# Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2010

### done BCECE Engineering Solved Paper-2010

• question_answer1) Find the dimensions of electric permittivity,

A) $\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{\text{4}}}\text{ }\!\!]\!\!\text{ }$

B) $\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }$

C) $\text{ }\!\![\!\!\text{ A}{{\text{M}}^{-3}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{4}}\text{ }\!\!]\!\!\text{ }$

D) $\text{ }\!\![\!\!\text{ }{{\text{A}}^{\text{2}}}{{\text{M}}^{0}}{{\text{L}}^{\text{-3}}}{{\text{T}}^{4}}\text{ }\!\!]\!\!\text{ }$

• question_answer2) A ship of mass $3\times {{10}^{7}}kg,$ initially at rest, is pulled by a force of $5\times {{10}^{4}}N$ through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

A) 1.5 m/s

B) 60 m/s

C) 0.1 m/s

D) 5 m/s

• question_answer3) If the external forces acting on a system have zero resultant, the centre of mass

A) may move but not accelerate

B) may accelerate

C) must not move

D) None of die above

• question_answer4) An object is placed on the surface of a smooth inclined plane of inclination 8. It takes time t to reach the bottom. If the same object is allowed to slide down a rough inclined plane of inclination$\theta ,$ it takes time $nt$ to reach the bottom, where n is a number greater than 1. The coefficient of friction u is given by

A) $\mu =\tan \,\theta \left( 1-\frac{1}{{{n}^{2}}} \right)$

B) $\mu =\cos \,\theta \left( 1-\frac{1}{{{n}^{2}}} \right)$

C) $\mu =\tan \,\theta \sqrt{1-\frac{1}{\sqrt{{{n}^{2}}}}}$

D) $\mu =\cot \,\theta \sqrt{1-\frac{1}{\sqrt{{{n}^{2}}}}}$

• question_answer5) A 500 kg horse pulls a can of mass 1500 kg along a level road with an acceleration of $1\,m/{{s}^{2}}$. If the coefficient of sliding friction is 0.2, then the horizontal force exerted by the earth on the horse is

A) 300 kg-wt

B) 400 kg-wt

C) 500 kg-wt

D) 600 kg-wt

• question_answer6) A spring is held compressed so that its stored energy is 2.4 J. its ends are in contact with masses 1 g and 48 g placed on a functionless table. When the spring is released, the heavier mass wilt acquire a speed of

A) $\frac{2.4}{49}m{{s}^{-1}}$

B) $\frac{2.4\times 48}{49}m{{s}^{-1}}$

C) $\frac{{{10}^{3}}}{7}cm{{s}^{-1}}$

D) $\frac{{{10}^{6}}}{7}cm{{s}^{-1}}$

• question_answer7) Two simple pendulums first of bob mass ${{M}_{1}}$ and length ${{L}_{1}},$ second of bob mass ${{M}_{2}}$ and length ${{L}_{2}}.\,{{M}_{1}}={{M}_{2}}$ and ${{L}_{1}}=2{{L}_{2}}$. If the vibrational energy of both is same. Then which of the following is correct?

A) Amplitude of B is greater than chat of A

B) Amplitude of B is smaller than that of A

C) Amplitude will be same

D) None of the above

• question_answer8) Which logic gate is represented by the following combination of logic gales?

A) OR

B) NAND

C) AND

D) NOR

• question_answer9) A body of mass m is situated on the earth in the gravitational field of sun. For the body to escape from die gravitation pull of the solar system the body must be imparted an escape velocity of (assume earth to be stationary)

A) 11.2km/s

B) 22.4 km/s

C) 33.6 km/s

D) 42 km/s

• question_answer10) Find the lifting force of a 4 kg cork life belt in sea water, if the densitites of cork and sea water are $0.2\,\times {{10}^{3}}kg/{{m}^{3}}$ and $1.03\,\times {{10}^{3}}kg/{{m}^{3}}$ respectively.

A) 163 N

B) 273 N

C) 119 N

D) 298 N

• question_answer11) Nitrogen $({{N}_{2}})$ is in equilibrium state at T = 421 K. The value of most probable speed, ${{v}_{mp}}$is

A) 400 m/s

B) 421 m/s

C) 500 m/s

D) 600 m/s

• question_answer12) The temperature at which the velocity of oxygen will be half that of hydrogen at NTP is

A) $1092{}^\circ C$

B) $1492{}^\circ C$

C) $273\text{ }K$

D) $819{}^\circ C$

• question_answer13) Two sound waves, each of amplitude A and frequency $\omega ,$ superpose at a point with phase difference of $\frac{\pi }{2}.$ The amplitude and frequency of the resultant wave are respectively

A) $\frac{A}{\sqrt{2}},\frac{\omega }{2}$

B) $\frac{A}{\sqrt{2}},\omega$

C) $\sqrt{2A,}\frac{\omega }{2}$

D) $\sqrt{2}A,\omega$

• question_answer14) A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to (1/4) as compared to intensity due to direct beam alone. The resultant intensity will be

A) (1/4) fold

B) (3/4) fold

C) (5/4) fold

D) (9/4) fold

• question_answer15) 15. A square of side 3, cm is located at a distance 25 cm from a concave mirror of focal length 10 cm. The centre of square is at the axis of the mirror and the plane is normal to axis of mirror. The area enclosed by the image of the square is

A) $4\,c{{m}^{2}}$

B) $6\,c{{m}^{2}}$

C) $16\,c{{m}^{2}}$

D) $36\,c{{m}^{2}}$

• question_answer16) A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal

A) $-\frac{Q}{2}$

B) $-\frac{Q}{4}$

C) $+\frac{Q}{4}$

D) $+\frac{Q}{2}$

• question_answer17) The numerical value of charge on either plate of capacitor C shown in figure

A) $CE$

B) $\frac{CE{{R}_{1}}}{{{R}_{1}}+r}$

C) $\frac{CE{{R}_{2}}}{{{R}_{2}}+r}$

D) $\frac{CE{{R}_{1}}}{{{R}_{2}}+r}$

• question_answer18) A proton enters a magnetic field of flux density $1.5\,Wb/{{m}^{2}}$ with a speed of $2\times {{10}^{7}}\,m/s$ at angle of 30? with the field. The force on a proton will be

A) $\text{0}\text{.24 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}$

B) $\text{2}\text{.4 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}$

C) $\text{24 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}$

D) $\text{0}\text{.024 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-12}}}\,\text{N}$

• question_answer19) Two long straight wires are set parallel to each other at separation rand each carries a current in the same direction. The strength of the magnetic field at any point midway between the two wires is

A) $\frac{{{\mu }_{0}}i}{\pi r}$

B) $\frac{2{{\mu }_{0}}i}{\pi r}$

C) $\frac{{{\mu }_{0}}i}{2\pi r}$

D) zero

• question_answer20) The work done in turning a magnet of magnetic moment At by an angle of 90? from the meridian is n times the corresponding work done to turn it through an angle of 60?

