Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2003

BCECE Engineering Solved Paper-2003 Total Questions - 150

1) The height y and distance x along the horizontal plane of projectile on a certain planet (with no surrounding) are given by: \[y=(8t-5{{t}^{2}})\] metre and x = 6t metre where t is in second. The velocity with which the projectile is projected is:

A)

8 m/s

B)

                                       6 m/s

C)

       10 m/s

D)

       data is not sufficient

View Answer
2) A body of mass a, moving with a velocity b collides with a body of mass c, at rest and sticks to it. They move together with a velocity given by:

A)

\[\frac{ac}{a+b}\]

B)

       \[\frac{ab}{a+c}\]

C)

       \[\frac{a+b}{ac}\]

D)

       \[\frac{b+c}{ab}\]

View Answer
3) The refractive index of a material is given by the equation \[n=\frac{A+B}{{{\lambda }^{2}}},\] where A and B are constants. The dimensional formula for B is:

A)

\[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]

B)

       \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{-2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]

C)

       \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]

D)

       \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{0}}}{{\text{L}}^{2}}{{\text{T}}^{0}}\text{ }\!\!]\!\!\text{ }\]

View Answer
4) A satellite is orbiting around the earth. By what percentage should we increase its velocity, so as to enable it escape away from the earth?

A)

41.4%

B)

       50%

C)

       82.8%

D)

       100%

View Answer
5) At what temperature, the hydrogen molecule will escape from earths surface?

A)

\[{{10}^{1}}K\]

B)

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

C)

       \[{{10}^{3}}K\]

D)

       \[{{10}^{4}}K\]

View Answer
6) If the earth is at one-fourth of its present distance from the sun, the duration of the year will be:

A)

half the present year

B)

       one-eighth the present year

C)

       one-fourth the present year

D)

       one-sixth the present year

View Answer
7) An observer moves towards a stationary source of sound with a velocity one-tenth the velocity of sound. The apparent increase in frequency is:

A)

zero

B)

       10%

C)

       5%

D)

       0.1%

View Answer
8) When two conductors of charges and potentials \[{{C}_{1}},\,{{V}_{1}}\] and \[{{C}_{2}},\,{{V}_{2}}\] respectively are joined, the common potential will be:

A)

\[\frac{{{V}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{V}_{1}}+{{V}_{2}}}\]

B)

       \[\frac{{{C}_{1}}{{V}_{1}}^{2}+{{C}_{2}}{{V}_{2}}^{2}}{{{V}_{1}}^{2}+{{V}_{2}}^{2}}\]

C)

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

D)

       \[\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}^{2}}{{{C}_{1}}+{{C}_{2}}}\]

View Answer
9) A weightless thread can bear tension upto 3.7 kg-wt. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g=10\,m/{{s}^{-2}},\] then the maximum angular velocity of the stone will be:

A)

4 rad/s

B)

       16 rad/s

C)

       \[\sqrt{21}\]rad/s

D)

       2 rad/s

View Answer
10) The effective length of a magnet is 31.4 cm and its pole strength is 0.5 Am. If it is bent in the form of semicircle, what will be its magnetic moment then?

A)

\[0.12\,A{{m}^{2}}\]

B)

       \[0.1\,A{{m}^{2}}\]

C)

       \[0.05\,A{{m}^{2}}\]

D)

       \[0.01\,A{{m}^{2}}\]

View Answer
11) Four molecules of a gas have speeds 1, 2, 3 and \[4\,km{{s}^{-1}}\]. The value of ms speed of the gas molecules is:

A)

\[\frac{\text{1}}{\text{2}}\sqrt{\text{15}}\text{km}{{\text{s}}^{\text{-1}}}\]

B)

       \[\frac{\text{1}}{\text{2}}\sqrt{\text{10}}\text{km}{{\text{s}}^{\text{-1}}}\]

C)

       \[\text{2}\text{.5km}{{\text{s}}^{\text{-1}}}\]

D)

       \[\sqrt{\frac{15}{2}}\text{km}{{\text{s}}^{\text{-1}}}\]

View Answer
12) If there is change of angular momentum from J to 5 J in 5 s, then the torque is:

A)

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

B)

       \[\frac{\text{4J}}{\text{5}}\]

C)

       \[\frac{\text{5J}}{4}\]

D)

       None of these

View Answer
13) Two springs having force constants k each are arranged in parallel and in series. A mass M is attached to two arrangements separately. If time period in first case is \[{{T}_{1}}\] and in second case is \[{{T}_{2}}\] then ratio \[\frac{{{T}_{1}}}{{{T}_{2}}}\] is:

A)

              1.5

B)

       3.2

C)

       0.5

D)

       2.1

View Answer
14) If the work done in blowing a bubble of volume V is W, then the work done in blowing a soap bubble of volume 2V will be:

A)

W

B)

       2 W

C)

       \[\sqrt{2}\]W

D)

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

View Answer
15) An ideal monoatomic gas is taken round the cycle ABCDA as shown in figure. The work done during the cycle is :

A)

\[PV\]

B)

\[2PV\]

C)

\[\frac{PV}{2}\]

D)

\[\text{zero}\]

View Answer
16) A proton of energy 2 MeV is moving in a circular path in a magnetic field. What should be the energy of a deuteron, so that it also describes circular path of radius equal to that of the proton?

