JKCET 2024 Question Paper (Avaliable): Download Solution PDF With Answer Key

Question 1:

What is the unit of measurement of solid angles?

• (a) Steradian
• (b) Degrees
• (c) Radians
• (d) Grades

If the unit of force and length are doubled, the unit of energy will be

• (a) 1/2 times
• (b) 2 times
• (c) 4 times
• (d) 1/4 times

A particle is moving with a constant speed along a straight-line path. A force is not required to

• (a) Change its direction
• (b) Decrease its speed
• (c) Keep it moving with uniform velocity
• (d) Increase its momentum

A ball tied at the end of a perfect string tied tightly (assume fixed) to a wooden bar at the other end is rotating with constant angular velocity. Its tangential velocity will

• (a) Increase with time
• (b) Decrease with time
• (c) Will remain constant
• (d) Will decrease exponentially

What may the cross product of two vectors be used for?

• (a) Area of rectangle
• (b) Area of square
• (c) Area of parallelogram
• (d) Perimeter of rectangle

The inherent property, with which a body resists any change in its state of motion is known as

• (a) Force
• (b) Momentum
• (c) Inertia
• (d) Acceleration

A bus that is travelling straight makes an abrupt right turn. What will happen to those who are on board the bus?

• (a) They will lean rightwards
• (b) They will lean leftwards
• (c) They will remain stationary
• (d) They will begin jumping

You lift a heavy book from the floor of the room and keep it in the bookshelf having a height of 2m. This process takes 5 seconds. The work done by you will depend on

• (a) Mass of the book and the time taken
• (b) Weight of the book and height of the bookshelf
• (c) Height of the bookshelf and the time taken
• (d) Mass of the book, height of the bookshelf and the time taken

Energy a system possesses because of the force exerted on its mass by a gravitational or electromagnetic field with respect to a reference surface.

• (a) Kinetic Energy
• (b) Potential Energy
• (c) Work
• (d) None of the mentioned

A boy of mass 50kg is standing on a frictionless surface. He throws a ball of mass 2kg away from him with a speed of 10m/s. Find the final speed of the centre of mass.

• (a) 0m/s
• (b) 20m/s
• (c) 10m/s
• (d) 0.4m/s

Point, where the total volume of the body is assumed to be concentrated is

• (a) Center of area
• (b) Centroid of volume
• (c) Centroid of mass
• (d) All of the mentioned

The displacement of the body is given to be proportional to the cube of time elapsed. The magnitude of acceleration of body is

• (a) Increasing with time
• (b) Decreasing with time
• (c) Constant but not zero
• (d) Zero

If the Earth loses its gravity, then for a body

• (a) Weight becomes zero
• (b) Mass becomes zero
• (c) Neither mass nor weight is zero
• (d) Both mass and weight are zero

The law which states that within elastic limits strain produced is proportional to the stress producing it is known as

• (a) Bernoulli’s law
• (b) Hooke’s law
• (c) Stress law
• (d) Poisson’s law

The slope of the stress-strain curve in the elastic deformation region is

• (a) Elastic modulus
• (b) Plastic modulus
• (c) Poisson’s ratio
• (d) None of the mentioned

Hess’s law states that a chemical reaction is independent of the route by which chemical reactions take place while keeping the same

• (a) initial conditions only
• (b) final conditions only
• (c) mid-conditions
• (d) initial and final conditions

Select the correct order of steps in which a working substance (gas) goes through in a refrigerator.

• (a) Expansion of gas, absorption of heat, heating of vapour, release of heat
• (b) Absorption of heat, expansion of gas, heating of vapour, release of heat
• (c) Heating of vapour, expansion of gas, absorption of heat, release of heat
• (d) Heating of vapour, absorption of heat, expansion of gas, release of heat

Which of the following is not a gas law?

• (a) Boyle’s law
• (b) Charles law
• (c) Hooke’s law
• (d) Gay Lussac’s law

The equation \( pv = RT \) is used for ideal gases. The right equation for real gases is van der Waals equation. What is the correct formula for the van der Waals equation? Where \(\frac{a}{v^2}\) is the force of cohesion and \( b \) is the coefficient related to volume of molecules.

• (a) \( \left(p + \frac{a}{v^2}\right) (v + b) = RT \)
• (b) \( \left(p - \frac{a}{v^2}\right) (v - b) = RT \)
• (c) \( \left(p + \frac{a}{v^2}\right) (v - b) = RT \)
• (d) \( \left(p - \frac{a}{v^2}\right) (v + b) = RT \)

Which of the following has a mole ratio 1:1?

• (a) 7g of N and 12g of Na
• (b) 20g of Na and 20g of Ca
• (c) 14g of N and 24g of Mg
• (d) 10g of Ca and 6g of C

What are the total degrees of freedom if the number of species are 8, total streams are 3, stream temperature 3, stream pressure 3 and heat released 1, extent of reaction 2?

• (a) 8
• (b) 12
• (c) 15
• (d) 17

Statement: The amplitude of an oscillating pendulum decreases gradually with time.
Reason: The frequency of the pendulum decreases with time.

• (a) Both statement and reason are true and the reason is the correct explanation of the statement
• (b) Both statement and reason are true but the reason is not the correct explanation of the statement
• (c) Statement is true, but the reason is false
• (d) Statement and reason are false

A particle is initially at the centre and going towards the left. Let \( T \) be the time period of the SHM it is undergoing. What will be its position and velocity at time \( 3T/4 \), if it starts from the centre at \( t = 0 \)?

• (a) At right extreme, zero velocity
• (b) At centre, maximum speed towards left
• (c) At centre, maximum speed towards right
• (d) Mid-way between centre and -A

What is meant by mean free path?

