Solved papers for VIT Engineering VIT Engineering Solved Paper-2007

VIT Engineering Solved Paper-2007 Total Questions - 120

1) Ionization power and penetration range of radioactive radiation increases in the order:

A)

\[\gamma ,\beta ,\alpha \,and\,\gamma ,\beta ,\alpha \,respectively\]

B)

\[\gamma ,\beta ,\alpha \,and\,\alpha ,\beta ,\gamma \,respectively\]

C)

\[\alpha ,\beta ,\gamma ,\,and\,\alpha ,\beta ,\gamma \,respectively\]

D)

\[\alpha ,\beta ,\gamma \,and\,\gamma ,\beta ,\alpha ,\,respectively\]

View Answer
2) The half-life of a radioactive element is 3.8 days. The fraction left after 19 days will be:

A)

0.124

B)

0.062

C)

0.093

D)

0.031

View Answer
3) Two identical p-n junctions are connected in series in three different ways as shown below to a battery. The potential drop across the p-n junctions are equal in:

A)

circuits 2 and 3

B)

circuits 1 and 2

C)

circuits 1 and 3

D)

none of the circuit

View Answer
4) The temperature coefficient of a zener mechanism is:

A)

negative

B)

positive

C)

infinity

D)

zero

View Answer
5) Identify the logic gate from the following truth table:

Input Output

A B Y

0 0 1

0 1 0

1 0 0

1 1 0

A)

NOR gate

B)

NOT gate

C)

AND gate

D)

NAND gate

View Answer
6) In Boolean algebra, \[\overline{\overline{A}.\overline{B}}\] is equal to:

A)

\[\overline{\text{A}}\cdot \overline{\text{B}}\]

B)

\[\overline{\text{A}}+\overline{\text{B}}\]

C)

\[\text{A}\cdot \text{B}\]

D)

\[\text{A+B}\]

View Answer
7) Radar waves are sent towards a moving aeroplane and the reflected waves are received. When the aeroplane is moving towards the radar, the wavelength of the wave:

A)

decreases

B)

increases

C)

remains the same

D)

sometimes increases or decreases .

View Answer
8) The transmission of high frequencies in a coaxial cable is determined by:

A)

\[\frac{1}{{{\left( LC \right)}^{1/2}}},\], where L and C are inductance and capacitance

B)

\[{{\left( LC \right)}^{2}}\]

C)

the impedance L alone

D)

the dielectric and skin effect

View Answer
9) The output stage of a television transmitter is most likely 10 be a:

A)

plate- modulated class C amplifier

B)

grid- modulated class C amplifier

C)

screen- modulated class C amplifier

D)

grid- modulated class A amplifier

View Answer
10) The antenna current of an AM transmitter is 8 A when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Find the percentage modulation.

A)

60.1%

B)

70.1%

C)

80.1%

D)

50.1%

View Answer
11) Two point like charges Q1 and Q2 of whose strengths are equal in absolute value are placed at a certain distance from each other. Assuming the field strength to be positive in the positive direction of x-axis, the signs of the charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\] for the graphs (field strength versus distance) shown in Fig. 1, 2, 3 and 4 are :

A)

\[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both positive; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both negative

B)

\[{{Q}_{1}}\] negative \[{{Q}_{2}}\] positive; \[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both positive; both negative

C)

\[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; both negative; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both positive

D)

both positive; \[{{Q}_{1}}\] positive, \[{{Q}_{2}}\] negative; \[{{Q}_{1}}\] negative, \[{{Q}_{2}}\] positive; both negative

View Answer
12)  ABCD is a rectangle. At comers B, C and D of the rectangle are placed charges \[+10\,\times \,{{10}^{-10}}\,C,-20\,\times \,{{10}^{-12}}\,and\,10\,\times \,{{10}^{-12}}C,\]respectively. Calculate the potential at the fourth comer. (The side \[AB=4\text{ }cm\] and \[BC=3\text{ }cm\])

A)

1.65 V

B)

0.165 V

C)

16.5 V

D)

2.65 V

View Answer
13) A parallel plate capacitor of capacitance 100 pF is to be constructed by using paper sheets of 1 mm thickness as dielectric. If the dielectric constant of paper is 4, the number of circular metal foils of diameter 2 cm each required for the purpose is:

A)

40

B)

20

C)

30

D)

10

View Answer
14) The electric field intensity \[\overrightarrow{E}\], due to an electric dipole of moment \[\overrightarrow{P}\], at a point on the equatorial line is:

A)

parallel to the axis of the dipole and opposite to the direction of the dipole moment \[\overrightarrow{P}\]

B)

perpendicular to the axis of the dipole and is directed away from it

C)

parallel to the dipole moment

D)

perpendicular to the axis of the dipole and is directed towards it

View Answer
15) Twelve wires of each of resistance 60 are connected to form a cube as shown in the figure. The current enters at a comer A and leaves at the diagonally opposite corner G. The joint resistance across the comers A and G are:

A)

12\[\Omega \]

B)

60\[\Omega \]

C)

30\[\Omega \]

D)

50\[\Omega \]

View Answer
16) A conductor and a semiconductor are connected in parallel as shown in the figure. At a certain voltage both ammeters register the same current. If the voltage of the DC source is increased then the:

A)

ammeter connected to the semiconductor will register higher current than the ammeter connected to the conductor

B)

ammeter connected to the conductor will register higher current than the ammeter connected to the semiconductor

C)

ammeters connected to both semiconductor and conductor will register the same current

D)

ammeters connected to both semiconductor and conductor will register no change in the current

View Answer
17) A uniform copper wire of length 1 m and cross-sectional area 8 x 10-7m2 carries a current of 1 A. Assuming that there are \[8\times {{10}^{28}}\]free electron/ m3 in copper, how long will an electron take to drift from one end of the wire to the other?