A)

1 MeV

B)

       2 MeV

C)

       4 MeV

D)

       0.5 MeV

View Answer
17) A gas at NTP is suddenly compressed to one-fourth of its original volume. If \[\gamma \] is supposed to be 3/2, then the final pressure is:

A)

4 atm

B)

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

C)

       8 atm

D)

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

View Answer
18) In   a   series   combination\[R=300\,\Omega ,\]\[\text{L=0}\text{.9H,}\]\[\text{C=2}\text{.0}\,\text{F,}\]\[\omega =1000\,\text{rad/s,}\]the impedance of the circuit is :

A)

1300\[\Omega \]

B)

       900\[\Omega \]

C)

       500\[\Omega \]

D)

       400\[\Omega \]

View Answer
19) n identical spherical drops each of radius r are charged to same potential V. They combine to form a bigger drop. The potential of the big drop will be:

A)

\[{{n}^{1/3}}V\]

B)

       \[{{n}^{2/3}}V\]

C)

       V

D)

       \[nV\]

View Answer
20) The wavelength of maximum energy, released during   an   atomic   explosion   was \[2.93\,\times {{10}^{-10}}\,m\]. Given that the Wiens constant is \[2.93\,\times {{10}^{-10}}m-K,\] the maximum temperature attained must be of the order of:

A)

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

B)

       \[{{10}^{7}}K\]

C)

       \[{{10}^{-3}}K\]

D)

       \[5.86\,\times {{10}^{7}}K\]

View Answer
21) The pressure and density of a diatomic gas \[\left( \gamma =\frac{7}{5} \right)\]change adiabatically from (P, d) to (P, d). If \[\frac{d}{d}=32,\] then\[\frac{P}{P}\] should be:

A)

\[\frac{1}{128}\]

B)

                                      32

C)

       128

D)

       None of these

View Answer
22) A piece of wax weighs 18.03 g in air. A piece of metal is found to weigh 17.03 g in water. It is tied to the wax and both together weigh 15.23 g in water. Then, the specific gravity of wax is:

A)

\[\frac{18.03}{17.03}\]

B)

       \[\frac{17.03}{18.03}\]

C)

       \[\frac{18.03}{19.83}\]

D)

       \[\frac{15.03}{17.83}\]

View Answer
23) If a mica sheet of thickness t and refractive index \[\mu \] is placed in the path of one of interfering beams in a double slit experiment, then displacement of fringes will be:

A)

\[\frac{D}{d}\mu t\]

B)

       \[\frac{D}{d}(\mu -1)t\]

C)

       \[\frac{D}{d}(\mu +1)t\]

D)

       \[\frac{D}{d}({{\mu }^{2}}-1)t\]

View Answer
24) A ray of light propagates from glass (refractive index\[=\frac{3}{2})\] to water (refractive index\[=\frac{4}{3}).\]                                                                        The value of the critical angle is:

A)

\[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]

B)

       \[{{\sin }^{-1}}\left( \sqrt{\frac{9}{8}} \right)\]

C)

       \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]

D)

       \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]

View Answer
25) A ray of light suffers minimum deviation when incident at 60° prism of refractive index \[\sqrt{2.}\] The angle of incidence is:

A)

\[{{\sin }^{-1}}(0.8)\]

B)

       \[60{}^\circ \]

C)

       \[45{}^\circ \]

D)

       \[30{}^\circ \]

View Answer
26) Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B.

A)

\[R\]

B)

       \[5R\]

C)

       \[2R\]

D)

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

View Answer
27) A gas in an air tight container is heated from \[25{}^\circ C\] to \[90{}^\circ C\]. The density of gas will:

A)

increase slightly

B)

       remain the same

C)

       increase considerably

D)

       decrease slightly

View Answer
28) If 2% of the main current is to be passed through the galvanometer of resistance G, the resistance of the shunt required is:

A)

\[\frac{G}{49}\]

B)

       \[\frac{G}{50}\]

C)

       49 G

D)

       50 G

View Answer
29) The current in self-inductance L = 40 mH is increased uniformly from 1 A to 11 A in 4 milliseconds. The induced emf produced in L during this process will be:

A)

100 V

B)

                                       0.2V

C)

       440 V

D)

       40 V

View Answer
30) \[{{\text{H}}^{\text{+}}}\]\[\text{H}{{\text{e}}^{2+}}\] and \[{{\text{O}}^{\text{2-}}}\] all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of \[{{\text{H}}^{\text{+}}}\text{,}\] \[\text{H}{{\text{e}}^{\text{2+}}}\] and \[{{\text{O}}^{\text{2-}}}\] are 1 amu, 4 amu and 16 amu, respectively. Then:

A)

\[{{\text{H}}^{\text{+}}}\] will be deflected most

B)

       \[{{\text{O}}^{\text{2}}}\] will be deflected most

C)

       \[H{{e}^{\text{2+}}}\]and \[{{\text{O}}^{\text{2-}}}\] will be deflected most

D)

       all will be deflected most

View Answer
31) The current gain of a transistor in common emitter mode is 49. The change in collector current and emitter current corresponding to the change in base current by \[5.0\,\mu A\] are:

A)

\[\Delta iC=245\,\mu A,\]\[\Delta {{i}_{E}}=250\,\mu A\]

B)

       \[\Delta {{i}_{C}}=252\,\mu A,\,\]\[\,\Delta {{i}_{E}}=145\mu A\]

C)

       \[\Delta {{i}_{C}}=125\,\mu A,\,\]\[\Delta {{i}_{E}}=250\mu A\]

D)

       \[\Delta {{i}_{C}}=252\,\mu A,\]\[\Delta {{i}_{E}}=230\mu A\]

View Answer
32) In hydrogen atom when an electron jumps from second to first orbit, the wavelength of line emitted is :

A)

\[0.563\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

B)

       \[4861\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

C)

       \[4102\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

D)

       \[1213\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

View Answer
33) How does the magnetic susceptibility \[\chi \] of a paramagnetic material change with absolute temperature T?

