# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

### done Rajasthan PET Solved Paper-2007

• question_answer1) A Carnot's engine has an efficiency of 50% at sink temperature$50{}^\circ C$. Calculate the temperature of source.

A) $133{}^\circ C$

B) $143{}^\circ C$

C) $100{}^\circ C$

D) $373{}^\circ C$

• question_answer2) Which of the following is not a state function?

A) Work done at constant pressure

B) Enthalpy

C) Work done by conservative force

D) Work done by non-conservative force

• question_answer3) What is the Q-value of the reaction? $P{{+}^{7}}Li{{\xrightarrow[{}]{{}}}^{4}}He{{+}^{4}}He$ The atomic masses of $^{1}H,\,{{\,}^{4}}He\,\,and\,{{\,}^{7}}Li$are 1.0078254U, 4.0026034U and 7.016004U respectively

A) 17.35 MeV

B) 18.06 MeV

C) 177.35 MeV

D) 170.35 MeV

• question_answer4) If average velocity becomes 4 times then, what will be the effect on rms velocity at that temperature?

A) 1.4 times

B) 4 times

C) 2 times

D) $\frac{1}{4}$times

• question_answer5) An aluminium rod and a copper rod are taken such that their lengths are same and their resistances are also same. The specific resistance of copper is half that of aluminium, but its density is three times that of aluminium. The ratio of the mass of aluminium rod and that of copper rod will be

A) 1/6

B) 2/3

C) 1/3

D) 6

• question_answer6) In a potentiometer, the null point is received at 7th wire. If now we have to change the null point at 9th wire, what should we do?

A) Attach resistance in series with battery

B) Increase resistance in main circuit

C) Decrease resistance in main circuit

D) Decrease applied emf

• question_answer7) The earth moves in an elliptical orbit with the sun S at one of foci as shown in the figure. Its rotational kinetic energy is maximum at the point. A) A

B) B

C) C

D) D

• question_answer8) If BH = $\frac{1}{\sqrt{3}}{{B}_{V}},$find the angle of dip. (where symbols have at their usual meanings)

A) $60{}^\circ$

B) $30{}^\circ$

C) $45{}^\circ$

D) $90{}^\circ$

• question_answer9) Reverberation time does not depend upon

A) temperature

B) volume of room

C) size of window

D) carpet and curtain

• question_answer10) The water of volume$4\text{ }{{m}^{3}}$at the height 20 m is pressed by$2\times {{10}^{5}}N$pressure. The work done by motor is

A) $8\times {{10}^{5}}J$

B) $16\times {{10}^{5}}J$

C) $12\times {{10}^{5}}J$

D) $32\times {{10}^{5}}J$

• question_answer11) The wavelength of K $\alpha$ line in copper is 1.5$\overset{o}{\mathop{\text{A}}}\,$. The ionization energy of K electron in copper is

A) $11.2\times {{10}^{-17}}J$

B) $12.9\times {{10}^{-16}}J$

C) $1.7\times {{10}^{-15}}J$

D) $10\times {{10}^{-16}}J$

• question_answer12) If mass [M], length [L], time [T] and current [A] as fundamental units, the dimensional formula for permeability will be

A) $[{{M}^{-1}}L{{T}^{-2}}A]$

B) $[M{{L}^{-2}}{{T}^{-2}}{{A}^{-1}}]$

C) $[ML{{T}^{-2}}{{A}^{-2}}]$

D) $[ML{{T}^{-1}}{{A}^{-1}}]$

• question_answer13) If in the following figure, height of object is${{H}_{1}}=+$2.5 cm, then height of image${{H}_{2}}$formed is A) $-5\text{ }cm$

B) +5 cm

C) +7.5cm

D) $-7.5\text{ }cm$

• question_answer14) Moment of inertia of ring about its diameter is$I$. Then. moment of inertia about an axis passing through centre and perpendicular to its plane is

A) $2I$

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

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

D) $I$

• question_answer15) Which of the following is true regarding beats?

A) Frequency different, amplitude same

B) Frequency same, amplitude same

C) Frequency same, amplitude different

D) None of the above

• question_answer16) When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

A) More frequency, less wavelength

B) More frequency, more wavelength

C) Less frequency, less wavelength

D) More frequency, constant wavelength

• question_answer17) In which of the following, force is constant?

