KEAM 2024 Pharmacy Question Paper with Answer Key (June 10)

In the measurement of length 6 \(\mu\)m is equal to \(x\) pm. Then the value of \(x\) is

• (A) \(1.5 \times 10^{-5}\)
• (B) \(1.2 \times 10^{6}\)
• (C) \(3 \times 10^{-6}\)
• (D) \(6 \times 10^{6}\)
• (E) \(2 \times 10^{-12}\)

Dimensions of the physical quantity \(X\) in the equation \[ Force = \frac{X}{Volume} \]
are

• (A) \(ML^3T^2\)
• (B) \(MLT\)
• (C) \(ML^2T^2\)
• (D) \(MLT^{-2}\)
• (E) \(ML^4T^{-2}\)

A man loses 50% of his velocity after running a distance of 100 m. If his retardation is uniform, the distance he will cover before coming to rest is

• (A) \(45.2\) m
• (B) \(33.3\) m
• (C) \(27.5\) m
• (D) \(15.7\) m
• (E) \(50.5\) m

A projectile is given an initial velocity of \((\hat{i} + \hat{j})\) ms\textsuperscript{-1 where \(\hat{i}\) is along the ground and \(\hat{j}\) is along the vertical direction. The equation of its trajectory is \((g = 10\) ms\textsuperscript{-2\()\)

• (A) \(y^2 = 2x\)
• (B) \(y^2 - 1 = 5x\)
• (C) \(y = x - 5x^2\)
• (D) \(y = x^2\)
• (E) \(y = x^2 - 2\)

A particle is describing a uniform circular motion with a certain constant speed. The INCORRECT statement is

• (A) The velocity and acceleration vectors are perpendicular to each other
• (B) The velocity vector is tangential to the circular path
• (C) The centripetal acceleration is a variable acceleration
• (D) The acceleration vector points to the centre of the circle
• (E) The acceleration vector is tangential to the circular path

A particle moves under the influence of a force in the XY-plane such that the components of its linear momentum \(\vec{p}\) at any time \(t\) is \(p_x = p \sin t\) and \(p_y = p \cos t\). The angle between \(\vec{F}\) and \(\vec{p}\) at that time is

• (A) \(45^\circ\)
• (B) \(60^\circ\)
• (C) \(30^\circ\)
• (D) \(90^\circ\)
• (E) \(0^\circ\)

In a ‘tug of war’ game, two persons pull each other through a massless rope. The person who wins is

• (A) One whose weight is less
• (B) One who exerts more friction force (shearing force) on the ground
• (C) One who exerts more normal force (compressing force) on the ground
• (D) One who pulls the rope with a greater force
• (E) One whose weight is more

When a spring of spring constant \(k\) is cut into two pieces whose lengths are \(l_1\) and \(l_2\), then the ratio of their spring constants \(k_1\) and \(k_2\) is

• (A) \(\frac{l_2}{l_1}\)
• (B) \(\frac{l_1}{l_2}\)
• (C) \(\sqrt{l_1 l_2}\)
• (D) \(l_1 l_2\)
• (E) \(\frac{1}{l_1 l_2}\)

If \(P\) is the pressure at which the heart is pumping the blood and the volume of blood pumped per second is \(V\), then the power of the heart is given by

• (A) \(\frac{P}{V}\)
• (B) \(\frac{P^2}{V}\)
• (C) \(P V\)
• (D) \(\frac{P}{V_2}\)
• (E) \(P^2 V\)

A block of mass \(M\) moves with a velocity \(v\) along a frictionless horizontal surface towards another block of mass \(2M\) at rest. The velocity of the center of mass of the system of blocks is

• (A) \(\frac{v}{2}\)
• (B) \(2v\)
• (C) \(3v\)
• (D) \(\frac{v}{3}\)
• (E) \(\frac{v}{4}\)

The radius of gyration of a regular solid cylinder of radius \(R\) about its axis is

• (A) \(\frac{R}{2}\)
• (B) \(R\)
• (C) \(\frac{R}{\sqrt{2}}\)
• (D) \(2R\)
• (E) \(\frac{R}{4}\)

When two spheres of radii \(r\) and \(\frac{r}{2}\) are brought in contact, the gravitational force of attraction between them is proportional to

