The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $R =(1. 3 \times 10^{-15})A^{1/3}m$ . It
follows that the mass density of n nucleus is of the order of: $(M_{prot} ≅M_{neut\,} \simeq 1. 67 \times 10^{-27}\, kg)$
a.
$10^{3}\, kg \,m^{-3}$
b.
$10^{10\,} kg \,m^{-3}$
c.
$10^{24}\, kg \,m^{-3}$
d.
$10^{17}\, kg \,m^{-3}$
Correct Answer
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Q2mcq
Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode)
probes connected across a component, are just reversed?
a.
Multimeter shows an equal deflection in both
cases i.e., before and after reversing the probes if
the chosen component is resistor.
b.
Multimeter shows NO deflection in both cases
i.e. before and after reversing the probes if the
chosen component is capacitor
Correct Answer
c.
Multimeter shows a deflection, accompanied by a
splash of light out of connected component in
one direction and NO deflection on reversing the
probes if the chosen component is LED
d.
Multimeter shows NO deflection in both cases
i.e. before and after reversing the probes is the
chsosen component is metal wire.
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Q3nat
An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass $m$ situated at
its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is
$\frac{N}{20}ma^{2}$ where $N$ is an integer. The value of $N$ is ___________ .
✓ Accepted Answer:25
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Q4mcq
Two resistors $400\,\Omega$ and $800\,\Omega$ are connected in series across a $6\vee$ battery. The potential difference measured
by a voltmeter of $10\,k\Omega$ across $400\,\Omega$ resistor is close to:
a.
$2\,V$
b.
$1. 8\,V$
c.
$2. 05\,V$
d.
$1. 95\,V$
Correct Answer
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Q5mcq
A metallic sphere cools from $50\,^{\circ}C$ to $40\,^{\circ}C$ in $300\,s$ . If atmospheric temperature around is $20\,^{\circ}C$ , then the
sphere's temperature after the nest $5$ minutes will be close to:
a.
$31\,^{\circ}C$
b.
$33\,^{\circ}C$
Correct Answer
c.
$28\,^{\circ}C$
d.
$35\,^{\circ}C$
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Q6mcq
Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively.
Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to
the number density of photons of the visible light of the given wavelengths is:
a.
$\frac{1}{500}$
Correct Answer
b.
$250$
c.
$\frac{1}{250}$
d.
$500$
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Q7mcq
Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant.
Dimension of solar constant is:
a.
$ML^{2} T^{-2}$
b.
$ML^{0} T^{-3}$
Correct Answer
c.
$M^{2}L^{0}T^{-1}$
d.
$MLT^{-2}$
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Q8mcq
The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is
$\vec{E}= E_{0}jcos(\omega t -kx).$ The magnetic field $\vec{B},$ at the moment $t = 0$ is:
A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy
source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn
schematically and are not to scale):
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Q10mcq
The mass density of a planet of radius R varies with the distance r from its centre as $\rho (r)=\rho _{0}(1 - \frac{r^{2}}{R^{2}})$ Then
the gravitational field is maximum at:
a.
$r=\sqrt{\frac{3}{4}} R$
b.
$r=R$
c.
$r= \frac{1}{\sqrt{3}} R$
d.
$r=\sqrt{\frac{5}{9}}R$
Correct Answer
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A uniform rod of length ' $\ell '$ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft
rotates at angular speed $\omega$ the rod makes an angle $\theta$ with it (see figure). To find $\theta$ equate the rate of change of
angular momentum (direction going into the paper) $\frac{m\ell ^{2}}{12}\omega ^{2}sin\theta$ about the centre of mass (CM) to the torque
provided by the horizontal and vertical forces $F_{H}$ and $F_{v}$ about the CM. The value of $\theta$ is then such that:
a.
$cos\theta = \frac{2g}{3𝓁\omega ^{2}}$
b.
$cos\theta = \frac{g}{2\ell \omega ^{2}}$
c.
$cos\theta = \frac{g}{\ell \omega ^{2}}$
d.
$cos\theta = \frac{3g}{2\ell \omega ^{2}}$
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If a semiconductor photo diode can detect a photon with a maximum wavelength of $400\, nm$ , then its band gap
energy is: Planck's constant $h = 6. 63 \times 10^{-34}\,J. s$
Speed of light $c = 3 \times 10^{8}\,m\,s^{-1}$
a.
$1. 1\, eV$
b.
$2. 0\, eV$
c.
