A proton, a deuteron and an $\alpha$ -particle with same kinetic energy enter into a uniform magnetic field at right
angle to magnetic field. The ratio of the radii of their respective circular paths is :
a.
$1\, : \,\sqrt{2}\, : \,\sqrt{2}$
b.
$1 : \sqrt{2}: 1$
Correct Answer
c.
$\sqrt{2}\, : 1\, : 1$
d.
None of these
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Q2nat
Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string.
They interfere to produce a stationary wave whose equation is given by $y=(10 cos\pi xsin \frac{2\pi t}{T})cm$ . The
amplitude of the particle at $x= \frac{4}{3}\, cm$ will be _____ $cm.$
✓ Accepted Answer:5
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Q3mcq
A long cylindrical volume contains a uniformly distributed charge of density $\rho$ . The radius of cylindrical
volume is $R$ . A charge particle $(q)$ revolves around the cylinder in a circular path. The kinetic energy of the
particle is :
A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas
will be _____ $R$ during this transformation.
Where $R$ is the gas constant.
✓ Accepted Answer:2
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Q5mcq
The light of two different frequencies whose photons have energies $3. 8 eV$ and $1. 4 eV$ respectively, illuminate
a metallic surface whose work function is $0. 6 eV$ successively. The ratio of maximum speeds of emitted
electrons for the two frequencies respectively will be :
a.
$2 : 1$
Correct Answer
b.
$4 : 1$
c.
$1 : 2$
d.
$1 : 4$
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Q6mcq
The distance between Sun and Earth is $R$ . The duration of year if the distance between Sun and Earth becomes
$3R$ will be :
a.
$\sqrt{3}\, yr$
b.
$3\sqrt{3}\, yr$
Correct Answer
c.
$3\, yr$
d.
$9\, yr$
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Q7nat
A potentiometer wire of length $10\,m$ and resistance $20\,\Omega$ is connected in series with a $25\,V$ battery and an
external resistance $30\,\Omega$ . A cell of emf $E$ in secondary circuit is balanced by $250\, cm$ long potentiometer wire.
The value of $E$ (in volt) is $\frac{x}{10}$ . The value of $x$ is _____ .
✓ Accepted Answer:25
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Q8mcq
A $100\,g$ of iron nail is hit by a $1. 5\, kg$ hammer striking at a velocity of $60\, ms^{-1}$ . What will be the rise in the
temperature of the nail if one fourth of energy of the hammer goes into heating the nail ? [Specific heat capacity
of iron $= 0. 42 Jg^{-1}^{\circ }C^{-1}$ ]
a.
$16. 07^{\circ}C$
Correct Answer
b.
$6. 75^{\circ}C$
c.
$1600^{\circ}C$
d.
$675^{\circ}C$
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Q9mcq
An object of mass $5\, kg$ is thrown vertically upwards from the ground. The air resistance produces a constant
retarding force of $10\,N$ throughout the motion. The ratio of time of ascent to the time of descent will be equal to
: [Use $g= 10\,m\,s^{-2}$ ].
a.
$1 : 1$
b.
$\sqrt{2}: \sqrt{3}$
Correct Answer
c.
$\sqrt{3}: \sqrt{2}$
d.
$2 : 3$
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Q10mcq
An electric bulb is rated as $200\,W$ . What will be the peak magnetic field at $4\,m$ distance produced by the
radiations coming from this bulb? Consider this bulb as a point source with $3. 5%$ efficiency.
a.
$1. 19 \times 10^{-8}T$
b.
$1. 71 \times 10^{-8}T$
Correct Answer
c.
$0. 84 \times 10^{-8}T$
d.
$3. 36 \times 10^{-8}T$
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A Carnot engine takes $5000\, kcal$ of heat from a reservoir at $727^{\circ}C$ and gives heat to a sink at $127^{\circ}C$ . The work
done by the engine is
a.
$3 \times 10^{6}J$
b.
Zero
c.
$8. 4 \times 10^{6}\,J$
d.
