# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

### done Rajasthan PET Solved Paper-2012

• question_answer1) The unit of permittivity of free space${{\varepsilon }_{0}}$is

A) ${{C}^{2}}/N-{{m}^{2}}$

B) ${{C}^{2}}/{{(N-m)}^{2}}$

C) $N-{{m}^{2}}/{{C}^{2}}$

D) $C/N-m$

• question_answer2) How are the numerical value (N) and unit (U) of a physical quantity related to each other?

A) $N\propto \sqrt{U}$

B) $N\propto \frac{1}{\sqrt{U}}$

C) $N\propto \frac{1}{U}$

D) $N\propto U$

• question_answer3) If a ball is thrown vertically upwards with speed$u,$the distance covered during the last t second of its ascent is

A) $ut-\frac{1}{2}g{{t}^{2}}$

B) $\frac{1}{2}g{{t}^{2}}$

C) $(u+gt)t$

D) $ut$

• question_answer4) An electron starting from rest has a velocity$v$ that increases linearly with time t as$v=kt,$ where$k=2\text{ }m{{s}^{-2}}$. The distance covered by electron in first 3 s is

A) 9m

B) 11 m

C) 33m

D) 40m

• question_answer5) The excess of pressure inside a drop of soap solution is pj and that inside a soap bubble of same radius is${{p}_{b}}$. The correct relation between ${{p}_{d}}$and${{p}_{b,}}$is given by

A) $2{{p}_{d}}={{p}_{b}}$

B) ${{p}_{d}}={{p}_{b}}$

C) ${{p}_{d}}=2{{p}_{b}}$

D) None of these

• question_answer6) Two vectors A and B are such that,$A+B=C$ and${{A}^{2}}+{{B}^{2}}={{C}^{2}}$. If 9 is the angle between positive directions of A and B, then

A) $\theta =\frac{2\pi }{3}$

B) $\theta =\frac{\pi }{2}$

C) $\theta =\pi$

D) $\theta =0$

• question_answer7) Let two satellites X and Y revolves around a planet P in circular orbits of radii 4R and R respectively. If the speed of the satellite X is 3v, then the speed of satellite Y will be

A) $6v$

B) $\frac{3v}{4}$

C) $12v$

D) $\frac{3v}{2}$

• question_answer8) A bimetallic strip is made of two strips A and B having coefficient of linear expansion as${{\alpha }_{A}}$and da. If${{\alpha }_{A}}>{{\alpha }_{B}},$ which one of the following describes the behaviour of the metallic strip when heated?

A) Strip will bend only when $\frac{{{\alpha }_{A}}+{{\alpha }_{B}}}{2}>({{\alpha }_{A}}-{{\alpha }_{B}})$

B) Strip will bend but will not elongate

C) Strip will bend with metal A as the outer side

D) Strip will bend with metal B as The outer side

• question_answer9) An electron accelerated through a potential difference of V volts has a wavelength$\lambda$ associated with it. Mass of proton is nearly 2000 times that of an electron. In order to have the same wavelength$\lambda$for the proton, it must be accelerated through a potential difference of

A) 2000 V volt

B) 20 V volt

C) V/2000 volt

D) $\sqrt{2000}$V volt

• question_answer10) Two points charges of$+3C$and$+9C$repel each other with a force of 27 N. If charges of$-3C$ are given to each of these charges, then the new force of interaction will be

A) zero

B) 9 N

C) 18 N

D) 2 N

• question_answer11) In Young's double slit experiment the 7th maximum with wavelength${{\lambda }_{1}}$is at a distance${{d}_{1}}$and that with wavelength${{\lambda }_{2}}$is at distance${{d}_{2}}.$Then, ${{d}_{1}}/{{d}_{2}}=$

A) ${{\lambda }_{2}}/{{\lambda }_{1}}$

B) ${{\lambda }_{1}}/{{\lambda }_{2}}$

C) $\lambda _{2}^{2}/\lambda _{1}^{2}$

D) $\lambda _{1}^{2}/\lambda _{2}^{2}$

• question_answer12) The plates of a parallel air capacitor are 2 cm apart. If a slab of dielectric constant 5 and thickness 1 cm is placed between its plates, then to keep the capacitance of the capacitor unchanged. The plates of the capacitor should moved by a distance of

A) 3.2 cm

B) 3.0 cm

C) 2.8 cm

D) 2.2 cm

• question_answer13) If$W$units of works is required to turn a magnetic needle through$60{}^\circ$when it is lying parallel to a magnetic field, then amount of torque needed to maintain needle in this position will be

A) $W$

B) $2\,W$

C) $\sqrt{3}W$

D) $\frac{\sqrt{3}W}{2}$

• question_answer14) If two stars radiates maximum energy at wavelengths$316\times {{10}^{-7}}m$and$4.8\times {{10}^{-7}}m$ respectively, then ratio of their temperatures T/T? will be

A) $\frac{2}{3}$

B) $\frac{4}{3}$

C) $\frac{3}{4}$

D) $\frac{3}{2}$

• question_answer15) The diameter of the moon is$3.5\times {{10}^{3}}$km and its distance from the earth is$3.8\times {{10}^{5}}$km seen by a telescope having focal lengths of the objective and eye piece as 4 m and 10 cm respectively, the diameter of image of the moon will be approximately