$1. 5\, eV$
d.
$3. 1\, eV$
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A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic
substance. The whole system is placed in a uniform magnetic field $\vec{B}$ . Then the field inside the paramagnetic
substance is:
a.
$\vec{B}$
b.
Zero
c.
much large than $\vec{B}$ and parallel to $\vec{B}$ much large than $\vec{B}$ but opposite to $\vec{B}$
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Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference.
The ratio of final speeds of hydrogen and helium ions is close to:
a.
$1\, : \,2$
b.
$10 : 7$
c.
$2 : 1$
d.
$5 : 7$
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A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal
wire. The wire has a diameter of $4\, mm$ and a total length of $30\, cm.$ The magnetic field changes with time at a
steady rate $dB /dt = 0. 032 Ts^{-1}.$ The induced current in the $loop$ is close to (Resistivity of the metal wire is
$1. 23 \times 10^{-8}\,\Omega m$ )
a.
0.43 A
b.
0.61 A
c.
0.34 A
d.
0.53 A
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If minimum possible work is done by a refrigerator in converting 100 grams of water at $0\,^{\circ}C$ to ice, how much
heat (in calories) is released to the surroundings at temperature $27\,^{\circ}C$ (Latent heat of ice $= \,80\, Cal / gram$ ) to
the nearest integer?
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A calorimeter of water equivalent $20\,g$ contains $180\,g$ of water at $25^{\circ}C$ . $'m'$ ' grams of steam at $100^{\circ}C$ is mixed
in it till the temperature of the mixture is $31^{\circ}C$ . The value of $'m'$ is close to (Latent heat of water
$\, = 540\, cal \,g^{-1}$ , specific heat of water $= 1\, cal \,g^{-1^{\circ}}C^{-1}$ )
a.
$2$
b.
$4$
c.
$3. 2$
d.
$2. 6$
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A galvanometer coil has 500 turns and each turn has an average area of $3 \times 10^{-4}m^{2}$ . If a torque of $1. 5\, Nm$ is
required to keep this coil parallel to a magnetic field when a current of $0. 5A$ is flowing through it, the strength
of the field (in $T$ ) is _________ .
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Concentric metallic hollow spheres of radii R and 4R hold charges $Q_{1}$ and $Q_{2}$ respectively. Given that surface
charge densities of the concentric spheres are equal, the potential difference $V(R) -V(4R)$ is:
a.
$\frac{Q_{2}}{4\pi \epsilon _{0}R}$
b.
$\frac{3Q_{2}}{4\pi \epsilon _{0}R}$
c.
$\frac{3Q_{1}}{16\pi \epsilon _{0}R}$
d.
$\frac{3Q_{1}}{4\pi \epsilon _{0}R}$
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When an object is kept at a distance of $30\, cm$ from a concave mirror, the image is formed at a distance of
$10\, cm \,$ from the mirror. If the object is moved with a speed of $9\, cm \,s^{-1}$ , the speed (in $cm \,s^{-1}$ ) with which
image moves at that instant is
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To raise the temperature of a certain mass of gas by $50\,^{\circ}C$ at a constant pressure, $160$ calories of heat is
required. When the same mass of gas is cooled by $100^{\circ}C$ at constant volume, $240$ calories of heat is released.
How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?
a.
$5$
b.
$6$
c.
$3$
d.
$7$
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A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a
frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its
equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:
a.
$\frac{1}{\sqrt{2}}$
b.
$1$
c.
$\frac{1}{2}$
d.
$\sqrt{2}$
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A block of mass $1. 9\, kg$ is at rest at the edge of a table, of height 1 m. A bullet of mass $0. 1\, kg$ collides with the
block and sticks to it. If the velocity of the bullet is $20\,m\,s^{-1}$ in the horizontal direction just before the collision
then the kinetic energy just before the combined system strikes the floor, is [Take $g\, = \,10\,m\,s^{-2}$ . Assume there
is no rotational motion and loss of energy after the collision is negligible.]
a.
$21\,J$
b.
$20\,J$
c.
$19\,J$
d.
