# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2005

### done BCECE Engineering Solved Paper-2005

• question_answer1) Consider the following statements: The total energy of a particle executing simple harmonic motion depends on its:

 (I) amplitude (II) period (III) displacement
Of these statements:

A) $\text{I}$ and $\text{II}$ are correct

B) $\text{II}$ and $\text{III}$ are correct

C) $\text{I}$ and $\text{III}$ are correct

D) $\text{I, II }and\,\text{III}\,are\,correct$

• question_answer2) The maximum velocity of a simple harmonic motion represented by $y=3\sin \left( 100\,t+\frac{\pi }{6} \right)m$ is given by:

A) 300 m/s

B) $\frac{\text{3}}{\text{6}}\text{m/s}$

C) 100 m/s

D) $\frac{}{\text{6}}\text{m/s}$

• question_answer3) When earth moves round the sun, the quantity which remains constant is:

A) angular velocity

B) kinetic energy

C) potential energy

D) areal velocity

• question_answer4) 1 kg body explodes into three fragments. The ratio of their masses is 1:1:3. The fragments of same mass move perpendicular to each other with speeds 30 m/s, while the heavier part remains in the initial direction. The speed of heavier part is:

A) $\frac{10}{\sqrt{2}}\text{m/s}$

B) $\text{10}\sqrt{2\,}\text{m/s}$

C) $\text{20}\sqrt{2\,}\text{m/s}$

D) $\text{30}\sqrt{2\,}\text{m/s}$

• question_answer5) The dimensional formula for the gravitational constant is:

A) $\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }$

B) $\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }$

C) $\text{ }\!\![\!\!\text{ M}{{\text{L}}^{2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }$

D) $\text{ }\!\![\!\!\text{ }{{\text{M}}^{-1}}{{\text{L}}^{3}}\text{T }\!\!]\!\!\text{ }$

• question_answer6) A particle is moving in a circle of radius R with constant speed v. If radius is doubled, then its centripetal force to keep the same speed gets:

A) twice as great as before

B) half

C) one-fourth

D) remains constant

• question_answer7) If linear density of a rod of length 3 m varies as $\lambda =2+x,$ then the position of the centre of gravity of the rod is:

A) $\frac{7}{3}m$

B) $\frac{12}{7}m$

C) $\frac{10}{7}m$

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

• question_answer8) A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. The maximum compression in the spring is x then:

A) $mgh=\frac{1}{2}k\,{{x}^{2}}$

B) $mg(h+x)=\frac{1}{2}k\,{{x}^{2}}$

C) $mgh=\frac{1}{2}k\,{{(x+h)}^{2}}$

D) $mg(h+x)=\frac{1}{2}k\,{{(x+h)}^{2}}$

• question_answer9) A ball of mass m moves with speed v and it strikes normally with a wall and reflected back normally. If its time of contact with wall is t, then find force exerted by ball on the wall.

A) $\frac{2mv}{t}$

B) $\frac{mv}{t}$

C) $mvt$

D) $\frac{mv}{2t}$

• question_answer10) A wheel of radius 1m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is :

A) $2\pi$

B) $\sqrt{2\pi }$

C) $\sqrt{{{\pi }^{2}}+4}$

D) $\pi$

• question_answer11) Water is flowing in a pipe of diameter 4 cm with a velocity 3 m/s. The water then enters into a pipe of diameter 2 cm. The velocity of water in the other pipe is:

A) 3 m/s

B) 6 m/s

C) 12 m/s

D) 8 m/s

• question_answer12) The surface tension of a liquid is 5 N/m. If a film is held on a ring of area $0.02\,\,{{m}^{2}},$ its total surface energy is about:

A) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}$

B) $\text{2}\text{.5 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-2}}}\text{J}$

C) $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}$

D) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-1}}}\text{J}$

• question_answer13) A viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram:

A)

B)

C)

D) none of these

• question_answer14) A wire is stretched by 1 mm by a force of 1 k N. The work done in stretching the wire is :

A) 5 erg

B) 5 J

C) 0.5 erg

D) 0.5 J

A) $\Delta U=\Delta Q$

B) $\Delta Q=\Delta W$

C) $\Delta U=\Delta W$

D) none of these

• question_answer16) Which is not a path function?