• (A) \(r^6\)
• (B) \(r^4\)
• (C) \(r^{-6}\)
• (D) \(r^{-4}\)
• (E) \(r^{-2}\)

The gravitational potential energy of a system of two bodies each of mass \(m\) and distance \(r\) between them is (G = gravitational constant, g = acceleration due to gravity)

• (A) \(-\frac{Gm^2}{r^2}\)
• (B) \(-\frac{Gm^2}{r}\)
• (C) \(-\frac{gm^2}{r}\)
• (D) \(-G \frac{gm^2}{r}\)
• (E) \(\frac{Ggm}{r^2}\)

Which of the following has the maximum Young’s modulus value?

• (A) Aluminium
• (B) Copper
• (C) Brass
• (D) Steel
• (E) Iron (Wrought)

The energy stored in a soap bubble of diameter 4 cm is nearly (surface tension of soap solution is 0.07 Nm\textsuperscript{-1})

• (A) \(8.5 \times 10^{-3}\) J
• (B) \(2.75 \times 10^{-2}\) J
• (C) \(7 \times 10^{-4}\) J
• (D) \(4.5 \times 10^{-4}\) J
• (E) \(3.15 \times 10^{-3}\) J

When two different liquids of same mass but at two different temperatures \(27^\circ C\) and \(47^\circ C\) are mixed together, the resulting temperature of the mixture is \(35^\circ C\). The ratio of their specific heat capacities is

• (A) 1 : 3
• (B) 5 : 3
• (C) 3 : 2
• (D) 4 : 1
• (E) 2 : 7

Two perfectly black bodies are at temperatures \( T \) and \( 2T \). The ratio between the wavelengths corresponding to maximum energy emission by the two black bodies is

• (A) 2 : 1
• (B) 1 : 2
• (C) 2 : 3
• (D) 3 : 2
• (E) 1 : 4

When water is heated from \(0^\circ\)C to \(8^\circ\)C, its volume

• (A) first decreases upto \(4^\circ\)C and then increases
• (B) first increases upto \(4^\circ\)C and then decreases
• (C) increases continuously
• (D) decreases continuously
• (E) does not change

The pressure of an ideal gas is proportional to the cube of its temperature (on absolute scale) in an adiabatic process. Then the value of the ratio \(C_p/C_v\) is

• (A) \(\frac{7}{5}\)
• (B) \(\frac{5}{3}\)
• (C) \(\frac{4}{3}\)
• (D) \(\frac{3}{2}\)
• (E) \(\frac{7}{3}\)

The average kinetic energy per molecule of an ideal gas at \(27^\circ C\) is \(E\). The temperature of the gas at which the average kinetic energy per molecule will be \(2E\) is

• (A) \(127^\circ C\)
• (B) \(227^\circ C\)
• (C) \(327^\circ C\)
• (D) \(400^\circ C\)
• (E) \(527^\circ C\)

The instantaneous displacement of a particle executing simple harmonic motion is given by \(x = 2(\cos(\pi t) + \sin(\pi t))\). The amplitude of oscillation is

• (A) \(3\sqrt{2}\)
• (B) 4
• (C) \(4\sqrt{2}\)
• (D) \(2\sqrt{2}\)
• (E) \(8\sqrt{2}\)

The velocity of a travelling plane wave given by \[ y = 10^{-2} \sin \left( 200t - \frac{x}{5} \right) m, \]
is

• (A) \(10\) ms^{-1}
• (B) \(500\) ms^{-1}
• (C) \(400\) ms^{-1}
• (D) \(5\) ms^{-1}
• (E) \(1000\) ms^{-1}

When a glass rod is rubbed with silk thread, it loses 1000 electrons. Then the charge on the glass rod is (electronic charge \(e = 1.6 \times 10^{-19}\) C)

• (A) \(+1.6 \times 10^{-16}\) C
• (B) \(-1.6 \times 10^{-19}\) C
• (C) \(-1.6 \times 10^{-13}\) C
• (D) \(+1.6 \times 10^{-19}\) C
• (E) \(-1.6 \times 10^{-15}\) C

In bringing a proton towards another proton, the electrostatic potential energy of the system

• (A) decreases
• (B) increases
• (C) becomes zero
• (D) first increases and then decreases
• (E) remains the same