A)

\[\chi \propto T\]

B)

       \[\chi \propto {{T}^{-1}}\]

C)

       \[\chi =\] constant

D)

       \[\chi \propto {{e}^{T}}\]

View Answer
34) Two identical heaters of 220 V, 1000 W are placed in parallel with each other across 220 V line, then the combined power is:

A)

1000 W

B)

       2000 W

C)

       500 W

D)

       4000 W

View Answer
35) A bar of magnetic moment M is cut into two pans of equal length. The magnetic moment of either part is;

A)

\[M\]

B)

       \[2M\]

C)

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

D)

       zero

View Answer
36) A rain drop of radius 0.3 mm has a terminal velocity of 1 m/s and the viscosity of 1 m/s and the viscosity of air is \[18\times {{10}^{-5}}\] poise. The viscous force on the drop is:

A)

\[16.95\times {{10}^{-9}}\,N\]

B)

       \[1.695\times {{10}^{-9}}\,N\]

C)

       \[10.17\times {{10}^{-9}}\,N\]

D)

       \[101.17\times {{10}^{-9}}\,N\]

View Answer
37) If magnetic material moves from stronger to weaker parts of magnetic field, then it is known as:

A)

anti-ferromagnetic

B)

       ferromagnetic

C)

       diamagnetic

D)

       paramagnetic

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

A)

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

B)

       \[-\frac{Q}{4}\]

C)

       \[+\frac{Q}{4}\]

D)

       \[+\frac{Q}{2}\]

View Answer
39) The temperature of cold, hot junction of a thermocouple are \[0{}^\circ C\] and \[T{}^\circ C\] respectively. The thermo-emf produced is\[E=AT-\frac{1}{2}B{{T}^{2}}.\]If A = 16, B = 0.08, the temperature of inversion will be:

A)

\[100{}^\circ C\]

B)

       \[300{}^\circ C\]

C)

       \[400{}^\circ C\]

D)

       \[500{}^\circ C\]

View Answer
40) Two light springs of force constants \[{{k}_{1}}\] and \[{{k}_{2}}\] and a block of mass m are in one line AS on a smooth horizontal table, such that one end of each spring is fixed to rigid support and other end is attached to block of mass m kg as shown in figure. The frequency of vibration is:

A)

\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}+{{k}_{2}}}{m}}\]

B)

\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{m}}\]

C)

\[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}-{{k}_{2}}}{m}}\]

D)

none of these

View Answer
41) Pressure inside two soap bubbles are 1.01 and 1.02 atm. Ratio between their volumes is:

A)

102 : 101

B)

       \[{{(102)}^{3}}:{{(103)}^{3}}\]

C)

       8 : 1

D)

       2 : 1

View Answer
42) Two dielectrics of dielectric constants \[{{K}_{1}}\] and \[{{K}_{2}}\]are filled in gap of parallel plate capacitor as shown in figure The capacitance of capacitor will be:

A)

\[\frac{{{\varepsilon }_{0}}A({{K}_{1}}+{{K}_{2}})}{2d}\]

B)

\[\frac{{{\varepsilon }_{0}}A}{2d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]

C)

\[\frac{{{\varepsilon }_{0}}}{d}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]

D)

\[\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]

View Answer
43) For a series LCR circuit, the phase difference between current and voltage at the condition of resonance will be:

A)

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

B)

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

C)

       zero

D)

       nothing can be said

View Answer
44) A metallic rod of length \[l\] is placed normal to the magnetic field B and revolved in a circular path about one of the ends with angular frequency m. The potential difference across the ends will be:

A)

\[\frac{1}{2}{{B}^{2}}l\omega \]

B)

                                       \[\frac{1}{2}B\omega {{l}^{2}}\]

C)

       \[\frac{1}{8}B\omega {{l}^{3}}\]

D)

       \[B\omega {{l}^{3}}\]

View Answer
45) A magnetic needle suspended in a vertical plane at \[30{}^\circ \] from the magnetic meridian makes an angle \[45{}^\circ \] with the horizontal. What will be the true angle of dip?

A)

\[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

B)

       \[{{\tan }^{-1}}(\sqrt{3})\]

C)

       \[{{45}^{0}}\]

D)

       \[{{30}^{0}}\]

View Answer
46) A force F is given by \[f=at+b{{t}^{2}},\] where t is rime. What are the dimensions of a and b respectively?

A)

\[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ }\]

B)

       \[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-3}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ }\]

C)

       \[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-4}}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]

D)

       \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{2}}{{\text{T}}^{3}}\text{ }\!\!]\!\!\text{ and}\,\text{ }\!\![\!\!\text{ }{{\text{M}}^{-1}}{{\text{L}}^{2}}\text{T }\!\!]\!\!\text{ }\]

View Answer
47) In a triode valve, the plate resistance is 10000\[\Omega \] and the anode load resistance is 30000\[\Omega \]. If the amplification factor is 36, then the voltage gain is:

A)

9

B)

       27

C)

       36

D)

       108

View Answer
48) \[{{g}_{e}}\] and\[{{g}_{p}}\] denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then:

A)

\[{{g}_{p}}=\frac{{{g}_{e}}}{2}\]

B)

       \[{{g}_{p}}={{g}_{e}}\]

C)

       \[{{g}_{p}}=2{{g}_{e}}\]

D)

       \[{{g}_{p}}=\frac{{{g}_{e}}}{\sqrt{2}}\]

View Answer
49) Of the following which relation is true:

A)

\[\beta >\alpha \]

B)

\[\alpha >\beta \]

C)

\[\alpha \,\beta =1\]

D)

\[\alpha =\beta \]

View Answer
50) A soap bubble in vacuum has a radius 3 cm and another soap bubble in vacuum has radius 4 cm If two bubbles coalesce under isothermal condition, then the radius of the new bubble will be :

A)

7 cm

B)

       5 cm

C)

       4.5 cm

D)

       2.3 cm

View Answer
51) Out of Cu, Al Fe and Zn, metal which can displace all others from their salt solution is:

A)

Al

B)

Cu

C)

Zn

D)

Fe

View Answer
52) In which of the following reactions, hydrogen is acting as an oxidizing agent?

