Question # 1

If the angle between two vectors with magnitude 2 and 15 is 30°then their scalar product is

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15

30

Sine rule for a triangle states that

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a/sin A = b/sin B = c/sin C

sin A/a = sin B/b = sin C/c

a/sin A + b/sin B + c/sin C

2a/sin A = 2b/sin B = 2c/sin C

Which term of the A.P 5,8,11,24.............is 320

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104th

106th

105th

64th

Domain of cotθis

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i⁹ =

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i²

-1

1

i

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Period of cos 2x is ______

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3x + 4 < 0 is

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inequality

equation

identity

not inequality

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Reflexive property

Symmetric property

Transitive property

Additive property

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Commutative property of addition

Closure property of addition

Additive inverse

Associative property w.r.t. to addition

A rule or correspondence that assigns to each element x in X a unique element y in Y is called a function from

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X to X

X to Y

Y to X

none of these

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G is geometric mean between a and b if a, G, b is

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A.P.

G.P.

H.P.

None of these

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0

1

2

3

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none of these

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n if n is even

0 for any natural number n

1 if in odd

None of these

The period of 3 sin x is

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2π

9π

3π

5π

Let S_ndenote the sum of the first n terms of an A.P. If S_2n= 3 S_n: S_nis equal to

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4

6

8

10

If x,y are two positive distinct numbers then

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A>G>H

A<G<H

A=G=H

None of these

If f(x) = x²then f(-2) is

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-2

2

4

-4

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Evert element of A is in B

Every element of B is in A

Every element of A is in B'

Every element of A is in A

There are 25 tickets bearing number from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

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7 / 25

9 / 25

11 / 25

None of these

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x^-2+ c

not possible

The point of concurrency of the medians of a triangle is called

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incentre

circumcentre

e-centre

centroid

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

The equation of the circle with centre (-h, -k) and radius r is

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(x +h)²+ (y+k)²= r²

(x +h)²+ (y-k)²= r²

(x -h)²+ (y+k)²= r²

(x -h)²+ (y-k)²= r²

If A=B, then

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A⊂B and B⊂A

A⊆B and B⊈A

A⊆B and B⊆A

None of these

ⁿC₂= exists when n is ______

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The locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

If in a set of real no a is additive identity then

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a+a = 2a

a+a = 1

a+a = 0

None of these

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If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

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-i

2 + i

i

2 - i

If one end of the diameter of the circle x² + y²- 5x = 3y -22 = 0 is (3,4) the other end is:

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(2,7)

(-2,-7)

(-2,7)

(2,-7)

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Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

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0.28

0.13

0.12

0.42

The area under the curve y = 1/x² between x = 1 and x =4 is:

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-25

0.75

-0.35

-10

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5

25

3

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If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

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2

4

6

8

A function from X to X is denoted as

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f : X to Y

f : Y to Y

A quadratic equation has two

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roots

degree

variables

constants

Number of ways of writing the letters of WORD taken all at a time is

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24

4

12

6

0.25 is ______

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An irrational number

A natural number

A prime number

A rational number

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-a -b -c

1

0

-1

The number of words that can be formed out of the letters of the word ASSASSINATION is

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none of these

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sec 5x + c

- sec 5x + c

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x-axis

y-axis

z-axis

None of these

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tan^-1(1/4) + tan^-1(2/9) is equal to

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1/2 cos^-1(3/5)

1/2 sin^-1(3/5)

1/2 tan^-1(3/5)

tan^-11/2

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The value of the expression sinθ+ cosθlies between

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A circle which touches one side of a triangle extermally and the other two sides produced is called

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In-circle

Circumcircle

e-circle

Point circle

Range of cosθis

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The value of cos(cos-1 1/2) is

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1/2

√3/2

-1/2

1/√2

The solution set of the equation tan^-1x - cot^-1x = cos^-1(2 - x) is

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[0, 1]

[-1, 1]

[1, 3]

None of these

99th term of the series 2 + 7 + 14 + 23 + 34 + ..... is

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9998

9999

10000

None of these

The law of sines can be used to solve oblique triangle when following information is given:

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Two angles and a side

Two sides and an angle opposite one of the given sides

Two sides and the angle between two sided

Option a and b

The total cost of 2 apples and 3 oranges is $1.70, which of the following is true

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The cost of one apple

The cost of one orange

Both have equal cost per item

Cost of each single item can not be determined

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A point of a solution region where two of its boundary lines intersect, is called

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Boundary

Inequality

Half plane

Vertex

Sin^-1(-x)=

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Cos^-11/x

- Sin^-1X

Cot^-1X

None of these

Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is

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Derivative of strictly increasing function is always

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Zero

Positive

Negative

Both (A) and (B)

The parabola y2 + 2y + x = 0 lie in _____ quadrant.

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First

Second

Third

Fourth

Which of the following is the subset of all sets

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Φ

{1,2,3}

{Φ}

{0}

Which of the following is the definition of singleton

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The objects in a set

A set having no element

A set having no subset

None of these

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The range of the principal sine function is

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If b²- 4ac = 0 then the roots of the equation are

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Real and distinct

Real and equal

Imaginary

None of these

The set {-1, 1} is

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Group under the multiplication

Group under addition

Does not form a group

Contains no identity element

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0

3

9

-3

Let A and B be two sets. If every element of A is also an element of B then

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An improper rational fraction can be reduced by division to a

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Proper fraction

Polynomial

mixed form

The identity element of a set X with respect to intersection in P(x) is

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X

Does not exist

∅

None of these

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivations of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours per hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 15 per hectometer for wheat. The profit function for the farmer is

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P(x, y) = 20x + 15y

P(x, y) = 2x + 3y

P(x, y) = x + y

P(x, y) = 3x + 2y

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a₁+ a₂

a²₁+ a²₂

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A finite non-empty set

Null set

Both a and b

None of these

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sin h x

cos h x

sec h x

cosec h x

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

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quadratic function

constant function

trigonometric function

linear function

The distance between the points (2,3) and (3,2) is

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5

2

10

If the intersection of two sets is non-empty, but either is a subset of other are called

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Disjoint sets

Over lapping

Equal sets

None of these

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

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-5

5

0

1

I is not

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Real number

Natural number

Prime Number

Whole Number

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x = ________ is in the solution of 2x + 3 > 0

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1

-2

-3

-4

The sample space for tossing a coin once is

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{T, T}

{H, H}

{H, T}

None of these

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0

1

2

1/2

The√ is used for the

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Positive square root

Negative square root

+ve and -ve square root

Whole number

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none of these

1 radian = _____

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60°

57.296°

57.2°

180°

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

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m x m

m x n

n x n

n x m

A polynomial of arbitrary degree

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f(x) = o

f(x) = x

f(x) = a

f(x) = ax + b,a ≠ 0

If 0 = {1,3,5.......}, then n (0) =

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99

odd integers

Even numbers

Infinite

A function whose range is just one element is called

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One-one function

Constant function

Onto function

Identity function

When 6s orbital is complete then next electron goes to

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6p

6d

5d

4f

Synthesis rubber is made by polymerization :

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Chloroform

Acetylene

Divinyl acetylene

Butene

Solution which distill without change in composition or temperature are called

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Amorphous

Azeotropic mixture

Ideal

Super saturated

Quality of fuel is judged from its octane number. The best fuels are

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Straight chain hydrocarbons

Branched chain hydrocarbons

Cyclic compounds

Compounds containing benzene ring

Which of the following does give violet colour with neutral ferric chloride?

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Acetic acid

Salicaylic acid

Formine acid

Benzoic acid

How many are the zones through which the charge passes in a rotary kiln?

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4

3

2

5

For spontaneity of a cell, which is correct?

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ΔG = 0,ΔE = 0

ΔG = -ve ,ΔE = 0

ΔG = +ve ,ΔE = 0

ΔG = -ve

Hydrocarbons are organic compounds which contain elements such as

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Hydrogen

Carbon

Hydrogen and carbon

Halogens

In a group, the ionization energy

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Increase

Decreases

Remain constant

First increases then decreases

Acetic acid is manufactured by the fermentation of

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Ethanol

Methanol

Ethanal

Methanal

If half life period of a reaction is independent of the concentration of the reactants, then the reaction is

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Zero order

First order

Second order

Order is in fraction

ΔH is equal to

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E + PV

E + PΔV

ΔE + P

ΔE + PΔV

Which of the following aqueous solutions have the lowest freezing point

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5.85% NaCI

6% urea

34.2 sucrose

All of them have same freezing points

Which is used in navigational equipments?

