# Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2009

### done JCECE Engineering Solved Paper-2009

• question_answer1) The twinkling effect of star light is due to

A) total internal reflection

B) high dense matter of star

C) constant burning of hydrogen in the star

D) the fluctuating apparent position of the star being slightly different from the actual position of the star

• question_answer2) The width of the diffraction band varies

A) inversely as the wavelength

B) directly as the width of the slit

C) directly as the distance between the slit and the screen

D) inversely as the size of the source from which the slit is illuminated

• question_answer3) An unpolarised beam of intensity ${{I}_{0}}$ is incident on a pair of Nichols making an angle of ${{60}^{o}}$ with each other. The intensity of light emerging from the pair is

A) ${{I}_{0}}$

B) $\frac{{{I}_{0}}}{2}$

C) $\frac{{{I}_{0}}}{4}$

D) $\frac{{{I}_{0}}}{8}$

• question_answer4) When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. This is due to

A) diffraction of the signal received from the antenna

B) interference of the direct signal received by the antenna with the weak signal reflected by the passing aircraft

C) change of magnetic flux occurring due to the passage of aircraft

D) vibration created by the, passage of aircraft,

• question_answer5) A beam of light of wavelength $600\,\,nm$ from a distant source falls on a single slit $1\,\,mm$ wide and the resulting diffraction pattern is observed on a screen $2\,\,m$ away. The distance between the first dark fringes on either side of the central bright fringe is

A) $1.2\,\,cm$

B) $1.2\,\,mm$

C) $2.4\,\,cm$

D) $2.4\,\,mm$

• question_answer6) The physical quantity having the dimensions $[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]$is

A) resistance

B) resistivity

C) electrical conductivity

D) electromotive force

• question_answer7) A battery of emf $10\,\,V$ and internal resistance $3\Omega$ is connected to a resistor. The current in the circuit is$0.5\,\,A$ The terminal voltage of the battery when the circuit is closed is

A) $10\,\,V$

B) $0\,\,V$

C) $1.5\,\,V$

D) $8.5\,\,V$

• question_answer8) A galvanometer coil has a resistance of $15\Omega$ and gives full scale deflection for a current of$4\,\,mA$. To convert it to an am metal of range $0$ to$6\,\,A$

A) $10\,\,m\Omega$ resistance is to be connected in parallel to the galvanometer

B) $10\,\,m\Omega$ resistance is to be connected in series with the galvanometer

C) $0.1\,\,\Omega$ resistance is to be connected in parallel to the galvanometer

D) $0.1\,\,\Omega$ resistance is to be connected in series with the galvanometer

• question_answer9) The electron drift speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to

A) the conducting property of the conductor

B) the resistance of the conductor is small

C) the electron number density of the conductor is small

D) the electron number density of the conductor is enormous

• question_answer10) A straight wire of mass $200\,\,g$ and length $1.5\,\,m$ carries a current of$2\,\,A$. It is suspended in mid- air by a uniform horizontal magnetic field$B$. The magnitude of $B$ (in tesla) is (assume$g=9.8\,\,m{{s}^{-2}})$

A) $2$

B) $1.5$

C) $0.55$

D) $0.65$

• question_answer11) A Gaussian sphere encloses an electric dipole within it. The total flux across the sphere is

A) zero

B) half that due to a single charge

C) double that due to a single charge

D) dependent on the position of the dipole

• question_answer12) A parallel plate air capacitor has a capacitance$C$. When it is half filled with a dielectric of dielectric constant$5$, the percentage increase in the capacitance will be

A) $400%$

B) $66.6%$

C) $33.3%$

D) $200%$

• question_answer13) A comb run through one's dry hair attracts small bits of paper. This is due to

A) comb is a good conductor

B) paper is a good conductor

C) the atoms is the paper get polarised by the charged comb

D) the comb possesses magnetic properties

• question_answer14) The specific charge of a proton is$9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}$. The specific charge of an alpha particle will be

A) $9.6\times {{10}^{7}}C\,\,k{{g}^{-1}}$

B) $19.2\times {{10}^{7}}C\,\,k{{g}^{-1}}$

C) $4.8\times {{10}^{7}}C\,\,k{{g}^{-1}}$

D) $2.4\times {{10}^{7}}C\,\,k{{g}^{-1}}$

• question_answer15) When light of wavelength $300\,\,nm$ falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, light of wavelength $600\,\,nm$ is sufficient for liberating photoelectrons. The ratio of the work function of the two emitters is

A) $1:2$

B) $2:1$

C) $4:1$

D) $1:4$

• question_answer16) White light is passed through a dilute solution of potassium permanganate. The spectrum produced by the emergent light is

A) band emission spectrum

B) line emission spectrum

C) band absorption spectrum

D) line absorption spectrum

• question_answer17) If ${{\lambda }_{1}}$ and ${{\lambda }_{2}}$ are the wavelengths of the first members of the Lyman and Paschen series respectively, then ${{\lambda }_{1}}:{{\lambda }_{2}}$ is

A) $1:3$

B) $1:30$

C) $7:50$

D) $7:108$

• question_answer18) Activity of a radioactive sample decreases to ${{(1/3)}^{rd}}$ of its original value in $3$ days. Then, in $9$ days its activity will become

A) $(1/27)$ of the original value

B) $(1/9)$ of the original value

C) $(1/18)$ of the original value

D) $(1/3)$of the original value

• question_answer19) The working of which of the following is similar to that of a slide projector?

