Question # 1

Choose an answer

for n€ N, 3^{2n + 7 is divisible by}

Choose an answer

7

8

9

10

An equation containing at least one derivative of a depends variable with respect to independent variable is a (an)

Choose an answer

Implicit equation

Differential equation

General equation

None of these

Choose an answer

If a,b,c are three non-coplanar vector then [a +b,b +c,c +a] = _____

Choose an answer

[a.b.c]

2[a,b,c]

[abc]-2

2[abc]2

The greatest term in the expansion of (3+2x)⁹, when x=1 is

Choose an answer

4th

4th and 5th

5th

6th

Choose an answer

4

6

8

10

If sin x + sin²x = 1, then the value of Cos¹²x + 3cos¹⁰x + 3cos⁸x + cos⁶x + 2 cos⁴x + cos²x-2 is equal to

Choose an answer

0

1

2

sin²x

The statement that a group can have more than one identity elements is

Choose an answer

True

False

Fallacious

Some times true

Fifteen girls compete in a race. The first three places can be taken by them in

Choose an answer

3! ways

12! ways

15 x 14 x 13 ways

42 ways

Choose an answer

x^-2+ c

not possible

Choose an answer

Associative law of multiplication

Commutative law of addition

Commutative law of multiplication

Associative law of addition

The sum of the roots of the equation x2 -6x +2 = 0 is

Choose an answer

-6

2

-2

6

Choose an answer

If n(X) = 18, n(X∩Y) = 7, n(X∪ Y) = 40 then n(Y) =

Choose an answer

1

12

5

29

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

Choose an answer

A.P.

G.P.

H.P.

None of these

Number of combination of zero or more things out of n different things

Choose an answer

nPn

nPr

nCr

2n

If m and n be two scalars, then (m+n) g =

Choose an answer

0

m+n

m▁a+n▁a

ma - m▁a

If B⊆ A, then complement of B in A is = -----------------------

Choose an answer

A-B

A∩B

B-A

A∪B

Choose an answer

2 b

2 a

2 ab

a + b

The period of cos(7x-5) is

Choose an answer

π/7

7π/2

π/2

2π/7

Choose an answer

Closure law of addition

Associative law of addition

Commutative law of multiplication

Associative law of multiplication

The angle between lines xy =0 is

Choose an answer

45°

60°

90°

180°

A box containing 10 mangoes out of which 4 are rotter. Two mangoes are taken together from the box. If one of them is found to be good, the probability that the other is also good is

Choose an answer

1 / 3

8 / 15

5 / 13

5 / 9

Choose an answer

The period of the function csc x/4 us

Choose an answer

4x

π/4

8π

π/8

Choose an answer

If f(x) = x³- 2x²+ 4x -1, then f(-2) = ?

Choose an answer

0

-25

5

45

Choose an answer

184

none of these

a >b ⇒a +c >b +c is known as

Choose an answer

Trichotomy property

Additive property of inequality

Transitive property

Multiplicative property

The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is

Choose an answer

The sets {1, 2, 4} and {4, 6, 8, 10} are

Choose an answer

Equal sets

Equivalent sets

Disjoint sets

Over lapping sets

For a square matrix A, if A = A^t, then A is called

Choose an answer

matrix

Transpose

Symmetric

Non-symmetric

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

Choose an answer

Which one represents a sequence

Choose an answer

an

Sn

a(n)

{an}

The number of divisors of 1029, 1547 and 122 are in

Choose an answer

A.P.

G.P.

H.P.

None of these

If A ⊆ B then A ∪ B is

Choose an answer

A

B

A'

A ∩B

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

Choose an answer

5th term of a G.P. is 2, then the product of first 9 terms is

Choose an answer

256

128

512

None of these

For two vector a and b, a+b = _______

Choose an answer

a b

b+a

b-a

None

Choose an answer

all are correct

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

Choose an answer

10

5

2

The centre fo the circle x²+ y²+ 12x -10 = 0 is

Choose an answer

(12, -10)

(6, -5)

(-12, 10)

(-6, 5)

There is no integer n for which 3n is

Choose an answer

Even

Prime

Odd

Real

if a₁ =3, d=7 and a_n =59 , then the number of terms in A.P is

Choose an answer

7

9

11

13

Choose an answer

A

A'

U

None of these

√2 is a number

Choose an answer

Rational

Irrational

Even

Odd

Choose an answer

If sinθand cosθare the roots of the equation ax²- bx + c = 0, then a, b, c satisfy the relation

Choose an answer

b²- a²= 2ac

A²- b²= 2ac

A²+ b²= c²

B²+ a²= 2ac

The distance of the point (1.1) from the origin is

Choose an answer

0

2

Matrices are represented by

Choose an answer

Natural numbers

Real numbers

Small letters

Capital letters

The period of cot 8x is

Choose an answer

π/10

9π/7

π/9

π/8

Which of the following is a scalar.

