`The MHT CET 2025 PCM Exam Shift 1 for 26th April 2025 was conducted from 9:00 A.M. to 12:00 P.M. The MHT CET 2025 question paper for April 26 Shift 1 (PCM group) is available here with the solutions PDF.

The MHT CET 2025 Question Paper consists of 150 multiple-choice questions (MCQs) totaling 200 marks divided into 3 sections: Physics, Chemistry, and Mathematics, with 50 questions in each subject.

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MHT CET 2025 April 26 Shift 1 PCM Question Paper PDF Download

MHT CET 2025 PCM Question Paper With Answer Key Download PDF Check Solution

Question 1:

Which cation from following exhibits no magnetic moment?

  • (a) \(Cr^{3+}\)
  • (b) \(Sc^{3+}\)
  • (c) \(Cu^{2+}\)
  • (d) \(V^{3+}\)

Question 2:

What is the common name of Benzene-1,3-diol?

  • (a) Catechol
  • (b) Resorcinol
  • (c) Quinol
  • (d) Pyrogallol

Question 3:

What is the number of oxygen atoms bonded to chlorine in its strongest oxoacid?

  • (a) 1
  • (b) 2
  • (c) 3
  • (d) 4

Question 4:

Calculate the edge length of bcc unit cell if radius of a particle present in it is 186 pm.

  • (a) \(4.296\times10^{-8}\) cm
  • (b) \(7.301\times10^{-8}\) cm
  • (c) \(3.715\times10^{-8}\) cm
  • (d) \(5.419\times10^{-8}\) cm

Question 5:

If \(E^{\circ}(Cu^{2+}/Cu)=+0.34 V\). What is potential for \(Cu(s)\rightarrow Cu^{2+}(aq)(0.1M)+2e^{-}\) at 298 K?

  • (a) +0.3696 V
  • (b) -0.3696 V
  • (c) +0.3104 V
  • (d) -0.3104 V

Question 6:

Calculate \(\Delta S_{total}\) for a certain reaction if \(\Delta H=-150 kJ\) and \(\Delta S=32 J K^{-1}\) at 300 K.

  • (a) 266.00 \(J K^{-1}\)
  • (b) 532.00 \(J K^{-1}\)
  • (c) 798.00 \(J K^{-1}\)
  • (d) 468.00 \(J K^{-1}\)

Question 7:

Calculate the molality of the solution of nonvolatile solute if it freezes at \(-0.36^{\circ}C\). [\(K_{f}\) for solvent \(=1.86 K kg mol^{-1}\)]

  • (a) 0.218 \(mol kg^{-1}\)
  • (b) 0.193 \(mol kg^{-1}\)
  • (c) 0.401 \(mol kg^{-1}\)
  • (d) 0.520 \(mol kg^{-1}\)

Question 8:

Identify a pair of molecules having similar shapes of both members.

  • (a) \(NH_{3}, SO_{2}\)
  • (b) \(XeF_{4}, SF_{4}\)
  • (c) \(H_{2}O,SCl_{2}\)
  • (d) \(PCl_{5}, BrF_{5}\)

Question 9:

The compound forming ccp structure contains \(9.6\times10^{23}\) atoms. Find the number of tetrahedral voids formed in it.

  • (a) \(1.00\times10^{24}\)
  • (b) \(1.68\times10^{24}\)
  • (c) \(1.92\times10^{24}\)
  • (d) \(1.56\times10^{24}\)

Question 10:

In the equation, \(BiO_{3}^{-}+6H^{+}+xe^{-}\rightarrow Bi^{3+}+3H_{2}O\) What is the value of x?

  • (a) 2
  • (b) 3
  • (c) 4
  • (d) 6

Question 11:

Which from following compounds is obtained when phenol reacts with dilute nitric acid at low temperature?

  • (a) o-Nitrophenol only
  • (b) p-Nitrophenol only
  • (c) 2, 4, 6-trinitrophenol
  • (d) Mixture of ortho and para nitrophenols

Question 12:

Identify the technique used to know binding nature of nanomaterials?

  • (a) SEM
  • (b) TEM
  • (c) XRD
  • (d) FTIR

Question 13:

Which from following compounds is an example of primary amines?

  • (a) N-methylmethanamine
  • (b) 4-Bromobenzenamine
  • (c) N-Phenylbenzenamine
  • (d) N-Ethyl-N-methylpropan-2-amine

Question 14:

What are the compounds used to obtain nylon salt?

  • (a) Adipic acid and ammonia
  • (b) Terephthalic acid and hexamethylenediamine
  • (c) Adipic acid and hexamethylenediamine
  • (d) \(\beta\)-hydroxybutyric acid and hexamethylenediamine

Question 15:

For the cell reaction, \(A_{(s)}+B_{(aq)}^{2+}\rightarrow A_{(aq)}^{2+}+B_{(s)}\) if equilibrium constant of reaction is \(10^{4}\) at 298 K. What is standard emf of cell?

  • (a) 0.0592 V
  • (b) 0.1184 V
  • (c) 0.1776 V
  • (d) 0.2368 V

Question 16:

Calculate % by mass of a \(H_{2}O_{2}\) solution that is 67.2 by volume.

  • (a) 13.60% by mass
  • (b) 20.40% by mass
  • (c) 22.44% by mass
  • (d) 17.60% by mass

Question 17:

Which of the following compounds does not exhibit optical isomerism?

  • (a) 3-Iodohexane
  • (b) 2-Iodopentane
  • (c) 2-Iodo-2-methylbutane
  • (d) 2-Iodo-3-methylbutane

Question 18:

Identify the product when chlorobenzene is heated with nitrating mixture.

  • (a) Only 1-chloro-4-nitrobenzene
  • (b) Only 1-chloro-2-nitrobenzene
  • (c) Mixture of 1-chloro-2-nitrobenzene and 1-chloro-4-nitrobenzene
  • (d) 2,4,6-trinitrochlorobenzene

Question 19:

What is the difference in molar mass of Undecane and Dodecane?

  • (a) 10 \(g mol^{-1}\)
  • (b) 20 \(g mol^{-1}\)
  • (c) 140 \(g mol^{-1}\)
  • (d) 14 \(g mol^{-1}\)

Question 20:

Calculate rate constant of a first order reaction having pre-exponential factor \(1.6\times10^{-13}s^{-1}\). (\(E_{a}/2.303RT=21\))

  • (a) \(1.6\times10^{-13}\)
  • (b) \(3.2\times10^{-13}\)
  • (c) \(3.2\times10^{-8}\)
  • (d) \(1.6\times10^{-34}\)

Question 21:

Which of the following statements is false about oxygen and sulphur?

