Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2014

JCECE Engineering Solved Paper-2014 Total Questions - 150

1) A mass of \[0.5\,\,kg\] moving with a speed of \[1.5\,\,m{{s}^{-1}}\] on a horizontal smooth surface, collides with a nearly weightless spring of force constant\[k=50\,\,N{{m}^{-1}}\]. The maximum compression of the spring would be

A)

\[0.15\,\,m\]

B)

\[0.23\,\,m\]

C)

\[1.6\,\,m\]

D)

\[0.4\,\,m\]

View Answer
2) A particle of mass \[{{m}_{1}}\] moves with velocity \[{{\upsilon }_{1}}\] and collides with another particle at rest of equal mass. The velocity of the second particle after the elastic collision is

A)

\[3{{v}_{1}}\]

B)

\[{{v}_{1}}\]

C)

\[-{{v}_{1}}\]

D)

\[0\]

View Answer
3) The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axis is

A)

\[\sqrt{3}:\sqrt{2}\]

B)

\[1:\sqrt{2}\]

C)

\[\sqrt{3}:1\]

D)

\[\sqrt{5}:\sqrt{3}\]

View Answer
4) A wheel having moment of inertia\[2kg\,\,{{m}^{-2}}\] about its vertical axis, rotates at the rate of \[60\,\,rpm\] about this axis. The torque which can stop the wheel's rotation in one minute would be

A)

\[\frac{2\pi }{13}N-m\]

B)

\[\frac{\pi }{14}N-m\]

C)

\[\frac{\pi }{15}N-m\]

D)

\[\frac{\pi }{20}N-m\]

View Answer
5) A sphere of diameter \[0.2\,\,m\] and mass \[2\,\,kg\] is rolling on an inclined plane with velocity\[v=0.5m{{s}^{-1}}\]. The kinetic energy of the sphere is

A)

\[0.4\,\,J\]

B)

\[0.3\,\,J\]

C)

\[0.6\,\,J\]

D)

\[0.42\,\,J\]

View Answer
6) If a sphere rolling on an inclined plane with velocity v without slipping, the vertical height of the incline in terms of velocity will be

A)

\[\frac{7v}{10g}\]

B)

\[\frac{7{{v}^{2}}}{10g}\]

C)

\[\frac{2{{v}^{2}}}{5g}\]

D)

\[\frac{3v}{5g}\]

View Answer
7) The height vertically above the earth's surface at which the acceleration due to gravity becomes \[1%\] of its value at the surface is (\[R\] is the radius of the earth)

A)

\[8R\]

B)

\[9R\]

C)

\[10R\]

D)

\[20R\]

View Answer
8) The motion of a particle executing SHM in one dimension is described by\[x=-0.23\sin \left( t+\frac{\pi }{4} \right)\]where, \[x\] is in metre and t in second. The frequency of oscillation in \[Hz\] is

A)

\[3\]

B)

\[\frac{1}{2\pi }\]

C)

\[\frac{\pi }{2}\]

D)

\[\frac{1}{\pi }\]

View Answer
9) The change in the gravitational potential energy when a body of mass \[m\] is raised to a height \[nR\] above the surface of the earth is (here, \[R\] is the radius of the earth)

A)

\[\left( \frac{n}{n+1} \right)mgR\]

B)

\[\left( \frac{n}{n-1} \right)mgR\]

C)

\[nmgR\]

D)

\[\frac{mgR}{n}\]

View Answer
10) A satellite is rotating around a planet in the orbit of radius \[r\] with time period\[T\]. If gravitational force changes according to\[{{r}^{5/2}}\], the \[{{T}^{2}}\] will be

A)

\[\propto {{r}^{3}}\]

B)

\[\propto {{r}^{7/2}}\]

C)

\[{{\propto }^{9/12}}\]

D)

\[\propto {{r}^{3/2}}\]

View Answer
11) A liquid \[X\] of density \[3.36\,\,g/c{{m}^{3}}\] is poured in a U-tube in right arm with height\[10\,\,cm\], which contains\[Hg\]. Another liquid \[Y\] is poured in left arm with height\[8\,\,cm\]. Upper levels of \[X\] and \[Y\] are same. What is the density of\[Y\]?

A)

\[0.8\,\,g/cc\]

B)

\[1.2\,\,g/cc\]

C)

\[1.4\,\,g/cc\]

D)

\[1.6\,\,g/cc\]

View Answer
12) Wafer flows along a horizontal pipe whose cross-section is not, constant. The pressure is \[1\,\,cm\] of\[Hg\], where the velocity is\[35\,\,cm{{s}^{-1}}\]. At a point where the velocity is\[65\,\,cm{{s}^{-1}}\], the pressure will be

A)

\[0.89\,\,cm\]of\[Hg\]

B)

\[8.9\,\,cm\]of\[Hg\]

C)

\[0.5\,\,cm\]of\[Hg\]

D)

\[1\,\,cm\]of\[Hg\]

View Answer
13) A lead bullet of unknown mass is fired-with a speed of \[180\,\,m{{s}^{-1}}\] into a tree in which it stops. Assuming that in this process two-third of heat produced goes into the bullet and one-third into wood. The temperature of the bullet rises by

A)

\[{{140}^{o}}C\]

B)

\[{{106}^{o}}C\]

C)

\[{{90}^{o}}C\]

D)

\[{{100}^{o}}C\]

View Answer
14) 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

View Answer
15) Two monoatomic ideal gases \[A\] and \[B\] occupying the same volume \[V\] are at the same temperature \[T\] and pressure\[p\]. If they are mixed, the resultant mixture has volume \[V\] and temperature\[T\]. The pressure of the mixture is

A)

\[p\]

B)

\[\frac{p}{2}\]

C)

\[4p\]

D)

\[2p\]

View Answer
16) The temperature at which the mean \[KE\] of the molecules of gas is one-third of the mean \[KE\] of its molecules at \[{{180}^{o}}C\] is

A)

\[-{{122}^{o}}C\]

B)

\[-{{90}^{o}}C\]

C)

\[{{60}^{o}}C\]

D)

\[{{151}^{o}}C\]

View Answer
17) \[U\] is the \[PE\] of an oscillating particle and \[F\] is the force acting on it at a given instant. Which of the following is true?

A)

\[\frac{U}{F}+x=0\]

B)

\[\frac{2U}{F}+x=0\]

C)

\[\frac{F}{U}+x=0\]

D)

\[\frac{F}{2U}+x=0\]

View Answer
18) The density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is\[R\], the radius of the plane would be

A)

\[2R\]

B)

\[4R\]

C)

\[\frac{1}{4}R\]

D)

\[\frac{1}{2}R\]

View Answer
19) The half-life period of a radioactive substance is\[140\,\,days\]. After, how much time, \[15\,\,g\] will decay from a \[16\,\,g\] sample of the substance?

