Question # 1

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

Choose an answer

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

Choose an answer

Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

Geometrically, the modulus of a complex number represents its distance from the

Choose an answer

Point (1, 0)

Point (0, 1)

Point (1, 1)

Point (0, 0)

Choose an answer

The number of values of x in the interval [0, 5π] satisfying the equation 3 sin²x - 7 sinx + 2 = 0 is

Choose an answer

0

5

6

10

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

Choose an answer

Boundary

Inequality

Half plane

Vertex

Cycle tyres are supplied in lots of 10 and there is a chance if 1 in 500 tyres to be defective. Using Poisson distribution, the approximate number of lots containing no defective tyre in a consignment of 10, 0000 lots is

Choose an answer

9028

9208

9802

9820

The third term in the expansion of (1+2x) is

Choose an answer

-2x2

-4x2

2x2

4x2

The set of all points in the plane that are equally distant from a fixed point to called a

Choose an answer

Parabola

ellipse

Hyperbola

Circle

If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is

Choose an answer

8

12

10

14

A circle drawn inside a triangle and touching its sides is called

Choose an answer

In-circle

Circum circle

Escribed circle

None of these

A point where two of its boundary lines intersect is called

Choose an answer

Corner point

Feasible point

Vertex

Feasible solution

Choose an answer

Distance between A(3, 8), B(5, 6) is

Choose an answer

If A is a set then any subset R of A x A is called

Choose an answer

relation on A

relation on B

relation from A to B

relation from B to A

Choose an answer

0

1

2

4

Choose an answer

12

6

8

none of these

A fraction in which the degree of the numerator is less the degree of the denominator is called

Choose an answer

Polynomial

Proper fraction

Rational fraction

None

Choose an answer

Which one is not defined∀n∈Z+

Choose an answer

-n!

n!

(-n)!

n!+0!=n!+1

Choose an answer

There is no integer n for which 3ⁿis

Choose an answer

Odd

even

Natural

Prime

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

Choose an answer

Differential equation

Initial condition

General solution

Singular equation

tan(2π+θ) = ________;

Choose an answer

tanθ

-tanθ

cotθ

-cotθ

Choose an answer

i³=

Choose an answer

-1

i

-i

1

The difference of two consecutive terms of an A.P is called the

Choose an answer

Common difference

Common ratio

Geometric series

Geometric mean

Choose an answer

The equation of the circle with centre origin and radius r is

Choose an answer

x²+ y²= 1

x²+ y²= r²

x²+ y²= 0

x²- y²= r²

Choose an answer

a cosec(ax + b) + c

- a cosec(ax + b) + c

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

Choose an answer

12

8

24

-24

For any set B,B∪B' is

Choose an answer

Is set B

Set B'

Universal set

Which of the following is a factor of x³- 3x²+ 2x - 6

Choose an answer

x + 2

x + 3

x - 3

x - 4

If S_rdenotes the sum of the first r terms of a G.P., then S_n, S_2n- S_n, S_3n- S_2nare in

Choose an answer

A.P.

G.P.

H.P.

None of these

Choose an answer

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is

Choose an answer

120

100

140

160

If x,y are two -ve distinct numbers then

Choose an answer

A>G>H

A<G<H

A=G=H

None of these

Choose an answer

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

Choose an answer

14 / 29

20 / 39

1 / 2

n

A function from X to Y is written as

Choose an answer

f : X to Y

f : Y to Y

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

Choose an answer

an ellipse

a hyperbola

a circle

a parabola

If you are looking a high point from the ground, then the angle formed is

Choose an answer

Angle of elevation

Angle of depression

Right angle

Horizon

If A and B are two disjoint events then

Choose an answer

P(A∪B)=P(A)+P(B)

P(A∪B)=P(A)-P(A∪B)

P(A∪B)=P(A)or P(B)

None

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

Choose an answer

A = B iff

Choose an answer

All elements of A also the elements of B

A and B should be singleton

A and B have the same number of elements

If both have the same element

Choose an answer

tanθ/2

Choose an answer

The point which is closet to the focus of a parabola is:

Choose an answer

vertex

Chord

Focus

Directix

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

Choose an answer

a = 1 , b = 1

a = 1 , b = 0

0.25 is ______

Choose an answer

An irrational number

A natural number

A prime number

A rational number

The roots of ax2+bx+c=0 are

Choose an answer

Rational ⇔ b2 -4 ac ≥ 0

Irrational ⇔ b2-4 ac > 0

Real ⇔ b2-4 ac ≠ 0

Rational⇔ b2-4 ac = 0

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

Choose an answer

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

Choose an answer

A = B

B = C

A = C

None of these

Choose an answer

2 x 2

2 x 3

3 x 2

3 x 3

For any set B, BUB' is

Choose an answer

Is set B

Set B'