A) $10{}^\circ$

B) $20{}^\circ$

C) $35{}^\circ$

D) $50{}^\circ$

• question_answer16) The rms velocity of oxygen molecule at$27{}^\circ C$is (Atomic weight of oxygen =16)

A) $402.5\,m{{s}^{-1}}$

B) $400.5\text{ }m{{s}^{-1}}$

C) $483.5\text{ }m{{s}^{-1}}$

D) $532.5\text{ }m{{s}^{-1}}$

• question_answer17) If a constant volume gas thermometer records a pressure of 20 kPa at tripple point of water and pressure of 14.3 kPa at the dry ice, then the temperature of dry ice will be

A) $-77.85{}^\circ C$

B) $+77.85{}^\circ C$

C) $-66.05{}^\circ C$

D) None of these

• question_answer18) Two discs have same mass and thickness but are made, up of different materials having different densities. Which one of them will have larger moment of inertia?

A) Both disc have same moment of inertia

B) disc having less density have larger moment of inertia

C) disc having more density have larger moment of inertia

D) None of the above

• question_answer19) If a resistor of$30\,\Omega ,$is bent in the form of a circle as shown in figure, then the effective resistance' between points X and Y will be

A) $\frac{5}{6}\Omega$

B) $\frac{6}{5}\Omega$

C) $\frac{6}{25}\Omega$

D) $\frac{25}{6}\Omega$

• question_answer20) A radioactive nuclide decays to form a stable nuclide. If the half-life of nuclide is 3 min, then what fraction of its 1 g will remain radioactive after 9 min?

A) 0.125

B) 0.875

C) 1.125

D) 1.875

• question_answer21) If an$\alpha -$particle of energy 10 MeV is deflected back when its distance from the nucleus is $4\times {{10}^{-14}}m,$then the atomic number of the atom is

A) 129

B) 130

C) 139

D) 120

• question_answer22) Which of the following spectral series in hydrogen atom give spectral line of$4860\overset{o}{\mathop{\text{A}}}\,$?

A) Brackett

B) Paschen

C) Lyman

D) Balmer

• question_answer23) A bus starts from rest with an acceleration$1\,m{{s}^{-2}}$. A man who is 48 m behind the bus starts with a uniform velocity of$10\text{ }m{{s}^{-1}}$. Then the minimum rime after which the man will reach the bus

A) 4 s

B) 8 s

C) 10 s

D) 15 s

• question_answer24) The gravitational constant G is called universal constant because

A) It has no dimensions

B) It has no unit

C) It has same value in different systems of unit

D) It does not depend upon the nature of the medium in which the bodies lie

• question_answer25) If a metallic block had no potential difference applied across it, then the average velocity of free electrons in it

A) zero

B) proportional to T

C) proportional to$\sqrt{T}$

D) finite but independent of temperature

• question_answer26) A particle describes a horizontal circle on the smooth surface of an inverted cone. If the height of the plane of the circle above the vertex is 9.8 cm, then the speed of the particle will be (Take$g=9.8\text{ }m/{{s}^{2}}$)

A) $0.98\text{ }m{{s}^{-1}}$

B) $19.6\text{ }m{{s}^{-1}}$

C) $4.9\,m{{s}^{-1}}$

D) None of these

• question_answer27) The equation of a wave is represented by $y={{10}^{-4}}\sin \left( 100t-\frac{x}{10} \right)m,$the velocity of the wave will be

A) $0.1\text{ }m{{s}^{-1}}$

B) $10\text{ }m{{s}^{-1}}$

C) $100\text{ }m{{s}^{-1}}$

D) $1000\text{ }m{{s}^{-1}}$

• question_answer28) If two vessels of different materials identical in size and wall thickness are filled with equal quantities of ice at$0{}^\circ C$and ice melts completely in 10 and 25 min respectively, then the ratio of coefficients of thermal conductivies of the materials of the vessels will be

A) $\frac{5}{7}$

B) $\frac{5}{2}$

C) $\frac{2}{5}$

D) $\frac{7}{5}$

• question_answer29) The stress for elastic limit of a material is$3.5\times {{10}^{8}}N-{{m}^{-2}}$. The minimum diameter of a rod made of this material which can support 500 N load without exceeding elastic limit will be

A) 1.35 mm

B) 1.35 cm

C) $1.35\times {{10}^{-6}}m$

D) 2mm

• question_answer30) A ray of light passing through a prism having$\mu =\sqrt{2}$suffers minimum deviation. If the angle of incidence is double the angle of refraction within the prism, then the angle of the prism is

A) $45{}^\circ$

B) $90{}^\circ$

C) $60{}^\circ$

D) None of these

• question_answer31) A drop of olive oil is introduced in a mixture of alcohol and water. The density of the mixture is same as that of olive oil. The upward thrust on the drop is

A) zero

B) equal to weight of the drop

C) less than the weight of the drop

D) more than the weight of the drop

• question_answer32) A Carnot engine whose low temperature reservoir is at$7{}^\circ C$has an efficiency of 50%. If the efficiency of heat engine is to be increased more by 10% then the temperature of high temperature reservoir should be increased by

A) 107 K

B) 500 K

C) 140 K

D) 200 K

• question_answer33) An AC source of frequency 50 Hz is connected to 50 mH inductor and a bulb. To get the maximum brightness from the bulb, what should be the capacitance of a capacitor connected in series with the circuit?