A)

\[140\,\,days\]

B)

\[280\,\,days\]

C)

\[420\,\,days\]

D)

\[560\,\,days\]

View Answer
20) A tuning fork \[A\] produces 4 beats \[{{s}^{-1}}\] with another tuning fork \[B\] of frequency\[320\,\,Hz\]. On filing one of the prongs of\[A\], 4 beats \[{{s}^{-1}}\] 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)

\[320\,\,Hz\]

View Answer
21) Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of\[72\,\,km/h\]\[\text{and}\]\[36\,\,km/h\]. If first car blows horn of frequency\[280\,\,Hz\], then the frequency of horn heard by the driver of second car when line joining the car makes angle of \[{{45}^{o}}\] with the roads, will.be

A)

\[321\,\,Hz\]

B)

\[296\,\,Hz\]

C)

\[289\,\,Hz\]

D)

\[280\,\,Hz\]

View Answer
22) A particle moves along a straight line\[OX\]. At a time \[t\] (in second) the distance \[x\] of the particle from \[O\] is given by\[x=40+12t-{{t}^{3}}\]. How long would the particle travel before coming to rest?

A)

\[24\,\,m\]

B)

\[40\,\,m\]

C)

\[56\,\,m\]

D)

\[16\,\,m\]

View Answer
23) The capacitance of a spherical conductor with radius \[1\,\,m\] is

A)

\[9\times {{10}^{9}}F\]

B)

\[1\mu F\]

C)

\[1.1\times {{10}^{-10}}F\]

D)

\[1\times {{10}^{-6}}F\]

View Answer
24) The electric field due to an electric dipole at a distance \[r\] from its centre in axial position is\[E\]. If the dipole is rotated through an angle of \[{{90}^{o}}\] about its perpendicular axis, the electric field at the same point will be

A)

\[E\]

B)

\[\frac{E}{4}\]

C)

\[\frac{E}{2}\]

D)

\[2E\]

View Answer
25) Choose the correct statement.

A)

When we heat a semiconductor its resistance increases

B)

When we heat a semiconductor its resistance decreases

C)

When we cool a semiconductor to\[0\,\,K\], then it be cames superconductor

D)

Resistance of a semiconductor is independent of temperature

View Answer
26) A charge \[q\] coulomb makes \[n\] revolutions in one second in a circular orbit of radius r. The magnetic field at the centre of the orbit in\[N{{A}^{-1}}{{m}^{-1}}\]is.

A)

\[\frac{2\pi rn}{q}\times {{10}^{-7}}\]

B)

\[\left( \frac{2\pi q}{r} \right)\times {{10}^{-7}}\]

C)

\[\left( \frac{2\pi q}{nr} \right)\times {{10}^{-7}}\]

D)

\[\left( \frac{2\pi nq}{r} \right)\times {{10}^{-7}}\]

View Answer
27) The path of an electron in a uniform magnetic field may be

A)

circular but not helical

B)

helical but not circular

C)

neither helical nor circular

D)

either helical or circular

View Answer
28) The couple acting on a magnet of length \[10\,\,cm\] and pole strength\[125\,\,A-m\], kept in a field of \[B=2\times {{10}^{-5}}T\], at an angle of \[{{30}^{o}}\] is

A)

\[1.5\times {{10}^{-5}}N-m\]

B)

\[1.5\times {{10}^{-3}}N-m\]

C)

\[1.5\times {{10}^{-2}}N-m\]

D)

\[1.5\times {{10}^{-6}}N-m\]

View Answer
29) \[X\]and\[Y\], two metallic coils are arranged in such a way that, when steady change in current flowing in \[X\] coil is\[4\,\,A\], change in magnetic flux associated with coil \[Y\] is\[0.4\,\,Wb\]. Mutual inductance of the system of these coils is

A)

\[0.2\,\,H\]

B)

\[5\,\,H\]

C)

\[0.8\,\,H\]

D)

\[0.1\,\,H\]

View Answer
30) A sinusoidal voltage of peak value \[300\,\,V\] and an angular frequency \[\omega =400\,\,rad/s\] is applied to series \[L-C-R\] circuit, in which \[R=3\Omega ,\,\,L=20\,\,mH\]and\[C=625\mu F\]. The peak current in the circuit is

A)

\[30\sqrt{2}A\]

B)

\[60\,\,A\]

C)

\[100\,\,A\]

D)

\[60\sqrt{2}A\]

View Answer
31) A fire screen produces sensation of cooling as

A)

it allows both infrared and visible light but cuts off ultraviolet

B)

it allows infrared and cuts off shorter wavelengths

C)

it cuts off both visible light and infrared

D)

it allows only visible light and cuts off infrared

View Answer
32) If the angle of incidence is twice the angle of refraction in a medium of refractive index\[\mu \], then the angle of incidence is

A)

\[2{{\cos }^{-1}}\frac{\mu }{2}\]

B)

\[2{{\sin }^{-1}}\frac{\mu }{2}\]

C)

\[2{{\cos }^{-1}}\mu \]

D)

\[2{{\sin }^{-1}}\mu \]

View Answer
33) The magnification produced by an astronomical telescope for normal adjustment is 10 and the length of the telescope.is\[1.1\,\,m\]. The magnification, when the image is formed atleast distance of distinct vision is

A)

\[6\]

B)

\[14\]

C)

\[16\]

D)

\[18\]

View Answer
34) In Young's double slit experiment with sodium vapour lamp of wavelength \[589\,\,nm\] and the slits \[0.589\,\,mm\] apart, the half angular width of the central maximum is

A)

\[{{\sin }^{-1}}(0.01)\]

B)

\[{{\sin }^{-1}}(0.0001)\]

C)

\[{{\sin }^{-1}}(0.001)\]

D)

\[{{\sin }^{-1}}(0.1)\]

View Answer
35) When the angle of incidence is \[{{60}^{o}}\] on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass is

A)

\[\sqrt{2}\times {{10}^{8}}m{{s}^{-1}}\]

B)

\[\sqrt{3}\times {{10}^{8}}m{{s}^{-1}}\]

C)

\[2\times {{10}^{8}}m{{s}^{-1}}\]

D)

\[3\times {{10}^{8}}m{{s}^{-1}}\]

View Answer
36) Cathode rays of velocity \[{{10}^{6}}m{{s}^{-1}}\] describe an approximate circular path of radius \[1\,\,m\] in an electric field\[300\,\,Vc{{m}^{-1}}\]. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

