The Kirchhoff's first law $(\sum i= 0)$ and second law $(\sum iR=\sum E)$ , where the symbols have their usual
meanings, are respectively based on
a.
conservation of charge, conservation of energy
Correct Answer
b.
conservation of charge, conservation of
momentum
c.
conservation of energy, conservation of charge
d.
conservation of momentum, conservation of
charge
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Q2mcq
A whistle producing sound waves of frequencies $9500\,Hz$ and above is approaching a stationary person with
speed $v\,ms^{-1}$ . The velocity of sound in air is $300\,ms^{-1}$ . If the person can hear frequencies upto a maximum of
$10, 000\,Hz$ , the maximum value of $v$ upto which he can hear the whistle is
a.
$30\,ms^{-1}$
b.
$15\,ms\sqrt{2}^{-1}$
c.
$15/\,ms\sqrt{2}^{-1}$
d.
$15\,ms^{-1}$
Correct Answer
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Q3mcq
A material ' $B$ ' has twice the specific resistance of ' $A$ '. A circular wire made of ' $B$ ' has twice the diameter of
a wire made of ' $A$ '. Then for the two wires to have the same resistance, the ratio $\ell _{A}/\ell _{B}$ of their respective
lengths must be
a.
2
Correct Answer
b.
1
c.
$\frac{1}{2}$
d.
$\frac{1}{4}$
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Q4mcq
A string is stretched between fixed points separated by $75\,cm$ . It is observed to have resonant frequencies of
$420\,Hz$ and $315\,Hz$ . There are no other resonant frequencies between these two. Then, the lowest resonant
frequency for this string is
a.
$10.5\,Hz$
b.
$105\,Hz$
Correct Answer
c.
$1.05\,Hz$
d.
$1050\,Hz$
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Q5mcq
An inductor $(L= 100mH)$ , a resistor $(R= 100\Omega )$ and a battery $(E = 100\,V)$ are initially connected in series
as shown in the figure. After a long time the battery is disconnected after short circuiting the points $A$ and $B$ .
The current in the circuit $1\,mm$ after the circuit is
a.
$1\,A$
b.
$1/eA$
Correct Answer
c.
$e\,A$
d.
$0.1\,A$
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Q6mcq
The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is
gradually changed. The plate current $I$ of the photocell varies as follows :
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Q7mcq
The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7\,mm$ , is $4.4\,m/s$ .
The period of oscillation is
a.
$100\,s$
b.
$0.01\,s$
Correct Answer
c.
$10\,s$
d.
$0.1\,s$
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Q8mcq
Two insulating plates are both uniformly charged in such a way that the potential difference between them is
$V_{2}- V_{1} = 20\,V$ . (i.e. plate 2 is at a higher potential). The plates are separated by $d= 0.1\,m$ and can be treated
as infinitely large. An electron is released from rest on the inner surface of plate 1 . What is its speed when it
hits plate $2?(e = 1.6 \times 10^{-19}C, m_{e} = 9.11 \times 10^{-31}\,kg)$
a.
$32 \times 10^{-19}\,m/s$
b.
$2.65 \times 10^{6}\,m/s$
Correct Answer
c.
$7.02 \times 10^{12}\,m/s$
d.
$1.87 \times 10^{6}\,m/s$
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Q9mcq
A electric dipole is placed at an angle of $30^{\circ }$ to a non-uniform electric field. The dipole will experience
a.
a torque only
b.
a translational force only in the direction of the
field
c.
a translational force only in a direction normal to
the direction of the field
d.
a torque as well as a translational force
Correct Answer
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Q10mcq
The work of $146\,kJ$ is performed in order to compress one kilo mole of gas adiabatically and in this process
the temperature of the gas increases by $7^{\circ }C$ . The gas is $(R = 8.3\,J\,mol^{-1}\,K^{-1})$
a.
monoatomic
b.
diatomic
Correct Answer
c.
triatomic
d.
a mixture of monoatomic and diatomic
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A bomb of mass $16\,kg$ at rest explodes into two pieces of masses of $4\,kg$ and $12\,kg$ . The velocity of the $12\,kg$
mass is $4\,ms^{-1}$ . The kinetic energy of the other mass is
a.
$96\,J$
b.
$144\,J$
c.
$288\,J$
d.
$192\,J$
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A body falling from rest under gravity passes a certain point $P$ . It was at a distance of $400\,m$ from $P, 4\,s$ prior
to passing through $P$ . If $g= 10\,m/s^{2}$ , then the height above the point $P$ from where the body began to fall is
a.
