If an electron is moving in the $n^{th\,}$ orbit of the hydrogen atom, then its velocity $(v_{n})$ for the $n^{th\,}$ orbit is given
as:
a.
$v_{n} \propto n$
b.
$v_{n} \propto \frac{1}{n}$
Correct Answer
c.
$v_{n} \propto n^{2}$
d.
$v_{n} \propto \frac{1}{n^{2}}$
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Q2mcq
Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed so that there is no loss of energy. If $F_{1}$ and
$F_{2}, \,m_{1}$ and $m_{2}, \,n_{1}$ and $n_{2}$ be the degrees of freedom, masses, number of molecules of the first and second
gas respectively, the temperature of mixture of these two gases is:
A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference
$V = 12\,V$ between its plates. The charging battery is now disconnected and a porcelain plate with $k= 7$ is
inserted between the plates, then the plate would oscillate back and forth between the plates with a constant
mechanical energy of _______ $pJ.$
(Assume no friction)
✓ Accepted Answer:864
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Q4mcq
A triangular plate is shown. A force $\vec{F} = 4ˆi -3ˆj$ is applied at point $P.$ The torque at point $P$ with respect to
point $O$ and $Q$ are:
a.
$-15 -20, 15 -20\sqrt{3} \sqrt{3}$
Correct Answer
b.
$15 + 20, 15 -20\sqrt{3} \sqrt{3}$
c.
$15 -20, 15 + 20\sqrt{3} \sqrt{3}$
d.
$-15 + 20, 15 + 20\sqrt{3} \sqrt{3}$
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Q5mcq
The thickness at the centre of a plano convex lens is $3\, mm$ and the diameter is $6\, cm.$ If the speed of light in
the material of the lens is $2 \times 10^{8}\,m\,s^{-1}.$ The focal length of the lens is ___________.
a.
$0. 30\, cm$
b.
$15\, cm$
c.
$1. 5\, cm$
d.
$30\, cm$
Correct Answer
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Q6mcq
The vernier scale used for measurement has a positive zero error of $0. 2\, mm.$ If while taking a measurement it
was noted that $0$ on the vernier scale lies between $8. 5\, cm$ and $8. 6\, cm$ . Vernier coincidence is $6,$ then the
correct value of measurement is $cm.$
(least count $= 0. 01\, cm$ )
a.
$8. 36\, cm$
b.
$8. 54\, cm$
Correct Answer
c.
$8. 58\, cm$
d.
$8. 56\, cm$
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Q7mcq
An $AC$ current is given by $I =I_{1}sin\omega t+I_{2}cos\omega t.$
A hot wire ammeter will give a reading:
If $2. 5 \times 10^{-6}\,N$ average force is exerted by a light wave on a non-reflecting surface of $30\, cm^{2}$ area during
$40\, min$ of time span, the energy flux of light just before it falls on the surface is _______ $W\, cm^{-2}.$ (Round off
to the Nearest Integer), (Assume complete absorption and normal incidence conditions are there)
✓ Accepted Answer:25
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Q9nat
The radius in kilometer to which the present radius of earth $(R= 6400\, km)$ to be compressed so that the
escape velocity is increased $10$ time is _______.
✓ Accepted Answer:64
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Q10nat
The angular speed of truck wheel is increased from $900\, rpm$ to $2460\, rpm$ in $26$ seconds. The number of
revolutions by the truck engine during this time is ______.
(Assuming the acceleration to be uniform).
✓ Accepted Answer:728
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A current of $10\,A$ exists in a wire of cross-sectional area of $5\, mm^{2}$ with a drift velocity of $2 \times 10^{-3}\,m\,s^{-1}.$
The number of free electrons in each cubic meter of the wire is
a.
$2 \times 10^{6}$
b.
$625 \times 10^{25}$
c.
$2 \times 10^{25}$
d.
