# Solved papers for JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

### done Jamia Millia Islamia Solved Paper-2010

• question_answer1) A car leaves station$X$for station Y every 10 min. The distance between$X$and Y is 60 km. The car travels at a speed of 60 km/h. A man drives a car from Y station towards$X$station at speed 60 km/h. If he starts at the moment when one of the car leaves station$X$how many cars would be meet on route?

A) 10

B) 11

C) 20

D) 21

• question_answer2) A ball rolls off the stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?

A) First

B) Second

C) Third

D) Fourth

• question_answer3) A sphere of mass 0.20 kg is attached to an inextensible string of length 0.5m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be

A) 1.5 m/s

B) 2.5 m/s

C) 3.2 m/s

D) 4.7 m/s

• question_answer4) Steady rain giving 5 mm an hour, turns suddenly into a downpour 20 mm an hour and the speed of rain drops falling vertically on to a flat roof simultaneously doubles. The pressure exerted by the falling rain on the roof rises by a factor of

A) 2

B) $2\sqrt{2}$

C) $4\sqrt{2}$

D) 8

• question_answer5) An open knife edge of mass M is dropped from a height h on a wooden floor. If the blade penetrates distance into the wood, the average resistance offered by the wood to the blade is

A) $Mg$

B) $Mg\left( 1+\frac{h}{s} \right)$

C) $Mg\left( \frac{1-h}{s} \right)$

D) $Mg{{\left( \frac{1+h}{s} \right)}^{2}}$

• question_answer6) A particle moves in$X-Y$plane under the influence of a force$\overrightarrow{F}$such that its instantaneous momentum is$\overrightarrow{P}=\hat{i}2\cos t+\hat{j}2\sin t$. What is the angle between the force and instantaneous momentum?

A) $0{}^\circ$

B) $180{}^\circ$

C) $90{}^\circ$

D) $45{}^\circ$

• question_answer7) The KE of a body varies directly as the time (t) elapsed. The force acting varies directly as

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

B) ${{t}^{-1/2}}$

C) ${{t}^{1/2}}$

D) $t$

• question_answer8) A gas at the temperature 250 K is contained in a closed vessel. If the gas is heated through 1 K, then the percentage increase in its pressure will be

A) 0.4%

B) 0.2%

C) 0.1%

D) 0.8%

• question_answer9) A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20 n rad/s to 40 n rad/s in 10 s. How many rotations did it make in this period?

A) 80

B) 100

C) 120

D) 150

• question_answer10) A point P lies on the axis of a ring of mass M and radius R at a distance 2R from its centre$O$ A small particle starts from P and reaches Q under gravitational attraction only. Its speed at $O$will be

A) zero

B) $\sqrt{\frac{2GM}{R}}$

C) $\sqrt{\frac{2GM}{R}(\sqrt{5}-1)}$

D) $\sqrt{\frac{2GM}{R}\left( 1-\frac{1}{\sqrt{5}} \right)}$

• question_answer11) Two vertical glass plates 1 mm apart are dipped into water. How high will be the water rise between the plates, if the surface tension of water is$70\text{ }dyne/c{{m}^{2}}$?

A) 2.86cm

B) 1.43cm

C) 5.72cm

D) 1.63cm

• question_answer12) A steel ball is dropped from a height h and it makes a perfectly elastic collision with a horizontal plane. Following its initial release, it will make periodic motion with frequency

A) $2\pi \sqrt{\frac{g}{h}}$

B) $2\pi \sqrt{\frac{h}{g}}$

C) $\frac{1}{2}\sqrt{\frac{g}{2h}}$

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

• question_answer13) Two closed organ pipes A and B have the same length, A is wider than B. They resonate in the fundamental mode at frequencies${{n}_{A}}$and${{n}_{B}}$ respectively

A) ${{n}_{A}}={{n}_{B}}$

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

C) ${{n}_{A}}<{{n}_{B}}$

D) Either or depending on the ratio of their diameters

• question_answer14) Shown below is a distribution of charges. The flux of electric field due to these charges through the surface is

A) $\frac{3q}{{{\varepsilon }_{0}}}$

B) zero

C) $\frac{2q}{{{\varepsilon }_{0}}}$

D) $\frac{q}{{{\varepsilon }_{0}}}$

• question_answer15) A parallel plate capacitor is connected across a 2 V battery and charged. The battery is then disconnected and a glass slab is introduced between plates. Which of the following pairs of quantities decrease?

A) Charge and potential difference

B) Potential difference and energy stored

C) Energy stored and capacitance

D) Capacitance and charge

• question_answer16) Four resistances of$10\,\Omega ,60\,\Omega ,100\,\Omega$and$200\,\Omega$. respectively taken in order are used to form a Wheatstones bridge. A 15 V battery is connected to the ends of a$200\,\Omega$ resistance. The current through it will be

A) $7.5\times {{10}^{-5}}A$

B) $7.5\times {{10}^{-4}}A$

C) $7.5\times {{10}^{-3}}A$

D) $7.5\times {{10}^{-2}}A$

• question_answer17) Magnetic field at the centre of a circular loop of area A is B. The magnetic moment of the loop will be

A) $\frac{B{{A}^{2}}}{{{\mu }_{0}}\pi }$

B) $\frac{B{{A}^{3/2}}}{{{\mu }_{0}}\pi }$

C) $\frac{B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}$

D) $\frac{2B{{A}^{3/2}}}{{{\mu }_{0}}{{\pi }^{1/2}}}$

• question_answer18) A thin magnet is cut into two equal parts by cutting it parallel to its length. If the original time period of vibration is 4 s the time period of each part in the same field will be

A) $4s$

B) $2s$

C) $4\sqrt{2}s$

D) None of these

• question_answer19) The moment of magnet is$0.1\text{ }A{{m}^{2}}$and the force acting on each pole in a uniform magnetic field of 0.36 oersted is$1.44\times {{10}^{-4}}N$. The distance between the poles of magnet is

A) 2.5 cm

B) 5.0 cm

C) 1.25cm

D) 1.17cm

• question_answer20) A solenoid 600 mm long has 50 turns on it and is wound on an iron rod of 7.5 mm radius. Find the flux through the solenoid when the current in it is 3 A. The relative permeabillity of iron is 600.

