Question # 1

For any equilateral r :R :η :r1 :r2 :r3 =

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1:2:3:4:5

1:2:3:3:3

1:2:4:4:4

2:1 :2 :2 :2

The sum of infinite numbers of terms of an arithmetic series is

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Finite

Infinite

May or may not finite

None of these

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

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Orthogonal

Collinear

Perpendicular

None of these

Period of Tangent function is

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0°

-π

π

2π

If a is any real number and a = a is called

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symmetric property

Trichotomy Properties

Transitive Property

Reflexive Properties

i is equal

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(1 , 0)

(0 , 1)

(1 , 1)

(0 , 0)

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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Commutative law of addition

Associative law of addition

Additive identity

Additive inverse

0.25 is ______

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An irrational number

A natural number

A prime number

A rational number

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The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

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3x - 4y =0

3x - 4y =5

4x + 3y = 5

4x + 3y = 25

A relation in which the equality is true only for some values of the known is called ______

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An identity

An equation

A polynomial

None of these

In a country 55% of the male population has houses in cities while 30% have houses both in cities and in villages find the percentage of the population that has houses only in villages

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45

30

25

50

The number of triplets (x, y, z) satisfying sin^-1x +cos^-1y + sin^-1z = 2π is

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0

2

1

Infinite

The Principal value of sin-1 (-1/1/2)

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π/2

-π/2

π

-π

If ab > 0 and a < 0, which of the following is negative?

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b

-b

-a

(a - b)²

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0

2

4/3

5/3

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The matrix A is Hermitian when (A)' =

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A

-A

A

A'

The set {-1, 1} is closed under the binary operation of

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Addition

Multiplication

Subtraction

Division

The number of solution of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

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0

1

2

3

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0

-1

1

2

In R the right cancellation property w.r.t. addition is

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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

Every real number is

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A complex number

A rational number

A natural number

A prime number

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

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

The middle term of the expansion (1 + 2x)⁶is ______

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1st term

4th term

2nd term

5th term

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Projection of vector u along v is

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|v| cosθ

|u| cosθ

|v| sinθ

|u| sinθ

cos (180° -θ)=

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sinθ

- cosθ

- sinθ

None of above

∫f(x) is known as:

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Definite itegral

Indefinite integral

Fixed integral

Multiple integral

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2²- n - 1

1 - 2^-n

n + 2^-n-1

2ⁿ- 1

If A is a non-singular matrix then adj A is

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Non-singular

Symmetric

Singular

Non defined

(2 + w) (2 + w²) = ______

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1

2

3

0

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quadratic function

constant function

trigonometric function

linear function

An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

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3 / 10

5 / 10

7 / 10

9 / 10

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If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

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(2, 4)

(4, 8)

(0, 2)

(0, -2)

The proposition S(n) is true∀n∈N,S(k+1) true when ______is true

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S(1)

Both a & c

S(k)

None

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1

-1

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

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θ and 2kπ+θ are the ________ angles

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Quadrantal angles

Coterminal

Allied

None

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cos 2x + c

- cos 2x + c

tan 2x + c

cot 2x + c

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-3 -2i

3 +2i

1 + 2i

1 - 2i

The set of rational number is represented by

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W

R

Q'

Q

The set {1, -1, i, -i}

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Form a group w.r.t addition

Form a group w.r.t multiplication

Does not form a group w.r.t multiplication

Not closed under multiplication

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The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

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1 and 3

1 and 4

1 and 2

2 and 3

The liner equation ax + by = c is called _________ of the inequality ax +by > c.

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Associated equation

Non-associated equation

disjoint equation

Feasible equation

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a^x

a^xIn a

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The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

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(0, 2π)

(-π, -0)

(0,π)

None of these

For any positive integer n

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ABn = Bn A ⇔ AB = BA

ABn = Bn A⇔ A,B are square matrices and AB = BA

ABn = BnA⇔ A + B

ABn = BnA ⇔ A and B are square matries

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5x^{4 + c}

1/6 x⁶+ c

5x²+ c

1/5 x⁶+ c

w¹⁵= ______

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0

1

w

w²

i =

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The value of the expression 3 cosθ+ 4 sinθθlie between

