# Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2008

### done Manipal Engineering Solved Paper-2008

• question_answer1) One drop of soap bubble of diameter D breakes into 27 drops having surface tension T. The change in surface energy is

A) $2\pi T{{D}^{2}}$

B) $4\pi T{{D}^{2}}$

C) $\pi T{{D}^{2}}$

D) $8\pi T{{D}^{2}}$

• question_answer2) The period of a planet around sun is 27 times that of earth. The ratio of radius of planets orbit to the radius of earths orbit is

A) 4

B) 9

C) 64

D) 27

• question_answer3) Three particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is

A) zero

B) $\frac{3GM}{{{L}^{2}}}$

C) $\frac{9GM}{{{L}^{2}}}$

D) $\frac{12}{\sqrt{3}}\frac{GM}{{{L}^{2}}}$

• question_answer4) In a turbulent flow, the velocity of the liquid in contact with the walls of the tube is

A) zero

B) maximum

C) in between zero and maximum

D) equal to critical velocity

• question_answer5) A charge q is fixed. Another charge Q is brought near it and rotated in a circle of radius r around it. Work done during rotation is

A) zero

B) $\frac{Qq}{4\pi G{{\varepsilon }_{0}}r}$

C) $\frac{Qq}{2\pi G{{\varepsilon }_{0}}r}$

D) None of these

• question_answer6) A diode having potential difference 0.5 V across its junction which does not depend on current, is connected in series with resistance of 20 $\Omega$ across source. If 0.1 A current passes through resistance then what is the voltage of the source?

A) 1.5V

B) 2.0V

C) 2.5 V

D) 5 V

• question_answer7) Dipole is placed parallel to the electric field. If Q is the work done in rotating the dipole by 60?, then work done in rotating it by 180? is

A) 2W

B) 3W

C) 4W

D) W/2

• question_answer8) An electron of charge e moves in a circular orbit of radius r around the nucleus at a frequency v. The magnetic moment associated with the orbital motion of the electron is

A) $\pi ve{{r}^{2}}$

B) $\frac{\pi v{{r}^{2}}}{e}$

C) $\frac{\pi v\,e}{r}$

D) $\frac{\pi v{{r}^{2}}}{v}$

• question_answer9) A and B are two identical spherical charged bodies which repel each other with force F, kept at a finite distance. A third uncharged sphere of the same size is brought in contact with sphere B and removed. It is then kept at mid-point of A and B. Find the magnitude of force on C.

A) F/2

B) F/8

C) F

D) Zero

• question_answer10) A wave equation is $y=0.1\sin [100\pi t-kx]$and wave velocity is 100 m/s, its wave number is equal to

A) $1{{m}^{-1}}$

B) $2{{m}^{-1}}$

C) $\pi {{m}^{-1}}$

D) $2\pi {{m}^{-1}}$

• question_answer11) Volume-temperature graph at atmospheric pressure for a monoatomic gas $\left( V\text{ }in\text{ }{{m}^{3}},\text{ }T\text{ }in\text{ }{}^\circ C \right)$ is

A)

B)

C)

D)

• question_answer12) An optically active compound

A) rotates the plane polarized light

B) changing the direction of polarized light

C) do not allow plane polarized light to pass through

D) None of the above

• question_answer13) Power applied to a particle varies with time as $P=(3{{t}^{2}}-2t+1)$ W, where t is in second. Find the change in its kinetic energy between t = 1 s and t = 4 s.

A) 32 J

B) 46 J

C) 61 J

D) 102 J

• question_answer14) A hockey player receives a corner shot at a speed of 15 m/s at an angle of 30? with the y-axis and then shoots the ball of mass 100 g along the negative x-axis with a speed of 30 m/s. If it remains in contact with the hockey stick for 0.01 s, the force imparted to the ball in the x-direction is

A) 281.25 N

B) 187.5N

C) 562.5 N

D) 375 N

• question_answer15) Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance from centre will experience maximum coulomb force, when

A) $x=d/\sqrt{2}$

B) $x=d/2$

C) $x=d/2\sqrt{2}$

D) $x=d/2\sqrt{3}$

• question_answer16) The equivalent resistance between points A and B of an infinite network of resistance s each of $1\,\Omega ,$ connected as shown, is

A) infinite

B) 2$\Omega$

C) $\frac{1+\sqrt{5}}{2}\Omega$

D) zero

• question_answer17) A circular current carrying coil has a radius R The distance from the centre of the coil off the axis of the coil, where the magnetic induction is I/8th of its value at the centre of the coil is

A) $\sqrt{3}R$

B) $R/\sqrt{3}$

C) $\left( \frac{2}{\sqrt{3}} \right)R$

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

• question_answer18) A point source of light is placed 4m below he surface of water of refractive index 5/ 3. The minimum diameter of a disc, which should be placed over the source, on the surface of water to cut-off all light coming out of water is

A) infinite

B) 6 m

C) 4m

D) 3m

• question_answer19) A ray falls on a prism ABC (AB =BC) and travels as shown in figure. The minimum refractive index of the prism material should be

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

B) $\sqrt{2}$

C) 1.5

D) $\sqrt{3}$

• question_answer20) The plane face of a planoconvex lens is silvered. If u be the refractive index and R, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature

A) $\mu R$

B) $\frac{R}{(\mu -1)}$

C) $\frac{{{R}^{2}}}{\mu }$

D) $\left[ \frac{(\mu +1)}{(\mu -1)} \right]R$

• question_answer21) Two similar accumulators each of emf E and internal resistance r are connected as shown in the following figure. Then, the potential difference between x and y is

A) 2E

B) E

C) zero

D) None of these

• question_answer22) A conducting circular loop is placed in a uniform magnetic field of induction B tesla with its plane normal to the field. Now, the radius of the loop starts shrinking at the rate$\left( \frac{dr}{dt} \right)$. Then, the induced emf at the instant when the radius is r, is

A) $\pi rB\left( \frac{dr}{dt} \right)$

B) $2\pi rB\left( \frac{dr}{dt} \right)$

C) $\pi {{r}^{2}}\left( \frac{dr}{dt} \right)$

D) ${{\left( \frac{\pi {{r}^{2}}}{2} \right)}^{2}}B\left( \frac{dr}{dt} \right)$

• question_answer23) The first excitation potential of a given atom is 10.2V. Then, ionization potential must be

A) 20.4V

B) 13.6V

C) 30.6V

D) 40.8V

• question_answer24) A train is approaching with velocity 25 m/s towards a pedestrian standing on the track, frequency of horn of train is 1 kHz. Frequency heard by the pedestrain is (v= 350 m/s)

A) 1077 Hz

B) 1167 Hz

C) 985 Hz

D) 954 Hz

• question_answer25) Intensity of wave A is 91, while of wave B is 7. What is maximum and minimum intensity in YDSE?

A) 82$I$, 80$I$

B) 8$I$, 10$I$

C) 16$I$, 4$I$

D) 4$I$,$I$

• question_answer26) What happens inside optical fibre?

A) Diffraction

B) Polarization

C) Interference

D) Total internal reflection

• question_answer27) A manometer connected to a closed tap reads$3.5\times {{10}^{5}}\,N/{{m}^{2}}$. When the valve is opened, the reading of manometer falls to $3.0\times {{10}^{5}}\,N/{{m}^{2}}$, then velocity of flow of water is

A) 100 m/s

B) 10 m/s

C) 1m/s

D) $10\sqrt{10}$m/s

• question_answer28) Water is moving with a speed of 5.18 $m{{s}^{-1}}$ through a pipe with a cross-sectional area of 4.20$c{{m}^{2}}$. The water gradually descends 9.66 m as the pipe increase in area to 7.60$c{{m}^{2}}$. The speed of flow at the lower level is

A) 3.0$m{{s}^{-1}}$

B) 5.7$m{{s}^{-1}}$

C) 3.82$m{{s}^{-1}}$

D) 2.86$m{{s}^{-1}}$

• question_answer29) What is de-Broglie wavelength of electron having energy 10 keV?