  • (a) Atoms of oxygen and sulphur consist two unpaired electrons in valence shell.
  • (b) Oxygen and sulphur show -2, +4 and +6 oxidation states.
  • (c) Oxygen is gas while sulphur is solid at room temperature.
  • (d) Hydride of oxygen is more stable than hydride of sulphur.

Question 22:

"It is impossible to determine simultaneously the exact position and exact momentum of an electron." This statement is called

  • (a) Pauli's exclusion principle
  • (b) Hund's rule
  • (c) Aufbau rule
  • (d) Heisenberg uncertainty principle

Question 23:

Identify from following the correct set of thermodynamic conditions for a reaction to be nonspontaneous at all temperatures.

  • (a) \(\Delta H<0\) and \(\Delta S<0\)
  • (b) \(\Delta H>0\) and \(\Delta S>0\)
  • (c) \(\Delta H<0\) and \(\Delta S>0\)
  • (d) \(\Delta H>0\) and \(\Delta S<0\)

Question 24:

Calculate vapour pressure of volatile liquid A at given temperature if mole fraction and vapour pressure of volatile liquid B are 0.4 and 900 mm Hg respectively \([P_{total}=600 mmHg]\).

  • (a) 450 mm Hg
  • (b) 560 mm Hg
  • (c) 500 mm Hg
  • (d) 400 mm Hg

Question 25:

What is the numerical value of osmotic pressure of 1 M urea solution if numerical value of osmotic pressure of 0.5 M urea solution is 'x'?

  • (a) x
  • (b) x/2
  • (c) 2x
  • (d) 3x

Question 26:

Which among the following has highest boiling point?

  • (a) Butyric acid
  • (b) Valeric acid
  • (c) Acetic acid
  • (d) Formic acid

Question 27:

Identify a medicinal compound having amide linkage.

  • (a) Aspirin
  • (b) Methylsalicylate
  • (c) Curcumin
  • (d) Paracetamol

Question 28:

Which among the following compounds does NOT form intermolecular hydrogen bonding?

  • (a) Ethoxyethane
  • (b) Butane
  • (c) Phenol
  • (d) Butan-1-ol

Question 29:

Which lanthanoid from following may exhibit +4 oxidation state with \(f^{0}\) configuration?

  • (a) Eu
  • (b) Tb
  • (c) Ce
  • (d) Lu

Question 30:

Which among the following salt turns blue litmus red in its aqueous solution?

  • (a) \(CuSO_{4}\)
  • (b) \(Na_{2}CO_{3}\)
  • (c) \(Na_{2}SO_{4}\)
  • (d) \(NaNO_{3}\)

Question 31:

Find out the total number of electrons present in 3.2 g methane?

  • (a) \(6.022\times10^{23}\)
  • (b) \(1.204\times10^{24}\)
  • (c) \(3.201\times10^{23}\)
  • (d) \(4.821\times10^{22}\)

Question 32:

Rate of the reaction \(A+B\rightarrow\) product is \(3.6\times10^{-2} mol dm^{-3}s^{-1}\) and rate law is \(r=k[A][B]^{2}\). What is rate constant of the reaction if \([A]=0.2\) M and \([B]=0.1\) M?

  • (a) \(18 mol^{-2}dm^{6}s^{-1}\)
  • (b) \(10 mol^{-2}dm^{6}s^{-1}\)
  • (c) \(24 mol^{-2}dm^{6}s^{-1}\)
  • (d) \(4.8 mol^{-2}dm^{6}s^{-1}\)

Question 33:

Identify the product 'A' formed in the following reaction (Addition of \(Br_{2}\) to an alkene).


  • (a) 2,3-dibromopentane
  • (b) 2-Bromo-3-methylbutane
  • (c) 3-Bromo-2-methylbutane
  • (d) 2,3-dibromo-2-methylbutane

Question 34:

What are the positions of 'N' atoms present in purine ring of nucleic acids?

  • (a) 1, 3 and 5
  • (b) 1, 3 and 9
  • (c) 1, 5, 7 and 9
  • (d) 1, 3, 7 and 9

Question 35:

Which from following compounds contains complex anions?

  • (a) Sodium hexanitrocobaltate (III)
  • (b) Triamminetrinitrocobalt (III)
  • (c) Pentaammineaquacobalt (II)iodide
  • (d) Hexaamminecobalt (III) chloride

Question 36:

Which among the following gases is least adsorbed on solid at similar conditions of temperature and pressure?

  • (a) \(Cl_{2}\)
  • (b) \(NH_{3}\)
  • (c) \(SO_{2}\)
  • (d) \(H_{2}\)

Question 37:

Dissociation constant of 0.01 M weak acid is \(10^{-4}\). What is percent dissociation of acid?

  • (a) 2%
  • (b) 6%
  • (c) 10%
  • (d) 1.5%

Question 38:

Equal masses of helium and oxygen are mixed in an empty container at \(25^{\circ}C\). What is the fraction of the total pressure exerted by helium?

  • (a) \(1/2\)
  • (b) \(1/4\)
  • (c) \(8/9\)
  • (d) \(7/9\)

Question 39:

Calculate the change in internal energy of the system if work done by the system is 18 joule and absorbs heat 50 joule in a particular reaction.

  • (a) 20 J
  • (b) 32 J
  • (c) 48 J
  • (d) 68 J

Question 40:

What is the expected order of basic strength of different compounds from following (in gaseous phase)?

  • (a) \(R_{3}N\)
  • (b) \(NH_{3}\)
  • (c) \(R_{2}NH\)
  • (d) \(NH_{3}\)

Question 41:

Which of the following does NOT exhibit haloform reaction?

  • (a) Ethanal
  • (b) Propanal
  • (c) Propanone
  • (d) Butanone

Question 42:

Which from following polymers does NOT contain either -COO- or -CO-NH- linkage in it?

  • (a) Perspex
  • (b) Polyacrylamide
  • (c) Glyptal
  • (d) Thermocol

Question 43:

What is the coordination number of a particle in simple cubic close packed structure?

  • (a) 12
  • (b) 4
  • (c) 6
  • (d) 8

Question 44:

Identify the products of following reaction: Formaldehyde + Benzaldehyde \(\xrightarrow{i. conc. NaOH ii. H_3O^+}\) Products.

