Solved papers for RAJASTHAN PET Rajasthan PET Solved Paper-2005

Rajasthan PET Solved Paper-2005 Total Questions - 300

1) A body cools down from\[80{}^\circ C\]to\[70{}^\circ C\]in 6 min. The time taken to cool it from\[60{}^\circ C\]to\[50{}^\circ C\]will be

A)

less than 6 min

B)

6 min

C)

more than 6 min

D)

None of the above

View Answer
2) At temperature\[227{}^\circ C,\]the power radiated by a body is\[Q\text{ }cal/c{{m}^{^{2}}}\]. At the temperature\[727{}^\circ C\] the power radiated by it will be

A)

2Q

B)

4 Q

C)

16 Q

D)

32 Q

View Answer
3) A train of mass\[5\times {{10}^{6}}\]kg is moving with velocity 72 km/s. If it is sloped by applying break, then the value of heat generated will be

A)

\[1.2\times {{10}^{5}}k-cal\]

B)

\[2.4\times {{10}^{5}}k-cal\]

C)

\[4.8\times {{10}^{5}}k-cal\]

D)

\[6\times {{10}^{5}}k-cal\]

View Answer
4) For a gas, if ratio of specific heat is 7. If gas constant is R, then the value of specific heat at constant volume will be

A)

\[\frac{R}{(\gamma -1)}\]

B)

\[\frac{R}{\gamma +1}\]

C)

\[\frac{R}{\gamma }\]

D)

\[R(\gamma -1)\]

View Answer
5) The value of critical temperature in terms of van der Waal's constant a and b is

A)

\[1.2\,\times \,{{10}^{5}}k-cal\]

B)

\[2.4\,\times \,{{10}^{5}}k-cal\]

C)

\[4.8\,\times \,{{10}^{5}}k-cal\]

D)

\[6\,\times \,{{10}^{5}}k-cal\]

View Answer
6) The surface tension of a soap solution is\[2\times {{10}^{-2}}\]N/m. To blow a bubble of radius 2 cm from 1 cm, the work done is

A)

\[1.5\pi \times {{10}^{-4}}J\]

B)

\[1.2\pi \times {{10}^{-4}}J\]

C)

\[0.3\pi \times {{10}^{-4}}J\]

D)

\[0.6\pi \times {{10}^{-4}}J\]

View Answer
7) A second pendulum is taken in a satellite moving at a height of 2R from the earth's surface. At that position the time period (in second) of pendulum will be

A)

0

B)

2

C)

4

D)

\[\infty \]

View Answer
8) A space shuttle of mass 2500 kg is projected outside the gravitational field of the earth in space. The radius of earth is 6400 km. The minimum initial velocity of the shutle should be

A)

5.6 km/s

B)

7.25 km/s

C)

8.5 km/s

D)

11.2 km/s

View Answer
9) Where can a geostationary sattelite be placed?

A)

Above the city at equatorial

B)

Above the north pole or south pole

C)

In the orbit making\[23.5{}^\circ \]with equatorial plane

D)

In the orbit making\[66.5{}^\circ \]with equatorial plane

View Answer
10) \[n\] bullets of each of mass m hits the surface with velocity \[u\]. The force feet by surface will be

A)

\[mnu\]

B)

\[2\text{ }mnu\]

C)

\[4\text{ }mnu\]

D)

\[zero\]

View Answer
11) A particle is vibrating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, its energy half potential and half kinetic?

A)

\[2\sqrt{2}\,cm\]

B)

\[2\,cm\]

C)

\[\sqrt{2}\]

D)

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

View Answer
12) Inertia of a thin rod of mass M and length L about an axis making an angle\[90{}^\circ \]with its length is \[\frac{M{{L}^{2}}}{9}.\] The distance of this axis from the midpoint of rod will be

A)

\[\frac{L}{6}\]

B)

\[\frac{L}{3}\]

C)

\[\frac{L}{4}\]

D)

\[\frac{L}{2}\]

View Answer
13) A ball at angle\[30{}^\circ \]with velocity v0 through in the vertically direction. Which statement will be true?

A)

Gravitational potential energy at maximum height of projectile path will be minimum

B)

The kinetic energy of ball at maximum height of projectile path will be zero

C)

The horizontal component of momentum will not change

D)

The vertical component of momentum will not change

View Answer
14) A body is rotating with angular velocity\[\overrightarrow{\omega }\]and its angular momentum is L, then relation between T and L will be

A)

\[\overset{\to }{\mathop{T}}\,=\,{{\omega }^{\to }}\times {{L}^{\to }}\]

B)

\[{{L}^{\to }}=L\frac{\,\,\,{{\omega }^{\to }}}{dt}\]

C)

\[{{T}^{\to }}={{\omega }^{\to }}\frac{\,\,\,d{{L}^{\to }}}{dt}\]

D)

\[{{T}^{\to }}=\frac{\,\,\,d{{L}^{\to }}}{dt}\]

View Answer
15) Two masses of 4 kg and 5 kg are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of 5 kg mass is

A)

\[49\text{ }m/{{s}^{2}}\]

B)

\[5.44m/{{s}^{2}}\]

C)

\[19.5\text{ }m/{{s}^{2}}\]

D)

\[2.72\text{ }m/{{s}^{2}}\]

View Answer
16) The maximum angular displacement of simple pendulum of length\[l\]is\[\theta .\] Its maximum kinetic energy will be

A)

\[mgl\text{ }sin\theta \]

B)

\[mgl\text{ }(1+sin\theta )\])

C)

\[mgl(1+cos\theta )\]

D)

\[mgl\text{ }(1-\cos \theta )\]

View Answer
17) The height of water raised in capillary tube will be

A)

maximum at\[4{}^\circ C\]

B)

maximum at \[0{}^\circ C\]

C)

minimum at\[4{}^\circ C\]

D)

minimum at\[0{}^\circ C\]

View Answer
18) The two gases\[{{O}_{2}}\]and\[{{H}_{2}}\]have same temperature at TK. Mean kinetic energy of molecules of\[{{O}_{2}}\] compare to mean kinetic energy of molecule of\[{{H}_{2}}\]will be

A)

16 times

B)

8 times

C)

equal

D)

1/6 times

View Answer
19) The relation between relative change of volume \[\left( \frac{\Delta V}{V} \right)\] and relative change of pressure \[\left( \frac{\Delta p}{p} \right)\] in adiabatic process is

A)

\[\frac{1}{\gamma }\left( \frac{\Delta V}{V} \right)\]

B)

\[\frac{1}{{{\gamma }^{2}}}\left( \frac{\Delta V}{V} \right)\]

C)

\[-\gamma \left( \frac{\Delta V}{V} \right)\]

D)

\[\gamma \left( \frac{\Delta V}{V} \right)\]

View Answer
20) An iron nail of 200 g is fitted in a wood piece with a speed of 50 m/s by a hammer of 1 kg. If specific heat of iron is\[0.105\text{ }cal/g{}^\circ C\]and half of the total energy given to nail is transfered in heat, then what will be the rise in temperature of nail?

A)

\[1.42{}^\circ C\]

B)

\[9.2{}^\circ C\]

C)

\[10.5{}^\circ C\]

D)

\[12.1{}^\circ C\]

View Answer
21) There is a rough black spot on a polished metal plate. If the plate in heated up to\[1400{}^\circ C\]and taken in a dark room, then what will be the rise in temperature

A)

the spot will be brighter as compared to remaining part of plat.

B)

spot and remaining part of the plate will be equally bright

C)

Neither spot nor the remaining part of the plate will be bright

D)

the spot is less bright, as compared to remaining part of the plate

View Answer
22) The force due to surface tension of a capillary tube filled with water is balanced by the force of \[72\times {{10}^{-5}}\]N worked toward the base due to weight of water. The surface tension of water is 0.06 N/m. The internal radius of capillary tube will be will be

A)

0.5 mm

B)

2 mm

C)

1.1 mm

D)

1.75 mm

View Answer
23) The mass and radius of a planet have half the value of corresponding parameter of earth. Acceleration due to gravity on the surface the planet is

A)

\[4.9\text{ }m/{{s}^{2}}\]

B)

\[9.8\text{ }m/{{s}^{2}}\]

C)

\[19.6\text{ }m/{{s}^{2}}\]

D)

zero

View Answer
24) The time period of satellites nearing the planet of radius R is T. Find the time period of nearest satellite for planet of radius 3R.

A)

\[3\sqrt{3}\,T\]

B)

\[\frac{\sqrt{3}}{2}\,T\]

C)

\[\frac{1}{3\sqrt{3}}\,T\]

D)

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

View Answer
25) A body of mass m is taken from earth surface to the height A equal to radius of earth, the increase in potential energy will be

A)

\[\frac{mgR}{2}\]

B)

\[mgR\]

C)

\[2mgR\]

D)

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

View Answer
26) When a mass 5 kg attached to a spring, it normally extends by 12 cm. If the weighted spring oscillates, then its time period will be

A)

0.7 s

B)

0.9 s

C)

1.1 s

D)

1.4 s

View Answer
27) The average kinetic energy of helium atom at\[30{}^\circ C\]will be

A)

13.6 eV

B)

59.60 eV

C)

15 keV

D)

less from 1 eV

View Answer
28) Star A has radius r, surface temperature T while star B has radius 4r and surface \[\frac{T}{2}\] temperature. The ratio of radiated power \[{{P}_{A}}\,:\,{{P}_{B}}\]from, then will be

A)

1 : 4

B)

16 : 1

C)

1 : 16

D)

1 : 1

View Answer
29) A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity \[\omega \]. Two objects each of mass m, are kept gently to the opposite ends of two perpendicular diameter of the ring. The angular velocity of the ring will be

A)

\[\frac{M\omega }{2m}\]

B)

\[\frac{2M\omega }{M}\]

C)

\[\frac{(M+2m)}{M}\omega \]

D)

\[\left( \frac{M\omega }{M+2\omega } \right)\]

View Answer
30) A fan of moment of inertia\[0.6\text{ }kg-{{m}^{2}}\]is turned upto a working speed of 0.5 rev/s. The angular momentum of the fan is

A)

\[0.3\pi \,kg-{{m}^{2}}/s\]

B)

\[0.6\pi \,kg-{{m}^{2}}/s\]

C)

\[\frac{0.03}{\pi }\,kg-{{m}^{2}}/s\]

D)

\[\frac{0.6}{\pi }\,kg-{{m}^{2}}/s\]

View Answer
31) In an AC circuit L is 0.5 H and C is 8\[\mu \]F. In circuit for maximum current, angular frequency will be

A)

500 rad/s

B)

250 rad/s

C)

150 rad/s

D)

100 rad/s

View Answer
32) When 4 A current flows in a motor, the power loss in 20 W and the resultant potential difference is 220 V, emf will be

A)

220 V

B)

225 V

C)

240 V

D)

260 V

View Answer
33) A step up transformer operates on a 230 V line and supplies a load of 2 A. The ratio of the primary and secondary winding is 1 : 25. The current in the primary is

A)

50 A

B)

25 A

C)

12.5 A

D)

6.25 A

View Answer
34) The magnetic field at the rate of 0.4 T/s changes in perpendicular direction from square coil of an arm 4 cm. If the resistance of coil is \[2\times {{10}^{-3}}\Omega ,\] then induced current will be

A)

0.16 A

B)

0.32 A

C)

3.2 A

D)

1.6 A

View Answer
35) A magnet has length 0.2 m and its placed at angle \[30{}^\circ \]in magnetic field of\[30\text{ }Wb/{{m}^{2}}\]

A)

\[7.5\times {{10}^{-4}}N-m\]

B)

\[3.0\times {{10}^{-4}}N-m\]

C)

\[1.5\times {{10}^{-4}}N-m\]

D)

\[6.0\times {{10}^{-4}}N-m\]

View Answer
36) The atomic mass of ionic lithium atoms are 0.06 amu. If they are motion with energy 400 eV in magnetic field of 0.08 T, then radius of circular path will be

A)

8.83 cm

B)

9.23 cm

C)

10.5 cm

D)

11.25 cm

View Answer
37) In Young's double slit experiment, distance between two sources is 0.1 mm. The distance of screen from the sources is 20 cm. Wavelength of light used is 5460\[\overset{o}{\mathop{\text{A}}}\,\]. The distance between maxima will be

A)

0.5 mm

B)

1.1 mm

C)

1.5 mm

D)

2.2 mm

View Answer
38) The ratio of gravitational and electric forces between two electrons.