A) $0.12\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $1.2\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $12.2\,\overset{\text{o}}{\mathop{\text{A}}}\,$

D) None of these

• question_answer30) Find beat frequency? Motion of two particles is given by ${{y}_{1}}=0.25\sin (310t)$ ${{y}_{2}}=0.25\sin (316t)$

A) 3

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

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

D) 6

• question_answer31) Half-life of radioactive substance is 3.20 h. What is the time taken for a 75% of substance to be used?

A) 6.38 h

B) 12 h

C) 4.18 day

D) 1.2day

• question_answer32) A capacitor of capacitance 1 $\mu F$ is filled with two dielectrics of dielectric constants 4 and 6. What is the new capacitance?

A) 10$\mu F$

B) 5$\mu F$

C) 4$\mu F$

D) 7$\mu F$

• question_answer33) The given combination represents the following gate

A) OR

B) XOR

C) NAND

D) NOR

• question_answer34) In BJT, maximum current flows in which of the following?

A) Emitter region

B) Base region

C) Collector region

D) Equal in all the regions

• question_answer35) In semiconductors at a room temperature

A) the valence band is partially empty and the conduction band is partially filled

B) the valence band is completely filled and the conduction band is partially filled

C) the valence band is completely filled

D) the conduction band is completely empty

• question_answer36) If coil is open then L and R become

A) $\infty ,0$

B) $0,\infty$

C) $\infty ,\infty$

D) 0, 0

• question_answer37) In a coil when current changes from 10A to 2A in time 0.1 s, induced emf is 3.28V. What is self-inductance of coil?

A) 4H

B) 0.4H

C) 0.04H

D) 5H

• question_answer38) Resistance of rod is 1$\Omega$. It is bent in form of square. What is resistance across adjoint corners?

A) 1$\Omega$

B) 3$\Omega$

C) $\frac{3}{16}\Omega$

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

• question_answer39) In a circuit L, C and R are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45{}^\circ$. The value of C is

A) $\frac{1}{2\pi f(2\pi fL+R)}$

B) $\frac{1}{\pi f(2\pi fL+R)}$

C) $\frac{1}{2\pi f(2\pi fL-R)}$

D) $\frac{1}{\pi f(2\pi fL-R)}$

• question_answer40) What is angle between electric field and equipotential surface?

A) $90{}^\circ \text{ }always$

B) $0{}^\circ \text{ }always$

C) $0{}^\circ \text{ }to\text{ }90{}^\circ$

D) $0{}^\circ \text{ }to\text{ }180{}^\circ$

• question_answer41) A ball falls from 20 m height on floor and rebounds to 5m. Time of contact is 0.02s. Find acceleration during impact.

A) $1200\,m/{{s}^{2}}$

B) $1000\,m/{{s}^{2}}$

C) $2000\,m/{{s}^{2}}$

D) $1500\,m/{{s}^{2}}$

• question_answer42) Two drops of equal radius coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

A) ${{2}^{1/2}}:1$

B) $1:1$

C) ${{2}^{2/3}}:1$

D) None of these

• question_answer43) In any fission process the ratio $\frac{mass\,of\,fission\,products}{mass\,of\,parent\,nucleus}is$

A) less than 1

B) greater than 1

C) equal to 1

D) depends on the mass of parent nucleus

• question_answer44) In the phenomenon of diffraction of light. when blue light is used in the experiment instead of red light, then

A) fringes will become narrower

C) no change in fringe width

D) None of the above

• question_answer45) A glass slab $(\mu =1.5)$ of thickness 6 cm is placed over a paper. What is the shift in the letters?

A) 4 cm

B) 2 cm

C) 1 cm

D) None of these

• question_answer46) Two capacitors of capacitance C are connected in series. If one of them is filled with dielectric substance K, what is the effective capacitance?

A) $\frac{KC}{(1+K)}$

B) C (K + 1)

C) $\frac{2KC}{K+1}$

D) None of these

• question_answer47) A person is sitting in a lift accelerating upwards. Measured weight of person will be

A) less than actual weight

B) equal to actual weight

C) more than actual weight

D) None of the above

• question_answer48) By mistake a voltmeter is connected in series and an ammeter is connected in parallel with a resistance in an electrical circuit. What will happen to the instruments?

A) Voltmeter is damaged

B) Ammeter is damaged

C) Both are damaged

D) None is damaged

• question_answer49) The half-life of $A{{t}^{215}}$is 100 $\mu s$. If a sample contains 215 mg of $A{{t}^{215}}$, the activity of the sample initially is

A) ${{10}^{2}}Bq$

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

C) $4.17\times {{10}^{24}}Bq$

D) $1.16\times {{10}^{5}}Bq$

• question_answer50) The ratio of minimum to maximum wavelength in Balmer series is

A) 5 : 9

B) 5 : 36

C) 1 : 4

D) 3 : 4

• question_answer51) A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is

A) 1 : 2 : 3

B) 1 : 4 : 9

C) 1 : 3 : 5

D) 1 : 5 : 3

• question_answer52) A body of mass 2 kg moving with a velocity of 3 m/s collides head on with a body of mass 1 kg moving in opposite direction with a velocity of 4 m/s. After collision two bodies stick together and move with a common velocity which in m/s is equal to

A) 1/4

B) 1/3

C) 2/3

D) 3/4

• question_answer53) Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures $127{}^\circ C$ and $527{}^\circ C$ respectively. The energy radiated by P and Q is

A) 0.054

B) 0.0034

C) 1

D) 2

• question_answer54) A cane is taken out from a refrigerator at $0{}^\circ C$. The atmospheric temperature is $25{}^\circ C$. If ${{t}_{1}}$ is the time taken to heat from $0{}^\circ C$ to $5{}^\circ C$ and ${{t}_{2}}$ is the time taken from $10{}^\circ C$ to $15{}^\circ C$, then

A) ${{t}_{1}}>{{t}_{2}}$

B) ${{t}_{1}}<{{t}_{2}}$

C) ${{t}_{1}}={{t}_{2}}$

D) there is no relation

• question_answer55) If an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same

A) energy

B) momentum

C) velocity

D) angular momentum

• question_answer56) The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

A) 540 nm

B) 400 nm

C) 310nm

D) 220 nm

• question_answer57) Work function of a metal is 2.1 eV. Which of the waves of the following wavelengths will be able to emit photoelectrons from its surface?

A) $4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,7500\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $5500\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $4000\overset{\text{o}}{\mathop{\text{A}}}\,,\,6000\overset{\text{o}}{\mathop{\text{A}}}\,$

D) None of the above

• question_answer58) A laser beam of pulse power ${{10}^{12}}$W is focused on an object of area${{10}^{-4}}c{{m}^{2}}$. The energy flux in watt/$c{{m}^{2}}$ at the point of focus is

A) ${{10}^{20}}$

B) ${{10}^{16}}$

C) ${{10}^{8}}$

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

• question_answer59) A laser device produces amplification in the

A) microwave region

B) ultraviolet or visible region

C) infrared region

D) None of the above

• question_answer60) Which of the following circular rods. (given radius r and length 0 each made of the same material as whose ends are maintained at the same temperature will conduct most heat?

A) $r=2{{r}_{0}};l=2{{l}_{0}}$

B) $r=2{{r}_{0}};l={{l}_{0}}$

C) $r={{r}_{0}};l={{l}_{0}}$

D) $r={{r}_{0}};l=2{{l}_{0}}$

• question_answer61) Which of the following is diamagnetic?