720 m
b.
900 m
c.
320 m
d.
680 m
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The potential energy of a $1\,kg$ particle free move along the $x$ -axis is given by
$4 2$
$V(x) =( \frac{x}{4} - \frac{x}{2})J$
The total mechanical energy of the particle $2\,J$ . Then, the maximum speed (in $m/s$ ) is
a.
2
b.
$3/\sqrt{2}$
c.
$\sqrt{2}$
d.
$1/\sqrt{2}$
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A particle located at $x= 0$ at time $t= 0$ , starts moving along the positive $x$ -direction with a velocity ' $v$ ' that
varies as $v=\alpha \sqrt{x}$ . The displacement of the particle varies with time as
a.
$t^{3}$
b.
$t^{2}$
c.
$t$
d.
$t^{1/2}$
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Needles $N_{1}, \,N_{2}$ and $N_{3}$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance
respectively. A magnet when brought close to them will
a.
attract all three of them
b.
attract $N_{1}$ and $N_{2}$ strongly but repel $N_{3}$
c.
attract $N_{1}$ strongly, $N_{2}$ weakly and repel $N_{3}$
weakly
d.
attract $N_{1}$ strongly, but repel $N_{2}$ and $N_{3}$ weakly
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An alpha nucleus of energy $\frac{1}{2} mv^{2}$ bombards a heavy nuclear target of charge Ze. Then the distance of closest
approach for the alpha nucleus will be proportional to
a.
$\frac{1}{Ze}$
b.
$v^{2}$
c.
$\frac{1}{m}$
d.
$\frac{1}{v^{4}}$
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The resistance of a bulb filament is $100\Omega$ at a temperature of $100^{\circ }C$ . If its temperature coefficient of resistance
be $0.005$ per $^{\circ }C$ , its resistance will become $200\Omega$ at a temperature of
a.
$200^{\circ }C$
b.
$300^{\circ }C$
c.
$400^{\circ }C$
d.
$500^{\circ }C$
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In an $AC$ generator, a coil with $N$ turns, all of the same area $A$ and total resistance $R$ , rotates with frequency $\omega$
in a magnetic field $B$ . The maximum value of emf generated in the coil is "
a.
N.A.B. $\omega$
b.
N.A.B.R. $\omega$
c.
N.A.B
d.
N.A.B.R
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In a series resonant LCR circuit, the voltage across $R$ is 100 volts and $R= 1k\Omega$ with $C = 2\mu F$ . The resonant
frequency $\omega$ is $200rad/s$ . At resonance the voltage across $L$ is
a.
$4 \times 10^{-3}\,V$
b.
$2.5 \times 10^{-2}\,V$
c.
$40\,V$
d.
$250\,V$
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A particle of mass $100\,g$ is thrown vertically upwards with a speed of $5\,m/s$ . the work done by the force of
gravity during the time the particle goes up is
a.
$0.5\,J$
b.
$-0.5\,J$
c.
$-1.25\,J$
d.
$1.25\,J$
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A thermocouple is made from two metals, Antimony and Bismuth. If one junction of the couple is kept hot and
the other is kept cold then, an electric current will
a.
flow from Antimony to Bismuth at the cold
junction
b.
flow from Antimony to Bismuth at the hot
junction
c.
flow from Bismuth to Antimony at the cold
junction
d.
not flow through the thermocouple
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If the terminal speed of a sphere of gold (density $= 19.5\,kg/m^{3}$ ) is $0.2\,m/s$ in a viscous liquid (density
$= 1.5\,kg/m^{3}$ ) of the same size in the same liquid.
a.
$0.2\,m/s$
b.
$0.4\,m/s$
c.
$0.133\,m/s$
d.
$0.1\,m/s$
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Consider a two particle system with particles having masses $m_{1}$ and $m_{2}$ . If the first particle is pushed towards
the centre of mass through a distance $d$ , by what distance should the second particle be moved, so as to keep
the centre of mass at the same position?
a.
$d$
b.
$\frac{m_{2}}{m_{1}}\,d$
c.
$\frac{m_{1}}{m_{1}+m_{2}}d$
d.
$\frac{m_{1}}{\,m_{2}}\,d$
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A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$ . Two
objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates
with an angular velocity $\omega ' =$
a.
$\frac{\omega m}{(m+2M)}$
b.
$\frac{\omega (m+2M)}{m}$
c.
$\frac{\omega (m-2M)}{(m+2M)}$
d.