  • (a) Phenylmethanol and methanol
  • (b) Methanol and benzoic acid
  • (c) Methanoic acid and phenylmethanol
  • (d) Methanoic acid and benzoic acid

Question 45:

Identify the order of following reaction: \(2NO_{2}(g)\rightarrow2NO(g)+O_{2}(g)\).

  • (a) 1
  • (b) 1.5
  • (c) 2
  • (d) 3

Question 46:

Which from following is a weak field ligand?

  • (a) EDTA
  • (b) CO
  • (c) \(F^{-}\)
  • (d) \(NH_{3}\)

Question 47:

Identify neutral amino acid from following list represented by three letter symbols.

  • (a) Arg
  • (b) Asp
  • (c) Leu
  • (d) His

Question 48:

Which of the following changes takes place at positive electrode during recharging of lead accumulator?

  • (a) Pb is oxidised to \(PbSO_{4}\)
  • (b) \(PbSO_{4}\) is oxidised to \(PbO_{2}\)
  • (c) \(PbSO_{4}\) is reduced to Pb
  • (d) \(PbO_{2}\) is reduced to \(PbSO_{4}\)

Question 49:

Which of the following reagents is used to convert \(C\equiv C\) triple bond to \(C=C\) double bond to give Cis isomer of alkene?

  • (a) \(ZnCl_{2}/HCl\)
  • (b) Pd-C/quinoline
  • (c) Na / liquid \(NH_{3}\)
  • (d) Na/Hg in \(H_{2}O\)

Question 50:

The solubility product of AgBr is \(4.9\times10^{-13}\) at a certain temperature. Calculate the solubility.

  • (a) \(4\times10^{-6} mol dm^{-3}\)
  • (b) \(4\times10^{-7} mol dm^{-3}\)
  • (c) \(7\times10^{-7} mol dm^{-3}\)
  • (d) \(3\times10^{-8} mol dm^{-3}\)

Question 51:

Consider statements \(p\) : \(S_1\) is closed; \(q\) : \(S_2\) is closed; \(r\) : \(S_3\) is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively ______.

  • (a)
  • (b)
     
  • (c)
     
  • (d)

Question 52:

The volume of tetrahedron with co-terminus edges \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) is \(\frac{64}{3}\) cubic units, then volume of parallelopiped considering co-terminus edges given by the vectors \(\vec{a} + \vec{b}\), \(\vec{b} + \vec{c}\), \(\vec{c} + \vec{a}\) is ______ cubic units.

  • (a) 384
  • (b) \(\frac{128}{3}\)
  • (c) 256
  • (d) \(\frac{32}{3}\)

Question 53:

If \(y = \tan^{-1} \left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right)\), \(0 \le x < \frac{\pi}{2}\), then \(y' \left( \frac{\pi}{6} \right) = \) ______.

  • (a) \(-\frac{1}{4}\)
  • (b) \(\frac{1}{6}\)
  • (c) \(\frac{1}{4}\)
  • (d) \(\frac{1}{2}\)

Question 54:

If \(f(x) = \frac{\sin^2 x}{1+\cot x} + \frac{\cos^2 x}{1+\tan x}\), then the value of \(f'(\frac{\pi}{6})\) is equal to ______.

  • (a) 0
  • (b) \(\frac{1}{2}\)
  • (c) \(-\frac{1}{2}\)
  • (d) \(\frac{\sqrt{3}}{2}\)

Question 55:

\(\int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} \, dx = \) ______.

  • (a) \(2\sqrt{\sec x} + c\), where c is a constant of integration
  • (b) \(2\sqrt{\tan x} + c\), where c is a constant of integration
  • (c) \(\frac{2}{\sqrt{\tan x}} + c\), where c is a constant of integration
  • (d) \(\frac{2}{\sqrt{\sec x}} + c\), where c is a constant of integration

Question 56:

If \(\int \frac{dx}{x^4 + 5x^2 + 4} = A \tan^{-1} x + B \tan^{-1} \frac{x}{2} + c\) where \(c\) is a constant of integration, then ______.

  • (a) \(A = \frac{1}{2}\), \(B = \frac{1}{4}\)
  • (b) \(A = \frac{1}{3}\), \(B = -\frac{1}{6}\)
  • (c) \(A = \frac{1}{3}\), \(B = \frac{1}{6}\)
  • (d) \(A = \frac{1}{2}\), \(B = -\frac{1}{4}\)

Question 57:

The number of positive integral solutions of \(\tan^{-1} x + \cos^{-1} \left( \frac{y}{\sqrt{1+y^2}} \right) = \sin^{-1} \left( \frac{3}{\sqrt{10}} \right)\) are ______.

  • (a) 1
  • (b) 2
  • (c) 3
  • (d) 4

Question 58:

If the plane \(\frac{x}{2} + \frac{y}{3} + \frac{z}{6} = 1\) cuts the co-ordinate axes at points A, B, C respectively, then area of the triangle ABC is ______.

  • (a) \(\sqrt{14}\) sq. units
  • (b) \(3\sqrt{14}\) sq. units
  • (c) \(\frac{1}{\sqrt{14}}\) sq. units
  • (d) \(3\sqrt{13}\) sq. units

Question 59:

Matrix A is non-singular matrix and \((A - 3I)(A - 5I) = 0\), then \(\frac{15}{8} A^{-1} = \dots\dots\)

  • (a) \(I - 8A\)
  • (b) \(2I - \frac{1}{15} A\)
  • (c) \(I - \frac{1}{8} A\)
  • (d) \(8I - 15 A\)

Question 60:

\(\int_{1/2}^{2} \frac{1}{x} \csc^{101} \left( x - \frac{1}{x} \right) dx = \) ______.

  • (a) 0
  • (b) 1
  • (c) \(\frac{1}{4}\)
  • (d) \(\frac{101}{2}\)

Question 61:

The differential equation which represents the family of curves \(y = c_1 e^{c_2 x}\), where \(c_1, c_2\) are arbitrary constants is ______.

  • (a) \(y'' = y' y\)
  • (b) \(yy' = y'\)
  • (c) \(yy'' = (y')^2\)
  • (d) \(y' = y^2\)

Question 62:

\(\lim_{x \to \infty} \frac{(2x+1)^{50} + (2x+2)^{50} + (2x+3)^{50} + \dots + (2x+100)^{50}}{(2x)^{50} + (10)^{50}} = \) ______.

