When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as :
$_{92}U^{235}+_{0}n^{1} \rightarrow \rightarrow_{56}Ba^{141}+_{36}Kr^{92}+ 3x+ Q($ energy) where three particles named $x$ are produced and energy
$Q$ is released. What is the name of the particle $x$ ?
a.
electron
b.
$\alpha$ -particle
c.
neutron
Correct Answer
d.
neutrino
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Q2mcq
Photons of an electromagnetic radiation has an energy $11keV$ each. To which region of electromagnetic
spectrum does it belong ?
a.
X-ray region
Correct Answer
b.
Ultra violet region
c.
Infrared region
d.
Visible region
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Q3mcq
Two simple pendulums of length $1\,m$ and $4\,m$ respectively are both given small displacement in the same
direction at the same instant. They will be again in phase after the shorter pendulum has completed number of
oscillations equal to:
a.
2
Correct Answer
b.
7
c.
5
d.
3
No explanation saved for this question yet.
Q4mcq
In a metre bridge experiment null point is obtained at $40\,cm$ from one end of the wire when resistance $X$ is
balanced against another resistance $Y$ . If $X < Y$ , then the new position of the null point from the same end, if
one decides to balance a resistance of $3X$ against $Y$ , will be close to :
a.
$80\,cm$
b.
$75\,cm$
c.
$67\,cm$
Correct Answer
d.
$50\,cm$
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Q5mcq
This question has Statement-1 and Statement- 2 . Of the four choices given after the Statements, choose the one
that best describes the two Statetnents. Statement-1: A capillary is dipped in a liquid and liquid rises to a height
$h$ in it. As the temperature of the liquid is raised, the height $h$ increases (if the density of the liquid and the angle
of contact remain the same). Statement-2: Surface tension of a liquid decreases with the rise in its temperature.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation for
Statement-1.
b.
Statement-1 is false, Statement- 2 is true.
Correct Answer
c.
Statement-1 is true, Statement- 2 is false.
d.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation for
Statement-1.
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Q6mcq
Figure shows the variation in temperature $(\Delta T)$ with the amount of heat supplied $(Q)$ in an isobaric process
corresponding to a monoatomic $(M)$ , diatomic $(D)$ and a polyatomic $(P)$ gas. The initial state of all the gases
are the same and the scales for the two axes coincide. Ignoring vibrational degrees of freedom, the lines $a,b$ and
$c$ respectively correspond to :
a.
$P$ , $M$ and $D$
b.
$M$ , $D$ and $P$
Correct Answer
c.
$P$ , $D$ and $M$
d.
$D$ , $M$ and $P$
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Q7mcq
In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to
be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in $n^{th\,}$ excited
state, is :
a.
$(\frac{e}{2m} \frac{n^{2}h}{2\pi} )$
b.
$(\frac{e}{m})\frac{nh}{2\pi}$
c.
$(\frac{e}{2m})\frac{nh}{2\pi}$
Correct Answer
d.
$(\frac{e}{m})\frac{n^{2}h}{2\pi}$
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Q8mcq
Two coils, $X$ and $Y$ , are kept in close vicinity of each other. When a varying current, $I(t)$ , flows through coil $X$
, the induced $emf(V(t))$ in coil $Y$ , varies in the manner shown here. The variation of $I(t)$ , with time, can then
be represented by the graph labelled as graph :
(A)
(B)
(C)
(D)
a.
$A$
Correct Answer
b.
$C$
c.
$B$
d.
$D$
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Q9mcq
An engine approaches a hill with a constant speed. When it is at a distance of $0.9\,km$ , it blows a whistle whose
echo is heard by the driver after $5$ seconds. If the speed of sound in air is $330\,m/s$ , then the speed of the engine
is :
a.
$32\,m/s$
b.
$27.5\,m/s$
c.
$60\,m/s$
d.
