Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2006

1) Which of the following rays can be polarised?

A) Water wave and sound wave

B) Sound wave and radio wave

C) \[X-\]rays and water wave

D) Light wave and \[X-\] ray

View Answer

2) Quantum nature can prove :

A) interference

B) photoelectric effect

C) diffraction

D) polarisation

View Answer

3) Which one has highest binding energy per nucleon?

A) \[F{{e}^{56}}\]

B) \[L{{i}^{6}}\]

C) \[{{U}^{235}}\]

D) \[C{{a}^{40}}\]

View Answer

4) Huygen's wave theory can't explain:

A) interference

B) photoelectric effect

C) diffraction

D) all of these

View Answer

5) If the refractive index of a glass prism is \[\cot (A/2)\] and \[A\] is angle of prism, then angle of minimum deviation is:

A) \[\left( \frac{\pi }{2}-A \right)\]

B) \[\left( 2\pi -\frac{A}{2} \right)\]

C) \[\left( \frac{\pi -A}{2} \right)\]

D) \[(\pi -2A)\]

View Answer

6) If \[f\] is the frequency when mass m is attached to a spring of spring constant \[k\], then new frequency for this arrangement, is:

A) \[f/2\]

B) \[\sqrt{2f}\]

C) \[f/\sqrt{2}\]

D) \[2\sqrt{2f}\]

View Answer

7) What is equivalent capacitance of the network? Each capacitor has \[1\mu F\] capacitance:

A) \[\frac{1}{3}\mu F\]

B) \[2\mu F\]

C) \[\frac{3}{2}\mu F\]

D) \[3\mu F\]

View Answer

8) The two capacitors \[{{C}_{1}}\]and\[{{C}_{2}}\]are charged to potentials \[{{V}_{1}}\] and \[{{V}_{2}}\] then connected in parallel. There will be no flow of energy, if:

A) \[{{C}_{1}}{{V}_{1}}={{C}_{2}}{{V}_{2}}\]

B) \[{{V}_{1}}={{V}_{2}}\]

C) \[{{C}_{1}}={{C}_{2}}\]

D) \[\frac{{{C}_{1}}}{{{V}_{1}}}=\frac{{{C}_{2}}}{{{V}_{2}}}\]

View Answer

9) Which is not the unit of electric field?

A) \[\frac{N}{C}\]

B) \[\frac{N-m}{C}\]

C) \[\frac{V}{m}\]

D) \[\frac{J}{C\text{-}m}\]

View Answer

10) If a body moves for \[2\,\,s\] with \[15\,\,m/s\] velocity towards east and then moves with \[5\,\,m/s\] velocity for \[8\,\,s\] towards north, then average velocity is:

A) \[5\,\,m/s\]

B) \[15\,\,m/s\]

C) \[30\,\,m/s\]

D) \[7.5\,\,m/s\]

View Answer

11) For monoatomic gas which is correct?

A) \[CV=\frac{3}{5}R\]

B) \[{{C}_{P}}=\frac{5}{2}R\]

C) \[{{C}_{P}}-{{C}_{V}}=2R\]

D) \[\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{3}{5}\]

View Answer

12) Which is correct relationship for diode?

A)

B)

C)

D)

View Answer

13) In a properly biased transistor:

A) both depletion layers are equally large

B) both depletion layers are equally small

C) emitter-base depletion layer is large but base-collector depletion layer is small

D) emitter-base depletion layer is small but base-collector depletion layer is large

View Answer

14) A wire has resistance \[20\,\,\Omega \]. If its length is increased three times its initial length, then new resistance is:

A) \[40\Omega \]

B) \[80\Omega \]

C) \[60\Omega \]

D) \[180\Omega \]

View Answer

15) A circular coil of diameter \[d\] is rotated in electric field such that electric flux is changed from zero to maximum value \[\phi \] then, electric field is:

A) \[\frac{\phi }{\pi {{d}^{2}}}\]

B) \[\frac{2\phi }{\pi {{d}^{2}}}\]

C) \[\frac{4{{d}^{2}}}{\pi {{\phi }^{2}}}\]

D) \[\frac{4\phi }{\pi {{d}^{2}}}\]

View Answer

16) Work done in rotating a bar magnet from \[0\] to angle \[\theta \] is:

A) \[MH(1-\cos \theta )\]

B) \[\frac{M}{H}(1-\cos \theta )\]

C) \[\frac{M}{H}(\cos \theta -1)\]

D) \[MH(\cos \theta -1)\]

View Answer

17) If a convex lens of refractive index \[1.44\] is dipped in liquid of refractive index \[1.49\], then it behaves as:

A) concave lens

B) convex lens

C) mirror

D) none of these

View Answer

18) If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is \[6:5\], then velocity of source is:\[({{v}_{s}}=330\,\,m/s)\]

A) \[20\,\,m/s\]

B) \[10\,\,m/s\]

C) \[30\,\,m/s\]

D) \[33\,\,m/s\]

View Answer

19) If a boy swings in a circle so the minimum and maximum height from ground is\[3\,\,m\]and\[6\,\,m\], then, its maximum velocity is:

A) \[5\sqrt{2}m/s\]

B) \[2\sqrt{5}m/s\]

C) \[3\sqrt{5}m/s\]

D) \[5\sqrt{3}m/s\]

View Answer

20) If percentage decrease in radius of earth is \[1%\] without changing its mass, then percentage change in acceleration due to gravity is:

A) \[2%\] decrease

B) \[2%\] increase

C) \[1%\] decrease

D) \[1%\] increase

View Answer

21) A black body radiates at two temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] such that\[{{T}_{1}}<{{T}_{2}}\]. The frequency corresponding to maximum intensity is:

A) less at\[{{T}_{1}}\]

B) more at\[{{T}_{1}}\]

C) equally in the two cases

D) cannot say

View Answer

22) If temperature is increased by \[1\,\,K\] at constant volume, then work done on the gas is:

A) \[\frac{5}{2}R\]

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

C) \[zero\]

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

View Answer

23) A body cools from\[{{75}^{o}}C\] to\[{{70}^{o}}C\] in time \[{{t}_{1}}\], from \[{{70}^{o}}C\] to \[{{65}^{o}}C\] in time \[{{t}_{2}}\] and from \[{{65}^{o}}C\] to \[{{60}^{o}}C\] in timer\[3\], then:

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

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

C) \[{{t}_{2}}>{{t}_{1}}={{t}_{3}}\]

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

View Answer

24) A gas is at \[{{27}^{o}}C\]. Its volume is doubled keeping pressure constant, then final temperature is:

A) \[{{600}^{o}}C\]

B) \[327\,\,K\]

C) \[{{327}^{o}}C\]

D) \[{{273}^{o}}C\]

View Answer

25) If the volume of gas is changed from \[{{V}_{1}}\] to \[{{V}_{2}}\] isothermally, then work done is:

A) \[RT\ln \frac{{{V}_{1}}}{{{V}_{2}}}\]

B) \[RT\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]

C) \[R({{T}_{2}}-{{T}_{1}})\ln \frac{{{V}_{2}}}{{{V}_{1}}}\]

D) \[R({{V}_{2}}-{{V}_{1}})\ln \frac{{{T}_{2}}}{{{T}_{1}}}\]

View Answer

26) If energy is supplied to a gas is ochorically, increase in internal energy is \[dU\] then:

A) \[dQ=dU+dW\]

B) \[dQ=dU-dW\]

C) \[dQ=dU\]

D) \[dQ=-dU\]

View Answer

27) A nucleus \[_{Z}^{A}X\] emits one a and \[2\beta \] particles, then final nucleus is:

A) \[Y_{Z-2}^{A}\]

B) \[Y_{Z-4}^{A-4}\]

C) \[Y_{Z}^{A-4}\]

D) \[X_{Z}^{A}\]

View Answer

28) The fringe width for red light is approximately how many times that for violet light in Young's slit experiment?

A) \[2\] times

B) \[3\] times

C) Equal

D) \[1/2\] times

View Answer

29) A person sees clearly at a distance of \[100\,\,cm\], then power of lens used to see object at \[40\,\,cm\] is:

A) \[3D\]

B) \[-3D\]

C) \[-1.5D\]

D) \[+1.5D\]

View Answer

30) The electric potential \[V\] is given as a function of distance \[x\] (metre) by\[V=(5{{x}^{2}}+10x-4)V\]. Value of electric field at \[x=1\,\,m\] is:

A) \[-23\,\,V/m\]

B) \[11\,\,V/m\]

C) \[6\,\,V/m\]

D) \[-20\,\,V/m\]

View Answer

31) In an image converter tube fluorescent material is bombarded by:

A) visible radiation

B) electron radiation

C) infrared radiation

D) ultra violet radiation

View Answer

32) A particle executes simple harmonic motion with a frequency\[f\]. The frequency with which its kinetic energy oscillates is:

A) \[f/2\]

B) \[f\]

C) \[2f\]

D) \[4f\]

View Answer

33) The work done by the centripetal force \[F\] when the body completes one rotation around the circle of radius \[R\] is:

A) \[2\pi RF\]

B) \[2RF\]

C) \[RF\]

D) \[zero\]

View Answer

34) The unit mass having \[\overset{\to }{\mathop{\mathbf{r}}}\,=8\widehat{\mathbf{i}}-4\widehat{\mathbf{j}}\] and \[\overset{\to }{\mathop{\mathbf{v}}}\,=8\widehat{\mathbf{i}}+4\widehat{\mathbf{j}}\] in its angular momentum is:

A) \[64\] unit in \[-\mathbf{\hat{k}}\] direction

B) \[64\]unit in \[+\mathbf{\hat{k}}\] direction

C) \[64\]unit in \[+\widehat{\mathbf{j}}\] direction

D) \[64\]unit in \[+\widehat{\mathbf{i}}\] direction

View Answer

35) Which is nuclear fusion direction?