A parallel plate capacitor with a dielectric medium of dielectric constant 1.5 has a capacitance of \(C\). If the dielectric is removed, then the capacitance of the capacitor becomes

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

When \(n\) identical cells are connected in parallel, they give

• (A) less current
• (B) more current
• (C) less voltage
• (D) more voltage
• (E) variable voltage and variable current

Resistivity of a conductor increases with

• (A) increase in its length
• (B) decrease in its length
• (C) increase in its area of cross-section
• (D) decrease in its area of cross-section
• (E) increase in its temperature

Kirchhoff’s junction rule is based on conservation of

• (A) charge
• (B) energy
• (C) both energy and charge
• (D) angular momentum
• (E) linear momentum

The magnetic force acting on a charged particle carrying a charge \(3 \mu C\) in a magnetic field of \(5\) T acting in the \(y\)-direction, when the particle velocity is \[ (\hat{i} + \hat{j}) \times 10^5 ms^{-1} \]
is

• (A) \(0.5\) N in \(+x\) direction
• (B) \(0.2\) N in \(+y\) direction
• (C) \(2\) N in \(-x\) direction
• (D) \(1.5\) N in \(-z\) direction
• (E) \(1.5\) N in \(+z\) direction

The magnetic moment \(\mu\) associated with a charged particle carrying charge \(q\) moving in a circle of radius \(a\) with uniform speed \(v\) is

• (A) \(qva\)
• (B) \(\frac{qva}{4}\)
• (C) \(\frac{qva}{2}\)
• (D) \(\frac{qva}{16}\)
• (E) \(\frac{qva}{8}\)

For a paramagnetic material, the magnetic susceptibility \( \chi_m \) is

• (A) small, positive and varies inversely with temperature
• (B) small, negative and temperature independent
• (C) small, positive and temperature independent
• (D) very large, negative and temperature dependent
• (E) very large, positive and temperature independent

An alternating current having peak value 14.14 A is used to heat a metal wire. The value of the direct current \(i\) required to produce the same heating effect in the same wire is

• (A) 0.707 A
• (B) 28.28 A
• (C) 7.07 A
• (D) 10 A
• (E) 14 A

The number of windings in the primary and secondary of a transformer are 100 and 2000 respectively. If 50 V a.c is applied to the primary, the potential difference across the secondary is

• (A) 2000 V
• (B) 1000 V
• (C) 500 V
• (D) 1500 V
• (E) 2500 V

The correct order of arrangement of electromagnetic waves according to their wavelengths is

• (A) \(Gamma rays < AM radio waves < FM radio waves < Micro waves\)
• (B) \(Micro waves < AM radio waves < FM radio waves < Gamma rays\)
• (C) \(Gamma rays < Micro waves < AM radio waves < FM radio waves\)
• (D) \(Gamma rays < Micro waves < FM radio waves < AM radio waves\)
• (E) \(AM radio waves < FM radio waves < Gamma rays < Micro waves\)

An ink mark is made on a piece of paper and a glass slab of thickness \(t\) and refractive index \(\mu\) is placed on it. If the image of the ink mark appears to be at a distance of \(x\) from the top surface of the slab, then the value of \(x\) is

• (A) \(\mu t\)
• (B) \(\frac{t}{\mu}\)
• (C) \(\frac{\mu}{t}\)
• (D) \(\frac{\mu - 1}{t}\)
• (E) \(\frac{t}{\mu - 1}\)

If the ratio of amplitudes of two light waves is 2 : 1, then the ratio between the intensities of the two waves is

• (A) \(4 : 1\)
• (B) \(1 : 1\)
• (C) \(1 : 2\)
• (D) \(1 : 4\)
• (E) \(2 : 1\)

In Young’s double slit experiment, to change the bandwidth from \(\beta\) to \(\frac{\beta}{4}\) without changing the experimental setup, the wavelength of light \(\lambda\) used must be changed to

• (A) \(4\lambda\)
• (B) \(16\lambda\)
• (C) \(\frac{\lambda}{4}\)
• (D) \(\frac{\lambda}{16}\)
• (E) \(8\lambda\)

If the speed of a moving particle is decreased by 1%, the de Broglie wavelength of the wave associated with it