$12. 6 \times 10^{6}\,J$
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A sample contains $10^{-2}\, kg$ each of two substances $A$ and $B$ with half lives $4\,s$ and $8\,s$ respectively. The ratio
of their atomic weights is $1 : 2$ . The ratio of the amounts of $A$ and $B$ after $16\,s$ is $\frac{x}{100}$ . The value of $x$ is _____
.
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A fly wheel is accelerated uniformly from rest and rotates through $5 rad$ in the first second. The angle rotated by
the fly wheel in the next second, will be :
a.
$7. 5 rad$
b.
$15 rad$
c.
$20 rad$
d.
$30 rad$
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Given below are two statements :
Statement-I:The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an
inductor.
Statement-II:In ac circuit, the average power delivered by the source never becomes zero.
In the light of the above statements, choose the correct answer from the options given below
a.
Both Statement I and Statement II are true.
b.
Both Statement I and Statement II are false.
c.
Statement I is true but Statement II is false.
d.
Statement I is false but Statement II is true.
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What will be the most suitable combination of three resistors $A= 2\,\Omega , \,B= 4\,\Omega , \,C = 6\,\Omega$ so that $(\frac{22}{3} )\Omega$ is
equivalent resistance of combination?
a.
Parallel combination of $A$ and $C$ connected in series with $B$
b.
Parallel combination of $A$ and $B$ connected in series with $C$
c.
Series combination of $A$ and $C$ connected in parallel with $B$ .
d.
Series combination of $B$ and $C$ connected in parallel with $A$ .
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Potential energy as a function of $r$ is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$ , where $r$ is the interatomic distance, $A$ and $B$ are
positive constants. The equilibrium distance between the two atoms will be :
a.
$(\frac{A}{B})\frac{1}{5}$
b.
$(\frac{B}{A})\frac{1}{5}$
c.
$(\frac{2A}{B})\frac{1}{5}$
d.
$(\frac{B}{2A})\frac{1}{5}$
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Two massless springs with spring constants $2k$ and $9k$ , carry $50\,g$ and $100\,g$ masses at their free ends. These
two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective
amplitudes will be :
a.
$3 : 2$
b.
$1 : 2$
c.
$3 : 1$
d.
$2 : 3$
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A circular coil of 1000 turns each with area $1\,m^{2}$ is rotated about its vertical diameter at the rate of one
revolution per second in a uniform horizontal magnetic field of $0. 07\,T$ . The maximum voltage generation will
be _____ $V$ .
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A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2\,s$ is $20\,m\,s^{-1}$ .
The maximum height reached by the body during its motion is _____ $m$ . (use $g= 10\,m\,s^{-2}$ )
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Two identical charged particles each having a mass $10\,g$ and charge $2. 0 \times 10^{-7}C$ are placed on a horizontal
table with a separation of $L$ between them such that they stay in limited equilibrium. If the coefficient of
friction between each particle and the table is $0. 25$ , find the value of $L$ . [Use $g = 10\, ms^{-2}$ ]
a.
$12\, cm$
b.
$10\, cm$
c.
$8\, cm$
d.
$5\, cm$
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A ray of light is incident at an angle of incidence $60^{\circ}$ on the glass slab of refractive index $\sqrt{3}$ . After refraction,
the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is
$4\, cm\sqrt{3}$ . The thickness of the glass slab is _____ $cm$ .
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An antenna is placed in a dielectric medium of dielectric constant $6. 25$ . If the maximum size of that antenna is
$5. 0\, mm$ , it can radiate a signal of minimum frequency of _____ $GHz$ .
(Given $\mu _{r} = 1$ for dielectric medium)
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In Bohr's atomic model of hydrogen, let $K,P$ and $E$ are the kinetic energy, potential energy and total energy
of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level
:
a.
All $K,P$ and $E$ increase.
b.
$K$ decreases, $P$ and $E$ increase.
c.
$P$ decreases, $K$ and $E$ increase.
d.
$K$ increases, $P$ and $E$ decrease
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In an experiment to verify Newton's law of cooling. a graph is plotted between. the temperature difference
$(\Delta T)$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as
$80^{\circ}C$ . The value of $t_{2}$ as mentioned in the graph will be
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When $200\, mL$ of $0. 2\,M$ acetic acid is shaken with $0. 6\,g$ of wood charcoal, the final concentration of acetic
acid after adsorption is $0. 1\,M$ . The mass of acetic acid adsorbed per gram of carbon is $g$ .