  • (a) 50
  • (b) 100
  • (c) 25
  • (d) 200

Question 63:

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is ______.

  • (a) 2002
  • (b) \(^{20}C_{11}\)
  • (c) \(^{20}C_6\)
  • (d) \(^{14}C_5\)

Question 64:

A box contains 8 red and \(x\) number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is \(\frac{7}{15}\), then number of green balls is ______.

  • (a) 2
  • (b) 4
  • (c) 3
  • (d) 5

Question 65:

The equation of a curve passing through (1,0) and having slope of tangent at any point (x, y) of the curve as \(\frac{y-1}{x^2+x}\) is ______.

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

Question 66:

If \(y = \alpha \log x + \beta x^2 - x\) has extreme values at \(x = -1\) and \(x = 1\), then \(\alpha\) and \(\beta\) are respectively ______.

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

Question 67:

The equation of the tangent to the curve \((1 + x^2)y = 2 - x\), where it crosses the X-axis, is ______.

  • (a) \(x + 5y = 2\)
  • (b) \(x - 5y = 2\)
  • (c) \(5x - y = 10\)
  • (d) \(5x + y - 10 = 0\)

Question 68:

The following is p.d.f. of continuous random variable X: \(f(x) = \frac{x}{8}\) for \(0 < x < 4\). Then \(F(0.5)\), \(F(1.7)\) and \(F(5)\) is respectively ______.

  • (a) \(\frac{1}{64}\), 1, 0.18
  • (b) 0.0156, 0.18, 1
  • (c) 0.18, 0.0156, 1
  • (d) 1, 0.0156, 0.18

Question 69:

A manufacturer sells \(x\) items at a price of ₹\((6 - \frac{x}{40})\) each. The cost price of \(x\) items is ₹\((\frac{x}{5} + 193)\). The maximum profit in ₹ is ______.

  • (a) 134.4
  • (b) 144.3
  • (c) 143.4
  • (d) 133.4

Question 70:

The mirror image of the point \(P(-1, 2, -4)\) in the plane \(x - y - 2z + 1 = 0\) is ______.

  • (a) (3, -4, 1)
  • (b) (1, 0, 0)
  • (c) (4, 1, 0)
  • (d) (2, -3, 0)

Question 71:

The cumulative distribution function of a discrete random variable X is given. Then \(\frac{P(X \le 0)}{P(X > 0)} = \) ______.


 

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

Question 72:

If \(\vec{a} = \lambda x \hat{i} + y \hat{j} + 4z \hat{k}\), \(\vec{b} = x \hat{i} + y \hat{j} + 3y \hat{k}\), and \(\vec{c} = -2 \hat{i} - 2z \hat{j} - (\lambda + 1) \hat{k}\) such that \(\vec{a} + \vec{b} - \vec{c} = \vec{0}\), then the value of \(\lambda\) is ______.

  • (a) 0
  • (b) 1
  • (c) 2
  • (d) 3

Question 73:

A triangle ABC is formed by A(1, -1, 0), B(3, 5, 3), C(-11, -5, 6). The equation of the internal angle bisector of angle A is ______.

  • (a) \(\frac{1-x}{2} = \frac{y-(-1)}{2} = \frac{z}{3}\)
  • (b) \(\frac{x+1}{2} = \frac{y-1}{2} = \frac{z}{3}\)
  • (c) \(\frac{x-1}{2} = \frac{y+1}{2} = \frac{z}{3}\)
  • (d) \(\frac{x-2}{1} = \frac{y+3}{2} = \frac{z}{3}\)

Question 74:

The circumcenter of the triangle formed by lines \(xy + 2x + 2y + 4 = 0\) and \(x + y + 2 = 0\) is ______.

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

Question 75:

The angle between lines whose direction cosines satisfy the equation \(l + m + n = 0\) and \(l^2 - m^2 - n^2 = 0\), is ______.

  • (a) \(\pi/2\)
  • (b) \(\pi/3\)
  • (c) \(\pi/4\)
  • (d) \(\pi/6\)

Question 76:

The solution for minimizing the function \(z = x + y\) under an L.P.P. with constraints \(x + y \ge 2\), \(x + 2y \le 8\), \(y \le 3\), \(x, y \ge 0\) is ______.

  • (a) at the point (0, 3)
  • (b) at the point (8, 0)
  • (c) at infinite number of points but bounded set
  • (d) at unbounded set

Question 77:

The angle between the tangents drawn from the point (1, 4) to the parabola \(y^2 = 4x\), is ______.

  • (a) \(\pi/6\)
  • (b) \(\pi/2\)
  • (c) \(\pi/3\)
  • (d) \(\pi/4\)

Question 78:

If \(\int \frac{(x^4+1)}{x(x^2+1)^2} \, dx = A \log |x| + \frac{B}{1+x^2} + c\), then \(A - B\) is ______.

  • (a) 0
  • (b) 1
  • (c) 2
  • (d) -1

Question 79:

Let \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be vectors of magnitude 2, 3 and 4 respectively. If \(\vec{a} \cdot (\vec{b} + \vec{c}) = 0\), \(\vec{b} \cdot (\vec{c} + \vec{a}) = 0\) and \(\vec{c} \cdot (\vec{a} + \vec{b}) = 0\), then the magnitude of \(\vec{a} + \vec{b} + \vec{c}\) is ______.

  • (a) 29
  • (b) \(\sqrt{28}\)
  • (c) \(\sqrt{29}\)
  • (d) 28

Question 80:

If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three coplanar vectors such that \(|\vec{a}| = 1\), \(|\vec{b}| = 2\), \(\vec{b} \cdot \vec{c} = 8\), the angle between \(\vec{b}\) and \(\vec{c}\) is \(45^\circ\), then \(|\vec{a} \times (\vec{b} \times \vec{c})| = \) ______.

  • (a) 8
  • (b) \(4\sqrt{2}\)
  • (c) \(\sqrt{2}\)
  • (d) \(8\sqrt{2}\)

Question 81:

In a triangle ABC, with usual notations, \((a + b + c)(a + b - c) = 3ab\), then \(\angle C = \) ______.

  • (a) \(\pi/2\)
  • (b) \(\pi/4\)
  • (c) \(\pi/3\)
  • (d) \(\pi/6\)

Question 82:

In a triangle ABC, with usual notations, \(\cot\left(\frac{A+B}{2}\right) \cdot \tan\left(\frac{A-B}{2}\right) = \) ______.