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-7 and 7

-25 and 25

-1 and 1

-5 and 5

Which is an explicit function

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y = x²+ 2x - 1

x²+ xy + y²= 2

x²+ y²= xy + 2

All are

The general term of a sequence is denoted by

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a₁

a_n

n

s_n

The range of y = sin x is ______

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[1, -1]

[-1, 1]

[0, -1]

[-∞+∞]

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sin -1(sin2π/3) =

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π/2

2π/3

-3π/2

π/3

Which of the following is a scalar

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weight

force

speed

momentum

Form a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

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1/4

1/3

1/2

1/6

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1

0

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

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N

r

2r

π

The distance between the points A(-8,3) and B(2,-1) is

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116

none of these

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The set of rationals numbers between 0 and I is

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Finite

Null set

Infinite

None of these

A,G,H are in

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A.P

G.P

H.P

None of these

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1/x

-x

2x

0.5 x

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

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2 AB

2 BA

A + B

AB

The roots of the equations will be equal if b²- 4ac is

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Positive

Negative

1

Zero

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Biconditional

Implication

Antecedent

Hypothesis

A subset of set of complex number whose elements are of the form (a,0) is called

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Real number

Complex number

Rational number

Irrational number

πis the period of the function

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|sin x| + |sin x|

sin⁴x + cos x

sin (sin x) + sin (cos x)

None of these

A tower subtends an angle of 30° at a point distant d from the foot of the tower and on the same level as the foot of the tower. At a second point, h vertically above the firs, the angle of depression of the foot of the tower, is 60°. The height of the tower is

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h/3

h/3d

3h

3h / d

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If a₁, r are first term and the common ratio respectively then the sum of an infinite geometric series is

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If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______

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-1

1

-4

4

The set of all positive even integers is

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Not a group

A group w.r.t subtraction

A group w.r.t division

A group w.r.t multiplication

The angle AOP which the ray from an observer's eye at O to an object at P at a lower level makes with horizontal ray OA through O is called the

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Angle of depression

Angle of elevation

Acute angle

Obtuse angle

If c is a constant number and if f is the function defined by the equation f(x) =c for all values of x, then f is differentiable at every x and f is defined by the equation f(x)

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f

1

C

0

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Rational fraction

Proper fraction

Improper rational fraction

None of these

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2

4

6

8

Choose an answer

2

4

3

16

A square matrix A for which A^t= -A is called a

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Column matrix

Symmetric matrix

Skew-symmetric matrix

Row matrix

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

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1/2

√3/2

-1/2

1/√2

The trigonometric function are continuous whenever

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They are defined

their limit exist

Their period is given

All are incorrect

The order of the matrix [1 2 3] is

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1 x 1

3 x 3

3 x 1

1 x 3

If b₁, b₂, b₃, ... are in G.P. with first term unity and common ratio r, then the minimum value of b₁- b₃+ b₅is equal to

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3/4

1/4

1

None of these

Which of the following is a polar molecules

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Carbon dioxide

Carbon tetrachloride

Methanol

Ethane

An electron with n = 3 , l = 2 will be in the sub-shell

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3p

3d

3f

3s

When rain is accompanied by a thunderstorm, the collected rain water will have a pH value

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Uninfluenced by occurrence of thuderstorm

Which depends on the amount of dust in air

Slightly lower than that of rain water without thunderstorm

Slighlty higher than that when the thunderstom is not there

When a carbon atom forms single bonds with other carbon atoms, these hybrid orbitals overlap with the orbitals of hydrogen to form four bonds which are

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Three sigma and one P_i

Two sigma and two P_i

One sigma and three P_i

sigma

The nature of the positive rays depend on

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The nature of the electrode

The nature of the discharge tube

The nature of the residual gas

All of the above

Standard reduction of Zn = -0.76 V and that of Ni is -0.25 V. On coupling them by a salt bridge which of these will act as anode

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Salt bridge will act as anode

Zn will act as anode

Ni will act as anode

None of these

The widely used nitrogen fertilizer that contains about 46% nitrogen is

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Ammonia

Ammonium nitrate

Ammonium sulphate

Urea

The branch of chemistry which deals with thermal energy changes in chemical reactions is called

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Chemical kinetic

Thermodynamics

Thermochemistry

Mechanics

Primary and secondary alcohols on action of red hot copper give

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Aldehydes and ketones respectilvely

ketones and aldehydes respectively

Only aldehydes

Only ketones

Lithium reacts with air to form

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Peroxide

Normal oxide

Superoxide

None of these

The shape of methanol, ammonia and water molecule can be explained by assuming

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Sp³hybridization

Sp²hybridization

Sp hybridization

All of these

Which responds to +ve iodoform test?