A) 1.66 Wb

B) 1.66 N Wb

C) 1.66 m Wb

D) $1.66\text{ }\mu \,Wb$

• question_answer21) A transformer has an efficiency of 80%. It works at 4 kW and 100 V. If secondary voltage is 240 V the current in primary coil is

A) 0.4 A

B) 4 A

C) 10 A

D) 40 A

• question_answer22) sIn a plane electromagnetic wave, the electric field oscillates sinusoid ally at a frequency $2\times {{10}^{10}}Hz$and amplitude 48V/m. The wavelength of the wave is

A) $24\times {{10}^{-10}}m$

B) $1.5\times {{10}^{-2}}m$

C) $4.16\times {{10}^{8}}m$

D) $3\times {{10}^{8}}m$

• question_answer23) A parallel beam of monochromatic unpolarised light is incident on a transparent dielectric plate of refractive indie$\frac{1}{\sqrt{3}}$. The reflected beam is completely polarised. Then the angle of incidence is

A) $30{}^\circ$

B) $60{}^\circ$

C) $45{}^\circ$

D) $75{}^\circ$

• question_answer24) A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark again in focus?

A) 2 cm upward

B) 1 cm upward

C) 4.5 cm downward,

D) 1 cm downward

• question_answer25) The wavelength of 1 keV photon is$1.24\times {{10}^{-9}}$ m What is the frequency of 1 MeV photon?

A) $2.4\times {{10}^{15}}Hz$

B) $2.4\times {{10}^{20}}Hz$

C) $1.24\times {{10}^{15}}Hz$

D) $1.24\times {{10}^{20}}Hz$

• question_answer26) An electron revolving in an orbit of radius 0.5 A in a hydrogen atom executes${{10}^{16}}rev/s$. The magnetic moment of electron due to its orbital motion will be,

A) $1256\times {{10}^{-26}}A{{m}^{2}}$

B) $6.53\times {{10}^{-26}}A{{m}^{2}}$

C) zero

D) $256\times {{10}^{-26}}A{{m}^{2}}$

• question_answer27) The ratio of electron and hole currents in a semiconductor is 7/4 and the ratio of drift velocities of electrons and holes is 5/4 then ratio of concentrations of electrons and holes will be

A) 5/7

B) 7/5

C) 25/49

D) 49/25

• question_answer28) In a common base transistor circuit, the current gain is 0.98 on changing emitter current by 5 mA, the change in collector current is

A) 0.196mA

B) 2.45mA

C) 4.9mA

D) 5.1mA

• question_answer29) A bus starts moving with acceleration$2\text{ }m/{{s}^{2}}$. A cyclist 96 m behind the bus starts simultaneously towards the bus of 20 m/s. After what time will he be able to overtake the bus?

A) $4s$

B) $8s$

C) $12s$

D) $16s$

• question_answer30) Geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then the time period of a spy satellite orbiting a 500 km above the earths surface (radius of earth = 6400 km) will approximately be

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

B) $1\,h$

C) $2\,h$

D) $4\,h$

• question_answer31) The upper end of a wire 1 m long and 2 mm radius is clamped. The lower end is twisted through an angle of$45{}^\circ$. The angle of shear is

A) $0.09{}^\circ$

B) $0.9{}^\circ$

C) $9{}^\circ$

D) $90{}^\circ$

• question_answer32) An air filled parallel plate capacitor charged to potential${{V}_{1}}$is connected to an uncharged identical parallel plate capacitor with dielectric constant K. The common potential is${{V}_{2}}$. The value of K is

A) $\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}$

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

C) $\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{2}}}$

D) $\frac{{{V}_{1}}-{{V}_{2}}}{{{V}_{1}}}$

• question_answer33) Three charged particles are initially in position$-1$. They are free to move and they come to position-2, after some time. Let${{U}_{1}}$and${{U}_{2}}$be the electrostatic potential energies in position$-1$and 2 then

A) ${{U}_{1}}={{U}_{2}}$

B) ${{U}_{2}}\ge {{U}_{1}}$

C) ${{U}_{2}}>{{U}_{1}}$

D) ${{U}_{1}}>{{U}_{2}}$

• question_answer34) In Youngs double slit experiment one slit is covered with red filter and another slit is covered by green filter, then interference pattern will be

A) red

B) green

C) yellow

D) invisible

• question_answer35) Two plano-convex lenses of radius of curvature R and refractive index$\mu =1.5$will have equivalent focal length equal to R when they are placed

A) at distance R/4

B) at distance R/2

C) at distanced

D) in contact with each other

• question_answer36) If energy E, velocity v and time T were taken as fundamental units, the dimensions for surface tension in these units are

A) $[{{E}^{-2}}{{V}^{1}}{{T}^{-2}}]$

B) $[{{E}^{-2}}{{V}^{-2}}{{T}^{1}}]$

C) $[{{E}^{1}}{{V}^{-2}}{{T}^{-2}}]$

D) $[{{E}^{-2}}{{V}^{-2}}{{T}^{-2}}]$

• question_answer37) The angle between$(\overrightarrow{A}\times \overrightarrow{B})$and$(\overrightarrow{A}+\overrightarrow{B})$is

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

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

C) $\pi$

D) zero

• question_answer38) Two stones are projected with the same velocity but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is$\frac{\pi }{3}$and maximum height is${{y}_{1}}$, then the maximum height of other will be

A) $3{{y}_{1}}$

B) $2{{y}_{1}}$

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

D) $\frac{{{y}_{1}}}{3}$

• question_answer39) A disc of mass 10 g is kept horizontally in air by firing bullets of mass 5 g each at the rate of 10 per second. If the bullets rebound with the same speed, what is the velocity with which the bullets are fired?