A) $50\times {{10}^{-4}}F$

B) $1\times {{10}^{-4}}F$

C) $2.03\times {{10}^{-4}}F$

D) $3\times {{10}^{-4}}F$

• question_answer34) Two long straight wires are connected by a circular section that has a radius r as shown in figure. All segments of the wire lie in the same place and carry steady current I. The magnetic field at centre O of the circular segment will be

A) $\frac{B{{\mu }_{0}}I}{4\pi r}$

B) $\frac{B{{\mu }_{0}}I}{r}$

C) $\frac{B{{\mu }_{0}}I}{2\pi r}$

D) $\frac{{{\mu }_{0}}I}{4\pi r}$

• question_answer35) If two wires made of tinned copper having identical cross-section but different lengths ${{l}_{1}}$and${{l}_{2}}$respectively are used as fuse wires, then the fuses will melt at same value of current in both of them

A) True

B) False

C) Insufficient data

D) None of the above

• question_answer36) A wave is represented by $y=a\cos (\omega t+kx+\phi )$ where$\omega ,\phi$and$\phi$are three constants. The dimensions of$\omega ,k$and$\phi$are respectively

A) $[T],[{{L}^{-1}}],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]$

B) $[T],[L],[M]$

C) $[T],[{{L}^{-1}}],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]$

D) $[{{T}^{-1}}],[L],[{{M}^{0}}{{L}^{0}}{{T}^{0}}]$

• question_answer37) Two blocks of masses ${{m}_{1}}$ and ${{m}_{2}}$ are placed in contact with each other on a rough horizontal surface having coefficient of friction$\mu$as shown in figure. The minimum horizontal force F required to move the block${{m}_{1}}$

A) $\mu ({{m}_{1}}-{{m}_{2}})g$

B) $\mu ({{m}_{2}}-{{m}_{1}})g$

C) $\mu {{m}_{1}}g$

D) $\mu ({{m}_{1}}+{{m}_{2}})g$

• question_answer38) A ball of mass m moving with a velocity$\mu$collides head-on with another ball of mass m initially at rest. If the coefficient of restitution be e, then the ratio of the final and initial velocities of the first ball is

A) $\frac{1-e}{2}$

B) $\frac{1+e}{2}$

C) $\frac{1-e}{1+e}$

D) $\frac{1+e}{1-e}$

• question_answer39) If${{I}_{A}},{{K}_{A}}$and${{I}_{B}},{{K}_{B}}$are the moments of interia and kinetic energies of two freely rotating bodies A and B respectively, such that${{I}_{A}}>{{I}_{B}}$and their angular mements are equal, then

A) ${{K}_{A}}<{{K}_{B}}$

B) ${{K}_{A}}>{{K}_{B}}$

C) ${{K}_{A}}={{K}_{B}}$

D) ${{K}_{A}}=2{{K}_{B}}$

• question_answer40) The angular frequency and the amplitude of a simple pendulum are$\omega$and a respectively. If the pendulum is displaced through a distance$x$ from the mean position then the ratio of its kinetic energy (K) and potential energy (U) will be

A) $\frac{K}{U}=\frac{{{a}^{2}}-{{x}^{2}}{{\omega }^{2}}}{{{x}^{2}}{{\omega }^{2}}}$

B) $\frac{K}{U}=\frac{{{a}^{2}}-{{x}^{2}}}{{{x}^{2}}}$

C) $\frac{K}{U}=\frac{{{x}^{2}}}{{{a}^{2}}-{{x}^{2}}}$

D) $\frac{K}{U}=\frac{{{x}^{2}}{{\omega }^{2}}}{{{a}^{2}}-{{\omega }^{2}}{{x}^{2}}}$

• question_answer41) Self-condensation of two moles of ethyl acetate in presence of sodium ethoxide yields

A) ethyl butyrate

B) acetoacetic ester

C) methyl acetoacetate

D) ethyl propionate

• question_answer42) End product of the following reaction is$C{{H}_{3}}C{{H}_{2}}COOH\xrightarrow[red\,P]{C{{l}_{2}}}\xrightarrow[{}]{Alcoholic\text{ }KOH}$

A) $\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C{{H}_{3}}CHCOO}}\,$

B) $\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C{{H}_{2}}C{{H}_{2}}COO}}\,H$

C) $C{{H}_{2}}=CHCOOH$

D) $\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,COOH$

• question_answer43) ${{S}_{N}}1$reaction is feasible in

A)

B)

C)

D)

• question_answer44) Maximum dehydration takes place in that of

A)

B)

C)

D)

• question_answer45) The volume of 2.8 g of CO at$27{}^\circ C$and 0.821 atm pressure is (R = 0.0821 L atm mol${{s}^{-1}}{{K}^{-1}}$)