$23\,J$
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A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$ . It comes back to its
initial position with velocity $\frac{v_{0}}{2}.$ The value of the coefficient of kinetic friction between the block and the
inclined plane is close to $\frac{1}{1000},$ The nearest integer to $I$ is :
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$| |$
Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a
path $L_{1}$ through a medium of refractive index $n_{1}$ while the second wave travels a path of length $L_{2}$ through a
medium of refractive index $n_{2}$ . After this the phase difference between the two waves is:
Three isomers A, B and C (mol. formula $C_{8}H_{11}N$ ) give the following results:
$--A$ and $C^{Dianotization}\rightarrow \rightarrow P + Q_{(ii)\, acidation(KMnO}^{(i)\, Hydrolyds}_{_{4}+H}\rightarrow \rightarrow_{^{+})} R\,(product \, of \,A) + S\,(product \, of \,C)$
R has lower boiling point than S
$-B^{C_{6}H_{5}SO_{2}}\rightarrow \rightarrow^{Cl}$ alkali-insoluble product
$A, \,B$ and $C,$ respectively are:
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Complex A has a composition of $H_{12}O_{6}Cl_{3}Cr$ . If the complex on treatment with conc. $H_{2}SO_{4}$ loses $13. 5%$
of its original mass, the correct molecular formulas of $A$ is:
[Given : atomic mass of $Cr= 52$ amu and $CI = 35\,$ amu]
a.
$[Cr(H_{2}O_{6}] Cl_{3}$
b.
$[Cr (H_{2}O)_{3}Cl_{3}] \cdot 3H_{2}O$
c.
$[Cr (H_{2}O)_{5}Cl] Cl_{2}\cdot H_{2}O$
d.
$[Cr (H_{2}O)_{4}Cl_{2}]Cl \cdot 2H_{2}O$
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The compound A in the following reactions is:
$--A\,^{(i)\, CH_{3}MgBr /H}\rightarrow \rightarrow^{_{2}O} B\,^{(i)\,O_{3}} C + D$
$(ii)\, Conc.\,H_{2}SO_{4}/\Delta (ii)\, Zn /H_{2}\vec{O}$
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The incorrect statement(s) among (a) - (d) regarding acid rain is (are):
a) It can corrode water pipes
(b) It can damage structures made up of stone.
(c) It cannot cause respiratory ailments in animals
(d) It is not harmful for trees
a.
(a), (c) and (d)
b.
(c) only
c.
(a), (b) and (d)
d.
(c) and (d)
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$0. 023 \times 10^{22}$ molecules are present in $10g$ of a substance $'x'.$ The molarity of a solution containing $5g$ of
substance 'x' in 2 L solution is $_________ \times 10^{-3}$
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If $250 cm^{3}$ of an aqueous solution containing $0. 73g$ of a protein $A$ is isotonic with one litre of another aqueous
solution containing $1. 65g$ of a protein $B,$ at $298K$ , the ratio of the molecular masses of $A$ and $B$ is
$___________ \times 10^{-2}$ (to the nearest integer).
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Consider the following reaction:
The product $'P'$ gives positive ceric ammonium nitrate test. This is because of the presence of which of these
$- OH$ group(s)?
a.
(b) only
b.
(c) and (d)
c.
(d) only
d.
(b) and (d)
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An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation
$Cr_{2}O^{2}_{7} + 14H^{+}+ 6e^{-} \rightarrow 2 Cr\rightarrow^{3+}+ 7H_{2}O$
The amount of $Cr^{3+}$ . obtained was $0. 104g$ . The efficiency of the process $(in %)$ is (Take : $F = 960000C$ , At.
mass of chromium $= 52$ )
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Consider the hypothetical situation where the azimuthal quantum number, , takes values𝓁
$0, \,1, \,2, \, … … . . n\, + \,1$ . Where n is the principal quantum number. Then, the element with atomic number:
a.
9 is the first alkali metal
b.
13 has a half-filled valence subshell
c.
8 is the first noble gas
d.
6 has a 2p-valence subshell
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Match the following drugs with their therapeutic actions:
(i) Ranitidine (a) Antidepressant
(ii) Nardil (Phenelzine) (b) Antibiotic
(iii) Chloramphenicol (c) Antihistamine
(iv) Dimetane (Brompheniramine) (d) Antacid
(e) Analgesic
a.
(i)-(a); (ii)-(c); (iii)-(b); (iv)-(e);
b.
(i)-(d); (ii)-(a); (iii)-(b); (iv)-(c);
c.
(i)-(e); (ii)-(a); (iii)-(c); (iv)-(d);
d.
(i)-(d); (ii)-(c); (iii)-(a); (iv)-(e);
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The strengths of $5. 6$ volume hydrogen peroxide (of density $1\,g/ mL$ ) in terms of mass percentage and
molarity $(M)$ respectively, are: (Take molar mass of hydrogen peroxide as $34\,g/ mol$ )
a.