A) Hydrogen to helium

B) Uranium to krypton

C) Hydrogen to water

D) Neutron to proton

View Answer

36) If an \[AC\] produces same heat as that produced by a steady current of \[4\,\,A\], then peak value of current is:

A) \[4\,\,A\]

B) \[1.56\,\,A\]

C) \[5.6\,\,A\]

D) \[1.41\,\,A\]

View Answer

37) In\[LCR\]circuit \[f=\frac{50}{\pi }Hz,\] \[V=50\,\,volt,\]\[R=300\Omega \]. If\[L=1\,\,H\]and\[C=20\,\,\mu C\], then voltage across capacitor is:

A) \[zero\]

B) \[20\,\,V\]

C) \[30\,\,V\]

D) \[50\,\,V\]

View Answer

38) If two forces each of \[2\,\,N\] are inclined at \[{{60}^{o}}\], then resultant force is:

A) \[2\,\,N\]

B) \[2\sqrt{5}N\]

C) \[3\sqrt{2}N\]

D) \[4\sqrt{2}N\]

View Answer

39) A block of mass \[10\,\,kg\] is placed on a rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of \[100\,\,N\] is applied on it, then acceleration of block will be:

A) \[10\,\,m/{{s}^{2}}\]

B) \[5\,\,m/{{s}^{2}}\]

C) \[15\,\,m/{{s}^{2}}\]

D) \[0.5\,\,m/{{s}^{2}}\]

View Answer

40) The potential difference across an instrument in a \[AC\] circuit of frequency \[f\] is \[V\] and the current through it is \[I\] such that \[V=5\cos 2\pi ft\,\,volt\] and \[I=2\sin 2\pi ft\,\,amp\]. The power dissipated in the instrument is:

A) \[zero\]

B) \[10\,\,W\]

C) \[5\,\,W\]

D) \[2.5\,\,W\]

View Answer

41) If ratio of intensities of interfering waves is \[16:9\], then ratio of maximum to minimum intensity is:

A) \[49:1\]

B) \[225:81\]

C) \[3:1\]

D) \[9:1\]

View Answer

42) The power of a lens, a short sighted person uses is \[-2\,\,D\]. Find the maximum distance of an object which he can see without spectacles:

A) \[25\,\,cm\]

B) \[50\,\,cm\]

C) \[100\,\,cm\]

D) \[10\,\,cm\]

View Answer

43) The first overtone frequency of a wave on string of length \[2\,\,m\] is \[250\,\,Hz\]. Then, its velocity is:

A) \[1000\,\,m/s\]

B) \[25\,\,m/s\]

C) \[100\,\,cm\]

D) \[10\,\,cm\]

View Answer

44) What is the current flowing in arm\[AB\]?

A) \[\frac{35}{4}A\]

B) \[\frac{13}{7}A\]

C) \[\frac{5}{7}A\]

D) \[\frac{7}{5}A\]

View Answer

45) A projectile is fired making an angle \[2\theta \] with horizontal with velocity\[4\,\,m/s\]. At any instant it makes an angle \[\theta \], then its velocity is:

A) \[4\cos \theta \]

B) \[4(2\cos \theta -\sec \theta )\]

C) \[2(\sec \theta +4\cos \theta )\]

D) \[4(\sec \theta +\cos \theta )\]

View Answer

46) If path difference becomes \[(2n-1)\frac{\lambda }{2}\] then:

A) white fringe is formed

B) bright fringe is formed

C) uniform illumination is obtained

D) dark fringe is formed

View Answer

47) If the intensity of fringe at wavelength\[\lambda \]is\[K\], then its intensity at wavelength \[\lambda /2\] is:

A) \[\frac{K}{2}\]

B) \[K\]

C) \[zero\]

D) \[\sqrt{2}K\]

View Answer

48) A positively charged particle moving with velocity \[v\] enters a region of space having a uniform magnetic field \[B\]. The particle will experience the large deflecting force, when the angle between \[v\] and \[B\] is:

A) \[{{0}^{o}}\]

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

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

D) \[{{180}^{o}}\]

View Answer

49) In a step-up transformer the turn ratio is\[1:8\]. A lead accumulator \[(emf=6\,\,V)\] is connected across the primary coil of the transformer. The voltage across the secondary coil is:

A) \[48\,\,V\]

B) \[0.75\,\,V\]

C) \[14\,\,V\]

D) \[zero\]

View Answer

50) The mass of a lift is\[500\,\,kg\]. When it ascends with an acceleration of \[2m/{{s}^{2}}\] the tension in the cable will be:\[(g=10\,\,m/{{s}^{2}})\]

A) \[6000\,\,N\]

B) \[5000\,\,N\]

C) \[4000\,\,N\]

D) \[1000\,\,N\]

View Answer

51) A water molecule can form maximum number of \[H-\]bond which is equal to:

A) \[1\]

B) \[2\]

C) \[3\]

D) \[4\]

View Answer

52) Bond angle in \[{{H}_{2}}O\] is:

A) \[{{109}^{o}}28'\]

B) \[{{107}^{o}}10\]

C) \[{{104.5}^{o}}\]

D) \[{{92}^{o}}\]

View Answer

53) Calamine is:

A) \[ZnS\]

B) \[PbC{{O}_{3}}\]

C) \[ZnC{{O}_{3}}\]

D) \[MgC{{O}_{3}}\]

View Answer

54) Which is extremely stable?

A) \[N{{F}_{3}}\]

B) \[NC{{l}_{3}}\]

C) \[NB{{r}_{3}}\]

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

View Answer

55) \[C{{H}_{3}}COCl\]does not react with:

A) diethyl ether

B) phenol

C) ethanol

D) aniline

View Answer

56) In \[S{{O}_{2}}\] hybridisation is:

A) \[sp\]

B) \[s{{p}^{3}}\]

C) \[ds{{p}^{2}}\]

D) \[s{{p}^{2}}\]

View Answer

57) Lowest melting point chloride is:

A) \[LiCl\]

B) \[NaCl\]

C) \[KCl\]

D) \[CsCl\]

View Answer

58) Half-life of a substance is\[6\min \]. If its initial amount is\[32\,\,g\], then amount present after \[18\,\,\min \] is:

A) \[4\,\,g\]

B) \[8\,\,g\]

C) \[16\,\,g\]

D) \[2\,\,g\]

View Answer

59) If calcium acetate and calcium for mate react, then product formed is:

A) acetaldehyde

B) acetic acid

C) formic acid

D) ethyl for mate

View Answer

60) Reduction with aluminium isopropoxide in excess of isopropyl alcohol is called Meer we in Pond or f Verley reduction\[(MPV)\]. What will be the firal product when cyclohex-2-enone is selectively reduced in \[MPV\] reaction?