Choose an answer

electric field

magnetic field

weight

mass

A fixed point which lies on the axis of the cone is called its:

Choose an answer

axis

apex

plane

diameter

Choose an answer

If w is a cube root of unity then 1 + w + w²= ______

Choose an answer

1

2

0

-1

Choose an answer

1/2

2

1/4

4

Choose an answer

none of these

Choose an answer

If z₁ = 1 + 2i, z₂ = 3 + 4i then

Choose an answer

z₁ > z₂

z₁ = z₂

z₁ < z₂

None of these

Identity w.r.t intersection in a power set of any set is

Choose an answer

∅

Set itself

Singleton set

{0}

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

Choose an answer

0

1

2

Infinite

How many arrangements of the letters of the word MATHEMATICS can be made

Choose an answer

An even function is symmetric about the line

Choose an answer

y = x

x = 0

y = -x

y = 0

The law of tangents is ______

Choose an answer

The points (x, y) which satisfy a linear inequality in two variables x and y from its

Choose an answer

domain

range

solution

none of these

The range of the principal sine function is

Choose an answer

202.04 is an example of

Choose an answer

Recurring decimals

Non-recurring decimals

Terminating decimals

None of these

The first three terms in the expansion of (1 - x)^-3are

Choose an answer

1 + 3x + 6x²

1 - 3x + 6x²

-3 - 3x - 6x²

1 - 3x - 6x²

If the sum of even coefficients in the expansion of (1+x)n is 128 then

Choose an answer

n=7

n=9

n=8

None

Choose an answer

Equation of parabola with focus F(-3,1) directrix x=3 is

Choose an answer

(y -1)2 =-12x

(y-1)2 =4x

(x+3)2 =4a(y-1)

y2 =-12(x-1)

The order of the matrix A is 3 x 2 and that of B is 2 x 3. The order of the matrix BA is

Choose an answer

3 x 3

3 x 2

2 x 5

5 x 2

Choose an answer

If B-A≠φ , then n(B-A) is equal to

Choose an answer

n(a)+n(c)

n(c)-n(a)

n(a)-n(c)

None of these

A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining a head and an even number is

Choose an answer

1/8

2/8

3/8

None of these

What is range of the function g (x) =|x-3|?

Choose an answer

[0 ,∞ )

(0 ,∞)

(-∞ ,3]

[0,∞)

Choose an answer

Square matrix

Row matrix

Symmetric matrix

Null matrix

7²ⁿ+ 3^n-1. 2^3n-3is divisible by

Choose an answer

24

25

9

13

Choose an answer

-a -b -c

1

0

-1

If u = xi + yj, then|u|

Choose an answer

x² + y²

(x² +y²)²

x²-y²

√(x²+y²)

If circumference of circle is divided into 360 congruent parts the angle subtended by one part at the centre of circle is

Choose an answer

1 degree

1 second

1 minute

1 radian

The differential equations of all conis whose axes coincide with the co-ordinate axis is

Choose an answer

The set of the first elements of the orders pairs forming a relations is called its

Choose an answer

Relation in B

Range

Domain

Relation in A

The domain of a finite sequence is a

Choose an answer

Set of natural numbers

R

Subset of N

Proper subset of N

Choose an answer

The number of non zero rows in echelon form of a matrix is called

Choose an answer

Order of matrix

Rank of matrix

Row operation

None of these

A box contains 10 red 30 white and 20 black marbles When a marble is drawn at random the probability that it is either red or white is

Choose an answer

1/6

1/3

1/2

2/3

Choose an answer

range of f

domain of f

both (a) and (b)

none of these

The line 3x - 4y = 0

Choose an answer

Is a tangent to the circle x²+ y²= 25

Is a normal to the circle x²+ y²=25

Does not meet the circle x²+ y²= 25

Does not pass thro' the origin

Inverse of the function y-10x is

Choose an answer

y=logx

y=lnx

x=10y

Which is used as a coagulant:

Choose an answer

Ferric Salts

Potash alum

a and b both

Chlorine

Chromium (VI) is highly toxic and can cause

Choose an answer

Blindness

Cancer

Liver problems

Blood problems

Which is not a component of environment

Choose an answer

Biosphere

Lithospahre

Hydrosphere

None of these

Standard reduction electrode potential of three metals A, B and C are erespectively + 0.05 V, -3.0 and -1.2V. The reducting power of

Choose an answer

B > C > A

A > B > C

C > B > A

A > C > B

The osmotic pressure of a dilute solution is directly proportional to the

Choose an answer

Diffusion rate of the solute

Ionic concentration

Elevation in boiling point

Flow of solvent from a concentrated to a dilute solution

Turnbull's blue is a compound called?