$30\,m/s$
Correct Answer
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Q10mcq
There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a
partition wall dividing the chambers in two compartments. Compartment $1$ is filled with an ideal gas and
Compartment $3$ is filled with a real gas. Compartments $2$ and $4$ are vacuum. A small hole (orifice) is made in
the partition walls and the gases are allowed to expand in vacuum. $Statement -1 :$ No change in the
temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas
goes down (cooling) when it expands in vacuum. $Statement -2 :$ The internal energy of an ideal gas is only
kinetic. The internal energy of a real gas is kinetic as well as potential.
a.
Statement-1 is false and Statement-2 is true.
Correct Answer
b.
Statement-1 and Statement-2 both are true.
Statement-2 is the correct explanation of
Statement-1.
c.
Statement-1 is true and Statement- 2 is false.
d.
Statement-1 and Statement-2 both are true.
Statement-2 is not correct explanation of
Statement-1.
No explanation saved for this question yet.
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If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a,b$ and $c$ respectively,
then the corresponding ratio of increase in their lengths is :
a.
$\frac{3c}{2ab^{2}}$
b.
$\frac{2a^{2}c}{b}$
c.
$\frac{3a}{2b^{2}c}$
d.
$\frac{2ac}{b^{2}}$
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A letter $'A'$ is constructed of a uniform wire with resistance $1.0\Omega$ per $cm$ , The sides of the letter are $20\,cm$ and
the cross piece in the middle is $10\,cm$ long. The apex angle is 60 . The resistance between the ends of the legs
is close to:
a.
$50.0\Omega$
b.
$10\Omega$
c.
$36.7\Omega$
d.
$26.7\Omega$
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A ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in diagram. It undergoes
partial reflection and refraction. At each reflection, $25%$ of incident energy is reflected. The rays $AB$ and $A'B'$
undergo interference. The ratio of $I_{max}$ and $I_{min}$ is :
a.
$49 : 1$
b.
$7 : 1$
c.
$4 : 1$
d.
$8 : 1$
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On a linear temperature scale $Y$ , water freezes at $-160^{\circ }Y$ and boils at $-50^{\circ }Y$ . On this $Y$ scale, a temperature of
$340\,K$ would be read as : (water freezes at $273\,K$ and boils at $373\,K$ )
a.
$-73.7^{\circ }Y$
b.
$-233.7^{\circ }Y$
c.
$-86.3^{\circ }Y$
d.
$-106.3^{\circ }Y$
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When two sound waves travel in the same direction in a medium, the displacements of a particle located at ' $x$ '
$y_{1} = 0.05 cos(0.50\pi x-100\pi t)$
at time ' $t$ ' is given by : where $y_{1},y_{2}$ and $x$ are in meters and $t$ in seconds. The
$y_{2} = 0.05 cos(0.46\pi x-92\pi t)$
speed of sound in the medium is :
a.
$92\,m/s$
b.
$200\,m/s$
c.
$100\,m/s$
d.
$332\,m/s$
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A person lives in a high-rise building on the bank of a river $50\,m$ wide. Across the river is a well lit tower of
height $40\,m$ . When the person, who is at a height of $10\,m$ , looks through a polarizer at an appropriate angle at
light of the tower reflecting from the river surface, he notes that intensity of light coming from distance $X$
from his building is the least and this corresponds to the light coming from light bulbs at height ' $Y$ ' on the
tower. The values of $X$ and $Y$ are respectively close to (refractive index of water $\simeq \frac{4}{3}$ )
a.
$25\,m, 10\,m$
b.
$13\,m, 27\,m$
c.
$22\,m, 13\,m$
d.
$17\,m, 20\,m$
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A shunt of resistance $1\,\Omega$ is connected across a galvanometer of $120\,\Omega$ resistance. A current of $5.5$ ampere
gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of
the shunt is nearly :
a.
$5.5$ ampere
b.
$0.5$ ampere
c.
$0.004$ ampere
d.