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

Question 83:

If the truth value of the expression \([(p \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q)\) is False, then truth values of p, q, r are respectively ______.

  • (a) T, T, T
  • (b) T, F, F
  • (c) F, F, F
  • (d) F, T, T

Question 84:

\(\int_0^1 \tan^{-1} x \, dx = \) ______.

  • (a) \(\pi/4 - \log 2\)
  • (b) \(\pi/4 - \log \sqrt{2}\)
  • (c) \(\pi/4 + \log 2\)
  • (d) \(\pi/4 + \log \sqrt{2}\)

Question 85:

If \(f(x) = \frac{\cos ax - \cos bx}{\cos cx - \cos bx}\) for \(x \ne 0\) and \(f(0) = -1\) is continuous at \(x = 0\), then \(a^2, b^2, c^2\) are in ______.

  • (a) Geometric progression
  • (b) Arithmetic progression
  • (c) Harmonic progression
  • (d) Arithmetico-Geometric progression

Question 86:

The area of smaller part between the circle \(x^2 + y^2 = 4\) and the line \(x = 1\) is ______ sq. units.

  • (a) \(\frac{4\pi}{3} - \sqrt{3}\)
  • (b) \(\frac{8\pi}{3} - \sqrt{3}\)
  • (c) \(\frac{4\pi}{3} + \sqrt{3}\)
  • (d) \(\frac{5\pi}{3} + \sqrt{3}\)

Question 87:

If \([x]^2 - 5[x] + 6 = 0\), where \([.]\) denotes the greatest integer function, then ______.

  • (a) \(x \in (2, 4)\)
  • (b) \(x \in [2, 4]\)
  • (c) \(x \in [2, 4)\)
  • (d) \(x \in (2, 4]\)

Question 88:

The modulus of the square root of the complex number \(6 + 8i\) (where \(i = \sqrt{-1}\)) is ______.

  • (a) \(\sqrt{5}\)
  • (b) \(2\sqrt{5}\)
  • (c) \(\sqrt{2} \cdot \sqrt{5}\)
  • (d) \(2\sqrt{10}\)

Question 89:

If \(f(x) = \sqrt{1 + \cos^2(x^2)}\), then \(f'(\frac{\sqrt{\pi}}{2})\) is ______.

  • (a) \(\frac{\sqrt{\pi}}{6}\)
  • (b) \(-\frac{\sqrt{\pi}}{6}\)
  • (c) \(\frac{\pi}{\sqrt{6}}\)
  • (d) \(\sqrt{\frac{\pi}{6}}\)

Question 90:

The equation of the directrix of the parabola \(y^2 + 4y + 4x + 2 = 0\) is ______.

  • (a) \(x = -1\)
  • (b) \(x = 1\)
  • (c) \(x = -\frac{3}{2}\)
  • (d) \(x = \frac{3}{2}\)

Question 91:

Let \(\vec{a} = \alpha\hat{i} + 3\hat{j} - \hat{k}\), \(\vec{b} = 3\hat{i} - \hat{j} + \beta\hat{k}\) and \(\vec{c} = \hat{i} + 2\hat{j} - 2\hat{k}\) where \(\alpha, \beta \in \mathbb{R}\), be three vectors. If the projection of \(\vec{a}\) on \(\vec{c}\) is \(\frac{10}{3}\) and \(\vec{b} \times \vec{c} = -6\hat{i} + 10\hat{j} + 7\hat{k}\), then the value of \((\alpha + \beta)\) is ______.

  • (a) 5
  • (b) 3
  • (c) 4
  • (d) 6

Question 92:

If \(\sin^{-1}(4x) + \sin^{-1}(4\sqrt{3}x) = -\frac{\pi}{2}\), then the value of \(x\) is ______.

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

Question 93:

In a triangle ABC, with usual notations, if \(a = 5\), \(b = 7\), \(\sin A = \frac{3}{4}\), then total number of triangles possible are ______.

  • (a) 1
  • (b) 0
  • (c) 2
  • (d) 5

Question 94:

If the foot of the perpendicular drawn from the origin to a plane is P(-1, -1, 2), then the equation of the plane is ______.

  • (a) \(x + y - 2z + 6 = 0\)
  • (b) \(2x + y + z + 1 = 0\)
  • (c) \(x + y + 2z - 2 = 0\)
  • (d) \(x - y - z + 2 = 0\)

Question 95:

The least distance of the point A(10, 7) from the circle \(x^2 + y^2 - 4x - 2y - 20 = 0\) is length of seg AM. If MM' is the diameter of the circle, then the lengths of AM and AM' are respectively ______, ______ units.

  • (a) 5, 10
  • (b) 5, 15
  • (c) 4, 15
  • (d) 2, 10

Question 96:

The money invested in a company is compounded continuously. If Rs. 400 invested today becomes Rs. 800 in 6 years, then at the end of 30 years, it will become (in Rs.) ______.

  • (a) 18101.76
  • (b) 12800
  • (c) 9050.88
  • (d) 12804

Question 97:

The line MN whose equation is \(x - y - 2 = 0\) cuts the X-axis at M and coordinates of N are (4, 2). The line MN is rotated about M through \(45^{\circ}\) in anticlockwise direction. The equation of the line MN in the new position is ______.

  • (a) \(y = -\sqrt{2}\)
  • (b) \(y = 2\)
  • (c) \(x = -2\)
  • (d) \(x = 2\)

Question 98:

If \(\tan(\pi \cos \theta) = \cot(\pi \sin \theta)\), then \(\sin\left(\frac{\pi}{4} + \theta\right) = \) ______.

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

Question 99:

The probability that a person is not a sportsperson is \(1/6\). Then the probability that out of 6 members of the family, 5 are sportspersons is ______.

  • (a) \((5/6)^5\)
  • (b) \(6(5/6)^5\)
  • (c) \(5(5/6)^6\)
  • (d) \((5/6)^6\)

Question 100:

The general solution of the differential equation \(\frac{dy}{dx} = \cot x \cdot \cot y\) is ______.

  • (a) \(\cos x = c \csc y\)
  • (b) \(\sin x = c \sec y\)
  • (c) \(\sin x = c \cos y\)
  • (d) \(\cos x = c \sin y\)

Question 101:

In series LCR circuit C = 2\(\mu\)F, L = 5mH and R = 5\(\Omega\). The ratio of energy stored in the inductor to that in capacitor, when maximum current flows through the circuit is ______.