A) $\Delta Q$

B) $\Delta Q+\Delta W$

C) $\Delta W$

D) $\Delta Q-\Delta W$

• question_answer17) The work done, V/during an isothermal process in which 1 mole of the gas expands from an initial volume ${{V}_{1}}$ to a final volume ${{V}_{2}}$ is given by: (R=gas constant, T= temperature)

A) $R({{V}_{2}}-{{V}_{1}}){{\log }_{e}}\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)$

B) $R({{T}_{2}}-{{T}_{1}}){{\log }_{e}}\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)$

C) $RT{{\log }_{e}}\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)$

D) $2RT{{\log }_{e}}\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)$

• question_answer18) The P-V diagram of a system undergoing thermodynamic transformation is shown in figure. The work done by the system in going from$A\to B\to C$ is 30 J, and 40 J heat is given to the system. The change in internal energy between A and C is:

A) 10 J

B) 70 J

C) 84 J

D) 134 J

• question_answer19) The degrees of freedom of a molecule of a triatomic gas are:

A) 2

B) 4

C) 6

D) 8

A) less than $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\text{m}$

B) equal to $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\text{m}$

C) more than $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\text{m}$

D) all of the above

• question_answer21) Two simple harmonic waves of the same amplitude and frequency differ by a phase$\text{/2}$ When they are fed simultaneously to the X and Y-plates of a CRO, the screen would display the trace of:

A) a circle

B) an ellipse

C) a straight line

D) a square

• question_answer22) The speed of a wave is 360 m/s and frequency is 500 Hz. Phase difference between two consecutive particles is $60{}^\circ$, then path difference between them will be:

A) 0.72 cm

B) 120 cm

C) 12 cm

D) 7.2 cm

• question_answer23) A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 Hz, then the waves would travel on it with a velocity of:

A) 125 m/s

B) 250 m/s

C) 500 m/s

D) 1000 m/s

• question_answer24) The fundamental frequency of a sonometer wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be:

A) $n$

B) $\frac{n}{\sqrt{2}}$

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

D) $\frac{n}{2\sqrt{2}}$

• question_answer25) In open organ pipe, if fundamental frequency is n, then the other frequencies are:

A) n, 2 n, 3n, 4n

B) n, 3n, 5n

C) n, 2n, 4n, 8n

D) none of these

• question_answer26) A sound wave of frequency $f$ propagating through air with a velocity c, is reflected from a surface which is moving away from the source with a constant speed v. The frequency of the reflected wave, measured by the observer at the position of the source, is:

A) $\frac{f(c-v)}{c+v}$

B) $\frac{f(c+v)}{c-v}$

C) $\frac{f(c+2v)}{c+v}$

D) $\frac{f(c-v)}{c-2v}$

• question_answer27) A convex lens of focal length 10 cm and image formed by it, is at least distance of distinct vision then the magnifying power is:

A) 3.5

B) 2.5

C) 1.5

D) 1.4

• question_answer28) If two +5 D, lenses are mounted at some distance apart, the equivalent power will always be negative, if the distance is:

A) greater than 40 cm

B) equal to 40 cm

C) equal to 10 cm

D) less than 10 cm

• question_answer29) A Galilean telescope has an objective of focal length 100 cm and magnifying power 50. The distance between the two lenses in normal adjustment will be:

A) 98 cm

B) 100 cm

C) 150 cm

D) 200 cm

• question_answer30) A film projector magnifies a $100\,c{{m}^{2}}$ film strip on a screen. If the linear magnification is 4, the area of the magnified film on the screen is:

A) $1600\,c{{m}^{2}}$

B) $400\,c{{m}^{2}}$

C) $800\,c{{m}^{2}}$

D) $200\,c{{m}^{2}}$

• question_answer31) The exposure time of a camera lens at$f/2.8$ setting is 1/200 s. The correct exposure time at $f/5.6$setting is:

A) 0.02 s

B) 0.04 s

C) 0.20 s

D) 0.40 s

• question_answer32) In Youngs double slit experiment, the slit width and the distance of slits from the screen both are doubled. The fringe width:

A) increases

B) decreases

C) remains unchanged

D) none of the above

• question_answer33) In Youngs double slit experiment, the aperture screen distance is 2 m. The slit width is 1 mm. Light of 600 nm is used. If a thin plate of glass $(\mu =1.5)$ of thickness 0.06 mm is placed over one of the slits, then there will be a lateral displacement of the fringes by:

A) zero

B) 6 cm

C) 10 cm

D) 15 cm

• question_answer34) A single slit is used to observe diffraction pattern with red light. on replacing the red light with violet light the diffraction pattern would:

A) remain unchanged

B) become narrower

D) disappear

• question_answer35) The resistance of a discharge tube is:

A) zero

B) ohmic

C) non-ohmic

D) infinity

• question_answer36) Which one of the following processes depends on gravity?