Choose an answer

Ferricyanide

Ferrous ferricyanide

Ferrous cyanide

Ferri - Ferro cyanide

Antibonding MO is formed by

Choose an answer

Addition of atomic orbitals

Substraction of atomic orbitals

Multiplication of atomic orbitals

None of these

Which of the following represents elements in order of increasing atomic size?

Choose an answer

I, Br, Cl

Na, Mg, C

C, N, O

Li, Na, K

The reaction is galvanic cell is

Choose an answer

Spontaneous

Non-spontaneous

Acid-base

None of these

The de-Brogile wavelength of a particle with mass 1g and velocity 100 m/s is

Choose an answer

6.63 x 10^-33m

6.63 x 10^-34m

6.63 x 10^-35m

6.65 x 10^-35m

In thermal decomposition of N₂O the half life period for two different initial concentrations of N₂O are

(i) 255 second for initial N₂O 290 mm Hg

(ii) 212 second for initial N₂O 360 mm Hg then it is

Choose an answer

Zero order

First order

Second order

Third order

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

Choose an answer

Zn

Fe²⁺

Ni³⁺

Cu⁺

The period table contains elements in vertical column. these vertical column are called

Choose an answer

Groups

Periods

Blocks

Sub group

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

Choose an answer

H₂SO₄

CuSO₄

ZnSO₄

Na₂SO₄

When an electric current is passed through discharge tube at low pressure, cathode rays are emitted from cathode these rays consist of:

Choose an answer

Alpha rays.

Negative particles.

Electromagnetic rays.

Positive particles.

In the manufacture of iron from haematitie,limestone is added to act as

Choose an answer

Flux

A reducing agent

Slag

An oxidizing agent

Fungicides are the pesticides which

Choose an answer

Control the growth of fungus

Kill insects

Kill plants

Kill herbs

Choose an answer

Alkyl

Alkyl nitrile

Cyanogens

Amine

Which of the following phosphorus is most reactive?

Choose an answer

Red phosphorus

White phosphorus

Scrlet phosphorus

Violet phosphorous

What is the shape of Fe(CO)₅molecule?

Choose an answer

Tetrahedral

Octahedral

Trigonal bipyramidal

Square pyramidal

Major food factors are:

Choose an answer

Fats and oils

Carbohydrates

Protiens

All of these

The total number of transition elements is

Choose an answer

10

14

40

50

Chloroform is carcinogenic:

Choose an answer

Heart

Lungs

Liver

Kidney

(CH₂O)_nis general formula for

Choose an answer

Monosaccharides

Oiligosaccharides

Polysaccharides

None of these

Smallest particle of an element which may or may not have independent existence is known as:

Choose an answer

A molecule

An ion

An atom

An electron

The relative lowering of vapour pressure is equal to the mole fraction of the solute, This law is called

Choose an answer

Henry's law

Raoult's law

Ostwald's law

Arrhenius law

Which of the following process is employed to convert alkyl halide into alcohol?

Choose an answer

Addition

Substitution

Dehydrohalogenation

Molecular rearrangement

The compound which gives oxygen on moderate heating is

Choose an answer

Zinc oxide

Mercuric oxide

Aluminium oxide

Ferric oxide

CL₂, N₂ and O_{2 are:}

Choose an answer

Diatomic molecules

Hetero atomic molecules

Poly-atomic molecules

Mono-atomic molecules

Which of the following is an isomer of ethanol

Choose an answer

CH₃OCH₃

C₂H₅OC₂H₅

CH₃OH

C₂H₅OH

Which woody raw material is used for manufacture of paper pulp?

Choose an answer

Cotton

Bagasse

Popular

Rice straw

The substance which is present in large quantity is called a :

Choose an answer

Solute

Solvent

solutiion

None of Above

Choose an answer

High temperature and low pressure

Low temperature and high pressure

Low temperature and low pressure

High temperature and high pressure

B.O.D is connected with

Choose an answer

Organic matter

Microbes

Mircrobes and organic matter

None of the above

The charge of an electron is determined by

Choose an answer

J.J. Thomson

Crooks

Perrin

R.A.Millikan

Boiling point of acetic acid is°C:

Choose an answer

116

117

118

119

Besides Zn and Cu , German silver contains the metal

Choose an answer

Sn

Ag

Ni

Mg

The carbon of a carbonyl group is:

Choose an answer

sp hybridized

sp²hybridized

sp³Hybidized

None of these

Best medhod of preparation of alkyl halide from alcohals is by its reaction with:

Choose an answer

HX

SOCl₂

Px₅ and PX₃

All

To determine the rate of reaction chemically a graphical method is applied. A graph is plotted between the amount or reactant decomposed or product formed against the time. The rate d_x/d_tat any time is equal to

Choose an answer

k

Tangentθ

1/a, a is initial conc.

