COMEDK UGET 2021 Question Paper(Available): Download Solution PDF with Answer Key PDF

The Lyman series of a hydrogen atom belongs in which category

• (1) ultraviolet region
• (2) infrared region
• (3) visible region
• (4) None of these

Insulators can be charged by which of the following process?

• (1) Induction
• (2) Diverging
• (3) Friction
• (4) Heating

In an adiabatic process with the ratio of two specific heat, \( \gamma = \frac{3}{2} \), pressure is increased by \( \frac{2}{3} % \), then decrease in the volume will be

• (1) \( \frac{4}{9}% \)
• (2) \( \frac{2}{3}% \)
• (3) 4%
• (4) \( \frac{9}{4}% \)

Two converging lenses of focal length 20 cm and 40 cm are placed in contact. The effective power of the combination is

• (1) 5.25 D
• (2) 7.25 D
• (3) 2.75 D
• (4) 7.5 D

The formula of capacitative reactance is

• (1) \( 2 \pi f C \)
• (2) \( \frac{fC}{2\pi} \)
• (3) \( \frac{C}{2\pi f} \)
• (4) \( \frac{1}{2\pi f C} \)

Which graph shows the correct \( v \)–\( x \) graph of a freely falling body?

The displacement \( x \) of a particle varies with time \( t \), \( x = ae^{-pt} + be^{qt} \), where \( a, b, p, q \) are positive constants. The velocity of the particle will

• (1) go on increasing forever
• (2) be independent of \( p \) and \( q \)
• (3) drop to zero when \( p = q \)
• (4) go on decreasing with time

Which of the following quantity represents the dimensions of momentum?

• (1) Impulse
• (2) Pressure
• (3) Viscosity
• (4) Power

The angle of projection with the horizontal in terms of maximum height attained and horizontal range is given by

• (1) \( \tan^{-1} \left( \frac{2H}{3R} \right) \)
• (2) \( \tan^{-1} \left( \frac{4R}{3H} \right) \)
• (3) \( \tan^{-1} \left( \frac{4H}{R} \right) \)
• (4) \( \tan^{-1} \left( \frac{R}{H} \right) \)

For the same resonant frequency, if \( L \) is changed from \( L \) to \( \frac{L}{3} \), then capacitance should change from \( C \) to

• (1) \( \frac{C}{3} \)
• (2) \( 3C \)
• (3) \( \frac{2}{3}C \)
• (4) \( 2C \)

The velocity of the proton is one-fourth the velocity of the electron. What is the ratio of the de-Broglie wavelength of an electron to that of a proton?

• (1) 1
• (2) \( \frac{1}{2} \)
• (3) \( \frac{1}{3} \)
• (4) \( \frac{1}{4} \)

For an ideal gas, coefficient of volume expansion is given by

• (1) \( \frac{1}{p} \)
• (2) \( \frac{1}{pV} \)
• (3) \( \frac{1}{R} \)
• (4) \( \frac{1}{T} \)

Which of the following is not a greenhouse gas?

• (1) CH\textsubscript{4}
• (2) CO\textsubscript{2}
• (3) O\textsubscript{3}
• (4) H\textsubscript{2}O

Two particles of masses \( m_1 = m \), \( m_2 = 2m \) and charges \( q_1 = q \), \( q_2 = 2q \) entered into uniform magnetic field. Find \( \frac{F_1}{F_2} \) (force ratio).

• (1) \( \frac{1}{2} \)
• (2) 1
• (3) \( \frac{1}{3} \)
• (4) 2

Work done in moving a charge of 25 C is 50 J. Calculate the potential difference between two points.

• (1) 0.5 V
• (2) 1 V
• (3) 2 V
• (4) 2.5 V

The correct arrangement in increasing order of wavelength of X-rays, UV rays, and microwaves is

• (1) microwave, X-rays, UV rays
• (2) UV rays, X-rays, microwave
• (3) X-rays, UV rays, microwave
• (4) microwave, UV rays, X-rays

What is the electric field near an infinite plane sheet of charge density \( \sigma \)?

• (1) \( \frac{\sigma}{2\varepsilon_0} \)
• (2) \( \frac{\sigma A}{2\varepsilon_0} \)
• (3) \( \frac{\sigma}{2\varepsilon_0 A} \)
• (4) \( \frac{\sigma}{\varepsilon_0} \)

Which of the following waves are used in the treatment of muscle ache?

• (1) Ultraviolet
• (2) Infrared
• (3) Microwave
• (4) X-rays

Find the logic gate, when both the inputs are high the output is low and vice-versa.

• (1) AND
• (2) OR
• (3) NAND
• (4) NOR

What is the minimum band-gap of the LED diode?

• (1) 1.5 eV
• (2) 1.7 eV
• (3) 1.8 eV
• (4) 0.8 eV

The displacement of a wave is given by \( y = 20 \cos(\omega t + 4x) \). The amplitude of the wave is

• (1) 10
• (2) 20
• (3) \( 20\sqrt{2} \)
• (4) \( 10\sqrt{2} \)

If frequencies are \( (v - 1) \) and \( (v + 2) \), then find the value of beats.

