Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

CET - Karnataka Engineering Solved Paper-2003 Total Questions - 180

1) The dimensions of \[\frac{a}{b}\] in the equation\[P=\frac{a-{{t}^{2}}}{bx}\]where P is pressure, \[x\] is distance and t is time, are:

A)

\[\left[ {{M}^{2}}L{{T}^{-3}} \right]\]

B)

\[\left[ M{{T}^{-2}} \right]\]

C)

\[\left[ L{{T}^{-3}} \right]\]

D)

\[\left[ M{{L}^{3}}{{T}^{-1}} \right]\]

View Answer
2) Three vectors satisfy the relation \[\overrightarrow{A.}\overrightarrow{B}=0\] and \[\overrightarrow{A.}\overrightarrow{C}=0,\]then A is parallel to:

A)

\[\overrightarrow{C}\]

B)

\[\overrightarrow{B}\]

C)

\[\overrightarrow{B}\times \overrightarrow{C}\]

D)

\[\overrightarrow{B}.\overrightarrow{C}\]

View Answer
3) A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \[1\text{ }m{{s}^{-2}}\], the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of n, so that the student is able to catch the bus is:

A)

\[8\text{ }m{{s}^{-1}}\]

B)

\[5\text{ }m{{s}^{-1}}\]

C)

\[12\text{ }m{{s}^{-1}}\]

D)

\[10\text{ }m{{s}^{-1}}\]

View Answer
4) For a given velocity, a projectile has the same range R for two angles of projection if \[{{t}_{1}}\] and \[{{t}_{2}}\] are the time of flight in the two cases, then:

A)

\[{{t}_{1}}{{t}_{2}}\propto R\]

B)

\[{{t}_{1}}{{t}_{2}}\propto {{R}^{2}}\]

C)

\[{{t}_{1}}{{t}_{2}}\propto \frac{1}{{{R}^{2}}}\]

D)

\[{{t}_{1}}{{t}_{2}}\propto \frac{1}{R}\]

View Answer
5) Weight of a body of mass m decreases by 1% when it is raised to height h above the earths surface. If the body is taken to a depth h in a mine, change in its weight is:

A)

0.5% decrease

B)

2% decrease

C)

                0.5% increase

D)

                1% increase

View Answer
6) The displacement time graph of a particle executing S.H.M. is as shown in the figure. The corresponding force-time graph of the particle is:

A)



B)



C)



D)



View Answer
7) Which of the following sets of concurrent forces maybe in equilibrium?

A)

\[{{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=1N\]

B)

(b \[{{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=9N\]

C)

\[{{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{1}}=6N\]

D)

\[{{F}_{1}}=3N,{{F}_{2}}=5N,\,{{F}_{3}}=15N\]

View Answer
8) Youngs modulus of perfectly rigid body material is:

A)

infinite

B)

zero

C)

\[10\times {{10}^{10}}N/{{m}^{2}}\]

D)

\[1\times {{10}^{10}}N/{{m}^{2}}\]

View Answer
9) An ideal monoatomic gas at \[{{27}^{o}}C\] is compressed adiabatically to 8/27 times of its present volume. The increase in temperature of the gas is:

A)

\[{{375}^{o}}C\]

B)

\[{{402}^{o}}C\]

C)

\[{{175}^{o}}C\]

D)

\[{{475}^{o}}C\]

View Answer
10) A sample of ideal monoatomic gas is taken round the cycle ABCA as shown in the figure. The work done during the cycle is:

A)

3 PV

B)

zero

C)

9 PV

D)

6 PV

View Answer
11) A bucket full of hot water is kept in a room. It cools from \[{{75}^{o}}C\] to \[{{70}^{o}}C\] in \[{{t}_{1}}\] minutes, from \[{{70}^{o}}C\] to \[{{65}^{o}}C\] in \[{{t}_{2}}\] minutes and from \[{{65}^{o}}C\]to \[{{60}^{o}}C\] in \[{{t}_{3}}\] minutes. Then:

A)

\[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]

B)

\[{{t}_{1}}={{t}_{2}}={{t}_{3}}\]

C)

\[{{t}_{1}}<{{t}_{2}}>{{t}_{3}}\]

D)

\[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]

View Answer
12) A fish, looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is:

A)

\[\frac{12\times 3}{\sqrt{5}}\]

B)

\[12\times 3\times \sqrt{5}\]

C)

\[\frac{12\times 3}{\sqrt{7}}\]

D)

\[12\times 3\times \sqrt{7}\]

View Answer
13) A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and material are now added to P, as shown in the figure. The ray will suffer:

A)

same deviation

B)

greater deviation

C)

total internal reflection

D)

no deviation

View Answer
14) The aperture of the objective lens of a telescope is made large so as to:

A)

increase the resolving power of the telescope

B)

increase the magnifying power of the telescope

C)

to focus on distant objects

D)

make image aberrationless

View Answer
15) A lamp hanging 4 metres above the table is lowered by 1 metre. The illumination on the table:

A)

decreased by 25%

B)

increased by 25%

C)

decreased by 66.7%

D)

increased by 77.7%

View Answer
16) The equation of a transverse wave travelling along positive \[x\] axis with amplitude 0.2 m, velocity 360 m/sec and wavelength 60 m can be written as:

A)

\[y=0.2\sin \pi \left[ 6t+\frac{x}{60} \right]\]

B)

\[y=0.2\sin \pi \left[ 6t-\frac{x}{60} \right]\]

C)

\[y=0.2\sin 2\pi \left[ 6t-\frac{x}{60} \right]\]

D)

\[y=0.2\sin 2\pi \left[ 6t+\frac{x}{60} \right]\]

View Answer
17) If \[{{\upsilon }_{m}}\], is the velocity of sound in moist air, \[{{\upsilon }_{d}}\]is the velocity of sound in dry air, under identical conditions of pressure and temperature:

A)

\[{{\upsilon }_{d}}<{{\upsilon }_{d}}\]

B)

\[{{\upsilon }_{m}}>{{\upsilon }_{d}}\]

C)

\[{{\upsilon }_{m}}\,{{\upsilon }_{d}}=1\]

D)

\[{{\upsilon }_{m}}={{\upsilon }_{d}}\]

View Answer
18) If T is the reverberation time of an auditorium of volume V, then

A)

\[T\propto {{V}^{2}}\]

B)

\[T\propto V\]

C)

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

D)

\[T\propto \frac{1}{{{V}^{2}}}\]

View Answer
19) Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the higher frequency in the setting is 360 Hz, the beat frequency when the two wires are sounded together, is:

A)

8

B)

5

C)

10

D)

6

View Answer
20) A sound source is moving towards stationary listener with \[\frac{1}{10}\]th of the speed of sound. The ratio of apparent to real frequency is:

A)

\[{{\left( \frac{9}{10} \right)}^{2}}\]

B)

\[\frac{10}{9}\]

C)

\[\frac{11}{10}\]

