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

- their velocities depend on their masses
- V
_{B}> V_{A} - V
_{A}= V_{B} - V
_{A}> V_{B}

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

- ML
^{-2}T^{-2} - MLT
^{-1} - ML
^{-1}T^{-1} - ML
^{-1}T^{-2}

Dimensions of 1/μ_{o}ε_{o}, where symbols have their usual meaning, are

- [L
^{2}T^{–2}] - [LT
^{–1}] - [L
^{–2}T^{2}] - [L
^{–1}T]

Which of the following units denotes the dimensions ML^{2}/Q^{2}, where Q denotes the electric charge?

- weber (Wb)
- H/m
^{2} - Wb/m
^{2} - henry (H)

The physical quantities not having same dimensions are

- torque and work
- stress and Young's modulus
- speed and (μ
_{0}ε_{0})^{–1/2} - momentum and Planck's constant

Identify the pair whose dimensions are equal

- force and work
- torque and work
- stress and energy
- force and stress

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

- MT
^{–1}C^{–1} - MLT
^{–1}C^{–1} - MT
^{2}C^{–2} - MT
^{–2}C^{–1}

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

- √3 + 1
- √5 + 1
- 2 + √2
- 2

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

- (1, 1)
- (1, 0)
- (0, 1)
- (-1, 1)

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

- 0
- 1
- 2
- infinity

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

- i - j - 2k
- i + j - 2k
- 2i - j + 2k
- -i + j - 2k

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

- 14
- 16
- 36
- 48

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
- 0
- -7
- 7

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

- π/4
- π/6
- π/2
- π/3

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

- x
^{2}+ 18x + 16 = 0 - x
^{2}- 18x - 16 = 0 - x
^{2}- 18x + 16 = 0 - x
^{2}+ 18x - 16 = 0

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

- 18 months
- 19 months
- 20 months
- 21 months

If α ≠ β but α^{2} = 5α - 3 and β^{2} = 5β - 3, then the equation having α/β and β/α as its roots is

- 3x
^{2}- 19x - 3 = 0 - 3x
^{2}- 19x + 3 = 0 - x
^{2}- 5x + 3 = 0 - 3x
^{2}+ 19x - 3 = 0

Let a and b be roots of the equation px^{2} + 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

- 2√17 / 9
- √61 / 9
- √34 / 9
- 2√13 / 9

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

- (0,∞)
- (-∞,0)
- (-∞,∞)
- (-∞,∞) - {0}

The function f(x) = log (x + √(x^{2} +1)) is

- an even function
- an odd function
- neither an even nor an odd function
- a periodic function

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

- not symmetric
- transitive
- reflexive
- a function

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

- (-1, 0) U (0, 1)
- (-2, -1)
- (1, 2)
- (-∞, -2) U (2, ∞)

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

- 510
- 256
- 275
- 219

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

- B = C
- A = C
- A ∩ B = φ
- A = B

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

- - 6.8 eV
- - 3.4 eV
- + 6.8 eV
- + 13.6 eV

The ionic radii (in Å) of N^{3–}, O^{2–} and F^{–} are respectively

- 1.36, 1.71 and 1.40
- 1.71, 1.40 and 1.36
- 1.71, 1.36 and 1.40
- 1.36, 1.40 and 1.71

The color of KMnO_{4} is due to

- d – d transition
- L → M charge transfer transition
- σ – σ* transition
- M → L charge transfer transition

Which of the following compounds is not an antacid?

- Cimetidine
- Phenelzine
- Ranitidine
- Aluminium hydroxide

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

- Al
_{2}O_{3}is mixed with CaF_{2}which lowers the melting point of the mixture and brings conductivity - Al
^{3+}is reduced at the cathode to form Al - Na
_{3}AlF_{6}serves as the electrolyte - CO and CO
_{2}are produced in this process

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

- Glyptal
- Polypropene
- Poly vinyl chloride
- Bakelite

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

- C
_{9}H_{12}N_{3} - C
_{3}H_{4}N - C
_{6}H_{8}N_{2} - C
_{2}H_{6}N_{2}

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

- twice that in 60 g carbon
- half that in 8 g He
- 6.023 × 10
^{22} - 558.5 × 6.023 × 10
^{23}

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)

- 10
^{–16}metres - 10
^{–31}metres - 10
^{–33}metres - 10
^{–25}metres

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

- NH
_{3} - SH
_{2} - SO
_{2} - OH
_{2}

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

- P/RT
- PT/R
- RT/P
- PRT

The enthalpy change for a reaction does not depend upon the

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

Butene-1 may be converted to butane by reaction with

- Zn-Hg
- Sn-HCl
- Zn-HCl
- Pd/H
_{2}

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

- neopentane
- pentane
- propane
- isopentane

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

- 2-bromo-2-methylbutane
- 1-bromo-3-methylbutane
- 2-bromo-3-methylbutane
- 1-bromo-2-methylbutane

Presence of a nitro group in a benzene ring

- deactivates the ring towards nucleophilic substitution
- activates the ring towards electrophilic substitution
- renders the ring basic
- deactivates the ring towards electrophilic substitution

The reaction of toluene with Cl_{2} in presence of FeCl_{3} gives predominantly

- benzoyl chloride
- m-chlorobenzene
- benzyl chloride
- o- and p-chlorotoluene

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

- C
_{2}H_{2}+ 2HBr → - CH
_{3}CHCH_{2}+ 2HBr → - CH
_{3}CHCHBr + HBr → - CH
_{3}CCH + 2HBr →

The hydrocarbon which can react with sodium in liquid ammonia is

- CH
_{3}CHCHCH_{3} - CH
_{3}CH_{2}C≡CCH_{2}CH_{3} - CH
_{3}CH_{2}CH_{2}C≡CCH_{2}CH_{2}CH_{3} - CH
_{3}CH_{2}C≡CH

The alkene that exhibits geometrical isomerism is

- 2-methyl propene
- 2 methyl 2 butene
- 2-Butene
- propene

The IUPAC name of neopentane is

- 2 – methylpropane
- 2, 2 – dimethylpropane
- 2 – methylbutane
- 2, 2 – dimethylbutane

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-butene
- 2-butene
- propene
- ethene

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

- an acetylenic triple bond
- a vinyl group
- two ethylenic double bonds
- an isopropyl group

Alkyl halides react with dialkyl copper reagents to give

- alkenes
- alkenyl halides
- alkanes
- alkyl copper halides

During dehydration of alcohols to alkenes by heating with concentrated H_{2}SO_{4} the initiation step is

- protonation of alcohol molecule
- formation of an ester
- formation of carbocation
- elimination of water

Among the following compounds which can be dehydrated very easily?

- CH
_{3}CH_{2}CH_{2}CH_{2}CH_{2}OH - CH
_{3}CH_{2}CH_{2}CHOHCH_{3} - CH
_{3}CH_{2}CHCH_{3}CH_{2}CH_{2}OH - CH
_{3}CH_{2}CH_{3}COHCH_{2}CH_{3}