  • (a) 200 : 1
  • (b) 100 : 1
  • (c) 300 : 1
  • (d) 500 : 1

Question 102:

A boy throws a ball vertically upwards from a bridge with velocity 5 m/s. It strikes water surface after 2 s. The height of the bridge is (Take g = 10 m/s\(^2\)) ______.

  • (a) 20 m
  • (b) 15 m
  • (c) 12 m
  • (d) 10 m

Question 103:

In Sonometer experiment, the frequency of a tuning fork used is 288 Hz. Harmonics will 'NOT' be produced at the frequency ______.

  • (a) 288 Hz
  • (b) 576 Hz
  • (c) 844 Hz
  • (d) 864 Hz

Question 104:

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) third to 2nd energy level and (ii) highest energy level to 3rd level is ______.

  • (a) 3 : 2
  • (b) 5 : 4
  • (c) 5 : 3
  • (d) 8 : 3

Question 105:

A magnetic field \(4 \times 10^{-2}\) T acts at right angles to a coil of area \(100\) cm\(^2\) with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in time 't'. The value of 't' is ______.

  • (a) 0.02 second
  • (b) 0.05 second
  • (c) 0.2 second
  • (d) 2 second

Question 106:

A sphere of mass 'm', moving with velocity '3u' collides head-on with another identical sphere at rest. If 'e' is coefficient of restitution then what will be the ratio of velocity of the second sphere to that of first sphere after collision?

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

Question 107:

In Paschen series, wavelength of first line is '\(\lambda_1\)' and for Brackett series, wavelength of first line is '\(\lambda_2\)' then ratio \(\frac{\lambda_1}{\lambda_2}\) is ______.

  • (a) \(\frac{7}{400}\)
  • (b) \(\frac{9}{144}\)
  • (c) \(\frac{81}{175}\)
  • (d) \(\frac{108}{509}\)

Question 108:

An air column is of length 17 cm. The ratio of frequencies of 5th overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air = 340 ms\(^{-1}\)) ______.

  • (a) \(\frac{9}{11}\)
  • (b) \(\frac{5}{7}\)
  • (c) \(\frac{11}{12}\)
  • (d) \(\frac{13}{9}\)

Question 109:

A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be ______.

  • (a) 20 N
  • (b) 22.5 N
  • (c) 30 N
  • (d) 36 N

Question 110:

Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is '\(I_1\)'. The same rod is bent into a ring and its moment of inertia about the diameter is '\(I_2\)'. Then \(I_1/I_2\) is ______.

  • (a) \(\frac{3\pi^2}{2}\)
  • (b) \(\frac{2\pi^2}{3}\)
  • (c) \(\frac{\pi^2}{3}\)
  • (d) \(\frac{\pi^2}{9}\)

Question 111:

The potentiometer wire is 5 m long and potential difference of 4 V is maintained between the ends. The e.m.f. of the cell which balances against a length of 200 cm of the potentiometer wire is ______.

  • (a) 0.4 V
  • (b) 0.8 V
  • (c) 1.2 V
  • (d) 1.6 V

Question 112:

The error in the measurement of length and mass is 3% and 4% respectively. The error in the measurement of density will be ______.

  • (a) 6%
  • (b) 13%
  • (c) 9%
  • (d) 15%

Question 113:

A bar of iron having magnetic moment 2.4 Am\(^2\) weighs 66 g. If the density of the material of the bar is 7700 kg/m\(^3\), the intensity of magnetisation in Am\(^{-1}\) is ______.

  • (a) \(1.4 \times 10^5\)
  • (b) \(2.8 \times 10^5\)
  • (c) \(1.4 \times 10^4\)
  • (d) \(2.8 \times 10^4\)

Question 114:

L, C and R are connected in series to an a.c. source. Which one of the following is true? Phase relation between current and voltage is such that ______.

  • (a) both are out of phase with each other in 'R'.
  • (b) both are in phase in 'L' and out of phase in 'C'.
  • (c) both are out of phase in 'L' and in phase in 'C'.
  • (d) both are out of phase in both 'C' and 'L'.

Question 115:

In Young's double slit experiment, the distance between the slits is 2 mm and the slits are 1 m away from the screen. Two interference patterns can be obtained on the screen due to light of wavelength '\(\lambda_1\)' and '\(\lambda_2\)' respectively. The separation on the screen between the 3rd order bright fringes on the two interference patterns is (\(\lambda_2 = 1.5\lambda_1\)) ______.

  • (a) \((0.75 \times 10^{-3})\lambda_1\)
  • (b) \((1.75 \times 10^{-3})\lambda_1\)
  • (c) \((2.00 \times 10^{-3})\lambda_1\)
  • (d) \((0.75 \times 10^3)\lambda_1\)

Question 116:

A source of sound emits sound wave of frequency 'f' and moves towards an observer with a velocity \(V/3\) where \(V\) is the velocity of sound. If the observer moves away from the source with a velocity \(V/5\) the apparent frequency heard by him will be ______.

  • (a) \(\frac{15}{2}f\)
  • (b) \(\frac{8}{15}f\)
  • (c) \(\frac{6}{5}f\)
  • (d) \(\frac{15}{18}f\)

Question 117:

The ratio of the frequencies of two simple pendulums is 4 : 3 at the same place. The ratio of their respective lengths is ______.

  • (a) 3 : 4
  • (b) 4 : 3
  • (c) 9 : 16
  • (d) 16 : 9

Question 118:

Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances are \(L_A = 10\) H and \(L_B = 10\) mH. The total resistance of each circuit is 40 \(\Omega\). The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is ______.

  • (a) 800
  • (b) 1000
  • (c) 1200
  • (d) 1400

Question 119:

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is ______.

  • (a) \(I/44\)
  • (b) \(I/188\)
  • (c) \(I/204\)
  • (d) \(I/243\)

Question 120:

Fundamental frequency of sonometer wire is 'n'. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be ______.

  • (a) \(2n\)
  • (b) \(\frac{\sqrt{3}}{2}n\)
  • (c) \(\frac{n}{2\sqrt{3}}\)
  • (d) \(\sqrt{3}n\)

Question 121:

Let \(R_1, R_2\) and \(R_3\) be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is ______.

  • (a) \((R_1^3 + R_2^3 + R_3^3)^{1/3}\)
  • (b) \((R_1^3 + R_2^3 - R_3^3)^{1/3}\)
  • (c) \((R_1^3 + R_2^3 + R_3^3)\)
  • (d) \((R_1 + R_2 + R_3)^3\)

Question 122:

An infinitely long straight conductor carrying current 'I' is bent into a shape as shown in figure. The radius of the circular loop is 'r'. The magnetic induction at the centre of the loop at point 'O' is ______.



