with a screw gauge having 50 divisions on circular scale and by one complete rotation of circular scale, main scale moves 0.5 mm. If reading of screw gauge is 0.250 cm. The minimum percentage error in the reading will be

1. 0.4

2. 0.8

3. 4

4. 5

The pitch of a screw gauge is 1 mm and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is:

1. 2.71 mm

2. 2.67 mm

3. 2.63 mm

4. 2.65 mm

What are the dimensions of electrical permittivity?

1. ${\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}{\mathrm{Q}}^{-2}$

2. ${\mathrm{M}}^{-1}{\mathrm{L}}^{2}{\mathrm{T}}^{-3}{\mathrm{Q}}^{-1}$

3. ${\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{T}}^{2}{\mathrm{Q}}^{2}$

4. ${\mathrm{M}}^{-1}{\mathrm{L}}^{3}{\mathrm{T}}^{-2}{\mathrm{Q}}^{-2}$

We have error in the measurement of length, radius, mass and current of a wire are 2%, 3%, 2% and 1% then error in its density will be

1. 11%

2. 8%

3. 10%

4. 7%

The velocity of water waves may depend on their wavelength $\mathrm{\lambda}$, the density of water $\mathrm{\rho}$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

1. ${\mathrm{v}}^{2}\propto {\mathrm{\lambda g}}^{-1}{\mathrm{\rho}}^{-1}$

2. ${\mathrm{v}}^{2}\propto \mathrm{g\lambda}$

3. ${\mathrm{v}}^{2}\propto \mathrm{\lambda g\rho}$

4. ${\mathrm{v}}^{2}\propto {\mathrm{g}}^{-1}{\mathrm{\lambda}}^{-2}$

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as $\mathrm{v}=\mathrm{\alpha}\sqrt{\mathrm{x}}$ . The displacement of the particle varies with time as

1. ${\mathrm{t}}^{3}$

2. ${\mathrm{t}}^{2}$

3. t

4. ${\mathrm{t}}^{1/2}$

Position-time curve of a body moving along a

straight line is shown in figure. The velocity-time

curve for the motion of the particle will be

1.

2.

3.

4.

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement(s) – velocity (v) graph of this object is

1.

2.

3.

4.

A body is thrown up in a lift with an upward velocity u relative to the lift from its floor and the time of flight is found to be t. The acceleration of the lift will be

1. $\frac{\mathrm{u}-\mathrm{gt}}{2}$

2. $\frac{\mathrm{u}+\mathrm{gt}}{2}$

3. $\frac{2\mathrm{u}-\mathrm{gt}}{2}$

4. $\frac{\mathrm{u}}{\mathrm{t}}-g$

In a car race, car A takes t0 time less to finish than car B and passes the finishing point with a velocity v_{0} more than car B. The cars start from rest and travel with constant accelerations a_{1} and a_{2}. Then the ratio $\frac{{\mathrm{v}}_{0}}{{\mathrm{t}}_{0}}$ is equal to

1. $\frac{{\mathrm{a}}_{1}^{2}}{{\mathrm{a}}_{2}}$

2. $\frac{{\mathrm{a}}_{1}+{\mathrm{a}}_{2}}{2}$

3. $\sqrt{{\mathrm{a}}_{1}{\mathrm{a}}_{2}}$

4. $\frac{{\mathrm{a}}_{2}^{2}}{{\mathrm{a}}_{1}}$

Acceleration of a particle moving along a straight line is a function of velocity as $\mathrm{a}=2\sqrt{\mathrm{v}}$. At t = 2s, its velocity v = 16 ${\mathrm{ms}}^{-1}$. Its velocity at t = 3s will be

1. 20 ${\mathrm{ms}}^{-1}$

2. 25 ${\mathrm{ms}}^{-1}$

3. 30 ${\mathrm{ms}}^{-1}$

4. 22.5 ${\mathrm{ms}}^{-1}$

A particle moving with uniform retardation along a straight line covers distances a and b in successive intervals p and q seconds. The acceleration of the particle is