A)

With Li to form \[LiH\]

B)

With \[{{I}_{2}}\] to give HI

C)

With S to give \[{{H}_{2}}S\]

D)

None of the above

View Answer
53) Our cells get energy by the conversion of:

A)

ATP \[\xrightarrow{{}}\] Adenine

B)

ATP \[\xrightarrow{{}}\]ADP

C)

ADP\[\xrightarrow{{}}\]AMP

D)

CDP\[\xrightarrow{{}}\] CTP

View Answer
54) The number of optically active isomers of tartaric acid are:

A)

1

B)

       3

C)

4

D)

       2

View Answer
55) The hardness of water is estimated by:

A)

conductivity method

B)

titrimetric method

C)

EDTA method

D)

distillation method

View Answer
56) \[N{{a}_{2}}O,\,MgO,\,A{{l}_{2}}{{O}_{3}}\] and \[Si{{O}_{2}}\]have heat of formation equal to \[-416,-602,-1676\] and \[-911\,kJ\,mo{{l}^{-1}}\]respectively. The most stable oxide is:

A)

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

B)

       \[MgO\]

C)

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

D)

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

View Answer
57) A photon having a wavelength of \[845\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,,\] causes the ionization of N atom. What is the ionization energy of N?

A)

\[1.4\,kJ\]

B)

       \[1.4\,\times {{10}^{4}}\,kJ\]

C)

\[1.4\,\times {{10}^{2}}\,kJ\]

D)

       \[1.4\,\times {{10}^{3}}\,kJ\]

View Answer
58) The electronic theory of bonding was proposed by:

A)

Pauling

B)

       Lewis

C)

Hronsted

D)

       Mullikan

View Answer
59) An azeotropic mixture of two liquids has boiling point lower than either of them, when it:

A)

shows a negative deviation from Raoults law

B)

shows no deviation from Raoults law

C)

shows positive deviation from Raoults law

D)

is saturated

View Answer
60) Troutons rule gives the relation between:

A)

\[{{T}_{b}}\] and\[{{T}_{c}}\]

B)

\[{{T}_{b}}\] and critical pressure

C)

enthalpy of vaporization and boiling point

D)

normal boiling point and boiling point

View Answer
61) The product X, in the following reaction is:

A)

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

B)

\[C{{H}_{3}}-\overset{Br}{\mathop{\overset{|}{\mathop{C}}\,}}\,=C{{H}_{2}}\]

C)

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

D)

none of the above

View Answer
62) What are the products in the following reaction? \[{{C}_{2}}{{H}_{5}}O{{C}_{2}}{{H}_{5}}\xrightarrow[cold]{HI}X+Y\]

A)

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

B)

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

C)

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

D)

None of the above

View Answer
63) Which of the following reagent can distinguish between butyne-1 and butyne-2?

A)

Bromine water

B)

Aqueous

C)

Fehlings solution

D)

Ammoniacal\[AgN{{O}_{3}}\]

View Answer
64) Which of the following will have maximum pH?

A)

\[\frac{M}{10}HCl\]

B)

       \[\frac{M}{100}HCl\]

C)

\[\frac{M}{10}NaOH\]

D)

       \[\frac{M}{100}NaOH\]

View Answer
65) What is AE for system that does 500 cal of work on surrounding and 300 cal of heat is absorbed by the system?

A)

\[-200\]cal

B)

       \[-300\]cal

C)

\[+\,200\]cal

D)

       \[+\text{ }300\]cal

View Answer
66) The rate of a chemical reaction:

A)

increase as the reaction proceeds

B)

decrease as the reaction proceeds

C)

may increase or decrease during reaction

D)

remain constant as the reaction

View Answer
67) A carbonate ore is:

A)

camallite

B)

       limonite

C)

siderite

D)

       horn silver

View Answer
68) Cadmium in a nuclear reactor acts as:

A)

nuclear fuel

B)

neutron absorber

C)

a moderator

D)

neutron liberator to start the chain

View Answer
69) Cement does not contain:

A)

calcium

B)

       aluminium

C)

sulphur

D)

       iron

View Answer
70) The simplest way, to check whether a system is a colloid, is by:

A)

Tyndall effect

B)

Brownian movement

C)

Electrodialysis

D)

finding out particle size

View Answer
71) What is Z in the following reaction?

A)

Benzoic acid

B)

       Cyanobenzoic acid

C)

Benzamide

D)

       Aniline

View Answer
72) The reaction, \[RCOOH\xrightarrow{Na{{N}_{3}}/conc.{{H}_{2}}S{{O}_{4}}}\]                 \[RN{{H}_{2}}+{{N}_{2}}+C{{O}_{2}}\] is known as:

A)

Curtius reaction

B)

Lossen reaction

C)

Schmidt reaction

D)

      Hofmann reaction

View Answer
73) What is the product in the reaction? \[C{{H}_{3}}MgBr\xrightarrow[(ii)\,{{H}_{2}}O]{(i)\,C{{O}_{2}}}X\]

A)

Acetaldehyde

B)

Acetic acid

C)

Formic acid

D)

Formaldehyde

View Answer
74) What is the value of \[{{E}_{cell}}\] \[Cr|C{{r}^{3+}}(0.1M)||F{{e}^{2+}}(0.01\,M)|Fe\] Given,   \[E_{C{{r}^{3+}}/Cr}^{o}=-0.74\,V\] and        \[E_{F{{e}^{2+}}/Fe}^{o}=-0.44\,V\]

A)

\[~+\text{ }0.2941\,V\]

B)

       \[~+\text{ }0.5212\,V\]

C)

\[+\text{ }0.1308\,V\]

D)

       \[-\,0.2606\,V\]