$\frac{\omega m}{(m+M)}$
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Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at
temperature $T_{0}$ , while Box $B$ contains one mole of helium at temperature $(7/3)T_{0}$ . The boxes are then put into
thermal contact with each other and heat flows between them until the gases reach a common final
temperature. (Ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_{f}$ , in terms of $T_{0}$ is
a.
$T_{f} = \frac{5}{2}\,T_{0}$
b.
$T_{f} = \frac{3}{7}\,T_{0}$
c.
$T_{f} = \frac{7}{3}\,T_{0}$
d.
$T_{f} = \frac{3}{2}T_{0}$
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A ball of mass $0.2\,kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2\,m$ which
applying the force and the ball goes upto $2\,m$ height further, find the magnitude of the force. Consider
$g = 10\,m/s^{2}$
a.
$22\,N$
b.
$4\,N$
c.
$16\,N$
d.
$20\,N$
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In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each
other. A charged particle is released from rest in this region. The path of the particle will be a
a.
circle
b.
helix
c.
straight line
d.
ellipse
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Four point masses, each of value $m$ , are placed at the corners of a square $ABCD$ of side $\ell$ . The moment of
inertia through $A$ and parallel to $BD$ is
a.
$m\ell ^{2}$
b.
$2\,m\ell ^{2}$
c.
$3m\ell ^{2}$
d.
$3\,m\ell ^{2}$
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Starting from the origin, a body oscillates simple harmonically with a period of $2\,s$ . After what time will its
kinetic energy be $75%$ of the total energy?
a.
$\frac{1}{12}\,s$
b.
$\frac{1}{6}\,s$
c.
$\frac{1}{4}\,s$
d.
$\frac{1}{3}s$
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In a Wheatstone's bridge, there resistances $P, Q$ and $R$ connected in the three arms and the fourth arm is
formed by two resistances $S_{1}$ and $S_{2}$ connected in parallel. The condition for bridge to be balanced will be
A wire elongates by $\ell mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$
each are hung at the two ends, the elongation of the wire will be (in $mm$ )
a.
$\ell /2$
b.
$\ell$
c.
$2\ell$
d.
zero
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Assuming the sun to be a spherical body of radius $R$ at a temperature of $TK$ , evaluate the total radiant power,
incident on Earth, at a distance $r$ from the Sun.
a.
$\frac{R^{2}\sigma T^{4}}{r^{2}}$
b.
$\frac{4\pi r^{2}_{0}R^{2}\sigma T^{4}}{r^{2}}$
c.
$\frac{\pi r^{2}_{0}R^{2}\sigma T^{4}}{r^{2}}$
d.
$\frac{r^{2}_{0}R^{2}\sigma T^{4}}{4\pi r^{2}}$
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The threshold frequency for a metallic surface corresponds to an energy of $6.2eV$ , and the stopping potential
for a radiation incident on this surface $5\,V$ . The incident radiation lies in
a.
X-ray region
b.
ultra-violet region
c.
infra-red region
d.
visible region
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A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular
frequency $\omega$ . The amplitude of oscillation is gradually increased. The coin will leave contact with the platform
for the first time
a.
at the highest position of the platform
b.
at the mean position of the platform
c.
for an amplitude of $\frac{g}{\omega ^{2}}$
d.
for an amplitude of $\frac{g^{2}}{\omega ^{2}}$
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A mass of $Mkg$ is suspended by a weightless string. The horizontal force that is required to displace it until the
string makes an angle of $45^{\circ }$ with the initial vertical direction is
a.
$Mg(\sqrt{2}-1)$
b.
$Mg(\sqrt{2}+ 1)$
c.
$Mg\sqrt{2}$
d.
$\frac{Mg}{\sqrt{2}}$
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The refractive index of glass is $1.520$ for red light and $1.525$ for blue light. Let $D_{1}$ and $D_{2}$ be an of minimum
deviation for red and blue light respectively in a prism of this glass. Then
a.
$D_{1} >D_{2}$
b.
$D_{1} < D_{2}$
c.
$D_{1} =D_{2}$
d.
$D_{1}$ can be less than or greater than depending
upon the angle of prism
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A player caught a cricket ball of mass $150\,g$ moving at a rate of $20\,m/s$ . If the catching process is completed in
$0.1\,s$ , the force of the blow exerted by the ball on the hand of the player is equal to
a.
$300\,N$
b.
$150\,N$
c.
$3\,N$
d.
$30\,N$
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Two spherical conductors $A$ and $B$ of radii $1\,mm$ and $2\,mm$ are separated by a distance of $5\,cm$ and are
uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio
of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is
a.