$0.045$ ampere
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From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as
well as correct order of magnitude, vis-a-vis typical atomic size, is:
a.
$\frac{e^{2}}{4\pi \epsilon _{0}mc^{2}}$
b.
$\frac{4\pi \epsilon _{0}e^{2}}{me^{2}}$
c.
$\frac{me^{2}}{4\pi \epsilon _{0}b^{2}}$
d.
$\frac{4\pi \epsilon _{0}mc^{2}}{e^{2}}$
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Light is incident from a medium into air at two possible angles of incidence (A) $20^{\circ }$ and (B) $40^{\circ }$ . In the
medium light travels $3.0\,cm$ in $0.2\,ns$ . The ray will :
a.
suffer total internal reflection in both cases (A)
and (B)
b.
suffer total internal reflection in case (B) only
c.
have partial reflection and partial transmission in
case (B)
d.
have $100%$ transmission in case (A)
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Two springs of force constants $300\,N/m$ (Spring A) and $400\,N/m$ (Spring B) are joined together in series. The
combination is compressed by $8.75\,cm$ . The ratio of energy stored in $A$ and $B$ is $\frac{E_{A}}{E_{B}}$ . Then $\frac{E_{A}}{E_{B}}$ is equal to:
a.
$\frac{4}{3}$
b.
$\frac{16}{9}$
c.
$\frac{3}{4}$
d.
$\frac{9}{16}$
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If a carrier wave $c(t) = A sin\omega _{c}t$ is amplitude modulated by a modulator signal $m(t) = A$ sin $\omega _{m}t$ then the
equation of modulated signal $[C_{m}(t)]$ and its modulation index are respectively
a.
$C_{m}(t) =A(1 + sin\omega _{m}t) sin\omega _{c}t$ and 2
b.
$C_{m}(t) =A(1 + sin\omega _{m}t) sin\omega _{m}t$ and 1
c.
$C_{m}(t) =A(1 + sin\omega _{m}t) sin\omega _{c}t$ and 1
d.
$C_{m}(t) =A(1 + sin\omega _{c}t) sin\omega _{m}t$ and 2
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Two point dipoles of dipole moment $\vec{p}_{1}$ and $\vec{p}_{2}$ are at a distance $x$ from each other and $\vec{p}_{1}||\vec{p}_{2}$ . The force
between the dipoles is :
A bullet of mass $10\,g$ and speed $500\,m/s$ is fired into a door and gets embedded exactly at the centre of the
door. The door is $1.0\,m$ wide and weighs $12\,kg$ . It is hinged at one end and rotates about a vertical axis
practically without friction. The angular speed of the door just after the bullet embeds into it will be :
a.
$6.25rad/sec$
b.
$0.625rad/sec$
c.
$3.35rad/sec$
d.
$0.335rad/sec$
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The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been
'removed out'), at a very far off point, $P$ , located as shown, would be (nearly) :
a.
$\frac{5}{6} \frac{GM}{x^{2}}$
b.
$\frac{8}{9} \frac{GM}{x^{2}}$
c.
$\frac{7}{8} \frac{GM}{x^{2}}$
d.
$\frac{6}{7} \frac{GM}{x^{2}}$
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Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$ . At electrostatic
equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is
proportional to :
a.
$l$
b.
$l^{2}$
c.
$l^{2/3}$
d.
$l^{1/3}$
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A uniform electric field $\vec{E}$ exists between the plates of a charged condenser. A charged particle enters the space
between the plates and perpendicular to $\vec{E}$ . The path of the particle between the plates is a:
a.
straight line
b.
hyperbola
c.
parabola
d.
circle
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An electric current is flowing through a circular coil of radius $R$ . The ratio of the magnetic field at the centre
of the coil and that at a distance $2\sqrt{2}R$ from the centre of the coil and on its axis is :
a.
$2\sqrt{2}$
b.
27
c.
36
d.