D)

\[{{\left( \frac{11}{10} \right)}^{2}}\]

View Answer
21) If v is the speed of sound in air then the shortest length of the closed pipe which resonates to a frequency n, is:

A)

\[\frac{v}{2n}\]

B)

\[\frac{v}{4n}\]

C)

\[\frac{4n}{v}\]

D)

\[\frac{2n}{v}\]

View Answer
22) Cavitation is a special application property exhibited only by:

A)

ultrasonics

B)

electromagnetic waves

C)

audible sound

D)

infrasonics

View Answer
23) In Youngs double slit experiment, the fringe width is \[\beta \], If the entire arrangement is placed in a liquid of refractive index n, the fringe width becomes:

A)

\[n\beta \]

B)

\[\frac{\beta }{n+1}\]

C)

\[\frac{\beta }{n-1}\]

D)

\[\frac{\beta }{n}\]

View Answer
24) Yellow light is used in single slit diffraction experiment with slit width 0.6 mm. If yellow light is replaced by X-rays, then the pattern will reveal that:

A)

no diffraction pattern

B)

that the central maxima narrower

C)

less number of fringes

D)

more number of fringes

View Answer
25) In an interference experiment, third bright fringe is obtained at a point on the screen with a light of 700 nm. What should be the wavelength of die light source in order to obtain 5th bright fringe at the same point?

A)

630 nm

B)

500 nm

C)

420 nm

D)

750 nm

View Answer
26) If a ray of light in a denser medium enters into a rarer medium at an angle of incidence i, the angle of reflection and refraction are respectively r and r. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is:

A)

                \[{{\sin }^{-1}}\left( \tan r \right)\]

B)

                \[{{\sin }^{-1}}\left( \tan r \right)\]

C)

\[ta{{n}^{-1}}\left( \sin i \right)\]

D)

\[cot\left( \tan i \right)\]

View Answer
27) Waves that cannot be polarized are:

A)

electromagnetic waves

B)

light waves

C)

longitudinal waves

D)

transverse waves

View Answer
28) The phenomenon of rotation of plane of plane polarized light is called:

A)

Kerr effect

B)

double refraction

C)

optical activity

D)

dichroism

View Answer
29) As a result of interference of two coherent sources of light energy is:

A)

redistributed and the distribution does not very with time

B)

increased

C)

redistributed and that distribution changes with time

D)

decreased

View Answer
30) There are \[{{n}_{1}}\] photons of frequency \[{{v}_{1}}\] in a beam of light. In an equally energetic beam there are \[{{n}_{2}}\] photons of frequency \[{{v}_{2}}\]. Then the correct relation:

A)

\[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{1}}}{{{v}_{2}}}\]

B)

\[\frac{{{n}_{1}}}{{{n}_{2}}}=1\]

C)

\[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}\]

D)

\[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{v}_{2}}^{2}}{{{v}_{1}}^{2}}\]

View Answer
31) A charge q is placed at the centre of the line joining two equal point charges each equal to Q. The system of 3 charges will be in equilibrium if q is equal to:

A)

\[+Q/4\]

B)

\[-Q/2\]

C)

\[+Q/2\]

D)

\[-Q/4\]

View Answer
32) The inward and outward electric flux from a closed surface are respectively \[8\times {{10}^{3}}\] and \[4\times {{10}^{3}}\] units. Then the net charge inside the closed surface is:

A)

\[-4\times {{10}^{3}}\] coulomb

B)

\[4\times {{10}^{3}}\] coulomb

C)

\[\frac{-4\times {{10}^{3}}}{{{\varepsilon }_{0}}}\] coulomb

D)

\[-4\times {{10}^{3}}{{\varepsilon }_{0}}\]coulomb

View Answer
33) In the circuit as shown in the figure, the effective capacitance between A and B is:

A)

\[2~\mu F\]

B)

\[2~\mu F\]

C)

\[8~\mu F\]

D)

\[4~\mu F\]

View Answer
34) Capacitance of a parallel plate capacitor becomes \[\frac{4}{3}\] times its original value, if a dielectric slab of thickness \[t=d/2\] is inserted between the plates [d is the separation between the plates]. The dielectric constant of the slab is:

A)

4

B)

8

C)

2

D)

6

View Answer
35) A charged particle of mass m and charge if is released from rest in an uniform electric field E neglecting the effect of gravity, the kinetic energy of the charged particle after t second is:

A)

\[\frac{2{{E}^{2}}{{t}^{2}}}{mq}\]

B)

\[\frac{E{{q}^{2}}m}{2{{t}^{2}}}\]

C)

\[\frac{Eqm}{t}\]

D)

\[\frac{{{E}^{2}}{{q}^{2}}{{t}^{2}}}{2m}\]

View Answer
36) Two wires of the same dimensions but resistivities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] are connected in series. The equivalent resistivity of the combination is:

A)

\[\frac{{{\rho }_{1}}+{{\rho }_{2}}}{2}\]

B)

\[{{\rho }_{1}}+{{\rho }_{2}}\]

C)

\[2\left( {{\rho }_{1}}+{{\rho }_{2}} \right)\]

D)

\[\sqrt{{{\rho }_{1}}\,{{\rho }_{2}}}\]

View Answer
37) If a 30V, 90W bulb is to be worked in 120V line, the resistance to be connected in series with the bulb is:

A)

\[20~\,\Omega \]

B)

\[10~\,\Omega \]

C)

\[40~\,\Omega \]

D)

\[30~\,\Omega \]

View Answer
38) The potential difference between me terminals of a cell in open circuit is 2.2 volt with resistance of 5 ohm across the terminals of a cell, the terminal potential difference is 1.8 volt. The internal resistance of the cell is:

A)

\[\frac{9}{10}\] ohm

B)

\[\frac{10}{9}\] ohm

C)

\[\frac{7}{12}\] ohm

D)

\[\frac{12}{7}\] ohm

View Answer
39) Thirteen resistances each of resistance R ohm are connected in the circuit as shown in the figure. The effective resistance between A and B is:

A)

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

B)

\[2R\Omega \]

C)

\[R\Omega \]

D)

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

View Answer
40) A group of N cells whose emf varies directly with the internal resistance as per the equation \[{{E}_{N}}=1.5\,{{r}_{N}}\] are connected as shown in the figure above. The current I in the circuit is:

A)

5.1 A

B)

0.51 A

C)

1.5 A

D)

0.15 A

View Answer
41) The temperature coefficient of resistance of a wire is \[0.00125/{{\,}^{o}}C\]. Its resistance is 1 ohm at 300 K. Its resistance will be 2 ohm at:

A)

1127 K

B)

1400 K

C)

1154 K

D)

1100 K

View Answer
42) A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is \[{{10}^{-7}}\] ohm-metre and the current passing through it is 0.1 ampere, cross-section of the wire is 10 m. The potential gradient along the potentiometer wire is:

A)

\[{{10}^{-6}}V/m\]