A)

\[0.8\times {{10}^{3}}s~\]

B)

\[1.6\times {{10}^{3}}s\]

C)

\[3.2\times {{10}^{3}}s\]

D)

\[6.4\times {{10}^{3}}s\]

View Answer
18) The temperature coefficient of resistance of a wire is 0.00125 / K. At 300 K, its resistance is 1\[\Omega \]. The resistance of the wire will be 2 0 at:

A)

1154 K

B)

1100 K

C)

1400 K

D)

1127 K

View Answer
19) A rectangular coil ASCD which is rotated at a constant angular velocity about an horizontal as shown in the figure. The axis of rotation of the coil as well as the magnetic field B are horizontal. Maximum current will flow in the circuit when the plane of the coil is:

A)

inclined at \[30{}^\circ \] to the magnetic field

B)

perpendicular to the magnetic field

C)

inclined at \[45{}^\circ \] to the magnetic field

D)

parallel to the magnetic field

View Answer
20) If the total emf in a thermocouple is a parabolic function expressed as \[E=at+\frac{1}{2}b{{t}^{2}},\]which of the following relation does not hold good?

A)

neutral temperature \[{{t}_{n}}=-\frac{a}{b}\]

B)

temperature of inversion, \[{{t}_{i}}=\frac{-2a}{b}\]

C)

thermoelectric power \[P=a+bt\]

D)

\[{{t}_{n}}=\frac{a}{b}\]

View Answer
21) The proton of energy \[1MeV\] describes a circular path in plane at right angles to a uniform magnetic field of \[6.28\times {{10}^{-4}}T\]. The mass of the proton is \[1.7\times {{10}^{-27}}kg\]. The cyclotron frequency of the proton is very nearly equal to:

A)

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

B)

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

C)

\[{{10}^{6}}Hz\]

D)

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

View Answer
22) The magnetic field at the centre of a loop of a circular wire of radius r carrying current I may be taken as B0. If a panicle of charge q moving with speed v passes the centre of a semicircular wire, as shown in figure, along the axis of the wire, the force on it due to the current is:

A)

zero

B)

\[\frac{1}{4}\]B0 qv

C)

\[\frac{1}{2}q{{B}_{0}}v\]

D)

\[q{{B}_{0}}v\]

View Answer
23) There are two solenoids of same length and inductance L but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series. (1) They are connected in series but separated by large distance, (2) they are connected in series with one inside the other and senses of the turns coinciding, (3) both are connected in series with one inside the other with senses of the turns opposite as depicted in figures 1, 2 and 3, respectively. The total inductance of the solenoids in each of the case 1, 2 and 3 are respectively:

A)

\[0,4{{L}_{0}},2{{L}_{0}}\]

B)

\[4{{L}_{0}},2{{L}_{0}},0\]

C)

\[2{{L}_{0}},0,4{{L}_{0}}\]

D)

\[2{{L}_{0}},4{{L}_{0}},0\]

View Answer
24) From figure shown below a series L-C-R circuit connected to a variable frequency\[200\text{ }V\]source. \[L=5H,\]\[\text{C=80 }\!\!\mu\!\!\text{ F}\]and \[\text{R = 40 }\Omega \]. Then the source frequency which drive the circuit at resonance is:

A)

25 Hz

B)

\[\frac{25}{\pi }\] Hz

C)

50 Hz

D)

\[\frac{50}{\pi }\]Hz

View Answer
25) If the coefficient of mutual induction of the primary and secondary coils of an induction coil is\[\text{5 H}\]and a current of \[10\text{ A}\] is cut-off in \[5\times {{10}^{-4}}s\], the emf inducted (in volt) in the secondary coil is:

A)

\[5\times {{10}^{4}}\]

B)

\[1\times {{10}^{5}}\]

C)

\[25\times {{10}^{5}}\]

D)

\[5\times {{10}^{6}}\]

View Answer
26) A voltage of peak value 283 V and varying frequency is applied to a series L-C-R combination in which \[R=3\,\Omega \], \[\text{L = 25 mH}\]and \[\text{C = 400 }\!\!\mu\!\!\text{ F}\]. The frequency (in Hz) of the source at which maximum power is dissipated in the above, is:

A)

51.5

B)

50.7

C)

51.1

D)

50.3

View Answer
27) Pour independent waves are represented by equations: (1) \[{{X}_{1}}={{a}_{1}}\,\sin \,\omega t\] (2) \[{{X}_{2}}={{a}_{1}}\,\sin \,2\omega t\] (3) \[{{X}_{3}}={{a}_{1}}\,\sin \,{{\omega }_{1}}t\] (4) \[{{X}_{4}}={{a}_{1}}\,\sin \,\left( \omega t+\delta \right)\] Interference is possible between waves represented by equations:

A)

3 and 4

B)

1 and 2

C)

2 and 3

D)

1 and 4

View Answer
28) Following diffraction pattern was obtained using a diffraction grating using two different wavelengths \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\]. With the help of the figure identify which is the longer wavelength and their ratios.