1. $\frac{2\left(\mathrm{aq}-\mathrm{bp}\right)}{\mathrm{q}\left(\mathrm{p}+\mathrm{q}\right)}$

2. $\frac{2\left(\mathrm{bp}-\mathrm{aq}\right)}{\mathrm{q}\left(\mathrm{p}+\mathrm{q}\right)}$

3. $\frac{2\left(\mathrm{aq}+\mathrm{bp}\right)}{\mathrm{q}\left(\mathrm{p}+\mathrm{q}\right)}$

4. $\frac{2\left(\mathrm{aq}-\mathrm{bp}\right)}{\mathrm{q}\left(\mathrm{p}+\mathrm{q}\right)}$

A bus is beginning to move with an acceleration of 1 m/s^{2}. A boy who is 48 m behind the bus starts running with constant speed of 10 m/s. The earliest time when the boy can catch the bus is

1. 8 sec

2. 10 sec

3. 12 sec

4. 14 sec

A particle has an initial velocity 11 m/s due east and a constant acceleration of 2 m/s^{2} due west. The distance covered by the particle in sixth second is

1. zero

2. 0.5 m

3. 1 m

4. 2 m

A point moves in a straight line so that its displacement x metre at time t sec is given by ${\mathrm{x}}^{2}=1+{\mathrm{t}}^{2}$ . Its acceleration in m/s^{2 }at time t sec is

1. $\frac{1}{{\mathrm{x}}^{3}}$

2. $\frac{1}{\mathrm{x}}-\frac{1}{{x}^{2}}$

3. $\frac{1}{\mathrm{x}}-\frac{{t}^{2}}{{x}^{3}}$

4. $\frac{-\mathrm{t}}{{\mathrm{x}}^{2}}$

A body starts from rest with uniform acceleration and remains in motion for n seconds. If its final velocity after n second is v, then its displacement in the last two seconds will be

1. $\frac{2\mathrm{v}\left(\mathrm{n}+1\right)}{\mathrm{n}}$

2. $\frac{\mathrm{v}\left(\mathrm{n}+1\right)}{\mathrm{n}}$

3. $\frac{\mathrm{v}\left(\mathrm{n}-1\right)}{\mathrm{n}}$

4. $\frac{2\mathrm{v}\left(\mathrm{n}-1\right)}{\mathrm{n}}$

Two particles A and B are separated from each other by a distance l. At time t = 0, particle A starts moving with uniform acceleration a along a line perpendicular to the initial line joining A and B. At the same moment, particle B starts moving with acceleration of constant magnitude b (> a) such that particle B always points towards the instantaneous position of A. The distance travelled by B till the moment B converges with A will be

1. $\frac{{\mathrm{b}}^{2}\mathrm{l}}{{\mathrm{b}}^{2}-{\mathrm{a}}^{2}}$

2. $\frac{{a}^{2}\mathrm{l}}{{\mathrm{b}}^{2}-{\mathrm{a}}^{2}}$

3. $\frac{\left({b}^{\mathit{2}}\mathit{+}{a}^{2}\right)\mathrm{l}}{{\mathrm{b}}^{2}-{\mathrm{a}}^{2}}$

4. $\frac{\left({b}^{\mathit{2}}\mathit{-}{a}^{2}\right)\mathrm{l}}{{\mathrm{b}}^{2}+{\mathrm{a}}^{2}}$

An aeroplane is rising vertically with acceleration f. Two stones are dropped from it at an interval of time t. The distance between them at time t' after the second stone is dropped will be

1. $\frac{1}{2}\left(g+f\right)tt\text{'}$

2. $\frac{1}{2}\left(g+f\right)\left(t+2t\text{'}\right)t$

3. $\frac{1}{2}\left(g+f\right){\left(t-t\text{'}\right)}^{2}$

4. $\frac{1}{2}\left(g+f\right){\left(t+t\text{'}\right)}^{2}$

The moment of the force, $\overrightarrow{\mathrm{F}}=4\hat{i}+5\hat{j}-6\hat{k}$ at (2, 0, -3), about point (2, -2, -2), is given by