A)

\[2400\,\,V\,\,c{{m}^{-1}}\]

B)

\[600\,\,V\,\,c{{m}^{-1}}\]

C)

\[1200\,\,V\,\,c{{m}^{-1}}\]

D)

\[12000\,\,V\,\,c{{m}^{-1}}\]

View Answer
37) The de-Broglie wavelength of an electron and the wavelength of a photon are the same. The ratio between the energy of that photon and the momentum of that electron is (\[c=\]velocity of light, \[h=\]Planck's constant)

A)

\[h\]

B)

\[c\]

C)

\[\frac{1}{h}\]

D)

\[\frac{1}{c}\]

View Answer
38) When \[1\,\,cm\]thick surface is illuminated with light of wavelength\[\lambda \], the stopping potential is\[V\]. When the same surface is illuminated by light of wavelength\[2\lambda \], the stopping potential is\[\frac{V}{3}\]. Threshold wavelength for metallic surface is

A)

\[\frac{4\lambda }{3}\]

B)

\[4\lambda \]

C)

\[6\lambda \]

D)

\[\frac{8\lambda }{3}\]

View Answer
39) For photoelectric emission, tungsten requires light of\[2300\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. If light of \[1800\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\] wavelength is incident, then emission

A)

takes place

B)

doesn't take place

C)

may or may not take place

D)

depends on frequency

View Answer
40) X-rays are used in determining the molecular structure of crystalline, because

A)

its energy is high

B)

it can penetrate the material

C)

its wavelength is comparable to interatomic distance

D)

its frequency is low

View Answer
41) The frequency of vibration of string is given by                 \[v=\frac{p}{2l}{{\left[ \frac{F}{m} \right]}^{1/2}}\] Here, \[p\] is the number of segments m the string and \[l\] is the length. The dimensional formula for \[m\] will be

A)

\[[{{M}^{0}}L{{T}^{-1}}]\]

B)

\[[M{{L}^{0}}{{T}^{-1}}]\]

C)

\[[M{{L}^{-1}}{{T}^{0}}]\]

D)

\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\]

View Answer
42) A stone is thrown vertically upwards. When the stone is at a height equal to half of its maximum height its speed will be\[10\,\,m/s\], then the maximum height attained by the stone (Take\[g=10\,\,m/{{s}^{2}})\]

A)

\[3\,\,m\]

B)

\[15\,\,m\]

C)

\[1\,\,m\]

D)

\[10\,\,m\]

View Answer
43) A string of length /fixed at one end carries mass \[m\] at the other end. The string makes\[\frac{2}{\pi }\,\,rev/s\] around the horizontal axis through the it fixed end as shown in the figure, the tension in the string is

A)

\[16\,\,ml\]

B)

\[6\,\,ml\]

C)

\[5\,\,ml\]

D)

\[3\,\,ml\]

View Answer
44) A gardener pushes a lawn roller through distance\[20\,\,m\]. If he applies a force of \[20\,\,kg-w\] in a direction inclined at \[{{60}^{o}}\] to the ground, the work done by him is

A)

\[1960\,\,J\]

B)

\[196\,\,J\]

C)

\[1.96\,\,J\]

D)

\[196\,\,kJ\]

View Answer
45) The breaking stress of a wire depends upon

A)

material of wire

B)

length of wire

C)

radius of wire

D)

shape of cross-section

View Answer
46) \[Li\] nucleus has three protons and four neutrons. Mass of lithium nucleus is\[7.016005\,\,amu\]. Mass of proton is \[1.007277\,\,amu\] and mass of neutron is\[1.008665\,\,amu\]. Mass defect for lithium nucleus in \[amu\] is

A)

\[0.04048\]

B)

\[0.04050\]

C)

\[0.04052\]

D)

\[0.04055\]

View Answer
47) A voltmeter of range \[2V\] and resistance \[300\Omega \] cannot be converted into ammeter of range

A)

\[1\,\,A\]

B)

\[1\,\,mA\]

C)

\[100\,\,mA\]

D)

\[10\,\,mA\]

View Answer
48) The values of two resistors are \[{{R}_{1}}=(6+0.3)k\Omega \] and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when, they are connected in parallel is

A)

\[5.125%\]

B)

\[2%\]

C)

\[10.125%\]

D)

\[7%\]

View Answer
49) A body of mass \[2\,\,kg\] is projected from the ground with a velocity \[20\,\,m{{s}^{-1}}\] at an angle \[{{30}^{o}}\] with the vertical. If \[{{t}_{1}}\] is the time in second at which the body is projected and \[{{t}_{2}}\] is the time in second at which it reaches the ground, the change in momentum in \[kgm{{s}^{-1}}\] during the time \[({{t}_{2}}-{{t}_{1}})\] is

A)

\[40\sqrt{2}\]

B)

\[40\sqrt{3}\]

C)

\[25\sqrt{3}\]

D)

\[45\]

View Answer
50) The position vector of a particle is\[r=(a\cos \omega t)\widehat{\mathbf{i}}+(a\sin \omega t)\widehat{\mathbf{j}}\]. The velocity vector of the particle is

A)

parallel to position vector

B)

perpendicular to position vector

C)

directed towards the origin

D)

directed away from the origin

View Answer
51) The major product of the reaction between m-dinitrobenzene and \[N{{H}_{4}}HS\]is

A)

B)

C)

D)

View Answer
52) Correct order of nucleophilicity is

A)

\[CH_{3}^{-}<NH_{2}^{-}<O{{H}^{-}}<{{F}^{-}}\]

B)

\[{{F}^{-}}<O{{H}^{-}}<CH_{3}^{-}<NH_{2}^{-}\]

C)

\[O{{H}^{-}}<NH_{2}^{-}<{{F}^{-}}<CH_{3}^{-}\]

D)

\[{{F}^{-}}<O{{H}^{-}}<NH_{2}^{-}<CH_{3}^{-}\]

View Answer
53) The main product of the reaction would be 2-butene + chloroform\[\xrightarrow{NaOH}\]?

A)

butanoic acid

B)

2-methyl butanoic acid

C)

1, 1, 1-trichloro-2-methyl butane

D)

1, 4-butane diol

View Answer
54) The end product of\[C{{H}_{3}}COOH\xrightarrow{CaC{{O}_{3}}}A\xrightarrow{Heat}B\xrightarrow{N{{H}_{2}}OH}C\]

A)

acetaldehyde

B)

acetoxime

C)

  formaldehyde

D)

  methyl cyanide

View Answer
55) Calorific value is in the order

A)

Fats > Carbohydrates > Proteins

B)

Carbohydrates > Fats > Proteins

C)

Proteins > Carbohydrates > Fats

D)

Fats > Proteins > Carbohydrates

View Answer
56) The monomeric unit of orlon molecule is

A)

\[C{{H}_{2}}=CH-Cl\]

B)

\[C{{H}_{3}}COO-CH=C{{H}_{2}}\]

C)

\[C{{H}_{2}}=CH-CN\]

D)

\[{{C}_{6}}{{H}_{5}}-CH=C{{H}_{2}}\]

View Answer
57) Which of the following acids possesses oxidising, reducing and complex forming properties?