A) $H_{2}^{+}$

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

C) $L{{i}_{2}}$

D) $He_{2}^{+}$

A) $NO_{2}^{-}$

B) ${{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,C{{H}_{2}}C{{H}_{2}}\overset{\centerdot \,\,\,\centerdot }{\mathop{N}}\,{{H}_{2}}$

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

D) $:N{{H}_{3}}$

• question_answer63) By heating phenol with chloroform in alkali, it is converted into

A) salicylic acid

B) salicylaldehyde

C) anisole

D) phenyl benzoate

• question_answer64) Osmotic pressure observed when benzoic acid is dissolved in benzene is less than that expected from theoretical considerations. This is because

A) benzoic acid is an organic solute

B) benzoic acid has higher molar mass than benzene

C) benzoic acid gets associated in benzene

D) benzoic acid gets dissociated in benzene

• question_answer65) The formula mass of Moms salt is 392. The iron present in it is oxidized by$KMn{{O}_{4}}$in acid medium. The equivalent mass of Mohrs salt is

A) 392

B) 31.6

C) 278

D) 156

• question_answer66) Solubility product of a salt$AB$is$1\times {{10}^{-8}}{{M}^{2}}$in a solution in which the concentration of${{A}^{+}}$ions is${{10}^{-3}}M$. The salt will precipitate when the concentration of${{B}^{-}}$ions is kept

A) between${{10}^{-8}}M$to${{10}^{-7}}M$

B) between${{10}^{-7}}M$to${{10}^{-8}}M$

C) $>{{10}^{-5}}M$

D) $<{{10}^{-8}}M$

• question_answer67) The decomposition of a certain mass of$CaC{{O}_{3}}$gave$11.2\,\,d{{m}^{3}}$of$C{{O}_{2}}$gas at STP. The mass of$KOH$required to completely I neutralize the gas is

A) 56 g

B) 28 g

C) 42 g

D) 20 g

• question_answer68) The basicity of aniline is less than that of cyclohexylamine. This is due to

A) $+R-$effect of$-N{{H}_{2}}$group

B) $-I-$effect of$-N{{H}_{2}}$group

C) $-R-$effect of$-N{{H}_{2}}$group

D) hyperconjugation effect

• question_answer69) A distinctive and characteristic functional group of fats is

A) a peptide group

B) an ester group

C) an alcoholic group

D) a ketonic group

• question_answer70) Which of the following compound is expected to be optically active?

A) ${{(C{{H}_{3}})}_{2}}CHCHO$

B) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CHO$

C) $C{{H}_{3}}C{{H}_{2}}CHBrCHO$

D) $C{{H}_{3}}C{{H}_{2}}CB{{r}_{2}}CHO$

• question_answer71) Which cycloalkane has the lowest heat of combustion per$C{{H}_{2}}$group?

A) Cyclopropane

B) Cyclobutane

C) Cyclopentane

D) Cyclohexane

• question_answer72) The physical states of dispersing phase and dispersion medium in colloid like pesticide spray respectively, are

A) gas, liquid

B) solid, gas

C) liquid, solid

D) liquid, gas

• question_answer73) Potassium dichromate is used

A) in electroplating

B) as a reducing agent

C) it oxidizes ferrous ions into ferric ions in acidic media as an oxidizing agent

D) as an insecticide

• question_answer74) Which one of the following statements is incorrect for the sucrose?

A) It is obtained from cane sugar

B) It is not reducing sugar

C) On hydrolysis, it gives equal quantities of D-glucose and D-fructose

D) It gives aspartame when it is heated at${{210}^{o}}C$

A) displacement of $\sigma$-electrons

B) delocalisation of $\pi$-electrons

C) delocalisation of $\sigma$-electrons

D) displacement of $\pi$-electrons

• question_answer76) The atomic number of$Ni$and$Cu$are 28 and 29 respectively. The electronic configuration $1{{s}^{2}},\,\,2{{s}^{2}},\,\,2{{p}^{6}},\,\,3{{s}^{2}}\,\,3{{p}^{6}}\,\,3{{d}^{10}}$represents

A) $C{{u}^{+}}$

B) $C{{u}^{2+}}$

C) $N{{i}^{2+}}$

D) $Ni$

• question_answer77) In which of the following complex ion, the central metal ion is in a state of$s{{p}^{3}}{{d}^{2}}$hybridisation?

A) ${{[CoF]}^{3-}}$

B) ${{[CO{{(N{{H}_{3}})}_{6}}]}^{3+}}$

C) ${{[Fe{{(CN)}_{6}}]}^{3-}}$

D) ${{[Cr{{(N{{H}_{3}})}_{6}}]}^{3+}}$

• question_answer78) The formation of$O_{2}^{+}{{[Pt{{F}_{6}}]}^{-}}$is the basis for the formation of xenon fluorides. This is because

A) ${{O}_{2}}$and$Xe$have comparable sizes

B) Both${{O}_{2}}$and$Xe$are gases

C) ${{O}_{2}}$and$Xe$have comparable ionization energies

D) Both (a) and (c)

• question_answer79) The density of a gas is$1.964\,\,g\,\,d{{m}^{-3}}$at$273\,\,K$and$76\,\,cm\,\,Hg$. The gas is

A) $C{{H}_{4}}$

B) ${{C}_{2}}{{H}_{6}}$

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

D) $Xe$

• question_answer80) $\Delta {{G}^{o}}vs\,\,T$plot in the Ellinghams diagram slopes downwards for the reactions

A) $Mg+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}MgO$

B) $2Ag+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}A{{g}_{2}}O$

C) $CO+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}$

D) All of the above

• question_answer81) When a mixture of calcium benzoate and calcium acetate is dry distilled, the resulting compound is

A) acetophenone

B) benzaldehyde

C) benzophenone

D) acetaldehyde

• question_answer82) In a metallic crystal

A) the valence electrons constitute a sea of mobile electrons

B) the valence electrons are localized in between the kernels

C) the valence electrons remain within the field of influence of their own kernels

D) None of the above

• question_answer83) Which of the following is correct, based on molecular orbital theory for peroxide ion?

A) Its bond order is one and it is paramagnetic

B) Its bond order is two and it is diamagnetic

C) Its bond order is one and it is diamagnetic

D) Its bond order is two and it is paramagnetic

• question_answer84) Insulin regulates the metabolism of

A) minerals

B) ammo acids

C) glucose

D) vitamins

• question_answer85) Which of the following electrolyte will have maximum flocculation value for$Fe{{(OH)}_{3}}$sol?

A) $NaCl$

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

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

D) ${{K}_{2}}S{{O}_{4}}$

• question_answer86) The concentration of a reactant X decreases from$0.1M$to$0.005M$in 40 min. If the reaction follows first order kinetics, the rate of the reaction when the concentration of$X$is $0.01\,\,M$will be

A) $1.73\times {{10}^{-4}}M\,\,{{\min }^{-1}}$

B) $3.47\times {{10}^{-4}}M\,\,{{\min }^{-1}}$

C) $3.47\times {{10}^{-5}}M\,\,{{\min }^{-1}}$

D) $7.5\times {{10}^{-4}}M\,\,{{\min }^{-1}}$

• question_answer87) At$pH=4$, glycine exists as

A) ${{H}_{3}}N-C{{H}_{2}}-CO{{O}^{-}}$

B) ${{H}_{3}}N-C{{H}_{2}}-COOH$

C) ${{H}_{2}}N-C{{H}_{2}}-COOH$

D) ${{H}_{2}}N-C{{H}_{2}}-CO{{O}^{-}}$

• question_answer88) Which of the following taking place in the blast furnace is endothermic?

A) $CaC{{O}_{3}}\xrightarrow{{}}CaO+C{{O}_{2}}$

B) $2C+{{O}_{2}}\xrightarrow{{}}2CO$

C) $C+{{O}_{2}}\xrightarrow{{}}C{{O}_{2}}$

D) $F{{e}_{2}}{{O}_{3}}+3CO\xrightarrow{{}}2Fe+3C{{O}_{2}}$

• question_answer89) The$emf\,\,{{E}^{o}}$of the following cells are: $AG|A{{g}^{+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=-0.46\,\,V$ $Zn|Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)|Cu;\,\,{{E}^{o}}=1.10\,\,V$ emf of the following cell is $Zn|Z{{n}^{2+}}(1M)||A{{g}^{+}}(1M)|Ag$

A) $0.64\,\,V$

B) $1.10\,\,V$

C) $1.56\,\,V$

D) $-0.64\,\,V$

• question_answer90) The formation of cyanohydrin from acetone is which type of reaction?