View Answer
75) Elevation in boiling point was \[0.52{{\,}^{o}}C\]when 6g of a compound was dissolved in 100 g of   water. Molecular weight of X is (\[{{K}_{b}}\]of water is \[5.2{{\,}^{o}}C\] per 100 g of water):

A)

120

B)

60

C)

600

D)

       180

View Answer
76) The solubility of \[PbC{{l}_{2}}\]is:

A)

\[\sqrt{{{K}_{sp}}}\]

B)

       \[{{({{K}_{sp}})}^{1/3}}\]

C)

\[{{({{K}_{sp/4}})}^{1/3}}\]

D)

       \[{{(8{{K}_{sp}})}^{1/2}}\]

View Answer
77) Equilibrium constant K, for the reaction, \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\] at room temperature is 2.85 and that at 698 K is \[1.4\times {{10}^{-2}}.\] This implies that the forward reaction is:

A)

exothermic

B)

       endothermic

C)

exergonic

D)

       unpredictable

View Answer
78) Which of the following represents hexadentate ligand?

A)

2, 2-bipyridyl

B)

       DMG

C)

       Ethylenediamine

D)

      None of these

View Answer
79) The amount of substance that gives \[3.7\times {{10}^{7}}\] dps, is:

A)

one becquerel

B)

       one curie

C)

       one millicurie

D)

       one Rutherford

View Answer
80) The reaction, \[A{{g}^{2+}}(aq)+Ag(s)2A{{g}^{+}}(aq)\] is an example of:

A)

reduction

B)

oxidation

C)

       comproportionation

D)

disproportionation

View Answer
81) DDT is obtained by the reaction, of chlorobenzene with:

A)

chloral

B)

chloroform

C)

dichloromethane

D)

acetaldehyde

View Answer
82) Which of the following is false?

A)

Glycerol has strong hydrogen bonding

B)

Glycol is a poisonous alcohols

C)

Waxes are esters of higher alcohols with higher acids

D)

Alkyl halides have higher b. p. than corresponding alcohols

View Answer
83) Which of the following oxides is most acidic?

A)

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

B)

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

C)

       \[{{P}_{2}}{{O}_{5}}\]

D)

       \[MgO\]

View Answer
84) Glaubefs salt is:

A)

\[N{{a}_{2}}C{{O}_{3}}.10{{H}_{2}}O\]

B)

\[N{{a}_{2}}S{{O}_{4}}.10{{H}_{2}}O\]

C)

\[MgS{{O}_{4}}.7{{H}_{2}}O\]

D)

\[CaS{{O}_{4}}.5{{H}_{2}}O\]

View Answer
85) Enthalpy change when \[1\,g\]water is frozen at \[(\Delta {{H}_{fus}}=1.435\,\text{kcal}\text{mo}{{\text{l}}^{\text{-1}}})\]

A)

\[0.0797\text{ }kcal~~\]

B)

\[-0.0797\text{ }kcal\]

C)

\[1.435\text{ }kcal\]

D)

\[-1.435\text{ }kcal\]

View Answer
86) Which of the following statement is true?

A)

Some complex metal oxides behave as superconductor

B)

Zinc oxide can act as superconductor

C)

An impurity of tetravalent germanium in trivalent gallium creates electron deficiency

D)

A Frenkel defect is formed when an ion is displaced from its lattice site to an interstitial site

View Answer
87) The correct set of four quantum number for the valence electron of rubidium \[(Z=37)\] is:

A)

\[n=5,\,l=0,\,m=0,\,s=+\,1/2\]

B)

\[n=5,\,l=1,\,m=1,\,s=+\,1/2\]

C)

\[n=5,\,l=1,\,m=1,\,s=+\,1/2\]

D)

\[n=6,\,l=0,\,m=0,\,s=+\,1/2\]

View Answer
88) \[s{{p}^{3}}-\]hybridisation is not found in:

A)

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

B)

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

C)

       \[BC{{l}_{3}}\]

D)

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

View Answer
89) Chalcopyrites is an ore of:

A)

gallium

B)

copper

C)

       calcium

D)

       magnesium

View Answer
90) Which of the following statement is correct?

A)

Acidity increases with increase in carbon atoms in carboxylic acids

B)

Solubility of carboxylic adds increases with increase in carbon atoms

C)

Boiling points of acids are higher than corresponding alcohols

D)

None of the above

View Answer
91) Which temperature is most suitable for fermentation?

A)

273 K

B)

298 K

C)

       350 K

D)

       330 K

View Answer
92) In the reaction, \[HCHO+N{{H}_{3}}\xrightarrow{{}}X,X\]is:

A)

meta-formaldehyde

B)

para-formaldehyde

C)

urotropine

D)

                                none of the above

View Answer
93) Which of the following have highest melting points?

A)

p-block elements

B)

s-block elements

C)

d-block elements

D)

None of the above

View Answer
94) An acid has \[pH=5\]and its concentration is 1M. What is the value of \[{{K}_{a}}\]for the acid?

A)

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

B)

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

C)

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

D)

\[{{10}^{-8}}\]

View Answer
95) Fatty acid is to fat as glucose is to:

A)

cellulose

B)

glycogen

C)

starch

D)

       all of these

View Answer
96) In aerosol, the dispersion medium is:

A)

solid

B)

liquid

C)

gas

D)

       any of these

View Answer
97) Peptisation denotes:

A)

digestion of food

B)

hydrolysis of protein

C)

breaking and dispersion into colloidal state

D)

precipitation of solid from colloidal state

View Answer
98) Buna-N is a polymer of:

A)

butadiene and isoprene

B)

butadiene and acrylonitrile

C)

isoprene and ethylene diamine

D)

isoprene and butyl diamine

View Answer
99) Which of the following is an engrain dye?