A) 30 mL

B) 3 L

C) 0.3 L

D) 1.5 L

• question_answer46) An electron having highest energy in the set

A) $3,2,1,\frac{1}{2}$

B) $4,2,-1,\frac{1}{2}$

C) $4,1,0,-\frac{1}{2}$

D) $5,0,0,\frac{1}{2}$

• question_answer47) On heating benzyl amine with chloroform and ethanolic KOH, product obtained is

A) benzyl alcohol

B) benzaldehyde

C) benzonitrile

D) benzyl isocyanide

• question_answer48) In which of the following pairs are both the ions coloured in aqueous solution? (At. no. : Sc = 21, Ti = 22, Ni = 28, Cu = 29, Co =27)

A) $N{{i}^{2+}},T{{i}^{3+}}$

B) $S{{c}^{3+}},T{{i}^{3+}}$

C) $S{{c}^{3+}},C{{o}^{2+}}$

D) $N{{i}^{2+}},C{{u}^{+}}$

• question_answer49) The number of lone pairs on$Xe$in$Xe{{F}_{2}},Xe{{F}_{4}},$ arid$Xe{{F}_{5}}$respectively are

A) 3, 2, 1

B) 2, 4, 6

C) 1, 2, 3

D) 6, 4, 2

• question_answer50) A solution of Baeyer's reagent

A) contains cold dilute$CuC{{l}_{2}}$and$HCl$

B) contains cold dilute alkaline$KMn{{O}_{4}}$solution

C) can be used for reduction purpose

D) can be used to detect unsaturation in phenol

• question_answer51) Gold number is the index for

A) protective colloid

B) purity of gold

C) metallic gold

D) electroplated gold

• question_answer52) The standard emf of the cell $Zn+C{{u}^{2+}}\xrightarrow[{}]{{}}Cu+Z{{n}^{2+}}$is 1.10 at$25{}^\circ C$. The emf of the cell when$0.1\text{ }M\,C{{u}^{2+}}$and$0.1\text{ }M\,Z{{n}^{2+}}$solution are used will be

A) 1.10V

B) $+\text{ }0.110\text{ }V$

C) $-1.10V$

D) $-0.11\,V$

• question_answer53) Given: The mass of electron is$9.11\times {{10}^{-31}}kg$and Planck constant is$6.626\times {{10}^{-34}}Js,$the uncertainty involved in the measurement of velocity within a distance of$0.1\overset{o}{\mathop{\text{A}}}\,$is

A) $5.79\times {{10}^{6}}m{{s}^{-1}}$

B) $5.79\times {{10}^{7}}m{{s}^{-1}}$

C) $5.79\times {{10}^{8}}m{{s}^{-1}}$

D) $5.79\times {{10}^{5}}m{{s}^{-1}}$

• question_answer54) If $E_{F{{e}^{2+}}/Fe}^{o}=-0.441V$ and $E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=0.771V$the standard emf of the reaction $Fe+3F{{e}^{3+}}\xrightarrow[{}]{{}}3F{{e}^{2+}}$will be

A) 0.330V

B) 1.653V

C) 1.212V

D) 0.111 V

• question_answer55) The enthalpy of combustion of${{H}_{2}},$cyclohexene$({{C}_{6}}{{H}_{10}})$and cyclohexane$({{C}_{6}}{{H}_{12}})$are$-241,~-3800$ and$-3920\text{ }kJ$per mol respectively. Heat of hydrogenation of cyclohexene is

A) $-121\text{ }kJ$ per mol

B) $+121\text{ }kJ$ per mol

C) $+242\text{ }kJ$ per mol

D) $-242\text{ }kJ$ per mol

• question_answer56) In which of the following molecules are all the bonds not equal?

A) $CI{{F}_{3}}$

B) $B{{F}_{3}}$

C) $Al{{F}_{3}}$

D) $N{{F}_{3}}$

• question_answer57) Half-life period of a substance is 1600 min. How much fraction of the substance will remain after 6400mm?

A) $\frac{1}{16}$

B) $\frac{1}{4}$

C) $\frac{1}{8}$

D) $\frac{1}{2}$

• question_answer58) Compound A given below is

A) antiseptic

B) antibiotic

C) analgesic

D) pesticide

• question_answer59) For the following cell with hydrogen electrodes at two different pressures${{p}_{1}}$and${{p}_{2}},$emf is given by $\underset{{{p}_{1}}}{\mathop{pt({{H}_{2}})}}\,|\underset{1M}{\mathop{{{H}^{+}}(aq)}}\,|\underset{{{p}_{2}}}{\mathop{Pt({{H}_{2}})}}\,$

A) $\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}$

B) $\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{1}}}{{{p}_{2}}}$

C) $\frac{RT}{F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}$

D) $\frac{RT}{2F}{{\log }_{e}}\frac{{{p}_{2}}}{{{p}_{1}}}$

• question_answer60) Consider the following two reactions, $A\xrightarrow[{}]{{}}$Product; $-\frac{d[A]}{dt}={{k}_{1}}{{[A]}^{0}}$ $B\xrightarrow[{}]{{}}$Product; $-\frac{d[B]}{dt}={{k}_{2}}[B]$ ${{k}_{1}}$and${{k}_{2}}$are expressed in terms of molarity (mol${{L}^{-1}}$) and time$({{s}^{-1}})$as