$1 : 4$
b.
$4 : 1$
c.
$1 : 2$
d.
$2 : 1$
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A long solenoid has 200 turns per $cm$ and carries a current $i$ . The magnetic field at its centre is $6.28 \times 10^{-2}$
Weber $/m^{2}$ . Another long solenoid has 100 turns per $cm$ and it carries a current $i/3$ . The value of the magnetic
field at its centre is
a.
$1.05 \times 10^{-4}$ Weber/m
b.
$1.05 \times 10^{-2}$ Weber $/m^{2}$
c.
$1.05 \times 10^{-5}Weber/m^{2}$
d.
$1.05 \times 10^{-3}Weber/m^{2}$
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The molar conductivities $\wedge ^{\circ }_{NaOAC}$ and $\wedge ^{\circ }_{HCl}$ at infinite dilution in water at $25^{\circ }C$ are $91.0$ and $426.2\,S\,cm^{2}/mol$
respectively. To calculate $\wedge ^{O}_{HOAc}$ , the additional value required is
a.
$\wedge ^{\circ }_{H_{2}O}$
b.
$\wedge ^{\circ }_{KCl}$
c.
$\wedge ^{\circ }_{NaOH}$
d.
$\wedge ^{\circ }_{NaCl}$
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Uncertainty in the position of an electron (mass $= 9.1 \times 10^{-31}\,kg$ ) moving with a velocity $300\,ms^{-1}$ , accurate
upto $0.001%$ , will be
The following mechanism has been proposed for the reaction of $NO$ with $Br_{2}$ to form $NOBr$ :
$NO(g) + Br_{2}(\,g)\rightleftharpoons NOBr_{2}(\,g)$
$NOBr_{2}(\,g) + NO(g)\longrightarrow 2NOBr(g)$
If the second step is the rate determining step, the order of the reaction with respect to $NO(g)$ is
a.
1
b.
0
c.
3
d.
2
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A reaction was found to be second order with respect to the concentration of carbon monoxide. If the
concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will
a.
remain unchanged
b.
triple
c.
increase by a factor of 4
d.
double
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If the ratio of the concentration of electrons that of holes in a semiconductor is $\frac{7}{5}$ and the ratio of currents is $\frac{7}{4}$ ,
then what is the ratio of their drift velocities?
a.
$\frac{4}{7}$
b.
$\frac{5}{8}$
c.
$\frac{4}{5}$
d.
$\frac{5}{4}$
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An ideal gas is allowed to expand both reversibly and irreversibly in an isolated system. If $T_{i}$ is the initial
temperature and $T_{f}$ is the final temperature, which of the following statements is correct?
a.
$(T_{f})_{irev\,} > (T_{f})_{rev\,}$
b.
$T_{f} >T_{i}$ for reversible process but $T_{f} =T_{i}$ for
irreversible process
c.
$(T_{f})_{rev\,} = (T_{f})$ irrev
d.
$T_{f} =T_{i}$ for both reversible and irreversible
processes
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In a common base mode of a transistor, $t$ collector current is $5.488\,mA$ for an emit current of $5.60 mA$ . The
value of the base current amplification factor $(\beta )$ will be
a.
48
b.
49
c.
50
d.
51
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The equilibrium constant for the reaction
$SO_{3}(\,g)\rightleftharpoons SO_{2}(\,g) + \frac{1}{2} O_{2}(\,g)$
is $K_{c} = 4.9 \times 10^{-2}$ . The value of $K_{c}$ for the reaction
$2SO_{2}(\,g) + O_{2}(\,g)\rightleftharpoons 2SO_{3}(\,g)$
will be
a.
416
b.
$2.40 \times 10^{-3}$
c.
$9.8 \times 10^{-2}$
d.
$4.9 \times 10^{-2}$
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Phosphorus pentachloride dissociates as follows, in a closed reaction vessel, $PCl_{5}(\,g)\rightleftharpoons PCl_{3}(\,g) + Cl_{2}(\,g)$
If total pressure at equilibrium of the reaction mixture is $P$ and degree of dissociation of $PCl_{5}$ is $x$ , the partial
pressure of $PCl_{3}$ will be
a.
$(\frac{x}{x+1} )P$
b.
$(\frac{2x}{1-x})P$
c.
$(\frac{x}{x-1} )P$
d.