A)

\[HCl\]

B)

\[HN{{O}_{2}}\]

C)

\[{{H}_{2}}S{{O}_{4}}\]

D)

\[HN{{O}_{3}}\]

View Answer
58) Cassiterite is concentrated by

A)

levigation

B)

electromagnetic separation

C)

floatation

D)

liquefaction

View Answer
59) The stability of the following alkali metal chlorides follows the order

A)

\[LiCl>KCl>NaCl>CsCl\]

B)

\[CsCl>KCl>NaCl>LiCl\]

C)

\[NaCl>KCl>LiCl>CsCl\]

D)

\[KCl>CsCl>NaCl>LiCl\]

View Answer
60) The complex \[{{[Fe{{({{H}_{2}}O)}_{5}}NO]}^{2+}}\] is formed in the brown ring test for nitrates when freshly prepared \[FeS{{O}_{4}}\] solution is added to aqueous solution of \[NO_{3}^{-}\] followed by addition of conc. \[{{H}_{2}}S{{O}_{4}}\]. Select the correct statement about this complex.

A)

Colour change is due to charge transfer

B)

It has iron in \[+1\] oxidation state and nitrosyl as\[N{{O}^{+}}\]

C)

It has, magnetic moment of \[3.87\,\,BM\] confirming three unpaired electrons in\[Fe\]

D)

All the above are correct statements

View Answer
61) Consider the following statements. I. Colour of a transition metal complex is dependent on energy difference between two \[d-\]levels. II. Colour of the complex is dependent on the nature of the ligand and the type of complex formed. III. \[ZnS{{O}_{4}}\] and \[Ti{{O}_{2}}\] are white as in both,\[d-d\] spectra are impossible. Select the correct statements.

A)

I, II and III

B)

I and II

C)

  II and III

D)

  I and III

View Answer
62) The outermost electronic configuration of the most electronegative element is

A)

\[n{{s}^{2}}n{{p}^{3}}\]

B)

\[n{{s}^{2}}n{{p}^{4}}\]

C)

\[n{{s}^{2}}n{{p}^{5}}\]

D)

\[n{{s}^{2}}n{{p}^{6}}\]

View Answer
63) Standard enthalpy and standard entropy change for the oxidation of \[N{{H}_{3}}\] at \[298\,\,K\] are \[-382.64\,\,kJ\,\,mo{{l}^{-1}}\]and\[-145.6\,\,J\,\,mo{{l}^{-1}}\]respectively. Standard Gibbs energy change for the same reaction at \[298\,\,K\] is

A)

\[+339.3\,\,kJ\,\,mo{{l}^{-1}}\]

B)

\[-439.3\,\,kJ\,\,mo{{l}^{-1}}\]

C)

\[-339.3\,\,kJ\,\,mo{{l}^{-1}}\]

D)

\[-393.3\,\,kJ\,\,mo{{l}^{-1}}\]

View Answer
64) According to the Arrhenius equation, a straight line is to be obtained by plotting the logarithm of the rate constant of a chemical reaction \[(\log k)\] against

A)

\[T\]

B)

\[\log T\]

C)

\[\frac{1}{T}\]

D)

\[\log \frac{1}{T}\]

View Answer
65) Which of the following is not a reducing agent?

A)

\[S{{O}_{2}}\]

B)

\[{{H}_{2}}{{O}_{2}}\]

C)

\[C{{O}_{2}}\]

D)

\[N{{O}_{2}}\]

View Answer
66) For a dilute solution, Raoult's law states that

A)

the lowering of vapour pressure is equal to the mole fraction of the solute

B)

the relative lowering of vapour pressure is equal to the mole fraction of solute

C)

the relative lowering of vapour pressure is equal to the amount of the solution

D)

the vapour pressure of the solution, is equal to the mole fraction of the solvent

View Answer
67) The bond dissociation energies of gaseous \[{{H}_{2}},\,\,C{{l}_{2}}\] and \[HCl\] are \[104,\,\,58\] and \[103\,\,kcal\] respectively. The enthalpy of formation of \[HCl\] gas would be

A)

\[-44\,\,kcal\]

B)

\[44\,\,kcal\]

C)

\[-22\,\,kcal\]

D)

\[22\,\,kcal\]

View Answer
68) Species acting both as Bronsted acid and base is

A)

\[HSO_{4}^{-}\]

B)

\[N{{a}_{2}}C{{O}_{3}}\]

C)

\[N{{H}_{3}}\]

D)

\[O{{H}^{-}}\]

View Answer
69) The solubility of \[Agl\] in \[Nal\] solution is less than that in pure water because

A)

\[Agl\] forms complex with\[Nal\]

B)

of common ion effect

C)

solubility product of \[Agl\] is less

D)

the temperature of the solution decreases

View Answer
70) \[Zn|Z{{n}^{2+}}(a=0.1\,\,M)||F{{e}^{2+}}(a=0.01\,\,M)|Fe.\]The emf of the above cell is\[0.2905\,\,V\]. Equilibrium constant for the cell reaction is

A)

\[{{10}^{0.32/0.0591}}\]

B)

\[{{10}^{0.32/0.0295}}\]

C)

\[{{10}^{0.26/0.0295}}\]

D)

\[{{10}^{0.26/0.0295}}\]

View Answer
71) \[50\,\,mL\] of \[1\,\,M\] oxalic acid (molar mass\[=126\]) is shaken with \[0.5\,\,g\] of wood charcoal. The final concentration of the solution after adsorption is\[0.5\,\,M\]. What is the amount of oxalic acid adsorbed per gram of carbon?

A)

\[3.15\]

B)

\[1.575\]

C)

\[6.30\]

D)

\[12.60\]

View Answer
72) A dust particle has mass equal to\[{{10}^{-11}}g\], diameter \[{{10}^{-4}}cm\] and velocity\[{{10}^{-4}}cm/s\]. The error in measurement of velocity is\[0.1\,\,%\]. What will be the uncertainty in its position?