A)

\[{{\lambda }_{2}}\]is longer than \[{{\lambda }_{1}}\]and the ratio of the longer to the shorter wavelength is 1.5

B)

\[{{\lambda }_{1}}\] is longer than \[{{\lambda }_{2}}\] and the ratio of the longer to the shorter wavelength is 1.5

C)

\[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are equal and their ratio is 1.0

D)

\[{{\lambda }_{2}}\] is longer than \[{{\lambda }_{1}}\] and the ratio of the longer to the shorter wavelength is 2.5

View Answer
29) In Youngs double slit experiment, the interference pattern is found to have an intensity ratio between bright and dark fringes is 9. This implies that:

A)

the intensities at the screen due to two slits are 5 units and 4 units respectively

B)

the intensities at the screen due to the two slits are 4 units and 1 units, respectively

C)

the amplitude ratio is 7

D)

the amplitude ratio is 6

View Answer
30) Rising and setting sun appears to be reddish because:

A)

diffraction sends red rays to earth at these times

B)

scattering due to dust panicles and air molecules are responsible

C)

refraction is responsible

D)

polarization is responsible

View Answer
31) The magnetic moment of the ground state of an atom whose open sub-shell is half-filled with five electrons is:

A)

\[\sqrt{35}\sqrt{{{\mu }_{B}}}\]

B)

\[35{{\mu }_{B}}\]

C)

\[35\sqrt{{{\mu }_{B}}}\]

D)

\[{{\mu }_{B}}\sqrt{35}\]

View Answer
32) Indicate which one of the following statements is not correct?

A)

Intensities of reflections from different crystallographic planes are equal

B)

According to Braggs law higher order of reflections have high 9 values for a given wavelength of radiation

C)

For a given wavelength of radiation, there is a smallest distance between the crystallographic planes which can be determined

D)

Braggs law may predict a reflection from a crystallographic plane to be present but it may be absent due to the crystal symmetry

View Answer
33) Identify the graph which correctly represents the Moseleys law?

A)



B)



C)

D)



View Answer
34) Assuming f to be frequency of first line in Burner series, the frequency of the immediate next (i.e., second) line is:

A)

0.50 f

B)

1.35 f

C)

2.05 f

D)

2.70 f

View Answer
35) The velocity of a panicle at which the kinetic energy is equal to its rest energy is:

A)

\[\left( \frac{3c}{2} \right)\]

B)

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

C)

\[\frac{{{\left( 3c \right)}^{1/2}}}{2}\]

D)

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

View Answer
36) One electron and one proton is accelerated by equal potential. Ratio in their de- Broglie wavelength is:

A)

1

B)

\[\frac{{{m}_{e}}}{{{m}_{p}}}\]

C)

\[\sqrt{\frac{{{m}_{p}}}{{{m}_{e}}}}\]

D)

\[\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}\]

View Answer
37) Two electrons are moving in opposite direction with speeds 0.8 c and 0.4 c, where c is the speed of light in vacuum. Then the relative speed is about:

A)

0.4 c

B)

0.8 c

C)

0.9 c

D)

1.2 c

View Answer
38) A photo-sensitive material would emit electrons, if excited by photons beyond a threshold. To overcome the threshold, one would increase the:

A)

voltage applied to the light source

B)

intensity of light

C)

wavelength of light

D)

frequency of light

View Answer
39) The radius of nucleus is:

A)

proportional to its mass number

B)

inversely proportional to its mass number

C)

proportional to the cube root of its mass number

D)

not related to its mass number

View Answer
40) Radio carbon dating is done by estimating in specimen the:

A)

amount of ordinary carbon still present

B)

amount of radio carbon still present

C)

ratio of amount of \[^{14}{{C}_{6}}\] to \[^{12}{{C}_{6}}\] still present

D)

ratio of amount of \[^{12}{{C}_{6}}\] to \[^{14}{{C}_{6}}\] still present

View Answer
41) An ion leaves its regular site occupy a position in the space between the lattice sites is called:

A)

Frenkel defect

B)

Schottky defect

C)

impurity defect

D)

vacancy defect

View Answer
42) The 8: 8 type of packing is present in:

A)

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

B)

\[CsCl\]

C)

\[KCl\]

D)

\[NaCl\]

View Answer
43) 43. When a solid melts reversibly:

A)

H decreases

B)

G increases

C)

E decreases

D)

S increases

View Answer
44) Enthalpy is equal to:

A)

\[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}\]

B)

\[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{P}}\]

C)

\[{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{V}}\]

D)

\[-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{V}}\]

View Answer
45) Condition for spontaneity in an isothermal process is:

A)

\[\Delta A+W<0\]

B)

\[\Delta G+U<0\]

C)

\[\Delta G+U>0\]

D)

\[\Delta G-U<0\]

View Answer
46) Given: \[2C+2{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g);\] \[\Delta H=-787kJ\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\] \[\Delta H=-286kJ\] \[{{C}_{2}}{{H}_{2}}(g)+2\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}2C{{O}_{2}}(g)+{{H}_{2}}O(l);\] \[\Delta H=-1310kJ\] The heat of formation of acetylene is :

A)

\[-1802kJ\]

B)

\[+1802kJ\]

C)

\[+237kJ\]

D)

\[-800kJ\]

View Answer
47) Given the equilibrium system : \[N{{H}_{4}}Cl(s)\xrightarrow{{}}NH_{4}^{+}(aq)+C{{l}^{-}}(aq)\] \[(\Delta H=+3.5kcal/mol.)\] What change will shift the equilibrium to the right?

A)

Decreasing the temperature

B)

Increasing the temperature

C)

Dissolving \[NaCl\]   crystals   in   the equilibrium mixture

D)

Dissolving \[N{{H}_{4}}N{{O}_{3}}\] crystals in the equilibrium mixture

View Answer
48) According to Arrhenius equation, the rate constant (K) is related to temperature (T) as:

A)

In \[\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\]

B)

In \[\frac{{{k}_{2}}}{{{k}_{1}}}=-\frac{{{E}_{a}}}{R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]\]

C)

In \[\frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{R}\left[ \frac{1}{{{T}_{1}}}+\frac{1}{{{T}_{2}}} \right]\]

D)

In \[\frac{{{k}_{2}}}{{{k}_{1}}}=-\frac{{{E}_{a}}}{R}\left[ \frac{1}{{{T}_{1}}}+\frac{1}{{{T}_{2}}} \right]\]

View Answer
49) Equivalent amounts of \[{{H}_{2}}\] and \[{{I}_{2}}\] are heated in a closed vessel till equilibrium is obtained. If 80% of the hydrogen can be converted to \[HI\], the \[{{k}_{c}}\] at this temperature is:

A)

\[64\]

B)

\[16\]

C)

\[0.25\]

D)

\[4\]

View Answer
50) For the reaction \[{{H}_{2}}(g)+{{I}_{2}}(g)\xrightarrow{{}}2HI(g),\] the equilibrium constant \[{{K}_{p}}\] changes with:

A)

total pressure

B)

catalyst

C)

the amount \[{{H}_{2}}\] and \[{{I}_{2}}\]

D)

temperature

View Answer
51) How long (in hours) must a current of 5.0 A be maintained to electroplate 60 g of calcium from molten \[CaC{{l}_{2}}\]?

A)

\[27h\]

B)

\[8.3h\]

C)

\[11h\]

D)

\[16h\]

View Answer
52) For strong electrolytes the plot of molar conductance vs\[\sqrt{C}\] is:

A)

parabolic

B)

linear

C)

sinusoidal

D)

circular

View Answer
53) If the molar conductance values of \[C{{a}^{2+}}\] and \[C{{l}^{-}}\] at infinite dilution are respectively \[118.88\times {{10}^{-4}}{{m}^{2}}mho\,mo{{l}^{-1}}\] and \[77.33\times {{10}^{-4}}{{m}^{2}}m\hom o{{l}^{-1}}\] then that of \[CaC{{l}_{2}}\] is (in \[{{m}^{2}}\,mho\,mo{{l}^{-1}}\]):

A)

\[118.88\times {{10}^{-4}}\]

B)

\[154.66\times {{10}^{-4}}\]

C)

\[273.54\times {{10}^{-4}}\]

D)

\[196.21\times {{10}^{-4}}\]

View Answer
54) The standard reduction potentials at 298 K for the following half reactions are given against each: \[Z{{n}^{2+}}(aq)+2{{e}^{-}}\to Zn(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.762V\] \[C{{r}^{3+}}(aq)+3{{e}^{-}}\to Cr(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.740V\] \[2{{H}^{+}}(aq)+2{{e}^{-}}\to {{H}_{2}}(s)\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.00V\] \[F{{e}^{3+}}(aq)+3{{e}^{-}}\to F{{e}^{2+}}(aq)\,\,\,\,\,\,\,\,\,\,{{E}^{o}}=-0.762V\] The strongest reducing agent is:

A)

\[Zn(s)\]

B)

\[Cr(s)\]

C)

\[{{H}_{2}}(g)\]

D)

\[F{{e}^{2+}}(aq)\]

View Answer
55) The epoxide ring consists of which of the following :

A)

three .membered ring with two carbon and one oxygen

B)

four membered ring with three carbon and one oxygen

C)

five membered ring with four carbon and one oxygen

D)

six membered ring with five carbon and one oxygen

View Answer
56) In the Grignard reaction, which metal forms an organometallic bond?