A) Uniform circular motion

B) Elliptical motion

C) Uniform linear motion

D) Projectile motion

• question_answer18) The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which car can be driven round a curve of radius 40 m without skidding is (assume $g=10m/{{s}^{2}}$)

A) 40 m/s

B) 20 m/s

C) 15 m/s

D) 10 m/s

• question_answer19) A bomb of mass 3 kg explodes in air and splits in two parts of 2 kg and 1 kg. Small peace moves with a speed of 80 m/s, then the total energy of both the pieces will be

A) 1.07 kJ

B) 2.14 kJ

C) 2.4 kJ

D) 4.8 kJ

• question_answer20) If${{k}_{s}}$and${{k}_{p}}$respectively are effective spring constant in series and parallel combination of springs as shown in figure, find $\frac{{{k}_{s}}}{{{k}_{p}}}$ A) $\frac{9}{2}$

B) $\frac{3}{7}$

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

D) $\frac{7}{3}$

• question_answer21) A bob of pendulum was filled with Hg and entire Hg is drained out, then the time period of pendulum A) remains unchanged

B) decreases

C) increases

D) first increases then decreases

• question_answer22) The minimum force required to move a body of mass m vertically upward is

A) $mg$

B) $mg/2$

C) more than 2 mg

D) more than mg

• question_answer23) The uncertainty in the momentum of a particle is${{10}^{-30}}kg-m/s$. The minimum uncertainty in its position will be

A) ${{10}^{-8}}m$

B) ${{10}^{-12}}m$

C) ${{10}^{-16}}m$

D) ${{10}^{-4}}m$

• question_answer24) If distance between earth and sun become four times than time period becomes

A) 4 times

B) 8 times

C) 1/4 times

D) 1/8 times

• question_answer25) An air bubble is contained inside water. It behaves as

A) concave lens

B) convex lens

C) neither convex nor concave

D) Cannot say

• question_answer26) The power dissipated across resistance R which is connected across a battery of potential V is P. If resistance is doubled, then the power becomes

A) 1/2

B) 2

C) 1/4

D) 2

• question_answer27) BE/nucleon relation with mass number

A) first decreases then increases

B) first increases then decreases

C) increases

D) decreases

• question_answer28) A 100 V, AC source of frequency 500 Hz is connected to an L-C-R circuit with L = 8.1 mH, C = 12.5 $\mu$ F, R = 10 $\Omega$ all connected. What is the quality factor of circuit?

A) 2.02

B) 2.5434

C) 20.54

D) 200.54

• question_answer29) The inductance of a coil is L = 10 H and resistance R = 5$\Omega$. If applied voltage of battery is 10 V and it switches off in 1 millisecond, find induced emf of inductor.

A) $2\times {{10}^{4}}V$

B) $1.2\times {{10}^{4}}V$

C) $2\times {{10}^{-4}}V$

D) None of these

• question_answer30) Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momenta of B to A is

A) 1 : 3

B) 3 : 1

C) 1 : $\sqrt{3}$

D) $\sqrt{3}$: 1

• question_answer31) Which of the following four fundamental forces has shortest range?

A) Nuclear

B) Gravitational

C) Electromagnetic

D) Weak force

• question_answer32) A proton is moving in a uniform magnetic field B in a circular path of radius a in a direction perpendicular to Z axis along which field B exists. Calculate the angular momentum, if the radius is a and charge on proton is e.

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

B) $e{{B}^{2}}a$

C) ${{a}^{2}}eB$

D) $aeB$

• question_answer33) If acceleration of a particle at any time is given by $a=2t+5$ Calculate, the velocity after 5s, if it starts from rest.

A) 50 m/s

B) 25 m/s

C) 100 m/s

D) 75 m/s

• question_answer34) To look inside an atom of diameter 100 pm we have to penetrate it upto a breadth of 10 pm. If we use an electron microscope, the minimum required energy will be

A) 1.5 keV

B) 15 keV

C) 150 keV

D) 1.05 keV

• question_answer35) A body from height h is dropped. If the coefficient of restitution is e, then calculate the height achieved after one bounce.

A) ${{h}_{1}}={{e}^{2}}h$

B) ${{h}_{1}}={{e}^{4}}h$

C) ${{h}_{1}}=eh$

D) ${{h}_{1}}=h/e$

• question_answer36) A body moves with uniform acceleration, then which of the following graph is correct?

A) B) C) D) • question_answer37) Two vectors are perpendicular, if

A) $A\to .B\to =1$

B) $A\to \times B\to =0$

C) $A\to .B\to =0$

D) $A\to \times B\to =AB$

• question_answer38) If coefficient of static friction is ${{\mu }_{s}}$and coefficient of kinetic friction is ${{\mu }_{k}}$, which is correct?

A) ${{\mu }_{s}}={{\mu }_{k}}$

B) ${{\mu }_{s}}>{{\mu }_{k}}$

C) ${{\mu }_{s}}<{{\mu }_{k}}$

D) Cannot predicted

• question_answer39) Light year is used to measure

A) distance between stars

B) distance between atoms

C) revolution time of earth around sun

D) None of the above

• question_answer40) Electromagnetic waves are produced by

A) accelerated charged particle

B) decelerated charged particle

C) charge in uniform motion

D) None of the above

• question_answer41) A beam of proton with velocity$4\times {{10}^{5}}m/s$enters a uniform magnetic field of 0.3 T at an angle of $60{}^\circ$to the magnetic field. Find the radius of the helical path taken by the proton beam.