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Butanol-1

Butan-1-al

Butanol-2

2-pentanone

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

Given below are some statements concerning formic acid, which of them is true?

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It is a weaker acid than acetic acid

It is a reducing agent

When its calcium salt is heated, it forms a ketone

It is an oxidizing agent

The spectrum of He is expected to be similar to that of

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H

Na

He⁺

Li⁺

Analytical chemistry is the science of

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Chemical characterization

Physical characterization

Biological characterization

Biochemical characterization

Glass calorimeter reaction is one which we measure

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Enthalpy of combustion

Enthalpy of reaction

Pressure volume work

None of above

For preparing an alkane, a concentrated aqueous solution of sodium or potassium salt of saturated carboxylic acid is subjected to

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Hydrolysis

Oxidation

Hydrogenation

Electrolysis

The increase in size of the anion is due to:

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Increase in electron-electron repulsion

Increase in valence shell electrons.

Decrease in valence shell electrons.

Both (a) and (b).

A 4f orbital has

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one node

two node

three node

four nodes

The elements like boron, chlorine, cobalt, copper etc are added in small amounts to the soil. They are called

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Macrountrients

Trace elemetns

Micronutrients

Additives

The ratio of the ionization energy of H and Be³⁺is

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1 : 1

1 : 3

1 : 9

1 : 16

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

Which of the following react with NaOH to produce an acid and an alcohol?

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NCHO

CH₃COOH

CH₃CH₂COOH

C₆H₅COOH

Which carbon is more electronegative?

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sp³- hybridized carbon

sp-hybridized carbon

sp²-hybridized carbon

always same irrespective of its hybrid state

Potable water is considered to be

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Safe for human consumption

Not safe for human consumption

The surface water

The ground water

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0 1

0 2

1 1

1 2

A set of compounds in which reactivity of halogen atom in the ascending order is

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Chlorobenzene, vinyl chloride, chloroethane

Chloroethane, chlorobenzene, vinyl chloride

Vinyl chloride,chlorobenzene chloroethane

Vinyl chloride, chloroethane,chlorobenzene

Formalin is an aqueous solution of

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Furfural

Fluorescein

Formaldehyde

Formic acid

Which one of the following is not a nucleophile

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H₂O

H₂S

BF₃

NH₃

Which of the following undergoes uncleophilic substitution exclusively by S_N1 mechanism?

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Benzyl chloride

Ethyl chloride

Chlorobenzene

Isopropyl choride

Two elements whose electronegativities are 1.2 and 3.0, the formed between them would be

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Ionic

Covalent

Coordinate

Metallic

In a reversible chemical reaction having two reactants in equilibrium, if the concentration of the reactants are doubled then the equilibrium constant will

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Also be doubled

Be halved

Becomes one fourth

Remains the same

If the value of azimuthal quantum number is 3, then values of m the magnetic quantum no. will be

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0, 1, 2, 3

+3, +2, +1, -1, -2, -3

0, -1, -2 ,-3

-3, 0, +3

The attraction that an atom exerts on a pair of electrons that are being shared with another atom for forming covalent bond is referred to as its

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Electron affinity

Electronegativity

Ionisation energy

Valency

Which of the following element is responsible for oxidation of water to O₂in biological process?

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Fe

Mn

Cu

Mo

The boiling point of an a zeotropic mixture of water and ethye alcohol is less than that of water and alcohol. The mixture shows

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That solution is highly saturated

No deviation from Raoult's law

Positive deviation from Raoult's law

Negative deviation from Raoult's law

Neutron was discovered by:

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Chadwick.

Bohr.

Rutherford.

Plank.