• (A) decreases by 1%
• (B) increases by 1%
• (C) decreases by 2%
• (D) increases by 2%
• (E) decreases by 5%

The photoelectric work function for a photosensitive material is 5.2 eV. The energy of the incident radiation for which the stopping potential is 6 V is

• (A) 1.2 eV
• (B) 5.6 eV
• (C) 6 eV
• (D) 10 eV
• (E) 11.2 eV

When the hydrogen atom is excited from the ground state,

• (A) potential energy increases but kinetic energy decreases
• (B) both potential energy and kinetic energy decrease
• (C) both potential energy and kinetic energy increase
• (D) potential energy decreases but kinetic energy increases
• (E) there is no change in the total energy

In a nuclear decay, after the emission of one \(\alpha\)-particle and one \(\beta\)-particle

• (A) atomic number remains unchanged
• (B) mass number is reduced by 4 units
• (C) mass number is reduced by 8 units
• (D) mass number increases by 4 units
• (E) atomic number is increased by 2 units

If nuclear radius of \(^{125}_{52}Te\) is 6 fermi, then the nuclear radius of \(^{27}_{13}Al\) in fermi is

• (A) \(3.6\)
• (B) \(5\)
• (C) \(2.5\)
• (D) \(1.7\)
• (E) \(4.2\)

Half-life of radon is 3.5 days. The amount of radon left out of 12 mg mass undecayed after 35 days is nearly

• (A) \(0.006\) mg
• (B) \(0.012\) mg
• (C) \(0.024\) mg
• (D) \(0.036\) mg
• (E) \(0.048\) mg

In a p-n junction diode, reverse biasing

• (A) increases the number of majority charge carriers
• (B) decreases the number of minority charge carriers
• (C) increases the potential barrier
• (D) decreases the potential barrier
• (E) increases the number of both majority and minority charge carriers

Which one of the following is not a semiconductor?

• (A) Si
• (B) Sb
• (C) Ge
• (D) CdS
• (E) GaAs

The number of significant figures in 0.0500L is

• (A) one
• (B) two
• (C) three
• (D) four
• (E) five

Isobars are atoms with the same

• (A) atomic number
• (B) mass number
• (C) number of electrons
• (D) number of protons
• (E) number of neutrons

The element with atomic number 111 was first named as Unununnium. What is its IUPAC name?

• (A) Nobelium
• (B) Bohrium
• (C) Lawrencium
• (D) Roentgenium
• (E) Rutherfordium

Octet rule is obeyed in

• (A) \(SCl_2\)
• (B) \(PF_5\)
• (C) \(SF_6\)
• (D) \(BCl_3\)
• (E) \(H_2SO_4\)

A particular color of light has a wavelength of 663 nm. What is the energy possessed by the light?
(Planck’s constant \(h = 6.63 \times 10^{-34}\) J·s; Velocity of light \(c = 3 \times 10^8\) m/s)

• (A) \(6.63 \times 10^{-19}\) J
• (B) \(6.63 \times 10^{-20}\) J
• (C) \(1.5 \times 10^{-19}\) J
• (D) \(3.0 \times 10^{-20}\) J
• (E) \(3.0 \times 10^{-19}\) J

The molar enthalpy of vaporization of water at 1 bar and \(100^\circ\)C is 41 kJ mol\textsuperscript{-1. What is the internal energy change, when 1 mol of water is vaporized at 1 bar pressure and \(100^\circ\)C? Assume water vapor as a perfect gas. (R = 8.3 J K\textsuperscript{-1 mol\textsuperscript{-1)

• (A) \(37.9\) kJ mol^{-1}
• (B) \(44.1\) kJ mol^{-1}
• (C) \(34.7\) kJ mol^{-1}
• (D) \(47.9\) kJ mol^{-1}
• (E) \(34.9\) kJ mol^{-1}

0.1 M HCl and 0.1 M H_{2}SO_{4} each of volume 2 mL are mixed and the volume is made up to 6 mL by adding 2 mL of 0.01 N NaCl solution. The pH of the resulting mixture is

• (A) \(1.17\)
• (B) \(1.0\)
• (C) \(0.3\)
• (D) \(\log 2 - \log 3\)
• (E) \(\log 3 - \log 2\)

Which of the following molecules has two sigma (\(\sigma\)) and two pi (\(\pi\)) bonds?