Universal set

None of these

An open sentence formed by using the sign of equality "=" is called

Choose an answer

Equation

In equation

True sentence

False sentence

Choose an answer

none of these

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

Choose an answer

1/2

√3/2

-1/2

1/√2

Choose an answer

The line y =mx +1 is tangent to the parabola y2 =4x if

Choose an answer

m=1

m=2

m=3

m=4

{x : xε Z and x < 1} is

Choose an answer

Singleton set

A set with two points

Empty set

None of these

Choose an answer

The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if

Choose an answer

A = B≠ 0

A≠ B and both are of same sign

A≠ B both are of opposite sign

Either A = 0 or B =0

Choose an answer

12

13

14

15

45° = ______

Choose an answer

If Z₁ = 1+ i, Z₂ = 2+3i , then |Z₁ -Z₂| =?

Choose an answer

√5

√7

-1-2i

√3

Choose an answer

x = f(y)

y = f(x)

x = f(x)

y = f(y)

The seventh term of an A.P whose first term is P and common difference is q. is

Choose an answer

P-6q

P+6q

P-4q

P-nq

tan (π-θ) = ______

Choose an answer

- sinθ

- tanθ

- cosθ

- cotθ

When rational fraction is separated into partial fractions, the result is

Choose an answer

an identity

A fraction

A partial sum

Improper fraction

The sum of coefficients in the binomial expansion equals to

Choose an answer

2

2ⁿ⁺¹

2^n-1

2ⁿ

Minor of an element a_ijis denoted by

Choose an answer

M_ij

A_ij

|A|

None of these

Choose an answer

1, 1/2, 0

1, 2, 1

1, 2, 3

1, 2, 0

Z is the set of integers (Z.*) is a group with a * b = a +b +1, a,b ∈ G.then inverse of a is

Choose an answer

-a

a +1

-1-a

None of these

Which of the following is not a quadrantal angle

Choose an answer

90°

100°

180°

270°

Choose an answer

For f(x) = x2, what is the value of f(a) +f (-a) in terms of a?

Choose an answer

3a2

2a2

2a

-7a

The velocity and acceleration at any point t of a particle which moves along straight line x = 5r-3

Choose an answer

5,3

5,-3

5,0

10,0

To each element of a group there corresponds ______ inverse element

Choose an answer

Two

One

No

Three

Z is a group under

Choose an answer

Subtraction

Multiplication

Addition

None of these

Roots of the equation x²+ 5x - 1 = 0 are

Choose an answer

Rational

Irrational

Complex

None of these

Range of 3 sin x is ______

Choose an answer

[ -3, 3]

[-1, 1]

R

None of these

If one end of the diameter of the circle 2x²+ 2y²-8x - 4y = 2 = 0 is (2 ,3), the other end is:

Choose an answer

(2,1)

(-2,1)

(2,-1)

(1,-1)

What is the circular measure of the angles between the hands of which at 4 o clock

Choose an answer

π/6

3π/2

π/4

2π/3

Choose an answer

A prime number

An integer

A whole number

An irrational number

Choose an answer

f(x) = C is

Choose an answer

identity function

constant function

linear function

quadratic function

For all points (x,y) in third quadrant

Choose an answer

x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

Choose an answer

2, 3

3, 3

2, 6

2, 4

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

Choose an answer

128π sq. units

64π sq. units

32π sq.units

None of these

For each natural number n, n (n+1) is

Choose an answer

an even

an odd

multiple of 3

Irrational

Choose an answer

An expression

Rational fraction

Equation

Identity

The product of complex numbers (a,b) and (c,d) is

Choose an answer

(ac, bd)

(ac-bd, ad+bc)

(ab,cd)

(ac+bd,ad-bc)

Each complex cube root of unity is square of

Choose an answer

itself

1

-1

the other

5-d series is in the period :

Choose an answer

4th

5th

6th

7th

The shape of CIO^-₃according to valence shell electron pair repulsion theory will be

Choose an answer

Planar triangle

Pyramidal

Tetrahedral

Square planar

Hydroxyl amine is a derivative of::

Choose an answer

Alcohol

Aldehyde

Ammonia

Ketone

In the manufacture of NH₃by Haber's process catalyst used is iron its catalytic efficiency is poisoned by

