# Solved papers for VIT Engineering VIT Engineering Solved Paper-2007

### done VIT Engineering Solved Paper-2007

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) $\alpha ,\beta ,\gamma \,and\,\gamma ,\beta ,\alpha ,\,respectively$

• question_answer2) 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

• question_answer3) 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

• question_answer4) The temperature coefficient of a zener mechanism is:

A) negative

B) positive

C) infinity

D) zero

• question_answer5) 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

• question_answer6) 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)  $\text{A+B}$

• question_answer7) 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 .

• question_answer8) 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

• question_answer9) 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

• question_answer10) 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%

• question_answer11) 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

• question_answer12) 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

• question_answer13) 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

• question_answer14) 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

• question_answer15) 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$\Omega$

• question_answer16) 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

• question_answer17) 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) $6.4\times {{10}^{3}}s$

• question_answer18) 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

• question_answer19) 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

• question_answer20) 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) ${{t}_{n}}=\frac{a}{b}$

• question_answer21) 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) ${{10}^{4}}Hz$

• question_answer22) 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) $q{{B}_{0}}v$

• question_answer23) 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) $2{{L}_{0}},4{{L}_{0}},0$

• question_answer24) 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

• question_answer25) 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) $5\times {{10}^{6}}$

• question_answer26) 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

• question_answer27) 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

• question_answer28) 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

• question_answer29) 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

• question_answer30) 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

• question_answer31) 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) ${{\mu }_{B}}\sqrt{35}$

• question_answer32) 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

• question_answer33) Identify the graph which correctly represents the Moseleys law?

A)

B)

C)

D)

• question_answer34) 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

• question_answer35) 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) $\frac{c\sqrt{3}}{2}$

• question_answer36) 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) $\sqrt{\frac{{{m}_{e}}}{{{m}_{p}}}}$

• question_answer37) 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

• question_answer38) 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

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

• question_answer40) 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

• question_answer41) 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

• question_answer42) The 8: 8 type of packing is present in:

A) $Mg{{F}_{2}}$

B) $CsCl$

C) $KCl$

D) $NaCl$

• question_answer43) 43. When a solid melts reversibly:

A) H decreases

B) G increases

C) E decreases

D) S increases

• question_answer44) 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) $-{{T}^{2}}{{\left[ \frac{\delta (G/T)}{\delta T} \right]}_{V}}$

• question_answer45) Condition for spontaneity in an isothermal process is:

A) $\Delta A+W<0$

B) $\Delta G+U<0$

C) $\Delta G+U>0$

D) $\Delta G-U<0$

• question_answer46) 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) $-800kJ$

• question_answer47) 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

• question_answer48) 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 $\frac{{{k}_{2}}}{{{k}_{1}}}=-\frac{{{E}_{a}}}{R}\left[ \frac{1}{{{T}_{1}}}+\frac{1}{{{T}_{2}}} \right]$

• question_answer49) 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) $4$

• question_answer50) 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

• question_answer51) 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) $16h$

• question_answer52) For strong electrolytes the plot of molar conductance vs$\sqrt{C}$ is:

A) parabolic

B) linear

C) sinusoidal

D) circular

• question_answer53) 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) $196.21\times {{10}^{-4}}$

• question_answer54) 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) $F{{e}^{2+}}(aq)$

• question_answer55) 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

• question_answer56) In the Grignard reaction, which metal forms an organometallic bond?

A) Sodium

B) Titanium

C) Magnesium

• question_answer57) Phenol is more acidic than:

A) p-chlorophenol

B) p-nitrophenol

C) o-nitrophenol

D) ethanol

• question_answer58) Aldol condensation is given by:

A) trimethylacetaldehyde

B) acetaldehyde

C) benzaldehyde

D) formaldehyde

• question_answer59) 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

• question_answer60) 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

• question_answer61) The catalyst used in Rosenmund reaction is:

A) $Zn/Hg$

B) $Pd/BaS{{O}_{4}}$

C) Raney $Ni$

D) $Na$ in ethanol

• question_answer62) ${{(C{{H}_{2}}CO)}_{2}}O+RMgX\xrightarrow{{{H}_{2}}O}$?

A) $ROOC(C{{H}_{2}})COOR$

B) $RCOC{{H}_{2}}C{{H}_{2}}COOH$

C) $RCOOR$

D) $RCOOH$

• question_answer63) Identify, which of the below does not possess any element of symmetry?