8
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$(I) H_{2}(g) + \frac{1}{2}O_{2}(g) \rightarrow H\rightarrow_{2}O(l); (II) H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H\rightarrow_{2}O(g);$
Given: The molar enthalpy of
$\Delta H^{\circ }_{298\,K} = -285.9\,kJ\,mol^{-1} \Delta H^{\circ }_{298\,K} = -241.8\,kJ\,mol^{-1}$
vapourisation of water will be :
a.
$241.8\,kJ\,mol^{-1}$
b.
$22.0\,kJ\,mol^{-1}$
c.
$44.1\,kJ\,mol^{-1}$
d.
$527.7\,kJ\,mol^{-1}$
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Solid $Ba(NO_{3})_{2}$ is gradually dissolved in a $1.0 \times 10^{-4}\,M\,Na_{2}CO_{3}$ solution. At which concentration of $Ba^{2+}$ ,
precipitate of $BaCO_{3}$ begins to form ? $(K_{sp}$ for $BaCO_{3} = 5.1 \times 10^{-9})$
a.
$5.1 \times 10^{-5}M$
b.
$7.1 \times 10^{-8}M$
c.
$4.1 \times 10^{-5}M$
d.
$8.1 \times 10^{-7}M$
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Given : $XNa_{2}HAsO_{3}+ YNaBrO_{3}+ ZHCl \rightarrow NaBr + H\rightarrow_{3}AsO_{4}+ NaCl$ The values of $X, Y$ and $Z$ in the
above redox reaction are respectively :
a.
$2, 1, 2$
b.
$2, 1, 3$
c.
$3, 1, 6$
d.
$3, 1, 4$
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An ether (A), $C_{5}H_{12}O$ , when heated with excess of hot concentrated $HI$ produced two alkyl halides which
when treated with $NaOH$ yielded compounds (B) and (C). Oxidation of (B) and (C) gave a propanone and an
ethanoic acid respectively. The IUPAC name of the ether (A) is :
a.
$2-$ ethoxypropane
b.
ethoxypropane
c.
methoxybutane
d.
$2-$ methoxybutane
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By how many folds the temperature of a gas would increase when the root mean square velocity of the gas
molecules in a container of fixed volume is increased from $5 \times 10^{4}\,cm/s$ to $10 \times 10^{4}\,cm/s$ ?
a.
Two
b.
Three
c.
Six
d.
Four
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$Cu^{+}/Cu = +0.52\,V,$
$Fe^{3+}/Fe^{2+} = +0.77\,V,$
Electrode potentials $(E^{\circ })$ are given below : Based on the above potentials, strongest
$\frac{1}{2}I_{2}(\,s)/I^{-} = +0.54\,V,$
$Ag^{+}/Ag = +0.88\,V.$
oxidizing agent will be :
a.
$Cu^{+}$
b.
$Fe^{3+}$
c.
$Ag^{+}$
d.
$I_{2}$
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Sodium Carbonate cannot be used in place of $(NH_{4})_{2}CO_{3}$ for the identification of $Ca^{2+}, Ba^{2+}$ and $Sr^{2+}$ ions
(in group $V$ ) during mixture analysis because :
a.
$Mg^{2+}$ ions will also be precipitated.
b.
Concentration of $CO_{3}^{2-}$ ions is very low.
c.
Sodium ions will react with acid radicals.
d.
$Na^{+}$ ions will interfere with the detection of
$Ca^{2+}, Ba^{2+}, Sr^{2+}$ ions.
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$12\,g$ of a nonvolatile solute dissolved in $108\,g$ of water produces the relative lowering of vapour pressure of
$0.1$ . The molecular mass of the solute is :
a.
$80$
b.
$60$
c.
$20$
d.
$40$
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The instantaneous rate of disappearance of $MnO^{-}_{4}$ ion in the following reaction is $4.56 \times 10^{-3}Ms^{-1}$
$2MnO^{-}_{4} + 10I^{-} + 16H^{+} \rightarrow 2Mn\rightarrow^{2+}+ 5I_{2}+ 8H_{2}O$ The rate of appearance $I_{2}$ is :
a.