B)

\[{{10}^{-4}}V/m\]

C)

\[{{10}^{-8}}V/m\]

D)

\[{{10}^{-2}}V/m\]

View Answer
43) A fuse wire with radius 1 mm blows at 1.5 ampere. The radius of the fuse wire of the same material to blow at 3A will be:

A)

\[{{3}^{1/4}}mm\]

B)

\[{{4}^{1/3}}mm\]

C)

\[{{3}^{1/2}}mm\]

D)

\[{{2}^{1/3}}mm\]

View Answer
44) A wire in the form of a circular loop of one turn carrying a current produces a magnetic field B at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is:

A)

3 B

B)

5 B

C)

4 B

D)

2 B

View Answer
45) To send 10% of the main current through a moving coil galvanometer of resistance 99 ohm, the shunt required is:

A)

10 ohm

B)

9.9 ohm

C)

9 ohm

D)

11 ohm

View Answer
46) The magnetic flux linked with a coil at any   instant t is given by \[\phi =5{{t}^{3}}-100t+300,\] the emf induced in the coil at \[t=2\] second is:

A)

40 V

B)

- 40 V

C)

300 V

D)

140 V

View Answer
47) A charged particles moves along the line AB which lies in the same plane of a circular loop of conducting wire as shown in the figure. Then:

A)

no current will be induced in the loop

B)

the current induced in the loop will change its direction as the charged particle passes by

C)

the current induced will be anticlockwise

D)

the current induced, will be clockwise

View Answer
48) The time taken by A.C. of 50 Hz in reaching from zero to the maximum value is:

A)

\[50\times {{10}^{-3}}sec\]

B)

\[5\times {{10}^{-3}}sec\]

C)

\[1\times {{10}^{-3}}sec\]

D)

\[2\times {{10}^{-3}}sec\]

View Answer
49) The ratio of the secondary to the primary turns in a transformer is 3 : 2 and the output power is P. Neglecting all power losses, the input power must be:

A)

P/2

B)

P

C)

2 P/3

D)

3 P/2

View Answer
50) The material used for permanent magnet has:

A)

low retentivity, high coercivity

B)

high retentivity, low coercivity

C)

high retentivity, high coercivity

D)

low retentivity, low coercivity

View Answer
51) A particle of mass M at rest decays into two masses \[{{m}_{1}}\] and \[{{m}_{2}}\] with non zero velocities. The ratio of de-Broglie wavelengths of the particles \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}\] is:

A)

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

B)

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

C)

\[\frac{\sqrt{{{m}_{1}}}}{\sqrt{{{m}_{2}}}}\]

D)

\[1:1\]

View Answer
52) For an electron in the second orbit of Bohrs hydrogen atom, the moment of linear momentum is:

A)

\[\pi h\]

B)

\[2\pi h\]

C)

\[\frac{h}{\pi }\]

D)

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

View Answer
53) If elements with principal quantum number \[n>4\]were not allowed in nature, the number of possible elements would have been:

A)

32

B)

60

C)

64

D)

4

View Answer
54) In photoelectric effect, the number of electrons ejected per second is:

A)

proportional to the wavelength of light

B)

proportional to the intensity of light

C)

proportional to the work function of the metal

D)

proportional to the frequency of light

View Answer
55) Half life of a radioactive substance is 20 minutes. The time between 20% and 80% decay will be:

A)

40 minutes

B)

20 minutes

C)

25 minutes

D)

30 minutes

View Answer
56) A hypothetical radioactive nucleus decays according to the following series \[_{72}{{A}^{180}}\xrightarrow{\alpha }{{A}_{1}}\xrightarrow{{{\beta }^{-}}}{{A}_{2}}\xrightarrow{\alpha }{{A}_{3}}\xrightarrow{\gamma }{{A}_{4}}\] If the mass number and atomic number of A are respectively 180 and 72. Then the atomic number and mass number of A will respectively be:

A)

69, 171

B)

70, 172

C)

68, 172

D)

69, 172

View Answer
57) Nucleus A is converted into C through the following reactions: \[A\xrightarrow[{}]{{}}B+\alpha \] [\[\alpha \] - alpha particle \[B\xrightarrow[{}]{{}}C+2\beta \] \[\beta \]-electron] then:

A)

A and B are isotopes

B)

A and C are isobars

C)

A and B are isobars

D)

A and C are isotopes

View Answer
58) If \[m,\,{{m}_{n}}\] and \[{{m}_{p}}\] are the masses of \[_{Z}{{X}^{A}}\]nucleus, neutron and proton respectively:

A)

\[m=\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}\]

B)

\[m<\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}\]

C)

\[m>\left( A-Z \right){{m}_{n}}+Z{{m}_{p}}\]

D)

\[m=\left( A-Z \right){{m}_{p}}+Z{{m}_{n}}\]

View Answer
59) The electrical circuit used to get smooth D.C output from a rectifier circuit is called:

A)

filter

B)

oscillator

C)

logic gates

D)

amplifier

View Answer
60) In the case of constants \[\alpha \] and \[\beta \] of a transistor:

A)

\[\alpha =\beta \]

B)

\[\beta <1,\alpha >1\]

C)

\[\alpha \beta =1\]

D)

\[\beta >1,\alpha <1\]

View Answer
61) A colour less crystalline salt \[x\] is soluble in dilute \[HCl\]. On adding \[NaOH\] solution, it gives a white precipitate which is insoluble in excess of \[NaOH\]. \[x\] is :

A)

\[A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\]

B)

\[ZnS{{O}_{4}}\]

C)

\[MgS{{O}_{4}}\]

D)

\[SnC{{l}_{2}}\]

View Answer
62) Which metal is used to make alloy steel for armour plates, safes and helmets?

A)

Al

B)

Mn

C)

Cr

D)

Pb

View Answer
63) lodoform test is not answered by:

A)

\[{{C}_{2}}{{H}_{5}}OH\]

B)

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

C)

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

D)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\]

View Answer
64) A gaseous carbon compound is soluble in dilute \[HCl\]. The solution on treating with \[NaN{{O}_{2}}\] gives off nitrogen leaving behind a solution which smells of wood spirit. The carbon compound is:

A)

\[HCHO\]

B)

CO

C)

\[{{C}_{2}}{{H}_{5}}N{{H}_{2}}\]

D)

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

View Answer
65) Which of the following statements is incorrect regarding benzyl chloride?

A)

It gives white precipitate with alcoholic \[AgN{{O}_{3}}\]

B)

It is an aromatic compound with substitution in the side chain

C)

It undergoes nucleophilic substitution reaction

D)

It is less reactive than vinyl chloride

View Answer
66) Enthalpy of formation of HF and \[HCl\] are -161 kJ and -92 kJ respectively. Which of the following statements is incorrect?