 

  • (a) zero
  • (b) \(\frac{\mu_0 I}{4\pi r} (\pi - 1)\)
  • (c) \(\frac{\mu_0 I}{2\pi r} (\pi + 1)\)
  • (d) \(\frac{\mu_0 I}{2\pi r} (\pi - 1)\)

Question 123:

The difference in length between two rods A and B is 60 cm at all temperatures. If \(\alpha_A = 18 \times 10^{-6}/^\circ C\) and \(\alpha_B = 27 \times 10^{-6}/^\circ C\), then the length of rod A and rod B at \(0^\circ C\) is respectively ______.

  • (a) \(l_A = 120\) cm, \(l_B = 60\) cm
  • (b) \(l_A = 180\) cm, \(l_B = 120\) cm
  • (c) \(l_A = 240\) cm, \(l_B = 180\) cm
  • (d) \(l_A = 270\) cm, \(l_B = 210\) cm

Question 124:

Charges of \(2\mu C\) and \(-3\mu C\) are placed at two points A and B separated by distance of 1 m. The distance of the point from A where net potential is zero is ______.

  • (a) 0.667 m
  • (b) 0.5 m
  • (c) 0.4 m
  • (d) 0.6 m

Question 125:

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by \(48^\circ C\) at constant pressure is (Molecular weight of nitrogen = 28, R = gas constant, \(C_p = 7/2 R\) for diatomic gas) ______.

  • (a) 76 R
  • (b) 84 R
  • (c) 90 R
  • (d) 96 R

Question 126:

The wavelength '\(\lambda\)' of a photon and the deBroglie wavelength of an electron have same value. The ratio of kinetic energy of the electron to the energy of a photon is ______.

  • (a) \(\frac{2\lambda mc}{h}\)
  • (b) \(\frac{\lambda mc}{h}\)
  • (c) \(\frac{h}{2\lambda mc}\)
  • (d) \(\frac{h}{\lambda mc}\)

Question 127:

A monochromatic ray of light is incident normally on a thin prism of refracting angle A. The ray is deviated through an angle \((1.15)^\circ\) in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of \((6.3)^\circ\) with the incident ray. The refractive index of the prism is ______.

  • (a) 1.625
  • (b) 1.575
  • (c) 1.525
  • (d) 1.515

Question 128:

Two black spheres P & Q have radii in the ratio 4 : 3. The wavelength of maximum intensity of radiation are in the ratio 4 : 5 respectively. The ratio of radiated power by P to Q is ______.

  • (a) \(\frac{625}{144}\)
  • (b) \(\frac{125}{81}\)
  • (c) \(\frac{25}{9}\)
  • (d) \(\frac{5}{3}\)

Question 129:

The capacity of air filled parallel plate capacitor is \(C_0\). One-half of the space between the plates is filled with a dielectric constant 'K' as shown in figure. The new capacity becomes \(C_n\). The ratio \(C_n\) to \(C_0\) is ______.


 

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

Question 130:

A rigid body rotates about a fixed axis with variable angular velocity \((\alpha - \beta t)\) at time \(t\), where \(\alpha\) and \(\beta\) are constants. The angle through which it rotates before it comes to rest is ______.

  • (a) \(\frac{\alpha}{\beta}\)
  • (b) \(\frac{\alpha^2}{\beta}\)
  • (c) \(\frac{\alpha^2}{2\beta}\)
  • (d) \(\frac{\alpha}{2\beta}\)

Question 131:

A resistor of 5 \(\Omega\), inductor of self inductance \(\left(\frac{2}{\pi}\right)\) H and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V, 50 Hz supply. When the voltage and current are in phase, the value of capacitance is ______.

  • (a) \(\frac{10}{\pi}\) \(\mu\)F
  • (b) \(\frac{20}{\pi}\) \(\mu\)F
  • (c) \(\frac{40}{\pi}\) \(\mu\)F
  • (d) \(\frac{50}{\pi}\) \(\mu\)F

Question 132:

A single slit diffraction pattern is formed with white light. For what wavelength of light the 4th secondary maximum in diffraction pattern coincides with the 3rd secondary maximum in the pattern of light of wavelength '\(\lambda\)'?

  • (a) \(\frac{5\lambda}{7}\)
  • (b) \(\frac{7\lambda}{9}\)
  • (c) \(\frac{3\lambda}{4}\)
  • (d) \(\frac{9\lambda}{13}\)

Question 133:

The temperature at which oxygen molecules will have same r.m.s. speed as helium molecules at 57\(^\circ\)C is (molecular masses of oxygen and helium are 32 and 4 respectively.) ______.

  • (a) 1320 K
  • (b) 2240 K
  • (c) 2640 K
  • (d) 3230 K

Question 134:

Out of the following statements which is NOT the characteristics of electric lines of force? ______.

  • (a) Electric lines of force originate from a positively charged object and end on negatively charged object.
  • (b) The electric lines of force do not intersect each other.
  • (c) The electric lines of force pass through the conductor.
  • (d) The electric lines of force are crowded in a region where electric intensity is large.

Question 135:

An ideal gas expands adiabatically, (\(\gamma = 1.5\)). To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded ______.

  • (a) 256 times
  • (b) 128 times
  • (c) 64 times
  • (d) 8 times

Question 136:

The ratio of the distance of \(n^{th}\) bright band and \(m^{th}\) dark band from the central bright band in an interference pattern is ______.

  • (a) \(n : m\)
  • (b) \(m : n\)
  • (c) \(n : (m - 1/2)\)
  • (d) \((n - 1/2) : m\)

Question 137:

The material used for solar cell should have band gap ______.

  • (a) equal to zero.
  • (b) less than 1.0 eV (non-zero).
  • (c) more than 1.8 eV.
  • (d) between 1.0 eV and 1.8 eV.

Question 138:

A spring executes S.H.M. with mass 1 kg attached to it. The force constant of the spring is 4 N/m. If at any instant its velocity is 20 cm/s, the displacement at that instant is (Amplitude of S.H.M. is 0.4 m) ______.

  • (a) \(\sqrt{0.11}\) m
  • (b) \(\sqrt{0.15}\) m
  • (c) \(\sqrt{0.17}\) m
  • (d) \(\sqrt{0.19}\) m

Question 139:

Three capacitors are connected to a battery as shown in figure. The ratio of charge on capacitors \(C_3\) and \(C_1\) is ______.



