JEE Questions

Work Energy

From a building two balls A and B are thrown such that A is thrown upwards A and B downwards (both vertically). If vA and vB are their respective velocities on reaching the ground, then

  1. their velocities depend on their masses
  2. VB > VA
  3. VA = VB
  4. VA > VB

Measurement

Which one of the following represents the correct dimensions of the coefficient of viscosity?

  1. ML-2T-2
  2. MLT-1
  3. ML-1T-1
  4. ML-1T-2

Measurement

Dimensions of 1/μoεo, where symbols have their usual meaning, are

  1. [L2T–2]
  2. [LT–1]
  3. [L–2T2]
  4. [L–1T]

Measurement

Which of the following units denotes the dimensions ML2/Q2, where Q denotes the electric charge?

  1. weber (Wb)
  2. H/m2
  3. Wb/m2
  4. henry (H)

Measurement

The physical quantities not having same dimensions are

  1. torque and work
  2. stress and Young's modulus
  3. speed and (μ0ε0)–1/2
  4. momentum and Planck's constant

Measurement

Identify the pair whose dimensions are equal

  1. force and work
  2. torque and work
  3. stress and energy
  4. force and stress

Measurement

The dimension of magnetic field in M, L, T and C (coulomb) is given as

  1. MT–1C–1
  2. MLT–1C–1
  3. MT2C–2
  4. MT–2C–1

Complex Numbers

If |z - 4/z| = 2, then the maximum value of |Z| is equal to

  1. √3 + 1
  2. √5 + 1
  3. 2 + √2
  4. 2

Complex Numbers

If w (≠1) is a cube root of unity and (1 + w)7 = A + Bw. Then (A, B) equals to

  1. (1, 1)
  2. (1, 0)
  3. (0, 1)
  4. (-1, 1)

Complex Numbers

The Number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

  1. 0
  2. 1
  3. 2
  4. infinity

Vectors

Let  a = j - k  and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

  1. i - j - 2k
  2. i + j - 2k
  3. 2i - j + 2k
  4. -i + j - 2k

Vectors

If |a| = 4, |b| = 2 and the angle between a and b is π/6, then (a × b)2 is equal to

  1. 14
  2. 16
  3. 36
  4. 48

Vectors

a, b and c are 3 vectors, such that a + b + c = 0, |a| = 1, |b| = 2|c|, then a.b + b.c + c.a is equal to

  1. 1
  2. 0
  3. -7
  4. 7

Vectors

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b are perpendicular to each other, then the angle between a and b is

  1. π/4
  2. π/6
  3. π/2
  4. π/3

Quadratic Equations Sequences Series

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

  1. x2 + 18x + 16 = 0
  2. x2 - 18x - 16 = 0
  3. x2 - 18x + 16 = 0
  4. x2 + 18x - 16 = 0

Quadratic Equations

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

  1. 18 months
  2. 19 months
  3. 20 months
  4. 21 months

Quadratic Equations

If α ≠ β but α2 = 5α - 3 and β2 = 5β - 3, then the equation having α/β and β/α as its roots is

  1. 3x2 - 19x - 3 = 0
  2. 3x2 - 19x + 3 = 0
  3. x2 - 5x + 3 = 0
  4. 3x2 + 19x - 3 = 0

Quadratic Equations Sequences Series

Let a and b be roots of the equation px2 + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

  1. 2√17 / 9
  2. √61 / 9
  3. √34 / 9
  4. 2√13 / 9

Relations Functions

The domain of the function f(x) = 1/√(|x| - x) is

  1. (0,∞)
  2. (-∞,0)
  3. (-∞,∞)
  4. (-∞,∞) - {0}

Relations Functions

The function f(x) = log (x + √(x2 +1)) is

  1. an even function
  2. an odd function
  3. neither an even nor an odd function
  4. a periodic function

Relations Functions

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

  1. not symmetric
  2. transitive
  3. reflexive
  4. a function

Relations Functions

If a ϵ R and the equation -3(x - [x])2 + 2(x - [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

  1. (-1, 0) U (0, 1)
  2. (-2, -1)
  3. (1, 2)
  4. (-∞, -2) U (2, ∞)

Sets

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is

  1. 510
  2. 256
  3. 275
  4. 219

Sets

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

  1. B = C
  2. A = C
  3. A ∩ B = φ
  4. A = B

Atomic Structure

Which of the following is the energy of a possible excited state of hydrogen?

  1. - 6.8 eV
  2. - 3.4 eV
  3. + 6.8 eV
  4. + 13.6 eV

Periodic Properties

The ionic radii (in Å) of N3–, O2– and F are respectively

  1. 1.36, 1.71 and 1.40
  2. 1.71, 1.40 and 1.36
  3. 1.71, 1.36 and 1.40
  4. 1.36, 1.40 and 1.71

df-Block

The color of KMnO4 is due to

  1. d – d transition
  2. L → M charge transfer transition
  3. σ – σ* transition
  4. M → L charge transfer transition

Everyday Life Chem

Which of the following compounds is not an antacid?