A) Conduction

B) Convection

D) None of the above

• question_answer37) The radius of solid metallic non-conducting sphere is 60 cm and charge on the sphere is $500\,\mu C$. The electric field at a distance 10 cm from centre of sphere is:

A) $2\times {{10}^{6}}\,N/C$

B) $2\times {{10}^{8}}\,N/C$

C) $5\times {{10}^{6}}\,N/C$

D) $5\times {{10}^{8}}\,N/C$

• question_answer38) The equivalent capacitance between the points A and B in the following circuit is:

A) $1\mu F$

B) $2\mu F$

C) $4\mu F$

D) $8\mu F$

• question_answer39) The figure shows a network of currents. The magnitude of current is shown here. The current $I$ will be:

A) 3 A

B) 9 A

C) 13 A

D) 19 A

• question_answer40) If resistance of voltmeter is $10000\,\Omega$ and resistance of galvanometer is $2\,\,\Omega ,$ then find R when voltmeter reads 12 V and galvanometer reads 0.1 A.

A) $118\,\,\Omega$

B) $120\,\,\Omega$

C) $124\,\Omega$

D) $114\,\Omega$

• question_answer41) Two bulbs 25 W, 220 V and 100 W, 220 V are given. Which has higher resistance?

A) 25 W bulb

B) 100 W bulb

C) Both bulbs will have equal resistance

D) Resistance of bulbs cannot be compared

• question_answer42) An electron (mass $9.1\times {{10}^{31}}$ kg, charge $=1.6\times {{10}^{19}}C$) experiences no deflection, if subjected to an electric field of $3.2\times {{10}^{5}}V/m,$ and a magnetic field of $2.0\times {{10}^{3}}$ $Wb/{{m}^{2}}$. Both the fields are normal to the path of electron and to each other. If the electric field is removed, then the electron will revolve in an orbit of radius:

A) 45 m

B) 4.5 m

C) 0.45 m

D) 0.045 m

• question_answer43) An LCR circuit of R = 100 0 is connected to an AC source 100 V, 50 Hz. The magnitude of phase difference between current and voltage is $30{}^\circ$. The power dissipated in the LCR circuit is:

A) 50 W

B) 86.6 W

C) 100 W

D) 200 W

• question_answer44) If half-life of radium is 77 days, its decay constant will be:

A) $\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}$

B) $\text{9 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}$

C) $\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}$

D) $\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}$

• question_answer45) In a radioactive reaction$_{92}{{X}^{232}}{{\to }_{82}}{{X}^{204}}$ the number of $\alpha$-particles emitted is:

A) 7

B) 6

C) 5

D) 4

• question_answer46) According to Hubbles law, the red-shift (Z) of a receding galaxy and its distance r from aril are related as:

A) $Z\,\propto r$

B) $Z\,\propto \frac{1}{r}$

C) $Z\,\propto \frac{1}{{{r}^{2}}}$

D) $Z\,\propto {{r}^{3/2}}$

• question_answer47) The de-Broglie wavelength of a body of mass m and kinetic energy E is given by:

A) $\lambda =\frac{h}{mE}$

B) $\lambda =\frac{\sqrt{2mE}}{h}$

C) $\lambda =\frac{h}{2mE}$

D) $\lambda =\frac{h}{\sqrt{2mE}}$

• question_answer48) Different voltages are applied across a p-n junction and the currents are measured form each value. Which of die following graphs is obtained between voltage and current?

A)

B)

C)

D)

• question_answer49) A logic gate having two inputs A and B and output C has the following truth table

 A B C 1 1 0 1 0 1 0 1 1 0 0 1
It is :

A) an OR gate

B) an AND gate

C) a NOR gate

D) a NAND gate

• question_answer50) For sky wave propagation of 10 MHz signal, what should be the minimum electron density in ionosphere?

A) $\sim 1.2\times {{10}^{12}}{{m}^{-3}}$

B) $\sim {{10}^{6}}{{m}^{-3}}$

C) $\sim {{10}^{14}}{{m}^{-3}}$

D) $\sim {{10}^{22}}{{m}^{-3}}$

• question_answer51) The number of molecules of $C{{O}_{2}}$present in 44 g of $C{{O}_{2}}$is:

A) $6.0\times {{10}^{23}}$

B) $3\times {{10}^{23}}$

C) $12\times {{10}^{23}}$

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

• question_answer52) Magnitude of kinetic energy in an orbit is equal to:

A) half of the potential energy

B) twice of the potential energy

C) one fourth of the potential energy

D) none of the above

• question_answer53) A p-orbital in a given shell can accommodate upto:

A) four electrons

B) two electrons with parallel spin

C) six electrons

D) two electrons with opposite spin

• question_answer54) Which of the following is Heisenberg uncertainty principle?