$1 \times 10^{23}$
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Two blocks ( $m= 0. 5\, kg$ and $M = 4. 5\, kg$ ) are arranged on a horizontal frictionless table as shown in the
figure. The coefficient of static friction between the two blocks is $\frac{3}{7}.$ Then the maximum horizontal force that
can be applied on the larger block so that the blocks move together is $N.$ (Round off to the Nearest Integer)
[Take $g$ as $9. 8\,m\,s^{-2}$ ]
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Two identical metal wires of thermal conductivities $K_{1}$ and $K_{2}$ respectively are connected in series. The
effective thermal conductivity of the combination is:
a.
$\frac{2\,K_{1}K_{2}}{K_{1}+K_{2}}$
b.
$\frac{K_{1}+K_{2}}{2\,K_{1}K_{2}}$
c.
$\frac{K_{1}+K_{2}}{K_{1}K_{2}}$
d.
$\frac{K_{1}K_{2}}{K_{1}+K_{2}}$
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An electron of mass $m$ and a photon have same energy $E.$ The ratio of wavelength of electron to that of photon
is : ( $c$ being the velocity of light)
a.
$\frac{1}{c}(\frac{2m}{E} ) \frac{1}{2}$
b.
$\frac{1}{c}( \frac{E}{2m})\frac{1}{2}$
c.
$(\frac{E}{2\,m})\frac{1}{2}$
d.
$c(2mE) \frac{1}{2}$
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A boy is rolling a $0. 5\, kg$ ball on the frictionless floor with the speed of $20\,m\,s^{-1}.$ The ball gets deflected by an
obstacle on the way. After deflection it moves with $5%$ of its initial kinetic energy. What is the speed of the ball
now?
a.
$19. 0\,m\,s^{-1}$
b.
$4. 4\,m\,s^{-1}$
c.
$14. 41\,m\,s^{-1}$
d.
$1. 00\,m\,s^{-1}$
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The equivalent resistance of series combination of two resistors is $s.$ When they are connected in parallel, the
equivalent resistance is $p.$ If $s=np,$ then the minimum value for $n$ is ______.
(Round off to the Nearest Integer)
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A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed
$v.$ If the coefficient of static friction between the tyres and the track is $\mu _{s},$ then the magnitude of negative lift $F_{L}$
acting downwards on the car is:
a.
$m(\frac{v^{2}}{\mu _{s}R} +g)$
b.
$m(\frac{v^{2}}{\mu _{s}R} - g)$
c.
$m(g- \frac{v^{2}}{\mu _{s}R})$
d.
$-m(g+ \frac{v^{2}}{\mu _{s}R})$
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For VHF signal broadcasting, _______ $km^{2}$ of maximum service area will be covered by an antenna tower of
height $30\,m,$ if the receiving antenna is placed at ground. Let radius of the earth be $6400\, km.$ (Round off to
the Nearest Integer) (Take $\pi$ as $3. 14$ )
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A solenoid of $1000$ turns per metre has a core with relative permeability $500.$ Insulated windings of the
solenoid carry an electric current of $5\,A.$ The magnetic flux density produced by the solenoid is:
(Permeability of free space $= 4\pi \times 10^{-7}\,H\,m^{-1}$ )
a.
$(\pi )\,T$
b.
$(2 \times 10^{-3}\pi )\,T$
c.
$(\frac{\pi}{5})\,T$
d.
$(10^{-4}\pi )\,T$
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The following bodies,
$(1)$ a ring
$(2)$ a disc
$(3)$ a solid cylinder
$(4)$ a solid sphere,
of same mass $m$ and radius $R$ are allowed to roll down without slipping simultaneously from the top of the
inclined plane. The body which will reach first at the bottom of the inclined plane is
[Mark the body as per their respective numbering given in the question]
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A Carnot's engine working between $400\,K$ and $800\,K$ has a work output of $1200\,J$ per cycle. The amount of
heat energy supplied to the engine from the source in each cycle is:
a.
$3200\,J$
b.
$1800\,J$
c.
$1600\,J$
d.