A)

Congo-red

B)

Aniline black

C)

       Alizarin

D)

       Indigo

View Answer
100) Which of the following give an explosive, RDX, on nitration?

A)

Toluene

B)

Benzene

C)

       Guanidine

D)

       Urotropine

View Answer
101) If\[f(x)=\left\{ \begin{matrix}    \frac{\sin x}{x}+\cos x, & \text{when}\,\text{x}\ne \text{0} \\    2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,, & \text{when}\,x=0 \\ \end{matrix} \right.\]

A)

\[\underset{x\to {{0}^{+}}}{\mathop{\lim }}\,f(x)\ne 2\]

B)

                 \[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,f(x)=0\]

C)

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

D)

                 none of the above

View Answer
102) If \[y=f(x)=\frac{x+2}{x-1},\] then \[x\] is equal to:

A)

\[f(y)\]

B)

                 \[2f(y)\]

C)

                 \[\frac{1}{f(y)}\]

D)

                 none of these

View Answer
103) The value of b and c for which the identity\[f(x+1)-f(x)=8x+3\] is satisfied, where \[f(x)=b{{x}^{2}}+cx+d,\]are:

A)

\[b=2,\,c=1\]

B)

                 \[b=4,c=-1\]

C)

                 \[b=-1,c=4\]

D)

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

View Answer
104) The range of the function \[f(x)={{x}^{2}}-6x+7\]is:

A)

\[(-\infty ,0)\]

B)

                 \[[-2,\infty )\]

C)

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

D)

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

View Answer
105) If\[f(x)=x{{\tan }^{-1}}x,\] then \[f(1)\] is equal to:

A)

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

B)

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

C)

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

D)

                 2

View Answer
106) \[\frac{d}{dx}\sqrt{\frac{1-\sin 2x}{1+\sin 2x}}\]is equal to:

A)

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

B)

                 \[-{{\sec }^{2}}\left( \frac{\pi }{4}-x \right)\]

C)

                 \[{{\sec }^{2}}\left( \frac{\pi }{4}+x \right)\]

D)

                 \[{{\sec }^{2}}\left( \frac{\pi }{4}-x \right)\]

View Answer
107) If \[y={{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+\frac{1}{{{x}^{2}}+...\infty }}}\,\,,\]then \[\frac{dy}{dx}\]is equal to:

A)

\[\frac{2xy}{2y-{{x}^{2}}}\]

B)

                 \[\frac{xy}{y+{{x}^{2}}}\]

C)

                 \[\frac{xy}{y-{{x}^{2}}}\]

D)

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

View Answer
108) The function \[F(x)=\max [(1-x),(1+x),2],x\in (-\infty ,\infty )\]is:

A)

continuous at all points

B)

                 differentiable at all points

C)

                 differentiable at all points except at \[x=1\] and \[x=-1\]

D)

                 none of the above

View Answer
109) If \[f({{x}_{1}})-f({{x}_{2}})=f\left( \frac{{{x}_{1}}-{{x}_{2}}}{1-{{x}_{2}}{{x}_{2}}} \right)\]for \[{{x}_{1}},{{x}_{2}}\in [-1,1],\]then \[f(x)\]is equal to:

A)

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

B)

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

C)

                 \[\log \frac{(1+x)}{(1-x)}\]

D)

                 none of these

View Answer
110) \[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}}\]is equal to:

A)

\[n\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]

B)

                 \[n\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]

C)

                 \[\frac{1}{n}\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]

D)

                 \[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]

View Answer
111) \[\int_{{}}^{{}}{{{\{1+2\tan x(\tan x+\sec x)\}}^{1/2}}dx}\]is equal to:

A)

\[log(sec\text{ }x+tan\text{ }x)+c\]

B)

                 \[log{{(sec\text{ }x+tan\text{ }x)}^{1/2}}+\text{ }c\]

C)

                 \[~log\,sec\text{ }x\,(sec\text{ }x+tan\text{ }x)+c\]

D)

                 none of the above

View Answer
112) The value of \[\int_{0}^{\pi /2}{\frac{\cos \theta }{\sqrt{4-{{\sin }^{2}}\theta }}}d\theta \]is:

A)

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

B)

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

C)

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

D)

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

View Answer
113) If the ordinate\[x=a\] divides the area bounded by the curve\[y=\left( 1+\frac{8}{{{x}^{2}}} \right),\]\[x-\]axis and the ordinates \[x=2,\text{ }x=4,\]into two equal parts, then the value of a is:

A)

2a

B)

                 \[2\sqrt{2}\]

C)

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

D)

                 none of these

View Answer
114) Area included   between the two curves, \[{{y}^{2}}=4ax\]and \[{{x}^{2}}-4ay\]is equal to:

A)

\[\frac{32}{3}{{a}^{2}}\text{sq}\,\text{unit}\]

B)

                 \[\frac{64}{9}\,\text{sq}\,\text{unit}\]

C)

                 \[\frac{32}{3}\text{sq}\,\text{unit}\]

D)

                 \[\frac{16}{3}{{a}^{2}}\text{sq}\,\text{unit}\]

View Answer
115) The differential equation of the family of curves \[y=a\cos (x+b)\]is :

A)

\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-y=0\]

B)

                 \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y=0\]

C)

                 \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2y=0\]

D)

                 none of these

View Answer
116) The solution of the given differential equation\[\frac{dy}{dx}+2xy=y\]is:

A)

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

B)

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

C)

                 \[y=c{{e}^{x}}\]

D)

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

View Answer
117) If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in examination is:

A)

0.5

B)

                 0.44

C)

                 0.6

D)

                 none of these

View Answer
118) The plane\[\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1\] cuts the coordinate axes in A, B, C, then the area of the \[\Delta ABC\]is:

A)

\[\sqrt{29}\] sq unit

B)

                 \[\sqrt{41}\,\text{sq}\,\text{unit}\]