1. $-8\hat{\mathrm{i}}-4\hat{\mathrm{j}}-7\hat{\mathrm{k}}$

2. $-4\hat{\mathrm{i}}-\hat{\mathrm{j}}-8\hat{\mathrm{k}}$

3. $-7\hat{\mathrm{i}}-4\hat{\mathrm{j}}-8\hat{\mathrm{k}}$

4. $-7\hat{\mathrm{i}}-8\hat{\mathrm{j}}-4\hat{\mathrm{k}}$

A particle moves so that its position vector is given by $\overrightarrow{\mathrm{r}}=\mathrm{cos}\omega t\hat{x}+\hspace{0.17em}\mathrm{sin}\mathrm{\omega t}\hat{\mathrm{y}}$. Where $\mathrm{\omega}$ is a constant. Which of the following is true?

1. Velocity and acceleration both are perpendicular to $\overrightarrow{\mathrm{r}}$

2. Velocity and acceleration both are parallel to $\overrightarrow{\mathrm{r}}$

3. Velocity is perpendicular to $\overrightarrow{\mathrm{r}}$ and acceleration is directed towards the origin

4. Velocity is perpendicular to $\overrightarrow{\mathrm{r}}$ and acceleration is directed away from the origin.

The position vector of a particle $\overrightarrow{\mathrm{R}}$ as a function of time is given by :

$\overrightarrow{\mathrm{R}}=4\mathrm{sin}\left(2\pi t\right)\hat{i}+4\mathrm{cos}\left(2\pi t\right)\hat{j}$ . Where R is in meter, t is in seconds and $\hat{\mathrm{i}}\mathrm{and}\hat{\mathrm{j}}$ denote unit vectors along x- and y-directions, respectively ?

Which one of the following statements is wrong for the motion of particle ?

1. Magnitude of acceleration vector is $\frac{{\mathrm{v}}^{2}}{\mathrm{R}}$, where v is the velocity of particle

2. Magnitude of the velocity of particle is 8 meter/second

3. Path of the particle is a circle of radius 4 meter.

4. Acceleration vector is along $\overrightarrow{\mathrm{R}}$

If vector $\overrightarrow{\mathrm{A}}=\mathrm{cos}\omega t\hat{i}+\mathrm{sin}\omega t\hat{j}$ and $\overrightarrow{\mathrm{B}}=\mathrm{cos}\frac{\omega t}{2}\hat{i}+\mathrm{sin}\frac{\omega t}{2}\hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other will be:

1. $\mathrm{t}=\frac{\mathrm{\pi}}{2\mathrm{\omega}}$

2. $\mathrm{t}=\frac{\mathrm{\pi}}{\mathrm{\omega}}$

3. $\mathrm{t}=0$

4. $\mathrm{t}=\frac{\mathrm{\pi}}{4\mathrm{\omega}}$

Two forces are acting as shown in figure. The resultant of the two forces is

1. $5\sqrt{3}\mathrm{N}$

2. $10\sqrt{3}\mathrm{N}$

3. $5\sqrt{5}\mathrm{N}$

4. None of these

A ship A is moving Westwards with a speed of 10 $\mathrm{km}{\mathrm{h}}^{-1}$ and a ship B 100 km South of A, is moving Northwards with a speed of 10 $\mathrm{km}{\mathrm{h}}^{-1}$. The time after which the distance between them becomes shortest is :

1. 5 h

2. $5\sqrt{2}\mathrm{h}$

3. $10\sqrt{2}\mathrm{h}$

4. 0 h

A boat is moving with velocity 2i + 3j with respect to ground. The water in the river is moving with a velocity -2j -3j with respect to ground. The relative velocity of the boat with repect to water is

