The distance $x$ covered by a paritcle in one dimensional motion varies with time $t$ as $x^{2} =at^{2} + 2bt+c$ . If
the acceleration of the particle depends on $x$ as $x^{-n}$ , where $n$ is an integer, the value of $n$ is _________
✓ Accepted Answer:3
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Q2mcq
Two particles of equal mass $m$ have respective initial velocities $uˆi$ and $u(\frac{ˆi+ˆj}{2})$ . They collide completely
inelastically. The energy lost in the process is:
a.
$\frac{1}{3} mu^{2}$
b.
$\frac{1}{8} 2$
Correct Answer
c.
$\frac{3}{4} mu^{2}$
d.
$\frac{mu}{2}$
$\sqrt{\,} _{3} mu^{2}$
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Q3mcq
If the screw on a screw-gauge is given six rotations, it moves by $3mm$ on the main scale. If there are $50$
divisions on the circular scale the least count of the screw gauge is:
a.
$0.001cm$
Correct Answer
b.
$0.02m$
c.
$0.01cm$
d.
$0.001mm$
No explanation saved for this question yet.
Q4mcq
Water flows m a horizontal tube (see figure). The pressure of water changes by $700\,Nm^{-2}$ between $A$ and $B$
where the area of cross section are $40\,cm^{2}$ and $20\,cm^{2},$ respectively. Find the rate of flow of water through the
tube. (density of water $= 1000\,kgm^{-3}$ )
a.
$3020cm^{3}/s$
b.
$2720cm^{3}/s$
Correct Answer
c.
$2420cm^{3}/s$
d.
$1810cm^{3}/s$
No explanation saved for this question yet.
Q5mcq
$-$
A charged particle of mass ‘ $m$ ’ and charge ‘ $q$ ’ moving under the influence of uniform electric field $\vec{E}\,ˆi$ and a
$-$
uniform magnetic field $\vec{B}\,ˆk$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q
are respectively, $v\vec{i}$ and $-2v\vec{j}$ . Then which of the following statements (A, B, C, D) are the correct?
(Trajectory shown is schematic and not to scale)
$(A) E = \frac{3}{2} ( \frac{mv^{2}}{qa})$
$(B)$ Rate of work done by the electric field at P is $\frac{3}{2} ( \frac{mv^{3}}{a})$
$(C)$ Rate of work done by both the fields at Q is zero
$(D)$ The difference between the magnitude of angular momentum of the particle at P and Q is $2mav$ .
a.
$(A), (C), (D)$
b.
$(B), (C), (D)$
c.
$(A), (B), (C)$
Correct Answer
d.
$(A), (B), (C), (D)$
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Q6nat
One end of a straight uniform $1m$ long bar is pivoted on horizontal table. It is released from rest when it makes
an angle $30^{o}$ from the horizontal (see figure). Its angular speed when it hits the table is given as $\sqrt{n} rad s^{-1}$ ,
where $n$ is an integer. The value of $n$ is ____________
✓ Accepted Answer:15
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Q7mcq
$|$
$||$
$|$
In the given circuit diagram, a wire is joining points B and D. The current in this wire is:
a.
$0.4A$
b.
$2A$
Correct Answer
c.
$4A$
d.
zero
No explanation saved for this question yet.
Q8mcq
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the
figure? Where, $1 \rightarrow 2\rightarrow$ is adiabatic. (Graphs are schematic and are not to scale)
No explanation saved for this question yet.
Q9mcq
Radiation, with wavelength $6561\,$ Åfalls on a metal surface to produce photoelectrons. The electrons are made
to enter a uniform magnetic field of $3 \times 10^{-4}\,T$ . If the radius of the largest circular path followed by the
electrons is $10\,mm$ , the work function of the metal is close to:
a.
$1.6\,eV$
b.
$0.8eV$
c.
$1.1\,eV$
Correct Answer
d.
$1.8eV$
No explanation saved for this question yet.
Q10mcq
An electric dipole of moment $\vec{p}=(-ˆi-3ˆj+ 2ˆk)\times 10^{-29}\,C\,m$ at the origin $(0,0, 0)$ . The electric field due
to this dipole at $\vec{r}= +ˆi+ 3ˆj+ 5ˆk$ (note that $\vec{r}\cdot \vec{p}= 0$ ) is parallel to:
a.
$(+ˆi-3ˆj-2ˆk)$
b.
$(-ˆi+ 3ˆj-2ˆk)$
c.
$(+ˆi+ 3ˆj-2ˆk)$
Correct Answer
d.
$(-ˆi-3ˆj+ 2ˆk)$
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A long, straight Wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the
magnetic fields due to the wire at distance $\frac{a}{3}$ and $2a$ , respectively from the axis of the wire is:
a.