C)

                 \[\sqrt{61}\,\text{sq}\,\text{unit}\]

D)

                 none of these

View Answer
119) Let    \[~0<P(A)<1,0<P(B)<1~\] and \[P(A\cap B)=P(A)+P(B)-P(A)P(B),\]then:

A)

\[P(B/A)=P(B)-P(A)\]

B)

                 \[P({{A}^{c}}\cup {{B}^{c}})=P({{A}^{c}})+P({{B}^{c}})\]

C)

                 \[P{{(A\cup B)}^{c}}=P({{A}^{c}})P({{B}^{c}})\]

D)

                 \[P(A/B)=P(A)+P({{B}^{c}})\]

View Answer
120) If the plane \[x+2y+2z-15=0\]cuts the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0,\]then the radius of the circle is:

A)

\[\sqrt{3}\]

B)

                 \[\sqrt{5}\]

C)

                 \[\sqrt{7}\]

D)

                 \[\sqrt{11}\]

View Answer
121) Forces acting on a particle have a magnitude 5, 3 and 1 unit and act in the direction of the vectors   \[6\hat{i}+2\hat{j}+3\hat{k},3\hat{i}-4\hat{j}+6\hat{k}\] and \[2\hat{i}-3\hat{j}-6\hat{k}\]respectively. Then remain constant while the particle is displaced from the point \[A(2,-1,-3)\]to \[B(5,-1,-1),\]The work done is:

A)

11 unit

B)

                 33 unit

C)

                 10 unit

D)

                 30 unit

View Answer
122) If \[\vec{a},\vec{b},\vec{c}\]are three non-coplanar vectors, then the vector equation\[\vec{r}=(1-p-q)\vec{a}+p\vec{b}+q\vec{c}\] represents a:

A)

straight line

B)

                 plane

C)

                 plane passing through the origin

D)

                 sphere

View Answer
123) If angle between \[\vec{a}\]and\[\vec{b}\]is\[\frac{2\pi }{3}\] and if\[|\vec{a}|=5,|\vec{b}|=3,\]then\[|\vec{a}-\vec{b}|\]is equal to:

A)

23

B)

                 7

C)

                 17

D)

                 18

View Answer
124) Let p and q be two statements, then \[(p\ \vee q)\vee \tilde{\ }p\] is:

A)

tautology

B)

                 contradiction

C)

                 both (a) and (b)

D)

                 none of these

View Answer
125) The values of \[x\] and \[y\]satisfying the equation \[\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i\]are:

A)

\[x=-1,y=3\]

B)

                 \[x=3,y=-1\]

C)

                 \[x=0,y=1\]

D)

                 \[x=1,y=0\]

View Answer
126) The points \[{{z}_{1}},{{z}_{2}},{{z}_{3}},{{z}_{4}}\]in the complex plane are the vertices of a parallelogram taken in order, iff:

A)

\[{{z}_{1}}+{{z}_{4}}={{z}_{2}}+{{z}_{3}}\]

B)

                 \[{{z}_{1}}+{{z}_{3}}={{z}_{2}}+{{z}_{4}}\]

C)

                 \[{{z}_{1}}+{{z}_{2}}={{z}_{3}}+{{z}_{4}}\]

D)

                 none of these

View Answer
127) An OR gate is the boolean function defined of:

A)

\[f({{x}_{1}},{{x}_{2}})={{x}_{1}}{{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]

B)

                 \[f({{x}_{1}},{{x}_{2}})={{x}_{1}}+{{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]

C)

                 \[f({{x}_{1}},{{x}_{2}})={{x}_{1}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]

D)

                 \[f({{x}_{1}},{{x}_{2}})={{x}_{2}};{{x}_{1}},{{x}_{2}}\in \{0,1\}\]

View Answer
128) If the sum of the roots of the equation \[a{{x}^{2}}+bx+c=0\]be equal to the sum of the reciprocal of their squares, then \[b{{c}^{2}},c{{a}^{2}},a{{b}^{2}}\]will be in:

A)

AP

B)

                 GP

C)

                 HP

D)

                 none of these

View Answer
129) If\[x,y,z\] are in GP and \[{{a}^{x}}={{b}^{y}}={{c}^{z}},\]then:

A)

\[{{\log }_{a}}C={{\log }_{b}}a\]

B)

                 \[{{\log }_{b}}a={{\log }_{c}}b\]

C)

                 \[{{\log }_{c}}b={{\log }_{a}}c\]

D)

                 none of these

View Answer
130) The sum of the series \[1+\frac{1}{5}+\frac{1.3}{5.10}+\frac{1.3.5}{5.10.15}+....\]is equal to:

A)

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

B)

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

C)

                 \[\sqrt{3}\]

D)

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

View Answer
131) If \[x\]is real, then the value of \[\frac{x+2}{2{{x}^{2}}+3x+6}\]

A)

\[\left( \frac{1}{13},\frac{1}{3} \right)\]

B)

                 \[\left[ -\frac{1}{13},\frac{1}{3} \right]\]

C)

                 \[\left( -\frac{1}{3},\frac{1}{13} \right)\]

D)

                 none of these

View Answer
132) Let a and P be the roots of the equation \[{{x}^{2}}+x+1=0,\]then the equation whose roots area\[{{\alpha }^{19}},{{\beta }^{7}}\] is:

A)

\[~{{x}^{2}}-x-1=0\]

B)

                 \[~{{x}^{2}}-\text{ }x+1=0\]

C)

                 \[~{{x}^{2}}+x-1=0\]

D)

                 \[~{{x}^{2}}+\text{ }x+1=0\]

View Answer
133) For a particle moving in a straight line, if timer be regarded as a function of velocity v, then the rate of change of the acceleration a is given by:

A)

\[{{a}^{2}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]