1.7 and 0.5
b.
0.85 and 0.25
c.
1.7 and 0.25
d.
0.85 and 0.5
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$100\, mL$ of $0. 1\,M\, HCl$ is taken in a beaker and to it $100\, mL 0. 1\,M\, NaOH$ of is added in steps of $2\, mL$ and
the $pH$ is continuously measured. Which of the following graphs correctly depicts the change in $pH$ ?
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Among the statement (I - IV), the correct ones are:
(I) Be has smaller atomic radius compared to Mg.
(II) Be has higher ionization enthalpy than AI.
(III) Charge/radius ratio of Be is greater than that of Al.
(IV) Both Be and Al form mainly covalent compounds
a.
(I), (II) and (IV)
b.
(I), (III) and (IV)
c.
(II), (III) and (IV)
d.
(I), (II) and (III)
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A mixture of one mole each of $H_{2}$ , $He$ and $O_{2}$ each are enclosed in a cylinder of volume $V$ at temperature T.
If the partial pressure of $H_{2}$ is $2 atm,$ the total pressure of the gases in the cylinder is:
a.
$6\, atm$
b.
$38\, atm$
c.
$14\, atm$
d.
$22\, atm$
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Consider the following molecules and statements related to them:
(a) (B) is more likely to be crystaline than (A)
(b) (B) has higher boiling point than (A)
(c) (B) dissolves more readily than (A) in water
Identify the correct option from below:
a.
(a) and (b) are true
b.
(a) and (c) are true
c.
only (a) is true
d.
(b) and (c) are true
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The five successive ionization enthalpies of an element are $800, \,2427, \,3658, \,35024\,\,32824\, kJ \, mol^{-1}$ . The
number of valence electrons in the element is:
a.
5
b.
4
c.
3
d.
2
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If $\int sin^{-1}(\frac{\sqrt{x}}{1+x})dx=A(x) tan^{-1}(\sqrt{x})+B(x) +C$ , where $C$ is a constant of integration, then the
ordered pair $(A(x), \,B(x))$ can be :
a.
$(x-1, \,\sqrt{x})$
b.
$(x-1, \, - \sqrt{x})$
c.
$(x+ 1, \,\sqrt{x})$
d.
$(x+ 1, \, - \sqrt{x})$
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If the sum of the series $20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5}+. . . . . . . . . .$ up to $n^{th\,}$ term is $488\,$ and the $n^{th\,}$ term is
negative, then :
a.
$n^{th\,}$ term is $-4\frac{2}{5}$
b.
$n= 41$
c.
$n^{th\,}$ term is $-4$
d.
$n= 60$
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Let $S$ be the set of all integer solutions $(x, \,y, \,z)$ of the system of equations
$x-2\,y+ 5\,z= 0$
$-2\,x+ 4\,y+z= 0$
$-7\,x+ 14\,y+ 9\,z= 0$
such that $15 \leq x^{2} +y^{2} +z^{2} \leq 150$ . Then, the number of elements in the set $S$ is equal to ..........
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If the tangent to the curve $y=e^{x}$ at a point $(c, \,e^{c})$ and the normal to the parabola $y^{2} = 4x$ at the point $(1, \,2)$
intersect at the same point on the $x-$ axis, then the value of $c$ is .....
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Let $R_{1}$ and $R_{2}$ be two relations defined as follows :
$R_{1} ={(a, \,b) \in R^{2} :a^{2} +b^{2} \in Q}$ and $R_{2} ={(a, \,b) \in R^{2} :a^{2} +b^{2} ∉ Q}$ , where $Q$ is the set of all rational
numbers, then
a.
$R_{1}$ is transitive but $R_{2}$ is not transitive. $R_{2}$ is transitive but $R_{1}$ is not transitive.
c.
Neither $R_{1}$ nor $R_{2}$ is transitive.
d.
$R_{1}$ and $R_{2}$ are both transitive.
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Let $a, \,b, \,c\in R$ be such that $a^{2} +b^{2} +c^{2} = 1$ . If $acos\theta =bcos(\theta + \frac{2\pi}{3})=ccos(\theta + \frac{4\pi}{3})$ ,where $\theta = \frac{\pi}{9}$ , then
the angle between the vectors $aˆi+bˆj+cˆk$ and $bˆi+cˆj+aˆk$ is:
a.
$0$
b.