• (1) 2
• (2) 1
• (3) 3
• (4) 4

The function \( y = \log(\omega t) \) can represent

• (1) a periodic function
• (2) a non-periodic function
• (3) oscillatory function
• (4) circular motion

Two springs of force constants \( k_1 \) and \( k_2 \) are connected to a mass \( m \) as shown. The angular frequency of this configuration is:

• (1) \( \frac{k_1 + k_2}{m} \)
• (2) \( \sqrt{\frac{k_1 + k_2}{m}} \)
• (3) \( \sqrt{\frac{k_1}{k_2 m}} \)
• (4) \( \frac{k_2 m}{k_1} \)

The resistance of a wire is \( R \) ohm. If it is melted and stretched to \( n \) times its original length, its new resistance will be

• (1) \( nR \)
• (2) \( \frac{R}{n} \)
• (3) \( n^2 R \)
• (4) \( \frac{R}{n^2} \)

An unpolarised beam of intensity \( I_0 \) is incident on a pair of nicols making an angle of \( 60^\circ \) with each other. The intensity of light emerging from the pair is

• (1) \( I_0 \)
• (2) \( \frac{I_0}{4} \)
• (3) \( \frac{I_0}{2} \)
• (4) \( \frac{I_0}{8} \)

The collision of the molecules of an ideal gas is taken as

• (1) elastic
• (2) inelastic
• (3) partially elastic
• (4) partially inelastic

The average energy associated with a monoatomic molecule is

• (1) \( K_B T \)
• (2) \( \frac{1}{2} K_B T \)
• (3) \( \frac{3}{2} K_B T \)
• (4) \( 2 K_B T \)

For the given electrical arrangement, what is the value of current \( I \)?

• (1) 6 A
• (2) 5 A
• (3) 7 A
• (4) 8 A

If an electron in hydrogen atom jumps from an orbit of level \( n = 3 \) to an orbit at level \( n = 2 \), emitted radiation has a frequency of
\( (R = Rydberg’s constant, \ c = speed of light) \)

• (1) \( \frac{3Rc}{27} \)
• (2) \( \frac{Rc}{25} \)
• (3) \( \frac{8Rc}{9} \)
• (4) \( \frac{5Rc}{36} \)

Within the elastic limit, the corresponding stress is known as

• (1) tensile strength
• (2) yield strength
• (3) elastic fatigue
• (4) yield point

A wire is stretched to double of its length. The strain is

• (1) 1
• (2) 2
• (3) 3
• (4) 4

Kepler’s second law of planetary motion corresponds to

• (1) conservation of energy
• (2) conservation of angular momentum
• (3) conservation of linear momentum
• (4) conservation of mass

A constant potential energy of a satellite is given as \[ PE = r \cdot KE \]
where PE = potential energy and KE = kinetic energy.
The value of \( r \) will be

• (1) \( -1 \)
• (2) \( -2 \)
• (3) \( -\frac{1}{2} \)
• (4) \( -\frac{3}{2} \)

A long solenoid has 20 turns cm\(^{-1}\). The current necessary to produce a magnetic field of 20 mT inside the solenoid is approximately

• (1) 1 A
• (2) 2 A
• (3) 4 A
• (4) 8 A

A constant current flows from A to B as shown in the figure. What is the direction of current in the circle?

• (1) Clockwise
• (2) Anti-clockwise
• (3) Straight line
• (4) None of the above

According to Pascal’s law, pressure in a fluid at rest is the same at all points, if

• (1) they are at the same plane
• (2) they are at the same height
• (3) they are along same line
• (4) Both (a) and (b)

The surface tension of a liquid at its boiling point

• (1) becomes zero
• (2) becomes infinity
• (3) is equal to the value at room temperature
• (4) is half of the value at room temperature

Centre of mass of the given system of particles will be at

• (1) OA
• (2) OB
• (3) OC
• (4) OD

Newton’s second law of rotational motion of a system of particles having angular momentum \( L \) is given by

• (1) \( \frac{dp}{dt} = \tau_{ext} \)
• (2) \( \frac{dL}{dt} = \tau_{int} \)
• (3) \( \frac{dL}{dt} = \tau_{ext} \)
• (4) \( \frac{dL}{dt} = \tau_{int} + \tau_{ext} \)

The motion of a particle of mass \( m \) is described by \( y = ut + g t^2 \). The force acting on the particle will be

• (1) zero
• (2) \( 4mg \)
• (3) \( 3mg \)
• (4) \( 2mg \)

When a car of mass \( m \) is moving with speed \( v \) along a circle of radius \( r \) on a level road, the centripetal force is provided by \( f \), where \( f \) denotes

• (1) \( \frac{mv^2}{r} = f \leq \mu_s N \)
• (2) \( f < \mu_k = \frac{mv^2}{r} \)
• (3) \( f = \mu_s N = \frac{mv^2}{r} \)
• (4) \( f = \mu_k N = \frac{mv^2}{r} \)

Ba-122 has half-life of 2 min. Experiment has to be done using Ba-122 and it takes 10 min to set up the experiment. It initially had 80 g of Ba-122. How much Ba-122 was left when the experiment started?

• (1) 2.5 g
• (2) 5 g
• (3) 10 g
• (4) 20 g

When the speed of light becomes \( \frac{2}{3} \) of its present value, then the energy released in a given atomic explosion would

• (1) decrease by a factor \( \frac{2}{3} \)
• (2) decrease by a factor \( \frac{4}{9} \)
• (3) decrease by a factor \( \frac{5}{9} \)
• (4) decrease by a factor \( \frac{\sqrt{5}}{9} \)

What should be the value of self-inductance of an inductor that should be connected to 220 V, 50 Hz supply, so that a maximum current of 0.9 A flows through it?

• (1) 11 H
• (2) 2 H
• (3) 1.1 H
• (4) 5 H

The magnifying power of a telescope is 9. When adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm. The focal lengths of lenses are:

• (1) 10 cm, 10 cm
• (2) 15 cm, 5 cm
• (3) 18 cm, 2 cm
• (4) 11 cm, 9 cm

Two masses of 1g and 9g are moving with equal kinetic energy. The ratio of magnitude of their momentum is

• (1) 3 : 1
• (2) 1 : 3
• (3) 1 : 2
• (4) 2 : 1

When two bodies collide with each other such that their kinetic energy remains constant, their collision is said to be

• (1) elastic
• (2) inelastic
• (3) Both (a) and (b)
• (4) None of the above

In a detector, the output circuit consists of \( R = 10 \, k\Omega \) and \( C = 100 \, pF \). The frequency of carrier signal it can detect is:

• (1) \( \gg 1 \, MHz \)
• (2) 0.1 kHz
• (3) \( \gg 1 \, GHz \)
• (4) \( 10^3 \, Hz \)

For motion under central forces, which quantity will be conserved?