A) 49cm/s

B) 98 cm/s

C) 147 cm/s

D) 196 cm/s

• question_answer40) A sphere of mass 100 g is attached to an inextensible string of length 1.3m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm. The time period of the revolution is

A) 5.0s

B) 4.5s

C) 3.2s

D) 2.3s

• question_answer41) A uniform rod of length$l$is free to rotate in a vertical plane about a fixed horizontal axis through point B. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle$\theta$its angular velocity co is given as A) $\sqrt{\frac{6g}{l}}\sin \theta$

B) $\sqrt{\frac{6g}{l}}\sin \frac{\theta }{2}$

C) $\sqrt{\frac{6g}{l}}\cos \frac{\theta }{2}$

D) $\sqrt{\frac{6g}{l}}\cos \theta$

• question_answer42) The displacement of a particle executing periodic motion is given by $y=4{{\cos }^{2}}\frac{t}{2}\sin 1000t$ The expression may be considered to be a result of superposition of ......... independent harmonic motions.

A) 1

B) 3

C) 4

D) 5

• question_answer43) Oxygen gas is contained in a cylinder of volume $1\times {{10}^{-3}}{{m}^{3}}$at a temperature of 320 K and a pressure of$3.53\times {{10}^{5}}N/{{m}^{2}}$. After some of the oxygen is used at constant temperature, the pressure falls to$2.7\times {{10}^{5}}N/{{m}^{2}}$. The mass of oxygen used is

A) 0.01 kg

B) 0.001 kg

C) 0.002 kg

D) 0.003 kg

• question_answer44) A reversible engine working between the temperature limits of 600 K and 1200K receives 50 kJ of heat. The work done by the engine will be

A) 50 kJ

B) 100 kJ

C) 25 kJ

D) $-25\text{ }kJ$

• question_answer45) For the stationary wave$y=4\sin \frac{\pi x}{15}\cos 96\pi t$ The distance between a node and the next antinode is

A) 7.5cm

B) 15cm

C) 22.5cm

D) 30cm

• question_answer46) Two waves each of frequency 540 Hz travel at a speed of 330 m/s. If the source are in phase, in the beginning, the phase difference of the waves at a point 4 m from one source and 4.4 m from the other is

A) $59{}^\circ$

B) $118{}^\circ$

C) $177{}^\circ$

D) $236{}^\circ$

• question_answer47) Two point charges$+36\mu C$and$-16\mu C$are placed 10 cm apart. At a point$X$, there is no resultant force on unit positive charge. The distance of$X$from$+36\mu C$charge is

A) 10cm

B) 20cm

C) 30 cm

D) 35 cm

• question_answer48) Five resistors are connected between points$X$and V as shown in the diagram. A current of 10 A flows in the network from$X$to$Y$. A) The potential difference between X and Z is equal to that between Z and Y

B) The potential difference between X and Z is more than that between Z and Y

C) The potential difference between X and Z is less than that between Z and Y

D) The potential difference between Z and Y is 24V

• question_answer49) The resistance of a galvanometer is$25\,\Omega$, and it requires$50\,\mu A$for full deflection. The value of the shunt resistance required to convert it into an ammeter of 5 A is

A) $2.5\times {{10}^{-4}}\Omega$

B) $1.25\times {{10}^{-3}}\Omega$

C) $0.05\,\Omega$

D) $2.5\,\Omega$

• question_answer50) In circuit shown in figure if both the bulbs${{B}_{1}}$and${{B}_{2}}$are identical A) their brightness will be same

B) ${{B}_{1}}$will be brighter than${{B}_{2}}$

C) as frequency of supply voltage is increased, brightness of${{B}_{1}}$will increase and that of${{B}_{2}}$will decrease

D) only${{B}_{2}}$will glow because the capacitor has infinite impedance

• question_answer51) A certain radioactive substance has a half-life of 5 yr. Thus, for a nucleus in a sample of the element, the probability of decay in 10 yr is

A) 50%

B) 75%

C) 100%

D) 60%

• question_answer52) An$L-C$resonant circuit contains a 400 pF capacitor and a$100\,\mu H$inductor. It is set into oscillation coupled to an antenna. The wavelength of the radiated electromagnetic waves is

A) 377 mm

B) 377 m

C) 377cm

D) 3.77cm

• question_answer53) The potential difference between the target and the cathode of an X-ray tube is 50 kV and the current in tube is 20 mA. Only 1% of the total energy supplied is emitted as X-radiation. What is the maximum frequency of the emitted radiation?

A) $1.2\times {{10}^{17}}Hz$

B) $1.2\times {{10}^{19}}Hz$

C) $6\times {{10}^{15}}Hz$

D) $2.4\times {{10}^{18}}Hz$

• question_answer54) In the depletion region of an unbiased$p-n$ junction diode there are

A) only electrons

B) only holes

C) both electrons and holes

D) only fixed ions

• question_answer55) A particle of mass$m=5$is moving with a uniform speed$v=3\sqrt{2}$in the XOY plane along the line$y=x+4$. The magnitude of the angular momentum of the particle about the origin is

A) 7.5 unit

B) 60 unit

C) $40\sqrt{2}$unit

D) zero

• question_answer56) An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of faces of the cube. The empirical formula of the compound would be

A) AB

B) ${{A}_{2}}B$

C) $A{{B}_{3}}$

D) ${{A}_{3}}B$

• question_answer57) Acetylene hydrocarbons are acidic because

A) acetylene contains least number of hydrogen atoms

B) acetylene has only one hydrogen atom at each carbon atom

C) acetylene belongs to the class of alkynes with formula${{C}_{n}}{{H}_{2n-2}}$

D) sigma electron density of$C-H$bond in acetylene is nearer a carbon which has 50% $s-$character

• question_answer58) Which of the following does not contain $-COOH$group?

A) Aspirin

B) Benzoic acid

C) Picric acid

D) All have $-COOH$group

• question_answer59) Only an aldehyde having ... can undergoes the aldol condensation.