A)

\[0.527\times {{10}^{10}}cm\]

B)

\[5.27\times {{10}^{9}}cm\]

C)

\[0.527\times {{10}^{-15}}cm\]

D)

\[0.527\times {{10}^{-9}}cm\]

View Answer
73) The value of compression factor, \[Z\] for critical constants is

A)

\[\frac{1}{2}\]

B)

\[\frac{3}{4}\]

C)

\[\frac{2}{3}\]

D)

\[\frac{3}{8}\]

View Answer
74) At what temperature, the \[rms\] velocity of \[S{{O}_{2}}\] be same as that of \[{{O}_{2}}\] at\[303\,\,K\]?

A)

\[273\,\,K\]

B)

\[606\,\,K\]

C)

\[303\,\,K\]

D)

\[403\,\,K\]

View Answer
75) The percentage of water of crystallisation of a sample of blue vitriol is

A)

\[34.07%\]

B)

\[35.07%\]

C)

\[36.07%\]

D)

\[37.07%\]

View Answer
76) Which of the following series of elements have nearly the same atomic radii?

A)

\[F,\,\,Cl,\,\,Br,\,\,I\]

B)

\[Na,\,\,K,\,\,Rb,\,\,Cs\]

C)

\[Li,\,\,Be,\,\,B,\,\,C\]

D)

\[Fe,\,\,Co,\,\,Ni,\,\,Cu\]

View Answer
77) The volume strength of 1 molar solution of\[{{H}_{2}}{{O}_{2}}\]is

A)

\[11.2\]

B)

\[22.4\]

C)

\[5.6\]

D)

\[56\]

View Answer
78) Maximum amount of carbon is present in

A)

wrought iron

B)

cast iron

C)

stainless steel

D)

  German silver

View Answer
79) What is the best way to carry out the following transformation? \[1-\text{pentyne}\xrightarrow{{}}\text{pentanal}\]

A)

\[HgS{{O}_{4}}/{{H}_{2}}S{{O}_{4}}\]

B)

\[{{H}_{2}}/Lindlar's\,\,catalyst;\,\,{{O}_{3}};\,\,Zn-{{H}_{2}}O\]

C)

\[Hl{{O}_{4}}/{{H}_{2}}O\]

D)

\[B{{H}_{3}};\,\,{{H}_{2}}{{O}_{2}}/NaOH\]

View Answer
80) Product of this reaction is

A)

B)

C)

D)

View Answer
81) Etherates are

A)

ethers

B)

solution in ether

C)

complexes of ethers with Lewis acid

D)

complexes of ethers with Lewis base

View Answer
82) Tranquillisers are the substances used for the treatment of

A)

cancer

B)

AIDS

C)

mental diseases

D)

  physical disorders

View Answer
83) Which of the following carbonyl compounds on condensation gives an aromatic compound?

A)

\[C{{H}_{3}}CHO\]

B)

\[HCHO\]

C)

\[C{{H}_{3}}COC{{H}_{3}}\]

D)

\[C{{H}_{3}}C{{H}_{2}}CHO\]

View Answer
84) Iron crystallises in a bcc system with a lattice parameter of\[2.861\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. Calculate the density of iron in the bcc system (atomic weight of\[Fe=56,\,\,{{N}_{A}}=6.02\times {{10}^{23}}mo{{l}^{-1}})\].

A)

\[7.94\,\,g\,\,m{{L}^{-1}}\]

B)

\[8.96\,\,g\,\,m{{L}^{-1}}\]

C)

\[2.78\,\,g\,\,m{{L}^{-1}}\]

D)

\[6.72\,\,g\,\,m{{L}^{-1}}\]

View Answer
85) Which particle among the following will have the smallest de-Broglie wavelength, assuming that they have the same velocity?

A)

A positron

B)

A photon

C)

  An \[\alpha -\]particle

D)

  A neutron

View Answer
86) The equilibrium constant for the reaction,\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g)\]is 64. If the volume of the container is reduced to half of the original volume, the value of the equilibrium constant will be

A)

\[16\]

B)

\[32\]

C)

\[64\]

D)

\[128\]

View Answer
87) For the reaction,\[Zn(s)+C{{u}^{2+}}(0.1M)\xrightarrow{{}}Z{{n}^{2+}}(1M)+Cu(s)t\]akmg place in a cell;\[E_{cell}^{\text{o}}\]is\[1.10\,\,V\].\[{{E}_{cell}}\] for the cell will be\[\left( 2.303\frac{RT}{F}=0.0591 \right)\]

A)

\[1.80\,\,V\]

B)

\[1.07\,\,V\]

C)

\[0.82\,\,V\]

D)

\[2.14\,\,V\]

View Answer
88) Surface of the eye is protected from bacterial infection by enzyme

A)

carbonic enhydrase

B)

  urease

C)

  lysozyme

D)

  zymase

View Answer
89) The number of \[\sigma \]bonds in \[{{P}_{4}}{{O}_{10}}\] is

A)

\[6\]

B)

\[16\]

C)

\[20\]

D)

\[7\]

View Answer
90) Indicate the wrongly named compound.

A)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}-C{{H}_{2}}-CHO\]     (4-methyl-1-pentanal)

B)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C\equiv C-COOH\]    (4-methyl-2-pentyn-1-oic acid)

C)

\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-COOH\]    (2-methyl-1-pentanoic acid)

D)

\[C{{H}_{3}}C{{H}_{2}}-CH=CH-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\]                          (3-hexen-5-one)

View Answer
91) Identify the vitamin whose deficiency in our blood decreases reproductive power?

A)

Vitamin E

B)

Vitamin D

C)

  Vitamin A

D)

  Vitamin C

View Answer
92) Give the major product of the following reaction,

A)

B)

C)

D)

Cannot say

View Answer
93) \[Phenol\xrightarrow[(ii)\,\,C{{O}_{2}}/{{140}^{o}}C]{(i)\,\,NaOH}A\xrightarrow{{{H}^{+}}/{{H}_{2}}O}B\xrightarrow{A{{c}_{2}}O}C\]In this reaction, the end product \['C'\] is

A)

salicylaldehyde

B)

salicylic acid

C)

  phenyl acetate

D)

  aspirin

View Answer
94) What will be the degree of ionisation of \[0.05\,\,M\] acetic acid if its \[p{{K}_{a}}\] value is\[4.74\]?

A)

\[0.019%\]

B)

\[1.9%\]

C)

\[3.0%\]

D)

\[4.74%\]

View Answer
95) Which of the reactions defines\[\Delta H_{f}^{\text{o}}\]?