• (1) Kinetic energy
• (2) Mechanical energy
• (3) Potential energy
• (4) None of the above

Which of the following statement is incorrect?

• (1) Classical Physics deals with macroscopic phenomena and includes subject like mechanics, electrodynamics, optics and thermodynamics.
• (2) All Physics and also mathematics is based on assumptions each of which is variously called hypothesis or axiom or postulate etc.
• (3) A hypothesis is a supposition with assuming that is true.
• (4) An axiom is a self-evident truth, while a model is a theory proposed to explain observed phenomena.

If impedance is \( \sqrt{3} \) times resistance, then find phase difference.

• (1) Zero
• (2) \(30^\circ\)
• (3) \(60^\circ\)
• (4) Data is incomplete

A bar magnet is oscillating in the earth’s magnetic field with a period \( T \). What happens to its period and motion, if its mass is quadrupled?

• (1) Motion remains simple harmonic with time period \(4T\)
• (2) Motion remains simple harmonic with time period nearly constant.
• (3) Motion remains simple harmonic and time period becomes \( \frac{T}{2} \)
• (4) Motion remains simple harmonic with time period \(2T\)

The relative permeability of iron is 6000. Its magnetic susceptibility is

• (1) 5999
• (2) 6001
• (3) \(6000 \times 10^{-7}\)
• (4) \(6000 \times 10^7\)

Which of the following technique is \textbf{not} used for measuring small time intervals?

• (1) Electronic oscillator
• (2) Decay of elementary particles
• (3) Atomic clock
• (4) Spring oscillator

The relative errors in the measurement of two lengths \(1.02 \, cm \pm 0.01 \, cm\) and \(9.89 \, cm \pm 0.01 \, cm\) is

• (1) \(\pm 1% and \pm 0.1%\)
• (2) \(\pm 1% and \pm 0.2%\)
• (3) \(\pm 1% and \pm 1%\)
• (4) \(0.1% and 1%\)

In Young’s double slit experiment with sodium vapour lamp of wavelength 589 nm and slit 0.589 mm apart, the half angular width of the central maxima is

• (1) \(\sin^{-1}(0.01)\)
• (2) \(\sin^{-1}(0.0001)\)
• (3) \(\sin^{-1}(0.001)\)
• (4) \(\sin^{-1}(0.1)\)

From the figure describing photoelectric effect, we may infer correctly that

• (1) Na and Al both have the same threshold frequency
• (2) Maximum kinetic energy for both the metals depends linearly on the frequency
• (3) The stopping potential are different for Na and Al for the same change in frequency
• (4) Al is better photosensitive material than Na

Carnot cycle of an engine is given below. What is the total work done by the gas in one cycle?

• (1) \( \mu R T_2 \log\frac{V_2}{V_1} - \mu R T_1 \log\frac{V_3}{V_4} \)
• (2) \( \mu R T_1 \log\frac{V_2}{V_1} - \mu R T_2 \log\frac{V_3}{V_4} \)
• (3) \( \mu R T_1 \log\frac{V_2}{V_1} + \mu R T_2 \log\frac{V_3}{V_4} \)
• (4) Zero

An optical fibre communication system works on a wavelength of \( 1.3 \, \mu m \). The number of subscribers it can feed, if a channel requires 20 kHz, are:

• (1) \( 2.3 \times 10^{10} \)
• (2) \( 1.15 \times 10^{10} \)
• (3) \( 1 \times 10^5 \)
• (4) None of these

When the expansion of a gas occurs in vacuum and at constant volume, then:

• (A) \( \Delta U = qV \)
• (B) \( \Delta U = qp \)
• (C) \( \Delta H = qV \)
• (D) \( \Delta H = qp \)

Carbon monoxide is poisonous to human beings because:

• (A) it binds 300 times more strongly to hemoglobin than oxygen
• (B) it doesn’t bind to hemoglobin
• (C) it forms cyanide in the body
• (D) it leads to coagulation of blood

Which one of the following sets of monosaccharides forms sucrose?

• (a) \( \alpha \)-D-galactopyranose and \( \alpha \)-D-glucopyranose
• (b) \( \alpha \)-D-glucopyranose and \( \beta \)-D-fructofuranose
• (c) \( \beta \)-D-glucopyranose and \( \alpha \)-D-fructofuranose
• (d) \( \alpha \)-D-glucopyranose and \( \beta \)-D-fructopyranose

Under which of the following conditions, the gases does not follow Henry's law?

• (a) When gases are placed under high temperature.
• (b) When the molecules of the system are in equilibrium state.
• (c) When gases are placed under extremely high pressure.
• (d) All of the above

An aqueous solution of \( X \) on addition of hydrogen peroxide in ice-cold conditions gives blue colour to the ethereal layer. Then, \( X \) can be:

• (A) Acidified potassium chromate
• (B) Alkaline potassium dichromate
• (C) Acidified potassium manganate
• (D) Acidified potassium permanganate

Determine the specific rate constant of the reaction. If the half-life period of a first-order reaction is 1402 s, then the rate constant is:

• (A) \( 4.94 \times 10^{-3} \, s^{-1} \)
• (B) \( 0.49 \times 10^{-3} \, s^{-1} \)
• (C) \( 0.49 \times 10^{-4} \, s^{-1} \)
• (D) \( 4.94 \times 10^{-5} \, s^{-1} \)

Sodium metal crystallizes in a body-centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is:

• (A) 1.86 Å
• (B) 3.22 Å
• (C) 5.72 Å
• (D) 0.93 Å

Which of the following amino acids \( NH_2 CH RCOOH \) contains a polar R group?

• (A) Alanine
• (B) Valine
• (C) Glycine
• (D) Glutamine

Find the correct order of \( C - O \) bond length among \( CO, CO_3^{2-}, CO_2 \).