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

B) $n=2$

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

D) $n=1$

• question_answer21) An inductive coil has a resistance of 100$\Omega$ When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by $45{}^\circ$. The inductance of the coil is

A) $\frac{1}{10\pi }$

B) $\frac{1}{20\pi }$

C) $\frac{1}{40\pi }$

D) $\frac{1}{60\pi }$

• question_answer22) An inductor of 1 H is connected across a 220 V, 50 Hz supply. The peak value of the current is approximately

A) 0.5 A

B) 0.7 A

C) 1 A

D) 1.4 A

• question_answer23) The figure shows an equiconvex lens of focal length $f.$ If the lens is cut along PQ, the focal length of each half will be

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

B) $f$

C) $2f$

D) $4f$

• question_answer24) Light of two different frequencies whose photons have energies 1 eV and 2.5 eV successively illuminate a metal of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons will be

A) 1 : 5

B) 1 : 4

C) 1 : 2

D) 1 : 1

• question_answer25) An electron Jumps from the first excited state to the ground State of hydrogen atom. Whit will be the percentage change in the speed of electron?

A) 25%

B) 50%

C) 100%

D) 200%

• question_answer26) The mutual inductance of a pair of coils, each of N rums, is M henry If a current of i ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt will be

A) $\frac{Mi}{t}$

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

C) $\frac{MN}{it}$

D) $\frac{Mi}{Nt}$

• question_answer27) A body falls from rest. In the last second of its fall it covers half of the total distance. If g is $9.8\,\,m/{{s}^{2}},$ then the total time of its fall is (in second)

A) 2

B) $2+\sqrt{2}$

C) $2-\sqrt{2}$

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

• question_answer28) A force$\mathbf{\vec{F}}=a\mathbf{\vec{i}}+3\mathbf{\vec{j}}+\mathbf{6\vec{k}}$ is acting at a point $\mathbf{\vec{r}}=\mathbf{2\vec{i}}+\mathbf{6\vec{j}}+\mathbf{12\vec{k}}.$ The value of a for which angular momentum is conserved is

A) zero

B) 1

C) -1

D) 2

• question_answer29) A wooden block is floating in a liquid 50% of its volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration$a=g/3$ is

A) 30%

B) 50%

C) 60%

D) 67%

• question_answer30) Two resistors 400$\Omega$ and 800$\Omega$are connected in series with a 6 V battery- The potential difference measured by voltmeter of 10$k\Omega$ across $400\,\Omega$ resistor is

A) 2 V

B) 1.95 V

C) 3.8 V

D) 4 V

• question_answer31) An astronomical telescope in normal adjustment receives light from a distant source S the tube length is now decreased slightly, then

A) no image will be formed

B) a virtual image of S will be formed at a finite distance

C) a large, real image of S will be formed behind the eye-piece, far away from it

D) a small, real image of S will be formed behind the eye-piece close to it

• question_answer32) The potential difference in volt across the resistance R., in the circuit shown in figure, is $({{R}_{1}}=15\,\Omega ,\,{{R}_{2}}=15\,\Omega ,\,{{R}_{3}}=30\,\Omega ,\,{{R}_{4}}=35\,\Omega )$

A) 5

B) 7.5

C) 15

D) 12.5

• question_answer33) The ratio of molecular masses of two radioactive substances is 3/2 and the ratio of their decay constants is 4/3, Then, the ratio of their initial activities per mole will be

A) 2

B) 4/3

C) 8/9

D) 9/8

• question_answer34) The resultant of two forces P and Q is of magnitude p. If P be doubled, the resultant will be inclined to Q at an angle

A) $0{}^\circ$

B) $30{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

• question_answer35) A person is at a distance x from a bus when the bus begins 10 move with a constant acceleration a. What is the minimum velocity with which [he person should run towards the bus so as to catch it?

A) $2ax$

B) $\sqrt{2ax}$

C) $ax$

D) $\sqrt{ax}$

• question_answer36) A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at die rate of $a\,m/{{s}^{2}},$ then the resultant acceleration will be

A) $\left( \frac{{{v}^{2}}}{r}+a \right)$

B) ${{\left( \frac{{{v}^{2}}}{{{r}^{2}}}+a \right)}^{1/2}}$

C) ${{\left( \frac{{{v}^{4}}}{{{r}^{2}}}+{{a}^{2}} \right)}^{1/2}}$

D) ${{\left( \frac{{{v}^{2}}}{{{r}^{2}}}-{{a}^{2}} \right)}^{1/2}}$

• question_answer37) A body of mass 10 kg at rest explodes into two pieces of masses 7 kg and 3 kg. If the total increase in kinetic energy due to explosion is 1680 J, the magnitude of their relative velocity in m/s, after explosion is

A) 40

B) 50

C) 70

D) 80

• question_answer38) The moment of inertia of a body about a given axis is $1.2\,\,kg\,{{m}^{2}}$. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of $25\,rad/{{s}^{2}}$ must be applied about that axis for a duration of

A) 4 s

B) 2 s

C) 8 s

D) 10 s

• question_answer39) Steel and aluminium wires have equal resistances and masses. Which of die wires is longer and how many times? (Given, densities of steel and aluminium are $7.8\,\times {{10}^{3}}\,kg\,{{m}^{-3}}$ and $2.7\times {{10}^{3}}\,kg\,{{m}^{-3}}$ and their resistivities are $0.15\,\mu \Omega .m$ and$0.028\,\mu \Omega -m$ respectively)