A) Cyclohexanol

B) Cyclohex-2-enol

C) Cyclohexanone

D) Benzene

View Answer

61) If \[pH\] of a solution is\[4\], then \[{{H}^{+}}\] is:

A) \[{{10}^{4}}\]

B) \[{{10}^{10}}\]

C) \[{{10}^{-4}}\]

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

View Answer

62) When sodium nitrate is heated above\[{{6000}^{o}}C\], then:

A) only \[N{{a}_{2}}O\] is formed

B) only \[{{N}_{3}}\] is formed

C) only \[{{O}_{2}}\] is formed

D) all are formed

View Answer

63) Which of the following produces \[C{{l}_{2}}\] gas?

A) \[NaCl+HN{{O}_{3}}\]

B) \[Mn{{O}_{2}}+HCl\]

C) \[KMn{{O}_{4}}+HCl\]

D) \[HCl+HN{{O}_{3}}\]

View Answer

64) Which is correctly arranged as increasing size?

A) \[F<O<C<Cl<Br\]

B) \[C<O<F<Cl<Br\]

C) \[Cl<Br<F<C<O\]

D) \[O<F<C<Cl<Br\]

View Answer

65) \[N{{H}_{3}}\] is absorbed by:

A) ozone

B) \[CaO\]

C) pyrargallol

D) \[CaC{{l}_{2}}\]

View Answer

66) \[1.25\,\,g\]\[N{{H}_{3}}\] contains how many atoms?

A) \[{{10}^{23}}\]

B) \[2\times {{10}^{23}}\]

C) \[6\times {{10}^{13}}\]

D) \[4\times {{10}^{23}}\]

View Answer

67) Which of the following has smallest bond angle?

A) Ethane

B) Ethene

C) Ethyne

D) Ethanol

View Answer

68) Chloroform in air is oxidised to :

A) \[CC{{l}_{4}}\]

B) dichloromethane

C) phosgene

D) oxygen

View Answer

69) Gypsum is:

A) \[CaS{{O}_{4}}\cdot 2{{H}_{2}}O\]

B) \[CaS{{O}_{4}}\cdot \frac{1}{2}{{H}_{2}}O\]

C) \[MgS{{O}_{4}}\cdot 2{{H}_{2}}O\]

D) \[CuS{{O}_{4}}\]

View Answer

70) Which is not soluble in water?

A) \[PbS{{O}_{4}}\]

B) \[CdS{{O}_{4}}\]

C) \[Bi{{(S{{O}_{4}})}_{2}}\]

D) \[CuS{{O}_{4}}\]

View Answer

71) Which of the following is colour red?

A) \[C{{u}_{2}}O\]

B) \[CuF\]

C) \[Zn{{F}_{2}}\]

D) \[ZnC{{l}_{2}}\]

View Answer

72) How many unpaired electrons are present in\[[Cr{{(N{{H}_{3}})}_{5}}]B{{r}_{3}}\]?

A) \[1\]

B) \[2\]

C) \[3\]

D) \[4\]

View Answer

73) \[S+\frac{3}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=2x\],\[S{{O}_{2}}+\frac{1}{2}{{O}_{2}}\xrightarrow{{}}S{{O}_{3}}\Delta H=y\],then heat of formation of \[S{{O}_{2}}\] is:

A) \[2x-y\]

B) \[2x+y\]

C) \[x+y\]

D) \[\frac{2x-y}{2}\]

View Answer

74) Reagent (catalyst) used in Friedel-Craft's alkylation reaction is:

A) \[AlC{{l}_{3}}\]

B) \[anhyd.\,\,AlC{{l}_{3}}\]

C) \[{{N}_{2}}\]

D) \[He\]

View Answer

75) Catalyst used in making \[{{H}_{2}}S{{O}_{4}}\] in contact process is:

A) \[{{V}_{2}}{{O}_{5}}\]

B) \[F{{e}_{2}}{{O}_{3}}\]

C) \[C{{r}_{2}}{{O}_{3}}\]

D) \[Cr{{O}_{3}}\]

View Answer

76) When acetamide is reacted with \[NaOBr\], then product formed is:

A) ethanamine

B) methanamine

C) methanamide

D) ethanenitrile

View Answer

77) Isocyanide is prepared by :

A) Friedel Craft's reaction

B) Wurtz's reacdon

C) Williamson synthesis

D) Carbylamine reaction

View Answer

78) If rate of diffusion of \[C{{H}_{4}}\] is twice than that of a gas\[x\], then its molecular mass is:

A) \[64\,\,g\]

B) \[16\,\,g\]

C) \[32\,\,g\]

D) \[8\,\,g\]

View Answer

79) Which one is not Lewis acid?