A) Electrophilic substitution reaction

D) Nucleophilic substitution reaction

• question_answer91) Name the end product in the following series of reactions $C{{H}_{3}}COOH\xrightarrow{N{{H}_{3}}}A\xrightarrow{Heat}B\xrightarrow[\Delta ]{{{P}_{4}}{{O}_{14}}}C$

A) $C{{H}_{3}}OH$

B) $C{{H}_{4}}$

C) $C{{H}_{3}}COON{{H}_{4}}$

D) $C{{H}_{3}}CN$

• question_answer92) The presence of unpaired electron in phosphorous atom is explained by which principle?

A) Aufbau principle

B) Faults exclusion principle

C) Hunds rule

D) Heisenbergs principle

• question_answer93) If a cricket ball having mass of$200\,\,g$is thrown with a speed of$3\times {{10}^{3}}\,\,cm/s$, then calculate the wavelength related to it.

A) $2.2\times {{10}^{-27}}cm$

B) $1.104\times {{10}^{-32}}cm$

C) $1.104\times {{10}^{-32}}cm$

D) $1.104\times {{10}^{-33}}cm$

• question_answer94) Which type of stacking pattern is found in sodium chloride crystal lattice?

A) $a-b-a-b$

B) $a-a-a$

C) $a-b-c-a-b-c$

D) None of these

• question_answer95) Equivalent weight of a bivalent metal is 37.2. The molecular weight of its chloride is

A) 412.2

B) 216

C) 145.4

D) 108.2

• question_answer96) Phenolphthalein is obtained by heating phthalic anhydride with $conc.{{H}_{2}}S{{O}_{4}}$and

A) benzyl alcohol

B) benzene

C) phenol

D) benzoic acid

• question_answer97) Freezing point of urea solution is$-{{0.6}^{o}}C$. How much urea$(m.wt.=60g/mol)$will be required to dissolve in 3 kg water? $({{k}_{f}}={{1.5}^{o}}C\,\,kg\,\,mo{{l}^{-1}})$

A) 24 g

B) 36 g

C) 60 g

D) 72 g

• question_answer98) If$K<1.0$, what will be the value of$\Delta {{G}^{o}}$of the following?

A) Zero

B) 1.0

C) Positive

D) Negative

• question_answer99) The normality of a solution containing 32.5 g of${{(COOH)}_{2}}\cdot 2{{H}_{2}}O$per$0.5\,\,L$is

A) $10\,\,N$

B) $1\,\,N$

C) $2\,\,N$

D) $0.1\,\,N$

• question_answer100) For the titration of$KOH$vs${{(COOH)}_{2}}\cdot 2{{H}_{2}}O$, the suitable indicator is

A) methyl orange

B) phenolphthalein

C) methyl red

D) All can be used

• question_answer101) The radius of$N{{a}^{+}}$is$95\,\,\text{pm}$and that of$C{{l}^{-}}$ion is$181\,\,\text{pm}$. The coordination number of$N{{a}^{+}}$is

A) 8

B) 6

C) 4

D) unpredictable

• question_answer102) In van der Waals equation of state of the gas law, the constant V is a measure of

A) intermolecular repulsion

B) intermolecular attraction

C) volume occupied by the molecules

D) intermolecular collisions per unit volume

• question_answer103) Which reaction intermediate is formed during the condensation reaction between acetaldehyde and formaldehyde?

A) $:C{{H}_{2}}CHO$

B) $\overset{+}{\mathop{C}}\,{{H}_{2}}CHO$

C) $\overset{+}{\mathop{C}}\,{{H}_{2}}OH$

D) $:\bar{C}HCHO$

• question_answer104) $2,\,\,2\mathbf{-}$dichloro propane on hydrolysis yields

A) acetone

B) $2,\,\,2\mathbf{-}$propane diol

C) iso-propyl alcohol

D) acetaldehyde

• question_answer105) Phenols are more acidic than alcohols because

A) phenoxide ion is stabilized by resonance

B) phenols are more soluble in polar solvents

C) phenoxide ions do not exhibit resonance

D) alcohols do not lose H atoms at all

• question_answer106) Lemon gives sour taste because of

A) citric acid

B) tartaric acid

C) oxalic acid

D) acetic acid

• question_answer107) When ammonium chloride is added to ammonia solution, the pH of the resulting solution will be

A) increased

B) seven

C) decreased

D) unchanged

• question_answer108) Which of the following has highest second ionization energy?

A) Calcium

B) Chromium

C) Iron

D) Cobalt

• question_answer109) The standard reduction potentials at$298K$for the following half-cell reactions are given below $Z{{n}^{2+}}(aq)+2{{e}^{-}}Zn(s)-0.762$ $C{{r}^{3+}}(aq)+3{{e}^{-}}Cr(s)-0.74$ $2{{H}^{+}}(aq)+2{{e}^{-}}{{H}_{2}}(g)-0.00$ $F{{e}^{3+}}(aq)+{{e}^{-}}F{{e}^{2+}}(aq)-0.77$ Which one of the following is the strongest reducing agent?

A) $Zn(s)$

B) $Cr(s)$

C) ${{H}_{2}}(g)$

D) $F{{e}^{2+}}(aq)$

• question_answer110) Following reaction, ${{(C{{H}_{3}})}_{3}}CBr+{{H}_{2}}O\xrightarrow{{}}{{(C{{H}_{3}})}_{3}}COH+HBr$is an example of

A) elimination reaction

C) nucleophilic substitution

D) electrophilic substitution

• question_answer111) The unit of rate for a first order reaction is

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

B) $mo{{l}^{-1}}\,\,L\,\,{{s}^{-1}}$

C) $mol\,\,{{L}^{-1}}\,\,{{s}^{-1}}$

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

• question_answer112) $Iso-$propyl amine with excess of acetyl chloride will give

A) ${{(C{{H}_{3}}CO)}_{2}}N-C-{{(C{{H}_{3}})}_{3}}$

B) ${{(C{{H}_{3}})}_{2}}CH-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}$

C) ${{(C{{H}_{3}})}_{2}}CHN{{(CO{{H}_{3}})}_{2}}$

D) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{N}}\,-COC{{H}_{3}}$

• question_answer113) ${{C}_{2}}{{H}_{5}}CHO$and${{(C{{H}_{3}})}_{2}}CO$can be distinguished by testing with

A) phenyl hydrazine

B) hydroxyl amine

C) Fehling solution

D) sodium bisulphite

• question_answer114) Glucose molecule reacts with$X$number of molecules of phenylhydrazine to yield osazone. The value of T is

A) four

B) one

C) two

D) three

• question_answer115) The oxidation number of chromium in$Cr{{O}_{5}}$is

A) +3

B) + 5

C) + 10

D) + 6

• question_answer116) Liquor ammonia bottles are opened only after cooling. This is because

A) it is a mild explosive

B) it generates high vapour pressure

C) Both (a) and (b)

D) it is lachrymatory

• question_answer117) What will be the proportion of moles of metal $(Cu:Ni:Ag)$at cathode according to the second law of Faraday?

A) $1:2:1$

B) $2:2:1$

C) $1:2:2$

D) $1:1:2$

• question_answer118) Which equation is true to calculate the energy of activation, if the rate of reaction is doubled by increasing temperature from${{T}_{1}}K$to${{T}_{2}}K$?

A) ${{\log }_{10}}\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]$

B) ${{\log }_{10}}\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]$

C) ${{\log }_{10}}\frac{1}{2}=\frac{{{E}_{a}}}{2.303}\left[ \frac{1}{{{T}_{2}}}-\frac{1}{{{T}_{1}}} \right]$

D) ${{\log }_{10}}2=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]$

• question_answer119) For a reversible reaction : $X(g)+3Y(g)2Z(g);\,\,\Delta H=-40kJ$ the standard entropies of$X,\,\,Y$and$Z$are 60, 40 and 50 $J{{K}^{-1}}mo{{l}^{-1}}$respectively. The temperature at which the above reaction attains equilibrium is about

A) $400\,\,K$

B) $500\,\,K$

C) $273\,\,K$

D) $373\,\,K$

• question_answer120) Which of the following gives aldol condensation reaction?