$2400\,J$
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Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as
shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of
oscillation of the two SHM is $\frac{T_{b}}{T_{a}} = \sqrt{x},$ where value of $x$ is ______.
(Round off to the Nearest Integer)
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A mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$
moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular
motion with constant angular velocity $\omega .$ The angular momentum of $M$ about point $A$ is $L_{A}$ which lies in the
positive $z$ direction and the angular momentum of $M$ about $B$ is $L_{B}.$ The correct statement for this system is:
a.
$L_{A}$ and $L_{B}$ are both constant in magnitude and
direction
b.
$L_{B}$ is constant in direction with varying
magnitude
c.
$L_{B}$ is constant, both in magnitude and direction
d.
$L_{A}$ is constant, both in magnitude and direction
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A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to
come to rest. If the total time elapsed is t seconds, the total distance travelled is:
a.
$\frac{4\alpha \beta}{(\alpha +\beta )}t^{2}$
b.
$\frac{2\alpha \beta}{(\alpha +\beta )}t^{2}$
c.
$\frac{\alpha \beta}{2(\alpha +\beta )}t^{2}$
d.
$\frac{\alpha \beta}{4(\alpha +\beta )} t^{2}$
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Four identical rectangular plates with length, $l= 2\, cm$ and breadth, $b= \frac{3}{2}\, cm$ are arranged as shown in
figure. The equivalent capacitance between $A$ and $C$ is $\frac{x\epsilon _{0}}{d}.$ The value of $x$ is _______.
(Round off to the Nearest Integer)
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For a certain first order reaction $32%$ of the reactant is left after $570\,s.$ The rate constant of this reaction is
$\times 10^{-3}\,s^{-1}.$ (Round off to the Nearest Integer).
[Given: $log_{10}\,2 = 0. 301, \, ln 10 = 2. 303$ ]
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The standard enthalpies of formation of $Al_{2}O_{3}$ and $CaO$ are $-1675\, kJ \, mol^{-1}$ and $-635\, kJ \, mol^{-1}$
respectively.
For the reaction
$3CaO + 2Al \rightarrow 3Ca + Al\rightarrow_{2}O_{3}$ the standard reaction enthalpy $\Delta _{r}H^{0} =$ ________ $kJ.$
(Round off to the Nearest Integer).
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The INCORRECT statement(s) about heavy water is (are)
(A) used as a moderator in nuclear reactor
(B) obtained as a by-product in fertilizer industry.
(C) used for the study of reaction mechanism
(D) has a higher dielectric constant than water
Choose the correct answer from the options given below:
a.
(B) only
b.
(C) only
c.
(D) only
d.
(B) and (D) only
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$0. 01$ moles of a weak acid $HA \,(K_{a} = 2. 0 \times 10^{-6})$ is dissolved in $1. 0\,L$ of $0. 1M\, HCl$ solution. The degree
of dissociation of $HA$ is __________ $\times 10^{-5}$ (Round off to the Nearest Integer). [Neglect volume change on
adding $HA$ and assume degree of dissociation $<< 1$ ]
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Given below are two statements:
Statement-I: Retardation factor $(R_{f})$ can be measured in meter/centimetre.
Statement-II: $R_{f}$ value of a compound remains constant in all solvents.
Choose the most appropriate answer from the options given below:
a.
Statement-I is true but statement-II is false
b.
Both statement-I and statement-II are true
c.
Both statement-I and statement-II are false
d.
Statement-I is false but statement-II is true
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In the above reaction, $3. 9\,g$ of benzene on nitration gives $4. 92\,g$ of nitrobenzene. The percentage yield of
nitrobenzene in the above reaction is _________ $%$ . (Round off to the Nearest Integer).
(Given atomic mass : $C\, : 12. 0\,u, \,H\, : 1. 0\,u\,O\, : 16. 0\,u, N\, : 14. 0\,u$ )
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The mole fraction of a solute in a $100$ molal aqueous solution ________ $\times 10^{-2}.$
(Round off to the Nearest Integer).