  1. Cimetidine
  2. Phenelzine 
  3. Ranitidine
  4. Aluminium hydroxide

Isolation Metals

In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?

  1. Al2O3 is mixed with CaF2 which lowers the melting point of the mixture and brings conductivity
  2. Al3+ is reduced at the cathode to form Al
  3. Na3AlF6 serves as the electrolyte
  4. CO and CO2 are produced in this process

Polymers

Which polymer is used in the manufacture of paints and lacquers?

  1. Glyptal
  2. Polypropene
  3. Poly vinyl chloride
  4. Bakelite

Stoichiometry

In a compound C, H and N atoms are present in 9:1:3.5 by weight. Molecular weight of compound is 108. Molecular formula of compound is

  1. C9H12N3
  2. C3H4N
  3. C6H8N2
  4. C2H6N2

Atomic Structure

Number of atoms in 558.5 gram Fe (atomic weight of Fe = 55.85 g mol–1) is

  1. twice that in 60 g carbon
  2. half that in 8 g He
  3. 6.023 × 1022
  4. 558.5 × 6.023 × 1023

Atomic Structure

The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 metres per second is approximately (Planck's constant, h = 6.63 × 10–34 Js)

  1. 10–16 metres
  2. 10–31 metres
  3. 10–33 metres
  4. 10–25 metres

Chemical Bonding

Which one of the following compounds has the smallest bond angle in its molecule?

  1. NH3
  2. SH2
  3. SO2
  4. OH2

States Matter Gaseous State

For an ideal gas, number of moles per litre in terms of its pressure P, gas constant R and temperature T is

  1. P/RT
  2. PT/R
  3. RT/P
  4. PRT

Chemical Thermodynamics

The enthalpy change for a reaction does not depend upon the

  1. use of different reactants for the same product.
  2. nature of intermediate reaction steps.
  3. physical states of reactants and products.
  4. difference in initial or final temperatures of involved substances.

Hydrocarbons

Butene-­1 may be converted to butane by reaction with

  1. Zn-Hg
  2. Sn-HCl
  3. Zn-­HCl
  4. Pd/H2

Hydrocarbons Organic Halogens

On mixing a certain alkane with chlorine and irradiating it with ultraviolet light, it forms only one monochloroalkane. This alkane could be

  1. neopentane
  2. pentane
  3. propane
  4. isopentane

Organic Halogens

2-­Methylbutane on reacting with bromine in the presence of sunlight gives mainly

  1. 2-­bromo­-2-­methylbutane
  2. 1-­bromo-­3-­methylbutane
  3. 2-­bromo-­3-­methylbutane
  4. 1-­bromo-­2-­methylbutane

Organic Nitrogen

Presence of a nitro group in a benzene ring

  1. deactivates the ring towards nucleophilic substitution
  2. activates the ring towards electrophilic substitution
  3. renders the ring basic
  4. deactivates the ring towards electrophilic substitution

Hydrocarbons Organic Halogens

The reaction of toluene with Cl2 in presence of FeCl3 gives predominantly

  1. benzoyl chloride
  2. m-­chlorobenzene
  3. benzyl chloride
  4. o­- and p­-chlorotoluene

Hydrocarbons Organic Halogens

Which of the following reactions will yield 2, 2-­dibromopropane?

  1. C2H2 + 2HBr →
  2. CH3CHCH2 + 2HBr →
  3. CH3CHCHBr + HBr →
  4. CH3CCH + 2HBr →

Hydrocarbons

The hydrocarbon which can react with sodium in liquid ammonia is

  1. CH3CHCHCH3
  2. CH3CH2C≡CCH2CH3
  3. CH3CH2CH2C≡CCH2CH2CH3
  4. CH3CH2C≡CH

Hydrocarbons Basic Organic

The alkene that exhibits geometrical isomerism is

  1. 2-methyl propene
  2. 2 methyl 2 butene
  3. 2-Butene
  4. propene

Basic Organic

The IUPAC name of neopentane is

  1. 2 – methylpropane
  2. 2, 2 – dimethylpropane
  3. 2 – methylbutane
  4. 2, 2 – dimethylbutane

Hydrocarbons Organic Oxygen

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

  1. 1-butene
  2. 2-butene
  3. propene
  4. ethene

Hydrocarbons Organic Oxygen

Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of

  1. an acetylenic triple bond
  2. a vinyl group
  3. two ethylenic double bonds
  4. an isopropyl group

Hydrocarbons Organic Halogens

Alkyl halides react with dialkyl copper reagents to give

  1. alkenes
  2. alkenyl halides
  3. alkanes
  4. alkyl copper halides

Hydrocarbons Organic Oxygen

During dehydration of alcohols to alkenes by heating with concentrated H2SO4 the initiation step is

  1. protonation of alcohol molecule
  2. formation of an ester
  3. formation of carbocation
  4. elimination of water

Organic Oxygen

Among the following compounds which can be dehydrated very easily?

  1. CH3CH2CH2CH2CH2OH
  2. CH3CH2CH2CHOHCH3
  3. CH3CH2CHCH3CH2CH2OH
  4. CH3CH2CH3COHCH2CH3