A) The aluminium wire is 3.9 times longer

B) The aluminium wire is 1.3 times longer

C) The aluminium wire is 2.6 times longer

D) The steel wire is 3.9 times longer

• question_answer40) Two cells of emfs ${{E}_{1}}$ and${{E}_{2}}({{E}_{1}}>{{E}_{2}})$ are connected as shown in figure. When a potentiometer is connected between A and B, the balancing length of the potentiometer wire is 300 cm. On connecting the same potentiometer between A and C, the balancing length is 100 on. The ratio$\frac{{{E}_{1}}}{{{E}_{2}}}$is

A) 3 : 1

B) 1 : 3

C) 2 : 3

D) 3 : 2

• question_answer41) In hydrogen atom the electron is making $6.6\,\times {{10}^{15}}\,rev/s$ around the nucleus of radius $0.53\,\overset{\text{o}}{\mathop{\text{A}}}\,$. The magnetic field produced at the centre of the orbit is nearly

A) $0.12\,Wb/{{m}^{2}}$

B) $1.2\,Wb/{{m}^{2}}$

C) $12\,Wb/{{m}^{2}}$

D) $120\,Wb/{{m}^{2}}$

• question_answer42) An AC source is 120 V-60 Hz. The value of voltage after$\frac{1}{720}$ from start will be

A) 20.2 V

B) 42.4 V

C) 84.8 V

D) 106.8 V

• question_answer43) The energy difference between the first two levels of hydrogen atom is 10.2eV. For another element of atomic number 10 and mass number 20, this will be

A) 1020 eV

B) 2040 eV

C) 0.51 eV

D) 0.102 eV

• question_answer44) The following equation represents induced transmutation $_{4}B{{e}^{9}}{{+}_{2}}H{{e}^{4}}{{\xrightarrow{{}}}_{6}}{{C}^{12}}+X$ In this equation, X represents

A) one ${{\beta }^{-}}$ particle

B) $\alpha -$particle

C) a positron

D) a neutron

• question_answer45) The masses of neutron and proton are 1.0087 and 1.0073 amu respectively- If the neutrons and protons combine to form helium nucleus of mass 4.0015 amu the binding energy of the helium nucleus will be

A) 28.4 MeV

B) 20.8 MeV

C) 27.3 MeV

D) 14.2 MeV

• question_answer46) The activity of a radioactive sample is measured as 9750 count/min at t=0 and 975 count/min at t =5min. The decay constant is nearly

A) $0.922\,{{\min }^{-1}}$

B) $0.691\,{{\min }^{-1}}$

C) $0.461\,mi{{n}^{-1}}$

D) $0.230{{\min }^{-1}}$

• question_answer47) Light of wavelength $\lambda ,$ strikes a photoelectric surface and electrons are ejected with an energy E. Iff is to be increased to exactly twice its original value, the wavelength changes to$\lambda ;$ where

A) $\lambda$is less than $\frac{\lambda }{2}$

B) $\lambda$is greater than$\frac{\lambda }{2}$

C) $\lambda$ is greater than $\frac{\lambda }{2}$ but less than $\lambda ,$

D) $\lambda$ is exactly equal to$\frac{\lambda }{2}$

• question_answer48) Three point masses, each of mass m are placed at the corners of an equilateral triangle of side The moment of inertia of this system about, an axis along one side of the triangle is

A) $3\,m{{a}^{2}}$

B) $2\,m{{a}^{2}}$

C) $\frac{3}{4}m{{a}^{2}}$

D) $\frac{3}{2}m{{a}^{2}}$

• question_answer49) A pipe opened at both ends produces a note of frequency ${{f}_{1.}}$ When the pipe is kept with $\frac{3}{4}$th of its length in water, it produces a note of frequency ${{f}_{2.}}$ The ratio $\frac{{{f}_{1}}}{{{f}_{2}}}$ is of

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

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

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

D) $2$

• question_answer50) A solenoid is 1.5 m long and its inner diameter is 4.0 cm. It has 3 layers of windings of 1000 turns each and carries a current of 2.0A. The magnetic flux for a cross-section of the solenoid is nearly

A) $4.1\,\times {{10}^{-5}}Wb$

B) $5.2\,\times {{10}^{-5}}Wb$

C) $6.31\,\times {{10}^{-31}}Wb$

D) $2.5\,\times {{10}^{-7}}Wb$

• question_answer51) How many moles of helium gas occupy 22.4 L at $\text{0}{{\,}^{\text{o}}}\text{C}$and 1 atm pressure?

A) 0.11

B) 1.11

C) 0.90

D) 1.0

• question_answer52) The compound which contains both ionic and covalent bond

A) $KCl$

B) KCN

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

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

• question_answer53) The following is endothermic reaction

A) Decomposition of water

B) Conversion of graphite to diamond

C) Dehydrogenation of ethane to ethylene

D) All of the above

• question_answer54) A saturated solution of $\text{A}{{\text{g}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$is $\text{2}\text{.5}\times {{10}^{-2}}\,M.$ The value of its solubility product is

A) $62.5\times {{10}^{-6}}$

B) $62.5\times {{10}^{-4}}$

C) $15.625\times {{10}^{-6}}$

D) $3.125\times {{10}^{-6}}$

• question_answer55) The enthalpies of combustion of carbon and carbon monoxide are $~-393.5$ and $-283\text{ kJ mo}{{\text{l}}^{-1}}$respectively. The enthalpy of formation of carbon monoxide per mole is

A) $\text{110}\text{.5kJ}$

B) $\text{676}\text{.5 kJ}$

C) $-\text{676}\text{.5 kJ}$

D) $-\text{110}\text{.5kJ}$

• question_answer56) 1 g ice absorbs 335 J of heat to melt at $\text{0}{{\,}^{\text{o}}}\text{C}\text{.}$ The entropy change will be