A) \[Be{{F}_{2}}\]

B) \[SnC{{l}_{4}}\]

C) \[AlC{{l}_{3}}\]

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

View Answer

80) Natural gas mainly consists of:

A) methane

B) butane

C) propane

D) ethane \[+\] octane

View Answer

81) Phenol is treated with \[Zn\] to form:

A) benzoic acid

B) benzyl alcohol

C) benzene

D) benzoquinone

View Answer

82) Which one is isoelectronic with\[CO?\]

A) \[N_{2}^{-}\]

B) \[N_{2}^{+}\]

C) \[C{{N}^{-}}\]

D) \[NO\]

View Answer

83) How much volume of \[1\,\,M\,\,{{H}_{2}}S{{O}_{4}}\] is required to neutralize \[20\,\,mL\] of\[1M\,\,NaOH\]?

A) \[10\,\,mL\]

B) \[20\,\,mL\]

C) \[5\,\,mL\]

D) \[15\,\,mL\]

View Answer

84) Fenton's reagent is:

A) \[SnC{{l}_{2}}+HCl\]

B) \[AgN{{O}_{3}}+N{{H}_{4}}OH\]

C) \[CuS{{O}_{4}}+NaOH\]

D) \[FeS{{O}_{4}}+{{H}_{2}}{{O}_{2}}\]

View Answer

85) \[C{{u}^{2+}}+Ag\xrightarrow{{}}Cu+A{{g}^{+}}\] oxidation half reaction is:

A) \[C{{u}^{2+}}\to Cu\]

B) \[Ag\to A{{g}^{+}}\]

C) \[Cu\to C{{u}^{2+}}\]

D) all of these

View Answer

86) \[{{C}_{4}}{{H}_{10}}O\] has how many isomeric alcohols?

A) \[1\]

B) \[2\]

C) \[3\]

D) \[4\]

View Answer

87) \[IUPAC\]name of\[C{{H}_{3}}-C\equiv C-HC-{{(C{{H}_{3}})}_{2}}\]is:

A) 4-methyl-2-pentyne

B) 1, 1-dimethyl-2-butyne

C) 2-methyl-4-pentyne

D) 4, 4-dimethyl-2-butyne

View Answer

88) Fehling test is given by:

A) glucose

B) fructose

C) sucrose

D) all of these

View Answer

89) Number of isomeric primary amine of molecular formula \[{{C}_{4}}{{H}_{11}}N\] is:

A) \[1\]

B) \[2\]

C) \[3\]

D) \[4\]

View Answer

90) For reaction\[3X+Y{{X}_{3}}Y\]\[\Delta H=+ve\], amount of \[{{X}_{3}}Y\] can be changed by:

A) changing temperature

B) changing pressure

C) changing temperature, pressure,

D) changing temperature, pressure, adding catalyst

View Answer

91) Which one is most ionic?

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

B) \[Mn{{O}_{2}}\]

C) \[M{{n}_{2}}{{O}_{7}}\]

D) \[{{P}_{2}}{{O}_{3}}\]

View Answer

92) Which one gives \[{{I}_{2}}\] on reaction with\[KI?\]

A) \[A{{g}_{2}}S{{O}_{4}}\]

B) \[CuS{{O}_{4}}\]

C) \[PbS{{O}_{4}}\]

D) \[CdS{{O}_{4}}\]

View Answer

93) Colour of the solution when \[KI\] reacts with \[B{{r}_{2}}\] is:

A) blue

B) black

C) red

D) no change

View Answer

94) Finely divided iron combines with \[CO\] to give:

A) \[Fe{{(CO)}_{5}}\]

B) \[F{{e}_{2}}{{(CO)}_{9}}\]

C) \[F{{e}_{3}}{{(CO)}_{12}}\]

D) \[Fe{{(CO)}_{6}}\]

View Answer

95) Which of the following is pyramidal?

A) \[PC{{l}_{3}}\]

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

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

D) \[NO_{3}^{-}\]

View Answer

96) Which of the following conducts electricity?

A) Crystal\[NaCl\]

B) Diamond

C) Molten\[KBr\]

D) Sulphur

View Answer

97) Ratio of kinetic energy of hydrogen and helium gas at \[300\,\,K\] is:

A) \[2:1\]

B) \[4:5\]

C) \[1:1\]

D) \[1:2\]

View Answer

98) Which of the following has highest energy?

A) \[n=2,\,\,l=1\]

B) \[n=3,\,\,l=2\]

C) \[n=3,\,\,l=1\]

D) \[n=2,\,\,l=0\]

View Answer

99) Oxidation state of phosphorus in pyrophosphoric acid is:

A) \[+5\]

B) \[+3\]

C) \[+4\]

D) \[+1\]

View Answer

100) If the \[75%\] of a first order reaction is complete in\[8\min \], then time taken to decompose \[50%\] of its initial amount is:

A) \[2\min \]

B) \[4\min \]

C) \[12\min \]

D) \[1\min \]

View Answer

101) If\[a\ne \beta \]and\[{{\alpha }^{2}}=5\alpha -3,\,\,{{\beta }^{2}}=5\beta -3\]then the equation having \[\alpha /\beta \] and \[\beta /\alpha \] as its roots is:

A) \[3{{x}^{2}}+19x+3=0\]

B) \[3{{x}^{2}}-19x+3=0\]

C) \[3{{x}^{2}}-19x-3=0\]