A) $\Delta x.\Delta p\ge \frac{h}{4\pi }$

B) $\Delta x.\Delta p=\frac{h}{4\pi }$

C) $\Delta x.\Delta p\le \frac{h}{4\pi }$

D) $\Delta x.\Delta p<\frac{h}{4\pi }$

• question_answer55) Chromium is represented by the electronic configuration:

A) $\text{ }\!\![\!\!\text{ }Ne\text{ }\!\!]\!\!\text{ }3{{s}^{2}}\text{ }3{{P}^{6}}\text{ }3{{d}^{1}}\text{ }4{{s}^{2}}$

B) $\text{ }\!\![\!\!\text{ }Ne\text{ }\!\!]\!\!\text{ }3{{s}^{2}}\text{ }3{{p}^{6}}\text{ }3{{d}^{2}}\text{ }4{{s}^{1}}$

C) $\text{ }\!\![\!\!\text{ }Ne\text{ }\!\!]\!\!\text{ }3{{s}^{2}}\text{ }3{{p}^{6}}\text{ }3{{d}^{5}}\text{ }4{{s}^{1}}$

D) $~[Ne]\text{ }3{{s}^{2}}\text{ }3{{p}^{6}}\text{ }4{{s}^{2}}\text{ }3{{d}^{4}}$

• question_answer56) Number of neutron in ${{C}^{12}}$is:

A) 6

B) 7

C) 8

D) 9

• question_answer57) H-bond is not present in:

A) water

B) glycerol

C) hydrogen fluoride

D) hydrogen sulphide.

• question_answer58) Oxidation number of S in$SO_{4}^{2-}:$

A) + 6

B) + 3

C) + 2

D) - 2

• question_answer59) 2 g of ${{O}_{2}}$ at$~27{{\,}^{o}}C$ and 760 mm of Hg pressure has volume:

A) 1.4 L

B) 2.8 L

C) 11.2 L

D) 22.4 L

• question_answer60) If pressure increases then its effect on given equilibrium $2NO(g){{N}_{2}}(g)+{{O}_{2}}(g)$ is shift in:

A) forward direction

B) backward direction

C) no effect

D) none of the above

• question_answer61) Which is Lewis base: ${{I}_{2}}+{{I}^{-}}\xrightarrow{{}}{{I}_{3}}^{-}$?

A) ${{I}_{2}}$

B) $I_{3}^{-}$

C) ${{I}^{-}}$

D) None of these

• question_answer62) The heat of neutralization of any strong acid and a strong base is nearly equal to:

A) $-75.3\,kJ$

B) $~+\,57.3\,kJ$

C) $-57.3\,kJ$

D) $+\,75.3\,kJ$

• question_answer63) pH of ${{10}^{-8}}\,M\,HCl$solution is:

A) 8

B) between 7 and 8

C) between 6 and 7

D) between 8 and 9

• question_answer64) A reaction $A\xrightarrow{{}}B$follows a second order kinetic. Doubling the concentration of A will increase the rate of formation of B by a factor of:

A) 1/4

B) 4

C) 1/2

D) 2

• question_answer65) Which of the following is always negative for exothermic reaction?

A) $\Delta H$

B) $\Delta S$

C) $\Delta G$

D) None of these

• question_answer66) Unit of equivalent conductance is:

A) $oh{{m}^{-1}}\,c{{m}^{2}}\,{{(g-eq)}^{-1}}$

B) $ohm\,cm\,(g-eq)$

C) $ohm\,c{{m}^{2}}\,{{(g-eq)}^{-1}}$

D) $oh{{m}^{-1}}\,cm\,{{(g-eq)}^{-1}}$

• question_answer67) For cell reaction $Zn+C{{u}^{2+}}\xrightarrow{{}}Z{{n}^{2+}}+Cu$ cell representation is:

A) $Zn|Z{{n}^{2+}}||C{{u}^{2+}}|Cu$

B) $Cu|C{{u}^{2+}}||Z{{n}^{2+}}|Zn$

C) $Cu|Z{{n}^{2+}}||Zn|C{{u}^{2+}}$

D) $C{{u}^{2+}}|Zn||Z{{n}^{2+}}|Cu$

• question_answer68) Molal solution means 1 mole of solute present in:

A) $1000\,g$of solvent

B) 1 L of solvent

C) 1 L of solution

D) $1000\,g$of solution

• question_answer69) Which of the following shows maximum depression in freezing point?

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

B) $NaCl$

C) Urea

D) Glucose

• question_answer70) An emulsion is a colloidal dispersion of:

A) a liquid in a gas

B) a liquid in a liquid

C) a solid in a liquid

D) a gas in a solid

• question_answer71) Size of colloidal particle is:

A) $1\,nm$

B) $1-100\,nm$

C) $<\,100\,nm$

D) $>\,100\,nm$

• question_answer72) Ether show isomerism with:

A) alcohol

B) ethane

C) halide

D) aldehyde

• question_answer73) Which of the following shows geometrical isomerism?