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The resistance of a conductivity cell containing $0. 01\, MKCl$ solution at $298\,K$ is $1750\,\Omega$ . If the conductivity
of $0. 01\, MKCl$ solution at $298\,K$
is $0. 152 \times 10^{-3}\,S\, cm^{-1}$ , then the cell constant of the conductivity cell is____ $\times 10^{-3}\, cm^{-1}$
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$PCl_{5}$ dissociates as $PCl_{5}(g) \rightleftharpoons PCl_{3}(g) + Cl_{2}(g) 5$ moles of $PCl_{5}$ are placed in a $200$ litre vessel which
contains $2$ moles of $N_{2}$ and is maintained at $600\,K$ . The equilibrium pressure is $2. 46\, atm$ . The equilibrium
constant $K_{p}$ for the dissociation of $PCl_{5}$ is___ $\times 10^{-3}$ . (nearest integer) (Given: $R = 0. 082\,L$ atm $K^{-1}\, mol^{-1}$ ;
Assume ideal gas behaviour)
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Hex- $4$ -ene- $2$ -ol on treatment with $PCC$ gives ' $A$ '. ' $A$ ' on reaction with sodium hypoiodite gives ' $B$ ', which on
further heating with soda lime gives ' $C$ '. The compound ' $C$ ' is
a.
$2$ -pentene
b.
proponaldehyde
c.
$2$ -butene
d.
$4$ -methylpent- $2$ -ene
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For a first order reaction, the time required for completion of $90%$ reaction is ' $x$ ' times the half life of the
reaction. The value of ' $x$ ' is
(Given: $ln 10 = 2. 303$ and $log 2 = 0. 3010$ )
a.
1.12
b.
2.43
c.
3.32
d.
33.31
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The energy of one mole of photons of radiation of wavelength $300\, nm$ is (Given :
$h = 6. 63 \times 10^{-34}\,J\,s, N_{A} = 6. 02 \times 10^{23}\, mol^{-1}c = 3 \times 10^{8}\,m\,s^{-1}$ )
a.
$235\, kJ \, mol^{-1}$
b.
$325\, kJ \, mol^{-1}$
c.
$399\, kJ \, mol^{-1}$
d.
$435\, kJ \, mol^{-1}$
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$0. 2\,g$ of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of
$N_{2}$ evolved (at STP) was found to be $22. 400\, mL$ . The percentage of nitrogen in the compound is - [nearest
integer] (Given: Molar mass of $N_{2}$ is $28\,g\, mol^{-1}$ , Molar volume of $N_{2}$ at $STP : 22. 4\,L$ )
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$120\,g$ of an organic compound which contains only carbon and hydrogen on complete combustion gives $330\,g$
of $CO_{2}$ and $270\,g$ of water. The percentage of carbon and hydrogen in the organic compound are respectively
a.
$25$ and $75$
b.
$40$ and $60$
c.
$60$ and $40$
d.
$75$ and $25$
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Given below are two statements.
Statement I: The presence of weaker -bonds make alkenes less stable than alkanes$\pi$
Statement II: The strength of the double bond is greater than that of carbon-carbon single bond.
In the light of the above statements, choose the correct answer from the options : given below.
a.
Both Statement I and Statement II are correct.
b.
Both Statement I and Statement II are incorrect.
c.
Statement I is correct but Statement II is
incorrect.
d.
Statement I is incorrect but Statement II is
correct.
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At $25\,^{\circ}C$ and $1$ atm pressure, the enthalpies of combustion are as given below:
Substance $H_{2} C$ (graphite) $C_{2}H_{6}(g)$
$\frac{\Delta _{c}H^{Θ}}{kJmol^{-1}} -286. 0 -394. 0 -1560. 0$
The enthalpy of formation of ethane is
a.
$+54. 0\, kJ \, mol^{-1}$
b.
$-68. 0\, kJ \, mol^{-1}$
c.
$-86. 0\, kJ \, mol^{-1}$
d.