A)

\[{{10}^{-36}}\]

B)

\[{{10}^{-39}}\]

C)

\[{{10}^{-42}}\]

D)

\[{{10}^{-47}}\]

View Answer
39) Two charges \[4q\] and \[q\] are placed at distance\[l\]. In the middle adjoining line a charge\[Q\]is kept. If resultant force on \[q\] will be zero, then \[Q\] will be

A)

\[+q\]

B)

\[-q\]

C)

\[+2q\]

D)

\[-2g\]

View Answer
40) Suppose the electrical potential at any point is V, then electric field at that point along\[x-\]axis will be

A)

\[{{\int }^{\infty }}{{\,}_{0}}V\,dt\]

B)

\[\frac{dV}{dx}\]

C)

\[-\frac{dV}{dx}\]

D)

\[-V\frac{dV}{dx}\]

View Answer
41) The magnitude of charges in an electric dipole are \[3.2\times {{10}^{-19}}C\]and the distance between them is 2.4\[\overset{o}{\mathop{\text{A}}}\,\]. If its placed at the electric field of intensity \[4\times {{10}^{5}}\]V/m, then the electric dipole moment will be

A)

\[9.6\times {{10}^{-5}}C-m\]

B)

\[12.8\times {{10}^{-14}}C-m\]

C)

\[7.68\times {{10}^{-29}}C-m\]

D)

\[30\times {{10}^{-24}}C-m\]

View Answer
42) A helium nucleus makes a full rotation in a circle of radius 0.8 m in 2s. The value of the magnetic field at the centre of the circle will be

A)

\[{{\mu }_{0}}\,\times \,{{10}^{-19}}\,T\]

B)

\[1.6\,\times {{\mu }_{0}}\,\times \,{{10}^{-19}}\,T\]

C)

\[3{{\mu }_{0}}\,\times \,{{10}^{-19}}\,T\]

D)

\[2{{\mu }_{0}}\,\times \,{{10}^{-19}}\,T\]

View Answer
43) A sinusoidal voltage of peak value 200 V is connected to a diode and capacitance C in the circuit shown, so that half wave rectification occurs.

A)

500 V

B)

200 V

C)

283 V

D)

141 V

View Answer
44) The ratio of energies of photon of wavelength 6000\[\overset{o}{\mathop{\text{A}}}\,\] to wavelength 4000\[\overset{o}{\mathop{\text{A}}}\,\]

A)

2 : 3

B)

3 : 2

C)

1 : 5

D)

5 : 1

View Answer
45) The third harmonic of a closed organ pipe is in resonance with the fourth overtone of open organ pipe. The ratio of lengths of the pipes is

A)

\[\frac{8}{7}\]

B)

\[\frac{7}{8}\]

C)

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

D)

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

View Answer
46) Two coherent monochromatic light beam of intensities \[I\] and \[4I\] are superposed. The maximum and minimum possible intensities in the resulting beam are

A)

\[3I\] and \[2I\]

B)

\[25I\text{ }and\text{ }9I\]

C)

\[9I\text{ }and\,I\]

D)

\[5I\text{ }and\text{ }3I\]

View Answer
47) Two steady sound sources having same frequency are placed at a distance of 1 m. An observer is moving at a distance of 10 m along the line joining there source. If the observed distance between first two successive maxima is 0.11 m, then frequency of sources is (velocity of sound v = 330 m/s.)

A)

1000 Hz

B)

3000 Hz

C)

3500 Hz

D)

4000 Hz

View Answer
48) A car moving with a speed of 28 m/s and blowing the horn of 500 Hz frequency waves another car moving at 15 m/s. What will be the observed frequency is the dimer of second car? (speed of sound = 332 m/s)

A)

480 Hz

B)

500 Hz

C)

520 Hz

D)

580 Hz

View Answer
49) The average emf induced in a coil in which current changes from 2 A to 4 A in 0.05 s is 8 V. What is the self inductance of the coil?

A)

0.5 H

B)

0.35 H

C)

0.2 H

D)

2 mH

View Answer
50) In a potential meter, a voltage source and battery of 3 V are balance at length 60cm length 45 cm respectively. The emf unknown voltage will be

A)

3 V

B)

4 V

C)

4.5 V

D)

6 V

View Answer
51) The square coil of turn 60 has length 20 cm and breath 10 cm is rotating rate of 1800 rev/min in uniform magnetic field of intensity 0.5 T. the maximum emf of coil will be

A)

98 V

B)

110 V

C)

113 V

D)

118 V

View Answer
52) The number of turn in the primary coil of a transformer is 240. For an input of alternating voltage 20 V, output voltage is 2.5 V. 7 number of turns in the secondary coil is

A)

250

B)

100

C)

10

D)

30

View Answer
53) A light wave is moving along y-axis. If \[E\to \] at a time along the x-axis, then direction of \[B\to \] at that time will along

A)

\[y-\]axis

B)

\[x-\]axis

C)

\[\text{+ }z-\]axis

D)

\[-\text{ }z-\]axis

View Answer
54) The current of an AC circuit is \[I=2\text{ }cos\] \[(\omega t\,+\,\theta ),\]then\[{{I}_{rms}}\]

A)

\[\sqrt{2}A\]

B)

\[\frac{1}{\sqrt{2}}\,A\]

C)

\[2A\]

D)

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

View Answer
55) The intensity of magnetic field of a current carrying circular at a point on its axis at distance \[x(x>>R)\]will depends upon

A)

\[B\alpha \frac{1}{{{x}^{3/2}}}\]

B)

\[B\alpha \frac{1}{{{x}^{2}}}\]

C)

\[B\alpha \frac{1}{{{x}^{3}}}\]

D)

\[B\alpha \frac{1}{{{x}^{1/2}}}\]

View Answer
56) A given charge is situated at a certain distance from an electric dipole in the end on position experience a force F. If the distance of the charge is doubled, the force acting on the charge will be

A)

zero

B)

\[F/2\]

C)

\[F/4\]

D)

\[F/8\]

View Answer
57) In dielectric medium, the electric field is \[E\to \]. If permittivity of vacuum is \[{{\varepsilon }_{0}},\]then

A)

\[\frac{kE\to }{{{\varepsilon }_{0}}}\]

B)

\[\frac{E\to }{K{{\varepsilon }_{0}}}\]

C)

\[\frac{{{\varepsilon }_{0}}E\to }{k}\]

D)

\[k{{\varepsilon }_{0}}E\to \]

View Answer
58) The work done to complete one revolution in a circle of radius r by a charge Q, if a charge Q is placed at the centre of the circle will be

A)

\[\frac{Q}{4\pi {{\varepsilon }_{0}}r}\]

B)

\[\frac{{{Q}^{2}}al}{4\pi {{\varepsilon }_{0}}r}\]

C)

zero

D)

\[\frac{Qal}{2r}\]

View Answer
59) Two mirror are bended on each other in such a manner that the incident ray on first mirror, parallel to the second mirror, becomes parallel to first mirror by reflection through second mirror, then the angle between the two mirrors is

A)

\[30{}^\circ \]

B)

\[45{}^\circ \]

C)

\[60{}^\circ \]

D)

\[75{}^\circ \]

View Answer
60) The energy for ion on of a excited hydrogen atom is

A)

13.6

B)

3.4

C)

more than 13.6

D)

None of these

View Answer
61) The thickness of glass strip is t and refractive index n. If velocity of light in vacuum is c, then minimum time in cross the strip by light will be

A)

\[\frac{ct}{n}\]

B)

\[\frac{nt}{c}\]

C)

\[nct\]

D)

\[\frac{nc}{t}\]

View Answer
62) Some point in progressive waves are

A)

not remain at rest

B)

always move

C)

in each cycle two times at rest at the same time

D)

in each cycle one time at rest at the same time

View Answer
63) One end closed pipe of length L resonented at any frequency. The length of open both ends pipe, for resonant at same frequency will be

A)

L/2

B)

L

C)

3L/2

D)

2L

View Answer
64) The frequency of Piano of length 1.1 m and of mass 160 g is 33 Hz, the tension will be

A)

556 N

B)

3000 N

C)

843 N

D)

995 N

View Answer
65) A tuning forks gives 5 beats/s with 20 cm length of sonometer. If length of wire changes from 20 to 21, and not change in frequency, then frequency of tuning forks will be

A)

205 Hz

B)

210 Hz

C)

220 Hz

D)

195 Hz

View Answer
66) When semiconductor makes from Germanium doped by phosphorus, then in semiconductor

A)

quantity of negative electric charge will be maximum

B)

electrons will be maximum

C)

quantity of positive electric charge will be maximum

D)

holes will be maximum

View Answer
67) Two coils have a same centre, when the mutual inductance of both coil will be maximum, then axis of both will

A)

perpendicular

B)

make an angle\[45{}^\circ \]

C)

make an angle\[60{}^\circ \]

D)

parallel

View Answer
68) In insulator, energy interval of low order is

A)

zero

B)

0.7 eV

C)

1.1 eV

D)

5 eV

View Answer
69) In triode 8 amplifier voltage gain depends upon

A)

\[\mu ,\,{{R}_{L}}\,and\,input\,voltage\]

B)

\[{{R}_{p}},{{R}_{L}}\]and\[\mu \]

C)

\[\mu ,{{R}_{p}}\]and input voltage

D)

\[{{R}_{p}},\mu \]and\[{{g}_{m}}\]

View Answer
70) In hydrogen atom, the kinetic energy of moving electron in Bhor orbit of radius r will be

A)

\[Ke/2r\]

B)

\[\frac{K{{e}^{2}}}{2r}\]

C)

\[Ke/r\]

D)

\[2Ke/4\]

View Answer
71) A hydrogen atom is in first excited state, then ion energy will be

A)

13.1 eV

B)

3.4 eV

C)

1.51 eV

D)

1.9 eV

View Answer
72) An electron and positron have the same rest mass of 0.51 MeV. Find the wavelength of \[\gamma \] rays produced due to their fusion

A)

6.012\[\overset{o}{\mathop{\text{A}}}\,\]

B)

0.024\[\overset{o}{\mathop{\text{A}}}\,\]

C)

0.012 to\[\overset{o}{\mathop{\text{A}}}\,\]

D)

0.024 to\[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
73) Crod makes of soft iron in electromagnet, because its

A)

diathesis and retantivity are maximum

B)

diathesis is maximum and retantivity is minimum

C)

diathesis and retantivity are minimum

D)

retantivity is maximum and diathesis is minimum

View Answer
74) A converging lens is used to form an image on a screen. When half of the lens is covered by opaque screen.