A) 0.2 cm

B) 1.2 cm

C) 2.2 cm

D) 0.122 cm

• question_answer42) Three progressive waves A, B and C are shown in the figure with respect to A, the progressive wave A) B lags by $\frac{\pi }{2}$ and C leads by $\frac{\pi }{2}$

B) B lags by $\pi$ and C leads by $\pi$

C) B leads by $\frac{\pi }{2}$ and C lags by $\frac{\pi }{2}$

D) B leads by $\pi$ and C lags by $\pi$

• question_answer43) When light passes from one medium to other then which will not change?

A) Frequency

B) Wavelength

C) Amplitude

D) Velocity

• question_answer44) Total internal reflection takes place

A) When a ray moves from denser to rarer and incident angle is greater than critical angle.

B) When a ray moves from rarer to denser and incident angle is less than critical angle.

C) When a ray moves from rarer to denser and incident angle is equal to critical angle.

D) None of the above

• question_answer45) A beam of light travelling along z-axis is described by the electric field ${{E}_{y}}=(600\,V/m)\sin \omega \left( t-\frac{x}{c} \right)$ then maximum magnetic force on a charge$q=2e$ moving along y-axis with a speed of $3.0\times {{10}^{7}}m/s$is$(e=1.6\times {{10}^{-19}}C)$

A) $19.2\times {{10}^{-17}}N$

B) $1.92\times {{10}^{-17}}N$

C) 0.992 N

D) None of these

• question_answer46) In hydrogen atom, transition takes from state 2 to 1, an electromagnetic wave of frequency $2.7\times {{10}^{15}}$Hz is emitted. If this transition takes place from 3 to 1, emitted frequency will be

A) $3.2\times {{10}^{15}}z$

B) $32\times {{10}^{15}}Hz$

C) $1.6\times 15\text{ }Hz$

D) $16\times {{10}^{15}}Hz$

• question_answer47) The equipotential surface related to an electric field, increases in magnitude along$x-$axis is

A) plane parallel to y-z plane

B) plane parallel to x-y plane

C) plane parallel to x-z plane

D) equi axis cylinder of increasing radius about$x-$axis

• question_answer48) If 200 MeV energy is released in the fission of 92 U235. What will be the required number of fission per second to produce 1 kW of power?

A) $3.12\times {{10}^{13}}$

B) $3.12\times {{10}^{3}}$

C) $3.1\times {{10}^{17}}$

D) $3.12\times {{10}^{19}}$

• question_answer49) During projectile motion, the horizontal velocity

A) first increases then decreases

B) first decreases then increases

C) always increases

D) always constant

• question_answer50) Find the ratio of acceleration due to gravity g at depth d and at height A, where, d = 2h.

A) 1 : 1

B) 1 : 2

C) 2 : 1

D) 1 : 4

• question_answer51) What is the stoichiometry coefficient of$Ca$in the following reaction? $Ca+A{{l}^{3+}}\xrightarrow[{}]{{}}C{{a}^{2+}}+Al$

A) 2

B) 1

C) 3

D) 4

• question_answer52) What is the value of x in the potash alum ${{K}_{2}}S{{O}_{4}}.A{{l}_{x}}{{(S{{O}_{4}})}_{3}}.24{{H}_{2}}O$?

A) 4

B) 1

C) 2

D) None of these

• question_answer53) Ozone is useful in the purification of water because

A) it releases oxygen on dissociation

B) it does not give unpleasant smell like chlorine

C) it acts as bactericide and destroys the bacteria, fungi etc

D) All of the above

• question_answer54) Internal energy is the sum of

A) kinetic energy and potential energy

B) all types of energy of system

C) energies of internal system

D) None of the above

• question_answer55) Which of the following is a combustion reaction?

A) $C+{{O}_{2}}\xrightarrow[{}]{{}}C{{O}_{2}}$

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

C) $Mg+{{O}_{2}}\xrightarrow[{}]{{}}MgO$

D) All of the above

• question_answer56) ${{C}_{6}}{{H}_{5}}^{14}COOH$is heated with$N{{a}_{2}}C{{O}_{3}}$to release

A) $C{{O}_{2}}$

B) $^{14}C{{O}_{2}}$

C) CO

D) None of these

• question_answer57) The mass of two molecules A and B are 100 kg and 64 kg respectively. If the diffusion rate of A is$12\times {{10}^{-3}}$then, the diffusion rate of B will be

A) $15\times {{10}^{-3}}$

B) $64\times {{10}^{-3}}$

C) $5\times {{10}^{-3}}$

D) $46\times {{10}^{-3}}$

• question_answer58) Commercially ethyl bromide is manufactured by

A) ethyl alcohol $+HBr$

B) ethanol$+B{{r}_{2}}$

C) alcohol $+HBr$

D) None of the above

• question_answer59) In the presence of$Fe/HCl,$aniline obtains from which of the following?