A) ${{C}_{6}}{{H}_{5}}OH$

B) ${{C}_{6}}{{H}_{5}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}$

C) $C{{H}_{3}}C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$

D) ${{(C{{H}_{3}})}_{3}}C-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}$

• question_answer121) The range of the function$f\left( x \right)={{x}^{2}}+\frac{1}{{{x}^{2}}+1}$is

A) $[1,\,\,\infty )$

B) $[2,\,\,\infty )$

C) $\left[ \frac{3}{2},\,\,\infty \right)$

D) None of these

• question_answer122) If$f\left( x \right)=\left\{ \begin{matrix} a{{x}^{2}}+b, & b\ne 0,\,\,x\le 1 \\ b{{x}^{2}}+ax+c, & x>1 \\ \end{matrix} \right.$,then $f\left( x \right)$is continuous and differentiable at$x=1$, if

A) $c=0,\,\,a=2b$

B) $a=b,\,\,c\in R$

C) $a=b,\,\,c=0$

D) $a=b,\,\,c\ne 0$

• question_answer123) If a circle passes through the point$(1,\,\,2)$and cuts the circle${{x}^{2}}+{{y}^{2}}=4$orthogonally, then the equation of the locus of its centre is

A) ${{x}^{2}}+{{y}^{2}}-3x-8y+1=0$

B) ${{x}^{2}}+{{y}^{2}}-2x-6y-7=0$

C) $2x+4y-9=0$

D) $2x+4y-1=0$

• question_answer124) If$\int{f\left( x \right)}\sin x\cos x\,\,dx$ $=\frac{1}{2({{b}^{2}}-{{a}^{2}})}\log [f(x)]+c,$ then$f\left( x \right)$is equal to

A) $\frac{1}{{{a}^{2}}{{\sin }^{2}}x+{{b}^{2}}{{\cos }^{2}}x}$

B) $\frac{1}{{{a}^{2}}{{\sin }^{2}}x-{{b}^{2}}{{\cos }^{2}}x}$

C) $\frac{1}{{{a}^{2}}{{\cos }^{2}}x-{{b}^{2}}{{\sin }^{2}}x}$

D) $\frac{1}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}$

• question_answer125) The points representing complex number 2 for which$\left| z-3 \right|=\left| z-5 \right|$lie on the locus given by

A) an ellipse

B) a circle

C) a straight line

D) None of the above

• question_answer126) The value of$\alpha$, for which the equation${{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0$has roots whose sum of square is least, is

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

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

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

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

• question_answer127) For$n\in N,\,\,{{10}^{n-2}}\ge 81n$, is

A) $n>5$

B) $n\ge 5$

C) $n<5$

D) $n>8$

• question_answer128) The two consecutive terms in the expansion of${{(3+2x)}^{74}}$whose coefficients are equal are

A) 11, 12

B) 7, 8

C) 30, 31

D) None of these

• question_answer129) The value of$2.\overline{357}$is

A) $\frac{2355}{999}$

B) $\frac{2355}{1000}$

C) $\frac{2355}{1111}$

D) None of these

• question_answer130) Let${{S}_{n}}=\frac{1}{{{1}^{3}}}+\frac{1}{{{1}^{3}}}+\frac{2}{{{2}^{3}}}+...+\frac{1+2+...+n}{{{1}^{3}}+{{2}^{3}}+...+n}$ $n=1,2,3,...$. Then,${{S}_{n}}$is not greater than

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

B) 1

C) 2

D) 4

• question_answer131) If$E(\theta )=\left[ \begin{matrix} {{\cos }^{2}}\theta & \cos \theta \sin \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]$and$\theta$and$\phi$ differ by an odd multiple of$\frac{\pi }{2}$, then$E(\theta )E(\phi )$is a

A) unit matrix

B) null matrix

C) diagonal matrix

D) None of the above

• question_answer132) A parabola is drawn with its focus at$(3,\,\,4)$and vertex at the focus of the parabola${{y}^{2}}-12x-4y+4=0$. The equation of the parabola is

A) ${{y}^{2}}-8x-6y+25=0$

B) ${{y}^{2}}-6x+8y-25=0$

C) ${{x}^{2}}-6x-8y+25=0$

D) ${{x}^{2}}+6x-8y-25=0$

• question_answer133) If$p,\,\,p$denote the lengths of the perpendiculars from the focus and the centre of an ellipse with semi major axis of length a respectively on a tangent to the ellipse and$r$denotes the focal distance of the point, then

A) $ap=rp+1$

B) $rp=ap$

C) $ap=rp+1$

D) $ap=rp$

• question_answer134) 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_answer135) If$\cos \theta =-\frac{\sqrt{3}}{2}$and$\sin \alpha =-\frac{3}{5}$, where$\theta$does not lie in the third quadrant, then $\frac{2\tan \alpha +\sqrt{3}\tan \theta }{{{\cot }^{2}}\theta +\cos \alpha }$is equal to

A) $\frac{7}{22}$

B) $\frac{5}{22}$

C) $\frac{9}{22}$

D) $\frac{22}{5}$

• question_answer136) A parallelogram is constructed on the vectors $\overset{\to }{\mathop{\mathbf{a}}}\,=3\overset{\to }{\mathop{\alpha }}\,-\overset{\to }{\mathop{\beta }}\,,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\alpha }}\,+3\overset{\to }{\mathop{\beta }}\,$, if$\left| \overset{\to }{\mathop{\alpha }}\, \right|=\left| \overset{\to }{\mathop{\beta }}\, \right|=2$and angle between$\overset{\to }{\mathop{\alpha }}\,$and$\overset{\to }{\mathop{\beta }}\,$is$\frac{\pi }{3}$, then length of a diagonal of the parallelogram is

A) $4\sqrt{5}$

B) $4\sqrt{3}$

C) $4\sqrt{17}$

D) None of the above

• question_answer137) The value of$c$, so that for all real$x$, the vectors$cx\widehat{\mathbf{i}}-6\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}$,$x\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+2cx\widehat{\mathbf{k}}$make an obtuse angle, are

A) $c<0$

B) $0<c<\frac{4}{3}$

C) $-\frac{4}{3}<c<0$

D) $c>0$

• question_answer138) The solution of the equation $y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)$

A) $y=c(x+a)(1-ay)$

B) $y=c(x+a)(1+ay)$

C) $y=c(x-a)(1+ay)$

D) None of the above

• question_answer139) The order of the differential equation whose general solution is given by$y=({{c}_{1}}+{{c}_{2}})\cos (x+{{c}_{3}})-{{c}_{4}}{{e}^{x\_{{c}_{5}}}}$, where${{c}_{1}},\,\,{{c}_{2}},\,\,{{c}_{3}},\,\,{{c}_{4}},\,\,{{c}_{5}}$are arbitrary constants, is

A) 4

B) 3

C) 2

D) 5

• question_answer140) If$f(x)={{x}^{3}}+b{{x}^{2}}+cx+d$and$0<{{b}^{2}}<c$, then in$(-\infty ,\,\,\infty )$

A) $f(x)$is strictly increasing function

B) $f(x)$has a local maxima

C) $f(x)$strictly decreasing function

D) $f(x)$is bounded

• question_answer141) $\frac{d}{dx}{{\sin }^{-1}}(x\sqrt{1-x}+\sqrt{x}\sqrt{1-{{x}^{2}}})$

A) $-\frac{1}{2x\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}$

B) $\frac{1}{2\sqrt{x}\sqrt{1-x}}-\frac{1}{\sqrt{1-{{x}^{2}}}}$

C) $\frac{1}{2\sqrt{x}\sqrt{1-x}}+\frac{1}{\sqrt{1-{{x}^{2}}}}$

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

• question_answer142) $\int{\frac{x{{\tan }^{-1}}x}{{{(1+{{x}^{2}})}^{3}}}}dx$is equal to