• (A) \( CO_2 < CO_3^{2-} < CO \)
• (B) \( CO < CO_3^{2-} < CO_2 \)
• (C) \( CO_3^{2-} < CO_2 < CO \)
• (D) \( CO < CO_2 < CO_3^{2-} \)

The total number of nodes is given by:

• (A) \( (n+1) \)
• (B) \( (n-1) \)
• (C) \( (n) \)
• (D) \( (n+1+1) \)

In the equilibrium, \( AB \rightleftharpoons A + B \), if the equilibrium concentration of A is double, then the equilibrium concentration of B will be:

• (A) Half
• (B) Twice
• (C) \( \frac{1}{4} \)
• (D) \( \frac{1}{8} \)

Which of the following is used as a drug to reduce fever?

• (A) Antibiotic
• (B) Antipyretic
• (C) Analgesic
• (D) Tranquilizer

The reaction: \[ ArN^{+} Cl^{-} \xrightarrow{Cu/HCl} ArCl + N_2 + CuCl \]
is called as:

• (A) Sandmeyer reaction
• (B) Gattermann reaction
• (C) Claisen reaction
• (D) Carbamylamine reaction

In 3d-transition series, which one has the least melting point?

• (A) V
• (B) Zn
• (C) Mn
• (D) Cu

Among the following enzymes, which one is involved in the given below catalytic reaction? \[ C_6H_{12}O_6 (aq) \rightarrow 2C_2H_5OH (aq) + 2CO_2 (g) \]

• (A) Maltase
• (B) Urease
• (C) Zymase
• (D) Invertase

Which of the following is correct mixture of azeotrope?

• (A) Chlorobenzene + bromobenzene
• (B) \( C_2H_5Br + C_2H_5Cl \)
• (C) \( C_6H_{14} + C_7H_{16} \)
• (D) \( CCl_4 + CHCl_3 \)

Rate constant \( K \) of a reaction has least value at

• (A) High T and high \( E_a \)
• (B) High T and low \( E_a \)
• (C) Low T and low \( E_a \)
• (D) Low T and high \( E_a \)

Arrange stability of the given carbon cation in decreasing order:

• (A) (iii) > (ii) > (i) > (iv)
• (B) (i) > (iii) > (ii) > (iv)
• (C) (iii) > (i) > (ii) > (iv)
• (D) (ii) > (iii) > (i) > (iv)

Which of the following pairs of ions are iso-electronic and iso-structural?

• (A) \( CO_3^{2-} \) and \( NO_3^{-} \)
• (B) \( SO_3^{2-} \) and \( NO_3^{-} \)
• (C) \( ClO_3^{-} \) and \( CO_3^{2-} \)
• (D) \( SO_3^{2-} \) and \( CO_3^{2-} \)

How much part of any corner atom actually belongs to a particular unit cell?

• (A) \( \frac{1}{4} \)
• (B) \( \frac{1}{6} \)
• (C) \( \frac{1}{8} \)
• (D) \( \frac{1}{10} \)

For the equilibrium, \[ 2NOCl (g) \rightleftharpoons 2NO (g) + Cl_2 (g) \]
The value of the equilibrium constant, \( K_c \), is \( 3.75 \times 10^{-6} \) at 1069 K. The value of \( K_p \) for the reaction at this temperature will be:

• (A) 0.133
• (B) 1.242
• (C) 0.033
• (D) 0.00033

Arrange the following artificial sweetening agents in order of increasing sweetness: \[ Aspartame, Saccharin, Sucralose, Acesulfame \]

• (A) Acesulfame > Saccharin > Sucralose > Aspartame
• (B) Aspartame > Acesulfame > Saccharin > Sucralose
• (C) Acesulfame > Sucralose > Saccharin > Aspartame
• (D) Sucralose > Aspartame > Acesulfame > Saccharin

Coupling reaction is an example of:

• (A) Nucleophilic addition reaction
• (B) Nucleophilic substitution reaction
• (C) Electrophilic substitution reaction
• (D) Electrophilic addition reaction

The oxidation number of Cr in \(CrO_5\) which has the following structure, is:

• (A) +4
• (B) +5
• (C) +3
• (D) +6

Identify the pair of gases that have equal rates of diffusion:

• (A) CO, NO
• (B) \(N_2O\), CO
• (C) \(N_2O\), \(CO_2\)
• (D) \(CO_2\), \(NO_2\)

The reducing agent which is used to reduce iron oxide in blast furnace is:

• (A) CO
• (B) Coke
• (C) Silica
• (D) Lime

Given that molar conductances for \(Ba(OH)_2\), \(BaCl_2\) and \(NH_4Cl\) are 523.28, 280.0 and 129.8 \( \Omega^{-1}cm^2mol^{-1} \), respectively. What is the molar conductivity \( \Lambda \) of \(NH_4OH\) at this temperature will be:

• (A) 502.88
• (B) 251.44
• (C) 1005.76
• (D) 209.42

Xerophthalmia disease is caused by which deficiency of vitamin?

• (A) Vitamin-A
• (B) Vitamin-C
• (C) Vitamin-B
• (D) Vitamin-\(B_6\)

Find the final product for the reaction: \[ C_6H_5CHO + CH_3COC_6H_5 \xrightarrow{OH^-, 293 K} Product \]

• (A) \(C_6H_5CH=CHC_6H_5 \)
• (B) \(C_6H_5CH=CHC_6H_5 OH \)
• (C) \(C_6H_5OH \)
• (D) \(C_6H_5CH_2C_6H_5 \)

The melting of ice:

• (A) is the phase transformation
• (B) takes place at constant pressure and temperature
• (C) takes place at 373 K
• (D) Both (a) and (b)

Which of the following options represent the correct composition of Dettol?