• (a) It is the average distance a molecule travels without colliding
• (b) Average distance between 2 molecules
• (c) Average distance travelled by a molecule before colliding with a wall of the container
• (d) Sum of distance travelled by all molecules

The property which differentiates two kinds of charges is called

• (a) Equality of charge
• (b) Polarity of charge
• (c) Fraction of charge
• (d) None of the option

What happens when a glass rod is rubbed with silk?

• (a) Gains protons from silk
• (b) Gains electrons from silk
• (c) Gives electrons to silk
• (d) Gives protons to silk

Two charges \(Q_1\) and \(-Q_2\) are separated by a distance \(r\). The charges attract each other with a force \(F\). What is the new force between the charges if the distance is cut to one-fourth and the magnitude of each charge is doubled?

• (a) 16 \(F\)
• (b) 64 \(F\)
• (c) 48 \(F\)
• (d) \( \frac{1}{48}F \)

X is a substance which does not allow the flow of charges through it but permits them to exert electrostatic forces on one another through it. Identify X.

• (a) Polar molecule
• (b) Dielectric
• (c) Non-polar molecule
• (d) Equipotential

The opposition offered by the electrolyte of the cell to the flow of current through itself is known as .

• (a) External resistance
• (b) Internal resistance
• (c) Non-resistance
• (d) None of these options

A steady current flows in a metallic conductor of non-uniform cross-section. Which of the following quantities is constant along the conductor?

• (a) Drift Speed
• (b) Current Density
• (c) Current
• (d) None of these

Resistor Color codes were developed by:

• (a) Radio Manufacturers Association (RMA)
• (b) International Organization for Standardization (ISO)
• (c) Electronics Industries Alliance (EIA)
• (d) a \& b are correct

36 cells, each of emf 4V are connected in series and kept in a box. The combination shows an emf of 88V on the outside. Calculate the number of cells reversed.

• (a) 2
• (b) 5
• (c) 10
• (d) 7

If a coil carrying current is placed in a uniform magnetic field, then

• (a) emf is produced
• (b) Torque is produced
• (c) Force is produced
• (d) Torque and force is produced

If the current \( I \) flows through the coil of radius \( r \), then the field at the center of the circular coil is

• (a) Inversely proportional to \( I^2 \)
• (b) Directly proportional to \( I \)
• (c) Directly proportional to \( r \)
• (d) Inversely proportional to \( r^2 \)

Which among the following is denoted by \( \delta \)?

• (a) Horizontal component
• (b) Magnetic meridian
• (c) Magnetic declination
• (d) Magnetic inclination

How is a galvanometer converted into an ammeter?

• (a) By connecting a high resistance shunt in parallel to the galvanometer
• (b) By connecting a low resistance shunt in parallel to the galvanometer
• (c) By connecting a high resistance shunt in series with the galvanometer
• (d) By connecting a low resistance shunt in series with the galvanometer

A current-carrying rectangular coil placed in a uniform magnetic field. In which orientation will the coil rotate?

• (a) In any orientation
• (b) The magnetic field is parallel to the plane of the coil
• (c) The magnetic field is at 45° with the plane of the coil
• (d) The magnetic field is perpendicular to the plane

Which of the following factors is the self-inductance associated with a coil independent of?

• (a) induced voltage
• (b) current
• (c) time
• (d) coil resistance

Find the force due to a current element of length 2 cm and flux density of 12 tesla. The current through the element will be 5A.

• (a) 1 N
• (b) 1.2 N
• (c) 4 N
• (d) 1.6 N

Which of the following statement is valid?

• (a) Lenz’s law is a consequence of the law of conservation of energy
• (b) Lenz’s law is a consequence of the law of conservation of momentum
• (c) Lenz’s law is a consequence of the law of conservation of force
• (d) Lenz’s law is a consequence of the law of conservation of mass

_______ the resonant frequency, the current in the capacitor leads the voltage in a series RLC circuit.

• (a) Above
• (b) Below
• (c) Equal to
• (d) Depends on the circuit

Which of the following can be used to produce a propagating electromagnetic wave?

• (a) Charge moving at a constant speed
• (b) Chargeless particle
• (c) Stationary charge
• (d) An accelerating charge

Which type of transmission line accepts the Transverse electromagnetic wave?

• (a) Copper cables
• (b) Coaxial cable
• (c) Rectangular waveguides
• (d) Circular waveguides

Which of the following cannot travel in vacuum?

• (a) Radio waves
• (b) Gamma waves
• (c) Infrared waves
• (d) Infrasonic waves

Which of the following is a necessary condition for total internal reflection?

• (a) The angle of incidence in the denser medium must be greater than the critical angle for the two media
• (b) The angle of incidence in the rarer medium must be greater than the critical angle for the two media
• (c) The angle of incidence in the denser medium must be lesser than the critical angle for the two media
• (d) The angle of reflection in the denser medium must be greater than the critical angle for the two media

Multimode graded index fibers are manufactured from materials with _______.

• (a) Lower purity
• (b) Higher purity than multimode step index fibers
• (c) No impurity
• (d) Impurity as same as multimode step index fibers

A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then what is its focal length?

• (a) Focal length will become zero
• (b) Focal length will become infinite
• (c) Focal length will reduce, but not become zero
• (d) Remains unchanged

If the separation between the two slits in Double Slit Fraunhofer Diffraction is changed, what change will be observed in the diffraction pattern?

• (a) The fringe length will increase
• (b) The fringe length will decrease
• (c) Fringes will be colored
• (d) No change

Which element of the light microscope is in charge of regulating the amount of light that enters the viewing area?