A)

Half the image will disappear

B)

Upper half the image will disappear

C)

Complete image will be formed of decreased intensity

D)

Complete image will disappear

View Answer
75) In an X-rays tube, the electron accelerated by potential V volt, the minimum wavelength of X-rays will be

A)

\[\frac{2400}{V}\]\[\overset{o}{\mathop{\text{A}}}\,\]

B)

\[\frac{12400}{V}\]\[\overset{o}{\mathop{\text{A}}}\,\]

C)

\[\frac{12.4}{V}\]\[\overset{o}{\mathop{\text{A}}}\,\]

D)

\[\frac{V}{124000}\]\[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
76) The atomic weight of boran is 10.81 and it has two isotopes \[_{5}{{\beta }^{10}}\] and \[_{5}{{\beta }^{11}}\]. Then ratio of \[_{5}{{\beta }^{10}}\]: \[_{5}{{\beta }^{11}}\] in nature would be

A)

19 : 81

B)

10 : 11

C)

15 : 61

D)

81 : 19

View Answer
77) A galvanometer of\[10\,\Omega \]resistance gives full scale deflection with 0.01 A of current. It is to be converted into an ammeter for measuring 10 A current. The value of shunt resistance will be

A)

\[11\,\Omega \]resistance in series

B)

100 resistance in series

C)

990\[\Omega \] resistance in series

D)

0.10\[\Omega \] resistance in series

View Answer
78) Half year of a radioactive element is 5 days. The time during which quantity remains 7/8 of initial mass will be

A)

2, 5 days

B)

5 days

C)

10 days

D)

15 days

View Answer
79) When a choke coil of resistance zero works at 200 V, then the 5 mA current flows its. The power in choke coil is

A)

zero

B)

11 W

C)

\[44\times {{10}^{3}}W\]

D)

1.1 W

View Answer
80) The below diagram shows a parabola. Its physical quantities and y at constant acceleration represent respectively

A)

X = time, Y = velocity

B)

X = time, Y = displacement

C)

X = time, Y = acceleration

D)

X = velocity, Y = displacement

View Answer
81) The chemical equivalent of silver is 108. If the current in silver voltameter is 2 A; then the during time in collecting of 27 g silver will be

A)

8.75 h

B)

6.70 h

C)

3.35 h

D)

12.50 h

View Answer
82) The reactance of a coil at frequency 50 Hz is 1000, the reactance at frequency 100 Hz will be

A)

100\[\Omega \]

B)

300\[\Omega \]

C)

450\[\Omega \]

D)

600\[\Omega \]

View Answer
83) For iron magnet materials

A)

permeability is high and tendency is positive and low

B)

permeability is very high and tendency is negative and low

C)

permeability is very low and tendency is positive and high

D)

permeability is very low and tendency is negative and low

View Answer
84) The magnetic susceptibility of any paramagnetic material changes with absolute temperature T as

A)

\[\chi \,\alpha \,T\]

B)

\[\chi \,\alpha \,\frac{1}{T}\]

C)

\[\chi \,\alpha \,\frac{1}{(1-T)}\]

D)

constant

View Answer
85) The grid voltage of any triode valve is changed from\[-2.5\text{ }V\]to\[-4.5\text{ }V\]and the mutual conductance is\[8\times {{10}^{-4}}\]mho. The change in plate circuit current will be

A)

\[1.6\times {{10}^{-3}}A\]

B)

\[2.0\times {{10}^{-4}}A\]

C)

\[1.6\times {{10}^{-3}}A\]

D)

\[1.6\times {{10}^{-4}}A\]

View Answer
86) To obtain a P-type germanium semiconductor, it must be doped with

A)

boran

B)

antimany

C)

arsenic

D)

phosphorus

View Answer
87) In a triode amplifier,\[\mu =25,\]\[{{r}_{p}}=40\text{ }k\Omega \] and load resistance\[{{R}_{L}}=10\text{ }k\Omega \]. If the input signal voltage is 0.5 V, then output signal voltage will be

A)

1.25 V

B)

2.5 V

C)

5 V

D)

10 V

View Answer
88) The radius of the coil of a tangent galvanometer which has 10 turn is 0.1 m. The current required to produce a deflection of \[60{}^\circ \] is

A)

\[3A\]

B)

\[1.1A\]

C)

\[2.1A\]

D)

\[1.5A~\]

View Answer
89) The atomic weight of thorium is 232 and atomic no Z = 90. Disintegration of thorium finally gives Pb for which A = 208 and Z = 82. For this process the number of \[\alpha \] and\[\beta \] particles respectively are

A)

4 and 6

B)

6 and 4

C)

3 and 2

D)

2 and 3

View Answer
90) The work function of metal is 2.4 eV. The maximum wavelength of photon for emitted the electric light will be

A)

3000\[\overset{o}{\mathop{\text{A}}}\,\]

B)

3500 \[\overset{o}{\mathop{\text{A}}}\,\]

C)

4500 \[\overset{o}{\mathop{\text{A}}}\,\]

D)

5156 \[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
91) The ratio of ioning power of\[\alpha \]and\[\beta \]particle emitted from a radioactive element will be

A)

1 : 100

B)

100 : 1

C)

1000 : 1

D)

1 : 1000

View Answer
92) The momentum of X-ray photon of wavelength 0.01\[\overset{o}{\mathop{\text{A}}}\,\]in kg-m/s will be

A)

\[6.6\times {{10}^{-21}}\]

B)

\[6.6\times {{10}^{-32}}\]

C)

\[6.6\times {{10}^{-46}}\]

D)

\[6.6\times {{10}^{-22}}\]

View Answer
93) The minimum wavelength of X-rays achive from the\[\alpha -\]ray tube is 0.1 A. The maximum voltage

A)

\[1.25\times {{10}^{3}}V\]

B)

\[1.24\times {{10}^{4}}V\]

C)

\[1.24\times {{10}^{5}}V\]

D)

\[1.24\times {{10}^{6}}V\]

View Answer
94) An electron is accelerated through a potential of 50000 V. Its de-Broglie wavelength of electron will be

A)

0.55\[\overset{o}{\mathop{\text{A}}}\,\]

B)

0.055\[\overset{o}{\mathop{\text{A}}}\,\]

C)

0.077\[\overset{o}{\mathop{\text{A}}}\,\]

D)

0.095\[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
95) The wavelength of second line of Lyman series is 1025\[\overset{o}{\mathop{\text{A}}}\,\]. The wavelength of first line will be

A)

825\[\overset{o}{\mathop{\text{A}}}\,\]

B)

900\[\overset{o}{\mathop{\text{A}}}\,\]

C)

1215\[\overset{o}{\mathop{\text{A}}}\,\]

D)

1325\[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
96) In hydrogen atom, the momentum of electron in second orbit of radius r will be

A)

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

B)

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

C)

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

D)

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

View Answer
97) An electric heater of resistance 70, heats 0.1 kg of water of\[20{}^\circ C\]for 3 min. If it carries a current of 4 A, then what will be the final temperature (specific heat of water\[=4.2\times {{10}^{3}}J/kg\text{ }K\])

A)

\[28{}^\circ C\]

B)

\[48{}^\circ C\]

C)

\[52{}^\circ C\]

D)

\[68{}^\circ C\]

View Answer
98) In LCR circuit having C = 25\[\mu \]F, L = 02 H and R = 25\[\Omega \]. If a generator of E = 320 sin 314 t volt is connect in the circuit, then impedence will be

A)

57.320\[\Omega \]

B)

79.480\[\Omega \]

C)

89.50\[\Omega \]

D)

99.10\[\Omega \]

View Answer
99) In question 98, how much inductance is added the circuit so that reactance becomes minimum?

A)

0.31 H

B)

0.41 H

C)

1.25 H

D)

1.75 H

View Answer
100) In a circuit the current is given by\[I={{l}_{0}}sin\] \[(\omega t-\pi /2)\]and the potential is\[V={{V}_{0}}sin\] at, then

A)

\[\frac{1}{2}{{I}_{0}}{{e}_{0}}\,watt\]

B)

\[{{I}_{0}}{{\varepsilon }_{0}}\,watt\]

C)

\[{{I}_{0}}\,watt\]

D)

\[zero\]

View Answer
101) Which of the following has minimum energy?

A)

\[\sigma \]bond

B)

\[\pi \]bond

C)

ionic bond

D)

hydrogen bond

View Answer
102) The addition of a reagent to an unsymmetric alkene take place in such a way that the negative part of the reagent will be attached to the carbon atom which containing lesser number of H-atom. This statement belongs to

A)

Markownikoffs rule

B)

Peroxide effect

C)

Saytzeffs rule

D)

Le-Chatelier's principle

View Answer
103) The atomic mass of two elements is same. There are 27 protons in first element and 30 protons in second element. If 30 neutrons are present in first element then neutron in second element will be

A)

27

B)

30

C)

29

D)

28

View Answer
104) Which of the following alcohol will form the most stable carbonium ion on dehydration?

A)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}OH\]

B)

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

C)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}C{{H}_{3}}\]

D)

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

View Answer
105) Which of the following is strong reducing agent?

A)

\[Li\]

B)

\[Na\]

C)

\[Al\]

D)

\[Zn\]

View Answer
106) On moving top to bottom in a group

A)

ionisation potential increases

B)

electronegativity increases

C)

oxidising strength increases

D)

reducing strength increases

View Answer
107) Power alcohol is

A)

absolute alcohol\[+C{{H}_{3}}OH\]

B)

absolute alcohol\[+{{C}_{6}}{{H}_{5}}OH\]

C)

absolute alcohol + petrol + benzene

D)

absolute alcohol\[+C{{H}_{3}}COOH\]

View Answer
108) Which of the following is the most stable ion?