A)

Sodium

B)

Titanium

C)

Magnesium

D)

Palladium

View Answer
57) Phenol is more acidic than:

A)

p-chlorophenol

B)

p-nitrophenol

C)

o-nitrophenol

D)

ethanol

View Answer
58) Aldol condensation is given by:

A)

trimethylacetaldehyde

B)

acetaldehyde

C)

benzaldehyde

D)

formaldehyde

View Answer
59) Give the IUPAC name for \[{{H}_{3}}C-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-{{H}_{2}}C-C{{H}_{2}}-\overset{O}{\mathop{\overset{||}{\mathop{C}}\,}}\,-OC{{H}_{3}}\]

A)

ethyl-4-oxoheptanoate

B)

methyl-4-oxoheptanoate

C)

ethyl-4-oxohexanoate

D)

methyl-4-oxohexanoate

View Answer
60) In which of the below reaction do we find \[\alpha \], \[\beta \]-unsaturated carbonyl compounds undergoing a ring closure reaction with conjugated dienes?

A)

Perkin reaction

B)

Diels-Alder reaction

C)

Claisen rearrangement

D)

Hofmann reaction

View Answer
61) The catalyst used in Rosenmund reaction is:

A)

\[Zn/Hg\]

B)

\[Pd/BaS{{O}_{4}}\]

C)

Raney \[Ni\]

D)

\[Na\] in ethanol

View Answer
62) \[{{(C{{H}_{2}}CO)}_{2}}O+RMgX\xrightarrow{{{H}_{2}}O}\]?

A)

\[ROOC(C{{H}_{2}})COOR\]

B)

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

C)

\[RCOOR\]

D)

\[RCOOH\]

View Answer
63) Identify, which of the below does not possess any element of symmetry?

A)

(+)(-) tartaric acid

B)

Carbon tetrachloride

C)

Methane

D)

Meso-tartaric acid

View Answer
64) The weakest acid amongst the following is :

A)

\[ClC{{H}_{2}}COOH\]

B)

\[HCOOH\]

C)

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

D)

\[C{{H}_{2}}(I)COOH\]

View Answer
65) Urea on slow heating gives:

A)

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

B)

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

C)

\[HCNO\]

D)

\[N{{H}_{2}}CON{{H}_{2}}.HN{{O}_{3}}\]

View Answer
66) Trans esterification is the process of :

A)

conversion of an aliphatic acid to ester

B)

conversion of an aromatic acid to ester

C)

conversion of one ester to another ester

D)

conversion of an ester into its components namely acid and alcohol

View Answer
67) The correct sequence of base strengths in aqueous solution is:

A)

\[{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}>{{(C{{H}_{3}})}_{3}}N\]

B)

\[{{(C{{H}_{3}})}_{3}}N>{{(C{{H}_{3}})}_{2}}NH>C{{H}_{3}}N{{H}_{2}}\]

C)

\[{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}={{(C{{H}_{3}})}_{2}}NH\]

D)

\[{{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}\]

View Answer
68) When aqueous solution of benzene diazoniumchloride is boiled, the product formed is:

A)

\[{{C}_{6}}{{H}_{5}}C{{H}_{2}}OH\]

B)

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

C)

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

D)

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

View Answer
69) Carbylamine reaction is given by aliphatic :

A)

primary amine

B)

secondary amine

C)

tertiary amine

D)

quaternary ammonium salt

View Answer
70) \[{{C}_{6}}{{H}_{5}}CHO\xrightarrow{N{{H}_{3}}}\]?

A)

\[{{C}_{6}}{{H}_{5}}C{{H}_{2}}OH\]

B)

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

C)

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

D)

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

View Answer
71) In \[TeC{{l}_{4}}\], the central atom tellurium involves:

A)

\[s{{p}^{3}}\] hybridisation

B)

\[s{{p}^{3}}d\] hybridization

C)

\[s{{p}^{3}}{{d}^{2}}\] hybridisation

D)

\[ds{{p}^{2}}\] hybridization

View Answer
72) Which of the following compounds volatilises on heating?

A)

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

B)

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

C)

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

D)

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

View Answer
73) A nuclear reaction of \[_{92}^{235}U\] with a neutron produces \[_{36}^{90}Kr\] and two neutrons. Other element produced in this reaction is:

A)

\[_{52}^{137}Te\]

B)

\[_{55}^{144}Cs\]

C)

\[_{56}^{137}Ba\]

D)

\[_{56}^{144}Ba\]

View Answer
74) \[AgCl\] dissolves in a solution of \[N{{H}_{3}}\] but not in water because:

A)

\[N{{H}_{3}}\] is a better solvent than \[{{H}_{2}}O\]

B)

\[A{{g}^{+}}\] forms a complex ion with \[N{{H}_{3}}\]

C)

\[N{{H}_{3}}\]is a stronger base than \[{{H}_{2}}O\]

D)

the dipole moment of water is higher than \[N{{H}_{3}}\]

View Answer
75) Which of the following is hexadentate ligand?