• (A) Chloroxylenol and terpineol
• (B) Chloroxylenol and furacine
• (C) Terpineol and iodine
• (D) Iodine and furacine

The chemical formula of Hinsberg's reagent is:

• (A) H\(NO_2\)
• (B) NaOH + CaO
• (C) \(C_6H_5\)\(SO_2Cl\)
• (D) \(CH_3CO\)\(NH_2\)

The increasing order of atomic radii of the following group 13 elements is:

• (A) Al < Ga < In < Tl
• (B) Ga < Al < In < Tl
• (C) Al < In < Tl < Ga
• (D) Al < Ga < Tl < In

Which of the following colloids resemble the true solutions?

• (A) Macromolecular colloids
• (B) Micelles
• (C) Micromolecular colloids
• (D) Lyophobic colloids

The hydrocarbon that cannot be prepared effectively by the Wurtz reaction is:

Reaction:



Find the product B.

Why do ketones and carboxylic acids have higher boiling points as compared to aldehydes?

• (A) Due to \(—CHO\) group
• (B) Due to Fazan’s rule
• (C) Due to intermolecular hydrogen bonding
• (D) Due to intramolecular hydrogen bonding

The vacant space in the bcc lattice cell is:

• (A) 26%
• (B) 48%
• (C) 23%
• (D) 32%

In the chemical reaction, \[ N_2 + 3H_2 \rightleftharpoons 2NH_3 at equilibrium point. \]
Which statement is correct?

• (A) Equal volumes of N\(_2\) and H\(_2\) are reacting
• (B) Equal moles of N\(_2\) and H\(_2\) are reacting
• (C) The reaction has stopped.
• (D) The same amount of ammonia is formed, as it is decomposed into N\(_2\) and H\(_2\)

The change in the energy of the system if 500 cal of heat energy are added to a system and the system does 350 cal of work on the surroundings will be:

• (A) +150 cal
• (B) -150 cal
• (C) +350 cal
• (D) -850 cal

Which of the following is not an antacid?

• (A) Aluminium hydroxide
• (B) Cimetidine
• (C) Phenelzine
• (D) Ranitidine

Which of the following is most stable?

• (A) \(CH_3N_3X^-\)
• (B) \(C_6H_5N_2X^-\)
• (C) \(CH_3CH_2N_2X^-\)
• (D) \(C_6H_5CH_2N_2X^{2-}\)

Which type of ligand is EDTA?

• (A) Monodentate
• (B) Hexadentate
• (C) Bidentate
• (D) Tridentate

The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A. What will be the ratio of pressure acting on B and A?

• (A) \(\frac{1}{4}\)
• (B) \(\frac{7}{8}\)
• (C) \(\frac{2}{5}\)
• (D) \(\frac{1}{6}\)

Which of the following is the correct order of their increasing boiling points?

• (A) \( 10^{-4} \, M NaCl > 10^{-3} \, M MgCl_2 > 10^{-2} \, M NaCl > 10^{-4} \, M urea \)
• (B) \( 10^{-2} \, M NaCl > 10^{-3} \, M MgCl_2 > 10^{-4} \, M NaCl > 10^{-4} \, M urea \)
• (C) \( 10^{-4} \, M urea > 10^{-2} \, M NaCl > 10^{-3} \, M MgCl_2 > 10^{-4} \, M NaCl \)
• (D) \( 10^{-4} \, M NaCl > 10^{-3} \, M MgCl_2 > 10^{-4} \, M urea > 10^{-2} \, M NaCl \)

The specific conductivity of a solution containing 1.0 g of anhydrous BaCl\(_2\) in 200 cm\(^3\) of the solution has been found to be 0.0058 Scm\(^{-1}\). The molar and equivalent conductivity of the solution respectively are:

• (A) 120.83 \, \(cm^2\) \, \(eq^{-1}\) \, and \, 241.67 \, \(cm^2\) \, \(eq^{-1}\)
• (B) 150.5 \, \(cm^2\) \, \(eq^{-1}\) \, and \, 289.7 \, \(cm^2\) \, \(eq^{-1}\)
• (C) 241.6 \, \(cm^2\) \, \(mol^{-1}\) \, and \, 120.83 \, \(cm^2\) \, \(eq^{-1}\)
• (D) 248.6 \, \(cm^2\) \, \(mol^{-1}\) \, and \, 180.3 \, \(cm^2\) \, \(eq^{-1}\)

For the reaction \(2N_2O_5 \rightarrow 4NO_2 + O_2\), rate constant \(k = 4.48 \times 10^{-5} \, s^{-1}\) and the initial pressure is 600 atm. After 10 min, determine the final pressure of \(N_2O_5\):

• (A) 590 atm
• (B) 490 atm
• (C) 588 atm
• (D) 580 atm

Calculate the difference between \(C_p\) and \(C_v\) for 10 moles of an ideal gas:

• (A) 83.14 J/K
• (B) 8.314 J/K
• (C) 831.4 J/K
• (D) 0.831 J/K

Which of the following particulate matter is emitted from vehicles?

• (A) Co
• (B) Pb
• (C) Sn
• (D) Se

Arrange the hydrides of group 15 in correct decreasing order of reducing nature:

• (A) \( NH_3 > PH_3 > AsH_3 > SbH_3 > BiH_3 \)
• (B) \( PH_3 > AsH_3 > SbH_3 > BiH_3 > NH_3 \)
• (C) \( AsH_3 > SbH_3 > BiH_3 > NH_3 > PH_3 \)
• (D) \( BiH_3 > SbH_3 > AsH_3 > PH_3 > NH_3 \)

What would be the molarity of one litre solution of 22.2 g of CaCl\(_2\)?

• (A) 0.2 M
• (B) 0.4 M
• (C) 0.6 M
• (D) 0.8 M

For decolourisation of 1 mole of KMnO\(_4\), the moles of H\(_2\)O\(_2\) required is:

• (A) \( \frac{1}{2} \)
• (B) \( \frac{3}{2} \)
• (C) \( \frac{5}{2} \)
• (D) \( \frac{7}{2} \)

What is the IUPAC name of the following compound? \[ HC= C - C = CH \]

• (A) 3,3-diethynylpenta-1,4-diene
• (B) 3,3-diethynylpenta-1,4-dyne
• (C) 3,3-diethynyl-3,3-diethyln-methane
• (D) 3-ethyl-3-ethylpent-1-en-4-yne

Find the compound which has both polar and non-polar covalent bonds:

• (A) HCN
• (B) H\(_2\)O\(_2\)
• (C) NH\(_4\)Cl
• (D) CH\(_4\)

What is the product formed when benzene reacts with CO and HCl in presence of anhydrous AlCl\(_3\)?