A) Benzene

B) Nitrobenzene

C) Dinitrobenzene

D) None of these

• question_answer60) Which of the following is a strong base?

A) Benzamide

B) Butanamine

C) Nitrobenzene

D) Benzene

• question_answer61) On comparison of S and$S$the${{S}^{2-}}$has

A) large radius and large size

B) small radius and large size

C) large radius and small size

D) small radius and small size

• question_answer62) Which of the following is not correct?

A) ${{t}_{1/2}}=\frac{0.693}{k}$

B) $N={{N}_{0}}{{e}^{-kt}}$

C) $\frac{1}{N}-\frac{1}{{{N}_{0}}}=In\,k{{t}_{1/2}}$

D) None of these

• question_answer63) Which of the following is the second most electronegative element?

A) Oxygen

B) Nitrogen

C) Fluorine

D) Sulphur

• question_answer64) Which of the following is not correct according to Aufbau's rule?

A) B) C) D) • question_answer65) Which of the following has the lowest ionization potential?

A) Oxygen

B) Nitrogen

C) Fluorine

D) Sulphur

• question_answer66) On homolytic fission,$C{{H}_{3}}C{{H}_{2}}Cl$gives

A) $C{{H}_{3}}\overset{\bullet }{\mathop{C}}\,{{H}_{2}}$and$C\overset{\bullet }{\mathop{l}}\,$

B) $C{{H}_{3}}\overset{\oplus }{\mathop{C}}\,{{H}_{2}}$and$C{{l}^{-}}$

C) $C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}$and$C\overset{\bullet }{\mathop{I}}\,$

D) $C{{H}_{3}}\overset{\bullet }{\mathop{C}}\,{{H}_{2}}$

• question_answer67) If the diffusion rate of$N{{H}_{3}}$is double of X, then the molecular weight of X will be

A) 68

B) 48

C) 12

D) 8

• question_answer68) The bond order of$C-C$bond of benzene.

A) 1

B) 2

C) between 1 and 2

D) None of these

• question_answer69) The decreasing order of bond length of following , Ethane Ethene Ethyne

A) $A>B>C$

B) $B>A>C$

C) $C>B>A$

D) $C>A>B$

• question_answer70) What is the range of the size of colloidal particle?

A) 1 to 100 nm

B) 1 to 1000 cm

C) 1 to 1000 mm

D) 1 to 100 km

• question_answer71) $Z{{n}^{2+}}\xrightarrow[{}]{{}}Zn(s)$ $E{}^\circ =-0.76V$ $C{{u}^{2+}}\xrightarrow[{}]{{}}Cu(s)$ $E{}^\circ =-0.34V$ Which of the following is the spontaneous reaction?

A) $Z{{n}^{2+}}+Cu\xrightarrow[{}]{{}}Zn+C{{u}^{2+}}$

B) $C{{u}^{2+}}+Zn\xrightarrow[{}]{{}}Cu+Z{{n}^{2+}}$

C) $Z{{n}^{2+}}+C{{u}^{2+}}\xrightarrow[{}]{{}}Zn+Cu$

D) None of the above

• question_answer72) Which of the following element has the maximum electron affinity?

A) Fluorine

B) Chlorine

C) Sulphur

D) Xenon

• question_answer73) Which is the most reactive inert gas?

A) $He$

B) $Ne$

C) $Ar$

D) $Xe$

• question_answer74) Which type of bond presents in$Xe$molecule?

A) Covalent

B) lon-dipole

C) van der Waals

D) Dipole-dipole

• question_answer75) Which of the following is irreversible reaction?

A) $2N{{H}_{3}}\xrightarrow[{}]{{}}{{N}_{2}}+3{{H}_{2}}$

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

C) $KCl{{O}_{3}}\xrightarrow[{}]{{}}KCl+{{O}_{2}}$

D) $2S{{O}_{3}}\xrightarrow[{}]{{}}2S{{O}_{2}}+{{O}_{2}}$

A) ${{H}_{2}}O$

B) ${{D}_{2}}O$

C) ${{H}_{2}}{{O}_{2}}$

D) None of these

• question_answer77) ${{H}_{2}}S$is not a

A) reducing agent

B) acidic

C) oxidising agent

D) None of these

• question_answer78) At constant temperature, the curve between p and V is

A) straight line

B) increasing curve

C) straight line with slope

D) None of the above

• question_answer79) At constant temperature, on doubling the p and V, the reversible constant will become

A) constant

B) double

C) quarter

D) None of these

• question_answer80) The electronic configuration of$M{{n}^{2+}}$is

A) $[Ne]3{{d}^{5}},4{{s}^{0}}$

B) $[Ar]3{{d}^{5}},4{{s}^{2}}$

C) $[Ar]3{{d}^{5}},4{{s}^{0}}$

D) $[Ne]3{{d}^{5}},4{{s}^{2}}$

• question_answer81) Generally the +3 oxidation state is

A) Ni (28)