A) Electron microscope

B) Scanning electron microscope

C) Transmission electron microscope

D) Atomic force microscope

• question_answer20) In a transistor the collector current is always less than the emitter current because

A) collector side is reverse biased and the emitter side is forward biased

B) a few electrons are lost in the base and only remaining ones reach the collector

C) collector being reverse biased, attracts less electrons

D) collector side is forward biased and emitter side is reverse biased

• question_answer21) A transparent cube of $0.21\,\,m$ edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is $0.10\,\,m$ and when viewed from the opposite face is$0.04\,\,m$. The actual distance of the bubble from the second face of the cube is

A) $0.06\,\,m$

B) $0.17\,\,m$

C) $0.05\,\,m$

D) $0.04\,\,m$

• question_answer22) To a fish under water, viewing obliquely a fisherman standing on the bank of a lake, the man looks

A) taller than what he actually is

B) shorter that what he actually is

C) the same height as he actually is

D) depends on the obliquity

• question_answer23) If white light is used in the Newton's rings experiment, the colour observed in the reflected light is complementary to that observed in the transmitted light through the same point. This is due to

A) ${{90}^{o}}$ change of phase in one of the reflected waves

B) ${{180}^{o}}$ change of phase in one of the reflected waves

C) ${{145}^{o}}$ change of phase in one of the reflected waves

D) ${{45}^{o}}$ change of phase in one the reflected waves

• question_answer24) A satellite in a circular orbit of radius $R$ has a period of$4\,\,h$. Another satellite with orbital radius $3R$ around the same planet will have a period (in hours)

A) $16$

B) $4$

C) $4\sqrt{27}$

D) $4\sqrt{8}$

• question_answer25) The freezer in a refrigerator is located at the top section so that

A) the entire chamber of the refrigerator is cooled quickly due to convection

B) the motor is not heated

C) the heat gained from the environment is high

D) the heat gained from the environment is low

• question_answer26) A monoatomic gas is suddenly compressed to ${{(1/8)}^{th}}$ of its initial volume adiabatically. The ratio of its final pressure to the initial pressure is (Given the ratio of the specific heats of the given gas to be$5/3)$

A) $32$

B) $40/3$

C) $24/5$

D) $8$

• question_answer27) A Carnot engine takes heat from a reservoir at ${{627}^{o}}C$ and rejects heat to a sink at${{27}^{o}}C$. Its efficiency will be

A) $3/5$

B) $1/3$

C) $2/3$

D) $200/209$

• question_answer28) A $30\,\,V,\,\,90\,\,W$ lamp is to be operated on a $120\,\,V$$DC$ line. For proper glow, a resistor, of$...\Omega$ should be connected in series with the lamp.

A) $40$

B) $10$

C) $20$

D) $30$

• question_answer29) A tuning fork $A$ produces $4$ beats/s with another tuning fork $B$ of frequency$320\,\,Hz$. On filing one of the prongs of $A,\,\,4$ beats/s are again heard when sounded with the same fork$B$. Then, the frequency of the fork $A$ before filing is

A) $328\,\,Hz$

B) $316\,\,Hz$

C) $324\,\,Hz$

D) $320\,\,Hz$

• question_answer30) The sprinkling of water reduces slightly the temperature of a closed room because

A) temperature of water is less than that of the room

B) specific heat of water is high

C) water has large latent heat of vaporisation

D) water is a bad conductor of heat

• question_answer31) The equation of a simple harmonic wave is given by$y=5\sin \frac{\pi }{2}(100t-x)$, where $x$ and $y$ are in metre and time is in second. The period of the wave in second will be

A) $0.04$

B) $0.01$

C) $1$

D) $5$

• question_answer32) The loudness and pitch of a sound note depends on

A) intensity and frequency

B) frequency and number of harmonics

C) intensity and velocity

D) frequency and velocity

• question_answer33) For ordinary terrestrial experiments, the observer in an inertial frame in the following cases is

A) a child revolving in a giant wheel

B) a driver in a sports car moving with a constant high speed of $200\,\,km{{h}^{-1}}$ on a straight rod

C) the pilot of an aeroplane which is taking off

D) a cyclist negotiating a sharp curve

• question_answer34) A rectangular vessel when full of water, takes $10\,\,\min$ to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?

A) $9\,\,\min$

B) $7\,\,\min$

C) $5\,\,\min$

D) $3\,\,\min$

• question_answer35) If there were no gravity, which of the following will not be there for a fluid?

A) Viscosity

B) Surface tension

C) Pressure

D) Archimedes' upward thrust

• question_answer36) In a $LCR$ series circuit, the potential difference between the terminals of the inductance is$60\,\,V$, between the terminals of the capacitor is$30\,\,V$ and that across the resistance is$40\,\,V$. Then, supply voltage will be equal to

A) $50\,\,V$

B) $70\,\,V$

C) $130\,\,V$

D) $10\,\,V$

• question_answer37) When deuterium and helium are subjected to an accelerating field simultaneously then

A) both acquire same energy

B) deuterium accelerates faster

C) helium accelerates faster

D) neither of them is accelerated

• question_answer38) A solenoid $1.5\,\,m$ long and $0.4\,\,cm$ in diameter possesses $10$ turns per $cm$ length. A current of $5\,\,A$ falls through it. The magnetic field at the axis inside the solenoid is