• (a) Coarse adjustment screw
• (b) Fine adjustment screw
• (c) Diaphragm
• (d) Condenser lens

A convex lens of focal length \( f = 20 \, cm \) is combined with a diverging lens of power 65 D. The power and the focal length of the combination is

• (a) -1.5 D, 66.7 cm
• (b) 1.5 D, 33.7 cm
• (c) 5 D, 66.7 cm
• (d) 5 D, 33.6 cm

According to the thin lens formula, which one of the following is true regarding the focal length of the lens?

• (a) \( f \) is positive for concave lens
• (b) \( f \) is negative for convex lens
• (c) \( f \) is positive for a diverging lens
• (d) \( f \) is negative for concave lens

What happens to the kinetic energy of the emitted electrons when the light is incident on a metal surface?

• (a) It varies with the frequency of light
• (b) It varies with the light intensity
• (c) It varies with the speed of light
• (d) It varies irregularly

Which radiations will be most effective for the emission of electrons from a metallic surface?

• (a) Microwaves
• (b) X-rays
• (c) Ultraviolet
• (d) Infrared

Which of the following regions does X-ray lie between?

• (a) Visible and ultraviolet regions
• (b) Short radio waves and long radio waves
• (c) Short radio waves and visible region
• (d) Gamma rays and ultraviolet region

Which of the following is a stable nucleus?

• (a) The nucleus with even protons and odd electrons
• (b) The nucleus with even number of protons and neutrons
• (c) The nucleus with even neutrons and odd protons
• (d) The nucleus with odd protons and neutrons

Isotones have the same number of

• (a) Protons
• (b) Electrons
• (c) Neutrons
• (d) All of the above

The manifestation of the band structure in solids is due to which of the following?

• (a) Heisenberg’s uncertainty principle
• (b) Pauli’s exclusion principle
• (c) Bohr’s correspondence principle
• (d) Boltzmann’s law

Which of the following is not a characteristic of LED?

• (a) Fast action
• (b) High Warm-up time
• (c) Low operational voltage
• (d) Long life

Which of the following should not be the characteristic of the solar cell material?

• (a) High Absorption
• (b) High Conductivity
• (c) High Energy Band
• (d) High Availability

In Zener diode, for currents greater than the knee current, the v-i curve is almost

• (a) Almost a straight line parallel to y-axis
• (b) Almost a straight line parallel to x-axis
• (c) Equally inclined to both the axes with a positive slope
• (d) Equally inclined to both the axes with a negative slope

What did Dalton propose?

• (a) Law of Multiple Proportions
• (b) Avogadro's Law
• (c) Law of Definite Composition
• (d) Law of Conservation of Mass

The total value of the magnetic quantum number is

• (a) \( 2n \)
• (b) \( 2l \)
• (c) \( 2n + 1 \)
• (d) \( 2l + 1 \)

Identify the de-Broglie expression from the following

• (a) \( \lambda = h \times p \)
• (b) \( \lambda = h + p \)
• (c) \( \lambda = h - p \)
• (d) \( \lambda = \frac{h}{p} \)

In the reaction, \( H_2(g) + Br_2(g) = 2HBr(g) \), what will happen if there is a change in pressure?

• (a) Equilibrium moves left
• (b) Equilibrium moves right
• (c) There is no change in equilibrium
• (d) We cannot say

Which of the following statements is correct with respect to electrolytic solutions?

• (a) Its conductance increases with dilution
• (b) Its conductance decreases with dilution
• (c) Its conductivity increases with dilution
• (d) Its equivalent conductance decreases with dilution

Lewis concept does explain the behaviour of

• (a) Bases
• (b) Salts
• (c) Protonic acids
• (d) Amphoteric substances

Precipitate is formed if ionic product is

• (a) greater than the solubility product
• (b) less than the solubility product
• (c) equal to the solubility product
• (d) independent of the solubility product

The rate constant of a reaction is \( K = 3.28 \times 10^{-4} \, s^{-1} \). Find the order of the reaction.

• (a) Zero order
• (b) First order
• (c) Second order
• (d) Third order

What is the integrated rate equation for a first-order reaction?

• (a) \( [A] = [A_0] e^{-kt} \)
• (b) \( [A] = \frac{[A_0]}{e^{-kt}} \)
• (c) \( [A] = [A_0] e^{-t} \)
• (d) \( [A] = [A_0] e^{-k} \)

Which of the following is not an example of an ideal solution?

• (a) Benzene + Toluene
• (b) n-Hexane + n-Heptane
• (c) Ethyl alcohol + Water
• (d) Ethyl bromide + Ethyl chloride

What is the value of the Van't Hoff factor (i) for solutes that dissociate in water?

• (a) \( > 1 \)
• (b) \( < 1 \)
• (c) \( = 0 \)
• (d) Not defined

Calculate the internal energy change when 2 moles of water at 0 degrees converts into ice at 0-degree centigrade?

• (a) 12 KJ per mole
• (b) 6 KJ per mole
• (c) 1 KJ per mole
• (d) 102 KJ per mole

The enthalpy and internal energy are the function of temperature for

• (a) All Gases
• (b) Steam
• (c) Water
• (d) Ideal Gas

The entropy of an isolated system can never

• (a) Increase
• (b) Decrease
• (c) Be zero
• (d) None of the mentioned

Reaction is spontaneous if Gibbs free energy is

• (a) Greater than zero
• (b) Equal to zero
• (c) Less than zero
• (d) Infinity

The standard oxidation potential of Ni/Ni\(^{2+}\) electrode is 0.3 V. If this is combined with a hydrogen electrode in acid solution, at what pH of the solution will the measured e.m.f. be zero at 25°C? (Assume \([Ni^{2+}] = 1M\))

• (a) 5.08
• (b) 4
• (c) 4.5
• (d) 5.25

What is the EMF of a galvanic cell if \( E^\circ_{cathode} = 0.80 \, volts \) and \( E^\circ_{anode} = -0.76 \, volts?\)

• (a) 1.56 volts
• (b) 0.04 volts
• (c) -1.56 volts
• (d) -0.04 volts

Choose the correct order of molar ionic conductivities of the following ions.