A) ${{s}^{-1}},M\,{{s}^{-1}}{{L}^{-1}}$

B) $M\,{{s}^{-1}}M\,{{s}^{-1}}$

C) ${{s}^{-1}}{{M}^{-1}}{{s}^{-1}}$

D) $M\,{{s}^{-1}}{{s}^{-1}}$

• question_answer61) $CsBr$crystallises in a body centred cubic lattice. The unit cell length is 436.6 pm. Given that the atomic mass of Cs = 133 u and that of Br = 80 u and Avogadro number being $6.0.2\times {{10}^{23}}mo{{l}^{-1}},$ the density of$CsBr$is

A) $42.5g/c{{m}^{3}}$

B) $0.425g/c{{m}^{3}}$

C) $8.25\text{ }g/c{{m}^{3}}$

D) $4.25\text{ }g/c{{m}^{3}}$

• question_answer62) $-[NH(C{{H}_{2}})NHCO{{(C{{H}_{2}})}_{4}}CO]{{-}_{n}}$is a

A) copolymer

C) thermosetting polymer

D) homopolymer

• question_answer63) During the process of digestion, the proteins present in food materials are hydrolysed to amino acids. The two enzymes involved in the process Proteins $\xrightarrow[{}]{Enzyme(A)}$Polypeptides are respectively

A) amylase and maltase

B) diastase and lipase

C) pepsin and trypsin

D) invertase and zymase

• question_answer64) Hybridisation of the underlined atom changes in

A) $\underline{Al}{{H}_{3}}$changes to $AlH_{4}^{-}$

B) ${{H}_{2}}\underline{O}$changes to${{H}_{3}}{{O}^{+}}$

C) $\underline{N}{{H}_{3}}$changes to$NH_{4}^{-}$

D) All the above cases

• question_answer65) A metal M forms water soluble MS 04 and inert MO. MO in aqueous solution forms insoluble $M{{(OH)}_{2}}$which is soluble in$NaOH$. Metal M is

A) $Be$

B) $Mg$

C) $Ca$

D) $Si$

• question_answer66) In an organic compound of molar mass 108g $mo{{l}^{-1}},C,H$and N atoms are present in 9 : 1: 3.5 by weight. Molecular formula can be

A) ${{C}_{6}}{{H}_{8}}{{N}_{2}}$

B) ${{C}_{7}}{{H}_{10}}N$

C) ${{C}_{5}}{{H}_{6}}{{N}_{3}}$

D) ${{C}_{4}}{{H}_{18}}{{N}_{3}}$

• question_answer67) $[Co{{(N{{H}_{3}})}_{4}}{{(N{{O}_{2}})}_{2}}]Cl$exhibits

A) linkage isomerism, ionisation isomerism and optical isomerism

B) linkage isomerism, ionisation isomerism and geometrical isomerism

C) Ionisation isomerism, geometrical isomerism and optical isomerism

D) linkage isomerism, geometrical isomerism and optical isomerism

• question_answer68) The correct order of the mobility of the alkali metal ions in aqueous solution is

A) $L{{i}^{+}}>N{{a}^{+}}>{{K}^{+}}>R{{b}^{+}}$

B) $N{{a}^{+}}>{{K}^{+}}>R{{b}^{+}}>L{{i}^{+}}$

C) ${{K}^{+}}>R{{b}^{+}}>N{{a}^{+}}>L{{i}^{+}}$

D) $R{{b}^{+}}>{{K}^{+}}>N{{a}^{+}}>L{{i}^{+}}$

• question_answer69) Cyanide process is used for the extraction of

A) barium

B) silver

C) boron

D) zinc

• question_answer70) For an aqueous solution, freezing point is$-0.186{}^\circ C$. Elevation of the boiling point of the same solution is (${{K}_{f}}=1.86{}^\circ mo{{l}^{-1}}kg$and${{K}_{b}}=0.512{}^\circ mo{{l}^{-1}}kg$)

A) $0.186{}^\circ C$

B) $0.0512{}^\circ C$

C) $1.86{}^\circ C$

D) $5.12{}^\circ C$

• question_answer71) Assume each reaction is carried out in an open container. For which reaction will$\Delta H=\Delta E$?