A) $2\pi \times {{10}^{-3}}T$

B) $2\pi \times {{10}^{-5}}T$

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

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

• question_answer39) A wire $PQR$ is bent as shown in figure and is placed in a region of uniform magnetic field$B$. The length of $PQ=QR=l\,\,A$ current $l$ ampere flows through the wire as shown. The magnitude of the force on $PQ$ and $QR$ will be

A) $BIl,\,\,0$

B) $BIl,\,\,0$

C) $0,\,\,BIl$

D) $0,\,\,0$

• question_answer40) A choke is preferred to a resistance for limiting current in $AC$ circuit because

A) choke is cheap

B) there is no wastage of power

C) choke is compact in size

D) choke is a good absorber of heat

• question_answer41) If ${{r}_{1}}$ and ${{r}_{2}}$ are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio $({{r}_{1}}/{{r}_{2}})$ is

A) $\frac{64}{125}$

B) $\sqrt{\frac{64}{125}}$

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

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

• question_answer42) A motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n-$times the water through the same pipe in the same time the power of the motor must be increased as follows

A) $n-$times

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

C) ${{n}^{3}}-$times

D) ${{n}^{4}}-$times

• question_answer43) For a system to follow the law of conservation of linear momentum during a collision, the condition is (i) total external force acting on the system is zero. (ii) total external force acting on the system is finite and time of collision is negligible. (iii) total internal force acting on the system is zero.

A) (i) only

B) (ii) only

C) (iii) only

D) (i) or (ii)

• question_answer44) An air bubble of radius $1\,\,cm$ rises from the bottom portion through a liquid of density $1.5\,\,g/cc$ at a constant speed of$0.25\,\,cm\,\,{{s}^{-1}}$. If the density of air is neglected, the coefficient of viscosity of the liquid is approximately, (In$Pa)$

A) $13000$

B) $1300$

C) $130$

D) $13$

• question_answer45) A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately

A) $1.2$

B) $1.41$

C) $1.67$

D) $1.83$

• question_answer46) Two solid spheres $A$ and $B$ made of the same material have radii ${{r}_{A}}$ and ${{r}_{B}}$ respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature $A$ and $B$ is

A) $\frac{{{r}_{A}}}{{{r}_{B}}}$

B) $\frac{{{r}_{B}}}{{{r}_{A}}}$

C) $\frac{r_{A}^{2}}{r_{B}^{2}}$

D) $\frac{r_{B}^{2}}{r_{A}^{2}}$

• question_answer47) The effect due to uniform magnetic field on a freely suspended magnetic needle is as follows

A) both torque and net force are present

B) torque is present but no net force

C) both torque and net force are absent

D) net force is present but not torque

• question_answer48) When a positively charged particle enters a uniform magnetic field with uniform velocity, its trajectory can be (i) a straight line (ii) a circle (iii) a helix

A) (i) only

B) (i) or (ii)

C) (i) or (iii)

D) any one of (i), (ii) and (iii)

• question_answer49) An oil drop having a mass $4.8\times {{10}^{-10}}g$ and charge $24\times {{10}^{-18}}C$ stands still between two charged horizontal plates separated by a distance of$1\,\,cm$. If now the polarity of the plates is changed, instantaneous acceleration of the drop is$(g=10\,\,m{{s}^{-2}})$

A) $5\,\,m{{s}^{-2}}$

B) $10\,\,m{{s}^{-2}}$

C) $15\,\,m{{s}^{-2}}$

D) $20\,\,m{{s}^{-2}}$

• question_answer50) A free neutron decays spontaneously into

A) a proton, an electron and anti-neutrino

B) a proton, an electron and a neutrino

C) a proton and electron

D) a proton, and electron, a neutrino and an anti-neutrino

• question_answer51) What is the correct order of spin only magnetic moment (in$BM)$of$M{{n}^{2+}},\,\,\,C{{r}^{2+}}$and${{V}^{2+}}$?

A) $M{{n}^{2+}}>{{V}^{2+}}>C{{r}^{2+}}$

B) ${{V}^{2+}}>C{{r}^{2+}}>M{{n}^{2+}}$

C) $M{{n}^{2+}}>C{{r}^{2+}}>{{V}^{2+}}$

D) $C{{r}^{2+}}>{{V}^{2+}}>M{{n}^{2+}}$

• question_answer52) Which of the following is used for making optical instruments?

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

B) $Si$

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

D) $SiC$

• question_answer53) Which of the following is not correct?

A) $3{{O}_{2}}\underset{\text{discharge}}{\overset{\text{Silent}\,\,\text{electric}}{\longleftrightarrow}}2{{O}_{3}};\,\,\Delta H=-284.5\,\,kJ$

B) Ozone undergoes addition reaction with unsaturated carbon compounds

C) Sodium thio sulphate reacts with ${{I}_{2}}$ to form sodium tetrathionate and sodium iodide

• question_answer54) Which of the following reactions can produce aniline as main product?

A) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/KOH$

B) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/N{{H}_{4}}Cl$

C) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}+LiAl{{H}_{4}}$

D) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}+Zn/HCl$

• question_answer55) Which of the following reagents when heated with ethyl chloride, forms ethylene?