• (a) \( Li^+ < Na^+ < K^+ < Rb^+ \)
• (b) \( Li^+ < K^+ < Rb^+ < Na^+ \)
• (c) \( Li^+ < Na^+ < Rb^+ < K^+ \)
• (d) \( Li^+ < Rb^+ < Na^+ < K^+ \)

The graph for Boyle's law is called

• (a) Isotherm
• (b) Hypertherm
• (c) Hypotherm
• (d) None of above

The role of diffusion of gases is governed by

• (a) Graham's law
• (b) Dalton's law
• (c) Avogadro's law
• (d) Newton's law

The efficiency of packing is 68% in

• (a) BCC structure
• (b) CCP structure
• (c) FEC structure
• (d) HEP structure

Schottky defect in a crystal is observed when

• (a) The ion leaves its normal position and occupies an interstitial location
• (b) The unequal number of cation and anions are missing from the lattice
• (c) The density of the crystal increases.
• (d) An equal number of cations and anions are missing from the lattice.

According to Freundlich adsorption isotherm, which of the following is correct?

• (a) \( \frac{x}{m} \alpha P^1 \)
• (b) \( \frac{x}{m} \alpha P^{1/m} \)
• (c) \( \frac{x}{m} \alpha P^0 \)
• (d) All are correct for different ranges of pressure

Which theory best suits for homogeneous catalysis?

• (a) Intermediate
• (b) Absorption
• (c) Nucleate
• (d) Paratoid

The correct order of the first ionization potentials among the following elements: Be, B, C, N, O is

• (a) \(B < Be < C < O < N\)
• (b) \(B < Be < C < N < O\)
• (c) \(Be < B < C < N < O\)
• (d) \(Be < B < C < O < N\)

The attributes of corresponding elements are the periodic functions of the

• (a) Atomic Weights
• (b) Atomic Number
• (c) Chemical properties
• (d) No. of protons

Which of the following molecule doesn't involve covalent bond?

• (a) H\(_2\)O
• (b) CCl\(_4\)
• (c) NaCl
• (d) O\(_2\)

The shape and hybridisation in BF\(_3\) is

• (a) sp\(^2\), linear
• (b) sp\(^3\)d, planar
• (c) sp\(^2\), planar
• (d) sp\(^3\), planar

Which of the following is correct regarding repulsive interaction?

• (a) Lone pair-Lone pair is greater than Lone pair-Bond pair is greater than Bond pair-Bond pair
• (b) Lone pair-Lone pair is less than Lone pair-Bond pair is less than Bond pair-Bond pair
• (c) Lone pair-Bond pair is greater than Lone pair-Lone pair is greater than Bond pair-Bond pair
• (d) Lone pair-Lone pair is greater than Lone pair-Bond pair is less than Bond pair-Bond pair

Which of the following species have maximum number of unpaired electrons?

• (a) O\(_2\)
• (b) O\(_2^+\)
• (c) O\(_2^-\)
• (d) O\(_2^{2-}\)

Alkali metals are strongly

• (a) Neutral
• (b) Electropositive
• (c) Electronegative
• (d) Non-metallic

The relative Lewis acid strengths of boron trihalides are in the

• (a) BBr\(_3\) \(>\) BC\(_3\) \(>\) BF\(_3\)
• (b) BC\(_3\) \(>\) BF\(_3\) \(>\) BBr\(_3\)
• (c) BF\(_3\) \(>\) BC\(_3\) \(>\) BBr\(_3\)
• (d) BF\(_3\) \(>\) BBr\(_3\) \(>\) BC\(_3\)

How many types of oxides do Carbon family form?

• (a) 9
• (b) 4
• (c) 3
• (d) 2

The increasing order of reducing power of the halogen acids is

• (a) \(HF < HCl < HBr < HI\)
• (b) \(HI < HBr < HCl < HF\)
• (c) \(HBr < HCl < HF < HI\)
• (d) \(HCl < HBr < HF < HI\)

Which of the following is amphoteric?

• (a) CrO
• (b) CrO\(_4\)
• (c) Cr\(_2\)O\(_3\)
• (d) CrO\(_3\)

Which of the following is an alloy of iron?

• (a) Vitallium
• (b) Brass
• (c) Invar
• (d) Solder

The name of [Co(NH\(_2\))\(_3\)](NO\(_2\))\(_3\) is

• (a) Trinitrotriamminecobalt(III)
• (b) Trinitrotriamminecobalt(II)
• (c) Trinitrotriamminecobalt(III) ion
• (d) Trinitrotriamminecobaltate(III)

What was the term proposed by Werner for the number of groups bound directly to the metal ion in a coordination complex?

• (a) Primary valence
• (b) Secondary valence
• (c) Oxidation number
• (d) Polyhedra

Which of the following complexes shows zero crystal field stabilization energy?