Choose an answer

Presence of Al₂O₃

Presence of Cr₂O₃

MnO₂

CO present with H₂gas

Which one of the following does not belong to alkaline earth metals

Choose an answer

Be

Ra

Ba

Rn

A compound having empirical formula C₃H₃O and its molecular mass is 110.02. Its molecular formula is

Choose an answer

C₃H₃O

C₆H₆O₂

C₉H₉O₃

C₃H₆O₂

The lA elements are called

Choose an answer

Alkaline earth metal

Alkaline metals

The halogens

The inert gases

A compound R has all of the following properties. It is neutral; It gives an orange precipitate with 2,4-dinitrophenythydrazine; it evolves hydrogen chloride when treated with PCI₅in the cold What could R be

Choose an answer

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

Choose an answer

Mg > Sr

Ba > Mg

Lu > Ce

Cl > l

Direct conversion of solid into vapors is called :

Choose an answer

Crystallization

Sublimation

Obligation

Vaporization.

Which of the following order is incorrect w.r.t property indicated?

Choose an answer

Formic acid > Acetic acid > Propionic acid (ACID STRENGTH)

Cyclohexanol < Phenol < Benzoic acid ( ACID STRENGTH)

Benzamide < Aniline < Cyclohexylamine ( ACID STRENGTH)

FCH₂COOH > CICH₂COOH > BrCH₂COOH (ACID STRENGTH)

The addition of unsymmetrical reagent to unsymmetrical alkene is in accordance with the rule:

Choose an answer

Hund's rule

Markownikov's rule

Pauli's Exclusion Principle

Auf bau Principle

Number of elements in the first period of the periodic table are

Choose an answer

Two

Four

One

Eight

Bond angle is minimum for

Choose an answer

H₂O

H₂S

H₂Se

H₂Te

The simplest separating unit of a polymer is called:

Choose an answer

Monomer

Dimer

Trimmer

Macromer

Oxidation of ter-alcohol gives:

Choose an answer

Aldehyde

Formaldehyde

Ketone

Alkens

pH of 1 molar NaOH is

Choose an answer

7

zero

14

10

The substance upon which an enzyme acts is known as its

Choose an answer

Domain

Field

Substrate

Reactant

Which of the following species has unpaired electrons in ant-bonding molecular orbitals?

Choose an answer

O2⁺²

N2^-2

B₂

F₂

Which one gives acidic reactions?

Choose an answer

CH₃----C≡C-------CH₃

CH₃-----CH₂-----HC=CH----CH₂

CH₃----CH=CH₂

CH₃-----C≡CH

Formation of a cation is:

Choose an answer

Exothermic process

Non-endothermic process

Endothermic process

None of above

The degenerate orbitals p-sub shell are

Choose an answer

2

3

5

7

Which one of the following metal ions is colourless?

Choose an answer

V²⁺

Cr³⁺

Zn²⁺

Ti³⁺

Reaction of Griganard's reagent with CO₂gives:

Choose an answer

Aldehyde

Pri-alcohol

Sec-alcohal

Carboxylic acid

Lysine is ______ amino acid

Choose an answer

Acidic

Basic

Natural

None of these

Contamination of water of tanning industries is due to:

Choose an answer

Cr(III)

Cr(VI)

Mn(III)

Mn(VII)

The term cryoscopy is used for

Choose an answer

Depression of freezing point

Elevation in boiling poing

Lowering of vapour pressure

Osmotic pressure

Which gasoline is better?

Choose an answer

Of low boiling point

Of low molecular mass

Of high octane

All of these

[Co(NH₃)₆]³⁺will form ______ structure

Choose an answer

Square planar

Tetrahedral

Octahedral

Trigonal bipyamidal

When the solute is present in trace quantities the following expression is used

Choose an answer

Gram per million

Milligram percent

Microgram percent

Parts per million

Mustard gas is a :

Choose an answer

Gas

Liquid

Solid

High boiling point

The horizontal rows in the periodic table are called periods. The number of period are

Choose an answer

5

6

7

8

Choose an answer

The value of K_pfalls with a rise in temperature

The value of K_pfalls with increasing pressure

Adding V₂O₅catalyst increase the equilibrium yield of sulphur trioxide equilibrium yield of sulphur trioxide

The value of K_pis equal to K_c

The rate of reaction determined at a given time is called

Choose an answer

Average rate

Instantaneous rate

Specific rate

Overall rate

What is the name of the comlex [Ni(CO)₄]

Choose an answer

Tetracarbonylnickel (o)