A) $\frac{x-{{\tan }^{-1}}x}{1-{{x}^{2}}}+c$

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

C) $\frac{x-{{\tan }^{-1}}x}{\sqrt{1+{{x}^{2}}}}+c$

D) $\frac{x+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}}+c$

• question_answer143) Let$A=\left[ \begin{matrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \\ \end{matrix} \right]$, where$0\le \theta \le 2\pi$. Then, the range of$\left| A \right|$is

A) 0

B) {2, 4}

C) [2, 4]

D) None of the above

• question_answer144) If$y=\left| \cos x \right|+\left| \sin x \right|$, then$\frac{dy}{dx}$at$x=\frac{2\pi }{3}$is

A) 0

B) 1

C) $\frac{1-\sqrt{3}}{2}$

D) $\frac{\sqrt{3}-1}{2}$

• question_answer145) $\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{1}{1-{{n}^{2}}}+\frac{2}{1-{{n}^{2}}}+...+\frac{n}{1-{{n}^{2}}} \right)$is equal to

A) 0

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

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

D) None of these

• question_answer146) Let$f(x)=\left\{ \begin{matrix} \sin x, & x\ne n\pi \\ 2 & x=n\pi \\ \end{matrix} \right.$, where$n\in I$and$g(x)=\left\{ \begin{matrix} {{x}^{2}}+1, & x\ne 2 \\ 3, & x=2 \\ \end{matrix} \right.$, then$\underset{x\to 0}{\mathop{\lim }}\,g[f(x)]$is

A) 1

B) 0

C) 3

D) does not exist

• question_answer147) The intercept made by the tangent to the curve$y=\int_{0}^{x}{|t|}\,\,dt$,which is parallel to the line $y=2x$, on x-axis is equal to

A) 1

B) -2

C) 2

D) None of these

• question_answer148) If$P={{x}^{3}}-\frac{1}{{{x}^{3}}}$and$Q=x-\frac{1}{x},\,\,x\in (0,\,\,x)$, then minimum value of$\frac{P}{{{Q}^{2}}}$is

A) $2\sqrt{3}$

B) $-2\sqrt{3}$

C) does not exist

D) None of these

• question_answer149) Locus of the point which divides double ordinate of the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$in the ratio 1:2 internally, is

A) $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{9{{y}^{2}}}{{{b}^{2}}}=\frac{1}{9}$

B) $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1$

C) $\frac{9{{y}^{2}}}{{{a}^{2}}}+\frac{9{{y}^{2}}}{{{b}^{2}}}=1$

D) None of these

• question_answer150) From any point on the hyperbola$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$tangents are drawn to the hyperbola$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=2$. The area cut-off by the chord of contact on the asymptotes is equal to

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

B) $ab$

C) $2ab$

D) $4ab$

• question_answer151) The value of the sum of the series$3{{\cdot }^{n}}{{C}_{0}}-8{{\cdot }^{n}}{{C}_{1}}+{{13}^{n}}{{C}_{2}}-18{{\cdot }^{n}}{{C}_{3}}+...$upto$(n+1)$terms is

A) 0

B) ${{3}^{n}}$

C) ${{5}^{n}}$

D) None of these

• question_answer152) If$A$is a skew-symmetric matrix, then trace of$A$is

A) 1

B) -1

C) 0

D) None of these

• question_answer153) The arbitrary constant on which the value of the determinant $\left| \begin{matrix} 1 & \alpha & {{\alpha }^{2}} \\ \cos (p-d)a & \cos pa & \cos (p-d)a \\ \sin (p-d)a & \sin pa & \sin (p-d)a \\ \end{matrix} \right|$does not depend, is

A) $\alpha$

B) p

C) d

D) a

• question_answer154) The sum of the first n terms of the series$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...$is equal to

A) ${{2}^{n}}-n+1$

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

C) $n+{{2}^{-n}}-1$

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

• question_answer155) The base of a cliff is circular. From the extremities of a diameter of the base angles of elevation of the top of the cliff are ${{30}^{o}}$and${{60}^{o}}$. If the height of the cliff be 500 m, then the diameter of the base of the cliff is

A) $\frac{2000}{\sqrt{3}}m$

B) $\frac{1000}{\sqrt{3}}m$

C) $\frac{2000}{\sqrt{3}}m$

D) $1000\sqrt{3}\,m$

• question_answer156) The most general solutions of the equation$\sec x-1=(\sqrt{2}-1)\tan x$are given by

A) $n\pi +\frac{\pi }{8}$

B) $2n\pi ,\,\,2n\pi +\frac{\pi }{4}$

C) $2n\pi$

D) None of these

• question_answer157) The maximum value of$\sin \left( x+\frac{\pi }{6} \right)+\cos \left( x+\frac{\pi }{6} \right)$in the interval $\left( 0,\,\frac{\pi }{2} \right)$ is attained at

A) $x=\frac{\pi }{12}$

B) $x=\frac{\pi }{6}$

C) $x=\frac{\pi }{3}$

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

• question_answer158) If${{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{2}$, where$r=1,\,\,2,\,\,3,....,\,\,n,$then$\underset{n\to \infty }{\mathop{\lim }}\,\,\,{{z}_{1}},\,\,{{z}_{2}}...{{z}_{n}}$is equal to

A) $\cos \alpha +i\sin \alpha$

B) $\cos \left( \frac{\alpha }{2} \right)-i\sin \left( \frac{\alpha }{2} \right)$

C) ${{e}^{i\alpha /2}}$

D) $\sqrt[3]{{{e}^{i\alpha }}}$

• question_answer159) Negation of Paris is in France and London is in England is

A) Paris is in England and London is in France

B) Paris is not in France or London is not in England

C) Paris is in England or London is in France

D) None of the above

• question_answer160) The area enclosed between the curves$y={{x}^{3}}$and$y=\sqrt{x}$is

A) $\frac{5}{3}sq\,\,unit$

B) $\frac{5}{4}sq\,\,unit$

C) $\frac{5}{12}sq\,\,unit$

D) $\frac{12}{5}sq\,\,unit$

• question_answer161) Find the equation of the bisector of the obtuse angle between the lines$3x-4y+7=0$and$-12x-5y+2=0$,

A) $21x+77y-101=0$

B) $99x-27y+81=0$

C) $21x-77y+101=0$

D) None of the above

• question_answer162) The equation of curve passing through the point$\left( 1,\frac{\pi }{4} \right)$and having slope of tangent at any point$(x,\,\,y)$as$\frac{y}{x}-{{\cos }^{2}}\left( \frac{y}{x} \right)$is

A) $x={{e}^{1+\tan \left( \frac{y}{x} \right)}}$

B) $x={{e}^{1-\tan \left( \frac{y}{x} \right)}}$

C) $x={{e}^{1+\tan \left( \frac{x}{y} \right)}}$

D) $x={{e}^{1-\tan \left( \frac{x}{y} \right)}}$

• question_answer163) 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_answer164) The differential equation of all non-vertical lines in a plane is

A) $\frac{{{d}^{2}}y}{d{{x}^{2}}}=0$

B) $\frac{{{d}^{2}}x}{d{{y}^{2}}}=0$

C) $\frac{dy}{dx}=0$

D) $\frac{dx}{dy}=0$

• question_answer165) The unit vector in ZOX plane and making angle ${{45}^{o}}$and ${{60}^{o}}$respectively with$\overset{\to }{\mathop{\mathbf{a}}}\,=2\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}-\widehat{\mathbf{k}}$and$\overset{\to }{\mathop{\mathbf{b}}}\,=0\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}$, is

A) $-\frac{1}{\sqrt{2}}\widehat{\mathbf{i}}+\frac{1}{\sqrt{2}}\widehat{\mathbf{k}}$

B) $\frac{1}{\sqrt{2}}\mathbf{\hat{i}}-\frac{1}{\sqrt{2}}\mathbf{\hat{k}}$

C) $\frac{1}{3\sqrt{2}}\widehat{\mathbf{i}}+\frac{4}{3\sqrt{2}}\widehat{\mathbf{j}}+\frac{1}{3\sqrt{2}}\widehat{\mathbf{k}}$