1. 4 j

2. -4 + 6j

3. 4 i + 6j

4. 6 j

The equation of a projectile is y = $\sqrt{3\mathrm{x}}-\frac{g{x}^{2}}{2}$

The angle projection is given by

1. $\mathrm{tan}\theta =\frac{1}{\sqrt{3}}$

2. $\mathrm{tan}\theta =\sqrt{3}$

3. $\frac{\mathrm{\pi}}{2}$

4. zero

A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

1. $\frac{4{\mathrm{v}}^{2}}{5\mathrm{g}}$

2. $\frac{4\mathrm{g}}{5{\mathrm{v}}^{2}}$

3. $\frac{{\mathrm{v}}^{2}}{\mathrm{g}}$

4. $\frac{4{\mathrm{v}}^{2}}{\sqrt{5}\mathrm{g}}$

A projectile can have the same range R for two angles of projection. It ${\mathrm{t}}_{1}$ and ${\mathrm{t}}_{2}$ be the times of flight in the two cases, then what is the product of two times of flight?

1. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}\propto {\mathrm{R}}^{2}$

2. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}\propto \mathrm{R}$

3. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}\propto \frac{1}{\mathrm{R}}$

4. ${\mathrm{t}}_{1}{\mathrm{t}}_{2}\propto \frac{1}{{\mathrm{R}}^{2}}$

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity v and other with a acceleration a. If $\mathrm{\alpha}$ is the angle between the lines of motion of two particles then the least value relative velocity will be at a time given by

1. $\frac{\mathrm{v}}{\mathrm{\alpha}}\mathrm{sin}\mathrm{\alpha}$

2. $\frac{\mathrm{v}}{\mathrm{\alpha}}\mathrm{cos}\mathrm{\alpha}$

3. $\frac{\mathrm{v}}{\mathrm{\alpha}}\mathrm{tan}\mathrm{\alpha}$

4. $\frac{\mathrm{v}}{\mathrm{\alpha}}cot\mathrm{\alpha}$

A particle is projected over a traingle from one end of a horizontal base and grazing the vertex falls on thr other end of the base. If $\mathrm{\alpha}$ and $\mathrm{\beta}$ be the base angles and $\mathrm{\theta}$ the angle of projection, then the correct relation between $\mathrm{\alpha},\mathrm{\beta}$ and $\mathrm{\theta}$ is

1. $\mathrm{sin}\theta =\mathrm{cos}\alpha +\mathrm{tan}\beta $

2. $\mathrm{tan}\theta =\mathrm{tan}\alpha +\mathrm{tan}\beta $

3. $\mathrm{cos}\theta =\mathrm{cos}\alpha \mathit{}\mathit{+}\mathit{}\mathit{cos}\beta $

4. $\mathrm{sin}\alpha =\mathrm{sin}\theta +\mathrm{sin}\beta $

AB is an inclined plane of inclination ${30}^{\mathrm{o}}$ with horizontal. Point O (point of projection ) is 20 m above point A. A particle is projected horozontally and it collides with the plane AB, perpendicularly.

Speed of the particle must be (g = 10 $\mathrm{m}/{\mathrm{s}}^{2}$)

1. $13\mathrm{m}/\mathrm{s}$

2. $8\sqrt{3}\mathrm{m}/\mathrm{s}$

3. $4\sqrt{5}\mathrm{m}/\mathrm{s}$

4. $2\sqrt{5}\mathrm{m}/\mathrm{s}$

A cricket ball thrown across a field is at height ${\mathrm{h}}_{1}$ and ${\mathrm{h}}_{2}$ from point of projectoin at times ${\mathrm{t}}_{1}$ and ${\mathrm{t}}_{2}$ respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is

1. $\frac{{\mathrm{h}}_{1}{\mathrm{t}}_{2}^{2}-{\mathrm{h}}_{2}{\mathrm{t}}_{1}^{2}}{{\mathrm{h}}_{1}{\mathrm{t}}_{2}-{\mathrm{h}}_{2}{\mathrm{t}}_{1}}$