A)

\[HCl\] is more stable than HF

B)

HF and \[HCl\] arc exothermic compounds

C)

The affinity of fluorine to hydrogen is greater than the affinity of chlorine to hydrogen

D)

HF is more stable than \[HCl\]

View Answer
67) Heat liberated with 100 ml of 1 N \[NaOH\] is neutralised by 300 ml of IN \[HCl\]:

A)

11.56 kJ

B)

5.73 kJ

C)

22.92 kJ

D)

17.19 kJ

View Answer
68) For a reaction \[A+B\xrightarrow{{}}C+D\], if concentration of A is doubled without altering that of B, rate doubles. If concentration of B is increased nine times without altering that of A, rate triples. Order of the reaction is :

A)

2

B)

1

C)

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

D)

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

View Answer
69) In Goldschmidt aluminothermic process, thermite contains :

A)

3 parts of \[A{{l}_{2}}{{O}_{3}}\] and 4 parts of \[Al\]

B)

3 parts of \[F{{e}_{2}}{{O}_{3}}\] and 2 parts of \[Al\]

C)

3 parts of \[F{{e}_{2}}{{O}_{3}}\] and 1 part of \[Al\]

D)

1 part of \[F{{e}_{2}}{{O}_{3}}\] and 1 part of \[Al\]

View Answer
70) The structure of orthophosphoric acid is:

A)

\[H-O-\overset{\begin{smallmatrix} O \\ \uparrow \end{smallmatrix}}{\mathop{\underset{\begin{align} & | \\ & O \\ & | \\ & H \\ \end{align}}{\mathop{P}}\,}}\,-O-H\]

B)

\[O\leftarrow \overset{\begin{smallmatrix} O \\ | \end{smallmatrix}}{\mathop{\underset{\begin{align} & | \\ & O \\ & | \\ & H \\ \end{align}}{\mathop{P}}\,}}\,-O-H\]

C)

\[O\leftarrow \overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\mathop{P}}\,}}\,-O-H\]

D)

\[H-OP=O\]

View Answer
71) A galvanic cell is constructed using the redox reaction, \[\frac{1}{2}{{H}_{2}}(g)+AgCl(s){{H}^{+}}(aq)+C{{l}^{-}}\]\[(aq)+Ag(s)\]it is represented as :

A)

\[Pt|{{H}_{2}}(g)|HCl(sol.n)|l\,AgN{{O}_{3}}(sol.n)|Ag\]

B)

\[Ag|AgCl(s)|KCl(sol.n)|l\,HCl(sol.n)\]\[,\,{{H}_{2}}(g)|Pt\]

C)

\[Pt|{{H}_{2}}(g)|KCl(sol.n)|l\,AgCl(s)\,l\,Ag\]

D)

\[Pt|{{H}_{2}}(g)|HCl(sol.n)|l\,AgCl(s)\,l\,Ag\]

View Answer
72) Same amount of electric current is passed through solutions of \[AgN{{O}_{3}}\] and \[HCl\]. If 1.08 g of silver is obtained in the first case, the amount of hydrogen liberated at S.T.P. in the second case is :

A)

\[224\,c{{m}^{3}}\]

B)

1.008 g

C)

\[112\,c{{m}^{3}}\]

D)

\[22400\,c{{m}^{3}}\]

View Answer
73) The flame colours of metal ions are due to:

A)

Frenkel defect

B)

Schottky defect

C)

Metal deficiency defect

D)

Metal excess defect

View Answer
74) The order of reactivities of methyl halides in the formation of Grignard reagent is :

A)

\[C{{H}_{3}}>C{{H}_{3}}Br>C{{H}_{3}}Cl\]

B)

\[C{{H}_{3}}Cl>C{{H}_{3}}Br>C{{H}_{3}}I\]

C)

\[C{{H}_{3}}Br>C{{H}_{3}}CI>C{{H}_{3}}I\]

D)

\[C{{H}_{3}}Br>C{{H}_{3}}I>C{{H}_{3}}Cl\]

View Answer
75) The reaction of an organic compound with ammonia followed by nitration of the product gives a powerful explosive, called RDX. The organic compound is :

A)

phenol

B)

toluene

C)

glycerine

D)

formaldehyde

View Answer
76) A signature, written in carbon pencil weighs 1 mg. What is the number of carbon atoms present in the signature?

A)

\[5.02\times {{10}^{23}}\]

B)

\[5.02\times {{10}^{20}}\]

C)

\[6.02\times {{10}^{20}}\]

D)

\[0.502\times {{10}^{20}}\]

View Answer
77) \[N{{H}_{3}}\] and \[HCl\] gas are introduced simultaneously from the two ends of a long tube. A white ring of \[N{{H}_{4}}Cl\] appears first:

A)

nearer to the \[HCl\] end

B)

at the centre of the tube

C)

throughout the tube

D)

nearer to the \[N{{H}_{3}}\] end

View Answer
78) A gas formed by the action of alcoholic \[KOH\]on ethyl iodide, decolourises alkaline \[KMn{{O}_{4}}\]. The gas is :

A)

\[{{C}_{2}}{{H}_{6}}\]

B)

\[C{{H}_{4}}\]

C)

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

D)

\[{{C}_{2}}{{H}_{4}}\]

View Answer
79) Which of the following is not a characteristic of chemisorption?

A)

\[\Delta H\]is of the order of 400 kJ

B)

Adsorption is irreversible

C)

Adsorption may be multimolecular layer

D)

Adsorption is specific

View Answer
80) The concentration of electrolyte required to coagulate a given amount of \[A{{s}_{2}}{{S}_{3}}\] sol. is minimum in the case of :

A)

magnesium nitrate

B)

potassium nitrate

C)

potassium sulphate

D)

aluminium nitrate

View Answer
81) Identify the organic compound which, on heating with strong solution of \[NaOH\], partly converted into an acid salt and partly into alcohol :

A)

Benzyl alcohol

B)

Acetaldehyde

C)

Acetone

D)

Benzaldehyde

View Answer
82) The process by which synthesis of protein takes place based on the genetic information present in w-RNA is called :

A)

translation

B)

transcription

C)

replication

D)

messenger hypothesis

View Answer
83) The enthalpies of formation of \[A{{l}_{2}}{{O}_{3}}\] and \[C{{r}_{2}}{{O}_{3}}\] are \[-1596\text{ }kJ\] and \[-1134kJ\] respectively. \[\Delta H\] for the reaction, \[2Al+C{{r}_{2}}{{O}_{3}}\xrightarrow{{}}2Cr+A{{l}_{2}}{{O}_{3}}\] is:

A)

-2730 kJ

B)

-462 kJ

C)

-1365 kJ

D)

+2730 kJ

View Answer
84) The gaseous reaction \[A+B2C+D+Q\] is most favoured at :

A)

low temperature and high pressure

B)

high temperature and high pressure

C)

high temperature and low pressure

D)

low temperature and low pressure

View Answer
85) Temperature coefficient of a reaction is 2. When temperature is increased from \[{{30}^{o}}C\] to\[{{100}^{o}}C\], rate of the reaction increases by :