D) \[{{x}^{2}}-16x+1=0\]

View Answer

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

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

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

C) \[-y\]

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

View Answer

103) If\[1,\,\,{{\log }_{3}}\sqrt{({{3}^{1-x}}+2)},\,\,{{\log }_{3}}(4\cdot {{3}^{x}}-1)\]are in \[AP\], then \[x\] equals:

A) \[{{\log }_{3}}4\]

B) \[1-{{\log }_{3}}4\]

C) \[1-{{\log }_{4}}3\]

D) \[{{\log }_{4}}3\]

View Answer

104) A problem in mathematics is given to three students \[A,\,\,\,B,\,\,\,C\] and their respective probability of solving the problem is \[\frac{1}{2},\,\,\,\frac{1}{3}\] and\[\frac{1}{4}\]. Probability that the problem is solved, is:

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

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

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

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

View Answer

105) The angle of elevation of a tower at a point distant \[d\] metres from its base is\[{{30}^{o}}\]. If the tower is \[20\,\,m\] high, then the value of \[d\] is:

A) \[10\sqrt{3}m\]

B) \[\frac{20}{\sqrt{3}}m\]

C) \[20\sqrt{3}m\]

D) \[10\,\,m\]

View Answer

106) \[l,\,\,\,m,\,\,\,n\] are the \[p\text{th}\], \[q\text{th}\] and \[r\text{th}\] terms of a \[GP\] and all positive, then\[\left| \begin{matrix} \log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1 \\ \end{matrix} \right|\]equals:

A) \[3\]

B) \[2\]

C) \[1\]

D) \[zero\]

View Answer

107) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}\]is equal to:

A) \[\lambda \]

B) \[-1\]

C) zero

D) does not exist

View Answer

108) A triangle with vertices\[(4,\,\,0),\,\,(-1,\,\,-1),\,\,(3,\,\,5)\] is:

A) isosceles and right angled

B) isosceles but not right angled

C) right angled but not isosceles

D) neither right angled nor isosceles

View Answer

109) \[{{\cot }^{-1}}(\sqrt{\cos \alpha })-{{\tan }^{-1}}(\sqrt{\cos \alpha })=x\], then\[\sin x\]is equal to:

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

B) \[{{\cot }^{2}}\left( \frac{\alpha }{2} \right)\]

C) \[\tan \alpha \]

D) \[\cot \left( \frac{\alpha }{2} \right)\]

View Answer

110) A plane which passes through the point \[(3,\,\,2,\,\,0)\] and the line\[\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}\]is:

A) \[x-y+z=1\]

B) \[x+y+z=5\]

C) \[x+2y-z=1\]

D) \[2x-y+z=5\]

View Answer

111) The solution of the equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{e}^{-2x}}\] is:

A) \[\frac{{{e}^{-2x}}}{4}\]

B) \[\frac{{{e}^{-2x}}}{4}+cx+d\]

C) \[\frac{1}{4}{{e}^{-2x}}+c{{x}^{2}}+d\]

D) \[\frac{1}{4}{{e}^{-2x}}+c+d\]

View Answer

112) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}\]is equal to:

A) \[{{e}^{4}}\]

B) \[{{e}^{2}}\]

C) \[{{e}^{3}}\]

D) \[e\]

View Answer

113) The domain of\[{{\sin }^{-1}}\left[ {{\log }_{3}}\left( \frac{x}{3} \right) \right]\]is:

A) \[[1,\,\,9]\]

B) \[[-1,\,\,9]\]

C) \[[-9,\,\,1]\]

D) \[[-9,\,\,-1]\]

View Answer

114) The value of\[{{2}^{1/4}}\cdot {{4}^{1/8}}\cdot {{8}^{1/16}}...\infty \]is

A) \[1\]

B) \[2\]

C) \[3\]

D) \[4\]

View Answer

115) Fifth term of a \[GP\] is \[2\], then the product of its \[9\] terms is:

A) 256

B) 512

C) 1024

D) none of these

View Answer

116) \[\int_{0}^{10\pi }{|\sin x|}\,\,dx\]is:

A) \[20\]

B) \[8\]

C) \[10\]

D) \[18\]

View Answer

117) \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}x}\,\,dx\], then\[\underset{n\to \infty }{\mathop{\lim }}\,n[{{I}_{n}}+{{I}_{n+2}}]\] equal to:

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

B) \[1\]

C) \[\infty \]

D) \[zero\]

View Answer

118) \[\int_{-\pi }^{\pi }{\frac{2x(1+\sin x)}{1+{{\cos }^{2}}x}}dx\]is:

A) \[\frac{{{\pi }^{2}}}{4}\]

B) \[{{\pi }^{2}}\]

C) \[zero\]

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

View Answer

119) The period of the function\[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\] is:

A) \[\pi \]

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

C) \[2\pi \]

D) none of these

View Answer

120) If\[{{x}^{y}}={{e}^{x-y}}\], then\[\frac{dy}{dx}\]is:

A) \[\frac{1+x}{1+\log x}\]

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

C) not defined

D) \[\frac{\log x}{{{(1+\log x)}^{2}}}\]

View Answer

121) The two curves \[{{x}^{3}}-3x{{y}^{2}}+2=0\] and\[3{{x}^{2}}y-{{y}^{3}}-2=0\]

A) cut at right angles

B) touch each other

C) cut at an angle\[\frac{\pi }{3}\]