A) ${{H}_{2}}(g)+B{{r}_{2}}(g)\xrightarrow[{}]{{}}2HBr(g)$

B) $C(s)+2{{H}_{2}}O(g)\xrightarrow[{}]{{}}2{{H}_{2}}(g)+C{{O}_{2}}(g)$

C) $PC{{l}_{5}}(g)\xrightarrow[{}]{{}}PC{{l}_{3}}(g)+C{{l}_{2}}(g)$

D) $2CO(g)+{{O}_{2}}(g)\xrightarrow[{}]{{}}2C{{O}_{2}}(g)$

• question_answer72) The hydrogen ion concentration of a ${{10}^{-8}}M\,HCl$aqueous solution at 298 K$({{K}_{w}}={{10}^{-14}})$

A) $1.0\times {{10}^{-6}}M$

B) $1.0525\times {{10}^{-7}}M$

C) $9.525\times {{10}^{-8}}M$

D) $1.0\times {{10}^{-8}}M$

• question_answer73) Proteins are composed of

A) $\alpha -$amino acids

B) carbohydrates

C) vitamins

D) mineral salts

• question_answer74) A carbonyl compound reacts with hydrogen cyanide to form cyanbhydrin which on hydrolysis forms a racemic mixture of a$\alpha -$ydroxy acid. The carbonyl compound is

A) acetaldehyde

B) acetone

C) diethyl ketone

D) formaldehyde

• question_answer75) Following reaction ${{(C{{H}_{3}})}_{2}}CBr+{{H}_{2}}O\xrightarrow[{}]{{}}{{(C{{H}_{3}})}_{3}}COOH+HBr$ is an example of

A) elimination reaction

C) nucleophilic substitution

D) elecrophilic substitution

• question_answer76) Acetylene does not react with

A) Na

B) $HCl$

C) ammoniacal $AgN{{O}_{3}}$

D) $NaOH$

• question_answer77) The following reaction is described as

A) ${{S}_{E}}2$

B) ${{S}_{N}}2$

C) ${{S}_{N}}1$

D) ${{S}_{E}}1$

• question_answer78) Refining of impure copper with zinc impurity is to be done by electrolysis using electrodes as

A) Cathode-pure copper Anode-pure zinc

B) Cathode-pure zinc Anode- pure copper

C) Cathode-pure copper Anode-impure copper

D) Cathode-pure zinc Anode- impure zinc

• question_answer79) $A{{l}_{2}}{{O}_{3}}$can be converted to anhydrous$AlC{{l}_{3}}$by heating

A) $A{{l}_{2}}{{O}_{3}}$with$HCl$gas

B) $A{{l}_{2}}{{O}_{3}}$with$NaCl$in solid state

C) a mixture of$A{{l}_{2}}{{O}_{3}}$ and carbon in dry$C{{l}_{2}}$gas

D) $A{{l}_{2}}{{O}_{3}}$with$C{{l}_{2}}$gas

• question_answer80) Which one of the following is a redox reaction?

A) $NaCl+KN{{O}_{3}}\xrightarrow[{}]{{}}NaN{{O}_{3}}+KCl$

B) $Ca{{C}_{2}}{{O}_{4}}+2HCl\xrightarrow[{}]{{}}CaC{{l}_{2}}+{{H}_{2}}{{C}_{2}}{{O}_{4}}$

C) $Ca{{(OH)}_{2}}+2N{{H}_{4}}Cl\xrightarrow[{}]{{}}CaC{{l}_{2}}+2N{{H}_{3}}$ $+2{{H}_{2}}O$

D) $2K[Ag{{(CN)}_{2}}]+Zn\xrightarrow[{}]{{}}2Ag$ $+{{K}_{2}}[Zn{{(CN)}_{4}}]$

• question_answer81) The region of the argand diagram defined by$|z-1|+|z+1|\le 4$is

A) interior of an ellipse

B) exterior of a circle

C) interior and boundary of an ellipse

D) None of the above

• question_answer82) The smallest positive integer n for which${{(1+i)}^{2n}}={{(1-i)}^{2n}}$is

A) 1

B) 2

C) 3

D) 4

• question_answer83) If$a=\cos \alpha +i\sin \alpha ,$$b=\cos \beta +i\sin \beta ,$ $c=\cos \gamma +i\sin \gamma$and$\frac{b}{c}+\frac{c}{a}+\frac{a}{b}=1,$then $\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha +\beta )$is equal to

A) 0

B) 1

C) -1

D) None of the above

• question_answer84) If one root of the equation$lx+mx+n=0$is$\frac{9}{2}$ $(l,m$and n are positive integers) and$\frac{m}{4n}=\frac{l}{m},$then$l+n$is equal to

A) 80

B) 85

C) 90

D) 95

• question_answer85) If$\alpha$and$\beta$are the roots of the equation $a{{x}^{2}}+bx+c=0,$then$\frac{\alpha }{\alpha \beta +b}+\frac{\beta }{a\alpha +b}$is equal to

A) $\frac{2}{a}$

B) $\frac{2}{b}$

C) $\frac{2}{c}$

D) $\frac{-2}{a}$

• question_answer86) If${{H}_{1}}$and${{H}_{2}}$are two harmonic means between two positive numbers a and$b(a\ne b),$and G are the arithmetic and geometric means between a and b, then$\frac{{{H}_{2}}+{{H}_{1}}}{{{H}_{2}}{{H}_{1}}}$is

A) $\frac{A}{G}$

B) $\frac{2A}{{{G}^{2}}}$

C) $\frac{A}{2{{G}^{2}}}$

D) $\frac{A}{{{G}^{2}}}$

• question_answer87) Let${{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1+2}{{{1}^{3}}+{{2}^{3}}}+...+$$\frac{1+2+....+n}{{{1}^{3}}+{{2}^{3}}+...+{{n}^{3}}},n=1,2,3,.....$Then${{S}_{n}}$is not greater than