D) None of the above

• question_answer166) If$\int_{2}^{e}{\left( \frac{1}{\log x}-\frac{1}{{{(\log x)}^{2}}} \right)dx=a+\frac{b}{\log 2}}$,then

A) $a=e,\,\,b=-2$

B) $a=e,\,\,b=2$

C) $a=-e,\,\,b=2$

D) None of these

• question_answer167) The circle${{x}^{2}}+{{y}^{2}}-4x-4y+4=0$is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcentre of the triangle is$x+y-xy+k\sqrt{{{x}^{2}}+{{y}^{2}}}=0$, then the value of $k$is equal to

A) 2

B) 1

C) -2

D) 3

• question_answer168) The points of discontinuity of tan x are

A) $n\pi ,\,\,n\in I$

B) $2n\pi ,\,\,n\in I$

C) $(2n+1)\frac{\pi }{2},\,\,n\in I$

D) None of the above

• question_answer169) The two curves${{x}^{3}}-3x{{y}^{2}}+2=0$and$3{{x}^{2}}y-{{y}^{3}}-2=0$

A) cut at right angles

B) touch each other

C) cut at an angle$\frac{\pi }{3}$

D) cut at an angle$\frac{\pi }{4}$

• question_answer170) The period of the function $f(x)=\frac{\sin 8x\cos x-\sin 6x\cos 3x}{\cos 2x\cos x-\sin 3x\sin 4x}$

A) $\pi$

B) $2\pi$

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

D) None of these

• question_answer171) 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_answer172) If$a>0,\,\,b>0$the maximum area of the triangle formed by the points$O(0,\,\,0)$$A(a\cos \theta ,\,\,b\sin \theta )$and$B(a\cos \theta ,\,\,-b\sin \theta )$is (in sq unit)

A) $\frac{ab}{2}$when$\theta =\frac{\pi }{4}$

B) $\frac{3ab}{4}$when$\theta =\frac{\pi }{4}$

C) $\frac{ab}{2}$when$\theta =-\frac{\pi }{2}$

D) ${{a}^{2}}{{b}^{2}}$

• question_answer173) If the two curves $y={{a}^{x}}$and$y={{b}^{x}}$intersect at an angle$\alpha$, then tan a equals

A) $\frac{\log a-\log b}{1+\log a\log b}$

B) $\frac{\log a+\log b}{1-\log a\log b}$

C) $\frac{\log a-\log b}{1-\log a\log b}$

D) None of these

• question_answer174) The number of roots of the equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$

A) 1

B) 2

C) 0

D) infinitely many

• question_answer175) The vector $z=-4+5i$is turned counter clockwise through an angle of${{180}^{o}}$and stretched$1\frac{1}{2}$times. The complex number corresponding to newly obtained vector is

A) $-6+\frac{15}{2}i$

B) $6+\frac{15}{2}i$

C) $6-\frac{15}{2}i$

D) None of these

• question_answer176) If$A=[{{a}_{ij}}]$is a4$4\times 4$matrix${{C}_{ij}}$is the cofactor of the element${{a}_{ij}}$in$\left| A \right|$, then the expression${{a}_{11}}{{C}_{11}}+{{a}_{12}}{{C}_{12}}+{{a}_{13}}{{C}_{13}}+{{a}_{14}}{{C}_{14}}$equal to

A) 0

B) -1

C) 1

D) $\left| A \right|$

• question_answer177) If$A=\left\{ x:\frac{\pi }{6}\le x\le \frac{\pi }{3} \right\}$and $f(x)=\cos x-x(1+x)$, then$f(A)$is equal to

A) $\left[ -\frac{\pi }{3},\,\,-\frac{\pi }{6} \right]$

B) $\left[ \frac{\pi }{6},\,\,\frac{\pi }{3} \right]$

C) $\left[ \frac{1}{2}-\frac{\pi }{3}\left( 1+\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}-\frac{\pi }{6}\left( 1+\frac{\pi }{6} \right) \right]$

D) $\left[ \frac{1}{2}+\frac{\pi }{3}\left( 1-\frac{\pi }{3} \right),\,\,\frac{\sqrt{3}}{2}+\frac{\pi }{6}\left( 1-\frac{\pi }{6} \right) \right]$

• question_answer178) The contrapositive of$(p\vee q)\Rightarrow r$is

A) $\tilde{\ }r\Rightarrow (p\vee q)$

B) $r\Rightarrow (p\vee q)$

C) $\tilde{\ }r\Rightarrow (\tilde{\ }p\wedge \tilde{\ }q)$

D) $p\Rightarrow (q\vee r)$

• question_answer179) If the function$f(x)=a{{x}^{3}}+b{{x}^{2}}+11x-6$satisfies the condition of Rollers theorem in$[1,\,\,3]$and$f\left( 2+\frac{1}{\sqrt{3}} \right)=0$, then the values of $a,\text{ }b$are respectively

A) - 1, 6

B) - 2, 1

C) 1, -6

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

• question_answer180) If$f(x)=\cos (\log x)$, then $f\left( \frac{1}{x} \right)f\left( \frac{1}{y} \right)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]$ is equal to

A) $\cos (x-y)$

B) $\log (x-y)$

C) $\cos (x+y)$

D) None of these

• question_answer181) If$\alpha ={{\sin }^{-1}}\frac{\sqrt{3}}{2}+{{\sin }^{-1}}\frac{1}{3}$and$\beta ={{\cos }^{-1}}\frac{\sqrt{3}}{2}+{{\cos }^{-1}}\frac{1}{3}$, then

A) $\alpha >\beta$

B) $\alpha =\beta$

C) $\alpha <\beta$

D) $\alpha +\beta =2\pi$

• question_answer182) If$1+\sin \theta +{{\sin }^{2}}\theta +...\infty =4+2\sqrt{3},\,\,0<\theta <\pi$, $\theta \ne \frac{\pi }{2}$, then

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

B) $\theta =\frac{\pi }{6}$

C) $\theta =\frac{\pi }{3}$or$\frac{\pi }{6}$

D) $\theta =\frac{\pi }{3}$or$\frac{2\pi }{3}$

• question_answer183) A round balloon of radius$r$subtends an angle $\alpha$at the eye of the observer, while the angle of elevation of its centre is$\beta$. The height of the centre of balloon is

A) $r\cos ec\alpha \sin \frac{\beta }{2}$

B) $r\sin \alpha \cos ec\frac{\beta }{2}$

C) $r\sin \frac{\alpha }{2}\cos ec\beta$

D) $r\cos ec\frac{\alpha }{2}\sin \beta$

• question_answer184) In$\Delta ABC,\,\,{{(a-b)}^{2}}{{\cos }^{2}}\frac{C}{2}+{{(a+b)}^{2}}{{\sin }^{2}}\frac{C}{2}$is equal to

A) ${{a}^{2}}$

B) ${{b}^{2}}$

C) ${{c}^{2}}$

D) None of these

• question_answer185) In a triangle$\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)\left( 1-\frac{{{r}_{1}}}{{{r}_{2}}} \right)=2$, then the triangle is

A) right angled

B) isosceles

C) equilateral

D) None of these

• question_answer186) If$a+b+c=0$, then the roots of the equation $4a{{x}^{2}}+3bx+2c=0$are

A) equal

B) imaginary

C) real

D) None of these

A) Connected

B) Disconnected

C) Neither connected nor disconnected

D) None of the above

• question_answer188) The solution of${{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}$is

A) $-\frac{1}{\sqrt{3}}$

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

C) $-\sqrt{3}$

D) $\sqrt{3}$

• question_answer189) The conjugate of the complex number$\frac{{{(1+i)}^{2}}}{1-i}$is

A) $1-i$

B) $1+i$

C) $-1+i$

D) $-1-i$

• question_answer190) A graph$G$has$m$vertices of odd degree and $n$vertices of even degree. Then which of the following statements is necessarily true?