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B

Be

Mg

Al

The % of CO₂is the atmosphere is

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3.0%

0.03%

0.3%

0.5%

Antibonding MO is formed by

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Addition of atomic orbitals

Substraction of atomic orbitals

Multiplication of atomic orbitals

None of these

The formula of secondary alcohol is

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R - OH

R - CH₂OH

R₂CHOH

R₃COH

One of the followings is not type of polymer

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Homopolymer

Copolymer

Heteropolymer

Terpolymer

Which of the following does not reflect the periodicity of elements?

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Bonding behaviour

Electronegativity

Ionisation potential

Neutral/proton ratio

The comparative rates at which the solutes move in paper chromatography, depend on:

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the size of per sued.

R_f values of solutes

temperature of the experiment

size of the chromatography tank used.

The common name of propanoic acid is

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Acetic acid

Formic acid

Propionic acid

Butyric acid

A solution has 92 g of ethyl alcohol, 96 g of methyl alcohol and 90 g of water. Mole percentage of ethyl alcohol in the solution is

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10

20

25

50

Carboxylic acids generally exists in cyclic

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Monomers

Dimers

Trimers

Tetrameter

Plaster of pares is obtained by heating

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Gypsum

Epsom

Lime stone

Dolomite

Partial reduction of acetic acid happens with

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NH₃

LiAIH₄

P + HI

PCI₅

The presence of a double bond in a compound is the sign of

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Saturation

Unsaturation

Substitution

None of above

Zn + HCI are used in

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Clemenson reduction

Wof kishner reduction

Kolb's electrolysis

Wutruz reaction

What is the maximum mass of aluminium which can be obtained from 240g of aluminium oxide Al₂O₃?

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26 g

127 g

51 g

108 g

The active part in a molecule is called

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Homologous series

Functional group

Chemical bonding

Ionic complex

Ethyl acetate is obtained when methyl magnesium iodide reacts with

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Ethyl formate

Ethyl choroformate

Acetyl chloride

carbondioxide

Which of the following compound is no formed according to octet rule:

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KrF₂

XeF₂

XeO₃

SF₆

In endothermic reactions, the heat content of the

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Products is more than that of reactants

Reactants is more than that of products

Both a and b

None of the above

Which of the following element's outermost orbits last electron has magnetic quantum number m=0?

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Na

O

Cl

N

Which one is used as a fuel for internal combustion engines in many European countries and Brazil

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C₂H₅OH

CH₃OH

CH₃COOH

C₂H₂

Alkynes normally have ______ hybridization

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Sp

Sp²

SP³

d sp³

Which statement is incorrect for balancing of redox reactions by ion-electron method

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The reaction is splitted into two half reactions

H₂O and H⁺ions are added for acidic or neutral reaction to balance O and H atoms

To balance H, HCi, is added

To balance O and H in the alkaline reaction OH^-added

Aniline reacts with which of these to form Schiff base?

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Acetic acid

Bezaldehyde

Acetone

NH₃

The rate of reaction b/w two specific time intervals is called :

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Instantaneous rate of reaction.

Average rate of reaction.

Rate of a reaction.

Minimum rate of a reaction.