A)

\[{{C}_{diamond}}+{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\]

B)

\[\frac{1}{2}{{H}_{2}}(g)+\frac{1}{2}{{F}_{2}}(g)\xrightarrow{{}}HF(g)\]

C)

\[{{N}_{2}}(l)+3{{H}_{2}}(g)\xrightarrow{{}}2N{{H}_{3}}(g)\]

D)

\[CO(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}C{{O}_{2}}(g)\]

View Answer
96) The equivalent weight of \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\] in the following reaction is                 \[2N{{a}_{2}}{{S}_{2}}{{O}_{3}}+{{I}_{2}}\xrightarrow{{}}N{{a}_{2}}{{S}_{4}}{{O}_{6}}+2NaI\]

A)

\[M\]

B)

\[M/8\]

C)

\[M/0.5\]

D)

\[M/2\]

View Answer
97) The half-life period for first order reaction having activation energy \[39.3\,\,kcal\,\,mo{{l}^{-1}}\] at \[{{300}^{o}}C\] and frequency constant \[1.11\times {{10}^{11}}{{s}^{-1}}\] will be

A)

\[1\,\,h\]

B)

\[1.68\,\,h\]

C)

\[1.28\,\,h\]

D)

\[1.11\,\,h\]

View Answer
98) Water is brought to boil under a pressure of\[1.0\,\,atm\]. When an electric current of \[0.50\,\,A\] from a \[12\,\,V\] supply is passed for \[300\,\,s\] through a resistance in thermal contact with it, it is found that \[0.798\,\,g\] of water is vaporised. Calculate the molar internal energy change at boiling point\[(373.15\,\,K)\].

A)

\[375\,\,kJ\,\,mo{{l}^{-1}}\]

B)

\[3.75\,\,kJ\,\,mo{{l}^{-1}}\]

C)

\[42.6\,\,kJ\,\,mo{{l}^{-1}}\]

D)

\[4.26\,\,kJ\,\,mo{{l}^{-1}}\]

View Answer
99) The electrons, identified by quantum numbers\[n\] and\[l\], (i)\[n=4,\,\,l=1\](ii)\[n=4,\,\,l=0\] (iii)\[n=3,\,\,l=2\](iv)\[n=3,\,\,l=1\]can be placed in order of increasing energy, from the lowest to highest, as

A)

(iv) < (ii) < (iii) < (i)

B)

(ii) < (iv) < (i) < (iii)

C)

(i) < (iii) < (ii) < (ii)

D)

(iii) < (i) < (iv) < (ii)

View Answer
100) At certain temperature and a total pressure of\[{{10}^{5}}\,\,Pa\], iodine vapours contains \[40%\] by volume of iodine atoms. \[{{K}_{p}}\] for the equilibrium, \[{{I}_{2}}(g)2I(g)\];will be

A)

\[0.67\]

B)

\[1.5\]

C)

\[2.67\times {{10}^{4}}\]

D)

\[9.0\times {{10}^{4}}\]

View Answer
101) The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\] and\[x=a\], is

A)

\[2{{a}^{2}}\]

B)

\[\frac{{{a}^{2}}}{2}\]

C)

\[\frac{\sqrt{3}{{a}^{2}}}{2}\]

D)

\[\frac{2{{a}^{2}}}{\sqrt{3}}\]

View Answer
102) There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is

A)

6

B)

11

C)

13

D)

  None of these

View Answer
103) For which interval, the given function \[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\]is decreasing?

A)

\[(-2,\,\,\infty )\]

B)

\[(-2,\,\,-1)\]

C)

\[(-\infty ,\,\,-1)\]

D)

\[(-\infty ,\,\,-2)\]and\[(-1,\,\,\infty )\]

View Answer
104) The value of\[x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}\]is

A)

\[-1\]

B)

\[1\]

C)

\[2\]

D)

\[3\]

View Answer
105) For what value\[k\], will the equation \[{{x}^{2}}-(3k-1)x+2{{k}^{2}}+2k=11\]have equal roots?

A)

\[5\]

B)

\[9\]

C)

Both [a] and [b]

D)

\[0\]

View Answer
106) A student is to answer \[10\] out of \[13\] questions in an examination such that he must choose atleast \[4\] from the first five questions. The number of choices available to him is

A)

\[140\]

B)

\[196\]

C)

\[280\]

D)

\[346\]

View Answer
107) The equations of the tangent and normal at point \[(3,\,\,-2)\] of ellipse \[4{{x}^{2}}+9{{y}^{2}}=36\] are

A)

\[\frac{x}{3}-\frac{y}{2}=1,\,\,\frac{x}{2}+\frac{y}{3}=\frac{5}{6}\]

B)

\[\frac{x}{3}+\frac{y}{2}=1,\,\,\frac{x}{2}-\frac{y}{3}=\frac{5}{6}\]

C)

\[\frac{x}{2}+\frac{y}{3}=1,\,\,\frac{x}{3}-\frac{y}{2}=\frac{5}{6}\]

D)

None of the above

View Answer
108) The angle between the lines whose direction cosines satisfy the equations\[l+m+n=0,\,\,{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\], is given by

A)

\[\frac{2\pi }{3}\]

B)

\[\frac{\pi }{6}\]

C)

\[\frac{5\pi }{3}\]

D)

\[\frac{\pi }{3}\]

View Answer
109) The equation of the plane containing the line of intersection of the planes \[2x-y=0\] and \[y-3z=0\] and perpendicular to the plane \[4x+5y-3z-8=0\] is

A)

\[28x-17y+9z=0\]

B)

\[28x+17y+9z=0\]

C)

\[28x-17y-9z=0\]

D)

\[7x-3y+z=0\]

View Answer
110) If \[f(x)\] and \[g(x)\] are two functions with \[g(x)=x-\frac{1}{x}\]and \[fog(x)={{x}^{3}}-\frac{1}{{{x}^{3}}}\], then\[f'(x)\] is equal to

A)

\[3{{x}^{2}}+3\]

B)

\[{{x}^{2}}-\frac{1}{{{x}^{2}}}\]

C)

\[1+\frac{1}{{{x}^{2}}}\]

D)

\[3{{x}^{2}}+\frac{3}{{{x}^{4}}}\]

View Answer
111) The function \[f:R\to R\] defined as\[f(x)=(x-1)(x-2)(x-3)\]is

A)

one-one but not onto

B)

onto but not one-one

C)

both one-one and onto

D)

neither one-one nor onto

View Answer
112) If\[f(x)=\left\{ \begin{matrix} -{{x}^{2}}, & when\,\,x\le 0 \\ 5x-4, & when\,\,0<x\le 1 \\ 4{{x}^{2}}-3x, & when\,\,1<x<2 \\ 3x+4, & when\,\,x\ge 2 \\ \end{matrix} \right.\]then

A)

\[f(x)\]is continuous at\[x=0\]

B)

\[f(x)\]is continuous at\[x=2\]