• (A) \(N_2\)
• (B) \(C_2H_6\)
• (C) \(N_2F_2\)
• (D) HCN
• (E) \(C_2H_2Cl_2\)

The following results were obtained in the gas phase reaction between nitric oxide and oxygen at a given temperature.

(A) 3 and 2 
(B) 2 and 2 
(C) 2 and 1 
(D) 3 and 0 
(E) 3 and 1 

Which of the following is an example of pseudo first order reaction?

• (A) Thermal decomposition of \(N_2O_5\) gas
  (B) Decomposition of HI on gold surface
  (C) Decomposition of \(NH_3\) on platinum surface
  (D) Inversion of sucrose
  (E) Hydrogenation of ethene

Which of the following changes alone would cause increase in the value of the equilibrium constant of the reaction? \(PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g); \Delta H > 0\)

• (A) Increasing the volume of the reaction vessel
  (B) Decreasing the volume of the reaction vessel
  (C) Addition of catalyst to equilibrium mixture
  (D) Addition of \(PCl_5(g)\) to the equilibrium mixture
  (E) Increasing the temperature

For the gas phase homogeneous equilibrium, \[ 2X(g) \rightleftharpoons 2Y(g) + Z(g), \]
\(K_C\) at 400K is \(1 \times 10^{-3}\) mol L\textsuperscript{-1. What is the value of \(K_P\) for the equilibrium at 400K? \[ R = 0.082 L atm K^{-1} mol^{-1} \]

• (A) \(1 \times 10^{-3}\) atm
• (B) \(3.16 \times 10^{-4}\) atm
• (C) \(4.24 \times 10^{-4}\) atm
• (D) \(3.28 \times 10^{-2}\) atm
• (E) \(1.28 \times 10^{-2}\) atm

Which of the following pairs of aquated first transition metal ions have the same color?

• (A) \(Cr^{3+}, Mn^{3+}\)
• (B) \(Ti^{3+}, Cu^{2+}\)
• (C) \(Fe^{2+}, Co^{2+}\)
• (D) \(Fe^{2+}, Cu^{2+}\)
• (E) \(Fe^{3+}, Co^{3+}\)

For the reaction \[ 3Fe_{(s)} + 2O_2{(g)} \rightarrow Fe_3O_4{(s)}, \]
\(\Delta H = -1650\) kJ mol\textsuperscript{-1, \(\Delta S = -600\) J K\textsuperscript{-1 mol\textsuperscript{-1 at 300K. What is the value of free energy change for the reaction at 300K?

• (A) \(-1470\) J mol\textsuperscript{-1}
• (B) \(-1830\) J mol\textsuperscript{-1}
• (C) \(-147.02\) kJ mol\textsuperscript{-1}
• (D) \(-1830\) kJ mol\textsuperscript{-1}
• (E) \(-1470\) kJ mol\textsuperscript{-1}

In which of the following aqueous solutions of salt, is pH independent of the concentration of the salt?

• (A) Ammonium chloride
• (B) Ferric chloride
• (C) Ammonium acetate
• (D) Sodium acetate
• (E) Ammonium sulphate

The values of X, Y, and Z in the following chemical equation are respectively: \( S_8 + X HNO_3 (conc.) \rightarrow Y H_2SO_4 + X NO_2 + Z H_2O \)
(A) 24, 4, 8
(B) 36, 6, 18
(C) 48, 8, 24
(D) 48, 8, 16
(E) 24, 8, 12

Which of the 3d block element has the minimum melting point?

• (A) Ti
• (B) Fe
• (C) Cr
• (D) Mn
• (E) Ag

Iron does not exhibit ------- oxidation state.

• (A) \(+6\)
• (B) \(+4\)
• (C) \(+3\)
• (D) \(+5\)
• (E) \(+2\)

The correct electronic configuration of Uranium (Z=92) is

• (A) \([Rn] 5f^3 6d^1 7s^2\)
• (B) \([Rn] 5f^4 6d^0 7s^2\)
• (C) \([Rn] 5f^6 6d^3 7s^0\)
• (D) \([Rn] 5f^6 6d^1 7s^1\)
• (E) \([Rn] 5f^6 6d^1 7s^0\)

Which one of the following is an outer orbital complex?