A)

Ethylene diamine

B)

Ethylene diamine tetra acetic acid

C)

1, 10-phenanthroline

D)

Acetyl acetonato

View Answer
76) 76. A coordiante bond is a dative covalent bond. Which of the below is true?

A)

Three atom form bond by sharing their electrons

B)

Two atom form bond by sharing their electrons

C)

Two atoms form bond and one of them provides both electrons

D)

Two atoms form bond by sharing electrons obtained from third atom

View Answer
77) Which of the following complex has zero magnetic moment (spin only)?

A)

\[[Ni{{(N{{H}_{3}})}_{6}}]C{{l}_{2}}\]

B)

\[N{{a}_{3}}[Fe{{F}_{6}}]\]

C)

\[[Cr{{({{H}_{2}}O)}_{6}}]S{{O}_{4}}\]

D)

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

View Answer
78) The IUPAC name of \[{{[Ni{{(PP{{h}_{3}})}_{2}}C{{l}_{2}}]}^{2+}}\] is:

A)

bis dichloro (triphenylphosphine) nickel (II)

B)

dichloro bis (triphenylphosphine) nickel (II)

C)

dichloro triphenylphosphine nickel (II)

D)

triphenyl phosphine nickel (II) dichloride

View Answer
79) Among the following the compound that is both paramagnetic and coloured is:

A)

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

B)

\[{{(N{{H}_{4}})}_{2}}[TiC{{l}_{6}}]\]

C)

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

D)

\[{{K}_{3}}[Cu{{(CN)}_{4}}]\]

View Answer
80) On an X-ray diffraction photograph the intensity of the spots depends on:

A)

neutron density of the atoms/ions

B)

electron density of the atoms/ions

C)

proton density of the atoms/ions

D)

photon density of the atoms/ions

View Answer
81) If the normal to the curve \[y=f(x)\] at (3, 4) makes an angle \[\frac{3\pi }{4}\] with the positive x-axis, then \[f(3)\] is equal to :

A)

\[-1\]

B)

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

C)

\[1\]

D)

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

View Answer
82) The function\[f(x)={{x}^{2}}{{e}^{-2x}},\]\[x>0\]. Then the maximum value of \[f(x)\] is :

A)

\[\frac{1}{e}\]

B)

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

C)

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

D)

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

View Answer
83) If \[(x+y)\sin u={{x}^{2}}{{y}^{2}},\] then \[x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}\] is equal to :

A)

\[\sin u\]

B)

\[\text{cosec}\,u\]

C)

\[2\tan u\]

D)

\[3\tan u\]

View Answer
84) The angle between the tangents at those points on the curve \[x={{t}^{2}}+1\] and \[y={{t}^{2}}-t-6\]where it meets x-axis is :

A)

\[\pm {{\tan }^{-1}}\left( \frac{4}{29} \right)\]

B)

\[\pm {{\tan }^{-1}}\left( \frac{5}{49} \right)\]

C)

\[\pm {{\tan }^{-1}}\left( \frac{10}{49} \right)\]

D)

\[\pm {{\tan }^{-1}}\left( \frac{8}{29} \right)\]

View Answer
85) The value of \[\int_{1}^{4}{\left| x-3 \right|}\,dx\]is equal to :

A)

\[2\]

B)

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

C)

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

D)

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

View Answer
86) The area of the region bounded by the straight lines \[x=0\]and \[x=2,\] and the curves \[y={{2}^{x}}\] and \[y=2x-{{x}^{2}}\] is equal to :

A)

\[\frac{2}{\log 2}-\frac{4}{3}\]

B)

\[\frac{3}{\log 2}-\frac{4}{3}\]

C)

\[\frac{1}{\log 2}-\frac{4}{3}\]

D)

\[\frac{4}{\log 2}-\frac{3}{2}\]

View Answer
87) The value of \[\int_{0}^{\infty }{\frac{dx}{({{a}^{2}}+{{x}^{2}})}}\]is equal to:

A)

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

B)

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

C)

\[\frac{\pi }{a}\]

D)

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

View Answer
88) The value of the integral \[\int{{{e}^{x}}}{{\left( \frac{1-x}{1+{{x}^{2}}} \right)}^{2}}dx\]is:

A)

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

B)

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

C)

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

D)

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

View Answer
89) If \[x\sin \left( \frac{y}{x} \right)dy=\left[ y\,\sin \left( \frac{y}{x} \right)-x \right]dx\] and \[y(1)=\frac{\pi }{2},\]then the value of \[\cos \left( \frac{y}{x} \right)\] is equal to:

A)

\[x\]

B)

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

C)

\[\log x\]

D)

\[{{e}^{x}}\]

View Answer
90) The differential equation of the system of all circles of radius \[r\] in the \[xy\] plane is :

A)

\[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{2}}={{r}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}\]

B)

\[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{3}} \right]}^{2}}={{r}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}\]

C)

\[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3}}={{r}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{2}}\]

D)

\[{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3}}={{r}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}\]

View Answer
91) The general solution of the differential equation \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}+y=2{{e}^{3x}}\]is given by:

A)

\[y=({{c}_{1}}+{{c}_{2}}x){{e}^{x}}+\frac{{{e}^{3x}}}{8}\]

B)

\[y=({{c}_{1}}+{{c}_{2}}x){{e}^{-x}}+\frac{{{e}^{-3x}}}{8}\]

C)

\[y=({{c}_{1}}+{{c}_{2}}x){{e}^{-x}}+\frac{{{e}^{3x}}}{8}\]

D)

\[y=({{c}_{1}}+{{c}_{2}}x){{e}^{x}}+\frac{{{e}^{-3x}}}{8}\]

View Answer
92) The solution of the differential equation\[ydx+(x-{{y}^{3}})=0\]is:

A)

\[xy=\frac{1}{3}{{y}^{3}}+c\]

B)

\[xy={{y}^{4}}+c\]

C)

\[{{y}^{4}}=4xy+c\]

D)

\[4y={{y}^{3}}+c\]

View Answer
93) The number of integral solutions of\[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=0,\] with \[{{x}_{i}}\ge -\,5,\] is :

A)

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

B)

\[{}^{16}{{C}_{2}}\]

C)

\[{}^{17}{{C}_{2}}\]

D)

\[{}^{18}{{C}_{2}}\]

View Answer
94) Let A = {1, 2, 3,..., n} and B = {a, b, c}, then the number of functions from A to B that are onto is:

A)

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

B)

\[{{3}^{n}}-{{2}^{n}}-1\]

C)

\[3\,({{2}^{n}}-1)\]

D)

\[{{3}^{n}}-3\,({{2}^{n}}-1)\]

View Answer
95) Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is :

A)

9

B)

12

C)

10

D)

14

View Answer
96) In a group G = {1,3,7,9} under multiplication modulo 10, the inverse of 7 is :

A)

7

B)

3

C)

9

D)

1

View Answer
97) A box contains 9 tickets numbered 1 to 9 inclusive. If 3 tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even}is:

A)

\[\frac{5}{17}\]

B)

\[\frac{4}{17}\]

C)

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

D)

\[\frac{5}{18}\]

View Answer
98) If \[P(A)=\frac{1}{12},P(B)=\frac{5}{12}\] and \[P\left( \frac{B}{A} \right)=\frac{1}{15},\] then \[P(A\cup B)\]is equal to :

A)

\[\frac{89}{180}\]

B)

\[\frac{90}{180}\]

C)

\[\frac{91}{180}\]

D)

\[\frac{92}{180}\]

View Answer
99) If the probability density function of a random variable X is \[f(x)=\frac{x}{2}\] in \[0\le x\le 2,\]then \[P(X>1.5\left| X>1 \right.)\] is equal to :

A)

\[\frac{7}{16}\]

B)

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

C)

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

D)

\[\frac{21}{64}\]

View Answer
100) If X follows a binomial distribution with parameters n = 100 and \[p=\frac{1}{3},\] then \[P(X=r)\] is maximum when r is equal to :

A)

16

B)

32

C)

33

D)

none of these

View Answer
101) If \[A(\theta )=\left[ \begin{matrix} 1 & \tan \theta \\ -\tan \theta & 1 \\ \end{matrix} \right]\] and \[AB=I,\] then\[({{\sec }^{2}}\theta )B\] is equal to :

A)

\[A\,(\theta )\]

B)

\[A\,\left( \frac{\theta }{2} \right)\]

C)

\[A\,\left( -\,\theta \right)\]

D)

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

View Answer
102) If \[x=-\,5\] is a root of \[\left| \begin{matrix}   2x+1 & 4 & 8 \\    2 & 2x & 2 \\    7 & 6 & 2x \\ \end{matrix} \right|=0,\] then the other roots are :

A)

3, 3.5

B)

1, 3.5

C)

1, 7

D)

2, 7

View Answer
103) The simultaneous equations \[Kx+2y-z=1,\] \[(K-I)\,y-2z=2\]and \[(K+2)\,z=3\] have only one solution when :

A)

\[K=-\,2~\]

B)

\[K=-1\]

C)

\[K=0\]

D)

\[~K=1\]

View Answer
104) If the rank of the matrix \[\left| \begin{matrix} -1 & 2 & 5 \\ 2 & -4 & a-4 \\ 1 & -2 & a+1 \\ \end{matrix} \right|\] is 1 then the value of a is :

A)

\[-1\]

B)

\[2\]

C)

\[-6\]

D)

\[4\]

View Answer
105) If \[{{b}^{2}}\ge 4ac\]for the equation\[a{{x}^{4}}+b{{x}^{2}}+c=0,\] then all the roots of the equation will be real if:

A)

\[b>0,\text{ }a<0,\text{ }c>0\]

B)

\[b<0,\text{ }a>0,\text{ }c>0\]

C)

\[b>0,\text{ }a>0,\text{ }c>0\]

D)

\[b>0,\text{ }a>0,\text{ }c<0\]