1/a²

Nitrogen in NH₃is sp³hybridized but the bond angle in NH₃is 107° and not 109.5° due to

Choose an answer

sp³orbital planar

sp³orbital trigonal

Repulsion between lone pair and bonded pairs

None of them

Alkynes normally have ______ hybridization

Choose an answer

Sp

Sp²

SP³

d sp³

Fatty acids are:

Choose an answer

Allphatic monocarboxylic acids

Dicaroxylic acids

Tricarboxylic acids

Tetracarboxylic acids

Poly carboxylic acids

Spraying of DDT produces pollution of

Choose an answer

Air

Air and water

Air and soil

Air, water and soil

Rusting of iron is catalysed by

Choose an answer

Fe

O₂

Zn

H⁺

Isotopes differ in

Choose an answer

properties which depend upon mass

arrangement of electrons in orbitals

chemical properties

the extent to which they may be affected in electric fields

(A) is one molar NaCl solution and (b) is 1 molal NaCl solutin :

Choose an answer

A and B are of same strength.

A is more Concentrate than B.

b is more Concentrate than A.

None of above.

Across the lanthanide series, the basicity of the lanthanide hydroxides

Choose an answer

Increases

Decreases

First increases and then decreases

First decreases and then increases

The temp. and pressure used for PVC polymerization is

Choose an answer

10°C and 10 atm

20°C and 20 atm

52°C and 9 atm

100°C and 10 atm

Covalent compound s mostly exist in the form of:

Choose an answer

Protons

Atoms

Neutrons

Molecules

A buffer solution of 0.1 molar HCOOH and 0.1 molar HCCONa has pH = 3.78 To is 0.01 molar HCl is added, then pH of the buffer solution becomes

Choose an answer

2.78

4.78

3.78

3.70

Which is not property in ether:

Choose an answer

Very weak hydogen bonding

High b.p

Slightly soluble

Inflammable

In aldol condensation reaction, a double bond is formed between ______ and ______ carbon atoms

Choose an answer

αandβ

αandα

αand Y

None of these

DDT is

Choose an answer

Biodegradable pollutant

Nondegradable pollutant

Not a pollutant

An antibiotic

Which of the followingα-Amino acids has basic R-group

Choose an answer

Proline

Glutamic acid

Histidine

Valine

Which of the following does not give iodoform test?

Choose an answer

Ethanol

Ethanal

Acetophenone

Bezophenone

The energy required to break one mole of bonds to form neutral atoms is called

Choose an answer

Bond length

Bond strength

Bond energy

None of these

Which of the following may affect the rate constant (k) fro a reaction :

Choose an answer

Change in concentration.

Change in pressure.

Change in pH.

Change in temperature.

Sodium forms largely

Choose an answer

Normal oxides

Per-oxides

Superoxides

None of these

When a carboxylic acid reacts with a metal ______ gas is evolved

Choose an answer

H₂

CO₂

CI₂

None of these

When two hydrogen atoms approach each other.

Choose an answer

Forces of attraction operate.

Forces of repulsion operate.

Forces of attraction and repulsion operate simultaneously.

Nothing happens.

Preparation of vegetable ghee involves:

Choose an answer

Halogenation

Hydrogenation

Hydroxylation

Dehydrogenation

Enzymes catalyse all biological reactions occurring in the cell. What is true about an enzyme

Choose an answer

Enzyme is a small molecule

Enzyme is acidic in nature

Enzyme is a protein

Enzyme is a lipid

Simple sugars are :

Choose an answer

Monosacchrides

Disaccharides

Oligo saccharides

Trisaccharides

Phenol is used in the preparation of

Choose an answer

Bakelite

Phenatherene

Cellulose

All of these

The acid used in lead storage cells is

Choose an answer

Phosphoric acid

Nitric acid

Sulphuric acid

Hydrochloric acid

Which of the following will have the highest boiling point at 1 atm pressure?

Choose an answer

0.1 M NaCl

0.1 M Sucrose

0.1 M BaCl₂

0.1 M Glucose

Choose the correct answer of transition elements?