B) Fe (26)

C) Zn (30)

D) Cu (29)

• question_answer82) The structure of 1, 2-dihydroxy butane is

A) $C(OH)-C(OH)-C-C$

B) $C-C{{(OH)}_{2}}-C-C$

C) $(OH)C-C-C-C(OH)$

D) $C-C(OH)-C(OH)-C$

• question_answer83) The atomic size increases on moving downward because

A) the number of electrons increases

B) the number of protons and neutrons increases

C) the number of protons increases

D) the number of protons, neutrons and electrons increases

• question_answer84) The ionization energy decreases on moving downward because

A) charge increases

B) atomic size increases

C) atomic size decreases

D) screening effect decreases

• question_answer85) Which of the following is tribasic acid?

A) ${{H}_{3}}P{{O}_{2}}$

B) ${{H}_{3}}P{{O}_{4}}$

C) ${{H}_{4}}{{P}_{2}}{{O}_{7}}$

D) ${{H}_{3}}P{{O}_{3}}$

• question_answer86) Which has the maximum dipole moment?

A) B) C) D) • question_answer87) In electrolytic cell, the cathode acts as

A) oxidising agent

B) reducing agent

C) Either [a] or [b]

D) Neither [a] nor [b]

• question_answer88) The order of reaction may be

A) zero

B) fraction

C) whole number

D) zero, fraction, whole number

• question_answer89) Which has the maximum relative ionization power?

A) $\alpha -$rays

B) $\beta -$rays

C) $\gamma -$rays

D) $X-$rays

• question_answer90) Which of the following is a vitamin?

A) Benzoic acid

B) Ascorbic acid

C) Oxalic acid

D) Formic acid

• question_answer91) Which isomerism is shown by following compounds? $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH$and$C{{H}_{3}}C{{H}_{2}}OC{{H}_{3}}$

A) Position isomerism

B) Functional isomerism

C) Structural isomerism

D) Chain isomerism

A) $P{{b}_{3}}{{O}_{4}}$

B) $PbO$

C) $2PbC{{O}_{3}}.Pb{{(OH)}_{2}}$

D) $Pb{{(C{{H}_{3}}COO)}_{2}}.Pb{{(OH)}_{2}}$

• question_answer93) The blister copper is

A) impure copper

B) alloy of copper

C) pure copper

D) copper with 1% impurity

• question_answer94) Claisen condensation is not given by

A) B) C) D) • question_answer95) $AgN{{O}_{3}}$does not give precipitate with$CHC{{l}_{3}}$ because

A) $CHC{{l}_{3}}$does not dissociate in water

B) Chemically$AgN{{O}_{3}}$is unreactive

C) Chemically$CH{{l}_{3}}$is unreactive

D) None of the above

• question_answer96) In$_{90}T{{h}^{228}}{{\xrightarrow[{}]{{}}}_{83}}B{{i}^{212}},$the emitted$\alpha$and$\beta$ particles are

A) $4\alpha ,1\beta$

B) $4\alpha ,2\beta$

C) $5\alpha ,1\beta$

D) $5\alpha ,2\beta$

• question_answer97) Which of the following is obtained on the hydrolysis of$PC{{l}_{3}}$?

A) ${{H}_{3}}P{{O}_{3}}$

B) $P{{H}_{3}}$

C) ${{H}_{3}}P{{O}_{4}}$

D) $POC{{l}_{3}}$

• question_answer98) Which bond is presents in protein and peptides?

A) $-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-NH-$

B) $-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-O-$

C) $-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-O-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-$

D) $-NH-$

• question_answer99) Blood cells do not shrink in blood, because blood is

A) hypotonic

B) isotonic

C) isomolecular

D) hypertonic

• question_answer100) On isothermal expansion of ideal gas, its

A) internal energy increases

B) enthalpy increases

C) enthalpy becomes zero on decreasing

D) enthalpy remains unchanged

• question_answer101) Let the coordinates of P are (1,0) and point Q lies on the curve${{y}^{2}}=8x$. The locus of the midpoint of PQ is

A) ${{y}^{2}}-4x+2=0$

B) ${{y}^{2}}+4x+2=0$

C) ${{x}^{2}}+4y+2=0$

D) ${{x}^{2}}-4y+2=0$

• question_answer102) If${{A}^{2}}-A+I=O,$then inverse of A is

A) $A+I$

B) A

C) $A-I$

D) $I-A$

• question_answer103) If$1,\omega$and${{\omega }^{2}}$are the cube roots of unity, then the roots of the equation${{(x-1)}^{3}}+8=0$are