C)

\[f(x)\]is discontinuous at\[x=1\]

D)

None of the above

View Answer
113) \[f(x)=\sqrt{ax}+\frac{{{a}^{2}}}{\sqrt{ax}}\], then\[f'(\alpha )\] is equal to

A)

\[-1\]

B)

\[1\]

C)

\[0\]

D)

\[a\]

View Answer
114) If\[y={{t}^{10}}+1\]and\[x={{t}^{8}}\], then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is equal to

A)

\[\frac{5}{2}t\]

B)

\[20{{t}^{8}}\]

C)

\[\frac{5}{16{{t}^{6}}}\]

D)

  None of these

View Answer
115) The value of \[b\] such that scalar product of the vector \[(\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\] with the unit vector parallel to sum of the vectors \[(2\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}-5\widehat{\mathbf{k}})\] and \[(b\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}})\] is\[1\], is

A)

\[-2\]

B)

\[-1\]

C)

\[0\]

D)

\[1\]

View Answer
116) Angle between the vectors \[\sqrt{3}(\mathbf{a}\times \mathbf{b})\] and\[b-(\mathbf{a}\cdot \mathbf{b})\mathbf{a}\]

A)

\[\frac{\pi }{2}\]

B)

\[\frac{\pi }{4}\]

C)

\[0\]

D)

\[\frac{\pi }{3}\]

View Answer
117) The point of contact of the line \[y=x-1\] with\[3x-4{{y}^{2}}=12\]is

A)

\[(4,\,\,3)\]

B)

\[(3,\,\,4)\]

C)

\[(4,\,\,-3)\]

D)

None of these

View Answer
118) \[\int{\frac{\text{cosec}\,x}{{{\cos }^{2}}\left( 1+\log \tan \frac{x}{2} \right)}dx}\]axis equal to

A)

\[{{\sin }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\]

B)

\[\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\]

C)

\[{{\sec }^{2}}\left[ 1+\log \tan \frac{x}{2} \right]+C\]

D)

\[-\tan \left[ 1+\log \tan \frac{x}{2} \right]+C\]

View Answer
119) \[\int_{2}^{\pi }{\sqrt{\frac{1+\cos 2x}{2}}dx}\]is equal to

A)

\[0\]

B)

\[2\]

C)

\[1\]

D)

\[-1\]

View Answer
120) The distance of the point \[(-1,\,\,5,\,\,-10)\] from the point   of   intersection   of   the   line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\] and the plane\[x-y+z=5\], is

A)

\[10\]

B)

\[11\]

C)

\[12\]

D)

\[13\]

View Answer
121) The angle between two diagonals of a cube will be

A)

\[{{\sin }^{-1}}\left( \frac{1}{3} \right)\]

B)

\[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]

C)

variable

D)

None of these

View Answer
122) Domain of function \[f(x)={{\sin }^{-1}}5x\] is

A)

\[\left( -\frac{1}{5},\,\,\frac{1}{5} \right)\]

B)

\[\left[ -\frac{1}{5},\,\,\frac{1}{5} \right]\]

C)

\[R\]

D)

\[\left( 0,\,\,\frac{1}{5} \right)\]

View Answer
123) Range of the function \[f(x)={{\sin }^{2}}({{x}^{4}})+{{\cos }^{2}}({{x}^{4}})\]is

A)

\[(-\infty ,\,\,\infty )\]

B)

\[\{1\}\]

C)

\[(-1,\,\,1)\]

D)

\[(0,\,\,1)\]

View Answer
124) If\[x+y=10\], then the maximum value of \[xy\] is

A)

\[5\]

B)

\[20\]

C)

\[25\]

D)

None of these

View Answer
125) The value of\[\sin \frac{\pi }{14}\sin \frac{3\pi }{14}\sin \frac{5\pi }{14}\sin \frac{7\pi }{14}\sin \frac{9\pi }{14}\sin \frac{11\pi }{14}\sin \frac{13\pi }{14}\]is equal to

A)

\[\frac{1}{8}\]

B)

\[\frac{1}{16}\]

C)

\[\frac{1}{32}\]

D)

\[\frac{1}{64}\]

View Answer
126) \[\cos 2\theta +2\cos \theta \]is always

A)

greater than\[-\frac{3}{2}\]

B)

less than or equal to\[\frac{3}{2}\]

C)

greater than or equal to \[\frac{-3}{2}\] and less than or equal to\[3\]

D)

None of the above

View Answer
127) In the expansion of\[{{(1+3x+2{{x}^{2}})}^{6}}\], the coefficient of \[{{x}^{11}}\] is

A)

\[144\]

B)

\[288\]

C)

\[216\]

D)

\[576\]

View Answer
128) If the second, third and fourth terms in the expansion of \[{{(x+a)}^{n}}\] are \[240,\,\,\,720\] and \[1080\] respectively, then the value of \[n\] is

A)

\[15\]

B)

\[20\]

C)

\[10\]

D)

\[5\]

View Answer
129) The values of \[x\] and \[y\] for which the numbers \[3+i{{x}^{2}}y\]and \[{{x}^{2}}+y+4i\] are conjugate complex, can be

A)

\[(-2,\,\,-1)\]or\[(2,\,\,-1)\]

B)

\[(-1,\,\,2)\]or\[(-2,\,\,1)\]

C)

\[(1,\,\,2)\]or\[(-1,\,\,-2)\]

D)

None of these

View Answer
130) The value of the expression \[1\cdot (2-\omega )(2-{{\omega }^{2}})+2\cdot (3-\omega )(3-{{\omega }^{2}})+...\] \[+(n-1)(n-\omega )(n-{{\omega }^{2}})\], where \[\omega \] is an imaginary cube root of unity, is

A)

\[\frac{1}{2}(n-1)n({{n}^{2}}+3n+4)\]

B)

\[\frac{1}{4}(n-1)n({{n}^{2}}+3n+4)\]

C)

\[\frac{1}{2}(n+1)n({{n}^{2}}+3n+4)\]

D)

\[\frac{1}{4}(n+1)n({{n}^{2}}+3n+4)\]

View Answer
131) If the first term of a \[GP\,\,{{\alpha }_{1}},\,\,{{\alpha }_{2}},\,\,{{\alpha }_{3}},...\]is unity such that \[4{{\alpha }_{2}}+5{{\alpha }_{3}}\] is least, then the common ratio of \[GP\] is

A)

\[\frac{-2}{5}\]

B)

\[\frac{-3}{5}\]

C)

\[\frac{2}{5}\]

D)

None of these

View Answer
132) If the \[AM\] of two numbers is greater than \[GM\] of the numbers by \[2\] and the ratio of the numbers is\[4:1\], then the numbers are