B)

                 \[{{a}^{3}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]

C)

                  \[-{{a}^{3}}\frac{{{d}^{2}}t}{d{{v}^{2}}}\]

D)

                 none of these

View Answer
134) \[{{\,}^{47}}{{C}_{4}}+\sum\limits_{r=1}^{5}{{{\,}^{52-r}}{{C}_{3}}}\]is equal to:

A)

\[{{\,}^{47}}{{C}_{6}}\]

B)

                 \[{{\,}^{52}}{{C}_{5}}\]

C)

                 \[{{\,}^{52}}{{C}_{4}}\]

D)

                 none of these

View Answer
135) In how many ways can 21 English and 19 Hindi books be placed in a row so that no two Hindi books are together:

A)

1540

B)

                 1450

C)

                 1504

D)

                 1405

View Answer
136) How many words can be made from the letters of the word COMMITTEE:

A)

\[\frac{9!}{{{(2!)}^{2}}}\]

B)

                 \[\frac{9!}{{{(2!)}^{3}}}\]

C)

                 \[\frac{9!}{2!}\]

D)

                 9!

View Answer
137) Three forces P, Q, and R acting on a particle are in equilibrium. If the angle between P and Q is double the angle between P and R, then P is equal to:

A)

\[\frac{{{Q}^{2}}+{{R}^{2}}}{R}\]

B)

                 \[\frac{{{Q}^{2}}-{{R}^{2}}}{Q}\]

C)

                 \[\frac{{{Q}^{2}}-{{R}^{2}}}{R}\]

D)

                 \[\frac{{{Q}^{2}}+{{R}^{2}}}{Q}\]

View Answer
138) If n is an integer greater than 1, then \[a-{{\,}^{n}}{{C}_{1}}(a-1)+{{\,}^{n}}{{C}_{2}}(a-2)-....+{{(-1)}^{n}}(a-n)\] is equal to:

A)

\[a\]

B)

                 \[0\]

C)

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

D)

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

View Answer
139) Forces forming a couple are of magnitude 12N each and the arm of the couple is 8m. The tone of an equivalent couple whose arm is 6 m is of magnitude:

A)

8 N

B)

                 16 N

C)

                 12 N

D)

                 4 N

View Answer
140) In the expansion of \[2{{\log }_{e}}x-{{\log }_{e}}(x+1)-{{\log }_{e}}(x-1)\] the coefficient of \[{{x}^{-4}}\]is:

A)

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

B)

                 \[-1\]

C)

                 1

D)

                 none of these

View Answer
141) A tower subtends an angle \[\alpha \]at a point in the plane of its base and the angle of depression of the foot of the tower at a point b ft just above A is \[\beta .\]Then height of the tower is:

A)

\[b\text{ }tan\text{ }\alpha \text{ }cot\beta \]

B)

                 \[~b\text{ }cot\text{ }\alpha \text{ }tan\text{ }\beta \]

C)

                 \[b\text{ }tan\text{ }\alpha \text{ }tan\text{ }\beta \]

D)

                  \[b\cot \alpha \cot \beta \]

View Answer
142) The matrix \[\left[ \begin{matrix}    2 & 5 & -7 \\    0 & 3 & 11 \\    0 & 0 & 9 \\ \end{matrix} \right]\]is known as:

A)

symmetric matrix

B)

                 upper triangular matrix

C)

                 diagonal matrix

D)

                 skew-symmetric matrix

View Answer
143) Two bodies of different masses \[{{m}_{1}}\]and \[{{m}_{2}}\]are dropped from different heights \[{{h}_{1}}\]and \[{{h}_{2}}.\]he ratio of the times taken by the two bodies to fall through these distance is:

A)

\[{{h}_{1}}:{{h}_{2}}\]

B)

                 \[\sqrt{{{h}_{1}}}:\sqrt{{{h}_{2}}}\]

C)

                 \[{{h}_{1}}^{2}:h_{2}^{2}\]

D)

                 \[{{h}_{2}}:{{h}_{1}}\]

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

A)

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

B)

                 \[nA-I\]

C)

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

D)

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

View Answer
145) The value of the determinant \[\left| \begin{matrix}    x & a & b+c \\    x & b & c+a \\    x & c & a+b \\ \end{matrix} \right|=0\]if:

A)

\[x=a\]

B)

                 \[x=b\]

C)

                 \[x=c\]

D)

                 \[x\]has any value

View Answer
146) \[{{12}^{o}}\sin {{48}^{o}}\sin {{54}^{o}}\]is equal to:

A)

1/16

B)

                 1/32

C)

                 1/8

D)

                 1/4

View Answer
147) If\[\tan A=\frac{1-\cos B}{\sin B}.\]then:

A)

\[\tan 2A=\tan B\]

B)

                 \[\tan 2A=ta{{n}^{2}}B\]

C)

                 \[\tan 2A={{\tan }^{2}}B+2\tan B\]

D)

                 none of the above

View Answer
148) Three points are\[A(6,3),B(-3,5),C(4,-2)\]and \[P(x,y)\]is any point, then the ratio of area of \[\Delta PBC\]and \[\Delta ABC\]is:

A)

\[\frac{x+y-2}{7}\]

B)

                 \[\frac{x-y+2}{2}\]

C)

                 \[\frac{x-y-2}{7}\]

D)

                 none of these

View Answer
149) The circle \[{{x}^{2}}+{{y}^{2}}+4x-4y+4=0\]t touches:

A)

\[x-\]axis

B)

                 \[y-\]axis

C)

                 \[x-\] axis and \[y-\]axis

D)

                 none of the above

View Answer
150) Three normals to the parabola \[{{y}^{2}}=x\]are drawn a point (c, 0), then:

A)

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

B)

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

C)

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

D)

                 None of these

View Answer

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