$\frac{2\pi}{3}$
c.
$\frac{\pi}{2}$
d.
$\frac{\pi}{9}$
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Let $e_{1}$ and $e_{2}$ be the eccentricities of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{b^{2}} = 1\,(b< 5)$ and the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{b^{2}} = 1$
respectively satisfying $e_{1}e_{2} = 1$ . If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the
hyperbola respectively, then the ordered pair $(\alpha , \,\beta )$ is equal to:
a.
$(8, \,10)$
b.
$(\frac{20}{3}, \,12)$
c.
$(8, \,12)$
d.
$(\frac{24}{5}, \,10)$
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If $m$ arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between $3$ and $243$ such that $4^{th}$
A.M. is equal to $2^{nd}$ G.M., then $m$ is equal to:
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$2 -1 1$
$[ ]$
Let A be a $3 \times 3$ matrix such that $adjA= -1 0 2$ and $B=adj (adjA)$ . If $|A| =\lambda$ and
$[ ]$
$1 -2 -1$
$(B^{-1})^{⊤} =\mu$ , then the ordered pair $(|\lambda |, \,\mu )$ is equal to
a.
$(3, \,\frac{1}{81})$
b.
$(9, \,\frac{1}{9} )$
c.
$(3, \,81)$
d.
$(9, \,\frac{1}{81} )$
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Let $x_{i}(1 \leq i \leq 10)$ be ten observation of a random variable $X$ . If $\sum ^{10}_{i=1}(x_{i}-p) = 3$ and $\sum ^{10}_{i=1} (x_{i}-p)^{2} = 9$
where $0 \neq p \in R$ , then the standard deviation of these observations is:
a.
$\frac{4}{5}$
b.
$\sqrt{\frac{3}{5}}$
c.
$\frac{9}{10}$
d.
$\frac{7}{10}$
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If the surface area of a cube is increasing at a rate of $3. 6cm^{2}/sec$ , retaining its shape; then the rate of change
of its volume (in $cm^{3}/sec$ ), when the length of a side of the cube is $10cm$ , is:
a.
$20$
b.
$10$
c.
$18$
d.
$9$
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Let $p, \,q, \,r$ be three statements such that the truth value of $(p\wedge q) \rightarrow (~\rightarrow q\vee r)$ is $F$ . Then the truth values of
$p, \,q, \,r$ are respectively :
a.
$T, \,T, \,F$
b.
$T, \,T, \,T$
c.
$T, \,F, \,T$
d.
$F, \,T, \,F$
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Suppose $f(x)$ is a polynomial of degree four having critical points at $-1, \,0, \,1$ . If $T = {x\in R\,|f(x) =f(0)}$ ,
then the sum of squares of all the elements of $T$ is :
a.
$4$
b.
$6$
c.
$2$
d.
$8$
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If $z_{1}, \,z_{2}$ are complex numbers such that $Re (z_{1}) = |z_{1}-1|$ and $Re (z_{2}) = |z_{2}-1|$ and $arg(z_{1}- z_{2}) = \frac{\pi}{6}$
, then $Im(z_{1}+z_{2})$ is equal to :
a.
$2\sqrt{3}$
b.
$\frac{\sqrt{3}}{2}$
c.
$\frac{1}{\sqrt{3}}$
d.
$\frac{2}{\sqrt{3}}$
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Let a plane $P$ contain two lines $\vec{r}= ˆi+\lambda (ˆi+ ˆj), \,\lambda \in R$ and $\vec{r}= -ˆj +\mu (ˆj - ˆk), \,\mu \in R$ . If $Q(\alpha , \,\beta , \,\gamma )$ is
the foot of the perpendicular drawn from the point $M(1, \,0, \,1)$ to $P$ , then $3(\alpha +\beta +\gamma )$ equals .......
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The set of all real values of $\lambda$ for which the quadratic equation $(\lambda ^{2} + 1)x^{2} -4\lambda x+ 2 = 0$ always have
exactly one root in the interval $(0, \,1)$ is :
a.
$(-3, \, -1)$
b.
$(0, \,2)$
c.
$(1, \,3]$
d.
$(2, \,4]$
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Let the latus rectum of the parabola $y^{2} = 4x$ be the common chord to the circles $C_{1}$ and $C_{2}$ each of them
having radius $2\sqrt{5}$ . Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ is :
a.
$12$
b.
$8$
c.
$8\sqrt{5}$
d.
$4\sqrt{5}$
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