A)

\[4,\,\,1\]

B)

\[12,\,\,3\]

C)

\[16,\,\,4\]

D)

None of these

View Answer
133) If \[3x+2y=I\] and \[2x-y=O\], where \[I\] and \[O\] are unit and null matrices of order \[3\] respectively, then

A)

\[x=\frac{1}{7},\,\,y=\frac{2}{7}\]

B)

\[x=\frac{2}{7},\,\,y=\frac{1}{7}\]

C)

\[x=\left( \frac{1}{7} \right)l,\,\,y=\left( \frac{2}{7} \right)l\]

D)

\[x=\left( \frac{2}{7} \right)l,\,\,y=\left( \frac{1}{7} \right)l\]

View Answer
134) Matrix \[A\] is such that\[{{A}^{2}}=2A-I\], where \[I\] is the identity matrix. Then, for \[n\ge 2,\,\,{{A}^{n}}\] is equal to

A)

\[nA-(n-1)l\]

B)

\[nA-l\]

C)

\[{{2}^{n-1}}A-(n-1)l\]

D)

\[{{2}^{n-1}}A-l\]

View Answer
135) If\[3f(x)-2f\left( \frac{1}{x} \right)=x\], then \[f'(x)\] is equal to

A)

\[\frac{2}{7}\]

B)

\[\frac{1}{2}\]

C)

\[2\]

D)

\[\frac{7}{2}\]

View Answer
136) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{2}^{x}}-1}{{{(1+x)}^{1/2}}-1}\]is equal to

A)

\[\log 2\]

B)

\[\log 4\]

C)

\[\log \sqrt{2}\]

D)

None of these

View Answer
137) On the parabola\[y={{x}^{2}}\], the point least distant from the straight line \[y=2x-4\] is

A)

\[(1,\,\,1)\]

B)

\[(1,\,\,0)\]

C)

\[(1,\,\,-1)\]

D)

\[(0,\,\,0)\]

View Answer
138) The general value of \[\theta \] in the equation\[2\sqrt{3}\cos \theta =\tan \theta \]

A)

\[2n\pi \pm \frac{\pi }{6}\]

B)

\[2n\pi \pm \frac{\pi }{4}\]

C)

\[n\pi +{{(-1)}^{n}}\frac{\pi }{3}\]

D)

\[n\pi +{{(-1)}^{n}}\frac{\pi }{4}\]

View Answer
139) If\[\sec x\cos 5x+1=0\], where\[0<x<2\pi \], then the value of \[x\] is

A)

\[\frac{\pi }{5},\,\,\frac{\pi }{4}\]

B)

\[\frac{\pi }{5}\]

C)

\[\frac{\pi }{4}\]

D)

None of these

View Answer
140) The solution of the differential equation\[({{x}^{2}}-y{{x}^{2}})\frac{dy}{dx}+{{y}^{2}}+x{{y}^{2}}=0\]is

A)

\[\log \left( \frac{x}{y} \right)=\frac{1}{x}+\frac{1}{y}+C\]

B)

\[\log \left( \frac{y}{x} \right)=\frac{1}{x}+\frac{1}{y}+C\]

C)

\[\log (xy)=\frac{1}{x}+\frac{1}{y}+C\]

D)

\[\log (xy)+\frac{1}{x}+\frac{1}{y}=C\]

View Answer
141) The general solution of, the differential equation\[(x+y)dx+xdy=0\]is

A)

\[{{x}^{2}}+{{y}^{2}}=C\]

B)

\[2{{x}^{2}}-{{y}^{2}}=C\]

C)

\[{{x}^{2}}+2xy=C\]

D)

\[{{y}^{2}}+2xy=C\]

View Answer
142) The tangent to the curve \[y=a{{x}^{2}}+bx\] at\[(2,\,\,-8)\] is parallel to\[X-axis\]. Then,

A)

\[a=2,\,\,b=-2\]

B)

\[a=2,\,\,b=-4\]

C)

\[a=2,\,\,b=-8\]

D)

\[a=4,\,\,b=-4\]

View Answer
143) The mean of a set of observations is\[x\]. If each observation is divided by \[\alpha ,\,\,\alpha \ne 0\] and then is increased by\[10\], then the mean of the new set is

A)

\[\frac{{\bar{x}}}{\alpha }\]

B)

\[\frac{\bar{x}+10}{\alpha }\]

C)

\[\frac{\bar{x}+10\alpha }{\alpha }\]

D)

\[\alpha \bar{x}+10\]

View Answer
144) \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\]is logically equivalent to

A)

\[\tilde{\ }p\]

B)

\[p\]

C)

\[q\]

D)

\[\tilde{\ }q\]

View Answer
145) If \[\frac{|z-2|}{|z-3|}=2\] represents a circle, then its radius is equal to

A)

\[1\]

B)

\[\frac{1}{3}\]

C)

\[\frac{3}{4}\]

D)

\[\frac{2}{3}\]

View Answer
146) The angle of elevation of the top of a tower from the top of a house is \[{{60}^{o}}\] and the angle of depression of its base is\[{{30}^{o}}\]. If the horizontal distance between the house and the tower be \[12\,\,m\], then the height of the tower is

A)

\[48\sqrt{3}m\]

B)

\[16\sqrt{3}m\]

C)

\[24\sqrt{3}m\]

D)

\[\frac{16}{\sqrt{3}}m\]

View Answer
147) Period of\[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }\]is

A)

\[2\pi \]

B)

\[\pi \]

C)

\[\frac{2\pi }{3}\]

D)

\[\frac{\pi }{3}\]

View Answer
148) If \[x\] is parallel to \[y\] and\[z\], where\[\mathbf{x}=2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}+\alpha \widehat{\mathbf{k}}\],\[\mathbf{y}=\alpha \widehat{\mathbf{i}}+\widehat{\mathbf{k}}\]and\[\mathbf{z}=5\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\], then a is equal to

A)

\[\pm \sqrt{5}\]

B)

\[\pm \sqrt{6}\]

C)

\[\pm \sqrt{7}\]

D)

None of these

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149) If\[y={{(x+\sqrt{1+{{x}^{2}}})}^{n}}\], then\[(1+{{x}^{2}})\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is equal to

A)

\[{{n}^{2}}y\]

B)

\[-{{n}^{2}}y\]

C)

\[-y\]

D)

\[2{{x}^{2}}y\]

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150) The values of a for which\[({{a}^{2}}-1){{x}^{2}}+2(a-1)x+2\] is positive for any\[x\], are

A)

\[a\ge 1\]

B)

\[a\le 1\]

C)

\[a>-3\]

D)

\[a<-3\]or\[a>1\]

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