Which of the following series of transitions in the spectrum of hydrogen atom fall in the visible region?

• (A) Balmer series
• (B) Paschen series
• (C) Brackett series
• (D) Lyman series

The value of \( \Delta G^\circ \) for the phosphorylation of glucose in glycolysis is 13.8 kJ/mol. The value of \( K_C \) at 298 K is:

• (A) \( 7.72 \times 10^{-4} \)
• (B) \( 5.62 \times 10^{-3} \)
• (C) \( 4.81 \times 10^{-3} \)
• (D) \( 3.81 \times 10^{-3} \)

The Lyman series of hydrogen spectrum lies in which region?

• (A) Infrared region
• (B) Visible region
• (C) Ultraviolet region
• (D) X-ray region

The correct IUPAC name of the coordination compound \( K_3[Fe(CN)_5NO] \) is:

• (A) Potassium pentacyanonitrosylferrate (II)
• (B) Potassium pentacyanonitro-N-ferrate (III)
• (C) Potassium nitritopentacyanoiron (IV)
• (D) Potassium nitritopentacyanoiron (II)

Which of the following conditions are favourable for chemisorption?

• (A) Low temperature and high pressure
• (B) High temperature and low pressure
• (C) High temperature and high pressure
• (D) Low temperature and low pressure

Shade the feasible region for the inequalities \[ x + y \geq 2, \quad 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \]
in a rough figure.

The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \]
is:

• (1) 5
• (2) 4
• (3) 6
• (4) 3

Write the solution of the following LPP \[ Maximize Z = x + y \]
Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \]
Which point the value of \( Z \) is maximum?

• (1) \( (0, 4) \)
• (2) \( (4, 0) \)
• (3) \( (6, 0) \)
• (4) \( (0, 6) \)

The vector that must be added to \[ \mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \quad and \quad 3\mathbf{i} + 6\mathbf{j} - 7\mathbf{k} \]
so resultant vector is a unit vector along the X-axis is:

• (1) \( 4\mathbf{i} + 2\mathbf{j} + 5\mathbf{k} \)
• (2) \( -4\mathbf{i} + 2\mathbf{j} + 5\mathbf{k} \)
• (3) \( 3\mathbf{i} + 5\mathbf{k} \)
• (4) Null vector

If \( |\mathbf{a}| = 8 \), \( |\mathbf{b}| = 3 \) and \( |\mathbf{a} \times \mathbf{b}| = 12 \), then find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).

• (1) \( \frac{\pi}{3} \)
• (2) \( \frac{\pi}{6} \)
• (3) \( \frac{\pi}{4} \)
• (4) None of these

If for \(\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}\), \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), and \(\vec{c} = -3\hat{i} + \hat{j} + 2\hat{k}\), then find \([\vec{a} \, \vec{b} \, \vec{c}]\).

• (1) -15
• (2) -10
• (3) -30
• (4) -5

If for any \(2 \times 2\) square matrix \(A\), we have \(A \cdot adj(A) = \begin{bmatrix} 8 & 0
0 & 8 \end{bmatrix}\), then the value of \(\det(A)\) is:

• (1) 6
• (2) 5
• (3) 7
• (4) 8

If matrix \( A = \begin{bmatrix} 2 & -2
-2 & 2 \end{bmatrix} \) and \( A^2 = pA \), then the value of \( p \) is:

• (1) 6
• (2) -4
• (3) 4
• (4) 8

If \( A \cdot adj(A) = \begin{bmatrix} -2 & 0 & 0
0 & -2 & 0
0 & 0 & -2 \end{bmatrix} \), then \( |adj(A)| \) equals:

• (1) -2
• (2) -4
• (3) 4
• (4) 8

The coefficients \( a, b, c \) of the quadratic equation \( ax^2 + bx + c = 0 \) are obtained by throwing a die three times. The probability that this equation has equal roots is:

• (1) \( \dfrac{1}{72} \)
• (2) \( \dfrac{5}{216} \)
• (3) \( \dfrac{1}{36} \)
• (4) \( \dfrac{1}{54} \)

Evaluate: \( 8^{\log_5 5} \)

• (1) \( \log_5 25 \)
• (2) 120
• (3) 125
• (4) \( \log_5 15 \)

The equation of normal to the curve \( y = (1 + x)^y + \sin^{-1}(\sin^2 x) \) at \( x = 0 \) is:

• (a) \( x + y = 1 \)
• (b) \( x - y = 1 \)
• (c) \( x + y = -1 \)
• (d) \( x - y = -1 \)

If \( L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2}}{x^4} \), \( a > 0 \), then:

• (a) \( a = 2 \)
• (b) \( a = 1 \)
• (c) \( a = \frac{1}{3} \)
• (d) None of these

What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?

• (a) \( x^2 + y^2 - 2x - 4y + 1 = 0 \)
• (b) \( x^2 + y^2 + 2x + 4y + 1 = 0 \)
• (c) \( x^2 + y^2 - 2x - 4y - 1 = 0 \)
• (d) \( x^2 + y^2 + 2x + 4y - 1 = 0 \)

The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:

• (a) -34.995
• (b) -33.995
• (c) -33.335
• (d) -35.995

Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).

• (a) \( Center = \left( -\frac{3}{4}, -2 \right), \, Radius = 2 \)
• (b) \( Center = (1, -2), \, Radius = 1 \)
• (c) \( Center = (0, 0), \, Radius = 3 \)
• (d) \( Center = (2, 1), \, Radius = 4 \)

Find the maximum value of \( f(x) = \frac{1}{4x^2 + 2x + 1} \).