A) ${{C}_{2}}{{H}_{5}}Br$

B) $(C{{H}_{2}}){{(COOH)}_{2}}$

C) ${{(CH)}_{2}}{{(COOH)}_{2}}$

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

• question_answer74) Which of the following is present in natural gas?

A) $n-$butane

B) Ethane

C) Methane

D) Propane

• question_answer75) Which of the following have delocalized electron?

A) Benzene

B) Cyclohexane

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

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

• question_answer76) Nitration of benzene is:

A) electrophilic substitution

C) nucleophilic substitution

• question_answer77) Alkyl halide can be converted into alkene by:

A) nucleophilic substitution reaction

B) elimination reaction

C) both nucleophilic substitution and elimination reaction

D) rearrangement

• question_answer78) Which of the following compounds is most acidic?

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

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

C) $CH\equiv CH$

D) ${{C}_{2}}{{H}_{5}}OH$

• question_answer79) Which of the following reacts with $KMn{{O}_{4}}$but does not react with$AgN{{O}_{3}}$?

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

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

C) ${{C}_{2}}{{H}_{4}}$

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

• question_answer80) Which of the following compound does not show anti-Markownikoffs addition?

A) Propene

B) 1-butene

C) 2-butene

D) 2-pentene

• question_answer81) Methyl ketone is identified by:

A) lodoform test

B) Fehling solution

C) Tollens reagent

D) Schiffs reagent

• question_answer82) Which of the following does not give Fehling solution test?

A) Acetone

B) Propanal

C) Ethanal

D) Butanal

• question_answer83) Cyanide group on hydrolysis gives:

A) acid

B) acetamide

C) amine

D) hydrate

• question_answer84) In alkyl cyanide alkyl group attached with:

A) C of CN group

B) N of CN group

C) either C or N of CN group

D) both C and N of CN group

• question_answer85) Fat on hydrolysis gives which alcohol

A) Glycerol

B) Propanol

C) Butanol

D) Ethanol

• question_answer86) Which of the following is natural polymer?

A) PVC

B) Nylon 66

C) Teflon

D) Cellulose

• question_answer87) Condensation product of caprolactum is:

A) Nylon 6

B) Nylon 66

C) Nylon 60

D) Nylon 6, 10

• question_answer88) Which inert gas have highest boiling point

A) $Xe$

B) $Ar$

C) Kr

D) He

• question_answer89) In Ostwald process of manufacturing of $\text{HN}{{\text{O}}_{\text{3}}}\text{,}$catalyst used is:

A) Mo

B) Fe

C) Mn

D) Pt

• question_answer90) Important ore of Mg is:

A) Gypsum

B) Camallite

C) Magnatide

D) Camolite

• question_answer91) Purification of Al by electrolysis method is called:

A) Halls process

B) Baeyer process

C) Ostwald process

D) Hoopes process

• question_answer92) Decreasing size of ions is:

A) $\text{I}\,\text{}\,{{\text{I}}^{-}}>{{I}^{+}}$

B) $\text{I}{{\,}^{-}}\text{}\,\text{I}>{{I}^{+}}$

C) $\text{I}{{\,}^{+}}\text{}\,{{\text{I}}^{-}}>I$

D) $\text{I}\,\text{}\,{{\text{I}}^{+}}>{{I}^{-}}$

• question_answer93) Which of the following is kept in water?

A) White phosphorus

B) Sodium

C) Potassium

D) Calcium

• question_answer94) When heated$N{{H}_{3}}$ is passed over$CuO$gas evolved is:

A) ${{N}_{2}}$

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

C) $HN{{O}_{3}}$

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

• question_answer95) Formula of hypophosphorus acid is:

A) $H-\underset{H}{\overset{O}{\mathop{\underset{||}{\overset{||}{\mathop{P}}}\,}}}\,-OH$

B) $HO-\underset{OH}{\overset{O}{\mathop{\underset{||}{\overset{||}{\mathop{P}}}\,}}}\,-OH$

C) $H-\underset{H}{\overset{O}{\mathop{\underset{||}{\overset{||}{\mathop{P}}}\,}}}\,=OH$

D) $H-\underset{OH}{\overset{O}{\mathop{\underset{|}{\overset{||}{\mathop{P}}}\,}}}\,-OH$

• question_answer96) Most powerful reducing agent is:

A) $Li$

B) $Na$

C) $Ca$

D) $Mg$

• question_answer97) When calomel reacts with $N{{H}_{4}}OH$solution the compound formed is:

A) $N{{H}_{2}}-Hg-Cl$

B) $H{{g}_{2}}C{{l}_{2}}N{{H}_{3}}$

C) $Hg{{(N{{H}_{3}})}_{2}}C{{l}_{2}}$

D) $HgC{{l}_{2}}N{{H}_{3}}$

• question_answer98) Which of the following is colored compound?