D) cut at an angle\[\frac{\pi }{4}\]

View Answer

122) The function \[f(x)={{\cot }^{-1}}x+x\] increases in the interval:

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

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

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

D) \[(0,\,\,\infty )\]

View Answer

123) The greatest value of\[f(x)={{(x+1)}^{1/3}}-{{(x-1)}^{1/3}}\]on\[[0,\,\,1]\]is:

A) \[1\]

B) \[2\]

C) \[3\]

D) \[1/3\]

View Answer

124) \[\int{\frac{dx}{x({{x}^{n}}+1)}}\]is equal to:

A) \[\frac{1}{n}\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

B) \[\frac{1}{n}\log \left( \frac{{{x}^{n}}+1}{{{x}^{n}}} \right)+c\]

C) \[\log \left( \frac{{{x}^{n}}}{{{x}^{n}}+1} \right)+c\]

D) none of the above

View Answer

125) The area bounded by the curve \[y=2x-{{x}^{2}}\] and the straight line \[y=-x\] is given by:

A) \[\frac{9}{2}sq\,\,unit\]

B) \[\frac{43}{6}sq\,\,unit\]

C) \[\frac{35}{6}sq\,\,unit\]

D) none of these

View Answer

126) The differential equation of all non-vertical lines in a plane is:

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

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

C) \[\frac{dy}{dx}=0\]

D) \[\frac{dx}{dy}=0\]

View Answer

127) Given two vectors \[\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\] and \[\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}\] the unit vector coplanar with the two vectors and perpendicular to first is:

A) \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]

B) \[\frac{1}{\sqrt{5}}(2\widehat{\mathbf{i}}+\widehat{\mathbf{j}})\]

C) \[\pm \frac{1}{\sqrt{2}}(\widehat{\mathbf{i}}+\widehat{\mathbf{k}})\]

D) none of these

View Answer

128) The vector \[\widehat{\mathbf{i}}+x\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\] is rotated through an angle \[\theta \] and doubled in magnitude, then it becomes\[4\widehat{\mathbf{i}}+(4x-2)\widehat{\mathbf{j}}+2\widehat{\mathbf{k}}\]. The value of is:

A) \[\left\{ -\frac{2}{3},\,\,2 \right\}\]

B) \[\left\{ \frac{1}{3},\,\,2 \right\}\]

C) \[\left\{ \frac{2}{3},\,\,0 \right\}\]

D) \[\{2,\,\,7\}\]

View Answer

129) A parallelepiped is formed by planes drawn through the points \[(2,\,\,3,\,\,5)\] and \[(5,\,\,9,\,\,7)\] parallel to the coordinate planes. The length of a diagonal of the parallelepiped to piped is:

A) \[7\]

B) \[\sqrt{38}\]

C) \[\sqrt{155}\]

D) none of these

View Answer

130) The equation of the plane containing the line\[\frac{x-{{x}_{1}}}{l}=\frac{y-{{y}_{1}}}{m}=\frac{z-{{z}_{1}}}{n}\]is\[a(x-{{x}_{1}})+b(y-{{y}_{1}})+c(z-{{z}_{1}})=0\], where:

A) \[a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=0\]

B) \[al+bm+cn=0\]

C) \[\frac{a}{l}=\frac{b}{m}=\frac{c}{n}\]

D) \[l{{x}_{1}}+m{{y}_{1}}+n{{z}_{1}}=0\]

View Answer

131) \[A\] and \[B\] play a game where each is asked to select a number from \[1\] to\[25\]. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:

A) \[\frac{1}{25}\]

B) \[\frac{24}{25}\]

C) \[\frac{2}{25}\]

D) none of these

View Answer

132) The equation of the directrix of the parabola \[{{y}^{2}}+4y+4x+2=0\]is:

A) \[x=-1\]

B) \[x=1\]

C) \[x=-\frac{3}{2}\]

D) \[x=\frac{3}{2}\]

View Answer

133) Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of \[n\] sides. If\[{{T}_{n+1}}-{{T}_{n}}=21\], then n equals:

A) \[5\]

B) \[7\]

C) \[6\]

D) \[4\]

View Answer

134) In a triangle \[ABC\], \[\frac{A-B+C}{2}\]is equal to:

A) \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]

B) \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]

C) \[{{b}^{2}}-{{c}^{2}}-{{a}^{2}}\]

D) \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]

View Answer

135) For \[x\in R,\,\,\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{x-3}{x+2} \right)}^{x}}\] is equal to:

A) \[e\]

B) \[{{e}^{-1}}\]

C) \[{{e}^{-5}}\]

D) \[{{e}^{5}}\]

View Answer

136) The in centre of the triangle with vertices \[(1,\,\,\sqrt{3}),\,\,(0,\,\,0)\]and\[(2,\,\,0)\]is:

A) \[\left( 1,\,\,\frac{\sqrt{3}}{2} \right)\]

B) \[\left( \frac{2}{3},\,\,\frac{1}{\sqrt{3}} \right)\]

C) \[\left( \frac{2}{3},\,\,\frac{\sqrt{3}}{2} \right)\]

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

View Answer

137) If the vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,,\,\,\,\overset{\to }{\mathop{\mathbf{b}}}\,\] and \[\overset{\to }{\mathop{\mathbf{c}}}\,\] from the sides \[BC,\,\,\,CA\] and \[AB\] respectively, of a triangle \[ABC\], then:

A) \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,+\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=0\]

B) \[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0\]

C) \[\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,=\overset{\to }{\mathop{\mathbf{b}}}\,\cdot \overset{\to }{\mathop{\mathbf{c}}}\,=\overset{\to }{\mathop{\mathbf{c}}}\,\cdot \overset{\to }{\mathop{\mathbf{a}}}\,=0\]

D) \[\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,+\overset{\to }{\mathop{\mathbf{a}}}\,\times \overset{\to }{\mathop{\mathbf{c}}}\,+\overset{\to }{\mathop{\mathbf{c}}}\,\times \overset{\to }{\mathop{\mathbf{a}}}\,=0\]

View Answer

138) If \[\omega \] is an imaginary cube root of unity, then \[{{(1+\omega -{{\omega }^{2}})}^{7}}\]equals:

A) \[128\omega \]

B) \[-128\omega \]

C) \[128{{\omega }^{2}}\]

D) \[-128{{\omega }^{2}}\]

View Answer

139) \[{{\sin }^{2}}\theta =\frac{4xy}{{{(x+y)}^{2}}}\]is true, if and only if:

A) \[x+y\ne 0\]

B) \[x=y,\,\,x\ne 0,\,\,y\ne 0\]

C) \[x=y\]

D) \[x\ne 0,\,\,y\ne 0\]

View Answer

140) The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] and having its centre at\[(0,\,\,3)\] is:

A) \[4\]

B) \[3\]

C) \[\sqrt{12}\]

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

View Answer

141) If \[(\omega \ne 1)\] is a cubic root of unity, then\[\left| \begin{matrix} 1 & 1+1+{{\omega }^{2}} & {{\omega }^{2}} \\ 1-i & -1 & {{\omega }^{2}}-1 \\ -i & -1+\omega -i & -1 \\ \end{matrix} \right|\]equals:

A) \[zero\]

B) \[1\]

C) \[i\]

D) \[\omega \]

View Answer

142) Let\[f(2)=4\] and \[f'(2)=4\]. Then\[\underset{x\to 2}{\mathop{\lim }}\,\frac{x\,\,f(2)-2f(x)}{x-2}\]is given by:

A) \[2\]

B) \[-2\]

C) \[-4\]

D) \[3\]

View Answer

143) Three straight lines \[2x+11y-5=0\],\[24x+7y-20=0\]and\[4x-3y-2=0\]:

A) form a triangle

B) are only concurrent

C) are concurrent with on line bisecting the angle between the other two

D) none of the above

View Answer

144) A straight line through the point\[(2,\,\,2)\]intersects the line\[\sqrt{3}x+y=0\]and\[\sqrt{3}x-y=0\]at the points\[A\]and\[B\]. The equation to the line\[AB\], so that triangle\[AOB\]is equilateral is:

A) \[x-2=0\]

B) \[y-2=0\]

C) \[x+y-4=0\]

D) none of these

View Answer

145) The greatest distance of the point \[P(10,\,\,7)\] from the circle \[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\] is:

A) \[10\]

B) \[15\]

C) \[5\]

D) none of these

View Answer

146) The equation of the ellipse whose foci are \[(\pm \,\,2,\,\,0)\]and eccentricity \[\frac{1}{2}\] is:

A) \[\frac{{{x}^{2}}}{12}+\frac{{{y}^{2}}}{16}=1\]

B) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{12}=1\]

C) \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{8}=1\]

D) none of these

View Answer

147) The equation of the chord joining two points \[({{x}_{1}},\,\,{{y}_{1}})\] and \[({{x}_{2}},\,\,{{y}_{2}})\] on the rectangular hyperbola \[xy={{c}^{2}}\] is:

A) \[\frac{x}{{{x}_{1}}+{{x}_{2}}}+\frac{y}{{{y}_{1}}+{{y}_{2}}}=1\]

B) \[\frac{x}{{{x}_{1}}-{{x}_{2}}}+\frac{y}{{{y}_{1}}-{{y}_{2}}}=1\]

C) \[\frac{x}{{{y}_{1}}+{{y}_{2}}}+\frac{y}{{{x}_{1}}+{{x}_{2}}}=1\]

D) \[\frac{x}{{{y}_{1}}-{{y}_{2}}}+\frac{y}{{{x}_{1}}-{{x}_{2}}}=1\]

View Answer

148) Let \[R\] be the resultant of \[P\] and \[Q\] \[\text{and}\] if \[\frac{P}{3}=\frac{Q}{7}=\frac{R}{5}\], the angle between \[P\] and \[R\] is:

A) \[{{\cos }^{-1}}\left( \frac{11}{14} \right)\]

B) \[{{\cos }^{-1}}\left( -\frac{11}{14} \right)\]

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

D) \[\frac{5\pi }{6}\]

View Answer

149) Two bodies of different masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are dropped from different heights \[{{h}_{1}}\] and \[{{h}_{2}}\]. The ratio of the time taken by the two bodies to fall through these distances 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

150) If\[\operatorname{var}(x)=8.25,\,\,\operatorname{var}(y)=33.96\]and\[\operatorname{cov}(x,\,\,y)=10.2\], then the correlation coefficient is:

A) \[0.89\]

B) \[-0.98\]

C) \[0.61\]

D) \[-0.16\]

View Answer

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