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

If \( f(x) = \begin{cases} ax + 3 & for x \leq 2
a(x - 1) & for x > 2 \end{cases} \), then the values of \( a \) for which \( f \) is continuous for all \( x \) are:

• (a) 1 and -2
• (b) 1 and 2
• (c) -1 and 2
• (d) -1 and -2

The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:

• (a) \( (abc)^3 \)
• (b) \( abc \)
• (c) \( (abc)^{1/3} \)
• (d) None of these

What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?

• (a) \( x^2 + y^2 - 2x - 4y + 1 = 0 \)
• (b) \( x^2 + y^2 + 2x + 4y + 1 = 0 \)
• (c) \( x^2 + y^2 - 2x - 4y - 1 = 0 \)
• (d) \( x^2 + y^2 + 2x + 4y - 1 = 0 \)

The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:

• (a) \( 3x + 4y + 5z = 7 \)
• (b) \( 2x + 3y + 4z = 0 \)
• (c) \( x + y - z = 2 \)
• (d) \( 2x + y - 2z = 0 \)

The equation of a plane passing through the line of intersection of the planes \( x + 2y + 3z = 2 \) and \( x - y + z = 3 \) and at a distance \( \frac{2}{\sqrt{3}} \) from the point \( (3, 1, -1) \) is:

• (a) \( 5x - 11y + z = 17 \)
• (b) \( \sqrt{2}x + y = 3\sqrt{2} - 1 \)
• (c) \( x + y + z = \sqrt{3} \)
• (d) \( x - \sqrt{2}y = 1 - \sqrt{2} \)

The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:

• (a) \( 30^\circ \)
• (b) \( 45^\circ \)
• (c) \( 90^\circ \)
• (d) \( 0^\circ \)

The point of intersection of the lines \( \frac{x - 1}{3} = \frac{y - 2}{-3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z - 1}{-2} \) is:

• (a) \( (0, 0, 0) \)
• (b) \( (1, 1, 1) \)
• (c) \( (-1, -1, -1) \)
• (d) \( (1, 2, 3) \)

The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:

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

The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:

• (a) 2
• (b) 3
• (c) 0
• (d) 5

The integral of \( \int \frac{dx}{x^2[1 + x^4]^{3/4}} \) is:

• (a) \( 4(x^{1/4} + 1)^{1/4} + C \)
• (b) \( 4(x^{1/4} + 1)^{1/4} + C \)
• (c) \( 4(x^4 + 1)^{1/4} + C \)
• (d) None of these

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals:

• (a) \( \frac{1}{2} \)
• (b) \( \frac{1}{5} \)
• (c) \( \frac{1}{10} \)
• (d) \( \frac{1}{20} \)

Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is:

• (a) \( \frac{1}{4} \)
• (b) \( \frac{2}{3} \)
• (c) \( \frac{3}{5} \)
• (d) \( \frac{4}{5} \)

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that \( P(B) = \frac{3}{2} P(A) \) and \( P(C) = \frac{1}{2} P(B) \), then \( P(A \cup C) \) equals:

• (a) \( \frac{10}{13} \)
• (b) \( \frac{3}{13} \)
• (c) \( \frac{6}{13} \)
• (d) \( \frac{7}{13} \)

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is \( p \), \( 0 < p < 1 \). If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly is:

• (a) \( \frac{3p}{4p + 3} \)
• (b) \( \frac{5p}{3p + 2} \)
• (c) \( \frac{5p}{4p + 1} \)
• (d) \( \frac{4p}{3p + 1} \)

If \( x \) and \( y \) are acute angles, such that \[ \cos x + \cos y = \frac{3}{2} \quad and \quad \sin x + \sin y = \frac{3}{4}, \quad then \quad \sin(x + y) equals: \]

• (a) \( \frac{2}{5} \)
• (b) \( \frac{3}{4} \)
• (c) \( \frac{3}{5} \)
• (d) \( \frac{4}{5} \)

The expression \( \frac{\tan A + \cot A}{1 - \cot A} \) can be written as:

• (a) \( \sin A \cos A + 1 \)
• (b) \( \sec A \csc A + 1 \)
• (c) \( \tan A + \cot A \)
• (d) \( \sec A + \csc A \)

If \( \sin 2x = 4 \cos x \), then \( x \) is equal to:

• (a) \( \frac{n\pi}{2}, \, n \in \mathbb{Z} \)
• (b) no value
• (c) \( n\pi + (-1)^n \frac{\pi}{4}, \, n \in \mathbb{Z} \)
• (d) \( 2n\pi + \frac{\pi}{2}, \, n \in \mathbb{Z} \)

If \( f(x) \) satisfies the relation \( 2f(x) + f(1 - x) = x^2 \) for all real \( x \), then \( f(x) \) is:

• (a) \( x^2 + 2x - 1 \)
• (b) \( x^2 + 2x - 1 \)
• (c) \( x^2 + 4x - 1 \)
• (d) \( x^2 + 4x - 1 \)

If \( A = \{1, 2, 5, 6\} \) and \( B = \{1, 2, 3\} \), then \( A \times B \cap B \times A \) is equal to:

• (a) \( \{(1, 1), (2, 1), (6, 1), (3, 2)\}
• (b) \( \{(1, 1), (2, 1), (3, 2), (2, 2)\}
• (c) \( \{(1, 1), (2, 1), (6, 1), (2, 2), (3, 2)\}
• (d) \( \{(1, 1), (2, 1), (6, 1), (2, 2), (3, 2), (2, 5)\} \)

Total number of elements in the power set of a set \( A \) containing 15 elements is:

• (a) \( 2^{15} \)
• (b) \( 15^2 \)
• (c) \( 2^{15} - 1 \)
• (d) \( 2^{15} - 1 \)

What is the argument of the complex number \( \frac{(1 + i)(2 + i)}{3 - i} \), where \( i = \sqrt{-1} \)?