$+97. 0\, kJ \, mol^{-1}$
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A company dissolves ' $x$ ' amount of $CO_{2}$ at $298\,K$ in $1$ litre of water to prepare soda water. $X = \times 10^{-3}\,g$ .
(nearest integer)
(Given: partial pressure of $CO_{2}$ at $298\,K = 0. 835$ bar. Henry's law constant for $CO_{2}$ at $298\,K = 1. 67\, kbar$ .
Atomic mass of $H, C$ and $O$ is $1, 12$ , and $6\,g\, mol^{-1}$ , respectively)
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At $300\,K$ , a sample of $3. 0\,g$ of gas A occupies the same volume as $0. 2\,g$ of hydrogen at $200\,K$ at the same
pressure. The molar mass of gas $A$ is $g\, mol^{-1}$ . (nearest integer) Assume that the behaviour of gases as ideal.
(Given: The molar mass of hydrogen $(H_{2})$ gas is $2. 0\,g\, mol^{-1}$ .)
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$-$ Let $S =$ { $z\in ^{C}: |z-3| \leq 1$ and $z(4 + 3i) +z(4 -3i) \leq 24$ }. If $\alpha +i\beta$ is the point in $S$ which is closest to $4i$
, then $25(\alpha +\beta )$ is equal to ______.
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Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{4} = 1,a> 2$ , having one of its
vertices at one end of the major axis of the ellipse and one of its sides parallel to the $y$ -axis, be $6\sqrt{3}$ . Then the
eccentricity of the ellipse is:
a.
$\frac{\sqrt{3}}{2}$
b.
$\frac{1}{2}$
c.
$\frac{1}{\sqrt{2}}$
d.
$\frac{\sqrt{3}}{4}$
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Consider the following statements:
$A$ : Rishi is a judge.
$B$ : Rishi is honest.
$C$ : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is
a.
$B\rightarrow (\rightarrow A\vee C)$
b.
$(~B) \wedge (A\wedge C)$
c.
$B\rightarrow ((~\rightarrow A) \vee (~C))$
d.
$B\rightarrow (\rightarrow A\wedge C)$
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Let the system of linear equations
$x+y+az= 2$
$3x+y+z= 4$
$x+ 2z= 1$
have a unique solution ( $x^{∗},y^{∗},z^{∗})$ . If ( $(a,x^{∗}), (y^{∗},\alpha )$ and ( $x^{∗}, -y^{∗})$ are collinear points, then the sum of
absolute values of all possible values of $\alpha$ is:
a.
$4$
b.
$3$
c.
$2$
d.
$1$
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Let the hyperbola $H : \frac{x^{2}}{a^{2}} - y^{2} = 1$ and the ellipse $E : 3x^{2} + 4y^{2} = 12$ be such that the length of latus rectum
of $H$ is equal to the length of latus rectum of $E$ . If $e_{H}$ and $e_{E}$ are the eccentricities of $H$ and $E$ respectively,
then the value of $12(e^{2}_{H} +e^{2}_{E})$ is equal to _____.
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A random variable $X$ has the following probability distribution:
$X 0 1 2 3 4$
$P(X) k 2k 4k 6k 8k$
The value of $P(\frac{1<x<4}{x\leq 2})$ is equal to
a.
$\frac{4}{7}$
b.
$\frac{2}{3}$
c.
$\frac{3}{7}$
d.
$\frac{4}{5}$
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Let the area of the triangle with vertices $A(1,\alpha ),B(\alpha , 0)$ and $C(0,\alpha )$ be $4$ sq. units. If the points
$(\alpha , -\alpha ), (-\alpha ,\alpha )$ and $(\alpha ^{2},\beta )$ are collinear, then $\beta$ is equal to
a.
$64$
b.
$-8$
c.
$-64$
d.
$512$
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Let the points on the plane $P$ be equidistant from the points $(-4, 2, 1)$ and $(2, -2, 3)$ . Then the acute angle
between the plane $P$ and the plane $2x+y+ 3z= 1$ is
a.
$\frac{\pi}{6}$
b.
$\frac{\pi}{4}$
c.
$\frac{\pi}{3}$
d.