A) $m+n$is an odd number

B) $m+n$is an even number

C) $n+1$is an even number

D) $m+1$is an odd number

• question_answer191) The value of$\sin \left[ 2{{\cos }^{-1}}\frac{\sqrt{5}}{3} \right]$is

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

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

C) $\frac{4\sqrt{5}}{9}$

D) $\frac{2\sqrt{5}}{9}$

• question_answer192) In the group$(G,{{\otimes }_{15}})$, where$G=\{3,\,\,6,\,\,9,\,\,12\}$, ${{\otimes }_{15}}$is multiplication modulo 15, the identity element is

A) 3

B) 6

C) 12

D) 9

• question_answer193) A group$(G,\,\,*)$has 10 elements. The minimum number of elements of$G$, which are their own inverses is

A) 2

B) 1

C) 9

D) 0

• question_answer194) $\frac{3{{x}^{2}}+1}{{{x}^{2}}-6x+8}$is equal to

A) $3+\frac{49}{2(x-4)}-\frac{13}{2(x-2)}$

B) $\frac{49}{2(x-4)}-\frac{13}{2(x-2)}$

C) $\frac{-49}{2(x-4)}+\frac{13}{2(x-2)}$

D) $\frac{49}{2(x-4)}+\frac{13}{2(x-2)}$

• question_answer195) The orthocentre of the triangle with vertices$O(0,\,\,0),\,\,A\left( 0,\,\,\frac{3}{2} \right),\,\,B(-5,\,\,0)$is

A) $\left( \frac{5}{2},\,\,\frac{3}{4} \right)$

B) $\left( \frac{-5}{2},\,\,\frac{3}{4} \right)$

C) $\left( -5,\,\,\frac{3}{2} \right)$

D) $(0,\,\,0)$

• question_answer196) The range in which$y=-{{x}^{2}}+6x-3$increasing, is

A) $x<3$

B) $x>3$

C) $7<x<8$

D) $5<x<6$

• question_answer197) The area bounded by the curve$x=4-{{y}^{2}}$and the y-axis is

A) 16 sq unit

B) 32 sq unit

C) $\frac{32}{3}$sq unit

D) $\frac{16}{3}$sq unit

• question_answer198) The number of positive divisors of 252 is

A) 9

B) 5

C) 18

D) 10

• question_answer199) The remainder obtained when 5124 is divided by 124 is

A) 5

B) 0

C) 2

D) 1

• question_answer200) Which of the following is not a group with respect to the given operation?

A) The set of even integers including zero under addition

B) The set of odd integers under addition

D) {1,-1} under multiplication

• question_answer201) He is so ...... of his own idea that he will not entertain any suggestion from others.

A) hopeful

B) enamoured

C) jealous

D) possessed

• question_answer202) Undoubtedly, English is the most...... spoken language in the world today.

B) widely

C) greatly

D) beautifully

• question_answer203) I will be leaving for Delhi tonight and ...... to return by this weekend.

A) waiting

B) plan

C) going

D) making

• question_answer204) The vacancy ......... by the dismissal of the superintendent is expected to be filled up by the promotion of a U.D.C.

B) created

C) caused

D) generated

A) Postpone

B) Accept

C) Bargain

D) Reject

A) Awful

B) Irrelevant

C) Shallow

D) Profound

A) Like

B) Eagerness

C) Disability

D) Dislike

A) Deal

B) Return

C) Lend

D) Exchange

A) Gallows

B) Suicide

C) Euphoria

D) Euthanasia

• question_answer210) The act of killing ones wife

A) Avicide

B) Canicide

C) Uxoricide

D) Genocide

• question_answer211) Stage between boyhood and youth

A) Infancy

C) Puberty

D) Maturity

• question_answer212) Lack of enough blood

A) Amnesia

B) Insomnia

C) Anaemia

D) Allergy

• question_answer213) To set the people by ears

A) To box the people

B) To insult and disgrace the people

C) To punish heavily

D) To excite people to a quarrel

• question_answer214) To give chapter and verse for a thing

A) To produce the proof of something

B) To eulogise the qualities of a thing

C) To make publicity of a thing

D) To attach artificial value to a thing

• question_answer215) Dog in the manger

A) An undersized bull almost the shape of a dog

B) A dog that has no kennel of its own

C) A person who puts himself in difficulties an account of other people

D) A person who prevents others from enjoying something useless to himself

• question_answer216) To blow hot and cold

A) Changing weather

B) To be untrustworthy

C) To change opinion often

D) To be rich and poor frequently

A) Casual

B) Cunning

C) Foolish

D) False

A) Conversation

B) Dialogue

C) Dramatic

D) Prologue

A) Spicy

B) Unfavorable

C) Conspicuous

D) Condemnatory

A) Encircled

B) Groped

C) Disfigured

D) Detached

• question_answer221) Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?

A) Hill

B) Valley

C) Dam

D) River

• question_answer222) In a certain code CREAM is written as NBDBQ. How in BREAD written in that code?

A) EBFAQ

B) EBDAQ

C) BEDQA

D) BEFQA

• question_answer223) If black means white, white means red, red means yellow, yellow means blue, blue means green, green means purple and purple means orange, then what is the colour of lemon?

A) Green

B) Purple

C) Orange

D) Blue

• question_answer224) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Hot: Oven : : Cold :?

A) Ice cream

B) Air conditioner

C) Snow

D) Refrigerator

• question_answer225) Directions: In the following questions, find the word which holds the same relation with the third word as there in between the first two word. Push : Pull : : Throw :?

A) Jump

B) Collect

C) Pick

D) Game

• question_answer226) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? R, M, ?, F, D, ?

A) C, B

B) J, H

C) H, C

D) I, C

• question_answer227) Directions: In each of the following questions, one letter or a set of letter is missing, you have to understand the pattern of the series and insert the appropriate letter? - bcc - ac - aabb - ab -cc

A) aab ca

B) aba ca

C) ba cab

D) bca ca.

• question_answer228) How many 9s are there in the following number series which are immediately preceded by 3 and followed by 6? 3 9 6 9 3 9 3 9 3 9 6 3 9 3 6 3 9 5 6 9 5 6 9 3 9 6 3 9

A) 0

B) 3

C) 2

D) 4

• question_answer229) Some boys are sitting in a row, P in sitting fourteenth from the left and Q is seventh from the right. If these are four boys between P and Q, how many boys are there in the row?

A) 25

B) 23

C) 21

D) 19

• question_answer230) Pointing to a photograph, a woman says, this mans sons sister in my mother-in-law. How is the womans husband related to the man in the photograph?

A) Grandson

B) Son

C) Son-in-law

D) Nephew

• question_answer231) The longest canal in the world is

A) Volga Baltic

B) Beloye-more Baltic

C) Suez Canal

D) Grand China Canal

• question_answer232) The oldest Hindu epic is

A) Mahabhashya

B) Ramayan

C) Mahabharata

• question_answer233) Who among the following is not associated with the Swaraj Party?

A) C.R. Das

B) M.L. Kelkar

C) Motilal Nehru

D) Mahatma Gandhi

• question_answer234) Where is the City of palaces?

A) London

B) Kolkata

C) Patiala

D) Lucknow

• question_answer235) Our National Song is

A) Sare Jahan Se Achcha

B) Jana Gana Mana

C) Vande Mataram

D) All of the above

• question_answer236) The Constitution of India was adopted by the Constituent Assembly on

A) Dec 11, 1946

B) Aug 15, 1957

C) Nov 26, 1949

D) Jan 26, 1949

• question_answer237) Gandhijis Dandi March started from

A) Bardoli

C) Surat

D) Bombay

• question_answer238) Who was the viceroy of India at the time of formation of the Indian National Congress?

A) Lord Canning

B) Lord Dufferin

C) Lord Mayo

D) Lord Elgin

• question_answer239) Which country was a major donor in financing the SAARC?

A) Pakistan

B) Sri Lanka

C) India

• question_answer240) Where in the H. Q. of the European Economic Community?

A) Bonn

B) Rome

C) Brussels

D) Hague