A) at least one alpha H atom

B) at least one beta H atom

C) no alpha H atom

D) an aromatic ring

A) no action occurs

B) ${{H}_{2}}$is formed

C) $NaO{{C}_{2}}{{H}_{5}}$and${{O}_{2}}$are formed

D) $NaO{{C}_{2}}{{H}_{5}}$and${{H}_{2}}$are formed

• question_answer61) The gold number of some colloidal solutions are given below

 Colloidal solution Gold number A 0.01 B 2.5 C 20
The protective nature of these colloidal solutions follows the order

A) $C>B>A$

B) $~A>B>C$

C) $A=B=C$

D) $B>A>C$

• question_answer62) The reaction of$HBr$with$C{{H}_{3}}\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}$in the presence of peroxide will give

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

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

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

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

• question_answer63) The alcohol manufactured from water gas is

A) ethanol

B) methanol

C) isobutanol

D) butanol

• question_answer64) The iodoform test is not given by

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

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

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

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

• question_answer65) When 3,3-dimethyl-2-butanol is heated with ${{H}_{2}}S{{O}_{4}},$the major product obtained is

A) 2,2-dimethyl-l-butene

B) 2,3-dimethyl-l-butene

C) 2,3-dimethyl-2-butene

D) $cis$and trans isomers of 2,3-dimethyl-2- butane

• question_answer66) The correct order of basicity of amines in water is

A) ${{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N$

B) $C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N$

C) ${{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}$

D) None of the above

• question_answer67) The number of nodes present in radial wave function of 3d orbital is

A) 1

B) 2

C) 0

D) 3

• question_answer68) Which of the following has largest negative electron gain enthalpy?

A) $F$

B) $Cl$

C) $Br$

D) $I$

• question_answer69) Bromine belongs to period

A) third

B) fourth

C) fifth

D) second

• question_answer70) $PC{{l}_{5}}$molecule has the following geometry

A) trigonal bipyramidal

B) octahedral.

C) square planar

D) planar triangular

• question_answer71) In an octahedral structure, the pair of d-orbitals involved in${{d}^{2}}s{{p}^{3}}$hybridisation is

A) ${{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{xz}}$

B) ${{d}_{{{z}^{2}}}},{{d}_{zx}}$

C) ${{d}_{xy}},{{d}_{yz}}$

D) ${{d}_{{{x}^{2}}-{{y}^{2}}}},{{d}_{{{z}^{2}}}}$

• question_answer72) For the electrode reaction,${{M}^{n+}}(aq)+n{{e}^{-}}\xrightarrow[{}]{{}}M(s)$Nernst equation is

A) $E=E{}^\circ +\frac{RT}{nF}\log \frac{1}{[{{M}^{n+}}]}$

B) $E{}^\circ =E+RT\,in\,[{{M}^{n+}}]$

C) $E=E{}^\circ -\frac{RT}{nF}\,in\frac{1}{\,[{{M}^{n+}}]}$

D) $\frac{E}{E{}^\circ }=\frac{RT}{nF}\,in[{{M}^{n+}}]$

• question_answer73) Two liquids A and B boil at$145{}^\circ C$and $190{}^\circ C$ respectively. At$80{}^\circ C$which of them has higher vapour pressure?

A) Liquid A

B) Liquid B

C) Both have equal vapour pressure

D) None of the above

• question_answer74) What is the effect of carbon dioxide in water on corrosion?

A) Increase rusting of iron

B) Decrease rusting of iron

C) Does not affect

D) None of the above

• question_answer75) Delocalised electrons are present in

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

C) 1,3,5-hexatriene

D) All of these

• question_answer76) The chemical name of isoprene is

C) 2-methoxypropene

D) None of the above

• question_answer77) Assertion/Reason Type Question Answer Codes (i) Both Assertion and Reason (R) are correct and (R) is the correct explanation of (ii) Both and (R) are correct but (R) is not the correct explanation of (iii) is correct but (R) is incorrect (iv) is incorrect but (R) is correct Assertion Methyl cyanide on reaction with$LiAl{{H}_{4}}$does not form ethyl amine. Reason (R) Acidic hydrolysis, of JRCN forms$RCOOH$.

A) (i)

B) (ii)

C) (iii)

D) (iv)

• question_answer78) The Birch reduction of toluene gives

A) B) C) D) • question_answer79) Given below is the sketch of a plant for carrying out a process. Name the process occurring in the above plant.

A) Reverse osmosis

B) Osmosis

C) Diffusion

D) None of these

• question_answer80) In a reaction between A and B, the initial rate of reaction$({{r}_{o}})$was measured for different initial concentrations of A and B as given below

 $A/mol\,{{L}^{-1}}$ 0.20 0.20 0.40 $B/mol\,{{L}^{-1}}$ 0.30 0.10 0.05 ${{r}_{0}}/$$mol\,{{L}^{-1}}{{s}^{-1}}$ $5.07\times {{10}^{-5}}$ $5.07\times {{10}^{-5}}$ $1.43\times {{10}^{-4}}$
What is the order of the reaction with respect to A and B?

A) 2.5, 1.0

B) 1.5,0

C) 2.5,0

D) 1.5, 1

• question_answer81) The most stable conformation of 1,2-diphenyl ethane is

A) B) C) D) • question_answer82) According to nuclear reaction,$_{4}Be+_{2}^{4}He\xrightarrow[{}]{{}}_{6}^{12}C+_{0}^{1}n,$the mass number of Be atom is

A) 4

B) 8

C) 6

D) 9

• question_answer83) Formula of asbestos is

A) ${{[M{{g}_{3}}S{{i}_{4}}{{O}_{10}}{{(OH)}_{2}}]}_{n}}$

B) $C{{a}_{2}}M{{g}_{5}}{{(S{{i}_{4}}{{O}_{11}})}_{2}}{{(OH)}_{2}}$

C) $CaMg{{(Si{{O}_{3}})}_{2}}$

D) $C{{a}_{3}}S{{i}_{3}}{{O}_{9}}$

• question_answer84) Which of the following resonating structures is not correct for$C{{O}_{2}}$?