A) $\frac{1}{2}$

B) 1

C) 2

D) 4

• question_answer88) p points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

A) ${{p}^{3}}+3{{p}^{2}}$

B) $\frac{1}{2}({{p}^{3}}+p)$

C) $\frac{{{p}^{2}}}{2}(5p-3)$

D) ${{p}^{2}}(4p-3)$

• question_answer89) If$p(n):2+4+6+....+(2n),n\in N,$then$p(k)=k(k+1)+2$implies$p(k+1)=$ $(k+1)(k+2)+2$is true for all$k\in N$. So, statement$p(n)=n(n+1)+2$is true for

A) $n\ge 1$

B) $n\ge 2$

C) $n\ge 3$

D) None of these

• question_answer90) If in the expansion of${{(1+x)}^{m}}{{(1-x)}^{n}},$the coefficient of $x$and${{x}^{2}}$are 3 and$-6$respectively, then m is

A) 6

B) 9

C) 12

D) 24

• question_answer91) If A and B are square matrices of size$n\times n$such that${{A}^{2}}-{{B}^{2}}=(A\text{ }B)(A+B)$then which of the following will be always true?

A) $AB=BA$

B) Either$A=O$or$B=O$

C) Either$A=I$or$B=I$

D) $A=B$

• question_answer92) The values of $x$ for which the given matrix will be non-singular, are

A)  $-2\le x\le 2$

B)  for all$x$other than 2 and$-2$

C)  $x\ge 2$

D)  $x\le -2$

• question_answer93) If$f(\theta )=\left| \begin{matrix} {{\cos }^{2}}\theta & \cos \theta \sin \theta & -\sin \theta \\ \cos \theta & {{\sin }^{2}}\theta & \cos \theta \\ \sin \theta & -\cos \theta & 0 \\ \end{matrix} \right|$Then, for all$\theta$

A) $f(\theta )=0$

B) $f(\theta )=1$

C) $f(\theta )=-1$

D) None of these

• question_answer94) The system of equations$2x+y-5=0,$ $x-2y+1=0$and$2x-14y-a=0$is consistent. Then, a is equal to

A) 1

B) 2

C) 5

D) None of these

• question_answer95) Find imaginary part of${{\sin }^{-1}}(\cos ec\theta )$.

A) $\log \left( \cot \frac{\theta }{2} \right)$

B) $\frac{\pi }{2}$

C) $\frac{1}{2}\log \left( \cot \frac{\theta }{2} \right)$

D) None of these

• question_answer96) If$\tan \left( \frac{x}{2} \right).\coth \left( \frac{x}{2} \right)=1,$then the value of$\cos x.\cosh \,x$is

A) 1

B) $-1$

C) $co{{s}^{2}}\text{ }x$

D) $sin{{h}^{2}}\text{ }x$

• question_answer97) The$x-$axis, y-axis and a line passing through the point A(6, 0) form a$\Delta ABC$. If$\angle A=30{}^\circ ,$ then the area of the triangle (in sq unit) is

A) $6\sqrt{3}$

B) $12\sqrt{3}$

C) $4\sqrt{3}$

D) $8\sqrt{3}$

• question_answer98) The equation of perpendicular bisectors of sides AB and AC of a$\Delta ABC$are$x-y+5=0$and$x+2y=0,$respectively. If the coordinates of vertex A are$(1,-2),$the equation of BC is

A) $14x+23y-40=0$

B) $14x-23y+40=0$

C) $23x+14y-40=0$

D) $23x-14y+40=0$

• question_answer99) If two chords having lengths${{a}^{2}}-1$and$3(a+1),$where a is a constant of a circle bisect each other, then the radius of the circle is

A) 6

B) $\frac{15}{2}$

C) 8

D) $\frac{19}{2}$

• question_answer100) For an equilateral triangle the centre is the origin and the length of altitude is a. Then, the equation of the circumcircle is

A) ${{x}^{2}}+{{y}^{2}}={{a}^{2}}$

B) $3{{x}^{2}}+3{{y}^{2}}=2{{a}^{2}}$

C) $9{{x}^{2}}+9{{y}^{2}}=4{{a}^{2}}$

D) ${{x}^{2}}+{{y}^{2}}=4{{a}^{2}}$

• question_answer101) The equation of the plane passing through the mid-point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it, is

A) $x+y+z=9$

B) $x+y+z=-9$

C) $2x+3y+4z=9$

D) $2x+3y+4z=-9$

• question_answer102) The direction cosines$l,m$and n of two lines are connected by the relation$l+m+n=0,\text{ }lm=0,$then the angle between them is

A) $\frac{\pi }{3}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{2}$

D) 0

• question_answer103) If$f(x)=\frac{{{4}^{x}}}{{{4}^{x}}+2},$then $f\left( \frac{1}{97} \right)+f\left( \frac{2}{97} \right)+....+f\left( \frac{96}{97} \right)$ is equal to