$\frac{2}{3}$
b.
$2$
c.
$\frac{1}{2}$
d.
$\frac{3}{2}$
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A body A of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body B of mass $\frac{m}{2}$
collides with A with a velocity which is half $(\frac{\vec{v}}{2})$ the instantaneous velocity $\vec{v}$ of A. The collision is completely
inelastic. Then, the combined body:
a.
continues to move in a circular orbit
b.
Escapes from the Planet's Gravitational field
c.
Falls vertically downwards towards the planet
d.
starts moving in an elliptical orbit around the
planet
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A body of mass $m = 10\,kg$ is attached to one end of a wire of length $0.3\,m$ . What is the maximum angular
speed (in $rad\,s^{-1}$ ) with which it can be rotated about its other end in a space station without breaking the wire?
[Breaking stress of wire $(\sigma )= 4.8 \times 10^{7}\,N\,m^{-2}$ and area of cross-section of the wire $= 10^{-2}\,cm^{2}$ ]
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Consider a sphere of radius $R$ which carries a uniform charge density $\rho$ . If a sphere of radius $\frac{R}{2}$ is carved out
$-$
$--^{E}\vec{A}$
of it, as shown, the ratio of magnitude of electric field $E$ and $E$ , respectively, at points $A$ and $B$ due to
$-_{E_{\vec{B}}}^{\vec{A}}^{\vec{B}}$
the remaining portion is:
a.
$\frac{21}{34}$
b.
$\frac{18}{34}$
c.
$\frac{17}{54}$
d.
$\frac{18}{54}$
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A quantity $f$ is given by $f = \sqrt{\frac{hc}{G}}$ where $c$ is speed of light, $G$ univasal gravitational constant and $h$ is the
Planck’s constant. Dimension of $f$ is that of:
a.
area
b.
energy
c.
momentum
d.
volume
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A particle moving with kinetic energy $E$ has de Broglie wavelength $\lambda$ . If energy $\Delta E$ is added to its energy, the
wavelength become $\frac{\lambda}{2}$ . Value of $\Delta E,$ is:
a.
$E$
b.
$4E$
c.
$3E$
d.
$2E$
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A vessel of depth $2h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid
of refractive index $\sqrt{2}$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of
the vessel will be
a.
$\frac{h}{\sqrt{2}}$
b.
$\frac{h}{2(\sqrt{2}+1)}$
c.
$\frac{h}{3\sqrt{2}}$
d.
$\frac{3\sqrt{2}h}{4}$
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Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$ . Molecules of the gas $A$ are rigid, and have
a mass $m$ . Molecules of the gas $B$ have an additional vibrational mode and have a mass $\frac{m}{4}$ . The ratio of the
specific heats $(C_{V} )_{A}and\,( C_{V} )_{B}$ of gas $A$ and $B,$ respectively is:
a.
$7 : 9$
b.
$5 : 9$
c.
$3 : 5$
d.
$5 : 7$
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Consider a force $\vec{F} = -xˆi+yˆj$ . The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$
along the line segment is : (all quantities are in SI units)
a.
$2$
b.
$\frac{1}{2}$
c.
$1$
d.
$\frac{3}{2}$
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Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these
are forward biased. Built in potential in each diode is $0.7V$ . For the input voltages shown in the figure, the
voltage (in Volts) at point A is ________
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$-\rightarrow \rightarrow$
The electric fields of two plane electromagnetic plane waves in vacuum are given by $E_{1} =E_{0}ˆjcos(\omega t- kx)$
$-\rightarrow \rightarrow$
and $E_{2} =E_{0}ˆkcos(\omega t- ky)$ At $t= 0,$ a particle of charge $q$ is at origin with a velocity $\vec{v}= 08cˆj$ ( $c$ is the
speed of light in vaccum). The instantaneous force experienced by the particle is:
a.
$E_{0}q(0.8ˆi- ˆj+ 0.4ˆk)$
b.
$E_{0}q(0.4ˆi-3ˆj+ 0.8ˆk)$
c.
$E_{0}q(-0.8ˆi+ ˆj+ ˆk)$
d.
$E_{0}q(0.8ˆi+ ˆj+ 0.2ˆk)$
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Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres
form an equilateral triangle of side of length $d$ . The ratio $\frac{I_{0}}{I_{A}}$ of moment of inertia $I_{0}$ of the system about an
axis passing the centroid and about center of any of the spheres $I_{A}$ and perpendicular to the plane of the triangle
is:
a.
$\frac{13}{23}$
b.
$\frac{15}{13}$
c.
$\frac{23}{13}$
d.
$\frac{13}{15}$
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The aperture diameter of a telescope is $5m$ . The separation between the moon and the earth is $4 \times 10^{5}km$ .