A)

128 times

B)

100 times

C)

500 times

D)

250 times

View Answer
86) The volume of water to be added to \[\frac{N}{2}HCl\]to prepare \[500\,c{{m}^{3}}\] of \[\frac{N}{10}\] solution is :

A)

\[450\text{ }c{{m}^{3}}\]

B)

\[100\text{ }c{{m}^{3}}\]

C)

\[45\text{ }c{{m}^{3}}\]

D)

\[400\text{ }c{{m}^{3}}\]

View Answer
87) The equivalent weight of a certain trivalent element is 20. Molecular, weight of its oxide is:

A)

152

B)

56

C)

168

D)

68

View Answer
88) Identify the reaction that doesnt take place during the smelting process of copper extraction :

A)

\[2FeS+3{{O}_{2}}\xrightarrow{{}}2FeO+3S{{O}_{2}}\uparrow \]

B)

\[C{{u}_{2}}O+FeS\xrightarrow{{}}C{{u}_{2}}S+FeO\]

C)

\[2C{{u}_{2}}S+3{{O}_{2}}\xrightarrow{{}}2C{{u}_{2}}O+2S{{O}_{2}}\uparrow \]

D)

\[FeO+Si{{O}_{2}}\xrightarrow{{}}FeSi{{O}_{3}}\]

View Answer
89) Pick out the complex compound in which the central metal atom obeys EAN rule strictly :

A)

\[{{K}_{4}}[Fe{{(CN)}_{6}}]\]

B)

\[{{K}_{3}}[Fe{{(CN)}_{6}}]\]

C)

\[[Cr{{({{H}_{2}}O)}_{6}}]C{{l}_{3}}\]

D)

\[[Cu{{(N{{H}_{3}})}_{4}}]S{{O}_{4}}\]

View Answer
90) In a reversible reaction, the catalyst :

A)

increases the activation energy of the backward reaction

B)

increases the activation energy of the forward reaction

C)

decreases the activation energy of both, forward and backward reaction

D)

decreases the activation energy of forward reaction

View Answer
91) Solubility product of a salt AB is \[1\times {{10}^{-8}}\] in a solution in which concentration of A is \[{{10}^{-3}}M\]. The salt will precipitate when the concentration of B becomes more than :

A)

\[{{10}^{-4}}M\]

B)

\[{{10}^{-7}}M\]

C)

\[{{10}^{-6}}M\]

D)

\[{{10}^{-5}}M\]

View Answer
92) The standard reduction potentials of Zn and Ag in water at 298 K are, \[Z{{n}^{+2}}+2{{e}^{-}}Zn;\] \[{{E}^{o}}=-0.76\,V\] and \[A{{g}^{+}}+{{e}^{-}}Ag;\]\[{{E}^{o}}=+0.80\,V\]. Which of the following reactions take place?

A)

\[Z{{n}^{+2}}(aq)+2Ag(s)\xrightarrow{{}}2A{{g}^{+}}(aq)+Zn(s)\]

B)

\[Zn(s)+2A{{g}^{+}}(aq)\xrightarrow{{}}Z{{n}^{+2}}(aq)+2Ag(s)\]

C)

\[Z{{n}^{+2}}(aq)+A{{g}^{+}}(aq)\xrightarrow{{}}Zn(s)+Ag(s)\]

D)

\[Zn(s)+Ag(s)\xrightarrow{{}}Z{{n}^{+2}}(aq)+A{{g}^{+}}(aq)\]

View Answer
93) The ratio of cationic radius to anionic radius in an ionic crystal is greater than 0.732. Its co-ordination number is :

A)

6

B)

8

C)

1

D)

4

View Answer
94) Dacron is obtained by the condensation polymerization of :

A)

Dimethyl terephthalate and ethylene glycol

B)

Terephthalic acid and formaldehyde

C)

Phenol and phthalic acid

D)

Phenol and formaldehyde

View Answer
95) 4-chloro-3, 5-dimethyl phenol is called :

A)

Chloramphenicol

B)

Paracetamol

C)

Barbital

D)

Dettol

View Answer
96) The percentage s-character of the hybrid orbitals in methane, ethene and ethyne are respectively :

A)

25, 33, 50

B)

25, 50, 75

C)

50, 75, 100

D)

10, 20, 40

View Answer
97) In the manufacture of sulphuric acid by contact process, Tyndall box is used to :

A)

filter dust particles

B)

remove impurities

C)

convert \[S{{O}_{2}}\] to \[S{{O}_{3}}\]

D)

test the presence of dust particles

View Answer
98) The pH value of gastric juice in human stomach is about 1.8 and in the small intestine it is about 7.8. The \[p{{K}_{a}}\] value of aspirin is 3.5. Aspirin will be:

A)

completely ionized in the small intestine and in the stomach

B)

unionised in the small intestine and in the stomach

C)

ionised in the small intestine and almost unionised in the stomach

D)

ionised in the stomach and almost unionised in the small, intestine

View Answer
99) The number of a and P particles emitted during the transformation of \[_{90}T{{h}^{232}}\] to \[_{82}P{{b}^{208}}\] are respectively :

A)

4, 2

B)

2, 2

C)

8, 6

D)

6, 4

View Answer
100) When chlorine is passed through warm benzene in presence of the sunlight, the product obtained is :

A)

Benzotrichloride

B)

Chlorobenzene

C)

Gammexane

D)

D.D.T.

View Answer
101) Ethyl benzoate reacts with \[PC{{l}_{5}}\] to give :

A)

\[{{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}+HCl\]

B)

\[{{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}\]

C)

\[C{{H}_{3}}COCl+{{C}_{6}}{{H}_{5}}COCl+POC{{l}_{3}}\]

D)

\[{{C}_{2}}{{H}_{5}}Cl+{{C}_{6}}{{H}_{5}}COOH+POC{{l}_{3}}\]

View Answer
102) Pick out the statement which is not relevant in the discussion of colloids :

A)

Sodium aluminium silicate is used in the softening of hard water

B)

Potash alum is used in shaving rounds and as a styptic in medicine

C)

Artificial rain is caused by throwing electrified sand on the clouds from an aeroplane

D)

Deltas are formed at a place where the river pours its water into the sea

View Answer
103) A wooden box excavated from Indus valley had an activity of \[1.18\times {{10}^{13}}\] disintegration per minute per gm. of carbon. What is the approximate age of this civilisation?

A)

4000 years

B)

5700 years

C)

8100 years

D)

6000 years

View Answer
104) For a reaction if \[{{K}_{p}}>{{K}_{c}}\], the forward reaction is favoured by :

A)

low pressure

B)

high pressure

C)

high temperature

D)

low temperature

View Answer
105) In a lime kiln, to get higher yield of \[C{{O}_{2}}\], the measure that can be taken is :

A)

to remove CaO

B)

to add more \[CaC{{O}_{3}}\]

C)

to maintain high temperature

D)

to pump out \[C{{O}_{2}}\]

View Answer
106) What is the volume of 20 volume \[{{H}_{2}}{{O}_{2}}\] required to get \[5000\text{ }c{{m}^{3}}\] of oxygen at S.T.R?