A chemical inert and heat resistant plastic, that is made form tetrafluoroethlene, is called

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Teflon

PVC

Bakelite

Polyamide

N₂ + O₂ ⇌2NO

The unit of K_c for tis reaction will be:

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No unit

mol^-2 dm^-3

mol^-1 dm^-3

mol^-2 dm⁺³

Picric acid is

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2, 4, 6-Trinitrotoluene

2, 4, 6-Tribomoethanol

2, 4,6-Trinitrophenol

Para-Nitrophenol

Proteins and amino acid can be separated by:

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Filtration

^Sublimation

Chromatography

Suction

In CCL4 solvent I3 shows:

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Blue Color

Brown Color

Purple Color

Pink Color

Generally ionization energy of atoms decreases by

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Decreases in atomic size

Increase in atomic size

Increase in nuclear charge

None of these

Which of these polymers is an addition polymer

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Nylon 6,6

Polystyrene

Terylene

Epoxy resin

According to the SI-system heat contents are measured in units of

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Calorie

Joules

Ergs

Watts

Bakelite is obtained from phenol by reacting with

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Acetaldehyde

Acetal

Formaldehyde

Chlorobenzene

In the extraction of iron, slag is produced which is

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CO

FeSiO₃

MgSiO₃

CaSiO₃

The bond order O₂molecule is

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1

2

3

Zero

Formalin is an aqueous solution of

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Furfural

Fluorescein

Formaldehyde

Formic acid

The rules which describe the distribution of electron in atomic energy levels are Auf-ban principle, Pauli's exclusion principle. Hunds rule. The pauli exclusion principle refers to the

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Orientation of orbital in space

Fact that two electrons in the same orbital should have opposite spins

Energy of the orbital

Spin of the electron

The hydrocarbons having double bonds normally end with suffix

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Ane

Ene

Yne

Oic

The boiling points of alcohols are higher than the corresponding alkanes, This is because

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Of hydrogen bonding existing between molecules of alcohols

Alkanes are dipolar compounds

Alcohols are sweet in taste

Alcohols are soluble in water

Alcohals can be distinguished using test:

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Lucas

Tollen's

Koib's

William's

The shape of the molecule SF₂Cl₂is

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Trigonal bipyradmidal

Cubic

Octahedral

Tetrahedral

Contamination of water of tanning industries is due to:

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Cr(III)

Cr(VI)

Mn(III)

Mn(VII)

The ionic bonds are

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Unidirectional

Bi-directional

Non-directional

Multi-directional

What is the cause of water pollution

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Chemical and bacterial contents in live stock

The spilled oil in rivers and ponds

Wide spread use of pesticides

All of the above

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In a group form top to bottom, the hardness of alkali metals

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Remains unchanged

Increases

Decreases

None

The atomic mass is measured in atomic mass unit (a.m.u.) which is equal to

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1.661 x 10^{-27- Kg}

1.661 x 10^-24Kg

1.661 x 10^{-27- g}

1.661 x 10^-24mg

Which one of the following reagents will distinguish between C₆H₅CHO and C₆H₅COCH₃

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Aqueous bromine

Phosphorus pentachloride

2, 4 DNPH

Tollen's reagent

A solution containing 5.8 grams acetone (CH₃OCH₃), 4.6 gram ethyl alcohol (C₂H₅OH) and 12 grams chloroform (CHl₃) has mole fraction and mole percent of acetone

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0.11, 10%

0.33, 33%

0.22, 22%

0.11, 33%

Electron affinity of sulphur is

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More than O and Se

More than O but less than Se

Less than O but more than Se

Equal to O and Se

The weight of pure NaOH required to prepare 250 cm³of 0.1 N solution is

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4 g

1 g

2 g

5 g

The amount of electricity that can deposit 108 g of silver from silver nitrate solution is

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1 ampere

1 coulomb

1 faraday

2 ampere

I a chemical reaction equilibrium is said to have been established when :

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Rate of opposing reactions are equal.

Rate constants of opposing reactions are equal.

Opposing reactions stop.

Concentration of reactants and products are equal

Isopropyl alcohol on oxidation forms

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Acetone

Ether

Ethylene

Acetaldehyde

The colour of transition metal complexes is due to

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d-d transitions of electrons

Para magnetic nature of transition elements

Ionization

Loss of s-electrons

If the value of principal quantum number is 3. the total possible values for magnetic quantum number will be

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1

4

9

12

Grignard reagent on reaction with a ketone forms

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Tertiary alcohol

Secondary alcohol

Primary alcohol

Carboxylic acid

The substances which are added to the soil to provide one or more nutrient elements essential for plant growth are called

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Minerals

Hormones

Fertilizers

None of these

Which one is the most toxic?