2. $\frac{{\mathrm{h}}_{1}{\mathrm{t}}_{2}^{2}+{\mathrm{h}}_{2}{\mathrm{t}}_{1}^{2}}{{\mathrm{h}}_{1}{\mathrm{t}}_{2}+{\mathrm{h}}_{2}{\mathrm{t}}_{1}}$

3. $\frac{{\mathrm{h}}_{1}{\mathrm{t}}_{2}}{{\mathrm{h}}_{2}{\mathrm{t}}_{1}-{\mathrm{h}}_{1}{\mathrm{t}}_{2}}$

4. None

If the equation for the displacement of a particle moving on a circular path is given by ($\mathrm{\theta}$) = $2{\mathrm{t}}^{3}+0.5$, where $\mathrm{\theta}$ is in radian and t in second, then the angular velocity of the particle after 2 s from its start is :

1. 8 rad/s

2. 12 rad/s

3. 24 rad/s

4. 36 rad/s

The values of a, for which points A, B, C with position vectors $2\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}},\hat{\mathrm{i}}-3\hat{\mathrm{j}}-5\hat{\mathrm{k}}$ and $\mathrm{a}\hat{\mathrm{i}}-3\hat{\mathrm{j}}+\hat{\mathrm{k}}$ respectively are the vertices of a right angled traingle with angle, C = $\frac{\mathrm{\pi}}{2}$ are

1. 2 and 1

2. -2 and -1

3. -2 and 1

4. 2 and -1

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length s = ${\mathrm{t}}^{3}$ + 5, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t = 2 s is nearly.

1. 13 $\mathrm{m}/{\mathrm{s}}^{2}$

2. 12 $\mathrm{m}/{\mathrm{s}}^{2}$

3. 7.2 $\mathrm{m}/{\mathrm{s}}^{2}$

4. 14 $\mathrm{m}/{\mathrm{s}}^{2}$

A particle is projected from a tower as shown in figure, then the distance from the foot of the tower where it will strike the ground will be

1. 4000/3m

2. 2000/3m

3. 1000/3m

4. 2500/3m

A projectile is fired with a velocity v at the rigt angle to the slope which is inclined at an angle $\mathrm{\theta}$ with the horizontal. The range of the projectile along the inclined plane is :

1. $\frac{2{\mathrm{v}}^{2}\mathrm{tan\theta}}{\mathrm{g}}$

2. $\frac{{\mathrm{v}}^{2}\mathrm{sec\theta}}{\mathrm{g}}$

3. $\frac{2{\mathrm{v}}^{2}\mathrm{tan\theta}\mathrm{sec\theta}}{\mathrm{g}}$

4. $\frac{{\mathrm{v}}^{2}\mathrm{sin\theta}}{\mathrm{g}}$

If rain falls vertically with a velocity ${\mathrm{V}}_{\mathrm{r}}$ wrt wind and wind blows with a velocity ${\mathrm{V}}_{\mathrm{w}}$ from east to west, then a person standing on the roadside should hold the umbrella in the direction

1. $\mathrm{tan}\theta =\frac{{V}_{w}}{{V}_{r}}$

2. $\mathrm{tan}\theta \mathit{}\mathit{=}\mathit{}\frac{{\mathit{V}}_{\mathit{r}}}{{\mathit{V}}_{\mathit{w}}}$

3. $\mathrm{tan}\theta \mathit{}\mathit{=}\mathit{}\frac{{\mathit{V}}_{\mathit{r}\mathit{w}}}{\sqrt{\mathit{V}{\mathit{r}}^{\mathit{2}}\mathit{}\mathit{+}\mathit{}\mathit{V}{\mathit{w}}^{\mathit{2}}}}$

4. $\mathrm{tan}\theta \mathit{}\mathit{=}\mathit{}\frac{{\mathit{V}}_{\mathit{r}}}{\sqrt{\mathit{V}{\mathit{r}}^{\mathit{2}}\mathit{}\mathit{+}\mathit{}\mathit{V}{\mathit{w}}^{\mathit{2}}}}$

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