A)

\[250\text{ }c{{m}^{3}}\]

B)

\[50\text{ }c{{m}^{3}}\]

C)

\[100\text{ }c{{m}^{3}}\]

D)

\[125\text{ }c{{m}^{3}}\]

View Answer
107) The IUPAC name of \[{{(C{{H}_{3}})}_{3}}C-CH=C{{H}_{2}}\] is:

A)

1, 1, l-trimethyl-2-propene

B)

3, 3, 3-trimethyl-2-propene

C)

2, 2-dimethyl-3-butene

D)

3, 3-dimethyl-l-butene

View Answer
108) Railway wagon axles are made by heating iron rods embedded in charcoal powder. This process is known as:

A)

Tempering

B)

Case hardening

C)

Sherardising

D)

Annealing

View Answer
109) Thomas slag is ...

A)

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

B)

\[C{{a}_{3}}{{(P{{O}_{4}})}_{2}}\]

C)

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

D)

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

View Answer
110) Urea is preferred to ammonium sulphate as a nitrogenous fertilizer because :

A)

it is more soluble in water

B)

it is cheaper than ammonium sulphate

C)

it is quite stable

D)

it does not cause acidity in the soil

View Answer
111) Two gas cylinders having same capacity have been filled with 44 g of \[{{H}_{2}}\] and 44 g of \[C{{O}_{2}}\]respectively. If the pressure in \[C{{O}_{2}}\] cylinder is 1 atmosphere at a particular temperature, the pressure in the hydrogen cylinder at the same temperature is :

A)

2 atmosphere

B)

1 atmosphere

C)

22 atmosphere

D)

44 atmosphere

View Answer
112) Angular momentum of an electron in the nth orbit of hydrogen atom is given by :

A)

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

B)

\[nh\]

C)

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

D)

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

View Answer
113) The element with atomic number 36 belongs to ......... block in the periodic table :

A)

\[p\]

B)

\[s\]

C)

\[f\]

D)

\[d\]

View Answer
114) The function of \[AlC{{l}_{3}}\] in Friedel-Crafts reaction is :

A)

to absorb \[HCl\]

B)

to absorb water

C)

to produce nucleophiie

D)

to produce electrophile

View Answer
115)                 An important reaction of acetone is auto condensation in presence of concentrated sulphuric acid to give the aromatic compound ......

A)

mesitylene

B)

mesityl oxide

C)

trioxan

D)

phorone

View Answer
116) Kinetic energy of one mole of an ideal gas at 300 K in kJ is :

A)

3.74

B)

348

C)

34.8

D)

3.48

View Answer
117) The tripeptide hormone present in most living cells is :

A)

glutathione

B)

glutamine

C)

oxytocin

D)

ptyalin

View Answer
118) Phenol\[\xrightarrow{NaN{{O}_{2}}|{{H}_{2}}S{{O}_{4}}}B\xrightarrow{{{H}_{2}}O}C\xrightarrow{NaOH}D\]name of the reaction is :

A)

Liebermanns reaction

B)

Phthalein fusion test

C)

Reimer Tiemann reaction

D)

Schotten-Baumann reaction

View Answer
119) Energy is stored in our body in the form of:

A)

ATP

B)

ADP

C)

Fats

D)

Carbohydrates

View Answer
120) An organic compound answers Molischs test as well as Benedicts test. But it does not answer Scliwanoffs test. Most probably, it is :

A)

sucrose

B)

protein

C)

fructose

D)

maltose

View Answer
121) In Z, the set of all integers, the inverse of -7 w.r.t. *defined by \[a*b=a+b+7\] for all \[a,\,b\,\in Z\] is :

A)

-14

B)

7

C)

14

D)

-7

View Answer
122) \[(p\wedge \,\,\,\,\,\,\,p)\wedge (\sim p\wedge q)\]is:

A)

a tautology

B)

a contradiction

C)

tautology and contradiction

D)

neither a tautology nor a contradiction

View Answer
123) The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is :

A)

574

B)

36

C)

754

D)

144

View Answer
124) In \[\Delta \,ABC\] if \[\left| \begin{matrix}    1 & a & b \\    1 & c & a \\    1 & b & c \\ \end{matrix} \right|=0\] then\[{{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C\] is equal to :

A)

\[\frac{4}{9}\]

B)

\[\frac{9}{4}\]

C)

\[3\sqrt{3}\]

D)

1

View Answer
125) 7th term of an A.P. is 40. Then the sum of first 13 terms is :

A)

520

B)

53

C)

2080

D)

1040

View Answer
126) The coefficient of \[{{x}^{32}}\]in the expansion of\[{{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}\]is:

A)

\[^{-15}{{C}_{3}}\]

B)

\[^{15}{{C}_{4}}\]

C)

\[^{-15}{{C}_{5}}\]

D)

\[^{15}{{C}_{2}}\]

View Answer
127) Which of the following is a subgroup of\[a=\text{ }\!\!\{\!\!\text{ }0,1,2,3,4,5\text{ }\!\!\}\!\!\text{ },\] under addition modules 6?

A)

{0, 2}

B)

{0, 1}

C)

{0, 4}

D)

{0, 3}

View Answer
128) Assuming that the sums and products given below are defined which of the following is not true for matrices?

A)

\[AB=AC\] does not imply \[B=C\]

B)

\[A+B=B+A\]

C)

\[(AB)=BA\]

D)

\[AB=0\] implies \[A=0\] or \[B=0\]

View Answer
129) Inverse of the matrix \[\left[ \begin{matrix}    1 & -2 \\    3 & 4 \\ \end{matrix} \right]\] is :

A)

\[\frac{1}{10}\left[ \begin{matrix}    1 & -2 \\    3 & 4 \\ \end{matrix} \right]\]

B)

\[\frac{1}{10}\left[ \begin{matrix}    4 & 2 \\    -3 & 1 \\ \end{matrix} \right]\]

C)

\[\left[ \begin{matrix}    4 & 2 \\    -3 & 1 \\ \end{matrix} \right]\]

D)

\[\frac{1}{10}\left[ \begin{matrix}    4 & -2 \\    -3 & 1 \\ \end{matrix} \right]\]

View Answer
130) If the vectors \[4\hat{i}+11\hat{j}+m\hat{k}\], \[7\hat{i}+2\hat{j}+6\hat{k}\] and \[i+5j+4k\] arc coplanar then m is equal to :

A)

0

B)

38

C)

-10

D)

10

View Answer
131) \[\left| \begin{matrix}    {{b}^{2}}{{c}^{2}} & bc & b+c \\    {{c}^{2}}{{a}^{2}} & ca & c+a \\    {{a}^{2}}{{b}^{2}} & ab & a+b \\ \end{matrix} \right|\] is equal to :