A) $-1,-1+2\omega ,-1-2{{\omega }^{2}}$

B) $-1,-1,-1$

C) $-1,1-2\omega ,1-2{{\omega }^{2}}$

D) $-1,1+2\omega ,1+2{{\omega }^{2}}$

• question_answer104) The value of $\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{{{n}^{2}}}{{\sec }^{2}}\frac{1}{{{n}^{2}}}+\frac{2}{{{n}^{2}}}{{\sec }^{2}}\frac{4}{{{n}^{2}}}+...+\frac{1}{n}{{\sec }^{2}}1 \right]$is

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

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

C) $\tan 1$

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

• question_answer105) Area of the greatest rectangle that can be inscribed in the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$is

A) $2ab$

B) $ab$

C) $\sqrt{ab}$

D) $\frac{a}{b}$

• question_answer106) The order and degree of the differential equation of the family of curve ${{y}^{2}}=2c(x+\sqrt{c}),$where c is a arbitrary constant, is

A) order 1, degree 2

B) order 1, degree 1

C) order 1, degree 3

D) order 2, degree 2

• question_answer107) If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the rank of SACHIN is

A) 601

B) 600

C) 603

D) 602

• question_answer108) The value of$^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}}$is

A) $^{55}{{C}_{4}}$

B) $^{55}{{C}_{3}}$

C) $^{56}{{C}_{3}}$

D) $^{56}{{C}_{4}}$

• question_answer109) If the coefficient of${{x}^{4}}$in the expansion of ${{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}},$is equal to the coefficient of ${{x}^{-7}}$in the expansion of${{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},$then the relation between a and b is

A) $a-b=1$

B) $a+b=1$

C) $\frac{a}{b}=1$

D) $ab=1$

• question_answer110) Let$f:(-1,1)\to B$is defined as $f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}.$Function$f$is one-one and onto, then the interval B is

A) $\left( 0,\frac{\pi }{2} \right)$

B) $\left[ 0,\frac{\pi }{2} \right)$

C) $\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]$

D) $\left( -\frac{\pi }{2},\frac{\pi }{2} \right)$

• question_answer111) lf$w=\frac{z}{z-\frac{i}{3}}$and$|w|=1,$ then z lies on

A) a ellipse

B) a circle

C) a straight line

D) a parabola

• question_answer112) If${{a}^{2}}+{{b}^{2}}+{{c}^{2}}=-2$and $f(x)=\left| \begin{matrix} 1+{{a}^{2}}x & (1+{{b}^{2}})x & (1+{{c}^{2}})x \\ (1+{{a}^{2}})x & 1+{{b}^{2}}x & (1+{{c}^{2}})x \\ (1+{{a}^{2}})x & (1+{{b}^{2}})x & 1+{{c}^{2}}x \\ \end{matrix} \right|,$ then$f(x)$is a polynomial of power

A) 1

B) 0

C) 3

D) 2

• question_answer113) Let$f(x)$is differentiable at$x=1$and $\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}(1+h)=5,$then the value of$f'(1)$is

A) 3

B) 4

C) 5

D) 6

• question_answer114) The value of$\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{\int_{0}^{{{x}^{2}}}{{{\sec }^{2}}t\,dt}}{x\sin x} \right)$is

A) 3

B) 2

C) 1

D) 0

• question_answer115) In a triangle, let$\angle C=\pi /2$. If r is the radius of incircle and R is the radius of circumcircle, then value of$2(r+R)$is

A) $b+c$

B) $a+b$

C) $a+b+c$

D) $c+a$

• question_answer116) If${{\cos }^{-1}}x-{{\cos }^{-1}}\frac{y}{2}=\alpha ,$then the value of $4{{x}^{2}}-4xy\,cos\alpha +{{y}^{2}}$is

A) $2\text{ }si{{n}^{2}}\alpha$

B) 4

C) $\text{4 }si{{n}^{2}}\alpha$

D) $\text{-4 }si{{n}^{2}}\alpha$

• question_answer117) If$\alpha$and$\beta$are two unequal roots of the equation$a{{x}^{2}}+bx+c=0,$ then the value of$\underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}}$is

A) $\frac{{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}$

B) $0$

C) $\frac{-{{a}^{2}}}{2}{{(\alpha -\beta )}^{2}}$

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

• question_answer118) If$x\frac{dy}{dx}y=y(log\text{ }y-log\text{ }x+1),$then, the solution of the equation is

A) $y\log \left( \frac{x}{y} \right)=cx$

B) $x\log \left( \frac{y}{x} \right)=cy$

C) $\log \left( \frac{y}{x} \right)=cx$

D) $\log \left( \frac{x}{y} \right)=cy$

• question_answer119) The value of${{\int{\left\{ \frac{(\log x-1)}{1+{{(\log x)}^{2}}} \right\}}}^{2}}dx$is