View Answer
106) If \[x>0\]and \[{{\log }_{3}}x+{{\log }_{3}}(\sqrt{x})+{{\log }_{3}}(\sqrt[4]{x})\]\[+{{\log }_{3}}(\sqrt[8]{x})+{{\log }_{3}}(\sqrt[16]{x})+....=4,\]then \[x\]equals:

A)

9

B)

81

C)

1

D)

27

View Answer
107) The number of real roots of the equation\[{{\left( x+\frac{1}{x} \right)}^{3}}+x+\frac{1}{x}=0\]is :

A)

0

B)

2

C)

4

D)

6

View Answer
108) If \[H\]is the harmonic mean between P and Q, then the value of \[\frac{H}{P}+\frac{H}{Q}\]is:

A)

\[2\]

B)

\[\frac{PQ}{P+Q}\]

C)

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

D)

\[\frac{P+Q}{PQ}\]

View Answer
109) If \[\overrightarrow{b}\] is a unit vector, then\[(\overrightarrow{a}\cdot \overrightarrow{b})\overrightarrow{b}+\overrightarrow{b}\times (\overrightarrow{a}\times \overrightarrow{b})\]is:

A)

\[{{\left| \,\overrightarrow{a}\, \right|}^{2}}\overrightarrow{b}\]

B)

\[\left| \,\overrightarrow{a}\cdot \overrightarrow{b}\, \right|\,\overrightarrow{a}\]

C)

\[\overrightarrow{a}\]

D)

\[\overrightarrow{b}\]

View Answer
110) It \[\theta \] is the between the lines AB and AC where A, B and C are the three points with coordinates (1, 2, -1), (2, 0, 3), (3, -1, 2) respectively, then\[\sqrt{462}\]is equal to :

A)

20

B)

10

C)

30

D)

40

View Answer
111) Let the pairs \[\overrightarrow{a},\,\overrightarrow{b}\] and \[\overrightarrow{c},\,\overrightarrow{d}\] each determine a plane. Then the planes are parallel, if:

A)

\[(\overrightarrow{a}\times \overrightarrow{c})\times (\overrightarrow{b}\times \overrightarrow{c})=\overrightarrow{0}\]

B)

\[(\overrightarrow{a}\times \overrightarrow{c})\cdot (\overrightarrow{b}\times \overrightarrow{c})=0\]

C)

\[(\overrightarrow{a}\times \overrightarrow{b})\times (\overrightarrow{c}\times \overrightarrow{d})=\overrightarrow{0}\]

D)

\[(\overrightarrow{a}\times \overrightarrow{b})\cdot (\overrightarrow{c}\times \overrightarrow{d})=0\]

View Answer
112) Tile area of a parallelogram with \[3\hat{i}+\hat{j}-2\hat{k}\] and \[\hat{i}-3\hat{j}+4\hat{k}\] as diagonals is :

A)

\[\sqrt{72}\]

B)

\[\sqrt{73}\]

C)

\[\sqrt{74}\]

D)

\[\sqrt{75}\]

View Answer
113) If \[\cos x+{{\cos }^{2}}x=1,\]then the value of \[{{\sin }^{12}}x+3{{\sin }^{10}}x+3{{\sin }^{8}}x+{{\sin }^{6}}x-1,\] is equal to :

A)

2

B)

1

C)

-1

D)

0

View Answer
114) The product of all values of\[{{(\cos \alpha +i\sin \alpha )}^{3/5}}\]is :

A)

1

B)

\[\cos \alpha +i\sin \alpha \]

C)

\[\cos 3\alpha +i\sin 3\alpha \]

D)

\[\cos 5\alpha +i\sin 5\alpha \]

View Answer
115) The imaginary part of \[\frac{{{(1+i)}^{2}}}{i\,(2i-1)}\]is :

A)

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

B)

\[0\]

C)

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

D)

\[-\frac{4}{5}\]

View Answer
116) If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2},\] then \[{{\cos }^{-1}}x+{{\cos }^{-1}}y\]is equal to :

A)

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

B)

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

C)

\[\pi \]

D)

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

View Answer
117) The equation of a directrix of the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{25}=1\]is:

A)

3y = 5

B)

y = 5

C)

3y = 25

D)

y = 3

View Answer
118) If the normal at \[(a{{p}^{2}},\,\,2ap)\]on the parabola\[{{y}^{2}}=4ax,\]meets the parabola again at\[(a{{q}^{2}},\,\,2aq),\] then :

A)

\[{{p}^{2}}+pq+2=0\]

B)

\[{{p}^{2}}-pq+2=0\]

C)

\[{{q}^{2}}+pq+2=0\]

D)

\[{{p}^{2}}+pq+1=0\]

View Answer
119) The length of the straight line \[x-3y=1\]intercepted by the hyperbola \[{{x}^{2}}-4{{y}^{2}}=1\] is :

A)

\[\sqrt{10}\]

B)

\[\frac{6}{5}\]

C)

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

D)

\[\frac{6}{5}\sqrt{10}\]

View Answer
120) The curve described parametrically\[x={{t}^{2}}+2t-1,\]\[y=3t+5\]represents:

A)

an ellipse

B)

a hyperbola

C)

a parabola

D)

a circle

View Answer