A)

\[C{{H}_{3}}C{{H}_{2}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]

B)

\[C{{H}_{3}}-\overset{+}{\mathop{C}}\,H-C{{H}_{3}}\]

C)

\[{{(C{{H}_{3}})}_{3}}{{C}^{+}}\]

D)

\[\overset{+}{\mathop{C}}\,{{H}_{3}}\]

View Answer
109) \[{{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}+22.4\,k\,cal\] What are the favourable condition for the formation of ammonia in the above reaction?

A)

High temperature and low pressure

B)

Low temperature and high pressure

C)

High temperature and high pressure

D)

Low temperature and low pressure

View Answer
110) Homolytic fission produces

A)

free radical

B)

carbocation

C)

carbonion

D)

carbine

View Answer
111) \[C{{H}_{3}}C{{H}_{2}}OH\]and\[C{{H}_{3}}-O-C{{H}_{3}}\]is

A)

position isomers

B)

functional isomers

C)

chain isomers

D)

geometrical isomers

View Answer
112) The IUPAC name of \[C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{2}}-C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}\]

A)

3-ethyl-4-methyl hexane

B)

3-ethyl-3-methyl heptane

C)

5-methyl-5-ethyl heptane

D)

2-butyl-2-ethyl butane

View Answer
113) Alkaline\[KMn{{O}_{4}}\]is called

A)

Tollen's reagent

B)

Baeyefs reagent

C)

Benedict solution

D)

None of these

View Answer
114) Acidic hydrogen is present in:

A)

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

B)

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

C)

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

D)

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

View Answer
115) The dipole moment of\[CC{{l}_{4}}\]is zero. It is due to:

A)

planar structure

B)

tetrahedral structure

C)

same size of C and\[Cl\]atoms

D)

same electron affinity of C and\[Cl\]atoms

View Answer
116) What will obtain on adding 50%\[NaOH\]in bauxite?

A)

\[Al\]

B)

\[Al{{(OH)}_{3}}\]

C)

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

D)

\[Fe\]

View Answer
117) Which is deviated from Aufbau's principle?

A)

B)

C)

D)

View Answer
118) \[C{{H}_{3}}-C\equiv CH+{{H}_{2}}O\xrightarrow[{}]{{{H}^{+}}/H{{g}^{2+}}}X,\]Compound X, is

A)

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

B)

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

C)

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

D)

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

View Answer
119) \[X+CHC{{l}_{3}}+3KOH\xrightarrow[{}]{{}}Y\] Y is a abnoxious odour compound. The compound X, is

A)

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

B)

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

C)

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

D)

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

View Answer
120) The pH of solution which obtains on adding 10 mL 0.2 M\[NaOH\]solution with 10 mL 0.1 M \[{{H}_{2}}S{{O}_{4}}\]will be

A)

zero

B)

2.0

C)

4.0

D)

7.0

View Answer
121) The shape of electron cloud is determined by

A)

principal quantum number

B)

azimuthal quantum number

C)

spin quantum number

D)

All of the above

View Answer
122) The oxidation number of Cr in\[{{K}_{2}}Cr{{O}_{4}}\]is

A)

+3

B)

\[-3\]

C)

+6

D)

\[-6\]

View Answer
123) Which of the following compound contains both ionic and covalent bond?

A)

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

B)

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

C)

\[N{{H}_{4}}Cl\]

D)

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

View Answer
124) On moving left to right in a period, the electropositive character

A)

increases

B)

decreases

C)

first increases then decreases

D)

first decreases then increases

View Answer
125) Bond angle and bond length in benzene are

A)

\[120{}^\circ \]and 1.34\[\overset{o}{\mathop{\text{A}}}\,\]

B)

\[120{}^\circ \]and 1.39\[\overset{o}{\mathop{\text{A}}}\,\]

C)

\[180{}^\circ \]and 1.33\[\overset{o}{\mathop{\text{A}}}\,\]

D)

\[120{}^\circ \] and 1.54\[\overset{o}{\mathop{\text{A}}}\,\]

View Answer
126) The atomic number of a element is 33. It belongs to

A)

third period and IVA group

B)

fourth period and IIIA group

C)

fourth period and VA group

D)

third period and VA group

View Answer
127) Which of the following compound is used as both oxidant and reductant?

A)

\[NaOH\]

B)

\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]

C)

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

D)

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

View Answer
128) \[{{(C{{H}_{3}}CO)}_{2}}O+HCl\xrightarrow[{}]{{}}X+C{{H}_{3}}COOH\] Compound X, will be

A)

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

B)

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

C)

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

D)

None of these

View Answer
129) Which of the following is diamagnetic?

A)

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

B)

\[NO\]

C)

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

D)

\[{{F}_{2}}\]

View Answer
130) Lewis acid is

A)

\[C{{l}^{-}}\]

B)

\[B{{F}_{3}}\]

C)

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

D)

\[NO_{2}^{-}\]

View Answer
131) The above reaction is called

A)

Gattermann reaction

B)

Schmidt reaction

C)

Schotten-Baumann reaction

D)

Friedel-Craft's reaction

View Answer
132) Malachite is the ore of which metal?

A)

\[Fe\]

B)

\[Cu\]

C)

\[Al\]

D)

\[Ag\]

View Answer
133) Alkyl halide reacts with alcoholic KOH to give

A)

alcohol

B)

alkene

C)

alkane

D)

aldehyde

View Answer
134) The concentration of pyrite ore is done by which method

A)

calcination

B)

roasting

C)

froth floatation

D)

gravity separation

View Answer
135) Which of the following reaction will not happen?

A)

\[Fe+{{H}_{2}}S{{O}_{4}}\xrightarrow[{}]{{}}FeS{{O}_{4}}+{{H}_{2}}\]

B)

\[Cu+2AgN{{O}_{3}}\xrightarrow[{}]{{}}Cu{{(N{{O}_{3}})}_{2}}+2Ag\]

C)

\[2KBr+{{I}_{2}}\xrightarrow[{}]{{}}2KI+B{{r}_{2}}\]

D)

\[CuO+{{H}_{2}}\xrightarrow[{}]{{}}Cu+{{H}_{2}}O\]

View Answer
136) \[SnC{{l}_{4}}+2FeC{{l}_{2}}\xrightarrow[{}]{{}}SnC{{l}_{2}}+2FeC{{l}_{3}}\] In this reaction, oxidising agent and reducing agent are respectively

A)

\[SnC{{l}_{2}}\]and \[FeC{{l}_{3}}\]

B)

\[FeC{{l}_{3}}\]and\[SnC{{l}_{4}}\]

C)

\[FeC{{l}_{2}}\] and \[SnC{{l}_{4}}\]

D)

\[SnC{{l}_{4}}\]and \[FeC{{l}_{3}}\]

View Answer
137) The molecular weight of ethyl alcohol and dimethyl ether are equal but the boiling point of ethyl alcohol is greater than dimethyl ether. It is due to

A)

ether is insoluble in water

B)

methyl group is attached to oxygen in ether

C)

the dipole moment of ethanol is greater

D)

ethanol has H-bond

View Answer
138) Which of the following gives iodoform test and Fehling test?

A)

\[HCHO\]

B)

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

C)

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

D)

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

View Answer
139) \[C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}+C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}\xrightarrow[{}]{{}}\] \[C{{H}_{3}}COC{{H}_{2}}COO{{C}_{2}}{{H}_{5}}+{{C}_{2}}{{H}_{5}}OH\] This reaction is called

A)

Esterification

B)

Claisen condensation

C)

Williamson's synthesis

D)

Trans-esterification

View Answer
140) Which is correct for 2p-orbital?

A)

\[n=1,l=2\]

B)

\[n=2,l=1\]

C)

\[n=1,l=0\]

D)

\[n=2,l=0\]

View Answer
141) Mostly alloys are made by which block of elements

A)

s-block

B)

p-block

C)

d-block

D)

\[f-\]block

View Answer
142) \[C{{H}_{3}}MgI+C{{O}_{2}}\xrightarrow[{}]{{}}X\xrightarrow[{}]{{{H}_{2}}O}Y\] Compound Y, is

A)

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

B)

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

C)

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

D)

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

View Answer
143) Which of the following compound obtains on the reaction of formaldehyde with\[C{{H}_{3}}MgX\]?

A)

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

B)

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

C)

\[HCOOH\]

D)

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

View Answer
144) Which of the following is not soluble in cone. \[{{H}_{2}}S{{O}_{4}}\]?

A)

\[n-\]hexane

B)

hexene

C)

benzene

D)

ethanol

View Answer
145) Conjugated base of\[C{{H}_{2}}C{{l}_{2}}\]is

A)

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

B)

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

C)

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

D)

\[CO_{3}^{2-}\]

View Answer
146) Ethylene can obtained by the electrolysis of

A)

potassium fumarate

B)

potassium succinate

C)

potassium maleate

D)

potassium formate

View Answer
147) The electronic configuration of-alkaline earth metal is

A)

\[n{{s}^{1}}\]

B)

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

C)

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

D)

\[n{{s}^{2}}(n-1){{d}^{10}}\]

View Answer
148) The oxidation number of C-atom in\[C{{H}_{2}}C{{l}_{2}}\]and\[CC{{l}_{4}}\]is respectively

A)

zero and 4

B)

zero and -4

C)

2 and 4

D)

-2 and -4

View Answer
149) \[C{{H}_{3}}-O-{{C}_{3}}{{H}_{7}}\]and\[{{C}_{2}}{{H}_{5}}-O-{{C}_{2}}{{H}_{5}}\]show the following isomerism

A)

position

B)

functional

C)

metamerism

D)

tautomerism

View Answer
150) \[C{{H}_{3}}CHO+C{{H}_{3}}MgBr\xrightarrow[{}]{{}}A\] Compound A, is

A)

a perimary alcohol

B)

a secondary alcohol

C)

a tertiary alcohol

D)

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

View Answer
151) The electronic configuration of dication of a element is 2, 8, 14. The atomic number of this element will be

A)

26

B)

24

C)

25

D)

28

View Answer
152) \[RCOOH\xrightarrow[{}]{Soda\lim e}X+C{{O}_{2}}\] Compound X, is

A)

\[RH\]

B)

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

C)

\[R-R\]

D)

None of these

View Answer
153) \[RMgI+C{{H}_{3}}OH\xrightarrow[{}]{{}}X\] Compound X, is

A)

RH

B)

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

C)

\[ROH\]

D)

None of these

View Answer
154) On moving left to right in period, the ionization potential

A)

increases

B)

decreases

C)

first increases then decreases

D)

first decreases then increases

View Answer
155) Lithium and magnesium show the similarity in characteristics because

A)

both find in nature along

B)

both have approximately same size

C)

both have same electronic configuration

D)

their ratio of charge and size are approximately same

View Answer
156) Which of the following character always increases on moving top to bottom in group?