A) Aqueous$KOH$

B) $Zn/HCl$

C) Alcoholic$KOH$

D) $HI$

• question_answer56) The energy of a photon is$3\times {{10}^{-12}}erg$. What is its wavelength in$nm$? $(h=6.62\times {{10}^{-27}}erg-s;\,\,c=3\times {{10}^{10}}cm/s)$

A) $66.2$

B) $1324$

C) $66.2$

D) $6.62$

• question_answer57) What is the time (in sec) required for depositing all the Silver present in $125\,\,mL$ of $1\,\,M\,\,AgN{{O}_{3}}$ solution by passing a current of$241.25\,\,A$? $(1F=96500\,\,C)$

A) $10$

B) $50$

C) $1000$

D) $100$

• question_answer58) The disperse phase, dispersion medium and nature of colloidal solution (lyophilic or lyophobic) of ?gold sol? respectively, are

A) solid, solid, lyophobic

B) liquid, liquid, lyophobic

C) solid, liquid, lyophobic

D) solid, liquid, lyophilic

• question_answer59) The rate constant of a first order reaction at ${{27}^{o}}C$ is ${{10}^{-3}}{{\min }^{-1}}$. The temperature coefficient of this reaction is$2$. What is the rate constant (in${{\min }^{-1}})$ at ${{17}^{o}}C$ for this reaction?

A) ${{10}^{-3}}$

B) $5\times {{10}^{-4}}$

C) $2\times {{10}^{-3}}$

D) ${{10}^{-2}}$

• question_answer60) A solution of an acid has$[{{H}^{+}}]=2\times {{10}^{-5}}$. Find out the concentration of $O{{H}^{-}}$ ions.

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

B) $4\times {{10}^{-10}}N$

C) $2\times {{10}^{-5}}N$

D) $9\times {{10}^{-4}}N$

• question_answer61) Which of the following is added to chloroform to slow down its aerial oxidation in presence of light?

A) Carbonyl chloride

B) Ethyl alcohol

C) Sodium hydroxide

D) Nitric acid

• question_answer62) Which of the products is formed when acetone is reacted with barium hydroxide solution?

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

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

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

D) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}$

• question_answer63) When acetaldehyde is heated with Fehling solution, a red precipitate is formed. Which of the following is that?

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

B) $Cu$

C) $CuO$

D) $CuS{{O}_{4}}$

• question_answer64) What is the correct order of occurrence $(%$ by weight) in air of$Ne,\,\,\,Ar$and$Kr$?

A) $Ne>Ar>Kr$

B) $Ar>Ne>Kr$

C) $Ar>Kr>Ne$

D) $Ne>Kr>Ar$

• question_answer65) Which of the following compounds when heated with $CO$ at ${{150}^{o}}C$ and $500\,\,atm$ pressure in presence of $B{{F}_{3}}$ forms ethyl propionate?

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

B) $C{{H}_{3}}OC{{H}_{3}}$

C) ${{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}$

D) $C{{H}_{3}}O{{C}_{2}}{{H}_{5}}$

• question_answer66) Identify the reaction for which$\Delta H\ne \Delta E$.

A) $S(\text{rhombic})+{{O}_{2}}(g)\xrightarrow{{}}S{{O}_{2}}(g)$

B) ${{N}_{2}}(g)+{{O}_{2}}(g)\xrightarrow{{}}2NO(g)$

C) ${{H}_{2}}(g)+C{{l}_{2}}(g)\xrightarrow{{}}2HCl(g)$

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

• question_answer67) Hydrolysis of $N{{O}_{3}}$ gives $N{{H}_{3}}$ and$X$. Which of the following is$X$?

A) $HClO$

B) $HCl{{O}_{3}}$

C) $HOCl$

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

• question_answer68) What are the metal ions present in carnallite?

A) $Mg,\,\,K$

B) $Al,\,\,Na$

C) $Na,\,\,Mg$

D) $Zn,\,\,Mg$

• question_answer69) Ethyl chloride reacts with sodium ethoxide to form a compound$A$. Which of the following reactions also yields$A?$

A) ${{C}_{2}}{{H}_{5}}Cl,\,\,KOH(alc.),\,\,\Delta$

B) $2{{C}_{2}}{{H}_{5}}OH,\,\,conc.{{H}_{2}}S{{O}_{4}},\,\,{{140}^{o}}C$

C) ${{C}_{2}}{{H}_{5}}Cl,\,\,Mg$(dry ether)

D) ${{C}_{2}}{{H}_{2}}dil.\,\,{{H}_{2}}S{{O}_{4}},\,\,HgS{{O}_{4}}$

• question_answer70) The number of sigma and $pi(\pi )$ bonds present in benzene respectively are

A) $12,\,\,6$

B) $6,\,\,6$

C) $6,\,\,12$

D) $12,\,\,3$

• question_answer71) Edge length of a cube is $400\,\,pm$, its body diagonal would be

A) $566\,\,pm$

B) $600\,\,pm$

C) $500\,\,pm$

D) $693\,\,pm$

• question_answer72) The number of $\alpha -$particles emitted by$_{84}R{{a}^{218}}{{\xrightarrow{{}}}_{82}}P{{b}^{206}}$

A) $3$

B) $4$

C) $6$

D) $2$

• question_answer73) The $IUPAC$ name of the following compound is$C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ {{C}_{6}}{{H}_{5}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{3}}$

A) $2-$cyclohexylbutane

B) $\sec -$butylbenzene

C) $3-$cyclohexylbutane

D) $2-$phenylbutane

• question_answer74) The reaction of primary amine with chloroform and ethanolic solution of $KOH$ is called