• (a) [Co(H\(_2\)O)\(_6\)]\(^{3+}\)
• (b) [Fe(H\(_2\)O)\(_6\)]\(^{3+}\)
• (c) [Co(H\(_2\)O)\(_6\)]\(^{2+}\)
• (d) [Mn(H\(_2\)O)\(_6\)]\(^{3+}\)

Which of the following do not show geometrical isomerism? (Assume all ligands are unidentate)

• (a) Square planar [MXL\(_3\)]
• (b) Square planar [MX\(_2\)L\(_2\)]
• (c) Octahedral [MX\(_2\)L\(_4\)]
• (d) Octahedral [MX\(_3\)L\(_3\)]

The IUPAC name of acetylsalicylic acid is

• (a) 2-acetoxy benzoic acid
• (b) 1-acetoxy benzoic acid
• (c) 4-acetoxy benzoic acid
• (d) 3-acetoxy benzoic acid

The most stable carbanion among the following is:

Which of the following is incorrect for electrophilic substitution?

• (a) -NO\(_2\) is deactivating and m-directing
• (b) -Cl is activating and o, p-directing
• (c) -OH is activating and o, p-directing
• (d) -CH\(_3\) is activating and o, p-directing

If a compound has 3 chiral carbons, what is the number of optically active isomers?

• (a) 9
• (b) 3
• (c) 4
• (d) 8

Which of the following compound(s) is/are chiral?

• (a) Only A and B
• (b) Only B
• (c) Only B and C
• (d) Only A

What is the relationship between (1R,2S)-dibromocyclohexane and (1S,2R)-dibromocyclohexane?

• (a) Identical
• (b) Enantiomers
• (c) Diastereomers
• (d) Constitutional isomers

How are alcohols prepared from haloalkanes?

• (a) By treating with concentrated H\(_2\)SO\(_4\)
• (b) By heating with aqueous NaOH
• (c) By treating with a strong reducing agent
• (d) By treating with Mg metal

Iodoform can be prepared from all except:

• (a) Isopropyl alcohol
• (b) 3-methyl-2-butanone
• (c) Isobutyl alcohol
• (d) Ethyl methyl ketone

Which of the following methods cannot produce aldehydes?

• (a) Oxidation of primary alcohols
• (b) Dehydrogenation of secondary alcohols
• (c) Ozonolysis of alkenes
• (d) Hydration of ethyne with acid

Which of the following acids does not form anhydride?

• (a) Formic acid
• (b) Acetic acid
• (c) Propionic acid
• (d) n-butyric acid

Trans-esterification is a reaction between

• (a) two ester molecules
• (b) alcohol and carboxylic acid
• (c) alcohol and ether
• (d) alcohol and ester.

Hydrolysis of alkyl isocyanide yields

• (a) primary amine
• (b) tert. amine
• (c) alcohol
• (d) aldehyde

Which of the following statements concerning methylamine is correct?

• (a) Methylamine is stronger base than NH\(_3\)
• (b) Methylamine is less basic than NH\(_3\)
• (c) Methylamine is slightly acidic
• (d) Methylamine forms salts with alkali

Oxidation of aniline with K\(_2\)Cr\(_2\)O\(_7\)/H\(_2\)SO\(_4\) gives

• (a) phenylhydroxylamine
• (b) p-benzoquinone
• (c) nitrosobenzene
• (d) nitrobenzene

Molisch test is used for the detection of:

• (a) fats
• (b) carbohydrates
• (c) alkyl halide
• (d) alkaloid

Greenhouse gases causing a rise of 3°C rise in the overall global temperature in the past century are CFCs. The CFC used in refrigerators is

• (a) Ammonia
• (b) Freon
• (c) Methane
• (d) Carbon dioxide

This is not a possible adverse effect of global warming

• (a) Sea level rise
• (b) An increase of UVB radiation
• (c) Retreat of glaciers
• (d) Extraordinary weather patterns

Addition polymerization is also known as

• (a) Copolymerisation
• (b) Homopolymerisation
• (c) Step growth polymerisation
• (d) Chain growth polymerisation

Which of the following is not a natural polymer?

• (a) Rayon
• (b) Starch
• (c) Cellulose
• (d) RNA

Which of the following is a non-biodegradable polymer?

• (a) PHB
• (b) PGA
• (c) LDPE
• (d) PHBV

Which of the following statement is true?

• (a) \( 3 \in \{1, 3, 5\} \)
• (b) \( 3 \in \{1, 3, 5\} \)
• (c) \( \{3\} \in \{1, 3, 5\} \)
• (d) \( \{3,5\} \in \{1, 3, 5\} \)

Which of the following is a null set?

• (a) \( A = \{ x : x > 1 and x < 1 \} \)
• (b) \( B = \{ x : x + 3 = 3 \} \)
• (c) \( C = \emptyset \)
• (d) \( D = \{ x : x \geq 1 and x \leq 1 \} \)

Let \( f : x \to y \) be a given function, then \( f^{-1} \) exists if

• (a) \( f \) is one-one
• (b) \( f \) is onto
• (c) \( f \) is one-one but not onto
• (d) \( f \) is one-one and onto

If \( n(A) = 4 \) and \( n(B) = 2 \), then the number of surjections from A to B is:

• (a) 14
• (b) 2
• (c) 8
• (d) None of these

Let \( R \) be a relation on set \( A \) such that \( R = R^{-1} \), then \( R \) is

• (a) Reflexive
• (b) Symmetric
• (c) Transitive
• (d) None of these

Let \( R \) be a relation on \( \mathbb{N} \) defined as \( x R y \) iff \( x + 2y = 8 \), the domain of \( R \) is

• (a) \{2, 4, 8\}
• (b) \{2, 4, 6, 8\}
• (c) \{2, 4, 6\}
• (d) \{1, 2, 3, 4\}

The conjugate complex number of \[ \frac{2 - i}{1 - 2i^2} \]