A)

ionization potential

B)

electron affinity

C)

electronegativity

D)

atomic radius

View Answer
157) In the extraction of copper, its ore is heated at high temperature, in the presence of air. This process is called

A)

smelting

B)

calcination

C)

roasting

D)

distillation

View Answer
158) A white precipitate of silver chloride is obtained on adding silver nitrate in sodium chloride solution because

A)

\[NaCl\]is insoluble in water

B)

CF ion is present in\[NaCl\]

C)

\[AgN{{O}_{3}}\]is insoluble in\[NaCl\]solution

D)

\[NaCl\]is a inorganic compound

View Answer
159) Aromatic compounds give mainly following reaction

A)

electrophilic addition

B)

nucleophilic addition

C)

nucleophilic substitution

D)

electrophilic substitution

View Answer
160) The\[[{{H}^{+}}]\]of a solution is 1 mol/L. Its pH will be

A)

1.0

B)

10.0

C)

0.1

D)

zero

View Answer
161) On ozonolysis of a alkene, only single organic compound obtains. Alkene is

A)

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

B)

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

C)

\[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]

D)

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

View Answer
162) On adding\[N{{H}_{4}}OH\]in equilibrium \[N{{H}_{4}}ClNH_{4}^{+}+C{{l}^{-}}\]

A)

more\[C{{l}^{-}}\]will form

B)

more\[N{{H}_{4}}Cl\]will decompose

C)

more\[NH_{4}^{+}\]will form

D)

decomposition of\[N{{H}_{4}}Cl\]will reduce

View Answer
163) For an electron\[n=2,\text{ }l=1\]. Total magnetic quantum number for this will be

A)

3

B)

2

C)

1

D)

zero

View Answer
164) The aqueous solution of a salt is basic. It is the salt of

A)

strong acid and strong base

B)

strong acid and weak base

C)

weak acid and weak base

D)

weak acid and strong base

View Answer
165) During the extraction of aluminium, cryolite adds in alumina

A)

to obtain pure\[Al\]

B)

to dissolve alumina

C)

to remove impurities

D)

to catalysis

View Answer
166) The main product of the reaction of \[C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}\]with nitrous acid

A)

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

B)

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

C)

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

D)

\[C{{H}_{3}}-N=O\]

View Answer
167) \[A+NaN{{O}_{2}}+HCl\xrightarrow[{}]{{}}C{{O}_{2}}+{{N}_{2}}+{{H}_{2}}O\] Compound A, is

A)

\[N{{H}_{2}}CON{{H}_{2}}\]

B)

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

C)

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

D)

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

View Answer
168) If a system in equilibrium is subjected to a change of concentration, temperature or pressure the equilibrium shifts in a direction so as to undo the effect of the change imposed. This law is known as

A)

Le-Chatelier's principle

B)

Avogadro's principle

C)

Guldberg-Waage principle

D)

Gay-Lussac's principle

View Answer
169) Alkaline hydrolysis of ethyl acetate gives

A)

\[C{{H}_{3}}COOH\] and\[{{C}_{2}}{{H}_{5}}OH\]

B)

\[C{{H}_{3}}COONa\]and \[{{C}_{2}}{{H}_{5}}OH\]

C)

\[C{{H}_{3}}COOH\]and \[N{{H}_{3}}\]

D)

\[C{{H}_{3}}COONa\]and \[N{{H}_{3}}\]

View Answer
170) Which of the following will reduce the Tollen's reagent?

A)

\[HCOOH\]

B)

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

C)

\[HOOC-COOH\]

D)

\[{{C}_{6}}{{H}_{5}}COOH\]

View Answer
171) For the reaction, \[2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}\] the expression for the equilibrium constant \[({{K}_{c}})\]is

A)

\[\frac{2[S{{O}_{2}}][{{O}_{2}}]}{2[S{{O}_{3}}]}\]

B)

\[\frac{[S{{O}_{2}}][{{O}_{2}}]}{[S{{O}_{3}}]}\]

C)

\[\frac{{{[S{{O}_{3}}]}^{2}}}{[S{{O}_{2}}][{{O}_{2}}]}\]

D)

\[\frac{{{[S{{O}_{2}}]}^{2}}[{{O}_{2}}]}{{{[S{{O}_{3}}]}^{2}}}\]

View Answer
172) The electronic configuration of Fe is

A)

2, 8, 14, 2

B)

2, 8, 8. 6, 2

C)

2, 6, 18

D)

None of these

View Answer
173) The following reaction is called \[{{C}_{6}}{{H}_{5}}OH+3KOH+CHC{{l}_{3}}\to \] \[+3KCl+{{H}_{2}}O\]

A)

Kolbe-Schmidt reaction

B)

Gattermann reaction

C)

Fries rearrangement

D)

Reimer-Tiemann reaction

View Answer
174) The product of the reaction of chloroform with cone.\[HN{{O}_{3}}\]is

A)

chloretone

B)

chloropicrin

C)

nitromethane

D)

methyl nitrite

View Answer
175) At equilibrium in a reversible reaction the catalyst

A)

increases the rate of forward direction

B)

increases the rate of backward direction

C)

increases the rate of forward and backward direction equally

D)

None of the above

View Answer
176) The process of conversion of higher hydrocarbon to lower hydrocarbon is called

A)

isomerisation

B)

cracking

C)

hydroformation

D)

mining

View Answer
177) Which of the following reagent will differentiate in propene and propyne?

A)

Alkaline \[KMn{{O}_{4}}\]

B)

Bromine water

C)

\[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}\]

D)

None of these

View Answer
178) Which of the following is Hofmann bromamide reaction?

A)

\[RCN+4H\xrightarrow[{}]{{}}RC{{H}_{2}}N{{H}_{2}}\]

B)

\[C{{H}_{3}}COCl+C{{H}_{3}}OH\xrightarrow[{}]{{}}\] \[C{{H}_{3}}COOC{{H}_{3}}+HCl\]

C)

\[C{{H}_{3}}CN+{{H}_{2}}O\xrightarrow[{}]{NaOH}C{{H}_{3}}COONa+N{{H}_{3}}\]

D)

\[C{{H}_{3}}COON{{H}_{2}}+B{{r}_{2}}+4KOH\xrightarrow[{}]{{}}\] \[C{{H}_{3}}N{{H}_{2}}+{{K}_{2}}C{{O}_{3}}+2KBr+2{{H}_{2}}O\]

View Answer
179) The solubility product of PbS is\[3.4\times {{10}^{-28}}\]. If the concentration of\[P{{b}^{2+}}\]is\[1\times {{10}^{-2}}\]mol then the concentration of\[{{S}^{2-}}\]at which\[PbS\]will precipitated

A)

\[3.4\times {{10}^{-26}}\]

B)

\[3.4\times {{10}^{-30}}\]

C)

\[1\times {{10}^{-2}}\]

D)

\[3.4\times {{10}^{-22}}\]

View Answer
180) Formaldehyde reacts with ammonia to give following compound

A)

formalin

B)

formaldehyde ammonia

C)

hexamethylene tetraamine

D)

formamide

View Answer
181) Which of the following characteristics does not show byd-block elements?

A)

Variable valency

B)

Formation to complex compound

C)

Diamagnetism

D)

Paramagnetism

View Answer
182) \[RX+2Na+RX\xrightarrow[{}]{{}}R-R+2NaX\] The above reaction is called

A)

Wurtz reaction

B)

Williamson's synthesis

C)

Kolbe's electrolysis

D)

Sabatier-Sendern's reaction

View Answer
183) \[C{{H}_{3}}COOAg+B{{r}_{2}}\xrightarrow[{}]{\Delta }C{{H}_{3}}Br+AgBr+C{{O}_{2}}\] This reaction is called

A)

Hofmann mustard oil reaction

B)

Hell Volhard Zeiinsky reaction

C)

Hunsdiecker reaction

D)

Wurtz-Fittig reaction

View Answer
184) For precipitation

A)

Solubility product = ionic product

B)

Solubility product > ionic product

C)

Solubility product < ionic product

D)

None of the above

View Answer
185) HCHO + 40% strong alkaline solution\[\xrightarrow[{}]{{}}\] Products one of the product in this reaction is

A)

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

B)

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

C)

\[CH\equiv CH\]

D)

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

View Answer
186) Which of the following reaction will not affected by pressure?

A)

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

B)

\[{{N}_{2}}+{{O}_{2}}2NO\]

C)

\[2S{{O}_{2}}+{{O}_{2}}2S{{O}_{3}}\]

D)

\[PC{{l}_{3}}+C{{l}_{2}}PC{{l}_{5}}\]

View Answer
187) In an atom, two electrons do not have identical set of four quantum number. This statement is belong to

A)

Hund's law

B)

Aufbau's law

C)

\[(n+l)\] law

D)

Fault's law

View Answer
188) In froth floatation method of ore concen-tration, ore particles rise to the surface because

A)

they are light

B)

these are insoluble

C)

their surface do not wet with water easily

D)

these contain electric charge

View Answer
189) Which of the following is amphoteric oxide?

A)

\[MgO\]

B)

\[A{{l}_{2}}{{O}_{3}}\]

C)

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

D)

\[CuO\]

View Answer
190) Alkaline hydrolysis of a ester is called

A)

hydrolysis

B)

saponification

C)

neutralization

D)

hydrogenation

View Answer
191) The number of n electrons present in a aromatic ring are

A)

\[(4+2)n\]

B)

\[(4+2n)\]

C)

\[(4n+2)\]

D)

None of these

View Answer
192) Picric acid is

A)

ortho-nitrophenol

B)

2, 4, 6-trinitro benzoic acid

C)

2, 4, 6-trinitrophenol

D)

2, 4-dinitrophenol

View Answer
193) The correct radius order of atom, its cation and anion is

A)

atom < cation > anion

B)

atom > cation < anion

C)

atom = cation = anion

D)

atom > cation > anion

View Answer
194) \[C{{H}_{3}}C{{H}_{2}}I+NaOR\xrightarrow[{}]{{}}C{{H}_{3}}C{{H}_{2}}OR+NaI\] This reaction is

A)

Wurtz reaction

B)

Williamson's synthesis

C)

Wittig reaction

D)

Curtius reaction

View Answer
195) Saturated hydrocarbon gives

A)

free radical substitution

B)

free radical addition

C)

electrophilic substitution

D)

electrophilic addition

View Answer
196) \[{{N}_{2}}+{{O}_{2}}2NO;\] \[\Delta H=43.2\,kcal\] Equilibrium will go in forward direction

A)

on increasing temperature

B)

on decreasing temperature

C)

on increasing pressure

D)

on decreasing pressure

View Answer
197) Ethanal forms 3-hydroxy butanal on reaction with alkali. This reaction is

A)

Claisen condensation

B)

Polymerization

C)

Aldol condensation

D)

Reimer-Tiemann reaction

View Answer
198) Absolute alcohol can obtained from absolute spirit by which process

A)

steam distillation

B)

fractional distillation

C)

azerotropic distillation

D)

hydrolysis

View Answer
199) Ethyl alcohol is obtained from sugar by following enzyme reaction

A)

invertase

B)

zymase

C)

maltase

D)

diastase

View Answer
200) Brass is a

A)

alloy

B)

transition metal

C)

non-metal

D)

element

View Answer
201) If\[\frac{x-a}{b+c}+\frac{x-b}{c+a}+\frac{x-c}{a+b}=3,\]then the value of\[x\] is