A) $\overset{\bullet \,\,\bullet }{\mathop{{}_{\bullet }^{\bullet }O}}\,=C=\overset{\bullet \,\bullet }{\mathop{O_{\bullet }^{\bullet }}}\,$

B) $\underset{\bullet \,\,\,\bullet }{\mathop{^{-}\overset{\bullet \,\,\bullet }{\mathop{{}_{\bullet }^{\bullet }O}}\,}}\,=C=\overset{+}{\mathop{O_{\bullet }^{\bullet }}}\,$

C) $\underset{\,\,\,\,\,\,\bullet \,\,\bullet }{\mathop{\overset{+}{\mathop{{}_{\bullet }^{\bullet }O}}\,}}\,-C\equiv \underset{\bullet \,\bullet }{\mathop{O{{_{\bullet }^{\bullet }}^{-}}}}\,$

D) $\overset{+}{\mathop{{}_{\bullet }^{\bullet }O}}\,\equiv C-\overset{\bullet \,\bullet }{\mathop{\underset{\bullet \,\bullet }{\mathop{O{{_{\bullet }^{\bullet }}^{-}}}}\,}}\,$

• question_answer85) At$25{}^\circ C,$3 g of a solute A in 100 mi/of an aqueous solution gave an osmotic pressure of 2.5 atmosphere. What is the molar mas5 of solute?

A) 293

B) 239

C) 392

D) 932

• question_answer86) The correct IUPAC name of$C{{H}_{3}}C{{H}_{2}}CH(C{{H}_{3}})CH{{({{C}_{2}}{{H}_{5}})}_{2}}$is

A) 4-ethyl-3-methylhexane

B) 3-ethyl-4-metbylhexane

C) 3-methy-4-ethyihexane

D) 3-iso-pentylpropane

• question_answer87) Reduction of carbonyl compounds to alkanes with$N{{H}_{2}}N{{H}_{2}}$and$NaOH$is called

A) Ponndrof verley reduction

B) Clemmensens reduction

C) Wurtz reaction

D) Wolff-Kishner reduction

• question_answer88) General formula of alkynes is

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

B) ${{C}_{n}}{{H}_{2n+2}}$

C) ${{C}_{2n+2}}{{H}_{n}}$

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

• question_answer89) Alkaline$KMn{{O}_{4}}$oxidises acetylene to

A) acetic acid

B) ethyl alcohol

C) ethylene glycol

D) oxalic acid

• question_answer90) Dehydration of alcohol is an example of

A) redox reaction

B) elimination reaction

C) substitution reaction

A) $Cu,Zn,Sn$

B) $Cu,Zn,Ni$

C) $Cu,Zn,P$

D) $C,N,Fe$

• question_answer92) How many moles of nitrogen are needed to produce 8.2 moles of ammonia by reaction with hydrogen?

A) 2.1

B) 3.1

C) 3.2

D) 4.1

• question_answer93) The temperature of a gas in a closed container is$27{}^\circ C$. If the temperature is raised to$327{}^\circ C,$the pressure exerted is

A) reduced to half

B) doubled

C) reduced to one third

D) cannot be predicted

• question_answer94) Molar heat capacity of ethanol is$110.4\text{ }J{{K}^{-1}}$. Its specific heat capacity is

A) 2.4

B) 55.2

C) 5.078

D) 110.4

• question_answer95) For the water gas reaction,$C(s)+{{H}_{2}}O(g)CO(g)+{{H}_{2}}O(g)$the standard Gibbs energy at 1000 K is$-8.1\text{ }kJ\,mo{{l}^{-1}}$. What is its equilibrium constant?

A) 2.60

B) 4.62

C) 2.64

D) None of these

• question_answer96) For the reaction,$2NO(g)+C{{l}_{2}}(g)2NOCl(g)$which is true?

A) ${{K}_{p}}={{K}_{C}}\times RT$

B) ${{K}_{p}}={{K}_{C}}{{(RT)}^{2}}$

C) ${{K}_{p}}=\frac{{{K}_{C}}}{RT}$

D) ${{K}_{p}}=\frac{{{K}_{C}}}{{{(RT)}^{2}}}$

• question_answer97) Oxidation number of$Mn$in$MnO_{4}^{-}$ion is

A) $+1$

B) $-7$

C) $-1$

D) $+7$

• question_answer98) Which of the following is not alkali metal?

A) $Na$

B) $Fr$

C) $Ca$

D) $K$

• question_answer99) Inert pair effect is predominant in

A) $~Si$

B) $Pb$

C) $Ge$

D) $Sn$

• question_answer100) How many o and n bonds are there in the molecule of tetracyanoethene? ${{(NC)}_{2}}C=C{{(CN)}_{2}}$

A) $9\sigma ,7\pi$

B) $5\sigma ,9\pi$

C) $5\sigma ,8\pi$

D) $9\sigma ,9\pi$

A) aqueous $KMn{{O}_{4}}$

B) neutral$KMn{{O}_{4}}$

C) alkaline$KMn{{O}_{4}}$

D) aqueous bromine water

A) zero

B) 20

C) 80

D) 60

• question_answer103) Low spin complex is formed by

A) $s{{p}^{3}}{{d}^{2}}$hybridization

B) $s{{p}^{3}}d$hybridization

C) ${{d}^{2}}s{{p}^{3}}$hybridization

D) $s{{p}^{3}}$hybridization

• question_answer104) Hybrid state of central oxygen atom in ether is

A) $sp$

B) $s{{p}^{2}}$

C) $s{{p}^{3}}d$

D) $s{{p}^{3}}$

• question_answer105) Clemmensen reduction of a ketone is carried out in the presence of

A) $LiAl{{H}_{4}}$in ether

B) $Zn-Hg$with$HCl$

C) glycol with $KOH$

D) ${{H}_{2}}$with$Pd$as catalyst

• question_answer106) The electrophile involved in the nitration of benzene is

A) $NO$

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

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

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

• question_answer107) In the reaction,${{C}_{6}}{{H}_{5}}-{{N}^{+}}\equiv NC{{l}^{-}}+{{H}_{3}}P{{O}_{2}}+{{H}_{2}}O\xrightarrow[{}]{{}}?$the product formed will be