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Carbon

CO

CO₂

SO₂

The degree of unsaturation in fats or oils is usually measured by numbers of grams of iodine required by 100 grmas of fat, this is called

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Oil number

Saturation number

Iodine number

Un saturation number

The color of Cr³⁺ion is

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Violet

Blue

Pink

Green

Sodium can be obtained by :

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Electrolysis of acidified water.

By heating NaCl and water at 100°

Electrolysis of molten sodium chloride.

Electrolysis of aqueous sodium chloride.

Quantum number value for 2p orbitals are:

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n=2 ,l=1

n=1 ,l=2

n= ,l=0

n=2 ,l=0

Hydrochloric acid available in the laboratory is 36% w/w. The density of HCl solution is 1.19 g cm^-3. The molarity of HCl solution is

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10.23 moles dm^-3

11.55 moles dm^-3

11.73 moles dm^-3

12.67 moles dm^-3

Which of the following polymers is used for weather resistant paints

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Arcylic resins

Polyvinyl acetate

Polystyrene

PVC

Choose an answer

RCH(CH₃)CO₂H + CH₃OH

RCH(CH₃)CO₂H + HCO₂H

RCH(CH₃)OH + CO₂

RCH(CH₃)OH + HCO₂H

Rate of chemical reaction depends upon :

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The number of total collisions per second.

Number of molecules taking part in a chemical reaction.

Number of fruitful collisions per second

Number of fruitless collisions per second.

Which of the following does not turn Schiff's reagent to pink?

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Formaldehyde

Bezaldehyde

Aceton

Methyl chloride

How many alcohol (including both structural isomers and stereoisomers) can have the molecular formula C₄H₁₀O

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3

4

5

6

How many zones through which the charge passes in a rotary kiln

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4

3

2

5

An electron has principal quantum number 3. The number of its 1 subshell and 2 orbitals would be respectively

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3 and 5

3 and 7

3 and 9

2 and 5

Alcohol fermentation is brought about by the action of

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CO₂

O₂

Invertase

Yeast

Quantity of heat evolved or absorbed during the reaction is measured according to the equation

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3.01 x 10²²Ag⁺ions is present in

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85 grams AgNO₃

0.85 g AgNO₃

8.5 g AgNO₃

18.5 g AgNO₃

Given date

(i) heat of neutralization of HCl and NaOH is -57.3 KJ mole^-1

(ii) heat of neutralization of CH₃COOH with NaOH is 55.2 KJ mole^-1

The enthalpy of ionization of CH₃COOH is a determined according to Hess's law by

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Adding i and ii

Dividing i by ii

Subtracting i from ii

Subtracting ii from i

Replacement of hydrogen atom by - SO₃H group in benzene is called

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Nitration

Alkylation

Sulphonation

Acylation

Choose an answer

Ethanol in the presence of concentrated sulphuric acid

Potassium hydroxide

Sodium

Sodium carbonate

Acetic anhydride is obtained form acetyl chloride by the reaction of

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P₂O₅

H₂SO₄

CH₃COONa

CH₃COCH₃

Which of the following is a characteristic of a reversible reaction?

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It never proceeds to completion

It can be influenced by a catalyst

It proceeds only in the forward direction

Number of moles of reactants and products are equal

Which is used as an antifreeze?

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Glycol

Ethyl alcohol

Water

Methanol

During nitration of benzene, the active nitrating agent is

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NO3

NO2+

NO2-

HNO3

B-B'-dichloroethyl sulphide is commonly known as

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Mustard gas

Laughing gas

Phosgene gas

Bio gas

The amount of heat evolved or absorbed in a chemical reaction, when the molar quantities of products and reactants being the same as represented in chemical equation. is called

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Heat of reaction

Free energy of reaction

Entropy of reaction

None of these

Which compound is more soluble in water

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C₂H₅OH

C₆H₅OH

CH₃OCH₃

n-hexanol

The product of addition polymerization reaction is

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PVC

Nylon

Terylene

Polyamide

Which property depends on the state of system

Choose an answer

Enthaply

Free energy

Entropy

All these

Organic compounds are soluble in all except

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Benzene

Petroleum

Ether

Water