A)

\[a+b+c\]

B)

\[abc\]

C)

1

D)

0

View Answer
202) If one root of the equation\[{{x}^{2}}+px+12=0\]is 4 when equation\[{{x}^{2}}+px+q=0\]have equal roots, then the value of\[q\]is

A)

\[\frac{4}{49}\]

B)

\[\frac{49}{4}\]

C)

\[4\]

D)

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

View Answer
203) The   real   roots   of   the   equation\[{{x}^{2}}+5|x|+4=0\]are

A)

\[(-1,-4)\]

B)

\[(\pm 1,\pm 4)\]

C)

\[(-4,4)\]

D)

None of these

View Answer
204) In a GP,\[(p+q)\]th term is 211 and\[(p-q)\]th term is n, then the value of pth term is

A)

\[\frac{m}{n}\]

B)

\[\sqrt{\frac{m}{n}}\]

C)

\[\sqrt{mn}\]

D)

\[\sqrt{\left( \frac{n}{m} \right)}\]

View Answer
205) If a, b, c are in AP, then\[\frac{a}{bc},\frac{1}{c},\frac{1}{b}\]will be in

A)

AP

B)

GP

C)

HP

D)

None of these

View Answer
206) If\[{{a}^{1/x}}={{b}^{1/y}}={{c}^{1/z}}\]and\[a,b,c\]are in GP, then\[x,y,z\]will be in

A)

AP

B)

GP

C)

HP

D)

None of these

View Answer
207) In the expansion of\[{{\left( \frac{x}{3}-\frac{2}{{{x}^{2}}} \right)}^{10}},\]the rth term contains\[{{x}^{4}},\]then the value of r is

A)

2

B)

3

C)

4

D)

5

View Answer
208) Sum of the series\[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....\]is

A)

\[log\text{ }2\]

B)

\[log\text{ }3\]

C)

\[2\text{ }log\text{ }2-1\]

D)

\[2\text{ }log\text{ }3-1\]

View Answer
209) If\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1,\]then\[ab+bc+ca\]lies in the interval

A)

\[\left[ \frac{1}{2},2 \right]\]

B)

\[[-1,2]\]

C)

\[\left[ -\frac{1}{2},1 \right]\]

D)

\[\left[ -1,\frac{1}{2} \right]\]

View Answer
210) In the 13 cricket players, 4 are bowlers and 2 are wicket keepers, then in how many ways can form a cricket team of 11 players in which one wicket keeper and atleast 3 bowlers included, is

A)

112

B)

22

C)

8

D)

1

View Answer
211) Two dice are tossed together. The probability that the sum of the numbers appeared on both dice is 5, is

A)

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

B)

\[\frac{1}{9}\]

C)

\[\frac{1}{12}\]

D)

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

View Answer
212) Between two players a coin is tossed 4 times. The probability that both players get equal number of heads, is

A)

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

B)

\[\frac{5}{256}\]

C)

\[\frac{35}{128}\]

D)

None of these

View Answer
213) A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random from this pack without replacement. The probability that atleast one of them will be an aces, is

A)

\[\frac{1}{5}\]

B)

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

C)

\[\frac{9}{20}\]

D)

\[\frac{1}{9}\]

View Answer
214) If\[A=\left[ \begin{matrix}    1 & 2 \\    2 & 3 \\ \end{matrix} \right],\]then the value of\[{{A}^{-1}}\]is

A)

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

B)

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

C)

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

D)

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

View Answer
215) The value of\[\left| \begin{matrix} b+c & a+b & a \\ c+a & b+c & b \\ a+b & c+a & c \\ \end{matrix} \right|\]is

A)

\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]

B)

\[0\]

C)

\[2abc(a+b+c)\]

D)

1

View Answer
216) If\[f:R\to R\]and\[f(x)=tan\text{ }x,\]then value of\[{{f}^{-1}}(1)\]is

A)

\[\left\{ n\pi +\frac{\pi }{4},n\in Z \right\}\]

B)

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

C)

does not exist

D)

None of these

View Answer
217) The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{1-\cos x}{{{x}^{2}}}\]is

A)

0

B)

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

C)

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

D)

1

View Answer
218) If function \[f(x)=\left\{ \begin{matrix} {{x}^{2}}/a & ,0\le x<1 \\ a & ,1\le x<\sqrt{2} \\ \frac{(2{{b}^{2}}-4b)}{{{x}^{2}}} & \sqrt{2}\le x<\infty \\ \end{matrix} \right.\] is continuous for\[0<x<\infty ,\]then the values of\[a\] and\[b\]are

A)

\[a=1,b=-1\]

B)

\[a=-1,b=1\]

C)

\[a=-1,b\text{ }=1+\sqrt{2}\]

D)

\[a=-1,b=\sqrt{2}-1\]

View Answer
219) The value of\[\underset{x\to \infty }{\mathop{\lim }}\,=\frac{{{x}^{2}}\sin \left( \frac{1}{x} \right)-x}{1-|x|}\]is

A)

\[-1\]

B)

\[1\]

C)

0

D)

\[\infty \]

View Answer
220) If\[{{x}^{y}}.{{y}^{x}}=1,\]then\[\frac{dy}{dx}\]is equal to

A)

\[\frac{y(x+y\log x)}{x(y+x\log y)}\]

B)

\[\frac{y(y+x\log y)}{x(y\log x+y)}\]

C)

\[-\frac{y(y+x\log y)}{x(y\log x+x)}\]

D)

\[-\frac{y(x+y\log x)}{x(y+x\log y)}\]

View Answer
221) If\[{{y}^{2}}=a{{e}^{-2x}}+\frac{2}{5}(\cos x-2\sin x),\]then the value of\[y\frac{dy}{dx}+{{y}^{2}}+\sin x\] is

A)

0

B)

\[-1\]

C)

1

D)

None of these

View Answer
222) If\[p(x)\]is a cubic polynomial and\[p(0)=4,\] \[p'(0)=3,p''(0)=4,p'''(0)=6,\]then the value of\[p'(-1)\]is

A)

2

B)

\[-10\]

C)

10

D)

None of these

View Answer
223) The angle of intersection of the curves\[y={{x}^{2}}\] and\[6y=7-{{x}^{3}}\]at point (1,1), is

A)

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

B)

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

C)

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

D)

\[\pi \]

View Answer
224) Curves\[a{{x}^{2}}+b{{y}^{2}}=1\]and\[a'{{x}^{2}}+b'{{y}^{2}}=1\]intersect each other orthogonally, if

A)

\[\frac{1}{a}+\frac{1}{a'}=\frac{1}{b}+\frac{1}{b'}\]

B)

\[\frac{1}{a}+\frac{1}{b}=\frac{1}{a'}+\frac{1}{b'}\]

C)

\[\frac{1}{a}-\frac{1}{b}=\frac{1}{a'}-\frac{1}{b'}\]

D)

None of these

View Answer
225) In the interval\[[-1,2],\]function\[f(x)=|x|+|x-1|\]will be

A)

constant

B)

increasing

C)

decreasing

D)

None of these

View Answer
226) The equation of tangent to the parabola \[{{y}^{2}}=4x\]at point (1, 2) is

A)

\[x-y+1=0\]

B)

\[x+y+1=0\]

C)

\[x+y-1=0\]

D)

\[x-y-1=0\]

View Answer
227) The distance covered by a particle in t second is\[s=a{{e}^{t}}+b{{e}^{-t}}\]. At time t the acceleration of the particle is

A)

\[s\,m/{{s}^{2}}\]

B)

\[as\,m/{{s}^{2}}\]

C)

\[bs\text{ }m/{{s}^{2}}\]

D)

\[-bs\text{ }m/{{s}^{2}}\]

View Answer
228) The value of\[\int{{{x}^{2}}{{e}^{{{x}^{3}}}}}\cos ({{e}^{{{x}^{3}}}})dx\] is

A)

\[\sin ({{e}^{{{x}^{3}}}})+c\]

B)

\[\frac{1}{3}\sin ({{e}^{{{x}^{3}}}})+c\]

C)

\[-\frac{1}{3}\sin ({{e}^{{{x}^{3}}}})+c\]

D)

\[3\sin ({{e}^{{{x}^{3}}}})+c\]

View Answer
229) If \[\int_{0}^{\infty }{\frac{{{x}^{2}}dx}{({{x}^{2}}+{{a}^{2}})({{x}^{2}}+{{b}^{2}})({{x}^{2}}+{{c}^{2}})}}\] \[=\frac{\pi }{2(a+b)(b+c)(c+a)},\]then the value of \[\int_{0}^{\infty }{\frac{dx}{({{x}^{2}}+4)({{x}^{2}}+9)}}\]is

A)

\[\frac{\pi }{20}\]

B)

\[\frac{\pi }{40}\]

C)

\[\frac{\pi }{60}\]

D)

\[\frac{\pi }{80}\]

View Answer
230) If\[\int{\frac{dx}{x\sqrt{1-{{x}^{3}}}}=a\log \left| \frac{\sqrt{(1-{{x}^{3}})}-1}{\sqrt{(1-{{x}^{3}})}+1} \right|}+b,\]then the value of a is

A)

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

B)

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

C)

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

D)

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

View Answer
231) If\[f(a-x)=f(x),\]then the value of\[\int_{0}^{a}{xf(x)}dx\]is

A)

\[a\int_{0}^{a}{f(x)}dx\]

B)

\[\frac{a}{2}\int_{0}^{a}{x\,f(x)\,}dx\]

C)

\[\frac{{{a}^{2}}}{2}\int_{0}^{a}{f(x)\,}dx\]

D)

None of these

View Answer
232) The value of\[\int_{0}^{\pi /4}{\frac{\sec x\cos ecx}{\log (\tan x)}}dx\] is

A)

0

B)

1

C)

does not exist

D)

None of these

View Answer
233) The area of the region bounded by the parabola\[{{y}^{2}}=4\text{ a}x\]and its latusrectum is

A)

\[\frac{4a}{3}sq\,unit\]

B)

\[\frac{4{{a}^{3}}}{3}sq\,unit\]

C)

\[\frac{8a}{3}sq\,unit\]

D)

\[\frac{8{{a}^{2}}}{3}sq\,unit\]

View Answer
234) If in the interval\[\left[ 0,\frac{\pi }{2} \right]\]the area of the region bounded by the curve\[y=sin\text{ }x\]and\[x-\]axis is A sq unit, then in the same interval, the area of the region bounded by the curve\[y=cos\text{ }x\] and\[x-\]axis is

A)

A sq unit

B)

\[\frac{\pi }{2}-A\] sq unit

C)

\[-A\] sq unit

D)

None of these

View Answer
235) The equation of the curve which satisfies the differential equation\[(1+{{y}^{2}})dx-xy\,dy=0\] and passes through the point (1, 0) is

A)

\[{{x}^{2}}+{{y}^{2}}=1\]

B)

\[{{x}^{2}}-{{y}^{2}}=1\]

C)

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

D)