With light of wavelength of $5500$ Å, the minimum separation between objects on the surface of moon, so that
they are just resolved, is close to:
a.
$60m$
b.
$20m$
c.
$200m$
d.
$600m$
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In a fluorescent lamp choke (a small transformer) $100V$ of reverse voltage is produced when the choke current
changes uniformly from $0.25A$ to $0$ in a duration of $0.025ms$ . The self-inductance of the choke (in $mH$ ) is
estimated to be ________
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Three harmonic waves having equal frequency $v$ and same intensity $I_{0}$ , have phase angles $0, \frac{\pi}{4}$ and $- \frac{\pi}{4}$
respectively. When they are superimposed the intensity of the resultant wave is close to:
a.
$5.8I_{0}$
b.
$0.2I_{0}$
c.
$3I_{0}$
d.
$I_{0}$
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The hardness of a water sample containing $10^{-3\,}M\,MgSO_{4}$ expressed as $CaCO_{3}$ equivalents (in $ppm$ ) is .
(molar mass of $MgSO_{4}$ is $120.37\,g/mol$ )
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A chemist has $4$ samples of artificial sweetener $A, B, C$ and $D$ . To identify these samples, he performed
certain experiments and noted the following observations:
(i) $A$ and $D$ both form blue-violet colour with ninhydrin.
(ii) Lassaigne extract of $C$ gives positive $AgNO_{3}$ test and negative $Fe_{4}[Fe(CN)_{6}]_{3}$ test.
(iii) Lassaigne extract of $B$ and $D$ gives positive sodium nitroprusside test.
Based on these observations which option is correct?
a.
A : Aspartame; B : Saccharin; C : Sucralose; D :
Alitame
b.
A : Alitame; B : Saccharin; C : Aspartame; D :
Sucralose
c.
A : Saccharin; B : Alitame; C : Sucralose; D :
Aspartame
d.
A : Aspartame; B : Alitame; C : Saccharin; D :
Sucralose
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For the following reactions
$^{700K}Product$
$-A$
$-A_{cat}^{500K}_{\vec{a}\vec{l}yst} Product$
It was found that the $E_{a}$ is decreased by $30\,KJ/mol$ in the presence of catalyst. If the rate remains unchanged,
the activation energy for catalysed reaction is (Assume pre-exponential factor is same)
a.
$75\,KJ/mol$
b.
$105\,KJ/mol$
c.
$135\,KJ/mol$
d.
$198\,KJ/mol$
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$108\,g$ of silver (molar mass $108\,gmol^{-1}$ ) is deposited at cathode from $AgNO_{3}(aq)$ solution by a certain
quantity of electricity. The volume (in $L$ ) of oxygen gas produced at $273\,K$ and $1$ bar pressure from water by
the same quantity of electricity is ________
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How much amount of $NaCl$ should be added to $600\,g$ of water $($ $\rho$ $= 1.00g/mL)$ to decrease the freezing point
of water to $-0.2\,^{o}C$ ? ________. (The freezing point depression constant for water $= 2\,K\,kgmol^{-1}$ )
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$[Pd(F)(Cl)(Br)(I)]^{2-}$ has $n$ number of geometrical isomers. Then, the spin-only magnetic moment and crystal
field stabilization energy $[CFSE]$ of $[Fe(CN)_{6}]^{n-6}$ , respectively, are:
[Note: Ignore the pairing energy]
a.
$2.84\,BM$ and $-16\Delta _{0}$
b.
$5.92\,BM$ and $0$
c.
$1.73\,BM$ and $-2.0\Delta _{0}$
d.
$0\,BM$ and $-2.4\Delta _{0}$
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Complex $X$ Of composition $Cr(H_{2}O)_{6}Cl_{n}$ Has a spin only magnetic moment of $3.83\,B. M.$ It reacts with
$AgNO_{3}$ And shows geometrical isomerism. The IUPAC nomenclature of $X$ Is:
The $K_{sp}$ for the following dissociation is $1.6 \times 10^{-5}$
$PbCl_{2(s)} \rightleftharpoons Pb^{2+}_{(aq)} + 2Cl^{-}_{(aq)}$
Which of the following choices is correct for a mixture of $300\,mL\,0.134\,M\,Pb(NO_{3})_{2}$ and $100\,mL$
$0.4\,M\,NaCl?$
a.
Not enough data provided
b.
$Q < K_{sp}$
c.
$Q > K_{sp}$
d.
$Q = K_{sp}$
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$B$ has a smaller first ionization enthalpy than $Be$ . Consider the following statement:
(I) it is easier to remove $2p$ electron than $2s$ electron
(II) $2p$ electron of $B$ is more shielded from the nucleus by the inner core of electrons than the $2s$ electrons of
$Be$
(III) $2s$ electron has more penetration power than $2p$ electron
(IV) atomic radius of $B$ is more than $Be$
(atomic number $B : 5, \,Be = 4$ )
The correct statements are.
a.