(Assuming standard bridge configuration where \(C_1\) is in series with parallel \(C_2, C_3\) based on OCR artifacts, or the visual Delta where battery connects to the base)

  • (a) 1.5
  • (b) 2.5
  • (c) 3.5
  • (d) 4.5

Question 140:

If \(|\vec{a}| = \sqrt{26}\), \(|\vec{b}| = 7\), \(|\vec{a} \times \vec{b}| = 35\), find \(\vec{a} \cdot \vec{b}\)

  • (a) 4
  • (b) 5
  • (c) 6
  • (d) 7

Question 141:

125 small water drops of same size fall through air with constant velocity 4 cm/s. They coalesce to form a big drop. The terminal velocity of the big drop is ______.

  • (a) 0.5 m/s
  • (b) 1 m/s
  • (c) 1.5 m/s
  • (d) 2.5 m/s

Question 142:

At a place, the length of the oscillating simple pendulum is made \(1/4\) times keeping amplitude same then the total energy will be ______.

  • (a) 2 times
  • (b) 4 times
  • (c) 8 times
  • (d) 16 times

Question 143:

When magnetic flux changes from \(6.5 \times 10^{-2}\) Wb to \(11 \times 10^{-2}\) Wb and the change in current is 0.03 A, the coefficient of mutual inductance will be ______.

  • (a) 1.0 H
  • (b) 1.2 H
  • (c) 1.5 H
  • (d) 1.8 H

Question 144:

The work done in turning a magnet of magnetic moment 'M' by an angle of 90\(^\circ\) from the meridian is 'n' times the corresponding work done to turn it through an angle of 60\(^\circ\) where the value of 'n' is ______.

  • (a) 0.5
  • (b) 2
  • (c) 0.25
  • (d) 1

Question 145:

A capillary tube when immersed vertically in water, the rise of water column is upto height \(h_1\) on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is \(h_2\). If R is the radius of the earth, the ratio \(h_2/h_1\) is ______.

  • (a) \(\frac{R+d}{R}\)
  • (b) \(\frac{R-d}{R}\)
  • (c) \(\frac{R}{R+d}\)
  • (d) \(\frac{R}{R-d}\)

Question 146:

Light of incident frequency 3 times the threshold frequency is incident on a photosensitive material. If the incident frequency is made (1/4)th and intensity is tripled then the photoelectric current will ______.

  • (a) increase.
  • (b) decrease.
  • (c) be (1/3)rd
  • (d) be zero.

Question 147:

Applying forward bias to p-n junction, the potential barrier ______.

  • (a) increases.
  • (b) decreases.
  • (c) remains unchanged.
  • (d) becomes zero.

Question 148:

In case of free expansion, which one of the following statements is WRONG ______.

  • (a) It is an instantaneous change.
  • (b) The system is not in thermodynamic equilibrium.
  • (c) Free expansion can be plotted on a P-V diagram.
  • (d) It is an uncontrolled change.

Question 149:

In a common emitter transistor amplifier circuit, the input resistance is 1.8 k\(\Omega\) and output is obtained across a load resistance of 9 k\(\Omega\). The alternating current gain is 70. Corresponding to an a.c. input voltage of 6 mV, the output voltage will be ______.

  • (a) 0.7 V
  • (b) 1.4 V
  • (c) 2.1 V
  • (d) 4.2 V

Question 150:

When a resistance of 100 \(\Omega\) is connected in series with a galvanometer of resistance 'G', its range is 'V'. To double its range, a resistance of 1000 \(\Omega\) is connected in series. The value of 'G' is ______.

  • (a) 400 \(\Omega\)
  • (b) 800 \(\Omega\)
  • (c) 1000 \(\Omega\)
  • (d) 1200 \(\Omega\)

MHT CET 2025 PCM Subject-wise Weightage

MHT CET 2025 for PCM (Physics, Chemistry, Mathematics) exam is held for admission to B.Tech/B.E. and Pharmacy courses in Maharashtra.

The PCM paper has 150 questions (50 questions each of Physics, Chemistry, and Mathematics), with Mathematics having 2 marks per question and Physics and Chemistry having 1 mark each.

Also Check:

MHT-CET 2025 Topper’s Strategy: Scoring 90 Percentile

MHT CET 2025 PCM Chapter-wise Weightage (Expected)

Subject Important Chapters (Class 11 & 12) Expected Weightage
Physics
  • Motion in a Plane
  • Laws of Motion
  • Kinetic Theory
  • Oscillations
  • Current Electricity
  • Modern Physics
8–10 Questions
  • Rotational Motion
  • EM Waves
  • Semiconductors
  • Ray Optics
6–8 Questions
  • Thermodynamics
  • Magnetism
  • Work
  • Energy
  • Power
5–6 Questions
Chemistry
  • Chemical Thermodynamics
  • Electrochemistry
  • Chemical Kinetics
  • p-Block
  • Organic Compounds
10–12 Questions
  • Coordination Compounds
  • Solid State
  • Biomolecules
6–8 Questions
  • Surface Chemistry
  • Polymers
  • Alcohols
  • Ethers
5–7 Questions
Mathematics
  • Integration
  • Differentiation
  • Limits & Continuity
  • Vectors
  • 3D Geometry
10–12 Questions
  • Probability
  • Complex Numbers
  • Matrices
  • Determinants
7–9 Questions
  • Trigonometry
  • Binomial Theorem
  • Linear Programming
5–7 Questions

MHT CET 2025 Difficulty Level

MHT CET 2025, organized by the State CET Cell, Maharashtra, is likely to be patterned much the same as in previous years.The Exam is expected to be moderate in terms of difficulty, with Physics and Maths being more challenging than Chemistry.

As the exam is held online with no negative marking, the exam tends to test speed and accuracy rather than in-depth conceptual Knowledge.

MHT CET 2025 Subject-wise Expected Difficulty Level

Subject Expected Difficulty Level Nature of Questions
Physics Moderate to Difficult Conceptual and Numerical based questions (e.g., Current Electricity, Modern Physics)
Chemistry Easy to Moderate Fact-based and Some Organic Mechanism questions (e.g., Thermodynamics, Coordination Compounds)
Mathematics Moderate to Difficult Lengthy and heavy Calculation based (e.g., Calculus, Vectors, Probability)