None of these

View Answer
236) The solution of the differential equation \[\frac{dy}{dx}=\frac{x+y+7}{2x+2y+3}\]is

A)

\[6(x+y)-11\text{ }log\text{ (}3x+3y+10)=9x+c\]

B)

\[6(x+y)+11\text{ }log\text{ (}3x+3y+10)=9x+c\]

C)

\[6(x+y)-\log \left( x+y+\frac{10}{3} \right)=9x+c\]

D)

\[6(x+y)\left( x+y+\frac{10}{3} \right)=9x+c\]

View Answer
237) If \[{{\left( \frac{1-i}{1+i} \right)}^{100}}=a+ib,\]then

A)

\[a=1,b=0\]

B)

\[a=0,b=1\]

C)

\[a=-1,b=2\]

D)

\[a=2,b=-1\]

View Answer
238) If complex numbers\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]represents the vertices of an equilateral triangle such that\[|{{z}_{1}}|=|{{z}_{2}}|=|{{z}_{3}}|,\]then

A)

\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\le 0\]

B)

\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\ge 0\]

C)

\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]

D)

None of these

View Answer
239) If\[m\sin \theta =n\sin (\theta +2\alpha ),\]then the value of\[\tan (\theta +\alpha )\cot \alpha \]is

A)

\[\frac{m+n}{m-n}\]

B)

\[\frac{m-n}{m+n}\]

C)

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

D)

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

View Answer
240) If\[A+B+C=\pi ,\]then\[tan\text{ }A+tan\text{ }B+tan\text{ }C\]is equal to

A)

\[-1\]

B)

1

C)

\[tan\text{ }A\text{ }tan\text{ }B\text{ }tan\text{ }C\]

D)

\[cot\text{ }A\text{ }cot\text{ }B\text{ }cot\text{ }C\]

View Answer
241) The maximum value of\[a\text{ }cos\theta +b\text{ }sin\theta \]is

A)

\[a+b\]

B)

\[|a|+|b|\]

C)

\[a-b\]

D)

\[\sqrt{{{a}^{2}}+{{b}^{2}}}\]

View Answer
242) The general solution of the equation \[(\sqrt{3}-1)\sin \theta +(\sqrt{3}+1)\cos \theta =2\]is

A)

\[2n\pi \pm \frac{\pi }{4}+\frac{\pi }{12}\]

B)

\[n\pi +{{(-1)}^{n}}\frac{\pi }{4}+\frac{\pi }{12}\]

C)

\[2n\pi \pm \frac{\pi }{4}-\frac{\pi }{12}\]

D)

\[n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{12}\]

View Answer
243) The value of\[{{\cot }^{-1}}\left[ \frac{\sqrt{(1+\sin x)}+\sqrt{(1-\sin x)}}{\sqrt{(1-\sin x)}-\sqrt{(1+\sin x)}} \right]\] is

A)

\[\frac{x}{2}\]

B)

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

C)

\[\pi -x\]

D)

\[2\pi -x\]

View Answer
244) In\[\Delta ABC,\]the value of\[a(b\cos C-c\cos B)\]is

A)

0

B)

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

C)

\[{{b}^{2}}-{{c}^{2}}\]

D)

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

View Answer
245) In\[\Delta \]ABC, if\[\angle A=30{}^\circ ,c=7\sqrt{3}\]and\[\angle C=90{}^\circ ,\] then the value of a is

A)

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

B)

\[7\sqrt{3}\]

C)

\[\frac{7}{2}\sqrt{3}\]

D)

\[7\sqrt{2}\]

View Answer
246) The equation of straight line which cut equal intercepts on axes and passes through the point\[(1,-2)\]is

A)

\[x+y=1\]

B)

\[x-y=1\]

C)

\[x-y=2\]

D)

\[x+y+1=0\]

View Answer
247) If the equation of tangent to a circle at point (3, 5) is\[2x-y-1=0\]and its centre lies on \[x+y=5,\]then the equation of circle is

A)

\[{{x}^{2}}+{{y}^{2}}+6x-16y+28=0\]

B)

\[{{x}^{2}}+{{y}^{2}}-6x-16y+28=0\]

C)

\[{{x}^{2}}+{{y}^{2}}+6x+6y+28=0\]

D)

\[{{x}^{2}}+{{y}^{2}}-6x-6y-28=0\]

View Answer
248) The curve represented by the parametric equations \[x=3(\cos t+\sin t),y=4\]\[(cos\text{ }t-sin\text{ }t)\]is

A)

a parabola

B)

an ellipse

C)

a hyperbola

D)

None of these

View Answer
249) Eccentricity of the hyperbola\[{{x}^{2}}-{{y}^{2}}=4\]is

A)

\[\sqrt{2}\]

B)

\[2\sqrt{3}\]

C)

\[\sqrt{3}\]

D)

\[3\sqrt{3}\]

View Answer
250) The equation of the normal to the parabola \[{{y}^{2}}=4x\]which is parallel to the line \[y=2x-5,\]is

A)

\[y=2x\]

B)

\[y=2x-10\]

C)

\[y=2x+10\]

D)

\[y=2x-12\]

View Answer
251) If (2, 3, 5) is one end of a diameter of the sphere\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2z+20=0,\]then the coordinates of the other end of the diameter are

A)

\[(4,\text{ }3,\text{ }5)\]

B)

\[(4,9,-3)\]

C)

\[(4,\text{ }3,-3)\]

D)

\[(4,-9,3)\]

View Answer
252) If\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0},|\overrightarrow{a}|=3,|\overrightarrow{b}|=5,|\overrightarrow{c}|=7,\]then angle between a and b is

A)

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

B)

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

C)

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

D)

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

View Answer
253) If\[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\]are three unit vectors,\[\overrightarrow{b}\ne \overrightarrow{c}\]and \[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})=\frac{1}{2}\overrightarrow{b},\] then angle between\[\overrightarrow{a}\]and\[\overrightarrow{c}\]is

A)

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

B)

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

C)

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

D)

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

View Answer
254) The roots of the equation\[a{{x}^{2}}+bx+c=0\]are \[\alpha ,\beta \]and roots of\[A{{x}^{2}}+Bx+C=0\]are \[\alpha -k,\beta -k,\]then the value of\[\frac{({{B}^{2}}-4AC)}{({{b}^{2}}-4ac)}\]is

A)

\[{{\left( \frac{A}{a} \right)}^{2}}\]

B)

\[x\le 0\]

C)

\[0\]

D)

\[1\]

View Answer
255) The value of\[x\]which satisfied the in equation \[{{x}^{3}}+1>{{x}^{2}}+x,\]is:

A)

\[x\ge 0\]

B)

\[x\le 0\]

C)

\[x\ge -1\]

D)

\[-1\le x\le 1\]

View Answer
256) If\[\frac{1}{q+r},\frac{1}{r+p},\frac{1}{p+q}\]are in AP, then

A)

\[p,q,r\]will be in AP

B)

\[\frac{1}{p},\frac{1}{q},\frac{1}{r}\]will be in AP

C)

\[{{p}^{2}},{{q}^{2}},{{r}^{2}}\]will be in AP

D)

\[\frac{1}{{{p}^{2}}},\frac{1}{{{q}^{2}}},\frac{1}{{{r}^{2}}}\]will be in AP

View Answer
257) The roots of the equation\[{{x}^{2}}-3x+a=0\]are\[\alpha ,\beta \] and roots of the equation \[{{x}^{2}}-12x+b=0\]are\[\gamma ,\delta \]and\[\alpha ,\beta ,\gamma ,\delta \]are in GP, then

A)

\[a=2,b=32\]

B)

\[a=3,b=12\]

C)

\[a=4,b=16\]

D)

\[a=12,b=3\]

View Answer
258) The sum of the infinite terms of the series\[1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+...\]is

A)

\[\frac{16}{35}\]

B)

\[\frac{11}{8}\]

C)

\[\frac{35}{16}\]

D)

\[\frac{9}{16}\]

View Answer
259) If\[x,2x+2,3x+3,...\]are in GP, then fourth term of this series is

A)

13.5

B)

\[-13.5\]

C)

27

D)

\[-27\]

View Answer
260) The number of total terms in the expansion of\[{{(1+3\sqrt{2}x)}^{9}}+{{(1-3\sqrt{2}x)}^{9}}\]is

A)

9

B)

0

C)

5

D)

10

View Answer
261) The value of\[\frac{1+\frac{1}{2!}+\frac{2}{3!}+\frac{{{2}^{2}}}{4!}+\frac{{{2}^{3}}}{5!}+.....}{1+\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+...}\]is

A)

\[\frac{e}{4}\]

B)

\[\frac{e}{2}\]

C)

\[8e\]

D)

\[\frac{e({{e}^{2}}-1)}{2({{e}^{2}}+1)}\]

View Answer
262) If n is a multiple of 3, then coefficient of\[{{x}^{n}}\]in the expansion of\[log(1+x+{{x}^{2}})\]is (where\[|x|<2\])

A)

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

B)

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

C)

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

D)

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

View Answer
263) If a, b, c are different positive numbers, then the value of\[(b+ca)(c+a-b)(a+b-c)\]\[-abc\]will be

A)

positive

B)

negative

C)

zero

D)

None of these

View Answer
264) If set A have 10 elements, then the number of relations from A to A is

A)

\[10!\]

B)

\[{{10}^{10}}\]

C)

\[{{2}^{10}}\]

D)

\[{{2}^{10}}-1\]

View Answer
265) If two dice are thrown together. Probability that the sum of the numbers appearing on them is 7, is

A)

\[\frac{5}{36}\]

B)

\[\frac{1}{6}\]

C)

\[\frac{7}{36}\]

D)

\[\frac{8}{36}\]

View Answer
266) If \[A=\left[ \begin{matrix}    1 & 2 \\    3 & -5 \\ \end{matrix} \right],B=\left[ \begin{matrix}    1 & 0 \\    0 & 2 \\ \end{matrix} \right]\]and X is a matrix such that\[A=BX,\]then the value of X is

A)

\[\left[ \begin{matrix}    2 & 4 \\    3 & -5 \\ \end{matrix} \right]\]

B)

\[\frac{1}{2}\left[ \begin{matrix}    2 & 4 \\    3 & -5 \\ \end{matrix} \right]\]

C)

\[\left[ \begin{matrix}    -2 & 4 \\    3 & 5 \\ \end{matrix} \right]\]

D)

\[\frac{1}{2}\left[ \begin{matrix}    -2 & 4 \\    3 & 5 \\ \end{matrix} \right]\]

View Answer
267) The system of equations\[x+2y+3z=1,\]\[2x+y+3z=2,\]\[5x+5y+9z=4\]have

A)

no solution is possible

B)

only one solution

C)

infinite solutions

D)

None of the above

View Answer
268) If\[{{\left| \begin{matrix}    4 & 1 \\    2 & 1 \\ \end{matrix} \right|}^{2}}=\left| \begin{matrix}    3 & 2 \\    1 & x \\ \end{matrix} \right|-\left| \begin{matrix}    x & 3 \\    -2 & 1 \\ \end{matrix} \right|,\]then the value of\[x\]is