$4.56 \times 10^{-4}Ms^{-1}$
b.
$1.14 \times 10^{-2}Ms^{-1}$
c.
$1.14 \times 10^{-3}Ms^{-1}$
d.
$5.7 \times 10^{-3}Ms^{-1}$
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In reaction $A + 2\,B\rightleftharpoons 2C + D$ , initial concentration of $B$ was $1.5$ times of $[A]$ , but at equilibrium the
concentrations of $A$ and $B$ became equal. The equilibrium constant for the reaction is :
a.
$8$
b.
$4$
c.
$12$
d.
$6$
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In which of the following ionization processes the bond energy has increased and also the magnetic behaviour
has changed from paramagnetic to diamagnetic ?
a.
$NO \rightarrow NO\rightarrow^{+}$
b.
$N_{2} \rightarrow N\rightarrow^{+}_{2}$
c.
$C_{2} \rightarrow C\rightarrow^{+}_{2}$
d.
$O_{2} \rightarrow O\rightarrow^{+}_{2}$
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If a polythene sample contains two monodisperse fractions in the ratio $2 : 3$ with degree of polymerization $100$
and $200$ , respectively, then its weight average molecular weight will be :
a.
$4900$
b.
$4600$
c.
$4300$
d.
$5200$
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The probability of a man hitting a target is $\frac{2}{5}$ . He fires at the target $k$ times $(k$ , a given number). Then the
minimum $k$ , so that the probability of hitting the target at least once is more than $\frac{7}{10}$ , is :
a.
3
b.
5
c.
2
d.
4
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If each of the lines $5x+ 8y= 13$ and $4x- y= 3$ contains a diameter of the circle $x^{2} +y^{2} -2(a^{2} -7a+ 11)$
$x-2(a^{2} -6a+ 6)y+b^{3} + 1 = 0$ , then :
a.
$a= 5$ and $b∉(-1, 1)$
b.
$a= 1$ and $b∉(-1, 1)$
c.
$a= 2$ and $b∉(-\infty , 1)$
d.
$a= 5$ and $b\in (-\infty , 1)$
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A vector $n$ is inclined to $x$ -axis at $45^{\circ }$ , to $y$ -axis at $60^{\circ }$ and at an acute angle to $z$ -axis. If $n$ is a normal to a
plane passing through the point $(\sqrt{2}, -1, 1)$ then the equation of the plane is :
a.
$4\sqrt{2}x+ 7y+z-2$
b.
$2x+y+ 2z= 2\sqrt{2}+ 1$
c.
$3\sqrt{2}x-4y-3z= 7$
d.
$\sqrt{2}x- y- z= 2$
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If the lines $\frac{x+1}{2} = \frac{y-1}{1} = \frac{z+1}{3}$ and $\frac{x+2}{2} = \frac{y-k}{3} = \frac{z}{4}$ are coplanar, then the value of $k$ is :
a.
$\frac{11}{2}$
b.
$- \frac{11}{2}$
c.
$\frac{9}{2}$
d.
$- \frac{9}{2}$
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A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at
least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this
committee can be formed is :
a.
40
b.
41
c.
16
d.
32
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Let $\vec{a}= 2\hat{i}- \hat{j}+ \hat{k}, \vec{b}= \hat{i}+ 2\vec{j}- \hat{k}$ and $\vec{c}= \hat{i}+ \hat{j} \frac{-2}{2} \hat{k}$ be three vectors. A vector of the type $\vec{b}+\lambda \vec{c}$ for some
scalar $\lambda$ , whose projection on $\hat{a}$ is of magnitude $\sqrt{\,} _{3}$ is :
a.
$2\hat{i}+ \hat{j}+ 5\hat{k}$
b.