A) $1.2\text{ J}{{\text{K}}^{-1}}\text{mo}{{\text{l}}^{-1}}$

B) $335\text{ J}{{\text{K}}^{-1}}\text{ mo}{{\text{l}}^{-1}}$

C) $22.1\text{ J}{{\text{K}}^{-1}}\text{mo}{{\text{l}}^{-1}}$

D) $0.8\text{ J}{{\text{K}}^{-1}}\text{ mo}{{\text{l}}^{-1}}$

• question_answer57) An ideal gas cant be liquefied because

A) its critical temperature is always above $\text{0}{{\,}^{\text{o}}}\text{C}$

B) its molecules are relatively smaller in size

C) it solidifies before becoming a liquid

D) forces operative between its molecules are negligible

• question_answer58) What type of crystal defect is indicated in the diagram below? $N{{a}^{+}}C{{l}^{-}}N{{a}^{+}}C{{l}^{-}}N{{a}^{+}}C{{l}^{-}}$ $\begin{matrix} N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} \\ {} & C{{l}^{-}} & {} & C{{l}^{-}} & N{{a}^{+}} & N{{a}^{+}} \\ N{{a}^{+}} & C{{l}^{-}} & {} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} \\ {} & C{{l}^{-}} & N{{a}^{+}} & C{{l}^{-}} & N{{a}^{+}} & N{{a}^{+}} \\ \end{matrix}$

A) Frenkel defect

B) Schottky defect

C) Interstitial defect

D) Frenkel and Schottky defects

• question_answer59) A metal has bcc structure and the edge length of its unit cell is $\text{3}\text{.04}\overset{\text{o}}{\mathop{\text{A}}}\,\text{.}$ The volume of the unit cell in $\text{c}{{\text{m}}^{\text{3}}}$will be

A) $\text{1}\text{.6}\times {{10}^{-21}}c{{m}^{3}}$

B) $2.81\times {{10}^{-23}}\,c{{m}^{3}}$

C) $6.02\times {{10}^{-23}}\,c{{m}^{3}}$

D) $6.6\times {{10}^{-24}}\,c{{m}^{3}}$

A) digestion of food

B) hydrolysis of proteins

C) breaking and dispersion into the colloidal state

D) precipitation of solid from colloidal dispersion

• question_answer61) Plaster of Paris is

A) $CaS{{O}_{4}}.2{{H}_{2}}O$

B) $CaS{{O}_{4}}.{{H}_{2}}O$

C) $CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O$

D) $CaS{{O}_{4}}.4{{H}_{2}}O$

• question_answer62) Conc.$\text{HN}{{\text{O}}_{\text{3}}}$ reacts with${{\text{I}}_{\text{2}}}$to form

A) $\text{HI}$

B) $\text{HOI}$

C) $\text{HI}{{\text{O}}_{\text{2}}}$

D) $\text{HI}{{\text{O}}_{3}}$

• question_answer63) Coal gas is a mixture of

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

B) ${{H}_{2}},CO$and $C{{H}_{4}}$

C) ${{H}_{2}}$and $CO$

D) $C{{H}_{4}}$and $CO$

A) $\text{ }\!\!~\!\!\text{ Fe + Cr + Cu}$

B) $\text{Fe + Cu + Ni}$

C) $\text{Fe + Cr + Ni}$

D) $\text{Fe + Ni + Cu}$

• question_answer65) The isomers which can be converted into another form by rotation of the molecule around single bond are

A) geometrical isomers

B) conformers

C) enantiomers

D) diastereomers

• question_answer66) An organic compound contains 49.3% carbon, 6.84% hydrogen and its vapour density is 73. Molecular formula of the compound is

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

B) ${{C}_{4}}{{H}_{10}}{{O}_{2}}$

C) ${{C}_{6}}{{H}_{10}}{{O}_{4}}$

D) ${{C}_{3}}{{H}_{10}}{{O}_{2}}$

• question_answer67) Ozone in stratosphere is depleted by

A) $C{{F}_{2}}C{{l}_{2}}$

B) ${{C}_{7}}{{F}_{16}}$

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

D) ${{C}_{6}}{{F}_{6}}$

• question_answer68) Iodine is formed when $\text{KI}$reacts with a solution of

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

B) ${{(N{{H}_{4}})}_{2}}S{{O}_{4}}$

C) $ZnS{{O}_{4}}$

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

• question_answer69) Select the correct order of the strength of acids given below

A) $HCl{{O}_{4}}<HCl{{O}_{3}}<HClO<HCl{{O}_{2}}$

B) $HCl{{O}_{4}}<HCl{{O}_{3}}<HCl{{O}_{2}}<HClO$

C) $HClO<HCl{{O}_{2}}<HCl{{O}_{3}}<HCl{{O}_{4}}$

D) None of the above

• question_answer70) Which one of the following statements regarding helium .is incorrect?

A) It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable

B) It is used as a cryogenic agent for carrying out experiments at low temperatures

C) It is used to produce and sustain powerful superconducting magnets

D) It is used in gas-cooled nuclear reactors

• question_answer71) One would expect proton to have very large

A) ionization potential

C) charge

D) hydration energy

• question_answer72) What is the correct orbital designation of an electron with the quantum number, $n=4,l=3,m=-2,s=\frac{1}{2}?$

A) $3s$

B) $4f$

C) $~5p$

D) $6s$

• question_answer73) The energy of an electron in second Bohr orbit of hydrogen atom is

A) $-5.44\times {{10}^{-19}}eV$

B) $-5.44\times {{10}^{-19}}cal$

C) $-5.44\times {{10}^{-19}}kJ$

D) $-5.44\times {{10}^{-19}}J$

• question_answer74) One of the following has greatest electron affinity. Identify it.