• (a) \( \frac{2}{25} + \frac{11}{25} i \)
• (b) \( \frac{2}{25} - \frac{11}{25} i \)
• (c) \( \frac{-2}{25} + \frac{11}{25} i \)
• (d) \( \frac{-2}{25} - \frac{11}{25} i \)

The value of \( \left( \frac{1 + i\sqrt{3}}{1 - i\sqrt{3}} \right)^6 + \left( \frac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \right)^6 \) is

• (a) 2
• (b) 12
• (c) 14
• (d) 0

The maximum value of \( P = 8x + 3y \), subject to the constraints \( x + y \leq 6, x \geq 0, y \geq 0 \), is

• (a) 2
• (b) -2
• (c) 14
• (d) 16

"The maximum or the minimum of the objectives function occurs only at the corners points of the feasible region". This theorem is known as fundamental theorem of

• (a) Algebra
• (b) Arithmetic
• (c) Calculus
• (d) Extreme Points

The solution of the inequality \( \frac{1}{2x - 5} > 0 \) is

• (a) \( \left[ -\frac{5}{2}, \infty \right) \)
• (b) \( \left( \frac{5}{2}, \infty \right) \)
• (c) \( \left( -\infty, \frac{5}{2} \right) \)
• (d) \( \left( \frac{5}{2}, \infty \right) \)

If \( 2 < x < 3 \), then

• (a) \( |x - 3| < |x - 2| \)
• (b) \( (x - 3) > (x - 2) \)
• (c) \( (x - 3)(x - 2) < 0 \)
• (d) \( \frac{x - 3}{x - 2} > 0 \)

The value of \( n \), for which \( \frac{a^{n+1} + b^{n+1}}{a^n + b^n} \) is the A.M. between \( a \) and \( b \), is

• (a) 0
• (b) 1
• (c) \( -\frac{1}{2} \)
• (d) -1

In a G.P. of \( (m + n)^{th} \) term is \( P \) and the \( (m - n)^{th} \) term is \( q \), then its \( m^{th} \) term is

• (a) 0
• (b) \( Pq \)
• (c) \( \sqrt{Pq} \)
• (d) \( \frac{1}{2}(P + q) \)

5 books in Math and 3 books in Physics are placed on a shelf so that the books on the same subject always remain together. The possible arrangements are

• (a) 1440
• (b) 1956
• (c) 720
• (d) None of these

There are 15 points in a plane, no three of which are in a straight line, except 6, all of which are in a straight line. The number of straight lines which can be drawn by joining them is

For the positive integer \( n \),
\[ C_1^{n} + C_2^{n} + C_3^{n} + \dots + C_n^{n} is equal to \]

• (a) \( 2^n \)
• (b) \( 2^n - 1 \)
• (c) \( n^2 \)
• (d) \( n^2 - 1 \)

The term independent of \( x \) in the expansion of \[ \left( x - \frac{3}{x^2} \right)^{18} \]

• (a) \( C_6^{18} \)
• (b) \( C_6 \cdot 3^6 \)
• (c) \( C_6 \cdot 3^{-6} \)
• (d) \( 3^6 \)

If \( a^2 + b^2 + c^2 = 0 \) and \[ \left| \begin{array}{ccc} b^2 + c^2 & ab & ac
ab & c^2 + a^2 & bc
ac & bc & a^2 + b^2 \end{array} \right| = ka^2b^2c^2 \]
then \( k \) is equal to

• (a) 1
• (b) 2
• (c) 3
• (d) 4

If \( A = \begin{pmatrix} 2 & 0 & 0
0 & \cos x & \sin x
0 & -\sin x & \cos x \end{pmatrix} \), then \( Adj(A)^{-1} \) is

• (a) A
• (b) 2A
• (c) \( \frac{1}{2} A \)
• (d) None of these

The system of linear equations \[ x + y + z = 2, \quad 2x + y - 2 = 3, \quad 3x + 2y + kz = 4 has a unique solution if \]

• (a) \( k \neq 0 \)
• (b) \( k > -1 \)
• (c) \( -2 < 2 < 2 \)
• (d) \( k = 0 \)

If a matrix \( A \) is symmetric as well as skew symmetric then \( A \) is

• (a) Diagonal matrix
• (b) Null matrix
• (c) Unit matrix
• (d) None of these

The limit \( \lim_{x \to 0} \frac{5^x + 4^x}{4^x - 3^x} \) is equal to

• (a) 0
• (b) \( \frac{\log(5/4)}{\log(4/3)} \)
• (c) 1
• (d) None of these

The limit \( \lim_{x \to 0} \left( \frac{\tan x - x}{x} \right) \cdot \left( \sin \frac{1}{x} \right) \) is equal to

• (a) 0
• (b) 1
• (c) A real number other than 0 and 1
• (d) None of these

Let \( f(x) = \frac{1 - \cos{P x}}{x \sin{x}} \) when \( x \neq 0 \) and \( f(0) = \frac{1}{2} \). If \( f \) is continuous at \( x = 0 \), then \( P \) is equal to

• (a) 2
• (b) -2
• (c) 1 or -1
• (d) None of these

The derivative of \( f(x) = |x| \) at \( x = 0 \) is

• (a) 0
• (b) 1
• (c) -1
• (d) None of these

The derivative of
\[ \frac{d}{dx} \left( \tan^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right) \right) is equal to \]

• (a) \( \frac{3}{1 + x^2} \)
• (b) \( \frac{3}{1 + 9x^2} \)
• (c) \( \sec^2{3x} \)
• (d) \( \frac{1}{1 + x^2} \)

