Physics: Sample Paper MET-2025

• This document is a sample paper for the MET-2025 exam

Physics

• If potential V = -5x+3y+ √15z, the electric field E(x, y, z) is 5 unit

The Relation between field and potential

• Electric field is the negative of the potential gradient

Electron motion in a magnetic field

• An electron with a mass of 9.0 *10-31 kg and charge of 1.6 *10-19 coulomb, moving in a circular orbit in a magnetic field of 2 × 10-4 wb/m², has a time period of revolution equal to 5.6 * 10-8 sec
• The time period of a charged particle is independent of its speed

Electromagnetic Radiation Arrangement

• Arranging electromagnetic radiations per quantum in order of increasing energy: Radio wave < Yellow light < Blue light < X-ray

Escape and Orbital Velocity

• For a planet with an escape velocity of 10√2 km/sec, the orbital velocity of a satellite near the planet's surface is 10 km/sec
• Orbital velocity is given by:
• Escape velocity is given by:

Mean Value of Current

• The average value of alternating current for one complete cycle is zero
• The average value of AC over half cycle is defined as mean value

Time Difference in Pure Inductor Circuit

• The time difference value for voltage and current in a pure inductor circuit is
• Phase difference between alternating current and voltage is ø
• TD = T/4

Potentiometer and EMF

• In a potentiometer, a cell of EMF 1.25V yields a balance point at 35 cm, If replaced the balance point shifts to 70 cm, the EMF of the second cell is 2.5V
• To compare EMF of two primary cells. E1 and E2 represents each cell's EMF, K being the constant of proportionality Balancing lengths of both are proportional to cell EMF

Work Done in Rotation

• The work done in rotating an electric dipole with dipole moment P in an electric field E through an angle is PE (1 - cos θ)
• Formula used to calculate work done in rotation

Extrinsic Semiconductors and Doping

• For extrinsic semiconductors, when doping level is increased, the Fermi-level of p-type semiconductors goes downward and in n-type semiconductors goes upward.

Tension in a Lift

• A man in a lift holding a 5 kg bag. If the lift moves upwards with acceleration g/2, the tension in the bag handle is 75 N.

Electromagnetic Waves

• A plane electromagnetic wave has a frequency of 2.0 x 1010 Hz with an energy density of 1.02 x 10-8 J/m³ in vacuum, the amplitude of the magnetic field of the wave is close to 160 nT

Mass Defect and Energy

• A mass defect of 0.02866μ in a fusion reaction involving hydrogen changing to Helium releases 26.675 MeV of energy, where 1μ = 931MeV

Photoelectrons and Work Function

• When a metal surface is illuminated with photons of energy 4eV and 2.5eV respectively, If the ratio of maximum speeds of emitted photoelectrons in the two cases is 2, the work function of the metal is 2 eV

Carrier Wave Modulation

• In a 100 V carrier wave varying between 160 V and 40 V due to a modulating signal, the modulation index is 0.6

Chemistry

• 2,2-Dimethylbutane can be obtained by: [(CH3)3C]2LiCu + CH3CH2Br →
• Corey House Synthesis where, Gilman's reagent yields higher alkane by SN2 mechanism

Purity of Iron

• The purest form of commercial iron is wrought iron.

IUPAC Nomenclature

• The IUPAC name for H2N-CH2-CH2-OH is 2-aminoethanol

Flame test

• Mg does not give a flame test
• Both Be and Mg do not give flame test because strong forces bind electrons, preventing excitation by flame

Alkoxide Stability

• Corrected order statbility for the following alkoxides is: C>B>A (C) Negative charge is delocalised with NO2 group (B) The negative charge is delocalised with the carbon of the alkene (A) The negative charge is localised
• Presence of electron-withdrawing groups (like NO2) increases stability.

Bauxite Leaching

• Leaching of bauxite using concentrated NaOH gives sodium aluminate and sodium silicate.
• Formula used to calculate leaching

Temperature and Reaction Rate

• If a chemical reaction rate doubles for every 10°C increase, raising the temperature by 40°C increases the reaction rate by 16 times

Balancing A2 + 6B + 3C + 3D → AzByBC3 + ByDz

• Given reaction 2A2 + 6B + 3C + 3D → AzByBC3 + ByDz
• By equating moles of atoms the solution is : 4,2,3

Acidic Flux

• can be used as an acidic flux to remove basic impurities.
• Flux is a chemical added to an ore to form a easily fusible material.