A) O

B) S

C) Se

D) Te

• question_answer75) The ONO angle is maximum in

A) $\text{NO}_{3}^{-}$

B) $\text{NO}_{2}^{-}$

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

D) $\text{NO}_{2}^{+}$

• question_answer76) The pH value for $\frac{1}{1000}\text{N}-\text{KOH}$solution is

A) 3

B) ${{10}^{-11}}$

C) 2

D) 11

• question_answer77) The equilibrium constant for a reaction, ${{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g)$ is $4\times {{10}^{-4}}$ at $\text{2000}\,\text{K}\text{.}$ In the presence of catalyst, the equilibrium is attained 10 times faster. The equilibrium constant in presence of catalyst at 2000 K is

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

B) $4\times {{10}^{-2}}$

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

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

• question_answer78) Consider the following ${{\text{E}}^{\text{o}}}$values $E_{F{{e}^{3+}}/F{{e}^{2+}}}^{o}=+\,0.77\,V$ $E_{S{{n}^{2+}}/Sn}^{o}=-0.14\,V$ Under standard conditions the potential for the reaction, $Sn(s)+2F{{e}^{3+}}(aq)\xrightarrow{{}}2F{{e}^{2+}}(aq)+S{{n}^{2+}}(aq)$is

A) 1.68 V

B) 1.40 V

C) 0.91 V

D) 0.63 V

• question_answer79) The relationship between the values of osmotic pressure of 0.1 M solutions of $\text{KN}{{\text{O}}_{\text{3}}}\text{(}{{\text{p}}_{\text{1}}}\text{)}$and $C{{H}_{3}}COOH({{p}_{2}})$is

A) $\frac{{{p}_{1}}}{{{p}_{1}}+{{p}_{2}}}=\frac{{{p}_{2}}}{{{p}_{1}}+{{p}_{2}}}$

B) ${{p}_{1}}>{{p}_{2}}$

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

D) ${{p}_{1}}={{p}_{2}}$

• question_answer80) Volume of $\text{0}\text{.6 M NaOH}$required to neutralize $\text{30}\,\text{c}{{\text{m}}^{\text{3}}}$of $\text{0}\text{.4}\,\text{M}\,\text{HCl}$is

A) $30c{{m}^{3}}$

B) $45\,c{{m}^{3}}$

C) $~20\,c{{m}^{3}}$

D) $~50\,c{{m}^{3}}$

• question_answer81) For nth order reaction, the half-life period, ${{t}_{1/2}}$ is proportional to initial concentration as

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

B) ${{a}^{n+1}}$

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

D) $\frac{1}{{{a}^{n}}}$

• question_answer82) Thermite is a mixture of

A) $C{{r}_{2}}{{O}_{3}}+A{{l}_{2}}{{O}_{3}}$

B) $F{{e}_{2}}{{O}_{3}}+Al$

C) $F{{e}_{2}}{{O}_{3}}+A{{l}_{2}}{{O}_{3}}$

D) $A{{l}_{2}}{{O}_{3}}+2Cr$

• question_answer83) Of the ions$Z{{n}^{2+}},N{{i}^{2+}}ad\,C{{r}^{3+}}$ (atomic number of and Cr = 24)

A) all these are colourless

B) all these are coloured

C) only$\text{N}{{\text{i}}^{\text{2+}}}$ is coloured and$\text{Z}{{\text{n}}^{\text{2+}}}$ and $\text{C}{{\text{r}}^{\text{3+}}}$are colourless

D) only $\text{Z}{{\text{n}}^{\text{2+}}}$ is colourless and $\text{N}{{\text{i}}^{\text{2+}}}$and $\text{C}{{\text{r}}^{3+}}$ are coloured

• question_answer84) The coordination number of a central metal atom in a complex is determined by

A) the number of ligands around a metal ion bonded by $\sigma -$bonds

B) the number of ligands around a metal ion bonded by it $\pi -$bonds

C) the number of ligands around a metal ion bonded by $\sigma$ and $\pi -$bonds both

D) the number of only anionic ligands bonded to the metal ion

• question_answer85) Potassium ferricyanide on ionization produces

A) 2 ions

B) 1 ion

C) 3 ions

D) 4 ions

• question_answer86) The IUPAC name of $C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{2}}-\underset{OH}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}$is

A) $1,1-$dimethyl$-1,3-$butanediol

B) $2-$methyl$-2,4-$pentanediol

C) $4-$methyl$-2,4-$pentanediol

D) $1,3,3-$trimethyl$-1,3-$propane diol

• question_answer87) The order of decreasing stability of the carbanions is ${{(C{{H}_{3}})}_{3}}\bar{C}(1),{{(C{{H}_{3}})}_{2}}\bar{C}H(2),C{{H}_{3}}\bar{C}{{H}_{2}}(3),$${{C}_{6}}{{H}_{5}}\bar{C}{{H}_{2}}(4)$

A) 1 > 2 > 3 > 4

B) 4 > 3 > 2 > 1

C) 1 > 2 > 4 > 3

D) 4 > 1 > 2 > 3

• question_answer88) Which set of products is expected on reductive ozonolysis of the following diolefin? $C{{H}_{3}}CH=\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}$

A) $C{{H}_{3}}CHO;C{{H}_{3}}COCH=C{{H}_{2}}$

B) $C{{H}_{3}}CH=\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-CHO;C{{H}_{2}}O$

C) $C{{H}_{3}}CHO;C{{H}_{3}}COCHO;C{{H}_{2}}O$

D) $C{{H}_{3}}CHO;C{{H}_{3}}COC{{H}_{3}};C{{H}_{2}}O$

• question_answer89) Which of the following pairs is/are correctly matched?

 Reaction Product (i) $RX+AgCN$ $RNC$ (ii) $RX+KCN$ $RCN$ (iii) $RX+KN{{O}_{2}}$ (iv) $RX+AgN{{O}_{2}}$ $R-O-N=O$
Select the correct answer using the codes given below

A) I alone

B) I and II

C) III and IV

D) I, II, III and IV

• question_answer90) A mixture of benzaldehyde and formaldehyde on heating with aqueous NaOH solution gives

A) benzyl alcohol and sodium formate

B) sodium benzoate and methyl alcohol

C) sodium benzoate and sodium formate

D) benzyl alcohol and methyl alcohol

• question_answer91) Which of the following react with NaOH to produce an acid and an alcohol?

A) $HCHO$

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

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

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

• question_answer92) Which of the following has the maximum acidic strength?