A) (+)(-) tartaric acid

B) Carbon tetrachloride

C) Methane

D) Meso-tartaric acid

• question_answer64) The weakest acid amongst the following is :

A) $ClC{{H}_{2}}COOH$

B) $HCOOH$

C) $FC{{H}_{2}}C{{H}_{2}}COOH$

D) $C{{H}_{2}}(I)COOH$

• question_answer65) Urea on slow heating gives:

A) $N{{H}_{2}}CONHN{{O}_{2}}$

B) $N{{H}_{2}}CONHCON{{H}_{2}}$

C) $HCNO$

D) $N{{H}_{2}}CON{{H}_{2}}.HN{{O}_{3}}$

• question_answer66) 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

• question_answer67) 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) ${{(C{{H}_{3}})}_{2}}NH>{{(C{{H}_{3}})}_{3}}N>C{{H}_{3}}N{{H}_{2}}$

• question_answer68) 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) ${{C}_{6}}{{H}_{5}}OH$

• question_answer69) Carbylamine reaction is given by aliphatic :

A) primary amine

B) secondary amine

C) tertiary amine

D) quaternary ammonium salt

• question_answer70) ${{C}_{6}}{{H}_{5}}CHO\xrightarrow{N{{H}_{3}}}$?

A) ${{C}_{6}}{{H}_{5}}C{{H}_{2}}OH$

B) ${{C}_{6}}{{H}_{6}}+{{N}_{2}}$

C) ${{C}_{6}}{{H}_{5}}COOH$

D) ${{C}_{6}}{{H}_{5}}OH$

• question_answer71) 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

• question_answer72) Which of the following compounds volatilises on heating?

A) $MgC{{l}_{2}}$

B) $HgC{{l}_{2}}$

C) $CaC{{l}_{2}}$

D) $FeC{{l}_{3}}$

• question_answer73) 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) $_{56}^{144}Ba$

• question_answer74) $AgCl$ 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 $N{{H}_{3}}$

A) Ethylene diamine

B) Ethylene diamine tetra acetic acid

C) 1, 10-phenanthroline

D) Acetyl acetonato

• question_answer76) 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

• question_answer77) 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) ${{K}_{4}}[Fe{{(CN)}_{6}}]$

• question_answer78) 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

• question_answer79) 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) ${{K}_{3}}[Cu{{(CN)}_{4}}]$

• question_answer80) 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

• question_answer81) 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) $-\frac{3}{4}$

• question_answer82) 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) $\frac{4}{{{e}^{4}}}$

• question_answer83) 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) $3\tan u$

• question_answer84) 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) $\pm {{\tan }^{-1}}\left( \frac{8}{29} \right)$

• question_answer85) 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) $\frac{3}{2}$

• question_answer86) 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) $\frac{4}{\log 2}-\frac{3}{2}$

• question_answer87) 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) $\frac{1}{2a}$

• question_answer88) 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) ${{e}^{x}}(1-x)+c$

• question_answer89) 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) ${{e}^{x}}$

• question_answer90) 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) ${{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{3}}={{r}^{2}}{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}$

• question_answer91) 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) $y=({{c}_{1}}+{{c}_{2}}x){{e}^{x}}+\frac{{{e}^{-3x}}}{8}$

• question_answer92) 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) $4y={{y}^{3}}+c$

• question_answer93) 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) ${}^{18}{{C}_{2}}$

• question_answer94) 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) ${{3}^{n}}-3\,({{2}^{n}}-1)$

• question_answer95) 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

• question_answer96) 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

• question_answer97) 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) $\frac{5}{18}$

• question_answer98) 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) $\frac{92}{180}$

• question_answer99) 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) $\frac{21}{64}$

• question_answer100) 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

• question_answer101) 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) $A\,\left( \frac{-\,\theta }{2} \right)$

• question_answer102) 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

• question_answer103) 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) $~K=1$

• question_answer104) 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) $4$

• question_answer105) 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) $b>0,\text{ }a>0,\text{ }c<0$

• question_answer106) 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

• question_answer107) 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

• question_answer108) 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) $\frac{P+Q}{PQ}$

• question_answer109) 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) $\overrightarrow{b}$

• question_answer110) 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

• question_answer111) 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) $(\overrightarrow{a}\times \overrightarrow{b})\cdot (\overrightarrow{c}\times \overrightarrow{d})=0$

• question_answer112) 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) $\sqrt{75}$

• question_answer113) 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

• question_answer114) 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) $\cos 5\alpha +i\sin 5\alpha$

• question_answer115) The imaginary part of $\frac{{{(1+i)}^{2}}}{i\,(2i-1)}$is :

A) $\frac{4}{5}$

B) $0$

C) $\frac{2}{5}$

D) $-\frac{4}{5}$

• question_answer116) 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) $\frac{3\pi }{4}$

• question_answer117) 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

• question_answer118) 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) ${{p}^{2}}+pq+1=0$

• question_answer119) 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) $\frac{6}{5}\sqrt{10}$

• question_answer120) 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