A) $Cu{{F}_{2}}$

B) $CuI$

C) $NaCI$

D) $MgC{{l}_{2}}$

• question_answer99) ${{H}_{2}}{{O}_{2}}$is formed by which of the following compounds?

A) $N{{a}_{2}}{{O}_{2}}$

B) $NaOH$

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

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

• question_answer100) Copper sulphate solution reacts with KCN and gives:

A) ${{K}_{3}}[Cu{{(CN)}_{4}}]$

B) $CuCN$

C) $Cu{{(CN)}_{2}}$

D) ${{K}_{2}}[Cu{{(CN)}_{4}}]$

• question_answer101) If $A\subseteq B,$then $B\cup A$is equal to:

A) $B\cap A$

B) A

C) B

D) none of these

• question_answer102) The real value of $\alpha$for which the expression $\frac{1-i\sin \alpha }{1+2i\,\sin \alpha }$ is purely real, is:

A) $(2n+1)\frac{\pi }{2}$

B) $(n+1)\frac{\pi }{2}$

C) $n\pi$

D) none of these

• question_answer103) The medians AD and BE of the triangle with vertices A (0, b), B (0, 0) and C (a, 0) are mutually perpendicular, if:

A) $b=a$

B) $b=-2\sqrt{a}$

C) $a=\pm \sqrt{2b}$

D) $b=\sqrt{2}\,a$

• question_answer104) The equation of line parallel to the tangent to the circle ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$at the point $({{x}_{1}},{{y}_{1}})$ and passing through origin, is:

A) $x{{y}_{1}}+{{x}_{1}}y=0$

B) $x{{x}_{1}}-y{{y}_{1}}=0$

C) $x{{x}_{1}}+y{{y}_{1}}=0$

D) $xy-{{x}_{1}}y=0$

• question_answer105) $\sin {{200}^{o}}+\cos {{200}^{o}}$is:

A) positive

B) negative

C) zero

D) zero or positive

• question_answer106) The principal value of ${{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right)$is:

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

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

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

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

• question_answer107) If $xy+yz+zx=1,$then $\sum{\frac{x+y}{1-xy}}$is equal to:

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

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

C) $~xyz$

D) none of these

• question_answer108) A vertical pole (more than 100 m high) consists of two portions, the lower being one-third of the whole. If the upper portion subtends an angle ${{\tan }^{-1}}\frac{1}{2}$at a point in a horizontal plane through the foot of the pole and distance 40 ft from it, then the height of the pole is:

A) 100 ft

B) 120 ft

C) 150 ft

D) none of these

• question_answer109) When the three coins are tossed simultaneously, then the probability of getting one head will be:

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

B) $\frac{1}{7}$

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

D) $\frac{7}{8}$

• question_answer110) The cosine of the angle between any two diagonals of a cube is:

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

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

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

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

• question_answer111) If$f$is any function, then $\frac{1}{2}[f(x)+f(-x)]$is always:

A) odd

B) even

C) neither even nor odd

D) one-one

• question_answer112) If $f(x)=\log \left( \frac{1+x}{1-x} \right)$and $g(x)=\frac{3x+{{x}^{3}}}{1+3{{x}^{2}}},$then $f(g(x))$is equal to:

A) $f(3x)$

B) ${{(f(x))}^{3}}$

C) $3f(x)$

D) $-f(x)$

• question_answer113) $\underset{x\to 0}{\mathop{\lim }}\,[\cos x]$is equal to:

A) $-1$

B) 1

C) 0

D) none of these

• question_answer114) $\frac{d}{dx}({{\sin }^{-1}}2x\sqrt{1-{{x}^{2}}})$is equal to:

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

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

C) $cos\,2x$

D) none of these

• question_answer115) $\int_{0}^{\pi /2}{|\sin x-\cos x|}\,dx$ is equal to:

A) $2(\sqrt{2}+1)$

B) $\sqrt{2}-1$

C) $2(\sqrt{2}-1)$

D) 0

• question_answer116) If p and q are the roots of the equation ${{x}^{2}}+pq=(p+1)x,$, then $q$is equal to:

A) $~-1$

B) 2

C) 1

D) $-2$

• question_answer117) If a line lies in the octant OXYZ and it makes equal angle with the axes, then:

A) $l=m=n=\frac{1}{\sqrt{3}}$

B) $l=m=n=\pm \frac{1}{\sqrt{3}}$

C) $l=m=n=-\frac{1}{\sqrt{3}}$

D) $l=m=n=\pm \frac{1}{\sqrt{2}}$

• question_answer118) If a, b, c are in AP, a, mb, c are in GP, then $a,{{m}^{2}}b,c$care in:

A) HP

B) GP

C) AP

D) none of these

• question_answer119) If $p\Rightarrow (q\vee r)$is false, then the truth values of p, q, r are respectively:

A) $T,F,F$

B) $F,F,F$

C) $~F,T,T$

D) $T,T,F$

• question_answer120) In the expansion of ${{(3x+2)}^{4}}$ the coefficient of middle term is:

A) 36

B) 216

C) 54

D) 81

• question_answer121) For any $2\times 2$matrix A, if $A(adj\,A)=\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right],$ then | A | i.e., det A is equal to:

A) 20

B) 100

C) 10

D) 0

• question_answer122) The vectors $\vec{a}=3\hat{i}-\hat{k},\vec{b}=\hat{i}+2\hat{j}$are adjacent sides of a parallelogram. Its area is:

A) $\frac{1}{2}\sqrt{7}$

B) $\sqrt{41}$

C) $\frac{1}{2}\sqrt{41}$

D) $\frac{1}{2}\sqrt{17}$

• question_answer123) If a, b, care elements of a boolean algebra, then $a.b+c(a+b)$is equal to:

A) $a.b$

B) c

C) $a\,.\,b+c$

D) none of these

• question_answer124) $(\vec{a}+\vec{b}).(\vec{a}-\vec{b})=0$implies that:

A) $\vec{a}=-\vec{b}$

B) $\vec{a}\ne \vec{b}$

C) $|\vec{a}|=|\vec{b}|$

D) $\vec{a}=\vec{b}$

• question_answer125) 3 persons have 4 coats, 5 waist coats and 6 hats. The number of ways in which they put on the clothes are:

A) ${{4}^{3}}\times {{5}^{3}}\times {{6}^{3}}$

B) $4\times 5\times 6$

C) $4!5!6!$

D) none of these

• question_answer126) If an integer p is chosen at random in the interval $0\le p\le 5,$the probability that the roots of the equation ${{x}^{2}}+px+\frac{p}{4}+\frac{1}{2}=0$ are real, is:

A) $\frac{4}{5}$

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

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

D) none of these

• question_answer127) $\int_{0}^{1}{x{{(1-x)}^{4}}dx}$is equal to:

A) 1

B) 0

C) $\frac{1}{30}$

D) $\frac{1}{5}$

• question_answer128) The function$f(x)=2-3x$is:

A) increasing

B) decreasing

C) neither decreasing nor increasing

D) none of the above

• question_answer129) The value of $\int_{0}^{\pi /2}{\frac{\frac{\pi }{4}-x}{\sqrt{\sin x+\cos x}}dx}$is:

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

B) $\frac{\pi }{4\sqrt{2}}$

C) 0

D) none of these

• question_answer130) If $y=\sqrt{x+\sqrt{x+\sqrt{x+....\infty ,}}}$then $\frac{dy}{dx}$is equal to:

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

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

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

D) 1

• question_answer131) If $f:A\to B$is a bijection, then:

A) $n(A)=n(B)$

B) $n(A)\le n(B)$

C) $n(A)\ge n(s)$

D) none of these

• question_answer132) The equation of a straight line passing through $(-3,2)$ and cutting an intercept equal in magnitude but opposite in sign from axis, is given by:

A) $x-y+5=0$

B) $x+y-5=0$

C) $~x-y-5=0$

D) $~x+y+5=0$

• question_answer133) If $\frac{2{{z}_{1}}}{3{{z}_{2}}}$is a purely imaginary number, then $\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|$is equal to:

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

B) 1

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

D) $\frac{4}{9}$

• question_answer134) If $pth,\text{ }qth,\text{ }rth,\text{ }sth$terms of an arithmetic progression axe in geometric progression, then $p-q,\,q-r$ and $r-s$are in:

A) HP

B) GP

C) AP

D) no particular order

• question_answer135) Two bodies are projected from the same point with the same velocity but in different directions. If the range in each case be R and times of flight be ${{t}_{1}}$and ${{t}_{2}},$then R is equal to:

A) $\frac{1}{2}g\,{{t}_{1}}{{t}_{2}}$

B) $g\,{{t}_{1}}{{t}_{2}}$

C) $\frac{1}{4}g\,{{t}_{1}}{{t}_{2}}$

D) $2g\,{{t}_{1}}{{t}_{2}}$

• question_answer136) The reciprocal of the eccentricity of rectangular hyperbola is:

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

B) $\sqrt{2}$

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

D) 2

• question_answer137) If $y=\frac{{{a}^{{{\cos }^{-1}}x}}}{1+{{a}^{{{\cos }^{-1}}x}}},z={{a}^{{{\cos }^{-1}}x}},$then $\frac{dy}{dx}$is equal to:

A) $\frac{1}{1+{{a}^{{{\cos }^{-1}}x}}}$

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

C) $\frac{-1}{1+{{a}^{{{\cos }^{-1}}x}}}$

D) none of these

• question_answer138) The value of $\sin {{600}^{o}}\,\cos {{330}^{o}}+\cos {{120}^{o}}\sin {{150}^{o}}$is:

A) 1

B) $-1$

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

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

• question_answer139) The area of circle whose centre is $(h,k)$ and radius a is:

A) $\pi {{a}^{2}}hk\,\text{sq}\,\text{unit}$

B) $\pi {{a}^{2}}\,\text{sq}\,\text{unit}$

C) $\pi ({{h}^{2}}+{{k}^{2}}-{{a}^{2}})\text{sq}\,\text{unit}$

D) none of the above

• question_answer140) If $\left[ \begin{matrix} 3 & 1 \\ 4 & 1 \\ \end{matrix} \right]X=\left[ \begin{matrix} 5 & -1 \\ 2 & 3 \\ \end{matrix} \right]$, then X is equal to:

A) $\left[ \begin{matrix} -3 & 4 \\ -4 & 13 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 3 & 4 \\ 14 & 13 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -3 & 4 \\ 14 & -13 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 3 & -4 \\ -14 & 13 \\ \end{matrix} \right]$

• question_answer141) If$\vec{a},\vec{b},\vec{c}$ are coplanar vectors, then $[\vec{a}+\vec{b}\vec{b}+\vec{c}\vec{c}+\vec{a}]$ is equal to:

A) $2|\vec{a}\vec{b}\vec{c}|$

B) $|\vec{a}\vec{b}\vec{c}|$

C) $3|\vec{a}\vec{b}\vec{c}|$

D) 0

• question_answer142) If the resultant of two unlike parallel forces of magnitudes 10 N and 16 N act along a line at a distance of 24 cm from the line of action of the smaller force is 8 N, then the distance between the lines of action of the force is:

A) 12 cm

B) 8 cm

C) 10.66 cm

D) 18 cm

• question_answer143) The resultant of two forces $\vec{P}$and $\vec{Q}$is of magnitude P. If the force $\vec{P}$ is doubled, $\vec{Q}$remaining unaltered, then the new resultant will be:

A) along $\vec{P}$

B) along $\vec{Q}$

C) at ${{60}^{o}}$to$\vec{Q}$

D) at right angle to $\vec{Q}$

• question_answer144) If the ratio of the sum of m and $n$terms of an AP is ${{m}^{2}}:{{n}^{2}},$then the ratio of its $mth$and $nth$terms is:

A) $m-1:n-1$

B) $2m+1:2n+1$

C) $2m-1:2n-1$

D) none of these

• question_answer145) A body. dropped from a height $h$at time $t=0$reaches the ground at tune ${{t}_{0}}.$would have reached a height $h/2$at time:

A) $\frac{{{t}_{0}}}{2}$

B) $\frac{{{t}_{0}}}{\sqrt{2}}$

C) $t_{0}^{2}$

D) $\frac{1}{t_{0}^{2}}$

• question_answer146) The area in the first quadrant between ${{x}^{2}}+{{y}^{2}}={{\pi }^{2}}$and $y=\sin x$is:

A) $\frac{{{\pi }^{3}}}{4}sq$unit

B) $\frac{{{\pi }^{3}}-16}{4}\text{sq}\,\text{unit}$

C) $\frac{{{\pi }^{3}}-8}{2}\text{sq}\,\text{unit}$

D) $\frac{{{\pi }^{3}}-8}{4}sq\,unit$

• question_answer147) In triangle ABC, if$~3a=b+c,$ then $\cot \frac{B}{2}\cot \frac{C}{2}$ is equal to:

A) $\sqrt{3}$

B) 1

C) 2

D) 3

• question_answer148) If $f(x)=2x+{{\cot }^{-1}}x+\log (\sqrt{1+{{x}^{2}}}-x),$then $f(x)$:

A) increases in $(-\infty ,\infty )$

B) decreases in $(0,\infty )$

C) neither increases nor decreases in $(0,\infty )$

D) sometimes increases and sometimes decreases

• question_answer149) The series $(1+3){{\log }_{e}}3+\frac{1+{{3}^{2}}}{2!}{{({{\log }_{e}}3)}^{2}}$$+\frac{1+{{3}^{2}}}{3!}{{({{\log }_{e}}3)}^{2}}+...$is equal to:

A) 28

B) 30

C) 25

D) 0

• question_answer150) $\int_{{}}^{{}}{\frac{\cos 4x-1}{\cot x-\tan x}}dx$is equal to:

A) $-\frac{1}{2}\cos 4x+c$

B) $-\frac{1}{4}\cos 4x+c$

C) $-\frac{1}{2}\sin 2x+c$

D) none of these