Question # 1

If p, q, r and in A.P., a is G.M. between p and q and b is G.M. between q and r, then a², q², b²are in

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A.P.

G.P.

H.P.

None of these

The point of concurrency of the medians of the ΔABC is called its

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Orthocenter

Centriod

Circumcentre

Incentre

ᵨ is a

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variable

Positive constant

Positive variable

Directrix

A∪(A∪B)= --------------------

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B

A

A∪B

None of these

The point lying on the terminal rat of -270° is

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(1,0)

(0,-1)

(0,1)

(-1,0)

If A = {x / x ∈ R ∧ x² - 16 = 0} then A =

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- x

Infinite set

Φ

{-4,4}

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0

1

2

4

Inverse of the function y-10x is

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y=logx

y=lnx

x=10y

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tan 3x + c

cot 3x + c

- cot 3x + c

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A square matrix A = [aij] is lower triangular matrix when

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aij = 0 for all i<j

bij = 0

cij = 0

dij = 0

The identity element with respect to subtraction is

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0

1

-1

Does not exist

Considering Cosine Rule of any triangle ABC, possible measures of angle A includes

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Angle A is obtuse

Angle A is acute

Angle A is right-angle

All of above

E-radius corresponding to < A is

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Archimedes approximate the function by horizontal function and the area under f by the sum of small

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Parallelograms

Squares

Retangles

Polygons

The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is

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(√6,1)

(2,3)

(7,-2√6)

(4,-√6)

Three right angles is the angle of measure

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270°

180°

90°

270'

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Symmetric property

Cancellation property w.r.t. multiplication

Reflexive property

Transitive property

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

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a+b=c+d

a+c=b+d

a+d=b+c

All are correct

√-1 b=

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b

2

2b

None of these

Period of Tangent function is

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0°

-π

π

2π

If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a

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Circle

Hyperbola

Ellipse

Parabola

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additive property

multiplicative property

additive identity

multiplicative identity

If a set S contains "n" elements then P (S) has ...... number of elements

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2ⁿ

2²ⁿ

2 . n

n²

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The complement of set A relative to universal set U is the set

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{x / x∈ A∧ x∈ U}

{x / x∉ A∧ x ∈ U}

{x / x∈ A and x ∉ U}

A-U

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0

-1

1

f(x) = ax + b will be an identity function if

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a = 1 , b = 1

a = 1 , b = 0

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The radius of the circle x²+ y² - 6 x + 4 y +13 = 0 , is

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1

2

0

None of these

If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

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parabola

circle

hyperbola

ellipse

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Polynomial

Equation

Improper rational fraction

Proper rational fraction

The distance of the point (2,3) from y-axis is

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2

3

5

If a polynomial p(x) is divided by x-c, then the remainder is

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p(x)

x-c

c

P(c)

The radian measure of the central angle of an arc 50 m long on a circle of radius 25 m is

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3

2

1

If tan^-13 + tan^-1x = tan^-18, then x=

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5

1/5

5/14

14/5

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2

1

5

0

Domain of 2 cos x is ______

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[-2, 2]

R

Negative real numbers

None of these

The value of sin²20° + sin²70° is equal to

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1

2

-1

1/2

For Cosine Rule of any triangle ABC, b²is equal to

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a²- c²+ 2ab cos A

a³+ c³- 3ab cos A

a²+ c²- 2ac cos B

a²- c²4bc cos A

cotθ= sin 2θifθ=

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2^x

2^xIn x

2^xIn 2

Cot 45° = ______

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Cos-1(x)=

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cos x

x

tan-1(-x)

Sec-1 (1/x)

Multiplicative inverse of 0 is

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0

1

+-1

Does not exist

If n is a negative integer n! is

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1

0

Unique

Not defined

x = 0 is in the solution of the inequality

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x > 0

3x + 4 < 0

x + 3 < 0

x - 2 < 0

Which of the following integrals can be evaluated

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The product of cube roots of unity is

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Zero

1

-1

None of these

The measure of the angle subtended at the centre of the circle by an arc, whose length is equal to the radius of the circle is

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1⁰

1'

1"

1 rad

Apollonius was a:

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Rocket

Muslims scientist

Greek mathematicians

Method of finding conics

If ax + bx + c =0 is satisfied by every value of x,then

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b = 0,c = 0

c = 0

b = 0

a = b = c = 0

For any set B, BUB' is

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Is set B

Set B'

Universal set

None of these

If the roots of ax2 + b =0 are real and distinct then

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ab > 0

a = 0

ab < 0

a > 0,b > 0

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The solution of differential equation:

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dy/dx+y/x = x²is :

4xy = x⁴+ c

4x = x⁴= c

4 y = x⁴+ c

4x=4x³ + c

The polar form of complex number x ≠ I y =

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r cos θ+ r sin θ

r cos θ+ is sin θ

cos θ+ r sin θ

i cos θ+ i sin θ

The general term of a sequence is denoted by

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a₁

a_n

n

s_n

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

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Negative

Positive

Zero

Nothing can be said

If G is a G.M between a and b then a,G,b are in

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A.P

H.P

G.P

None of these

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2x cos x2

-2xcosxsinx

2x Sin x2

-Sin x2

Φ set is the _______ of all sets

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Subset

Union

Universal

Intersection

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15/23

7/15

7/8

15/7

Choose an answer

none of these

Roots of the equation x²- 7x + 10 = 0 are

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{2, 5}

{-2, 5}

{2,5}

{-2,-5}

A key ring is an example of

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Permutation

Circular permutation

Combination

None

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If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a hyperbola

a circle

a parabola

Cofactor of an element a_ijis defined by

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(-1)^i+j|A|

(-1)^i+jM_ij

(-1)^i+jM^-1

None of these

pth term of an H.P. is qr and qth term is pr then the rth term of the H.P. is

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pqr

1

pq

pqr²

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Principle of equality of fractions

Rule for product of fraction

Rule for quotient of fraction

Golden rule of fractions

If A is a subset of B and B contains at least one element which is not an element of A, then A is said to be

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Improper subset of B

Super set of B

Proper subset of B

None of these

4/√49 is a

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Irrational Number

Prime Number

Rational number

Whole number

{1, 2, 3} is _____

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an infinite set

A finite set

A singleton set

Universal set

Which one is a pair of allied angles

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(180° -θ)

(180° -θ,180° +θ)

(180° +θ)

None of these

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110

220

1320

None of these

Which symbolic notation represent unary operation ?

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-

∨

∧

⇔

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cos x

- sin x

- cos x

tan x

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None of these

Five engineering, four mathematics, two chemistry books are placed on a table at random.The probability that the books of each kind are all together is

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w^-12= ______

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0

1

w

w²

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

The physical quantity which possesses both magnitude and direction is called a

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scalar

vector

constant

none of these

If A ⊆ B then A ∪ B is

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A

B

A'

A ∩B

A function from X to X is denoted as

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f : X to Y

f : Y to Y

The set {1,-1, i, -i} form a group under

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Addition

Multiplication

Subtraction

None

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

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5

2

10

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

Second derivative of y = x⁹+ 10x²+ 2x - 1 at x = 0 is

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10

20

12

1

n! > 2ⁿ-1 is true when

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n≤ 3

n≤ 6

n≥ 4

n≤ 6

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

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7 / 40

5 / 40

11 / 40

None of these

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The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

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Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

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[0, 0, 0]

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

The first three terms in the expansion of (1 + x)^-2are ______

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1 - 2x + 3x²

1 - 2x - 3x²

1 + 2x + 3x²

-2 -2x + 3x²

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the co-ordinate plane. Let d = distance between P and Q

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Concentration of rectified spirit is:

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12%

14%

90%

95%

An element in +3 oxidation state has the electronic configuration (Ar) 3d³. Its atomic number is

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24

23

22

21

Which of the following is present in the stings of bees and wasps

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Formic acid

Citric acid

Carbolic acid

Formalin

Ozone depletion in stratosphere shall result in

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Forest fires

Increased incidence of skin cancer

Global warming

None of the above

Alkyl halides on treatment with aqueous KOH give

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Phenol

Alcohol

Aldehyde

Ketone

A condensation polymer among the following is

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Dacron

PVC

Polysterene

Teflon

Alcohols are derivatives of:

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Alkanes

Alkens

Alkynes

Benzene

If we remove one hydrogen atom from an alkane we obtain a group called

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Acetyle group

Formyle group

Alkyle group

Ketyle group

The sun of all the energies of atoms, molecule, ion, within system is called

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Enthalpy

K.E. of the system

Internal energy

None

The number of bonds in nitrogen molecule is

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In the presence of high temperature and pressure peat is converted to:

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Lignite

Polymorphism

Polymerization

Catenation

Which teat is not given by both glucose and fructose

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Give yellow ppt of CHl₃with alkaline aqueous iodine

With 2, 4-DNPH give yellow ppt of hydrazone

Evolve H₂gas with Na metal

Oxidised with [Ag(NH₃)₂]⁺i.e. Tollen's reagent

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0.02

0.2

50

25

The elements with atomic numbers 9, 17, 35, 53, 85 an all

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Noble gases

Halogens

Heavy metals

Light metals

The hydrocarbons having double bonds normally end with suffix

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Ane

Ene

Yne

Oic

Of the following four reactions, formic acid and acetic acid differ in which respect?

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Replacement of hydrogen by sodium

Formation of ester with alcohol

Reduction of Fehling solution

Blue litmus reaction

For which system does the equilibrium constant, kc has units of (concentration) ?

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N₂+3H_2-------2NH₃

H₂+L₂---------2HL

2NO₂----------N₂O₄

2HF--------H2+F₂

Analytical chemistry is the science of :

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Chemical Characterization.

Physical Characterization.

Biological Characterization.

Biochemical Characterization.

When two hydrogen atoms approach to form a chemical bond

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The repulsive forces dominate the attractive forces

The attractive forces, dominate the repulsive forces

The energy of atoms increases

The two atoms start ionization

The development of industries was a direct result of which major factor

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Population

Living standards

Depletion of resources

All of these

Choose an answer

32 g

3.2 g

5.6 g

9.6 g

Which gas is produced by treating CaC₂with water

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Methane

Ethane

Acetylene

HCI

Which is not true with respect to cathode rays?

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A stream of electrons

Charged particles

Move with speed as that of light

Can be deflected by magnetic fields

The other name of cross linked polymers is

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Linear polymer

Branched polymer

Inter connected polymers

None of these

In an experiment the concentration of a reactant 'A' is doubled the rate increases four times. If concentration in tripled, then rate increases nint times. Thus the rate is proportional to ______ of concentration of 'A'

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Square root

Square

Twice

Cube

Denaturation of protein means the structure of protein is disrupted, indicate which factor foes not denature protein

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Heating protein

pH changes

Oxidising agent

Keeping pH 7.35

Marsh gas was the name given to

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Methane

Ethane

Propane

Butane

The branch of chemistry which deals with the study of compounds containing carbon as an essential elements is called

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Physical

Inorganic

Nuclear

Organic

Isotopes differ in

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properties which depend upon mass

arrangement of electrons in orbitals

chemical properties

the extent to which they may be affected in electric fields

Ethyl acetate reacts with CH₃MgBr to form

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Secondary alcohol

Tertiary alcohol

Primary alcohol and acid

Acid

Which of the following oxides is unlikely to dissolve in aqueous hydroxide

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Al₂O₃

MgO

SO₂

SIO₂

Choose an answer

Condensation

Electrophilic substitution

Free radical substitution

Nucleophilic substitution

Among the nitrogen containing fertilizer, the one with about 82% nitrogen content is

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Ammonium nitrate

Ammonia

Ammonium phosphate

Ammonium sulphate

Choose an answer

Alkyl

Alkyl nitrile

Cyanogens

Amine

The sum of the exponents of the conc. terms in the rate equation is called

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Rate of reaction

Order of reaction

Specific rate constant

Average rate

The number of bonds in nitrogen molecule is

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Oneφ and one π

Oneφ and two π

three sigma only

Two φ and one π

Solvent extraction is an equilibrium process and it is controlled by :

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law of mass action.

the amount of solvent used.

distribution law.

the amount of solute.