Tetracabonylnickel

Tetracabonylnickel (II)

Tetracabonylnickel (IV)

First atomic theory was put forward by an English school teacher:

Choose an answer

Maxewell

Newton

Sanger

John Dalton

The group linkage present in fats is

Choose an answer

Peptide linkage

Ester linkage

Glycosidic linkage

None of these

The reactivity order of alkyl halides for a particular alkyl group is:

Choose an answer

F >Cl>Br>I

Cl>Br>F>l

l>Br>Cl>F

Br>l>Cl>F

Unpleasant smell of carbylamine is obtained when chloroform and alcoholic KOH are heated with

Choose an answer

Any aromatic amine

Any primary amine

Any amine

Any aliphatic amine

The other name for distribution law is

Choose an answer

Dispersive law

Partition law

Avogadro's law

separation law

Grignard reagent on reaction with a ketone forms

Choose an answer

Tertiary alcohol

Secondary alcohol

Primary alcohol

Carboxylic acid

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

Which of the following compounds is explosive in nature?

Choose an answer

Phosphorus trichloride

Nitrogen trichloride

Hyponitrous acid

Nitrosyl chloride

The functional group isomer of dimethylether is

Choose an answer

Ethyl alcohol

Propyl alcohol

Diethyl ether

Butyl alcohol

The hydration energy is the heat evolved when one mole of gaseous ion is dissolved in water. The hydration energy of an ion

Choose an answer

Increases with increase of charge to mass ratio

Decreases with increase of charge to mass ratio

Depends on sign of charge +ve or -ve

Depends upon the solvent

Homologues differ from each other by an integral number of

Choose an answer

CH₂groups

CH₃groups

CH groups

CH₄groups

In the ground state, an element has 13 electrons in its M shell. The element is

Choose an answer

Copper

Chromium

Nickel

Iron

Reaction of Grignard's reagent with ketones gives: Reaction of Grignard's reagent with formaldehyde gives:

Choose an answer

Pri-alcohol

Sec-Alcohol

Ter-alcohol

Carboxylic

Bakelite is obtained from phenol by reacting with

Choose an answer

Acetaldehyde

Acetal

Formaldehyde

Chlorobenzene

Glyptal polymer is obtained from glycerol on reacting with

Choose an answer

Malonic acid

Phthalic acid

Maleic acid

Acetic acid

Which of the following reactions is used for detecting presence of carbonyl group?

Choose an answer

Reaction with hydroxylamine

Reaction with hydrazine

Reaction with phenyl hydrazine

All

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

Choose an answer

Saturation

Unsaturation

Subsitution

None

In Lucas test primary alcohol make as oily layer

Choose an answer

Immediately

In 10 mins

On heating

Not

Which of the following has zero depole-moment?

Choose an answer

CIF

PCl₃

SiF₄

CFCl₄

As the nuclear charge increases, the pull on the electrons is increased and size of an atom:

Choose an answer

Decreases.

Remain same.

Increases.

Is negligible.

Choose an answer

s

p

d

f

Essentialα-amino acids are those which are necessary in the diet

Which one is an essentialα-amino acids

Choose an answer

Alanine

Aspartic acid

Glycine

Tryptophan

The human body can synthesize ______ amino acids

Choose an answer

1

10

20

19

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

Choose an answer

Henry's law

Raoult's law

Distribution law

Ostwald's dilution law

Lead accumulator contains

Choose an answer

30% NaCI solution as electrolyte

30% HCI solution as electrolyte

30% H₂SO₄solution as electrolyte

30% NaOH solution as electrolyte

Choose an answer

There is no change in temperature

No change in volume

Heat is absorbed

Heat is released

Generally the bond formed by metals with non-metals is

Choose an answer

Ionic

Covalent

Polar

Non- polar

According to VSEPR theory, the shape of the water molecule is

Choose an answer

Octahedral

Distorted tetrahedral

Planar triangle

Linear

Estimation of Na in sea water is an example of

Choose an answer

Numerical analysis

Qualitative analysis

Quantitative analysis

None of above

Of the following which is a step growth polymer

Choose an answer

Bakelite

Polyethylene

Teflon

PVC

Peroxyacetylnitrate (PAN) is an irritant to human beings and it affects:

Choose an answer

Eyes

Ears

Stomach

Nose

A fibre which is made from acrylonitrile as monomer

Choose an answer

PVC

Rayon fibre

Acrylic fibre

Polyester fibre

Variable valency is characteristic of

Choose an answer

Halogen

Transition elements

Alkali metals

Noble gas

Which reaction produces a free radical

Choose an answer

SN reaction

Homelytic fission reaction

Heterolytic fission reaction

Addition reaction

A reaction in which heat is given out is

Choose an answer

An endothermic reaction

An exothermic reaction

A thermochemical reaction

An energetic reaction

Ethanal may be converted into a three-carbon acid in a two-step process.