A) Hermann's reaction

B) Reimer-Tiemann's reaction

C) Carbylamine reaction

D) Kolbe's reaction

• question_answer75) $0.01$mole of a non-electrolyte is dissolved in $10\,\,g$ of water. The molality of the solution is

A) $0.1\,\,m$

B) $0.5\,\,m$

C) $1.0\,\,m$

D) $0.18\,\,m$

• question_answer76) Atoms with same atomic number and different mass numbers are called

A) isobars

B) isomers

C) isotones

D) isotopes

• question_answer77) The shape of the orbital with the value of$l=2$ and $m=0$is

A) spherical

B) dumb-bell

C) trigonal planar

D) square-planar

• question_answer78) In the following, the element with the highest ionisation energy is

A) $[Ne]3{{s}^{2}}3{{p}^{1}}$

B) $[Ne]3{{s}^{2}}3{{p}^{3}}$

C) $[Ne]3{{s}^{2}}3{{p}^{2}}$

D) $[Ne]3{{s}^{2}}3{{p}^{4}}$

• question_answer79) In the conversion of $B{{r}_{2}}$ to$BrO_{3}^{-}$, the oxidation number of $Br$ changes from

A) zero to$+5$

B) $+1$to$+5$

C) zero to$-3$

D) $+2$to$+5$

• question_answer80) Among the alkali metals cesium is the most reactive because

A) its incomplete shell is nearest to the nucleus

B) it has a single electron in-the valence shell

C) it is the heaviest alkali metal

D) the outermost electron is more loosely bound than the outermost electron of the other alkali metals

• question_answer81) Which of the following represents the Lewis structure of ${{N}_{3}}$ molecule?

A) $_{\text{X}}^{\text{X}}N\equiv N_{\text{X}}^{\text{X}}$

B) $_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,\equiv \overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}$

C) $_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,$

D) $\underset{\text{X}\,\,\text{X}}{\mathop{_{\text{X}}^{\text{X}}\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,}}\,_{\text{X}}^{\text{X}}-\underset{\text{X}\,\,\text{X}}{\mathop{\overset{\text{X}\,\,\text{X}}{\mathop{N}}\,_{\text{X}}^{\text{X}}}}\,$

• question_answer82) Hydrogen bond is strongest in

A) $S-H\cdot \cdot \cdot O$

B) $O-H\cdot \cdot \cdot S$

C) $F-H\cdot \cdot \cdot F$

D) $O-H\cdot \cdot \cdot N$

• question_answer83) The density of a gas is $1.964\,\,d{{m}^{-3}}$ 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_answer84) The shape of $PC{{l}_{3}}$ molecule is

A) trigonal bipyramidal

B) tetrahedral

C) pyramidal

D) square planar

• question_answer85) The concentration of a reactant $X$ decreases from $0.1\,\,M$ to $0.005\,\,M$ 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_answer86) Which of the following does not conduct electricity?

A) Fused$NaCl$

B) Solid$NaCl$

C) Brine solution

D) Copper

• question_answer87) 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_answer88) The $pH$ of ${{10}^{-8}}M\,\,HCl$ Solution is

A) $8$

B) more than$8$

C) between $6$ and $7$

D) slightly more than$7$

• question_answer89) For a reaction to be spontaneous, at all temperatures

A) $\Delta G$ and $\Delta H$ should be negative

B) $\Delta G$ and $\Delta H$ should be positive

C) $\Delta G=\Delta S=0$

D) $\Delta H<\Delta G$

• question_answer90) Which of the following electrolytes 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_answer91) What is the order of a reaction which has a rate expression$rate=k{{[A]}^{3/2}}{{[B]}^{-1}}$?

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

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

C) $0$

D) $\frac{4}{2}$

A) displacement of $\sigma -$electrons

B) delocalisation of $\pi -$electrons

C) delocalisation of $\sigma -$electrons

D) displacement of $\pi -$electrons

• question_answer93) 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_answer94) The catalyst used in the preparation of an alkyl chloride by the action of dry HC1 on an alcohol is

A) anhydrous$AlC{{l}_{3}}$

B) $FeC{{l}_{3}}$

C) anhydrous$ZnC{{l}_{2}}$

D) $Cu$

• question_answer95) By heating phenol with chloroform in alkali, it is converted into

A) salicylic acid

B) salicylaldehyde

C) anisole

D) phenyl benzoate

• question_answer96) Which of the following does not give benzoic acid on hydrolysis?

A) Phenyl cyanide

B) Benzoyl chloride

C) Benzyl chloride

D) Methyl benzoate

A) one secondary $-OH$ and four primary$-OH$ groups

B) one primary $-OH$ and four secondary $-OH$ groups

C) two primary $-OH$ and three secondary$-OH$ groups

D) three primary $-OH$ and two secondary $-OH$ groups

• question_answer98) The formula mass of Mohr's salt is$392$. The iron present in it is oxidised by $KMn{{O}_{4}}$ in acid medium. The equivalent mass of Mohr's salt is

A) $392$

B) $31.6$

C) $278$

D) $156$

• question_answer99) The brown ring test for nitrates depends on

A) the reduction of nitrate to nitric oxide

B) oxidation of nitric oxide to nitrogen dioxide

C) reduction of ferrous sulphate to iron

D) oxidising action of sulphuric acid

• question_answer100) Which of the following solutions will exhibit highest boiling point?