• (a) 0
• (b) \( \frac{\pi}{4} \)
• (c) \( -\frac{\pi}{4} \)
• (d) \( \frac{\pi}{2} \)

Evaluate \( \left[ i^{18} + \frac{1}{i} \right]^{25} \):

• (a) \( 2(1 - i) \)
• (b) \( 7(1 - i) \)
• (c) \( 8i + 4 \)
• (d) \( 7i - 1 \)

If \( (\sqrt{3} + i)^{100} = 2^{99} (a + ib) \), then \( a^2 + b^2 \) is equal to:

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

Using mathematical induction, the numbers \( a_n \)'s are defined by \( a_0 = 1 \), \( a_{n+1} = 3n^2 + n + a_n \), \( (n \geq 0) \). Then, \( a_n \) is equal to:

• (a) \( n^3 + n^2 + 1 \)
• (b) \( 3n^3 + 3n + 1 \)
• (c) \( n^3 - n^2 + 1 \)
• (d) \( n^3 + n^2 \)

If \( 49^n + 16n + P \) is divisible by 64 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is:

• (a) -2
• (b) 3
• (c) -4
• (d) -1

Evaluate \( 3^n - 7n - 1 \) is divisible by:

• (a) 64
• (b) 36
• (c) 49
• (d) 25

The solution of the differential equation \( \sec^2 x \, \tan y \, dx + \sec y \, \tan x \, dy = 0 \) is:

• (a) \( \tan x \, \tan y = C \)
• (b) \( \tan y = \tan x = C \)
• (c) \( \tan^2 x = C \)
• (d) None of these

The solution of the differential equation \[ y \frac{dy}{dx} = x \left[ \frac{y^2}{x^2} + \varphi \left( \frac{y^2}{x^2} \right) \right] \]
is:

• (a) \( \varphi \left( \frac{y^2}{x^2} \right) = Cx \)
• (b) \( x \frac{y^2}{x^2} = C \)
• (c) \( \left( \frac{y^2}{x^2} \right) = Cx^2 \)
• (d) \( x \varphi \left( \frac{y^2}{x^2} \right) = C \)

The solution of the differential equation \[ (1 + y^2) + (x - e^{\tan^{-1} y}) \frac{dy}{dx} = 0 \]
is:

• (a) \( 2x e^{\tan^{-1} y} = e^{2\tan^{-1} y} + C \)
• (b) \( x e^{\tan^{-1} y} = \tan^{-1} y + C \)
• (c) \( x e^{\tan^{-1} y} = e^{\tan^{-1} y} + C \)
• (d) \( (x - 2) = C e^{-\tan^{-1} y} \)

The value of \[ 1! + 2! + 2! + 3! + 3! + \cdots + n \cdot n! \]
is:

• (a) \( (n!) \)
• (b) \( (n + 1)! \)
• (c) \( (n! + 1)! - 1 \)
• (d) None of these

The sum of the series \( (1 + 2) + (1 + 2 + 2^2) + (1 + 2 + 2^2 + 2^3) + \cdots \) up to terms is:

• (a) \( 2n^2 + n - 4 \)
• (b) \( 2^n - 1 \)
• (c) \( 2n^2 + n - 1 \)
• (d) \( 2n^n - 1 \)

If \( a, b, c \) are in AP, \( b - a, c - b \) and \( a \) are in GP, then \( a : b : c \) is:

• (a) \( 1 : 2 : 3 \)
• (b) \( 1 : 3 : 5 \)
• (c) \( 2 : 3 : 4 \)
• (d) \( 1 : 2 : 4 \)

The number of triangles which can be formed by using the vertices of a regular polygon of \( (n + 3) \) sides is 220. Then, \( n \) is equal to:

• (a) 8
• (b) 9
• (c) 10
• (d) 11

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from these 8 points?

• (a) 26
• (b) 28
• (c) 27
• (d) 25

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

• (a) 12
• (b) 24
• (c) 36
• (d) 48

If a polygon of \( n \) sides has 275 diagonals, then \( n \) is equal to:

• (a) 25
• (b) 35
• (c) 20
• (d) 15

If two pairs of lines \( x^2 - 2mxy - y^2 = 0 \) and \( x^2 - 2nxy - y^2 = 0 \) are such that one of them represents the bisector of the angles between the other, then:

• (a) \( mn = 1 \)
• (b) \( m + n = mn \)
• (c) \( mn = -1 \)
• (d) \( m - n = mn \)

The distance of the point \( (1, 2) \) from the line \( x + y + 5 = 0 \) measured along the line parallel to \( 3x - y = 7 \) is:

• (a) \( \frac{4}{\sqrt{10}} \)
• (b) 40
• (c) \( \sqrt{40} \)
• (d) \( \frac{10}{\sqrt{2}} \)

The slopes of the lines, which make an angle 45° with the line \( 3x - y = -5 \), are:

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

If 3 and 4 are intercepts of a line \( L = 0 \), then the distance of \( L = 0 \) from the origin is:

• (a) 5 units
• (b) 12 units
• (c) \( \frac{5}{12} \) unit
• (d) \( \frac{12}{5} \) units

Number of terms in the binomial expansion of \( (x + a)^{53} + (x - a)^{53} \) is:

• (a) 25
• (b) 26
• (c) 27
• (d) 26.5

The coefficient of \( x^{10} \) in the expansion of \( 1 + (1 + x) + (1 + x)^2 + \cdots + (1 + x)^{20} \) is:

• (a) \( 19C9 \)
• (b) \( 20C10 \)
• (c) \( 21C11 \)
• (d) \( 22C12 \)

Middle term in the expansion of \( \left( x^2 + \frac{1}{x^2} + 2 \right)^n \) is:

• (a) \( \frac{n!}{(n/2)^2} \)
• (b) \( \frac{(2n)!}{(n!)^2} \)
• (c) \( \frac{(2n-1)!}{(n!)^2} \)
• (d) \( \frac{2n!}{n!} \)