A) $o-$nitrobenzoic acid

B) $m-$nitrobenzoic acid

C) $p-$nitrobenzoic acid

D) $p-$nitrophenol

A) $Zn+HCl$

B) $Sn+HCl$

C) $FeS{{O}_{4}}+{{H}_{2}}{{O}_{2}}$

D) None of these

• question_answer94) The energy stored in the cells of a living body is in the form of

A) fats

B) glucose

C) ATP

D) proteins

B) polynuclear compound

C) sweetening agent

D) sugar

• question_answer96) The nucleic acid the purine base having two possible binding sites is

A) thymine

B) cytosine

C) guanine

• question_answer97) On reduction secondary amine is given by

A) nitroethane

B) methylcyanide

C) methylisocyanide

D) nitrobenzene

• question_answer98) In chlorobenzene solution, the basic strength of amines increases in the order

A) ${{({{C}_{2}}{{H}_{5}})}_{3}}N<{{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{C}_{2}}{{H}_{5}}N{{H}_{2}}$

B) ${{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{({{C}_{2}}{{H}_{5}})}_{3}}N$

C) ${{({{C}_{2}}{{H}_{5}})}_{2}}NH<{{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{3}}N$

D) ${{({{C}_{2}}{{H}_{5}})}_{3}}N<{{C}_{2}}{{H}_{5}}N{{H}_{2}}<{{({{C}_{2}}{{H}_{5}})}_{2}}NH$

• question_answer99) Dimethyl terephthalate and ethylene glycol react to form

A) nylon-6

B) nylon-66

C) dacron

D) neoprene

• question_answer100) Gasoline is a mixture of

A) ${{C}_{6}}-{{C}_{11}}$alkanes

B) ${{C}_{3}}-{{C}_{5}}$ alkanes

C) ${{C}_{7}}-{{C}_{9}}$ alkanes

D) ${{C}_{15}}-{{C}_{20}}$alkanes

• question_answer101) If ${{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta ,}$ where n is a positive integer, then $n({{I}_{n-1}}+{{I}_{n+1}})$is equal to

A) 1

B) $n-1$

C) $\frac{1}{n-1}$

D) None of these

• question_answer102) The minimum value of${{2}^{{{({{x}^{2}}-3)}^{3}}}}+27$is

A) 1

B) 2

C) ${{2}^{27}}$

D) None of these

• question_answer103) The set of points of discontinuity of the function $f(x),$where$f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\sin x)}^{2n}}}{{{3}^{n}}-{{(2\cos x)}^{2n}}}$is

A) R

B) $\left\{ n\pi \mp \frac{\pi }{3},n\in I \right\}$

C) $\left\{ n\pi \pm \frac{\pi }{6},n\in I \right\}$

D) None of these

• question_answer104) The derivative of $\cos e{{c}^{-1}}\left( \frac{1}{2{{x}^{2}}-1} \right)$ with respect to $\sqrt{1-{{x}^{2}}}$at $x=\frac{1}{2}$is

A) - 4

B) 4

C) -1

D) None of these

• question_answer105) The equation of hyperbola conjugate to the hyperbola$~2{{x}^{2}}+3xy-2{{y}^{2}}-5x+5y+2=0$ is

A) $~2{{x}^{2}}+\text{ }3xy-2{{y}^{2}}-\text{ }5x\,\,+\,\,5y-8=0$

B) ${{x}^{2}}+3xy-2{{y}^{2}}-5x+5y+8=0$

C) $2{{x}^{2}}+3xy-2{{y}^{2}}+5x-5y+8=0$

D) None of these

• question_answer106) The sum of the focal distances of any point on the conic $\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1$is

A) 10

B) 9

C) 41

D) 18

• question_answer107) The focus of the parabola ${{y}^{2}}-x-2y+2=0$is

A) $\left( \frac{1}{4},0 \right)$

B) $(1,2)$

C) $\left( \frac{5}{4},1 \right)$

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

• question_answer108) Observe the following statements: (i) The circle ${{x}^{2}}+{{y}^{2}}-6x-4y-7=0$ touches y-axis (ii) The circle ${{x}^{2}}+\text{ }{{y}^{2}}+6x+4y-7=0$ touches $x-$axis Then, which of the following statements is/are correct?

A) Both I and II

B) Neither I nor II

C) Only I

D) Only II

• question_answer109) The line $x+y=a$meets the axes of X and Y at A and B respectively. $A\Delta AMN$is inscribed in the $\text{ }\!\!\Delta\!\!\text{ }\,\text{O}\,\text{A}\,\text{B,}$ O being the origin, with right angle at N. M and N lie on OB and AB respectively. If the area of the $\Delta AMN$is $\frac{3}{8}$ of the area of the $\Delta OAB,$ then$\frac{AN}{BN}$ is equal to

A)  $\frac{1}{3}$

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

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

D) $3$

• question_answer110) The intercept made by a line on y-axis is double to the intercept made by it on x-axis and if it passes through$(1,2),$then its equation is

A) $2x+y=4$

B) $2x+y+4=0$

C) $2x-y=4$

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

• question_answer111) The area of the triangle formed by the lines $4{{x}^{2}}-9xy-9{{y}^{2}}=0$ and $x=2$is equal to

A) $\frac{20}{3}\,\text{sq}\,\text{units}$

B) $3\,\text{sq}\,\text{units}$

C) $\frac{10}{3}\,\text{sq}\,\text{units}$

D) $\text{2}\,\text{sq}\,\text{units}$

• question_answer112) The area bounded by the parabolas ${{y}^{2}}=4a(x+a)$and ${{y}^{2}}=-4a(x-a)$is

A) $\frac{16}{3}{{a}^{2}}\text{sq units}$

B) $\frac{8}{3}\text{sq}\,\text{units}$

C) $\frac{\text{4}}{\text{3}}{{\text{a}}^{\text{2}}}\text{sq}\,\text{units}$

D) None of these

• question_answer113) If the vectors $\vec{a}=\hat{i}+a\hat{j}+{{a}^{2}}\hat{k},\vec{b}=\hat{i}+b\hat{j}+{{b}^{2}}\hat{k},$$\vec{c}=\hat{i}+c\hat{j}+{{c}^{2}}\hat{k}$are three non-coplanar vectors and $\left| \begin{matrix} a & {{a}^{2}} & 1+{{a}^{3}} \\ b & {{b}^{2}} & 1+{{b}^{3}} \\ c & {{c}^{2}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0,$ then the value of aback is