The derivative of
\[ \frac{d}{dx} \left( x \sqrt{a^2} - x^2 + a^2 \sin^{-1} \left( \frac{x}{a} \right) \right) is equal to \]

• (a) \( \sqrt{a^2 - x^2} \)
• (b) \( 2\sqrt{a^2 - x^2} \)
• (c) \( \frac{1}{\sqrt{a^2 - x^2}} \)
• (d) None of these

Let \( f(x) = x^3 - 6x^2 + 9x + 8 \), then \( f(x) \) is decreasing in

• (a) \( (-\infty, 1) \)
• (b) \( [1, 3] \)
• (c) \( [3, \infty) \)
• (d) \( (-\infty, 1) \cup (3, \infty) \)

The function \( f(x) = 2 + 4x^2 + 6x^4 + 8x^6 \) has

• (a) Only one maxima
• (b) Only one minima
• (c) No maxima and minima
• (d) Many maxima and minima

If \( \sin(\pi \cos \theta) = \cos(\pi \sin \theta) \), then the value of \[ \cos \left( \theta + \frac{\pi}{4} \right) \]

• (a) \( \frac{1}{\sqrt{2}} \)
• (b) \( \frac{2}{\sqrt{2}} \)
• (c) \( \frac{1}{\sqrt{2}} \)
• (d) \( -\frac{1}{\sqrt{2}} \)

The general solution of \( x \) satisfying the equation \( \sqrt{3} \sin x + \cos x = \sqrt{3} \), is given by

• (a) \( x = n\pi \pm \frac{\pi}{3} \)
• (b) \( x = n\pi \pm \frac{\pi}{6} \)
• (c) \( x = n\pi \pm (-1)^n \frac{\pi}{3} \)
• (d) \( x = n\pi \pm (-1)^n \frac{\pi}{4} \)

The domain of the function \( \sin^{-1} x \) is

• (a) \( [-\pi, \pi] \)
• (b) \( [-1, 1] \)
• (c) \( \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \)
• (d) \( [0, 2\pi] \)

The value of
\[ \tan^{-1} \left( \frac{x}{y} \right) - \tan^{-1} \left( \frac{x - y}{x + y} \right) is \]

• (a) \( \frac{\pi}{2} \)
• (b) \( \frac{\pi}{3} \)
• (c) \( \frac{\pi}{4} \)
• (d) None of these

If the length of a chord of a circle is equal to that of radius of the circle, then the angle subtended in radius, at the centre of the circle by the chord is

• (a) 1
• (b) \( \frac{\pi}{2} \)
• (c) \( \frac{\pi}{3} \)
• (d) \( \frac{\pi}{4} \)

If \( \tan x = \frac{m}{m+1} \), \( \tan \beta = \frac{1}{2m+1} \), then \( (\alpha + \beta) \) is equal to

• (a) \( \frac{\pi}{2} \)
• (b) \( \frac{\pi}{4} \)
• (c) \( \frac{\pi}{6} \)
• (d) None of these

The integral \( \int \frac{x e^x}{(1+x)^2} dx \) is equal to

• (a) \( \frac{-e^x}{1+x} \)
• (b) \( \frac{1 + 2x e^x}{1+x} \)
• (c) (\( \frac{1 + 2x e^x}{1+x} \) )
• (d) \( \frac{e^x}{1+x} \)

The integral \( \int \sqrt{x^2 + a^2} \, dx \) is equal to

• (a) \( \log |x + \sqrt{x^2 + a^2}| \)
• (b) \( \frac{x \sqrt{x^2 + a^2}}{2} - \frac{a^2 \log |x + \sqrt{x^2 + a^2}|}{2} \)
• (c) \( \frac{x \sqrt{x^2 + a^2}}{2} + \frac{a^2 \log |x + \sqrt{x^2 + a^2}|}{2} \)
• (d) None of these

The value of \[ \int_0^{2\pi} \sqrt{1 + \sin^2 \frac{x}{2}} \, dx is \]

• (a) 0
• (b) 2
• (c) 8
• (d) 4

If \[ \int_0^{2a} f(x) \, dx = 2 \int_0^a f(x) \, dx, then \]

• (a) \( f(2a - x) = -f(x) \)
• (b) \( f(2a - x) = f(x) \)
• (c) \( f(x) \) is an odd function
• (d) \( f(x) \) is an even function

The value of \[ \int_0^{\frac{\pi}{2}} \frac{\tan x}{\tan x + \cot x} \, dx is \]

• (a) 0
• (b) \( \frac{\pi}{2} \)
• (c) \( \frac{\pi}{4} \)
• (d) None of these

The order of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2} = \frac{d^2y}{dx^2} \]
is

• (a) 1
• (b) 2
• (c) 3
• (d) 4

The area enclosed between the curve \[ y^2 = 4x, \quad and the line y = x is \]

• (a) \( \frac{2}{3} \)
• (b) \( \frac{4}{3} \)
• (c) \( \frac{1}{2} \)
• (d) \( \frac{8}{3} \)

The points \[ (-a, -b), (0, 0), (a, b), and (a^2, ab) \]
are

• (a) Vertical of a triangle
• (b) Vertical of a square
• (c) Vertical of a parallelogram
• (d) Collinear

The inclination of the straight line passing through the point (-3, 6) and the mid point of the line joining the points (4,-5) and (-2,9) is

• (a) \( \frac{\pi}{4} \)
• (b) \( \frac{\pi}{6} \)
• (c) \( \frac{\pi}{3} \)
• (d) \( \frac{3\pi}{4} \)

The coordinates of the foot of the perpendicular from \( (a, 0) \) on the line \( y = mx + \frac{a}{m} \) are