Choose an answer

Transition elements have low melting points

Transition elements do not have catalytic activity

Transition elements exhibit variable oxidation states

Transition elements exhibit inert pair effect

Isotopes of an element differ in

Choose an answer

Number of protons

Number of electrons

Number of neutrons

Number of electrons and protons

Polysaccharides are also called

Choose an answer

Crystals

Sugars

Liquids

None sugars

Lattice energy of NaCI

Choose an answer

+5000 KJ

-344 KJ

-776 KJ

-411 KJ

When during electrolysis of a solution of AgNO₃, 9650 coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be

Choose an answer

1.08 g

10.8 g

21.6 g

108 g

Alcohals can be distinguished using test:

Choose an answer

Lucas

Tollen's

Koib's

William's

Which alcohol gives only one oxidation product when wormed with dil acidified K₂Cr₂O₇

Choose an answer

Butan-1-ol

Butan-2-ol

2-methyl propan-1-ol

2-methyl propan-2-ol

3-d series elements are present in:

Choose an answer

First period

Second Period

Third period

4th period

Which of the following metals is sometimes found in native state in nature?

Choose an answer

Al

Cu

Fe

Mg

Which on of the following compounds does not exist?

Choose an answer

NCl₅

AsF₅

SbCl₅

PF₅

Two or more similar monomers combine to form:

Choose an answer

Homopolymer

Copolymer

Ter Polymer

Thermoplastic polymers

Micro-nutrients are required in quantity ranging from

Choose an answer

4g-40g

6g-200g

6Kg-200Kg

4Kg-40Kg

The polymers which can be re-softened again and again are caled

Choose an answer

Thermoplastic

Thermosetting

Both a and b

None

Which one of the following step is not involved in determination of empirical formula

Choose an answer

Determination % of each element

Determination of gram atom of each element

Determination of isotopes of each element

Determination of atomic ratio of element

Tincal is a mineral of:

Choose an answer

Al

B

Si

C

Which of the following elements is most electronegative?

Choose an answer

Oxygen

Chlorine

Nitrogen

Fluorine

Protein may have

Choose an answer

Primary structure

Secondary structure

Tertiary structure

All of these

The order of reactivity of halogen acids towards alkenes

Choose an answer

HCl > HBr > Hl

HBr > HCl > HI

HCl > HBr

HI > HBr > HCl

The ionic bonds are

Choose an answer

Unidirectional

Bi-directional

Non-directional

Multi-directional

When 6d orbital is complete, the entering electron goes into:

Choose an answer

7f.

7s.

7p.

7d.

Choose an answer

1st order

2nd order

Zero order

3rd order

Minamata disease is due to pollution of

Choose an answer

Organic waste into drinking water

Oil spill in water

Industrial waste containing mercury into fishing water

Arsenic into the atmosphere

The chemist who synthesized urea from ammonium cyanate was

Choose an answer

Berzelius

Kolbe

Wholer

Lavoisier

Generally electron affinities for elements in a period from left to right

Choose an answer

Decreases

Increases

Remain same

Increases alternatively

The empirical formula of benzene is determined by

Choose an answer

IR spectra

U.V

Elemental analysis

NMR spectra

Alkyl halides are reactive :

Choose an answer

High

Medium

Less

Least

Sp³hybird orbitals are oriented at an angle of

Choose an answer

107.5°

108.5°

109.5°

103.5°

An ionic compound A+B is most likely to be formed when

Choose an answer

The ionization energy of A is high and electron affinity of B is low.

The ionization energy of A is low and electron affinity of B is high.

Both ionization energy of A and electron affinity of B are high.

Both ionization energy of A and electron affinity of B are low.

Which of the following chlorocompounds is heat easily hydrolysed by hydorxide ion to give the product indicated

Choose an answer

Value of chemical oxygen demand (COD) is a measure of chemically oxidizable matter in water. Which value of COD will indicate more polluted water

Choose an answer

Low value

Higher value

Both values

None of these

Dehydration of glycerol give

Choose an answer

Propane

Propene

Acrolein

Benzene

The galvanic or voltaic cells which are rechargeable called as

Choose an answer

Primary cells

Secondary cells

Dry cells

Infinite cells

In Lucas test teriary alcohol make an oily layer

Choose an answer

Immediately

In 10 mins

On heating

Not

Which statement is incorrect about standard hydrogen electrode

Choose an answer

Its oxidation and reduction potential is zero

It consists of Pt wire dipped on 1 molar HCI solution

The electrolyte is 1 molar NaOH solution

H₂gas is passes in it at 1 atmospheric pressure