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s

p

d

f

The colour of ppts formed by Fehling's test is

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Brick red

Red

Yellow

Orange

In alkynes the bonds between carbon atoms are

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All sigma bonds

All pi(π) bonds

One is sigma and two areπ(pi) bonds

One isπ(pi) and two are sigma bonds

Grignard reagent on reaction with a ketone forms

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Tertiary alcohol

Secondary alcohol

Primary alcohol

Carboxylic acid

The function of salt bridge is :

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To increase movement onions.

To increase the emf of cell.

To decrease the temperate

To maintain electrical neutrality

In the presence of Aluminium ethoxide, aldehydes get converted into esters. The reaction is known as

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Schmidt reaction

Aldol condensation

Beckmann's rearrangement reaction

Tischenko reaction

Which will have the maximum value of heat of hydration

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Na⁺

Cs⁺

Ba⁺²

Mg⁺²

The four bonds of carbon in methane are directed towards the corners of

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Cube

Pentagon

Hexagon

Tetrahedron

Choose an answer

Homogeneous

Heterogeneous

Isogeneous

None

Splitting of spectral lines when atoms are subjected to strong electron field is called

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Zeeman effect

Stark effect

Photoelectric effect

Compton effect

Polyester resins have special use in:

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Clothing

Paints

Emulsion

Floor covering

Azeotropic mixture of HCl and water has

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48% HCl

22.2% HCl

36% HCl

20.2% HCl

Rutherford's model of atom failed because:

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The atom did o have a nucleus and electrons

It did not account fro the attraction b/w protons and neutrons

It did no account for the stability of the atom.

There is actually no space b/w the nucleus ad the electrons.

Which of the following reaction is characteristic of benzene

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Electrophilic substitution reaction

Reduction

Oxidation

Ozonolysis

Which of the following statements is not true?

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Isotopes with even atomic masses are comparatively abundant

Isotopes with even atomic masses and even atomic numbers are comparatively abundant

Isotopes with even atomic masses and odd atomic number are comparatively abundant

A compound possessingα-hydrogen atom, in the presence of dilute alkali formsβ-hydroxy aldehyde. This product on heating with dilute acid forms an unsaturated crotonaldehyde. The compound is

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CH₃CHO

CH₃CH₂CHO

CH₂= CH - CHO

HC = C - CHO

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Treatment with HCN followed by acid hydrolysis

Oxidation of acetaldehyde followed by basic hydrolysis

Treatment with HCN followed by reduction

Treatment with HCN followed by oxidation

The reactivity order of alkyl halides for a paricular alkyl group is

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Fluoride > chloride > bromide > iodide

Chloride > bromide > fluoride > iodide

Iodide > bromide > chloride > fluoride

Bromide > iodide > chloride > fluoride

Which of the following pair contains isomers of each other

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Propanoic acid and propanone

Acetone and acetaldehyde

Ethyl alcohol and diethyl ether

Methyl alcohol and dimethyl ether

Major food factors are:

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Fats and oils

Carbohydrates

Proteins

All of these

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

When phenol is reduced in the presence of Zn dust, we get

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Cyclohexene

Cyclohexane

Benzene

Benzyne

The number of unpaired electrons in the p-subshell of oxygen atom

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1

2

3

4

Which of the following has the maximum number of unpaired d-electrons?

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Zn

Fe²⁺

Ni³⁺

Cu⁺

Which of the following statement about fluorine is not correct?

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Electron affinity of chlorine is greater than that of fluorine

Bond energy of fluorine is less than that of chlorine

Fluorine cannot be prepared by electrolysis of fused metal fluorides

Fluorine does not form oxoacid

Variable valency is generally exhibited by

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Normal elements

Transition elements

Metallic elements

None of these

Keeping in view the size of atoms, which order is the correct one

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Mg > Sr

Ba > Mg

Lu > Ce

Cl > l

A single chlorine free radical can destroy how many ozone molecules

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100

100000

10000

10

Which is used in navigational equipments?