A) $0.01\,\,M\,\,N{{a}_{2}}S{{O}_{4}}(aq)$

B) $0.01\,\,M\,\,KN{{O}_{3}}(aq)$

C) $0.015\,\,M\,\,urea(aq)$

D) $0.015\,\,M\,\,glucose(aq)$

• question_answer101) $\int_{0}^{\pi /2}{\frac{x\sin x\cdot \cos x}{{{\cos }^{4}}x+{{\sin }^{4}}x}}dx$is equal to

A) $\frac{{{\pi }^{2}}}{8}$

B) $\frac{{{\pi }^{2}}}{16}$

C) $1$

D) $0$

• question_answer102) Equation of the tangent to the hyperbola$2{{x}^{2}}-3{{y}^{2}}=6$. Which is parallel to the line $y-3x-4=0$is

A) $y=3x+8$

B) $y=3x-8$

C) $y=3x+2$

D) None of these

• question_answer103) If the coefficient of correlation between two variables is$0.32$, covariance is $8$ and variance of $x$ is$25$, then variance of $y$ is

A) $36$

B) $25$

C) $64$

D) None of these

• question_answer104) Ten coins are thrown simultaneously, the probability of getting at least $7$ heads is

A) $\frac{63}{256}$

B) $\frac{121}{172}$

C) $\frac{113}{512}$

D) $\frac{11}{64}$

• question_answer105) When ${{b}_{yx}}=0.03$ and${{b}_{xy}}=0.3$, then $r$ is equal to approximately

A) $0.003$

B) $0.095$

C) $0.3$

D) $-0.3$

• question_answer106) Use Simpson's$\frac{1}{3}$rule to find the value of $\int_{1}^{5}{f(x)}\,\,dx$given

 $x$ $1$ $2$ $3$ $4$ $4$ $y$ $10$ $50$ $70$ $80$ $100$

A) $140.88$

B) $256.66$

C) $160.26$

D) None of these

• question_answer107) The feasible region represented by${{x}_{1}}+{{x}_{2}}\le 1$,$-3{{x}_{1}}+{{x}_{2}}\ge 3,\,\,({{x}_{1}},\,\,{{x}_{2}}\ge 0)$is

A) a polygon

B) a singleton set

C) empty set

D) None of these

• question_answer108) The points on the curve ${{x}^{2}}=2y$ which are closest to the point $(0,\,\,5)$ are

A) $(2,\,\,2),\,\,(-2,\,\,2)$

B) $(2\sqrt{2},\,\,4),\,\,(-2\sqrt{2},\,\,4)$

C) $(\sqrt{6},\,\,3),\,\,(-\sqrt{6},\,\,3)$

D) $(2\sqrt{3},\,\,6),\,\,(-2\sqrt{3},\,\,6)$

• question_answer109) Solve$\left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y)$

A) $\sec x-\frac{1}{2}\tan y=c$

B) $\log \sin (x+y)=c$

C) $\sec x+\tan y=c$

D) $\sec y+2\cos x=c$

• question_answer110) $\overset{\to }{\mathop{\mathbf{A}}}\,\cdot \{(\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\times (\overset{\to }{\mathop{\mathbf{A}}}\,+\overset{\to }{\mathop{\mathbf{B}}}\,+\overset{\to }{\mathop{\mathbf{C}}}\,)\}$equals

A) $[\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]$

B) $[\overset{\to }{\mathop{\mathbf{B}}}\,\overset{\to }{\mathop{\mathbf{A}}}\,\overset{\to }{\mathop{\mathbf{C}}}\,]$

C) $0$

D) $1$

• question_answer111) If$y=\frac{{{y}^{3}}}{3}+\frac{{{y}^{5}}}{5}+...\infty =2\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+...\infty \right]$ then value of $y$ is

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

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

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

D) None of these

• question_answer112) If$x=\frac{1}{2}(\sqrt{3}+i)$, then ${{x}^{3}}$ is equal to

A) $1$

B) $-1$

C) $i$

D) $-i$

• question_answer113) if the complex numbers $\sin x+i\cos 2x$ and $\cos x-i\sin 2x$ are complex conjugate to each other, then the value of $x$ is

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

B) $\frac{\pi }{8}$

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

D) None of these

• question_answer114) $\underset{x\to {{2}^{+}}}{\mathop{\lim }}\,\frac{|x-2|}{x-2}$is equal to

A) $-1$

B) $1$

C) $2$

D) $-2$

• question_answer115) If$\left| \begin{matrix} x & {{x}^{2}} & 1+{{x}^{3}} \\ y & {{y}^{2}} & 1+{{y}^{3}} \\ z & {{z}^{2}} & 1+{{z}^{3}} \\ \end{matrix} \right|=0$, then

A) $z=xy$

B) $z=\frac{1}{xy}$

C) $z=-\frac{1}{xy}$

D) None of these

• question_answer116) ${{\cos }^{4}}\frac{\pi }{8}+{{\cos }^{4}}\frac{3\pi }{8}+{{\cos }^{4}}\frac{5\pi }{8}+{{\cos }^{4}}\frac{7\pi }{8}$is equal to

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

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

C) $-1$

D) $1$

• question_answer117) In a triangle$ABC$, if$\tan \frac{A}{2}=\frac{5}{6}$and$\tan \frac{B}{2}=\frac{20}{37}$, then $a+c$is equal to

A) $b$

B) $2b$

C) $3b$

D) $4b$

• question_answer118) Number of solutions of the equation $\tan x+\sec x=2\cos x$ lying in the interval$[0,\,\,2\pi ]$is