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

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

C) ${{C}_{6}}{{H}_{5}}Cl$

D) ${{C}_{6}}{{H}_{5}}-{{C}_{6}}{{H}_{5}}$

• question_answer108) Amylopectin is a polymer of

A) $\beta -D-$glucose

B) $\alpha -D-$glucose

C) $\beta -D-$fructose

D) $\alpha -D-$mannose

• question_answer109) Across the lanthanide series, the basicity of the lanthanide hydroxides

A) increases

B) decreases

C) first increases and then decreases

D) first decreases and then increases

• question_answer110) When sodium and chlorine ion react, energy is

A) released and ionic bonds are formed

B) released and covalent bonds are formed

C) absorbed and ionic bonds are formed

D) absorbed and covalent bonds are formed

• question_answer111) The value of$\sum\limits_{k=1}^{6}{\left( \sin \frac{2\pi k}{7}-i\cos \frac{2\pi k}{7} \right)}$is

A)

B) $-i$

C) 1

D) 0

• question_answer112) If${{a}_{n}}$be the nth term of an AP and if${{a}_{7}}=15,$then the value of the common difference that would make${{a}_{2}}{{a}_{7}}{{a}_{12}}$greatest is

A) 9

B) 9/4

C) 0

D) 18

• question_answer113) If${{a}_{1}},{{a}_{2}},{{a}_{3}},...,{{a}_{n}}$are in AP, where${{a}_{i}}>0$for all$i$, then value of the expression $\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+.....\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}$

A) $\frac{n-1}{\sqrt{{{a}_{n}}}-\sqrt{{{a}_{1}}}}$

B) $\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}$

C) $\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}$

D) None of these

• question_answer114) If one root of${{x}^{2}}-x-k=0$is square of the other, then k is equal to

A) $2\pm \sqrt{3}$

B) $3\pm \sqrt{2}$

C) $2\pm \sqrt{5}$

D) $5\pm \sqrt{2}$

• question_answer115) The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is

A) 27378

B) 27405

C) 27399

D) None of these

• question_answer116) The coefficient of${{x}^{n}}$in the expansion of ${{(1-4x)}^{-1/2}}$is

A) $\frac{(2n)!}{{{(n!)}^{2}}}$

B) $\frac{2n}{{{(n!)}^{2}}}$

C) $\frac{(2n)!}{{{n}^{2}}}$

D) None of these

• question_answer117) Let A and B be symmetric matrices of the same order, then

A) $A+B$is symmetric matrix

B) $AB-BA$is skew symmetric matrix

C) $AB+BA$is symmetric matrix

D) All of the above

• question_answer118) If$\alpha ,\beta ,\gamma$are the roots of${{x}^{3}}+a{{x}^{2}}+b=0,$then the value of$\left| \begin{matrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \\ \end{matrix} \right|$is

A) $-{{a}^{3}}$

B) ${{a}^{3}}-3b$

C) ${{a}^{3}}$

D) ${{a}^{2}}-3b$

• question_answer119) If the axes are shifted to the point$(1,-2)$without rotation the equation $2{{x}^{2}}+{{y}^{2}}-4x+4y=0$becomes

A) $2{{X}^{2}}+{{Y}^{2}}=6$

B) $2{{X}^{2}}+{{Y}^{2}}+6=0$

C) ${{X}^{2}}+2{{Y}^{2}}=6$

D) $2{{X}^{2}}+{{Y}^{2}}=0$

• question_answer120) The lines represented by the equation $A{{x}^{2}}+2Bxy+H{{y}^{2}}=0$are perpendicular, if

A) $A+B=0$

B) $B+H=0$

C) $A+H=0$

D) $AH=-1$

• question_answer121) The number of common tangents to the circles ${{x}^{2}}+{{(y-1)}^{2}}=9$and${{(x-1)}^{2}}+{{y}^{2}}=25$is

A) 0

B) 1

C) 2

D) 3

• question_answer122) The length of focal chord which makes an angle $\alpha$with the axis. of the parabola${{y}^{2}}=4ax$is

A) $2a\text{ }co{{t}^{2}}\alpha$

B) $4a\text{ }cose{{c}^{2}}\alpha$

C) $4a\text{ }cot\,\alpha$

D) None of these

• question_answer123) The point of intersection of the tangents at two points on the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,$whose eccentric angles differ by a right angle lies on the ellipse

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

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

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

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

• question_answer124) If the normal at$\left( ct,\frac{c}{t} \right)$on the curve$xy={{c}^{2}}$meets the curve again in t, then

A) $t=-\frac{1}{{{t}^{3}}}$

B) $t=-\frac{1}{t}$

C) $t=\frac{1}{{{t}^{2}}}$

D) $t{{}^{2}}=-\frac{1}{{{t}^{2}}}$

• question_answer125) If$f(x)=\left\{ \begin{matrix} \frac{|x-4|}{x-4}, & x\ne 4 \\ 0, & x=4 \\ \end{matrix} \right.$then$\underset{x\to 4}{\mathop{\lim }}\,f(x)$is equal to

A) 1

B) $-1$

C) 0

D) does not exist

• question_answer126) The equation$\left| \begin{matrix} x-a & x-b & x-c \\ x-b & x-c & x-a \\ x-c & x-a & x-b \\ \end{matrix} \right|=0$where a, b, c are different is satisfied by

A) $x=0$

B) $x=a$

C) $x=\frac{1}{3}(a+b+c)$

D) $x=a+b+c$

• question_answer127) The function$f(x)=\left\{ \begin{matrix} x & for & x<1 \\ 2-x & for & 1\le x\le 2 \\ -2+3x-{{x}^{2}} & for & x>2 \\ \end{matrix} \right.$is differentiable

A) at$x=2$and at$x=1$

B) at$x=2$but not at$x=1$

C) at$x=1$but not at$x=2$

D) neither at$x=2$nor at$x=1$

• question_answer128) Find the points on the curve$y={{x}^{3}}-2{{x}^{2}}-x$ at which the tangent lines are parallel to the line$y~=3x-2$

A) $(2,2),\left( -\frac{2}{3},-\frac{14}{27} \right)$

B) $(2,-2),\left( -\frac{2}{3},-\frac{14}{37} \right)$

C) $(2,-2),\left( -\frac{2}{3},-\frac{14}{27} \right)$

D) None of the above:

• question_answer129) If$f$and g are two increasing functions such that fog is denned, then

A) fog is an increasing function

B) fog is a decreasing function

C) fog is neither increasing nor decreasing

D) None of the above

• question_answer130) The value of the integral$\int{\frac{2x\,dx}{({{x}^{2}}+1)({{x}^{2}}+2)}}$is

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

B) $-[\log |{{x}^{2}}+1|+\log |{{x}^{2}}+2|+c$

C) $\log |{{x}^{2}}+1|-\log |{{x}^{2}}+2|+c$

D) $\log |{{x}^{2}}+2|-\log |{{x}^{2}}+1|+c$

• question_answer131) The area of the figure bounded by the curves $y=|x-1|$is$y=3|x|$

A) 1

B) 2

C) 3

D) 4

• question_answer132) If the unit vectors$\overrightarrow{a}$and$\overrightarrow{b}$are inclined at an angle$2\theta$such that$|\overrightarrow{a}-\overrightarrow{b}|<1$and$0\le \theta k,\pi$then $\theta$lies in the interval

A) $\left[ 0,\frac{\pi }{6} \right)$

B) $\left( \frac{5\pi }{6},\pi \right]$

C) Both and

D) Neither (a) nor (b)

• question_answer133) The plane$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$meets the coordinate axes at A, B and C respectively, find the equation of the sphere OABC

A) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+ax+by+cz=0$

B) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-ax-by-cz=0$

C) ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+ax-by+cz=0$

D) None of the above

• question_answer134) A bag contains 16 coins of which two are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is

A) $\frac{9}{16}$

B) $\frac{11}{16}$

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

D) None of these

• question_answer135) The value of$\sqrt{3}\cot 20{}^\circ -4\cos 20{}^\circ$is equal to

A) 1

B) $-1$

C) 0

D) None of these

• question_answer136) If$sin\text{ }x+cosec\text{ }x=2,$then${{\sin }^{n}}x+\cos e{{c}^{n}}x$is equal to

A) 2

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

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

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

• question_answer137) The number of solutions of the equation tan $x+sec\text{ }x=2\text{ }cos\text{ }x,$lying in the interval $[0,2\pi ]$is

A) 0

B) 1

C) 2

D) 3

• question_answer138) The arithmetic mean of a set of observations is $\overline{X}$. If each observation is divided by a and then is increased by 10, then the mean of the new series is

A) $\frac{\overline{X}}{\alpha }$

B) $\frac{\overline{X}+10}{\alpha }$

C) $\frac{\overline{X}+10\,\alpha }{\alpha }$

D) $\alpha \overline{X}+10$

• question_answer139) If$x$and y are two uncorrelated variables and if $u=x+y,v=x-y,$then$r(u,v)$is equal to

A) $\frac{\sigma _{x}^{2}+\sigma _{y}^{2}}{\sigma _{x}^{2}-\sigma _{y}^{2}}$

B) $\frac{\sigma _{x}^{2}-\sigma _{y}^{2}}{\sigma _{x}^{2}+\sigma _{y}^{2}}$

C) $\frac{\sigma _{x}^{2}+\sigma _{y}^{2}}{{{\sigma }_{x}}{{\sigma }_{y}}}$

D) None of these

• question_answer140) If$u$and$v$be the components of the resultant velocity w of a particle such that$u=v=w,$then the angle between the velocities is

A) $60{}^\circ$

B) $150{}^\circ$

C) $120{}^\circ$

D) $30{}^\circ$

• question_answer141) $\left\{ \frac{1+\cos \frac{\pi }{8}+i\sin \frac{\pi }{8}}{1+\cos \frac{\pi }{8}-i\sin \frac{\pi }{8}} \right\}$is equal to

A) $1+i$

B) $1-i$

C) 1

D) $-1$

• question_answer142) The arithmetic mean of two positive numbers and$b(a>b)$is twice their geometric mean, then$a:b$is

A) $2+\sqrt{3}:2-\sqrt{3}$

B) $7+4\sqrt{3}:7-4\sqrt{3}$

C) $2:7+4\sqrt{3}$

D) $2\sqrt{3}$

• question_answer143) Given that tan A and tan B are the roots of the equation${{x}^{2}}-px+q=0,$the value of ${{\sin }^{2}}(A+B)$is

A) $\frac{{{p}^{2}}}{{{p}^{2}}+{{(1-q)}^{2}}}$

B) $\frac{{{p}^{2}}}{{{p}^{2}}+{{q}^{2}}}$

C) $\frac{{{q}^{2}}}{{{p}^{2}}+{{(1-q)}^{2}}}$

D) $\frac{{{p}^{2}}}{{{(p+q)}^{2}}}$

• question_answer144) How many four letter words can be formed using the letters of the word FAILURE, so that F is included in each word?

A) 400

B) 420

C) 460

D) 480

• question_answer145) Find the coefficient of${{x}^{4}}$in the expansion of

A) 4

B) 8

C) 12

D) None of these

• question_answer146) If A is a skew symmetric matrix, then the matrix ${{B}^{T}}AB$is

A) symmetric

B) skew symmetric

C) cant say

D) None of these

• question_answer147) If the lines$x+2ay+a=0,\text{ }x+3by+b=0$and $x+4cy+c=0$are concurrent, then a, b, c are in

A) AP

B) GP

C) HP

D) None of these

• question_answer148) The distance between the parallel lines represented by the equation ${{x}^{2}}+6xy+9{{y}^{2}}+4x+12y-5=0$is

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

B) $\frac{6}{\sqrt{10}}$

C) $\frac{6}{\sqrt{5}}$

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

• question_answer149) If the lengths of the tangents from the point (1,2) to the circles${{x}^{2}}+{{y}^{2}}+x+y-4=0$and $3{{x}^{2}}+3{{y}^{2}}-x-y-\lambda =0$are in the ratio$4:3,$then the value of$\lambda$is