• (a) \( \left( 0, -\frac{a}{m} \right) \)
• (b) \( \left( \frac{a}{m}, 0 \right) \)
• (c) \( \left( 0, \frac{a}{m} \right) \)
• (d) None of these

If the line \( x - 1 = 0 \) is the direction of the parabola \( y^2 - kn + 8 = 0 \), then one of the values of \( k \) is

• (a) \( \frac{1}{8} \)
• (b) \( 8 \)
• (c) \( 4 \)
• (d) \( \frac{1}{4} \)

Equation of the ellipse with eccentricity \( \frac{1}{2} \) and foci at \( (\pm 1, 0) \) is

• (a) \( \frac{x^2}{3} + \frac{y^2}{4} = 1 \)
• (b) \( \frac{x^2}{4} + \frac{y^2}{3} = 1 \)
• (c) \( \frac{x^2}{4} + \frac{y^2}{3} = \frac{4}{3} \)
• (d) None of these

For a frequency distribution, the mean deviation about the mean is computed by

• (a) M.D = \( \frac{\Sigma d_i}{\Sigma f_i} \)
• (b) M.D = \( \frac{\Sigma f_i d_i}{\Sigma f_i} \)
• (c) M.D = \( \frac{\Sigma f_i |d_i|}{\Sigma f_i} \)
• (d) M.D = \( \frac{\Sigma f_i |d_i|}{\Sigma f_i} \)

The standard deviation of 25 numbers is \( \sigma \). If each of the numbers is increased by 5, then the new standard deviation will be

• (a) 40
• (b) 45
• (c) \( 40 + \frac{21}{25} \)
• (d) None of these

If \( P[E_1] = P_1 \) and \( E_1 \) and \( E_2 \) are mutually exclusive, then \( P[neither E_1 nor E_2] \) is equal to

• (a) \( (1 - P_1)(1 - P_2) \)
• (b) \( 1 - (P_1 + P_2) \)
• (c) \( P_1 + P_2 - 1 \)
• (d) None of these

A bag contains 5 white, 7 red, and 4 black balls. Four balls are drawn one by one with replacement. The chance that at least two balls are black is

• (a) \( \frac{67}{256} \)
• (b) \( \frac{54}{256} \)
• (c) \( \frac{243}{256} \)
• (d) None of these

If A and B are two events and \( P(A \cup B) = \frac{5}{6} \), \( P(A \cap B) = \frac{1}{3} \), \( P(\overline{B}) = \frac{1}{2} \), then A and B are

• (a) Dependent
• (b) Independent
• (c) Mutually Exclusive
• (d) None of these

A die is tossed 5 times, getting an odd number is considered a success. Then the variance of the distribution of number of successes is

• (a) \( \frac{8}{3} \)
• (b) \( \frac{3}{8} \)
• (c) \( \frac{4}{5} \)
• (d) \( \frac{5}{4} \)

If \( \vec{a} \) is a non-zero vector and \( k \) is a scalar such that \( |k \vec{a}| = 1 \), then \( k \) is equal to

• (a) \( |\vec{a}| \)
• (b) 1
• (c) \( \frac{1}{|\vec{a}|} \)
• (d) \( \pm \frac{1}{|\vec{a}|} \)

If \( \theta \) is the angle between two vectors \( \vec{a} \) and \( \vec{b} \), then \[ | \vec{a} \times \vec{b} | = | \vec{a} \cdot \vec{b} | \]
equals to

• (a) \( \cot \theta \)
• (b) \( -\cot \theta \)
• (c) \( \tan \theta \)
• (d) \( -\tan \theta \)

The unit vector perpendicular to each of the vectors \[ (2\hat{i} - \hat{j} + \hat{k}) and (3\hat{i} + 4\hat{j}) is \]

• (a) \( \frac{1}{\sqrt{146}} (4\hat{i} - 3\hat{j} + 11\hat{k}) \)
• (b) \( \frac{1}{\sqrt{146}} (-4\hat{i} + 3\hat{j} + 11\hat{k}) \)
• (c) \( \frac{1}{\sqrt{146}} (4\hat{i} + 3\hat{j} + 11\hat{k}) \)
• (d) \( \frac{1}{146} (-4\hat{i} + 3\hat{j} + 11\hat{k}) \)

The plane \( xoz \) divides the join of \( (1, -1, 5) \) and \( (2, 3, 5) \) in the ratio \( \lambda : 1 \), then \( \lambda \) is

• (a) -3
• (b) \( -\frac{1}{3} \)
• (c) 3
• (d) \( \frac{1}{3} \)

The value of \( k \) so that \[ \frac{x-1}{-3} = \frac{y-2}{2k} = \frac{z-3}{2} = \frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5} \]
may be perpendicular is given by

• (a) \( -10 \)
• (b) \( \frac{10}{7} \)
• (c) \( \frac{-10}{7} \)
• (d) \( \frac{-7}{10} \)

Angle between the line \[ \vec{r} = (2\hat{i} - \hat{j} + \hat{k}) + \lambda (-\hat{i} + \hat{j} + \hat{k}) \]
and the plane \[ \vec{r} \cdot (3\hat{i} + 2\hat{j} - \hat{k}) = 4 \]
is

• (a) \( \cos^{-1} \left( \frac{2}{\sqrt{42}} \right) \)
• (b) \( \cos^{-1} \left( \frac{-2}{\sqrt{42}} \right) \)
• (c) \( \sin^{-1} \left( \frac{2}{\sqrt{42}} \right) \)
• (d) \( \sin^{-1} \left( \frac{-2}{\sqrt{42}} \right) \)