A) $0$

B) $1$

C) $2$

D) $3$

• question_answer119) Equation of the pair of straight lines bisecting the angles between the lines represented by $a{{x}^{2}}+hxy+b{{y}^{2}}=0$is

A) $\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{2xy}{h}$

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

C) $\frac{{{x}^{2}}-{{y}^{2}}}{a-b}=\frac{xy}{h}$

D) None of these

• question_answer120) The equation of circle which touches the axes and the line $\frac{x}{3}+\frac{y}{4}=1$ and whose centre lies in the first quadrant is${{x}^{2}}+{{y}^{2}}-2cx-2cy+{{c}^{2}}=0$. Then, $c$ is equal to

A) $1$

B) $2$

C) $3$

D) .$6$

• question_answer121) Angle between any two diagonals of a cube is

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

B) ${{\cos }^{-1}}\left( \frac{1}{3} \right)$

C) ${{\cos }^{-1}}\left( \frac{1}{\sqrt{3}} \right)$

D) None of these

• question_answer122) If`${{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},...,{{a}_{n}}$are in$AP$. Where${{a}_{i}}>0$for all$i$. Find the sum of series $\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{1}{\sqrt{{{a}_{3}}+{{a}_{4}}}}+...$$+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}$

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

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

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

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

• question_answer123) The ratio in which the $xy-$plane meets the line joining the points $(-3,\,\,4,\,\,-8)$ and $(5,\,\,-6,\,\,4)$is

A) $2:3$

B) $2:1$

C) $4:5$

D) None of these

• question_answer124) The unit vector perpendicular to each of the vectors$3\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}$, and$2\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+4\widehat{\mathbf{k}}$

A) $\frac{\widehat{\mathbf{i}}-\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}$

B) $\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}}}{\sqrt{3}}$

C) $\frac{\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-\widehat{\mathbf{k}}}{\sqrt{3}}$

D) None of these

• question_answer125) $y={{\tan }^{-1}}\frac{\sqrt{(1+{{x}^{2}})}+\sqrt{(1-{{x}^{2}})}}{\sqrt{(1+{{x}^{2}})}-\sqrt{(1-{{x}^{2}})}}$, then$\frac{dy}{dx}$is equal to

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

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

C) $-\frac{x}{\sqrt{(1-{{x}^{4}})}}$

D) $\frac{x\sqrt{1+{{x}^{2}}}}{1-{{x}^{4}}}$

• question_answer126) $\overrightarrow{\mathbf{a}},\,\,\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{c}}$ are coplanar vectors, then which of the following is not correct?

A) $\overrightarrow{\mathbf{a}}\cdot (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0$

B) $\overrightarrow{\mathbf{a}}\times (\overrightarrow{\mathbf{b}}\times \overrightarrow{\mathbf{c}})=0$

C) $[\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}},\,\,\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}},\,\,\overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{a}}]=0$

D) $\overrightarrow{\mathbf{a}}=p\overrightarrow{\mathbf{b}}+q\overrightarrow{\mathbf{c}}$

• question_answer127) If$|A|\ne 0$and $A$ is of order n, then$adj\,\,(adj\,\,A)$is equal to

A) $|A{{|}^{n}}$

B) $|A{{|}^{2}}$

C) $|A{{|}^{n-1}}I$

D) $|A{{|}^{n-2}}\cdot A$

• question_answer128) $\int{\frac{x+\sin x}{1+\cos x}}dx$is equal to

A) $x\log (1+\cos x)+c$

B) $\frac{1}{x}\log (1+\cos x)+c$

C) $x\tan \frac{x}{2}+c$

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

• question_answer129) Find the differential equation of curves $y=A{{e}^{x}}+B{{e}^{-x}}$ for different values of $A$ and $B$

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

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

C) $\frac{{{d}^{2}}y}{d{{x}^{2}}}=4y+3$

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

• question_answer130) Solve$\frac{dy}{dx}=\frac{{{y}^{2}}}{xy-{{x}^{2}}}$

A) $y=c{{e}^{x/y}}$

B) $y=c{{e}^{-y/x}}+x$

C) $y=c{{e}^{y/x}}$

D) $xy=c{{e}^{y/x}}$

• question_answer131) If$\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1$, then

A) $a=1$

B) $a=0$

C) $a=e$

D) $a=\frac{1}{e}$

• question_answer132) If four digits are taken from the digits $1,\,\,2,\,\,3,\,\,4,$ $5,\,\,6,\,\,7$. The probability that the sum of digits is less than$12$, is

A) $\frac{3}{25}$

B) $\frac{4}{35}$

C) $\frac{2}{35}$

D) $\frac{1}{35}$

• question_answer133) The probability of happening exactly one of a two events $A$ and $B$ is

A) $P(A)+P(B)-2P(A\cap B)$

B) $P(A)+P(B)-P(A\cap B)$

C) $P(A)-P(B)$

D) None of the above

• question_answer134) Solve$x\cos x\left( \frac{dy}{dx} \right)+y(x\sin x+\cos x)=1$

A) $y=x\tan x+\sin x+c$

B) $x=y\tan x+c$

C) $yx\sec x=\tan x+c$

D) $xy\cos x=x+c$

• question_answer135) If the equation$({{a}^{2}}+4a+3){{x}^{2}}+({{a}^{2}}-a-2)x$$+a(a+1)=0$has more than two roots, then value of $a$ is