[Given : Atomic masses: $H\, : 1. 0\,u, \,O\, : 16. 0\,u$ ]
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The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of
product $A.$ The reaction $1\, mol$ of $A$ with excess of $AgNO_{3}$ in aqueous medium gives ________ mole(s) of
$Ag.$ (Round off to the Nearest Integer).
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$15\, mL$ of aqueous solution of $Fe^{2+}$ in acidic medium completely reacted with $20\, mL$ of $0. 03\,M$ aqueous
$Cr_{2}O_{7}^{2-}.$ The molarity of the $Fe^{2+}$ solution is _______ $\times 10^{-2}M$ (Round off to the Nearest Integer).
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Given below are two statements:
Statement I: Potassium permanganate on heating at $573\,K$ forms potassium manganate.
Statement II: Both potassium permanganate and potassium manganate are tetrahedral and paramagnetic in
nature.
In the light of the above statements, choose the most appropriate answer from the options given below:
a.
Statement I is true but statement II is false
b.
Both statement I and statement II are true
c.
Statement I is false but statement II is true
d.
Both statement I and statement II are false
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Hoffmann bromamide degradation of benzamide gives product $A,$ which upon heating with $CHCl_{3}$ and $NaOH$
gives product $B.$ The structures of $A$ and $B$ are:
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The pressure exerted by a non-reactive gaseous mixture of $6. 4\,g$ of methane and $8. 8\,g$ of carbon dioxide in a
$10\,L$ vessel at $27^{\circ}C$ is _____ $kPa.$ (Round off to the Nearest Integer).
[Assume gases are ideal, $R = 8. 314\,J\, mol^{-1}\,K^{-1}$ Atomic masses: $C\, : 12. 0\,u, \,H\, : 1. 0\,u, \,\,O\, : 16. 0\,u$ ]
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The oxygen dissolved in water exerts a partial pressure of $20\, kPa$ in the vapour above water. The molar
solubility of oxygen in water is ______ $\times 10^{-5}\, mol \, dm^{-3}.$
(Round off to the Nearest Integer).
[Given : Henry's law constant $= K_{H} = 8. 0 \times 10^{4}\, kPa$ for $O_{2}.$ Density of water with dissolved oxygen
$= 1. 0\, kg \, dm^{-3}$ ]
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Let $\vec{a}= 2ˆi-3ˆj+ 4ˆk$ and $\vec{b}= 7ˆi+ ˆj-6ˆk$ If $\vec{r}\times \vec{a}= \vec{r}\times \vec{b}, \vec{r}\cdot (ˆi+ 2ˆj+ ˆk)= -3,$ then $\vec{r}\cdot (2ˆi-3ˆj+ˆk)$ is
equal to:
a.
$12$
b.
$8$
c.
$13$
d.
$10$
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The value of $_{x}lim_{\rightarrow 0\rightarrow }_{+} \frac{cos^{-1}(x-[x]^{2})\cdot sin^{-1}(x-[x]^{2})}{x-x^{3}},$ where $[x]$ denotes the greatest integer $\leq x$ is:
a.
$\pi$
b.
$0$
c.
$\frac{\pi}{4}$
d.
$\frac{\pi}{2}$
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If $\vec{a}=\alpha ˆi+\beta ˆj+ 3ˆk, \,\vec{b}= -\beta ˆi- \alpha ˆj- ˆk$ and $\vec{c}= ˆi-2ˆj- ˆk$ such that $\vec{a}\cdot \vec{b}= 1$ and $\vec{b}\cdot \vec{c}= -3,$ then
$\frac{1}{3}((\vec{a}\times \vec{b})\cdot \vec{c})$ is equal to _______.
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In a school, there are three types of games to be played. Some of the students play two types of games, but
none play all the three games. Which Venn diagrams can justify the above statement?
a.
P and Q
b.
P and R
c.
Q and R
d.