A)

\[\frac{1}{abc}(ab+bc+ca)\]

B)

\[ab+bc+ca\]

C)

0

D)

\[a+b+c\]

View Answer
132) In \[\Delta \,ABC\] if \[\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}\] then \[\cos C\]is equal to :

A)

\[\frac{5}{7}\]

B)

\[\frac{7}{5}\]

C)

\[\frac{16}{17}\]

D)

\[\frac{17}{36}\]

View Answer
133) The value of \[\frac{\tan {{70}^{o}}-\tan {{20}^{o}}}{\tan {{50}^{o}}}\] is equal to:

A)

2

B)

1

C)

0

D)

3

View Answer
134) \[\cos {{1}^{o}}+\cos {{2}^{o}}+\cos {{3}^{o}}+....+\cos {{180}^{o}}\] is equal to :

A)

1

B)

0

C)

2

D)

-1

View Answer
135) If \[\left| \vec{a}\times \vec{b} \right|=4\] and \[\left| \vec{a}\,.\,\vec{b} \right|=2\] then \[{{\left| {\vec{a}} \right|}^{2}}{{\left| {\vec{b}} \right|}^{2}}\] is equal to :

A)

6

B)

2

C)

20

D)

8

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

A)

\[{{e}^{-a}}\]

B)

e

C)

\[{{e}^{a}}\]

D)

1

View Answer
137) Which of the following is not a proposition :

A)

3 is prime

B)

\[\sqrt{2}\] is irrational

C)

Mathematics is interesting

D)

5 is an even integer

View Answer
138) \[\underset{n\to \infty }{\mathop{\lim }}\,\,{{({{3}^{n}}+{{4}^{n}})}^{1/n}}\] is equal to :

A)

4

B)

3

C)

e

D)

\[\infty \]

View Answer
139) The distance between the directories of the hyperbola \[x=8\sec \theta ,\,y=8\,\tan \theta \] is :

A)

\[8\sqrt{2}\]

B)

\[16\sqrt{2}\]

C)

\[4\sqrt{2}\]

D)

\[6\sqrt{2}\]

View Answer
140) The general solution of the equation \[\tan 2\theta \,.\,\tan \theta =1\] for \[n\in z\] is, \[\theta \] is equal to:

A)

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

B)

\[(2n+1)\frac{\pi }{6}\]

C)

\[(2n+1)\frac{\pi }{2}\]

D)

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

View Answer
141) \[\sin \left( \frac{1}{2}{{\cos }^{-1}}\frac{4}{5} \right)\] is equal to :

A)

\[-\frac{1}{\sqrt{10}}\]

B)

\[\frac{1}{\sqrt{10}}\]

C)

\[-\frac{1}{10}\]

D)

\[\frac{1}{10}\]

View Answer
142) The angle between the vectors \[\vec{a}+\vec{b}\] and \[\vec{a}-\vec{b}\] when \[a=(1,1,4)\] and \[b=(1,-1,4)\]is:

A)

\[{{45}^{o}}\]

B)

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

C)

\[{{15}^{o}}\]

D)

\[{{30}^{o}}\]

View Answer
143) The angle between the lines in \[{{x}^{2}}-xy-6{{y}^{2}}-7x+31y-18=0\] is :

A)

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

B)

\[{{45}^{o}}\]

C)

\[{{30}^{o}}\]

D)

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

View Answer
144) The equation of line bisecting perpendicularly the segment joining the points (-4, 6) and (8,8) is :

A)

\[y=7\]

B)

\[6x+y-19=0\]

C)

\[x+2y-7=0\]

D)

\[6x+2y-19=0\]

View Answer
145) If the distance of any point P from the points \[A\,(a+b,\,\,a-b)\] and B \[B\,(a-b,\,\,a+b)\] are equal then the locus of P is :

A)

\[ax+by=0\]

B)

\[x-y=0\]

C)

\[x+y=0\]

D)

\[bx-ay=0\]

View Answer
146) If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b then :

A)

\[{{p}^{2}}={{a}^{2}}+{{b}^{2}}\]

B)

\[{{p}^{2}}={{a}^{2}}-{{b}^{2}}\]

C)

\[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\]

D)

\[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}-\frac{1}{{{b}^{2}}}\]

View Answer
147) If the slope of one of the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is 5 times the other then:

A)

\[5{{h}^{2}}=9ab\]

B)

\[5{{h}^{2}}=ab\]

C)

\[{{h}^{2}}=ab\]

D)

\[9{{h}^{2}}=5ab\]

View Answer
148) \[\int_{0}^{2\pi }{(\sin x+|\sin x|dx}\] is equal to :

A)

4

B)

0

C)

1

D)

8

View Answer
149) \[\int_{0}^{\pi }{\frac{x\,dx}{{{a}^{2}}{{\cos }^{2}}x+{{b}^{2}}{{\sin }^{2}}x}}\] is equal to :

A)

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

B)

\[\frac{\pi }{ab}\]

C)

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

D)

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

View Answer
150) The differential equation for which \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=c\] is given by :

A)

\[\sqrt{1-{{x}^{2}}}dy+\sqrt{1-{{y}^{2}}}\,dx=0\]

B)

\[\sqrt{1-{{x}^{2}}}dx+\sqrt{1-{{y}^{2}}}\,dy=0\]

C)

\[\sqrt{1-{{x}^{2}}}dx-\sqrt{1-{{y}^{2}}}\,dy=0\]

D)

\[\sqrt{1-{{x}^{2}}}dy-\sqrt{1-{{y}^{2}}}\,dx=0\]

View Answer
151) The derivative of \[{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\] w.r.t. \[{{\cos }^{-1}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)\]is :

A)

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

B)

1

C)

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

D)

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

View Answer
152) If \[x=a\,(\theta -\sin \theta ),\,y=a\,(1-\cos \theta )\] then \[\frac{dy}{dx}\] is equal to :

A)

\[\cot \theta /2\]

B)

\[\tan \theta /2\]

C)

\[\frac{1}{2}\cos e{{c}^{2}}\frac{\theta }{2}\]

D)

\[-\frac{1}{2}\cos e{{c}^{2}}\frac{\theta }{2}\]

View Answer
153) If \[y=1-x+\frac{{{x}^{2}}}{2!}-\frac{{{x}^{3}}}{3!}+\frac{{{x}^{4}}}{4\,!}....\]then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]is equal to :

A)

\[-x\]

B)

\[x\]

C)

\[y\]

D)

\[-y\]

View Answer
154) If \[\sqrt{x}+\frac{1}{\sqrt{x}}=2\,\cos \theta \] then \[{{x}^{6}}+{{x}^{-6}}\] is equal to:

A)

\[2\cos 12\theta \]

B)

\[2\cos 6\,\theta \]

C)

\[2\sin 3\,\theta \]

D)

\[2\cos 3\,\theta \]

View Answer
155) The slope of the tangent to the curve\[x=3{{t}^{2}}+1,\,y={{t}^{3}}-1\] at \[x=1\] is :

A)

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

B)

0

C)

-2

D)

\[\infty \]

View Answer
156) Which of the following is a fourth root \[\frac{1}{2}+\frac{\sqrt{3}}{2}\]?