A) $\frac{\log x}{{{(\log x)}^{2}}+1}+c$

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

C) $\frac{x{{e}^{x}}}{1+{{x}^{2}}}+c$

D) $\frac{x}{{{(\log x)}^{2}}+1}+c$

• question_answer120) Let$f:R\to R$is a differentiable function$f(2)=6,f'(x)=\frac{1}{48},$then$\underset{x\to 2}{\mathop{\lim }}\,\int_{6}^{f(x)}{\frac{4{{t}^{3}}}{x-2}}dt$is equal to

A) 24

B) 36

C) 12

D) 18

• question_answer121) Let a non-negative continuous function$f(x)$is such that the area of the region bounded by the curve$y=f(x),$$x-$axis and the lines$x=\frac{\pi }{4}$ands$x=\beta >\frac{\pi }{4}$is$\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right),$then the value of $f\left( \frac{\pi }{2} \right)$is

A) $\left( \frac{\pi }{4}+\sqrt{2}-1 \right)$

B) $\left( \frac{\pi }{4}-\sqrt{2}+1 \right)$

C) $\left( 1-\frac{\pi }{4}-\sqrt{2} \right)$

D) $\left( 1-\frac{\pi }{4}+\sqrt{2} \right)$

• question_answer122) The area of the region bounded by the curve $y=lo{{g}_{e}}(x+e)$and axes is

A) 1

B) 2

C) 3

D) 4

• question_answer123) The parabolas${{y}^{2}}=4x$and${{x}^{2}}=4y$divide the square region bounded by the lines$x=4,\text{ }y=4$and the coordinates axes. If ${{S}_{1}},{{S}_{2}},{{S}_{3}}$are respectively the areas of these parts numbered from top to bottom, then ${{S}_{1}}:{{S}_{2}}:{{S}_{3}}$is

A) 1 : 2 : 1

B) 1 : 2 : 3

C) 2 : 1 : 2

D) 1 : 1 : 1

• question_answer124) If the plane$2ax-3at+4az+6=0$passes through the midpoint of the line joining the centres of the spheres ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13$ and${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8,$then a equals

A) $-1$

B) 1

C) $-2$

D) 2

• question_answer125) The distance between the line$\overrightarrow{a}=2\hat{i}-2\hat{j}+3\hat{k}$ $\lambda (\hat{i}+5\hat{j}+\hat{k})=5$and the plane$\overrightarrow{r}.(\hat{i}+5\hat{j}+\hat{k})=5$is

A) $\frac{10}{9}$

B) $\frac{10}{3\sqrt{3}}$

C) $\frac{3}{10}$

D) $\frac{10}{3}$

• question_answer126) For any vector$\overrightarrow{a}$the value of${{(\overrightarrow{a}\times i)}^{2}}+{{(\overrightarrow{a}\times \hat{j})}^{2}}+{{(\overrightarrow{a}\times \hat{k})}^{2}}$is equal to

A) $3{{\overrightarrow{a}}^{2}}$

B) ${{\overrightarrow{a}}^{2}}$

C) $2{{\overrightarrow{a}}^{2}}$

D) $4{{\overrightarrow{a}}^{2}}$

• question_answer127) If non-zero numbers a, b, c are in HP, then line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$always passes through a fixed point. That point is

A) $(-1,2)$

B) $(-1,-2)$

C) $(1,-2)$

D) $\left( 1,-\frac{1}{2} \right)$

• question_answer128) If the circles ${{x}^{2}}+{{y}^{2}}+2ax+cy+a=0$and ${{x}^{2}}+{{y}^{2}}-3ax+dy-1=0$intersects at two different points P and Q, then the line $5x+by-a=0$passes through the points P and Q for

A) only one value of a

B) no value of a

C) infinite values of a

D) only two values of a

• question_answer129) In an ellipse OB is a semi-minor axis, F and F' are its focus and angle FBF' is right angle. Then, eccentricity of the ellipse is

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

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

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

D) $\frac{1}{\sqrt{3}}$

• question_answer130) If$y=ax+p$is a tangent to the hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,$then the locus of the point $P(\alpha ,\beta )$or is

A) an ellipse

B) a circle

C) a parabola

D) a hyperbola

• question_answer131) If the angle between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$and the plane$2x-y+\sqrt{\lambda z}+4=0$is$\theta$such that$\sin \theta =\frac{1}{3},$then the value of$\lambda$is,

A) $\frac{5}{3}$

B) $-\frac{3}{5}$

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

D) $-\frac{4}{3}$

• question_answer132) Let A and B be two events such that$P\overline{(A\cup B)}=\frac{1}{6},P(A\cap B)=\frac{1}{4}$an$P(\overline{A})=\frac{1}{4},$where A stands for complement of event A. Then, events A and B are

A) mutually exclusive and independent

B) independent but not equally likely

C) equally likely but not independent

D) equally likely and mutually exclusive

• question_answer133) Three houses are available in a locality. Three persons apply for the houses. Each applie for one house without consulting others. The probability that all three apply for the same house, is