$(\frac{x}{1-x})P$
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The standard enthalpy of formation $(\Delta _{f}H^{\circ })$ at $298\,K$ for methane, $CH_{4}(\,g)$ , is $-74.8\,kJ\,mol^{-1}$ . The
additional information required to determine the average energy for $C -H$ bond formation would be
a.
the dissociation energy of $H_{2}$ and enthalpy of
sublimation of carbon
b.
latent heat of vapourization of methane
c.
the first four ionization energies of carbon and
electron gain enthalpy of hydrogen
d.
the dissociation energy of hydrogen molecule, $H_{2}$
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$Cl_{2}(\,g) = 2Cl(g), 242.3\,kJ\,mol^{-1}$
$I_{2}(\,g) = 2I(g), 151.0\,kJ\,mol^{-1}$
The enthalpy changes for the following processes are listed below:
$ICl(g) = I(g) + Cl(g), 211.3\,kJ\,mol^{-1}$
$I_{2}(\,s) = I_{2}(\,g), 62.76\,kJ\,mol^{-1}$
Given that the standard states for iodine and chlorine are $I_{2}(\,s)$ and $Cl_{2}(\,g)$ , the standard enthalpy of formation
for $ICl(g)$ is
a.
$-14.6\,kJ\,mol^{-1}$
b.
$-16.8\,kJ\,mol^{-1}$
c.
$+16.8\,kJ\,mol^{-1}$
d.
$+244.8\,kJ\,mol^{-1}$
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Resistance of a conductivity cell filled with a solution of an electrolyte of concentration $0.1M$ is $100\Omega$ . The
conductivity of this solution is $1.29\,S\,m^{-1}$ . Resistance of the same cell when filled with $0.2M$ of the same
solution is $520\Omega$ . The molar conductivity of $0.02M$ solution of the electrolyte will be
a.
$124 \times 10^{-4}\,S\,m^{2}\,mol^{-1}$
b.
$1240 \times 10^{-4}\,S\,m^{2}\,mol^{-1}$
c.
$1.24 \times 10^{-4}\,S\,m^{2}\,mol^{-1}$
d.
$12.4 \times 10^{-4}\,S\,m^{2}\,mol^{-1}$
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Following statements regarding the periodic trends of chemical reactivity of the alkali metals and the halogens
are given. Which of these statements gives the correct picture?
a.
The reactivity decreases in the alkali metals but
increases in the halogens with increase in atomic
number down the group
b.
In both the alkali metals and the halogens the
chemical reactivity decreases with increase in
atomic number down the group
c.
Chemical reactivity increases with increase in
atomic number down the group in both the alkali
metals and halogens
d.
In alkali metals the reactivity increases but in the
halogens it decreases with increase in atomic
number down the group
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Given the data at $25^{\circ }C$ ,
$Ag + I^{-} \longrightarrow AgI + e^{-}; E^{\circ } = 0.152\,V$
$Ag\longrightarrow Ag^{+} + e^{-}; E^{\circ } = -0.800\,V$
What is the value of $log K_{sp}$ for $AgI$ ?
$(2.303 \frac{RT}{F} = 0.059\,V)$
a.
$-8.12$
b.
$+8.612$
c.
$-37.83$
d.
$-16.13$
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Nickel $(Z = 28)$ combines with a uninegative monodentate ligand $X^{-}$ to form a paramagnetic complex
$[NiX_{4}]^{2-}$ . The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively
a.
one, tetrahedral
b.
two, tetrahedral
c.
one, square planar
d.
two, square planar
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If the binding energy per nucleon in $^{7}_{3}Li$ and $^{4}_{2}He$ nuclei are $5.60MeV$ and $7.06MeV$ respectively, then in the
reaction $p +^{7}_{3}Li \rightarrow 2\rightarrow^{4}_{2}He$ energy of proton must be
a.
$39.2MeV$
b.
$28.24MeV$
c.
$17.28MeV$
d.
$1.46MeV$
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$CH_{3}Br + Nu^{-} \longrightarrow CH_{3}-Nu + Br^{-}$
The decreasing order of the rate of the above reaction with nucleophiles $(Nu^{-})A$ to $D$ is $[Nu^{-} = (A)PhO^{-}$ ,
(B) $AcO^{-}$ , (C) $HO^{-}$ , (D) $CH_{3}O^{-}]$
a.
D $>$ C $>$ A $>$ B
b.
D $>$ C $>$ B $>A$
c.
$A>B>C >D$
d.