$\frac{5\pi}{12}$
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Let $P_{1}$ be a parabola with vertex $(3, 2)$ and focus $(4, 4)$ and $P_{2}$ be its mirror image with respect to the line
$x+ 2y= 6$ . Then the directrix of $P_{2}$ is $x+ 2y=$ _____.
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Let $\lambda ^{*}$ be the largest value of $\lambda$ for which the function $f_{\lambda }(x) = 4\lambda x^{3} -36\lambda x^{2} + 36x+ 48$ is increasing for all
$x\in R$ . Then $f_{\lambda ^{*}}(1) +f_{\lambda ,*}(-1)$ is equal to:
a.
$36$
b.
$48$
c.
$64$
d.
$72$
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Let a circle $C : (x- h)^{2} + (y- k)^{2} =r^{2},k> 0$ , touch the $x$ -axis at $(1, 0)$ . If the line $x+y= 0$ intersects the
circle $C$ at $P$ and $Q$ such that the length of the chord $PQ$ is $2$ , then the value of $h+k+r$ is equal to _____.
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$-1 a$
Let $S ={( );a,b\in {1, 2, 3, … 100}}$ and let $T_{n} ={A\in S :A^{n(n+1)} =I}$ . Then the number of
$0 b$
elements in $_{n}^{100}\cap _{=1}T_{n}$ is _____.
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$\{\frac{sin(x-[x])}{x-[x]}, x\in (-2, -1)$
Let $f(x) =$
$max(2x, 3[|x|]), |x| < 1$
$\{$
$1, otherwise$
where $[t]$ denotes greatest integer $\leq t$ . If $m$ is the number of points where $f$ is not continuous and $n$ is the
number of points where $f$ is not differentiable, the ordered pair $(m,n)$ is:
a.
$(3, 3)$
b.
$(2, 4)$
c.
$(2, 3)$
d.
$(3, 4)$
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Let $x\times y=x^{2} +y^{3}$ and $(x\times 1) \times 1 =x\, \times (1 \times 1)$ . Then a value of $2 sin^{-1}( \frac{x^{4}+x^{2}-2}{x^{4}+x^{2}+2})$ is
a.
$\frac{\pi}{4}$
b.
$\frac{\pi}{3}$
c.
$\frac{\pi}{6}$
d.
$\pi$
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In an examination, there are $10$ true-false type questions. Out of $10$ , a student can guess the answer of $4$
questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$ . If the
probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27k}{4^{10}}$ , then $k$ is
equal to
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A particle is moving in the $xy$ -plane along a curve $C$ passing through the point $(3, 3)$ . The tangent to the curve
$C$ at the point $P$ meets the $x$ -axis at $Q$ . If the $y$ -axis bisects the segment $PQ$ , then $C$ is a parabola with
a.
length of latus rectum $3$
b.
length of latus rectum $6$
c.
focus $(\frac{4}{3} , 0)$
d.
focus $(0, \frac{3}{3})$
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$|||$
Let $a$ and $b$ be two unit vectors such that $|(a+b) + 2(a\times b)| = 2$ . If $\theta \in (0,\pi )$ is the angle between $ˆa$ and $ˆb$ ,
then among the statements:
$(S1) : 2 ˆa\times ˆb = ˆa- ˆb$
$(S2)$ : The projection of $ˆa$ on $(ˆa+ ˆb)$ is $\frac{1}{2}$
a.
Only $(S1)$ is true.
b.
Only $(S2)$ is true.
c.
Both $(S1)$ and $(S2)$ are true.
d.
Both $(S1)$ and $(S2)$ are false.
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The slope of normal at any point $(x,y),x> 0,y> 0$ on the curve $y=y(x)$ is given by $\frac{x^{2}}{xy-x^{2}y^{2}-1}$ . If the curve
passes through the point $(1, 1)$ , then $e\cdot y(e)$ is equal to
a.
$\frac{1-tan(1)}{1+tan(1)}$
b.
$tan(1)$
c.
$1$
d.
$\frac{1+tan(1)}{1-tan(1)}$
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If the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{\lambda}$ and $\frac{x-2}{1} = \frac{y-4}{4} = \frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$ , then the sum of all
possible values of $\lambda$ is:
a.
$16$
b.
$6$
c.
$12$
d.
$15$
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