A) 0

B) 1

C) 2

D) - 1

• question_answer114) If $4{{\sin }^{2}}x-8\sin x+3=0,$$0\le x\le 2\pi ,$ then the solution set for $x$is

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

B) $\left[ 0,\frac{5\pi }{6} \right]$

C) $\left[ \frac{5\pi }{6},2\pi \right]$

D) $\left[ \frac{5\pi }{6},\frac{\pi }{6} \right]$

• question_answer115) The value of $\left( 1+\cos \frac{\pi }{8} \right)\left( 1+\cos \frac{3\pi }{8} \right)$$\left( 1+\cos \frac{5\pi }{8} \right)\left( 1+\cos \frac{7\pi }{8} \right)$ is equal to

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

B) $\frac{1}{6}$

C) $\frac{1}{8}$

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

• question_answer116) If the probability of A to fail in an examination is $\frac{1}{5}$and that of B is $\frac{3}{10},$ then the probability that either A or B fails, is

A) $\frac{19}{50}$

B) $\frac{11}{25}$

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

D) None of these

• question_answer117) Which of the following is the empty set?

A) {$x:x$ is a real number and ${{x}^{2}}-1=0$}

B) {$x:x$ is a real number and$~{{x}^{2}}+1=0$}

C) {$x:x$ is real number and${{x}^{2}}-9=0$}

D) {$x:x$ is a real number and${{x}^{2}}=x+2$}

• question_answer118) If $f:[1,\infty )\to [2,\infty ]$is given by $f(x)=x+\frac{1}{x},$then ${{f}^{-1}}(x)$ is equal to

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

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

C) $\frac{x-\sqrt{{{x}^{2}}-4}}{2}$

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

• question_answer119) If$A=\left[ \begin{matrix} 1 & 3 \\ 2 & -2 \\ \end{matrix} \right],$ then ${{A}^{-1}}$is equal to

A) $-\frac{1}{8}\left[ \begin{matrix} 3 & 1 \\ -2 & 2 \\ \end{matrix} \right]$

B) $-\frac{1}{8}\left[ \begin{matrix} -2 & -3 \\ -2 & 1 \\ \end{matrix} \right]$

C) $\frac{1}{8}\left[ \begin{matrix} -1 & -3 \\ -2 & 2 \\ \end{matrix} \right]$

D) None of these

• question_answer120) The determinant $\left| \begin{matrix} \cos (\alpha +\beta ) & -\sin (\alpha +\beta ) & \cos 2\beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta \\ \end{matrix} \right|$ is independent of

A) $\alpha$

B) $\beta$

C) $\alpha$and$\beta$

D) Neither $\alpha$nor $\beta$

• question_answer121) The ninth term in the expansion of${{[{{3}^{{{\log }_{3}}\sqrt{{{25}^{x-1}}+7}}}+{{3}^{-\frac{1}{8}{{\log }_{3}}({{5}^{x-1}}+1)}}]}^{10}}$is equal to 180, then $x$is equal to

A) 1

B) 2

C) 3

D) None of these

• question_answer122) The number of diagonals that can be drawn by joining the vertices of an octagon, is

A) 28

B) 48

C) 20

D) None of these

• question_answer123) The coefficient of x in the quadratic equation $a{{x}^{2}}+bx+c=0$was wrongly taken as 17 in place of 13 and its roots were found to be - 2 and - 15, the actual roots of the equation are

A) - 2 and 15

B) - 3 and - 10

C) - 4 and- 9

D) -5 and -6

• question_answer124) It is given that $\sum\limits_{r=1}^{\infty }{\frac{1}{{{(2r-1)}^{2}}}}=\frac{{{\pi }^{2}}}{8},$then$\sum\limits_{r=1}^{\infty }{\frac{1}{{{r}^{2}}}}$is equal to

A) $\frac{{{\pi }^{2}}}{24}$

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

C) $\frac{{{\pi }^{2}}}{6}$

D) None of these

• question_answer125) The 10th common term between the series $3+7+11+...$.and $1+6+11+...$is

A) 191

B) 193

C) 211

D) None of these

• question_answer126) If $x=a+b,\,y=a\omega +b{{\omega }^{2}}$and $z=a{{\omega }^{2}}+b\omega ,$ then $xyz$is equal to

A) ${{(a+b)}^{2}}$

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

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

D) ${{(a+b)}^{3}}-3ab(a+b)$

• question_answer127) If C is an obtuse angle in a triangle, then

A) tan A tan B < 1

B) tan A tan B > 1

C) tan A tan B = 1

D) None of these

• question_answer128) In any $\Delta \,A \,B \,C,\frac{1}{r_{1}^{2}}+\frac{1}{r_{2}^{2}}+\frac{1}{r_{3}^{2}}+\frac{1}{{{r}^{2}}}$ is equal to

A)  $\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{2{{\Delta }^{2}}}$

B) $\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{{{\Delta }^{2}}}$

C) $\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{3{{\Delta }^{2}}}$

D) None of these

• question_answer129) $\tan \left[ {{\cos }^{-1}}\frac{4}{5}+{{\tan }^{-1}}\frac{2}{3} \right]$is equal to

A) $\frac{13}{6}$

B) $\frac{17}{6}$

C) $-\frac{13}{6}$

D) $-\frac{17}{6}$

• question_answer130) A man on the top of a cliff 100 m high, observe the angles of depression of two points on the opposite sides of the cliff as $\text{3}{{\text{0}}^{\text{o}}}$ and $\text{6}{{\text{0}}^{\text{o}}}$ respectively. Then, the distance between the two points is equal to

A) $400\sqrt{3}\,m$

B) $\frac{400}{\sqrt{3}}\,m$

C) $\frac{100}{\sqrt{3}}\,m$

D) $200\sqrt{3}\,m$

• question_answer131) The sum of square of deviations for 10 observations taken from mean 50 is 250. The coefficient of variation is

A) 10

B) 20

C) 30

D) 40

• question_answer132) The vector equation of a plane through the point $(2\hat{i}-\hat{j}-4\hat{k})$ and parallel to the plane $\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})-7=0$is

A) $\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=0$

B) $\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=32$

C) $\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=12$

D) None of the above

• question_answer133) The equation${{x}^{3}}-3x+4=0$ has only one real root. What is its first approximate value as obtained by the method of false position in$(-3,-2)?$