• (A) \([Co(NH_3)_6]^{3+}\)
• (B) \([Fe(CN)_6]^{3-}\)
• (C) \([CoF_6]^{3-}\)
• (D) \([Co(C_2O_4)_3]^{3-}\)
• (E) \([Fe(NH_3)_6]^{3+}\)

Conformational isomerism is not possible in

• (A) ethane
• (B) n-butane
• (C) 2,3-dimethylbutane
• (D) cyclohexane
• (E) ethene

When sodium nitroprusside is added to sodium fusion extract the presence of sulphur is indicated by the formation of a violet colored complex. Its formula is

• (A) \([Fe(CN)_5(NO)(SO_4)]^{4+}\)
• (B) \([Fe(CN)_5NOS]^{4-}\)
• (C) \([Fe(CN)_5(NO_2)(SO_4)]^{3-}\)
• (D) \([Fe(CN)_5(NO_3)(SO_4)]^{3-}\)
• (E) \([Fe(CN)_5(NO)(SO_4)]^{4-}\)

When n-hexane is heated to 773K at 10-20 atmosphere pressure in the presence of \(Cr_2O_3\), benzene is formed. This reaction is called

• (A) pyrolysis
• (B) refining
• (C) reforming
• (D) cracking
• (E) isomerisation

The decreasing order of reactivity of butyl bromides in \(S_N2\) reaction is

• (A) \((CH_3)_3CBr > CH_3CH_2CH_2CH_2Br > CH_3CH(CH_3)CH_2Br > CH_3CH_2CH(Br)CH_3\)
• (B) \(CH_3CH_2CH_2CH_2Br > CH_3CH(CH_3)_2Br > (CH_3)_3CBr > CH_3CH_2CH(Br)CH_3\)
• (C) \((CH_3)_3CBr > CH_3CH(CH_3)CH_2Br > CH_3CH_2CH_2CH_2Br > CH_3CH_2CH(Br)CH_3\)
• (D) \(CH_3CH_2CH_2CH_2Br > (CH_3)_3CBr > CH_3CH(CH_3)CHBr > CH_3CH(CH_3)CH_2Br\)
• (E) \(CH_3CH_2CH_2CH_2Br > CH_3CH(CH_3)_2Br > CH_3CH_2CH(Br)CH_3 > (CH_3)_3CBr\)

Which of the following is the most acidic compound?

• (A) p-Nitrophenol
• (B) o-Nitrophenol
• (C) o-Cresol
• (D) p-Cresol
• (E) Phenol

When propanoic acid is treated with bromine and red phosphorus in aqueous medium, 2-bromopropanoic acid is formed. This reaction is known as

• (A) Kolbe reaction
• (B) Wurtz reaction
• (C) Hell-Volhard-Zelinsky reaction
• (D) Etard reaction
• (E) Wurtz-Fittig reaction

Which of the following groups is deactivating ortho-para directing in aromatic electrophilic substitution?

• (A) \(-NO_2\)
• (B) \(-OCH_3\)
• (C) \(-CH_3\)
• (D) \(-Cl\)
• (E) \(-CHO\)

Gatterman reaction is used to convert benzene diazonium chloride to

• (A) benzene
• (B) nitrobenzene
• (C) phenetole
• (D) phenol
• (E) chlorobenzene

The correct increasing order of basic strength is

• (A) \(NH_3 < C_2H_5NH_2 < C_6H_5NH_2 < C_6H_5CH_2NH_2\)
• (B) \(C_6H_5NH_2 < NH_3 < C_6H_5CH_2NH_2 < C_2H_5NH_2\)
• (C) \(C_6H_5NH_2 < C_6H_5CH_2NH_2 < NH_3 < C_2H_5NH_2\)
• (D) \(C_6H_5CH_2NH_2 < NH_3 < C_2H_5NH_2 < C_6H_5NH_2\)
• (E) \(C_6H_5NH_2 < NH_3 < C_2H_5NH_2 < C_6H_5CH_2NH_2\)

Animal starch is

• (A) glycogen
• (B) lactose
• (C) cellulose
• (D) amylase
• (E) maltose