In the modern long form of the periodic table elements are arranged in the increasing order of

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Atomic mass

Atomic number

Mass number

Isotopic number

Acid rain is caused when various atmospheric gases dissolve in rain water. What are the gases that cause rain water

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SO₂

NO₂

CO

A and b only

Content is a combination of mainly:

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Calcarious

Argillaceous

Calcarious and argillaceous

Al₂O₃

Reason of pollution are:

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Population and Urbanization

Transportation

Urbanization industrialization

All of these

The reference calomel electrode is made from which of the following?

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ZnCl₂

CuSO₄

Hg₂Cl₂

HgCl₂

Solvay process is used in the manufacture of

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Na₂CO₃

NaHCO₃

CaCl₂

All

The protection of steel by chrome plating is due to

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Cathodic protection

Anodic protection

Covering of steel surface

Formation of alloy with iron

Partial pressure of a solution component is directly proportional to its mole fraction. This statement is known as

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Henry's law

Raoult's law

Distribution law

Ostwald's dilution law

Ionic radius, in a period from left to right

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Increases

Decreases

Decreases then increases

Increases and decreases

An azeotropic mixture of two liquids boils at a lower temperature than either of them when lower temperature

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It is saturated

it shows positive deviation from Raoult's law

It shows negative deviation form Raoult's law

It is metastable

Which of the following element is most reactive

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Li

Na

K

Cs

The elements of group lA are called

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Chalocogens

Halogens

Alkali metals

Alkaline earth metals

Phenol is also known as

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Acetic acid

Carbolic acid

Tararic acid

Trichloroacetic acid

K_bfor NH₄OH is 1.81 x 10^-5, then K_avalue of its conjugate base is

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1.81 x 10⁺⁵

1.81 x 10^-9

5.5 x 10^-9

5.5 x 10^-10

Ethyl alcohol prepared during fermentation is pure:

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20%

10%

11%

12%

Ethyl alcohol may be identified by

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Ring test

Iodoform test

Tollen's test

Bazeyer's test

Charge to mass ratio (e/m) of the electron is determined by

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R. A. Millikan

J. J. Thompson

G. J, Stoney

None of these

A compound is soluble in conc. H₂SO₄, it does not decolourise bromine in carbon tetrachloride but is oxidized by chromic anhydride in aqueous sulphuric acid within two seconds, turning orange solution to blue, green and then opaque. The original compound is

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Primary alcohol

Tertiary alcohol

alkene

ether

Plastics are a pollution problem because many plastics

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Are made from petroleum

Are very inflammable

Burn to produce toxic fumes

Decompose to produce toxic products

Soil remediation means

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To make it suitable for cultivation of crops

To make it acidic

To make it alkeline

To add manure into it

When aqueous solution of NaOH is electrolysed useing graphite electrodes, the product obtained at anode is

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O₂gas

H₂gas

Na metal

Na₂O

Oxalic acid oxidizes to:

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CO

CO₂

Oxalates

None of these

The oxidation number of each element of group l-A is

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0

+1

+2

-1

The nature of interparticle forces in benzene is

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Dipole-dipole interaction

Dispersion force

Ion-dipole interaction

H-bonding

A solution contains 1.2046 x 10²⁴hydrochloric acid molecules in one dm³of the solution. The strength of the solution is

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6 N

2 N

4 N

8 N

When an aqueous solution of potassium salt of monocarboxylic acid is subjected to electrolysis, corresponding alkane is formed. This reation is known as

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Cannizaro reaction

Sabatier-secderens reaction

Alkylation

Kolbe's reaction

Purification of an impure copper is made by electrolytic cell, in which impure copper is anode and pure copper is cathode, and the electrolyte used is

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H₂SO₄

CuSO₄

ZnSO₄

Na₂SO₄

Zeotropic mixture

Choose an answer

Obey Henry's law

Obey Raoult's law

Does not obey Raoult's law

Obey Dalton's law

In electrolysis of NaCl when Pt electrode is taken then H₂is liberated at cathode while with Hg cathode it forms sodium amalgam

Choose an answer

Hg is more inert than Pt

More voltage is required to deduce H⁺at Hg than Pt

Na is dissolved in Hg while it does not dissolve in Pt

Conc. of H⁺ions is larger when Pt electrode is taken

Rectified spirit contains alcohol about:

Choose an answer

80%

85%

90%

95%

Solutions with same osmotic pressures are called

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Hypertonic

Hypotonic

Isotonic

Normal

Which of the atoms has 1s², 2s², 2p_x²2p¹_y2p¹_zconfiguration

Choose an answer

Nitrogen

Carbon

Fluorine

Oxygen

Give IUPAC name fo Acetone

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Ethanal

Propanone

Butanone

Propanal

Which one of the following has discontinuous solubility curve

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CaCI₂6H₂O

NaCI

KCI

NaNO₃

Formic Acid is obtained from Red out by:

Choose an answer

Distillation

Crystallization

Filtration

sublimation

Odour of alkene is:

Choose an answer

Fruity

Odourless

Zarlic like

Irritating

How many mole of acidfied FeSO₄solution can be completely oxidized by one mole of KMNO₄?

Choose an answer

10

5

6

2

Corrosion may be prevented by

Choose an answer

Allcying

Paints

Metallic coatings

All

Choose an answer

[A] = [B]

[A] < [B]

[B] = [C]

[A] > [B]

Pauli's principle is applicable to

Choose an answer

Degenerate orbits

Two electrons in the same orbital

One electron

None

What is the structure of the ester formed from propanoic acid and ethanol

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Which element among the following belongs to Group IV-A of the periodic table?

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Barium

Iodine

Lead

Oxygen

Which of the following is not isoelectronic?

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Na⁺

Mg²⁺

O^2-

Cl^-

The molal elevation constant is the ratio of the elevation in boiling point to

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Molarity

Molality

Mole fraction of solute

Mole fraction of solvent

During electrolysis, the reaction that takes place at cathode is :

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Reduction

Both (a) and (c)

Oxidation

No reaction occurs

During oxidation in k₂Cr₂O_{7, Cr VI changes to :}

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I

II

III

IV

Cannizzzaro's reaction is not given by:

Choose an answer

Formaldehyde

Acetaldehyde

Benzaldehyde

Trimethyl

Choose an answer

High temperature and low pressure

Low temperature and low pressure

Low temperature and high pressure

High temperature and high pressure

Identification of a substance, determination of its structure and quantitative analysis of its composition are the aspects covered by

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Modern analytical physics

Mechanical chemistry

Biochemistry

Modern analytical chemistry

Alkyl halides are considered to be very reactive compounds towards nucleophiles because

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They have an electrophilic carbon

They have an electrophilic carbon and a good leaving group

They have an electrophilic carbon and a bad leaving group

They have a nucleophilic carbon and a good leaving group

The percentage of H is the highest in

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CH₄

NH₃

H₂SO₄

C₆H₁₂O₆

Which of the following is not the reactions of lithium

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Volcanoes produce SO₂:

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47%

57%

67%

77%

Elements in which f-orbitals are in the process of completion are called

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Outer transition element

Inner transition elements

Non-tranistion elements

Radioactive elements

Which of the following pair of atomic numbers represents s-block elements?

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7, 15

6, 12

9, 17

3, 20

Carboxylic acids on complete reduction in the presence of HI and red Phosphours gives:

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esters

alcohols

alkanes

aldehydes

Rosenmund's reduction of an acyl chloride gives

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An aldehydes

An alcohol

An ester

A hydrocarbon

When chloroform is boiled with NaOH, it gives

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Formic acid

Trihydroxymethane

Acetylene

Sodium formate

Introduction of a second methyl group in methylbenzene will give how many isomeric dimethyllenzenes

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2

1

3

4

Octane number is zero for

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n-Heptane

Isooctane

n-Hexane

Isoheptane

When alkyl halide is heated with aqueous solution of ammonia at 100°C the major product is

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Primary amine

Secondary amine

Tertiary amine

Mixture of amines and salt

6-d series is in the period :

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4th

5th

6th

7th

Alkanes normally have ______ hybridization

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Sp

Sp²

Sp³

d sp³

Synthetic polymer prepared from caprolactum is known is

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Nylon 610

Teflon

Terylene

Nylon-6