A) $\frac{21}{2}$

B) $\frac{21}{4}$

C) $\frac{21}{5}$

D) $\frac{21}{11}$

• question_answer150) If M is the foot of the perpendicular from a point P oh a parabola to its directrix and SPM is an equilateral triangle, where$S$is the focus, then PM is equal to

A) $a$

B) $2a$

C) $3a$

D) $4a$

• question_answer151) The equations of tangents to the ellipse $9{{x}^{2}}+16{{y}^{2}}=144$which pass through the point $(2,3)$are

A) $y=3,y=x+5$

B) $y=3,x=3$

C) $x=2,\text{ }y=x+5$

D) $y=3,\text{ }y=-x+5$

• question_answer152) Let and$e$be the eccentricities of a hyperbola and its conjugate, then$\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}$is equal to

A) 0

B) 1

C) 2

D) None of these

• question_answer153) If$f(x)$is an even differentiable function on R, then$f(x)$is

A) an even function

B) an odd function

C) cant say

D) cant be determined

• question_answer154) The inverse of the function$f(x)=\frac{{{10}^{x}}-{{10}^{-x}}}{{{10}^{x}}+{{10}^{-x}}}$is

A) ${{\log }_{10}}(2-x)$

B) $\frac{1}{2}{{\log }_{10}}\left( \frac{1+x}{1-x} \right)$

C) $\frac{1}{2}{{\log }_{10}}(2x-1)$

D) $\frac{1}{4}{{\log }_{10}}\left( \frac{2x}{2-x} \right)$

• question_answer155) The value of the$\underset{x\to \infty }{\mathop{\lim }}\,{{x}^{1/x}}$is equal to

A) 0

B) 1

C) $e$

D) ${{e}^{-1}}$

• question_answer156) If$f(x)={{e}^{x}}g(x),g(0)=2,g(0)=1,$then$f(0)$is equal to

A) 1

B) 3

C) 2

D) 0

• question_answer157) The slope of the tangent to the curve $x={{t}^{2}}+3t-8,\text{ }y=2{{t}^{2}}-2t-5$at the point $(2,-1)$is

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

B) $\frac{6}{7}$

C) $-\frac{6}{7}$

D) None of these

• question_answer158) The function$f(x)={{\cot }^{-1}}x+x$increases in the interval

A) $(1,\infty )$

B) $(-1,\infty )$

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

D) $(0,\infty )$

• question_answer159) The maximum slope of the curve $y=-{{x}^{3}}+3{{x}^{2}}+2x-27$is

A) 5

B) $-5$

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

D) None of these

• question_answer160) The integral$\int{{{\sin }^{3}}x}{{\cos }^{3}}x\,dx$is equal to

A) $\frac{1}{32}\left[ -\frac{3}{2}\cos 2x+\frac{1}{6}\cos 6x \right]+c$

B) $\frac{1}{32}\left[ -\frac{3}{2}\sin 2x+\frac{1}{6}\sin 6x \right]+c$

C) $-\frac{1}{32}\left[ -\frac{3}{2}\cos 2x+\frac{1}{6}\sin 6x \right]+c$

D) None of the above

• question_answer161) The value of$\int{\frac{{{e}^{x}}\,dx}{\sqrt{5-4{{e}^{x}}-{{e}^{2x}}}}}$is equal to

A) ${{\tan }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c$

B) ${{\sin }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c$

C) ${{\cos }^{-1}}\left( \frac{{{e}^{x}}+2}{3} \right)+c$

D) None of the above

• question_answer162) $\int_{0}^{1}{\frac{({{x}^{\alpha }}-1)dx}{\log x}}$equals

A) $\frac{1}{\alpha +1}$

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

C) $\alpha -1$

D) None of these

• question_answer163) Solution of${{e}^{(dy/dx)}}=x+1;y(0)=5$is

A) $y=x\text{ }log(x+1)-x-log(x+1)+5$

B) $y=x\text{ }log(x+1)+x+log(x+1)+5$

C) $y=x\text{ }log(x+1)-x+log(x+1)+5$

D) None of the above

• question_answer164) For any vector$\overrightarrow{a},|\overrightarrow{a}\times \hat{i}{{|}^{2}}+|\overrightarrow{a}\times \hat{j}{{|}^{2}}+|\overrightarrow{a}\times \hat{k}{{|}^{2}}$is equal to

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

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

C) $3|\overrightarrow{a}{{|}^{2}}$

D) None of these

• question_answer165) The shortest distance between the lines $\overrightarrow{r}=(4\hat{i}-\hat{j})+\lambda (\hat{i}+2\hat{j}-3\hat{k})$and $\overrightarrow{r}=(\hat{i}-\hat{j}+2\hat{k})+\mu (2\hat{i}+4\hat{j}-5\hat{k})$is equal to

A) $\frac{6}{\sqrt{10}}$

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

C) $\frac{6}{5}$

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

• question_answer166) If A and B are two independent events such that$P(\overline{A}\cap B)=\frac{2}{15}$and$P(A\cap \overline{B})=\frac{1}{6},$then P is

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

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

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

D) $\frac{7}{6}$

• question_answer167) Maximum and minimum values of$6\text{ }sin\text{ }x\text{ }cos\text{ }x+4\text{ }cos\text{ }2x$are respectively

A) 5 and$-5$

B) $2\sqrt{13}$and$-2\sqrt{13}$

C) 10 and$-10$

D) $\frac{5}{2}$and$-\frac{5}{2}$

• question_answer168) In a$\Delta ABC,$if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$and the side$a=2,$then area of the triangle is

A) 1

B) 2

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

D) $\sqrt{3}$

• question_answer169) The equation${{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)$has

A) no solution

B) unique solution

C) infinite number of solutions

D) None of the above

• question_answer170) A tower subtends an angle a at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is P. Then, height of the tower is

A) $b\text{ }tan\text{ }\alpha \text{ }cot\text{ }\beta$

B) $b~cot\text{ }\alpha \text{ }tan\text{ }\beta$

C) $b\text{ }tan\text{ }\alpha \text{ }tan\text{ }\beta$

D) $b\text{ }cot\text{ }\alpha \text{ }cot\text{ }\beta$

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