(I), (II) and (IV)
b.
(II), (III) and (IV)
c.
(I), (II) and (III)
d.
(I), (III) and (IV)
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Let the observation $x_{i}(1 \leq i\leq 10)$ satisfy the equations $\sum ^{10}_{i=1}(x_{i}-5) = 10$ , $\sum ^{10}_{i=1} (x_{i}-5)^{2} = 40$ . If $\mu$ and
$\lambda$ are the mean and the variance of the observations, $x_{1}-3,x_{2}-3, . . . . ,x_{10}-3,$ then the ordered pair $(\mu ,\lambda )$
is equal to:
a.
$(3,3)$
b.
$(6,3)$
c.
$(6,6)$
d.
$(3,6)$
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If $e_{1}$ and $e_{2}$ are the eccentricities of the ellipse $\frac{x^{2}}{18} + \frac{y^{2}}{4} = 1$ and the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ respectively and
$(e_{1},e_{2})$ is a point on the ellipse $15x^{2} + 3y^{2} =k$ , then the value of $k$ is equal to
a.
$16$
b.
$17$
c.
$15$
d.
$14$
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If for some $\alpha$ and $\beta$ in $R$ , the intersection of the following three planes
$x+ 4y-2z= 1$
$x+ 7y-5z=\beta$
$x+ 5y+\alpha z= 5$
is a line in $R^{3}$ , then $\alpha +\beta$ is equal to:
a.
$0$
b.
$10$
c.
$2$
d.
$-10$
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Let $D$ be the centroid of the triangle with vertices $(3, -1)$ , $(1, 3)$ and $(2, 4)$ . Let $P$ be the point of
intersection of the lines $x+ 3y-1 = 10$ and $3x- y+ 1 = 0$ . Then, the line passing through the points $D$ and
$P$ also passes through the point:
a.
$(-9, -6)$
b.
$(9,7)$
c.
$(7,6)$
d.
$(-9, -7)$
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$||$
The projection of the line segment joining the point $(1, -1, 3)$ and $(2, -4, 11)$ on the line joining the points
$(-1, 2, 3)$ and $(3, -2,10)$ is _______
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$\{ \frac{sin(a+2)x+sinx}{x} ;x< 0$
If $f(x) = b ;x= 0$ is continuous at $x= 0$ , then $a+ 2b$ is equal to:
$\{\frac{(x+3x^{2})^{1/3}-x^{1/3}}{x^{1/3}} ;x> 0$
a.
$1$
b.
$-1$
c.
$0$
d.
$-2$
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A spherical iron ball of $10cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of
$50cm^{3}/min$ . When the thickness of ice is $5cm$ , then the rate (in $cm/min$ .) at which of the thickness of ice
decreases, is:
a.
$\frac{5}{6\pi}$
b.
$\frac{1}{54\pi}$
c.
$\frac{1}{36\pi}$
d.
$\frac{1}{18\pi}$
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In a box, there are $20$ cards, out of which $10$ are labelled as $A$ and the remaining $10$ are labelled as $B$ . Cards
are drawn at random, one after the other and with replacement, till a second $A$ card is obtained. The probability
that the second $A$ card appears before the third $B$ card is:
a.
$\frac{9}{16}$
b.
$\frac{11}{16}$
c.
$\frac{13}{16}$
d.
$\frac{15}{16}$
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A circle touches the y-axis at the point $(0, 4)$ and passes through the point $(2, 0)$ . Which of the following lines
is not a tangent to this circle?
a.
$4x-3y+ 17 = 0$
b.
$3x-4y-24 = 0$
c.
$3x+ 4y-6 = 0$
d.
$4x+ 3y-8 = 0$
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If the vectors, $\vec{p}= (a+ 1)ˆi+aˆj+aˆk, \vec{q}=aˆi+ (a+ 1)ˆj+aˆk$ and $\vec{r}=aˆi+aˆj+ (a+ 1)ˆk(a\in R)$ are
coplanar and $3(\vec{p}. \vec{q})^{2} - \lambda \vec{r}\times \vec{q}^{2} = 0$ , then the value of $\lambda$ is ________
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Let $f$ be any function continuous on $[a,b]$ and twice differentiable on $(a,b)$ . If all $x\in (a,b),f'(x) > 0$ and
$f''(x) < 0$ , then for any $c\in (a,b), \frac{f(c)-f(a)}{f(b)-f(c)}$
a.
$\frac{b+a}{b-a}$
b.
$1$
c.
$\frac{b-c}{c-a}$
d.
$\frac{c-a}{b-c}$
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