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B

Be

Mg

Al

Alkanes normally have ______ hybridization

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Sp

Sp²

Sp³

d sp³

Which element has 4 unpaired electrons in 3d-orbital

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Chromium - 24

Manganese - 25

Iron - 26

Cobalt - 27

The term ebullioscopy is used for

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Depression of freezing point

Elevation in boiling point

Lower of vapour pressure

None of the above

Which is not state function

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Temperature

Enthaply

Entropy

Internal energy

Benzophenone can be converted into benzene using

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Fused alkali

Anhydrous AlCl₃

Sodium amalgam in water

Acidfied dichromate

Choose an answer

Le-chatlier's principle

Only adding catalyst

Decreasing pressure

Decreasing temperature

Any substance under going physical or chemical change is said to be

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Surrounding

System

Losphere

Lithosphere

Sulphuric acid has great affinity for water because

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It hydrolyses the acid

It decomposes the acid

Acid forms hydrates with water

Acid decomposes water

Selection of filter paper depends upon sizes of particles to be:

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Tested

^Filtered

Checked

All of above

White phosphorus is

Choose an answer

A mono atomic gas

P₄, a tetrahedral solid

P₈, a crown

A linear diatomic molecule

The relative lowering of vapour pressure is equal to the mole fraction of the solute is statement of

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Rault law

Henry law

Dalton law

Grahms law

Which compound will not dissolve in H₂O

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C₆H₆

C₂H₅OH

CH₃CH₂CH₂OH

CH₃- OH

Choose an answer

Small change in concentration of product

Small time internal

Co-efficient of the reactant

Co-efficient of the product

The sample being analyzed is called :

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Electrolyte.

Substance.

Analyte.

All of above.

A fat or oil is characterised for extent of unsaturation by one of the following number, which one

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Rancidity number

Acid number

Iodine number

Saponicfication number

Metallic conduction is due to the

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Movement of electrons

Movement of ions

Both a and b

None of these

Which of the statements given below concerning properties of solution, describe a colligative effect?

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Boiling point of pure water decreases by the addition of ethanol

Vapour pressure of pure water decreases by the addition of nitric acid

Vapour pressure of pure benzene decreases by the addition of naphthalene

Boiling point of pure benzene increases by the addition of toluene

The solubility product of Ca(OH)₂is 6.5 x 10^-6. The concentration of OH^-ions is

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1.175 x 10^-2

2.35 x 10^-2

3.25 x 10^-3

3.25 x 10^-4

Which of the following hydrides has the lowest boiling point?

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H₂O

H₂S

H₂S3

H₂Te

Hydrogenation of vegetable oils is accelerated by Ni catalyst. The catalytic activity of Bi is increased by a promoter of activator which is

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Na and K

Na and Hg

Hg and Zn

Cu and Te

During redox reaction an oxidizing agent

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Gains electrons

Is oxidized

Loses electrons

Hydrolysed

Which one of the following is not a nuclelphile

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H₂O

H₂S

BF₃

NH₃

Negatively charged particle nature of cathode rays was first demonstrated in 1895 by:

Choose an answer

Millikan.

J. Perrin.

Hittrof

J.J. Thomson.

A bond between two atoms may be obtained by sharing of electrons such a bond is called

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An ionic bond

A coordinate bond

A dative bond

A covalent bond

The geometry of [Co(NH₃)₆]³⁺is

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Tetrahedral

Square planar

Octahedral

None of these

Which of the following is known as wood spirit

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Ethyl alcohol

Propyl alcohol

Methyl alcohol

Butyl alcohol

Which statement about Arrhenius equation is incorrect

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Factor 'A' called Arrhenius constant depends upon collision frequency of reactants

Rate of reaction increase by increasing temperature

Rate constant k is increased

Activation energy Ea is decreased by rise in temperature

Determination of atomic masses and invention of system of writing symbols was made by:

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J. Berzelius

Democritus

Dalton

None of above

Synthesis of rubber is made by polymerization of

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Chloroform

Acetylene

Divinylacetylene

Butene

Compounds of carbon and hydrogen in which the tetra valency of carbon is fully satisfied are called,

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Saturated

Un-saturated

Magnetic

Para-magnetic

In which of the following theories the hybridizationis considered

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Vsepr

Lewis

Molecule orbital

Valence bond

Which is not a calcarious material?

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Lime

Clay

Marble

Marine shell

Which of the following groups will increase the acidity of phenol?

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-NO₂

-CN

-X (halogens)

All

Choose an answer

High temperature

Low temperature

Low pressure

High pressure