A) $-2.125$

B) $2.125$

C) $-2.812$

D) $~2.812$

• question_answer134) An oil company required 13000, 20000 and 15000 barrels of high grade, medium grade and low grade oil respectively. Refinery A produces 100, 300 and 200 barrels per day of high grade, medium grade and low grade oil respectively. While, refinery B produces 200, 400 and 100 barrels per day of high grade, medium grade and low grade oil respectively. If refinery A costs Rs 400 per day and refinery B costs Rs 300 per day to operate, then the days should each be run to minimize costs, while satisfying requirements are

A) 30, 60

B) 60, 30

C) 40, 60

D) 60, 40

• question_answer135) If in a$\text{ABC,}$ $a\tan A+b\,\tan \,B=(a+b)\tan \left( \frac{A+B}{2} \right),$then

A) $A=B$

B) $~A=-B$

C) $A=2B$

D) $B=2A.$

• question_answer136) If A and B are two events such that$P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P(\bar{B})=\frac{1}{2},$ then the events A and B are

A) dependent

B) independent

C) mutually exclusive

D) None of the above

• question_answer137) If $P(x,y,z)$is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that the projections of $\overrightarrow{\text{OP}}$on the axes are$\frac{13}{5},\frac{19}{5},\frac{26}{5}$ respectively, then P divides QR in the ratio

A) 1 : 2

B) 3 : 2

C) 2 : 3

D) 1 : 3

• question_answer138) The vector $\vec{c}$ is perpendicular to the vectors$\vec{a}=(2,-3,1),\vec{b}=(1,-2,3)$ and satisfies the condition $\vec{c}.(\hat{i}+2\hat{j}-7\hat{k})=10.$Then, $\vec{c}$ is equal to

A) $7\hat{i}+5\hat{j}+\hat{k}$

B) $-7\hat{i}-5\hat{j}-\hat{k}$

C) $\hat{i}+\hat{j}-\hat{k}$

D) $\hat{i}+\hat{j}+\hat{k}$

• question_answer139) Consider the differential equation $y=px+\sqrt{{{a}^{2}}{{p}^{2}}+{{b}^{2}}},$where$p=\frac{dy}{dx}.$The order and degree of the differential equation are

A) 1, 1

B) 1, 2

C) 2, 1

D) None of these

• question_answer140) Solution of the differential equation $y\left[ x\cos \left( \frac{y}{x} \right)+y\sin \left( \frac{y}{x} \right) \right]dx$ $-x\left[ y\sin \left( \frac{y}{x} \right)-x\cos \left( \frac{y}{x} \right) \right]dy=0$is

A) $xy\cos \left( \frac{y}{x} \right)=K$

B) $\cos \left( \frac{x}{y} \right)=K\,xy$

C) $\frac{x}{y}\cos \left( \frac{y}{x} \right)=K$

D) None of these

• question_answer141) The value of $\alpha \in (-\pi ,0)$satisfying $\sin \alpha +\int_{\alpha }^{2a}{\cos 2x\,dx=0}$is

A) 0

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

C) $-\pi$

D) All of these

• question_answer142) If curves $y=1-a{{x}^{2}}$ and $y={{x}^{2}}$intersect orthogonally, then the value of a is

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

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

C) 2

D) 3

• question_answer143) If $f(9)=9,$$f(9)=4,$then $\underset{x\to 9}{\mathop{\lim }}\,\frac{\sqrt{f(x)}-3}{\sqrt{x}-3}$ equals

A) 9

B) 4

C) 36

D) None of these

• question_answer144) Find the equation of chord of ${{x}^{2}}-{{y}^{2}}=9$which is bisected at $(5,-3).$

A) $5x+3y+16=0$

B) $~5x+3y-16=0$

C) $~3x+5y+16=0$

D) $3x+5y-16=0$

• question_answer145) The normal chord at a point t on the parabola ${{y}^{2}}=4ax$subtends a right angle at the vertex. Then,${{t}^{2}}$ is equal to

A) 2

B) $\sqrt{2}$

C) 4

D) None of these

• question_answer146) The equation of a circle of radius 5 which lies within the circle ${{x}^{2}}+{{y}^{2}}+14x+10y-26=0$and touches it at the point $(-1,3)$ is

A) ${{x}^{2}}+{{y}^{2}}+\text{ }8x+2y+8=0$

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

C) ${{x}^{2}}+{{y}^{2}}+8x+2y-14=0$

D) None of the above

• question_answer147) The sum of the series $\left[ 1+\left( \frac{1}{2}+\frac{1}{3} \right).\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right).\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\frac{1}{{{4}^{3}}}+...\infty \right]$is equal to

A) $\log \sqrt{12}$

B) $\log \sqrt{10}$

C) ${{e}^{12}}$

D) None of these

• question_answer148) If the AM and GM between two numbers are in the ratio m: n, then the numbers are in the ratio

A) $m+\sqrt{{{m}^{2}}-{{n}^{2}}}:n+\sqrt{{{m}^{2}}-{{n}^{2}}}$

B) $m+\sqrt{{{m}^{2}}-{{n}^{2}}}:m-\sqrt{{{m}^{2}}-{{n}^{2}}}$

C) $m+\sqrt{{{m}^{2}}+{{n}^{2}}}:n+\sqrt{{{m}^{2}}+{{n}^{2}}}$

D) $m+\sqrt{{{m}^{2}}+{{n}^{2}}}:m-\sqrt{{{m}^{2}}-{{n}^{2}}}$

• question_answer149) A line is drawn through a fixed point $(h,k)$ cutting the coordinate axes at P and Q respectively. The rectangle OPRQ is completed. Find the equation of locus of R.

A) $\frac{x}{h}+\frac{y}{k}=1$

B) $\frac{x}{y}+\frac{h}{k}=1$

C) $\frac{h}{x}+\frac{k}{y}=1$

D) $\frac{x}{k}+\frac{y}{h}=1$

• question_answer150) If the sum of m terms of an APIs the same as the sum of its n terms. The sum of its (m + n) terms is

A) 0

B) $1$

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

D) $\sqrt{mn}$