$B>D>C >A$
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Suppose a population $A$ has 100 observations $101, 102, … , 200$ , and another population $B$ has 100
observations $151, 152, … , 250$ . If $V_{A}$ and $V_{B}$ represent the variances of the two populations, respectively,
then $\frac{V_{A}}{V_{B}}$ is
a.
1
b.
9/4
c.
4/9
d.
2/3
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A particle has two velocities of equal magnitude inclined to each other at an angle $\theta$ . If one of them is halved,
the angle between the other and the original resultant velocity is bisected by the new resultant. Then $\theta$ is
a.
$90^{\circ }$
b.
$120^{\circ }$
c.
$45^{\circ }$
d.
$60^{\circ }$
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$----_{-}_{-}_{-}_{-}$
If $(a \times b) \times c = a \times (b \times c)$ , where $-a, b$ and $-c$ are any three vectors such that $-a \cdot b \neq 0$ , $b \cdot c \neq 0$ , then $a$ and
$c$ are
a.
inclined at an angle of $\pi /3$ between them
b.
inclined at an angle of $\pi /6$ between them
c.
perpendicular
d.
parallel
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Let $C$ be the circle with centre $(0, 0)$ and radius 3 units. The equation of the locus of the mid points of the
chords of the circle $C$ that subtend an angle of $\frac{2\pi}{3}$ at its centre is
a.
$x^{2} +y^{2} = \frac{3}{-}$
b.
$x^{2} +y^{2} = 1$
c.
$x^{2} +y^{2} = \frac{27}{4}$
d.
$x^{2} +y^{2} = \frac{9}{4}$
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$--$
$ABC$ is a triangle, right angled at $A$ . The resultant of the forces acting along $A\vec{B},A\vec{C}$ with magnitudes $\frac{1}{AB}$
$-$
and $\frac{1}{AC}$ respectively is the force along $A\vec{D}$ , where $D$ is the foot of the perpendicular from $A$ onto $BC$ . The
magnitude of the resultant is
a.
$\frac{AB^{2}+AC^{2}}{(AB)^{2}(AC)^{2}}$
b.
$\frac{(AB)(AC)}{AB+AC}$
c.
$\frac{1}{AB} + \frac{1}{AC}$
d.
$\frac{1}{AD}$
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If $z^{2} +z+ 1 = 0$ , where $z$ is a complex number, then the value of
$2 2 2 2$
$(z+ \frac{1}{z}) +(z^{2} + \frac{1}{z^{2}}) +(z^{3} + \frac{1}{z^{3}}) + \cdots +(z^{6} + \frac{1}{z^{6}})$
a.
18
b.
54
c.
6
d.
12
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A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two
sides having fence are of same length x. The maximum area enclosed by the park is
a.
$\frac{3}{2}x^{2}$
b.
$\sqrt{\,} \frac{x^{3}}{8}$
c.
$\frac{1}{2}x^{2}$
d.
$\pi x^{2}$
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The values of $a$ , for which the points $A,B,C$ with position vectors $2\hat{i}- \hat{j}+ \hat{k}, \hat{i}-3\hat{j}-5\hat{k}$ and $a\hat{i}-3\hat{j}+ \hat{k}$
respectively are the vertices of a right-angled triangle with $C = \frac{\pi}{2}$ are
a.
2 and 1
b.
-2 and -1
c.
-2 and 1
d.
2 and -1
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At an election, a voter may vote for any number of candidates, not greater than the number to be elected.
There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of
ways in which he can vote is
a.
5040
b.
6210
c.
385
d.
1110
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At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson
distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at
the most one phone call during a 10-minute time period is
a.
$\frac{6}{5^{e}}$
b.
$\frac{5}{6}$
c.
$\frac{6}{55}$
d.
$\frac{6}{e^{5}}$
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Let W denote the words in the English dictionary. Define the relation R by : $R= {(x,y) \in W \times W |$ the
words $x$ and $y$ have at least one letter in common $}$ . Then $R$ is
a.
not reflexive, symmetric and transitive
b.
reflexive, symmetric and not transitive
c.
reflexive, symmetric and transitive
d.
reflexive, not symmetric and transitive
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Let $a_{1},a_{2},a_{3}, …$ be terms of an A.P. If $\frac{a_{1}+a_{2}+\cdots a_{p}}{a_{1}+a_{2}+\cdots +a_{q}} = \frac{p^{2}}{q^{2}},p\neq q$ , then $\frac{a_{6}}{a_{21}}$ equals
a.
$\frac{41}{11}$
b.
$\frac{7}{2}$
c.
$\frac{2}{7}$
d.
$\frac{11}{41}$
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