$2\hat{i}+ 3\hat{j}-3\hat{k}$
c.
$2\hat{i}- \hat{j}+ 5\hat{k}$
d.
$2\hat{i}+ 3\hat{j}+ 3\hat{k}$
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Statement-1: The equation $xlogx= 2 - x$ is satisfied by at least one value of $x$ lying between 1 and 2.
Statement-2: The function $f(x) =xlogx$ is an increasing function in $[1, 2]$ and $g(x) = 2 - x$ is a decreasing
function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1, 2]$
a.
Statement-1 is true; Statement-2 is true;
Statement-2 is a correct explanation for
Statement-1.
b.
Statement-1 is true; Statement-2 is true;
Statement-2 is not correct explanation for
Statement-1.
c.
Statement-1 1 is false, Statement- 2 is true.
d.
Statement-1 1 is true, Statement- 2 is false.
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A light ray emerging from the point source placed at $P(1, 3)$ is reflected at a point $Q$ in the axis of $x$ . If the
reflected ray passes through the point $R(6, 7)$ , then the abscissa of $Q$ is:
a.
1
b.
3
c.
$\frac{7}{2}$
d.
$\frac{5}{2}$
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$||$
Statement-1: The slope of the tangent at any point $P$ on a parabola, whose axis is the axis of $x$ and vertex is at
the origin, is inversely proportional to the ordinate of the point $P$ . Statement-2: The system of parabolas
$y^{2} = 4ax$ satisfies a differential equation of degree 1 and order 1.
a.
Statement-1 is true; Statement- 2 is true;
Statement-2 is a correct explanation for
statement-1.
b.
Statement-1 is true; Statement-2 is true;
Statement- 2 is not a correct explanation for
statement-1.
c.
Statement-1 is true; Statement- 2 is false.
d.
Statement-1 is false; Statement- 2 is true.
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Let $a_{1},a_{2},a_{3}, …$ be an A.P, such that $\frac{a_{1}+a_{2}+…+a_{p}}{a_{1}+a_{2}+a_{3}+…+a_{q}} = \frac{p^{3}}{q^{3}};p\neq q$ . Then $\frac{a_{6}}{a_{21}}$ is equal to:
a.
$\frac{41}{11}$
b.
$\frac{31}{121}$
c.
$\frac{11}{41}$
d.
$\frac{121}{1861}$
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If $a$ and $c$ are positive real numbers and the ellipse $\frac{x^{2}}{4c^{2}} + \frac{y^{2}}{c^{2}} = 1$ has four distinct points ir common with the
circle $x^{2} +y^{2} = 9a^{2}$ , then
a.
$9ac-9a^{2} -2c^{2} < 0$
b.
$6ac+ 9a^{2} -2c^{2} < 0$
c.
$9ac-9a^{2} -2c^{2} > 0$
d.
$6ac+ 9a^{2} -2c^{2} > 0$
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Statement-1: The statement $A\rightarrow (\rightarrow B\rightarrow \rightarrow A)$ is equivalent to $A\rightarrow (\rightarrow A\vee B)$ . Statement-2: The statement
$\sim [(A \wedge B) \rightarrow (\sim A \vee B)]\rightarrow$ is a Tautology.
a.
Statement- 1 is false; Statement- 2 is true.
b.
Statement-1 is true; Statement-2 is true;
Statement- 2 is not correct explanation for
Statement-1.
c.
Statement-1 is true; Statement- 2 is false.
d.
Statement-1 is true; Statement-2 is true;
Statement- 2 is the correct explanation for
Statement-1.
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If $Z_{1} \neq 0$ and $Z_{2}$ be two complex numbers such that $\frac{Z_{2}}{Z_{1}}$ is a purely imaginary number, then $\frac{2Z_{1}+3Z_{2}}{2Z_{1}-3Z_{2}}$ is equal
to:
a.
2
b.
5
c.
3
d.
1
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