Which compound is the intermediate

Choose an answer

CH₃CO₂H

CH₃CN

CH₃CH₂CN

CH₃CH(OH)CN

Acetaldehyde is used to make

Choose an answer

Rubbber

Antiseptics

Phenolic resin

All of these

General formula of aromatic carboxyl acids

Choose an answer

R---------------OH

RCOOH

RCOR

ARCOOH

Choose an answer

Three times

Six times

Nine times

Two times

Alcohols reacts with Grignard reagent to form

Choose an answer

Alkanes

Alkenes

Alkynes

All

Al is the most element in earth crust:

Choose an answer

O

Si

Al

Pb

The reaction in which ketone is reduced to the alkane is called

Choose an answer

Kolb

Clemmensen

Cannizzaro

None

The C-C bond angles in benzene ring are

Choose an answer

119°

120°

121°

None

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

Which of the following statements about acetic, anhydride is not correct

Choose an answer

It is immiscible with water but is hydrolysed to give acetic acid

It is prepared by the action of actyl chloride on the sodium salt of acetic acid

it reacts with ammonia to give acetamide

it is a strong acid

Potassium ferrocyanide is a

Choose an answer

Mixed salt

Double salt

Complex salt

Normal salt

Fungicides are the pesticides which

Choose an answer

Control the growth of fungus

Kill insects

Kill plants

Kill herbs

Sodium forms largely

Choose an answer

Normal oxides

Per-oxides

Superoxides

None of these

Plastics are a pollution problem because many plastics

Choose an answer

Are made from petroleum

Are very inflammable

Burn to produce toxic fumes

Decompose to produce toxic products

Which of the following compounds on boiling with KMnO₄(alk) and subsequent acidification will not give benzoic acid?

Choose an answer

Benzyl alcohol

Acetophenone

Anisole

Toluene

E = hv is the

Choose an answer

Spectral equation

Plank's equation

de Broglie's equation

None of these

Which is used as a coagulant:

Choose an answer

Ferric Salts

Potash alum

a and b both

Chlorine

The number of amino acids found in proteins that a human body can synthesize is

Choose an answer

20

10

5

14

Oxidation of 2-propanol gives

Choose an answer

Propanone

Butanone

Pentanone

None of these

Saturated solution of NaCl on heating becomes

Choose an answer

Super saturated

Unsaturated

Remains saturated

None

A 4f orbital has

Choose an answer

one node

two node

three node

four nodes

Which one of the following is not air pollutant gas

Choose an answer

CO

CO₂

NO

SO₂

Which of the following molecules have its central atom sp²hybridized

Choose an answer

CH₄

C₂H₂

C₂H₄

CCl₄

The liquid obtained after passing the mixture through filter paper is termed as:

Choose an answer

Extract

Residue

Filtrate

Sample

Carbon monoxide, emitted by automobiles, prevents transport of oxygen in body due

Choose an answer

Combining with oxygen to form carbon dioxide

Destruction of hemoglobin

Preventing reaction between oxygen and hemoglobin

Forming stable compound with hemoglobin

Buffers having pH less than 7 are made

Choose an answer

Mixture of weak acid + salt of it with strong base

Mixture of weak acid + salt of it with weak base

Mixture of weak base + salt of it with strong acid

Mixture of weak base + salt of it with weak base

Compared to a 1.0M aqueous solution of calcium chloride will have

Choose an answer

The same freezing and boiling point

A lower freezing point and lower boiling point

A lower freezing point and higher boiling point

A higher freezing point and higher boiling point

The configuration 1s²2s²2p⁵3s¹shows

Choose an answer

Excited state of O₂

Excited state of neon

Excited state of fluorine

Ground state of fluorine atom

CO+ is an example of

Choose an answer

Stable molecule

Anionic molecule ion

Cationic molecular ion

Free radical

The radius of ion while considering it to be spherical in shape is called:

Choose an answer

Covalent radii.

Atomic radii.

Ionic radii.

Both (a) and (C).

Two moles of acetic acid are heated with P₂O₅the product formed is

Choose an answer

2 moles of ethyl alcohol

Formic anhydride

Acetic anhydride

2 moles of methyl cyanide