A) $0$

B) $1$

C) $-1$

D) None of these

• question_answer136) ${{S}_{1}},\,\,{{S}_{2}}$and ${{S}_{3}}$ are the sums of$n,\,\,2n$ and $3n$terms of an arithmetic progression respectively, then

A) ${{S}_{2}}=3{{S}_{3}}-2{{S}_{1}}$

B) ${{S}_{3}}=4({{S}_{1}}+{{S}_{2}})$

C) ${{S}_{3}}=3({{S}_{2}}-{{S}_{1}})$

D) ${{S}_{3}}=2({{S}_{2}}+{{S}_{1}})$

• question_answer137) If$^{n}{{C}_{r-1}}=36,\,{{\,}^{n}}{{C}_{r}}=84$and$^{n}{{C}_{r+1}}=126$, then $n$ is equal to

A) $8$

B) $9$

C) $10$

D) $11$

• question_answer138) The sides $AB,\,\,BC,\,\,CA$ of triangle $ABC$ have $3,\,\,\,4$ and $5$ interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

A) $201$

B) $120$

C) $205$

D) $435$

• question_answer139) Coefficient of ${{x}^{n}}$ in the expansion of$1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}+\frac{{{(a+bx)}^{3}}}{3!}+...$is

A) $\frac{{{e}^{a}}{{b}^{n}}}{n!}$

B) $\frac{{{(b\cdot a)}^{n}}}{n}$

C) $\frac{{{e}^{b}}\cdot {{b}^{n}}}{(n-1)!}$

D) $\frac{{{a}^{n}}\cdot {{b}^{n-1}}}{n!}$

• question_answer140) $\frac{{{C}_{0}}}{1}+\frac{{{C}_{2}}}{3}+\frac{{{C}_{4}}}{5}+\frac{{{C}_{6}}}{7}+...$is equal to

A) $\frac{{{2}^{n-1}}}{n-1}$

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

C) $\frac{{{2}^{n}}}{n+1}$

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

• question_answer141) The equation of the parabola having the focus at the point $(3,\,\,-1)$ and the vertex at $(2,\,\,-1)$ is

A) ${{y}^{2}}-4x-2y+9=0$

B) ${{y}^{2}}+4x+2y-9=0$

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

D) ${{y}^{2}}+4x-2y+9=0$

• question_answer142) The equation of lines joining the origin to the points of intersection of $y=x+3$ and $4{{x}^{2}}+4{{y}^{2}}=1$ is

A) $36({{x}^{2}}+{{y}^{2}})={{(x-y)}^{2}}$

B) $12({{x}^{2}}+{{y}^{2}})={{(x+y)}^{2}}$

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

D) None of the above

• question_answer143) The angle of elevation of a jet fighter from a point $A$ on the ground is${{60}^{o}}$. After a flight of$10\,\,s$, the angle of elevation changes to${{30}^{o}}$. If the jet is flying at a speed of$432\,\,km/h$. Find the constant height at which the jet is flying.

A) $200\sqrt{3}m$

B) $400\sqrt{3}m$

C) $600\sqrt{3}m$

D) $800\sqrt{3}m$

A) $(AB)'=B'A'$

B) ${{(AB)}^{\theta }}={{B}^{\theta }}{{A}^{\theta }}$

C) $\overline{AB}=\bar{B}\bar{A}$

D) ${{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}$

• question_answer145) Find the equation of plane through the line$\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-4}{5}$and parallel to $x-$axis.

A) $2x+3y+5z=1$

B) $2x-5y=4$

C) $5y-3z-3=0$

D) $3y+4z=0$

• question_answer146) Find the moment of the force$5\widehat{\mathbf{i}}+10\widehat{\mathbf{j}}+16\widehat{\mathbf{k}}$ acting at the point$2\widehat{\mathbf{i}}-7\widehat{\mathbf{j}}+10\widehat{\mathbf{k}}$, about the point $-5\widehat{\mathbf{i}}+6\widehat{\mathbf{j}}-10\widehat{\mathbf{k}}$

A) $41\widehat{\mathbf{i}}-8\widehat{\mathbf{j}}+55\widehat{\mathbf{k}}$

B) $-408\widehat{\mathbf{i}}-12\widehat{\mathbf{j}}+135\widehat{\mathbf{k}}$

C) $-36\widehat{\mathbf{i}}+14\widehat{\mathbf{j}}-35\widehat{\mathbf{k}}$

D) None of the above

• question_answer147) Find the equation of tangents to the ellipse$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$, which cut off equal intercepts or the axes.

A) $y=\sqrt{3}x\pm \sqrt{3{{a}^{2}}+{{b}^{2}}}$

B) $y=\pm x\mp \sqrt{{{a}^{2}}+{{b}^{2}}}$

C) $y=\sqrt{3}\pm \sqrt{{{a}^{2}}+3{{b}^{2}}}$

D) None of the above

• question_answer148) A square matrix $A$ is called an orthogonal matrix if

A) $A\bar{A}=I$

B) $AA'=I$

C) $A{{A}^{\theta }}=I$

D) ${{A}^{2}}=I$

• question_answer149) The value of $'c'$ Rolle's theorem for $f(x)={{e}^{x}}\sin x$in$[0,\,\,\pi ]$is given by

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

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

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

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

• question_answer150) $\int_{-a}^{a}{x\sqrt{({{a}^{2}}-{{x}^{2}})}}dx$is equal to

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

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

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

D) $0$