A)

\[cis\frac{\pi }{12}\]

B)

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

C)

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

D)

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

View Answer
157) If \[f(a)=2f(a)=1,\,g(a)=3,\,g(a)=-1\] then \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)\,g\,(x)-f(x)\,g\,(a)}{x-a}\] equal to :

A)

6

B)

1

C)

-1

D)

-5

View Answer
158) The rate of change of the surface area of the sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to :

A)

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

B)

\[\frac{1}{r}\]

C)

\[{{r}^{2}}\]

D)

\[r\]

View Answer
159) The amplitude of \[\sin \frac{\pi }{5}+i\left( 1-\cos \frac{\pi }{5} \right)\] is :

A)

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

B)

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

C)

\[\frac{\pi }{15}\]

D)

\[\frac{\pi }{10}\]

View Answer
160) For the curve \[xy={{c}^{2}}\] the subnormal at any point varies as :

A)

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

B)

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

C)

\[{{y}^{3}}\]

D)

\[\infty \]

View Answer
161) The function \[f(x)=\left| x \right|+\frac{\left| x \right|}{x}\] is :

A)

discontinuous at origin because \[\left| x \right|\] is discontinuous there

B)

continuous at origin

C)

discontinuous at origin because both \[\left| x \right|\] and \[\frac{\left| x \right|}{x}\] are discontinuous there

D)

discontinuous at the origin because is discontinuous there.

View Answer
162) \[\int{{{e}^{x}}\left( \frac{1+\sin x}{1+\cos x} \right)dx}\] is equal to :

A)

\[{{e}^{x}}{{\sec }^{2}}\frac{x}{2}+C\]

B)

\[{{e}^{x}}\tan \frac{x}{2}+C\]

C)

\[{{e}^{x}}\sec \frac{x}{2}+C\]

D)

\[{{e}^{x}}+\tan x+C\]

View Answer
163) \[\int{\sqrt{1+\sin \left( \frac{x}{4} \right)}\,dx}\] is equal to :

A)

\[8\,\left( \sin \frac{x}{8}+\cos \frac{x}{8} \right)+C\]

B)

\[8\,\left( \sin \frac{x}{8}-\cos \frac{x}{8} \right)+C\]

C)

\[8\,\left( \cos \frac{x}{8}-\sin \frac{x}{8} \right)+C\]

D)

\[8\,\left( \sin \frac{x}{8}-\cos \frac{x}{8} \right)+C\]

View Answer
164) \[\int_{0}^{\infty }{\frac{x\,dx}{(1+x)\,(1+{{x}^{2}})}}\] is equal to :

A)

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

B)

0

C)

1

D)

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

View Answer
165) If \[{{I}_{n}}\int{{{(\log \,x)}^{n}}dx}\] then \[{{I}_{n}}+n\,{{I}_{n-1}}\] is equal to :

A)

\[{{(x\,\log \,x)}^{n}}\]

B)

\[x\,{{(\log \,x)}^{n}}\]

C)

\[n\,{{(\log \,x)}^{n}}\]

D)

\[{{(\log \,x)}^{n-1}}\]

View Answer
166) The area included between the parabolas\[x=4y\] and \[y=4x\] is (in square units) :

A)

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

B)

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

C)

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

D)

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

View Answer
167) If \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z=3\pi \] then\[xy+yz+zx\] is equal to :

A)

1

B)

0

C)

-3

D)

3

View Answer
168) Which of the following is a group?

A)

{1, 2, 4, 8} under multiplication

B)

\[\{0,\pm \,2,\pm \,4,\pm \,6\text{ }...\}\] under addition

C)

\[\{1,-1\}\] under addition

D)

{0,1,2,3, 4} under multiplication module 5

View Answer
169) If the circles \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\] and\[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\] touch each other then :

A)

\[ff=gg\]

B)

\[fg=fg\]

C)

\[{{(fg)}^{2}}={{(fg)}^{2}}\]

D)

\[fg=fg\]

View Answer
170) The line \[3x-2y=k\] meets the circle\[{{x}^{2}}+{{y}^{2}}=4{{r}^{2}}\] at only one point if k is equal to:

A)

\[52{{r}^{2}}\]

B)

\[20{{r}^{2}}\]

C)

\[\frac{20}{9}{{r}^{2}}\]

D)

\[\frac{52}{9}{{r}^{2}}\]

View Answer
171) In three element group \[\{e,a,b\}\] where e is the identity a b is equal to :

A)

a

B)

e

C)

ab

D)

b

View Answer
172) The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is :

A)

a circle

B)

a straight line

C)

a hyperbola

D)

an ellipse

View Answer
173) The directrix of the parabola\[{{x}^{2}}-4x-8y+12=0\] is :

A)

\[y=0\]

B)

\[x=1\]

C)

\[y=-1\]

D)

\[x=-1\]

View Answer
174) Which of the following is a point on the common chord of the circle\[{{x}^{2}}+{{y}^{2}}+2x-3y+6=0\] and\[{{x}^{2}}+{{y}^{2}}+x-8y-13=0\]

A)

(1, 4)

B)

(1, -2)

C)

(1, -4)

D)

(1, 2)

View Answer
175) The locus of the point of intersection of the perpendicular tangents to ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1\] is:

A)

\[{{x}^{2}}+{{y}^{2}}=4\]

B)

\[{{x}^{2}}+{{y}^{2}}=9\]

C)

\[{{x}^{2}}+{{y}^{2}}=5\]

D)

\[{{x}^{2}}+{{y}^{2}}=13\]

View Answer
176) The sum of the coefficients in the expansion of \[{{(1+x-3{{x}^{2}})}^{3148}}\] is :

A)

8

B)

7

C)

1

D)

-1

View Answer
177) The relation \[R=((1,1),\text{(}2,\,2\text{)},\,\text{(}3,\,\,3\text{)}\}\] on the set \[\{1,2,3\}\] is :

A)

symmetric only

B)

reflexive only

C)

an equivalence relation

D)

transitive only

View Answer
178) The least remainder when \[{{17}^{30}}\] is divided by 5 is:

A)

2

B)

1

C)

4

D)

2

View Answer
179) The limiting points of the co-axial system of circles \[{{x}^{2}}+{{y}^{2}}+2\lambda y+4=0\] are :

A)

\[(0\pm 4)\]

B)

\[(\pm 2,\,0)\]

C)

\[(0,\pm 1)\]

D)

\[(0,\pm 2)\]

View Answer
180) The maximum of \[4{{\sin }^{2}}x+3{{\cos }^{2}}x\] is :

A)

4

B)

3

C)

7

D)

5

View Answer