None of these
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The minimum distance between any two points $P_{1}$ and $P_{2}$ while considering point $P_{1}$ on one circle and point
$P_{2}$ on the other circle for the given circles' equations
$x^{2} +y^{2} -10x-10y+ 41 = 0$
$x^{2} +y^{2} -24x-10y+ 160 = 0$ is ________
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The line $2x- y+ 1 = 0$ is a tangent to the circle at the point $(2, \,5)$ and the centre of the circle lies on
$x-2y= 4.$ Then, the radius of the circle is:
a.
$3\sqrt{5}$
b.
$5\sqrt{3}$
c.
$5\sqrt{4}$
d.
$4\sqrt{5}$
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$|$
$||$
In a triangle $PQR,$ the co-ordinates of the points $P$ and $Q$ are $(-2, 4)$ and $(4, -2)$ respectively. If the equation
of the perpendicular bisector of $PR$ is $2x- y+ 2 = 0,$ then the centre of the circumcircle of the $\Delta PQR$ is:
a.
$(-1, \,0)$
b.
$(-2, \,-2)$
c.
$(0, \,2)$
d.
$(1, \,4)$
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$||$
$||$
Let there be three independent events $E_{1},E_{2}$ and $E_{3}.$ The probability that only $E_{1}$ occurs is $\alpha$ only $E_{2}$ occurs
is $\beta$ and only $E_{3}$ occurs is $\gamma .$ Let $'p'$ denote the probability of none of events occurs that satisfies the equations
$(\alpha -2\beta )p =\alpha \beta$ and $(\beta -3\gamma )p = 2\beta \gamma .$ All the
given probabilities are assumed to lie in the interval $(0, \,1).$
Then, $\frac{\,Probability ofoccurrence of\,E_{1}}{\,Probability ofoccurrence of\,E_{3}}$ is equal to ________.
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Which of the following statement is correct for the function $g(\alpha )$ for $\alpha \in R$ such that
$g(\alpha ) =\int _{6}\frac{\pi}{\pi 3} \frac{sin^{\alpha }x}{cos^{\alpha }x+sin^{\alpha }x}dx$
a.
$g(\alpha )$ is a strictly increasing function
b.
$g(\alpha )$ has an inflection point at $\alpha = -\frac{1}{2}$
c.
$g(\alpha )$ is a strictly decreasing function
d.
$g(\alpha )$ is an even function
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Two dices are rolled. If both dices have six faces numbered $1, \,2, \,3, \,5, \,7$ and $11,$ then the probability that the
sum of the numbers on the top faces is less than or equal to $8$ is:
a.
$\frac{4}{9}$
b.
$\frac{17}{36}$
c.
$\frac{5}{12}$
d.
$\frac{1}{2}$
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If the equation of the plane passing through the line of intersection of the planes
$2x-7y+ 4z-3 = 0, \,3x-5y+ 4z+ 11 = 0$ and the point $(-2, \,1, \,3)$ is $ax+by+cz-7 = 0,$ then the
value of $2a+b+c-7$ is _________.
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If $f(x) = sin(cos^{-1}(\frac{1-2^{2}^{x}}{1+2^{2}^{x}}))$ and its first derivative with respect to $x$ is $-\frac{b}{a}log_{e}2$ when $x= 1,$ where $a$ and
$b$ are integers, then the minimum value of $a^{2} - b^{2}$ is _______.
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Team $'A'$ consists of $7$ boys and $n$ girls and Team $'B'$ has $4$ boys and $6$ girls. If a total of $52$ single matches can
be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is
equal to:
a.
$5$
b.
$2$
c.
$4$
d.
$6$
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Choose the incorrect statement about the two circles whose equations are given below:
$x^{2} +y^{2} -10x-10y+ 41 = 0$ and $x^{2} +y^{2} -16x-10y+ 80 = 0$
a.
Distance between two centres is the average of
radii of both the circles.
b.
Both circles' centres lie inside region of one
another.
c.
Both circles pass through the centre of each
other.
d.
Circles have two intersection points.
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