A)

6

B)

7

C)

8

D)

11

View Answer
269) If\[\left| \begin{matrix}    a+x & a-x & a-x \\    a-x & a+x & a-x \\    a-x & a-x & a+x \\ \end{matrix} \right|=0,\]then the values of \[x\]will be

A)

\[x=0,x=4a\]

B)

\[x=0,x=a\]

C)

\[x=0,\text{ }x=2a\]

D)

\[x=0,\text{ }x=3a\]

View Answer
270) If\[\Sigma x=15,\Sigma y=40,\Sigma xy=110\]and\[n=5,\]then the value of cov\[(x,y)\]is

A)

\[-2\]

B)

2

C)

22

D)

None of these

View Answer
271) If\[f:N\to R,f(x)=\frac{(2x-1)}{2}\]and\[g:Q\to R,g(x)=x+2\]are two functions, then the value of\[(gof)\left( \frac{3}{2} \right)\]is

A)

1

B)

3

C)

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

D)

None of these

View Answer
272) The value of\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{\left[ \frac{1}{2}(1-\cos 2x) \right]}}{x}\]is

A)

1

B)

\[-1\]

C)

0

D)

None of these

View Answer
273) If function \[f(x)=\left\{ \begin{matrix}    \frac{\sqrt{(1+px)}-\sqrt{(1-px)}}{x}, & x<0 \\    \frac{2x+1}{x-2} & ,0\le x\le 1 \\ \end{matrix} \right.\] is continuous in the interval\[[-1,1],\]then the value of p is

A)

\[-1\]

B)

\[-1/2\]

C)

1/2

D)

1

View Answer
274) If\[y=\log |x|\]and\[x\ne 0,\]then\[\frac{dy}{dx}\]is equal to

A)

\[\frac{1}{x}\]

B)

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

C)

\[\frac{1}{|x|}\]

D)

None of these

View Answer
275) If\[y={{\sin }^{-1}}\sqrt{(1-x)}+{{\cos }^{-1}}\sqrt{x},\]then\[\frac{dy}{dx}\]is equal to

A)

\[\frac{-1}{\sqrt{x(1-x)}}\]

B)

\[\frac{1}{\sqrt{x(1+x)}}\]

C)

\[\frac{1}{\sqrt{x(1-x)}}\]

D)

None of these

View Answer
276) If\[y=b\cos \left\{ n\log \left( \frac{x}{n} \right) \right\},\]then which of the following is correct?

A)

\[{{x}^{2}}{{y}_{2}}+x{{y}_{1}}-{{n}^{2}}y=0\]

B)

\[{{x}^{2}}{{y}_{2}}-x{{y}_{1}}-{{n}^{2}}y=0\]

C)

\[{{x}^{2}}{{y}_{2}}+x{{y}_{1}}+{{n}^{2}}y=0\]

D)

\[{{x}^{2}}{{y}_{2}}-x{{y}_{1}}+{{n}^{2}}y=0\]

View Answer
277) If tangent to the curve\[x=a{{t}^{2}},\text{ }y=2at\]is perpendicular to\[x-\]axis, then point of contact is

A)

(0, 0)

B)

(0, a)

C)

(a, 0)

D)

(a, a)

View Answer
278) The equation of ellipse whose vertex is (±5,0) and focus is (±4,0), is

A)

\[9{{x}^{2}}+25{{y}^{2}}=225\]

B)

\[25{{x}^{2}}+9{{y}^{2}}=225\]

C)

\[3{{x}^{2}}+4{{y}^{2}}=192\]

D)

None of these

View Answer
279) The value of\[\int{\frac{dx}{{{e}^{x}}+{{e}^{-x}}}}\]is

A)

\[{{\tan }^{-1}}({{e}^{x}})+c\]

B)

\[\log ({{e}^{x}}+{{e}^{-x}})+c\]

C)

\[\log ({{e}^{2x}}+1)+c\]

D)

None of these

View Answer
280) The value of\[\int{{{e}^{x}}\left\{ \frac{(x-1)}{{{(x+1)}^{3}}} \right\}}dx\]is

A)

\[\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+c\]

B)

\[\frac{{{e}^{x}}}{(x+1)}+c\]

C)

\[\frac{-{{e}^{x}}}{(x+1)}+c\]

D)

\[\frac{-{{e}^{x}}}{{{(x+1)}^{2}}}+c\]

View Answer
281) The value of\[\int_{-\pi /2}^{\pi /2}{\log \left( \frac{2-\sin \theta }{2+\sin \theta } \right)dx}\]is

A)

0

B)

1

C)

2

D)

None of these

View Answer
282) The value of\[\int_{0}^{\pi /4}{\log (1+\tan x)dx}\]is

A)

\[\frac{1}{2}\pi \log 8\]

B)

\[\frac{1}{4}\pi \log 2\]

C)

\[\frac{1}{8}\pi \log 2\]

D)

\[\frac{1}{4}\pi \log 8\]

View Answer
283) The maximum value of\[f(x)=\int_{1}^{x}{|t|}\,dt\]in the interval\[\left[ -\frac{1}{2},\frac{1}{2} \right]\]is

A)

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

B)

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

C)

\[-\frac{5}{8}\]

D)

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

View Answer
284) The area of the region bounded by the curve \[y=4+3x-{{x}^{2}}\]and\[x-\]axis is

A)

\[\left( \frac{125}{3} \right)sq\,units\]

B)

\[\left( \frac{125}{6} \right)sq\,units\]

C)

\[\left( \frac{125}{4} \right)sq\,units\]

D)

None of these

View Answer
285) If the area of the region bounded by the curve \[y=8{{x}^{2}}-{{x}^{5}},\]straight line\[x=0\]and\[x=a\]and the\[x-\]axis is\[\frac{16}{3},\]then the value of a is

A)

\[{{(8-4\sqrt{2})}^{1/3}}\]

B)

\[{{(8+\sqrt{2})}^{1/3}}\]

C)

no value of\[a\]

D)

None of these

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

A)

\[y+2x=\frac{{{c}^{2}}{{x}^{2}}}{y}\]

B)

\[y-2x=\frac{{{c}^{2}}{{x}^{2}}}{y}\]

C)

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

D)

None of these

View Answer
287) The solution of the differential equation \[\frac{dy}{dx}+\frac{1}{x}\tan y=\frac{1}{{{x}^{2}}}\tan y\sin y\]is

A)

\[2x=\frac{(1+2c{{x}^{2}})}{\sin y}\]

B)

\[2x=\sin y(1+2c{{x}^{2}})\]

C)

\[2x+\sin y(1+c{{x}^{2}})=0\]

D)

None of the above

View Answer
288) If\[{{\alpha }_{1}},{{\alpha }_{2}},....,{{\alpha }_{n-1}}\]are n roots of unity, then the value of\[(1-{{\alpha }_{1}})(1-{{\alpha }_{2}}).....(1-{{\alpha }_{n-1}})\]is

A)

\[n\]

B)

\[n-1\]

C)

\[-1\]

D)

\[1\]

View Answer
289) If\[\left| \frac{({{z}_{1}}-2{{z}_{2}})}{(2-{{z}_{1}}{{\overline{z}}_{2}})} \right|=1\]and\[|{{z}_{2}}|\ne 1,\]where\[{{z}_{1}}\]and\[{{z}_{2}}\]are complex numbers, then the value of\[|{{z}_{1}}|\]is

A)

1

B)

\[-1\]

C)

2

D)

\[-2\]

View Answer
290) The value of\[sin\text{ }20{}^\circ sin\text{ }40{}^\circ sin\text{ }60{}^\circ sin\text{ }80{}^\circ \]is:

A)

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

B)

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

C)

\[-\frac{5}{16}\]

D)

\[\frac{5}{16}\]

View Answer
291) If\[A+B+C=\frac{\pi }{2},\]then the value of \[sin\text{ }2A+sin\text{ }2B+sin\text{ }2C\]is

A)

\[2\text{ }sin\text{ }A\text{ }sin\text{ }B\text{ }sin\text{ }C\]

B)

\[2\text{ }cos\text{ }A\text{ }cos\,B\text{ }cos\text{ }C\]

C)

\[4\text{ }sin\text{ }A\text{ }sin\text{ }B\text{ }sin\text{ }C\]

D)

\[4\text{ }cos\text{ }A\text{ }cos\text{ B }cos\text{ }C\]

View Answer
292) The period of\[sin4\text{ }x+cos4\text{ }x\]is

A)

\[\pi \]

B)

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

C)

\[2\pi \]

D)

None of these

View Answer
293) In the interval\[0<x<2\pi ,\]the solution of \[(2\text{ }cos\text{ }x-1)(3+2\text{ }cos\text{ }x)=0\]is

A)

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

B)

\[\left\{ \frac{\pi }{3},\frac{5\pi }{3} \right\}\]

C)

\[\left\{ \frac{\pi }{3},\frac{5\pi }{3},{{\cos }^{-1}}\left( -\frac{3}{2} \right) \right\}\]

D)

None of the above

View Answer
294) If in the\[\Delta ABC,\angle A=30{}^\circ ,c=10,\angle C=90{}^\circ ,\]then the value of b is

A)

5

B)

\[5\sqrt{3}\]

C)

10

D)

None of these

View Answer
295) If\[{{\sin }^{-1}}\frac{x}{5}+\cos e{{c}^{-1}}\frac{5}{4}=\frac{\pi }{2},\]then the value of\[x\]is

A)

1

B)

3

C)

4

D)

5

View Answer
296) A line is perpendicular to the line\[3x+y=3\] and passes through the point\[(-2,2),\]then its intercept on y-axis is

A)

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

B)

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

C)

\[1\]

D)

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

View Answer
297) The locus of the foot of the perpendicular on the line\[\frac{x}{a}+\frac{y}{b}=1,\]where\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{c}^{2}}}\]from the origin, is

A)

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

B)

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

C)

\[{{x}^{2}}+{{y}^{2}}=\frac{c}{2}\]

D)

None of these

View Answer
298) The focus of parabola\[{{y}^{2}}=4y-4x\]is

A)

(0, 2)

B)

(1, 2)

C)

(2, 0)

D)

(2, 1)

View Answer
299) The focus of the hyperbola\[4{{x}^{2}}-9{{y}^{2}}-36=0\]are

A)

\[(\pm \sqrt{11},0)\]

B)

\[(0,\pm \sqrt{12})\]

C)

\[(\pm \sqrt{12},0)\]

D)

\[(\pm \sqrt{13},0)\]

View Answer
300) The equation of the tangent of the hyperbola \[2{{x}^{2}}-3{{y}^{2}}=6\]which is parallel to the line \[y=3x+4,\]is

A)

\[y=3x-5\]

B)

\[y=3x+5\]

C)

\[y=3x+5\]and\[y=3x-5\]

D)

None of the above

View Answer

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Rajasthan PET Solved Paper-2005 Total Questions - 300