A) $\frac{2}{9}$

B) $\frac{1}{9}$

C) $\frac{8}{9}$

D) $\frac{7}{9}$

• question_answer134) If$\overrightarrow{a}=\hat{i}-\hat{k},\overrightarrow{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$and$\overrightarrow{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k},$then$[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]$depends on

A) only y

B) only$x$

C) both$x$and y

D) neither$x$ nor y

• question_answer135) Let a, b and c are different non-negative numbers. If vectors$a\hat{i}+a\hat{j}+c\hat{k},\text{ }\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$lies in the same plane, then the value of c is

A) geometric mean of a and b

B) arithmetic mean of a and b

C) zero

D) harmonic mean of a and b

• question_answer136) If$\vec{a},\text{ }\overrightarrow{b}$and$\overrightarrow{c}$are non-coplanar vectors and$\lambda$is a real number, then $[\lambda (\overrightarrow{a}+\overrightarrow{b}){{\lambda }^{2}}\overrightarrow{b}\,\lambda \,\overrightarrow{c}]=[\overrightarrow{a}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{b}]$for

A) only one value of $\lambda$

B) no value of $\lambda$

C) only three values of$\lambda$

D) only two values of$\lambda$

• question_answer137) The value of$\int_{-\pi }^{\pi }{\frac{{{\cos }^{2}}x}{1+{{a}^{x}}}}dx,a>0$is

A) $a\pi$

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

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

D) $2\pi$

• question_answer138) The radius of the circle in which the sphere${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x+z-2=0$cuts by the plane $x+2y-z=4,$is

A) 3

B) 1

C) 2

D) $\sqrt{2}$

• question_answer139) The value of$\tan \left\{ {{\cos }^{-1}}\left( -\frac{2}{7} \right)-\frac{\pi }{2} \right\}$is

A) $\frac{2}{3\sqrt{5}}$

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

C) $\frac{1}{\sqrt{5}}$

D) $\frac{4}{\sqrt{5}}$

• question_answer140) If${{\tan }^{-1}}(x-1)+{{\tan }^{-1}}x+{{\tan }^{-1}}(x+1)$ $={{\tan }^{-1}}3x,$then the value of$x$is

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

B) $0,\frac{1}{2}$

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

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

• question_answer141) The sum of the sequence$1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+......\infty$is

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

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

C) $\frac{e-1}{2\sqrt{e}}$

D) $\frac{e+1}{2\sqrt{e}}$

• question_answer142) If${{x}_{0}}=1$is to find the real roots of the equation ${{x}^{2}}-x=2$by Newton-Raphson's method then the value of${{x}_{2}}$is

A) 9/15

B) 3

C) 11/5

D) 19/5

• question_answer143) Let$R=\{(1,\text{ }3),\text{(}4,\text{ }2),(2,\text{ }4),(2,\text{ }3),(3,\text{ }1)\}$is a relation on the set$A=\{1,2,3,4\}$. Then, relation R is

A) a function

B) transitive

C) not symmetric

D) reflexive

• question_answer144) Let z and w are two complex numbers such that$\overline{z}+i\overline{w}=0$and arg$zw=\pi ,$then arg z is equal to

A) $\pi /4$

B) $\pi /2$

C) $3\pi /4$

D) $5\pi /4$

• question_answer145) If$z=x-iy$and${{z}^{1/3}}=p+iq,$then${\left( \frac{x}{p}+\frac{y}{q} \right)}/{({{p}^{2}}+{{q}^{2}})}\;$equal to

A) 1

B) $-1$

C) 2

D) $-2$

• question_answer146) If $|{{z}^{2}}-1|=|{{z}^{2}}|+1,$.then z

A) lies on real axis

B) lies on imaginary axis

C) lies on a circle

D) lies on an ellipse

• question_answer147) Let$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right]$and$(10)B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right]$ If B is the inverse of matrix A, then the value of $\alpha$is

A) $-2$

B) $-1$

C) 2

D) 5

• question_answer148) If ${{a}_{1}},{{a}_{2}},{{a}_{3}},.....,{{a}_{n}}$are in GP, then the value of $\left| \begin{matrix} \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}} \\ \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}} \\ \log {{a}_{n+6}} & \log {{a}_{n+7}} & \log {{a}_{n+8}} \\ \end{matrix} \right|$is

A) 0

B) 1

C) 2

D) $-2$

• question_answer149) Let the arithmetic mean and geometric mean of two numbers are 9 and 4 respectively. Then, these numbers are the roots of following equation

A) ${{x}^{2}}+18x+16=0$

B) ${{x}^{2}}-18x+16=0$

C) ${{x}^{2}}+18x-16=0$

D) ${{x}^{2}}-18x-16=0$

• question_answer150) If$(1-p)$is one root of the equation ${{x}^{2}}+px+(1-p)=0,$then its roots are

A) $0,\text{ }1$

B) $-1,\text{ }1$

C) $0,-1$

D) $-1,\text{ }2$

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