A) 1

B) 48

C) $-48$

D) $-1$

• question_answer104) The range of the function $f(x)=\tan \sqrt{\frac{{{\pi }^{2}}}{9}-{{x}^{2}}}$is

A) $[0,3]$

B) $[0,\sqrt{3}]$

C) $(-\infty ,\infty )$

D) None of these

• question_answer105) If$f(x)=|\log |x||,$then

A) $f(x)$is continuous and differentiable for all $x$in its domain

B) $f(x)$is continuous for all$x$in its domain but not differentiable at$x=\pm 1$

C) $f(x)$is neither continuous nor differentiable at$x=\pm 1$

D) None of the above

• question_answer106) If$f(x)={{\cot }^{-1}}[(3x-{{x}^{3}})/(1-3{{x}^{2}})]$and $g(x)={{\cos }^{-1}}[(1-{{x}^{2}})/(1+{{x}^{2}})],$ then $\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)-f(a)}{g(x)-g(a)}\left[ 0<a<\frac{1}{2} \right]$is

A) $-\frac{3}{2}$

B) $\frac{1}{2}$

C) $\frac{3}{2}$

D) None of these

• question_answer107) If$f(x)=(x-2)(x-4)(x-6)...(x-2n),$then $f'(2)$is

A) ${{(-1)}^{n}}{{2}^{n-1}}.(n-1)!$

B) ${{(-2)}^{n-1}}(n-1)!$

C) ${{(-2)}^{n}}n!$

D) ${{(-1)}^{n-1}}{{2}^{n}}(n-1)!$

• question_answer108) The derivative of$f(\tan x)$w.r.t.$g(\sec x)$at $x=\frac{\pi }{4},$where$f'(1)=2$and$g'(\sqrt{2})=4$is

A) $\frac{1}{\sqrt{2}}$

B) $\sqrt{2}$

C) 1

D) None of these

• question_answer109) The minimum value of${{e}^{(2{{x}^{2}}-2x+1){{\sin }^{2}}x}}$is

A) 0

B) 1

C) 2

D) 3

• question_answer110) The function$f(x)={{\cot }^{-1}}x+x$increases in the interval

A) $(1,\infty )$

B) $(-1,\infty )$

C) $(-\infty ,\infty )$

D) $(0,\infty )$

• question_answer111) If$u=-f''(\theta ).\sin \theta +f'(\theta ).\cos \theta$and$v=f''(\theta ).\cos \theta +f'(\theta ).\sin \theta ,$then ${{\int{\left[ {{\left( \frac{du}{d\theta } \right)}^{2}}+{{\left( \frac{dv}{d\theta } \right)}^{2}} \right]}}^{1/2}}d\theta$is equal to

A) $f(\theta )-f''(\theta )+C$

B) $f(\theta )+f''(\theta )+C$

C) $f'(\theta )+f''(\theta )+C$

D) $f'(\theta )-f''(\theta )+C$

• question_answer112) If for every integer$n,\int_{n}^{n+1}{f(x)}\,dx={{n}^{2}},$then the value of$\int_{-2}^{4}{f(x)}\,dx$is

A) 16

B) 14

C) 19

D) None of these

• question_answer113) If$f(x)=\int_{-1}^{x}{|t|dt},$then for any$x\ge 0,f(x)$is equal to

A) $1-{{x}^{2}}$

B) $\frac{1}{2}(1+{{x}^{2}})$

C) $1+{{x}^{2}}$

D) $\frac{1}{2}(1-{{x}^{2}})$

• question_answer114) The area bounded by the parabola${{y}^{2}}=8x$ and its latusrectum, is

A) $\frac{16}{3}$sq units

B) $\frac{32}{3}$sq units

C) $\frac{8}{3}$sq units

D) $\frac{64}{3}$sq units

• question_answer115) The area bounded by the curve$y=2x-{{x}^{2}}$and the line$y=-x$is

A) $\frac{3}{2}$sq units

B) $\frac{9}{3}$sq units

C) $\frac{9}{2}$sq units

D) None of these

• question_answer116) If a, b and c are non-coplanar and$(a+\lambda b).[(b+3c)\times (c-4a)]=0,$then the value of$\lambda$is equal to

A) 0

B) $\frac{1}{12}$

C) $\frac{5}{12}$

D) $3$

• question_answer117) If a and b are unit vectors such that$[a\,b\,a\times b]=\frac{1}{4},$then angle between a and b is

A) $\frac{\pi }{3}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{6}$

D) $\frac{\pi }{2}$

• question_answer118) The area of the triangle having vertices as $i-2j+3k,-2i+3j-k,4i-7j+7k$is

A) 36 sq units

B) 0 sq unit

C) 39 sq units

D) 11 sq units

• question_answer119) If$P(A)=P(B)=x$and $P(A\cap B)=P(A'\cap B')=\frac{1}{3},$ then$x$is equal to

A) $\frac{1}{2}$

B) $\frac{1}{3}$

C) $\frac{1}{4}$

D) $\frac{1}{6}$

• question_answer120) A fair die is tossed eight times. The probability that a third six is observed on the eight throw is

A) $\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{7}}}$

B) $\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}$

C) $\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}$

D) None of the above