Conductance

• 500 ml of aqueous solution contains 0.1 mole of solute AB. If its specific conductance is x Scm-1, then its molar conductance is 200x (in Scm² mol-1)

Number of Atoms

• In 88 g of CO2, the mass of CO having the same number of oxygen atoms equals 112 g

Equivalent weight

• Equivalent of sulphur in SCl2, is 16.

Methane and carbon content

• By 1 mole in methane, the percentage composition of carbon. is 20

Volume occupied by gases

• Given reaction , for complete reaction if volumes of A2 and B at STP are 22.4L and 44.8L, respectively, the value of x, from Gay Lussac's Law is 2

Titration Completion

• Initially, 100 ml of 0.1 N HCl titrated with 0.2 N NaOH until 30 ml of NaOH is added. Completing the titratiion with 0.25 N KOH requires 16 ml of KOH

Maths

Solve DE equation

• Solution of the DE equation, is (sin x)/y=x-c

Matrix Product

• If A and B are two matrices with AB = B and BA = A, then A² + B² = A+B.

Modulus of z

• For origin, if z is origin, then |z| = 0.

Submultiples of an angle

• Given if sinA=⅔ the value of isin A/2 - cos A/2 is √3 /3

Complex Numbers

• Adding -1-4i to the complex number 2 + 3i results in 1-i

Intersecting plane

• The intersection of the planes x + y - 2z = 10 and 3x - y + z = 5 is (4x - 15) / 3 = (4y - 25) / 5 = z.

The magnitude of forces

• The magnitude of forces are 5 N , 13 N. If, the sum of two forces is 18 N where the resultant is at right angles to the smaller force and its value is 12 N

ARITHMETIC Mean

• The arithmetic mean of the following observations is 5.2, in the values x: 2, 5, 7, 9 f(frequency) = 5,2,5,2.

Triangle midpoints

• The median AD of triangle ABC is bisected at E, BE meets AC in F then AF:AC equals to 1/3 of the same

Quadratic Equations

• The product of roots of If -2-3i is a root of quadratic equation with real coefficient is 13

Theorem of Combinations

• Letters can be selected from a collection of m Objects one kind, then Objects the kind will be , where the other kind P. objects + 1 (M + 1)

Trigonometry

• If , (x->0) what is the ratio between lim sin3x to tan2x is 3/2

Determinants

• For what value If A cos B * sin C * tan3z, is there a relationship with A, B, C, E is symmetric

Cartesian Coordinates

• 'C' divides AB internally 1:1 and D divides externally in ratio 2:1. For In Cartesian coordinate system the Point A = (2, 7), C(the mid points, (5/2, 7/2) and D = (4, 13)Then

Midpoint Formula

• In Cartesian coordinate system Point: B[C/(5, 7/2(2,7), C= Point A+B and 'C'(points to in = 'C/2
• (4^n4 * A = 24 B = (2, 7) the segment 'C' is the point)
• (2 * B1y42. - + * (1/2 (7 C + B1.4( 2 the middle the (P . * ' - and )and '4- - ' /1

Coordinates

• = ( 4)4( + B5 - C points (0 * - * and * P = B 'where =/ in2 C if there4( segment line coordinate a 5 the in .A If21

Centroid

.4* + 4 and is equal to where of Centroid A .The a B C = Centroid21 B, = if coordinates Find2<

English

• Indiscipline among students and its causes” catches the central idea of the passage.

Correct tense

• I _______you the next week is will kill

Synonyms

• Alienate and marginalize mean to isolate is the given synonym:

Antonyms

• Exalt correct Deride
• Thus, it cannot be attributed to his serene(peaceful) nature is correct

Question format

• I said to my classmate, "Have you paid off the money to your teacher” is grammatically correct.

Noun

• Account is The countable is the noun with correct Q.10