Given below are two statements: one is labelled as Assertion $A$ and the other is labelled asReason $R$ .
Assertion A: Electromagnets are made of soft iron.
Reason R: Soft iron has high permeability and low retentivity.
In the light of above statements, choose the most appropriate answer from the options given below.
a.
$A$ is not correct but $R$ is correct
b.
$A$ is correct but $R$ is not correct
c.
Both $A$ and $R$ are correct and $R$ is the correct
explanation of $A$
d.
Both $A$ and $R$ are correct but $R$ is NOT the
correct explanation of $A$
Correct Answer
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Q2mcq
The orbital angular momentum of a satellite is $L$ , when it is revolving in a circular orbit at height $h$ from earth
surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the
new angular momentum will be
a.
$8\,L$
b.
$9\,L$
c.
$4\,L$
d.
$3\,L$
Correct Answer
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Q3mcq
A hydraulic automobile lift is designed to lift vehicles of mass $5000\, kg$ . The area of cross section of the
cylinder carrying load is $250\, cm^{2}$ . The maximum pressure the smaller piston would have to bear is [Assume
$g = 10\,m\,s^{-2}$ ]
a.
$20 \times 10^{6}\, Pa$
b.
$2 \times 10^{5}\, Pa$
Correct Answer
c.
$200 \times 10^{6}\, Pa$
d.
$2 \times 10^{6}\, Pa$
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Q4mcq
For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and regular velocity $\omega$ , as shown in
below figure, the projection of $OP$ on the $x$ -axis at time $t$ is
The ratio of wavelength of spectral lines $H_{\alpha }$ and $H_{\beta }$ in the Balmer series is $\frac{x}{20}$ . The value of $x$ is _____.
✓ Accepted Answer:8
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Q6mcq
The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ}C$ is
a.
$927^{\circ}C$
b.
$327^{\circ}C$
Correct Answer
c.
$1227^{\circ}C$
d.
$627^{\circ}C$
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Q7mcq
A guitar string of length $90\, cm$ vibrates with a fundamental frequency of $120\, Hz$ . The length of the string
producing a fundamental of $180\, Hz$ will be _____ $cm$
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Q8nat
A series combination of resistor of resistance $100\,\Omega$ inductor of inductance $1\,H$ and capacitor of capacitance
$6. 25\,$ $\mu$ $F$ is connected to an ac source. The quality factor of the circuit will be _____.
✓ Accepted Answer:75
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Q9mcq
Work done by a Carnot engine operating between temperatures $127^{\circ}C$ and $27^{\circ}C$ is $2\, kJ$ . The amount of heat
transferred to the engine by the reservoir is:
a.
$8\, kJ$
b.
$2. 67\, kJ$
c.
$2\, kJ$
d.
$4\, kJ$
Correct Answer
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Q10nat
An emf of $0. 08\,V$ is induced in a metal rod of length $10\, cm$ held normal to a uniform magnetic field of $0. 4\,T$ ,
when move with a velocity of:
✓ Accepted Answer:30
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The trajectory of projectile, projected from the ground is given by $y=x- \frac{x^{2}}{20}$ . Where $x$ and $y$ are measured in
meter. The maximum height attained by the projectile will be.
a.
$200\,m$
b.
$10\,m$
c.
$5\,m$
d.
$10\,m\sqrt{2}$
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In photoelectric effect
A. The photocurrent is proportional to the intensity of the incident radiation.
B. Maximum kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
C. Max K.E. with which photoelectrons are emitted depends on the frequency of incident light.
D. The emission of photoelectrons require a minimum threshold intensity of incident radiation.
E. Max K.E. of the photoelectrons is independent of the frequency of the incident light.
Choose the correct answer from the options given below:
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The width of fringe is $2\, mm$ on the screen in a double slit experiment for the light of wavelength of $400\, nm$ .
The width of the fringe for the light of wavelength $600\, nm$ will be:
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Two transparent media having refractive indices $1. 0$ and $1. 5$ are separated by a spherical refracting surface of
radius of curvature $30\, cm$ . The centre of curvature of surface is towards denser medium and a point object is
placed on the principal axis in rarer medium at a distance of $15\, cm$ from the pole of the surface. The distance
of image from the pole of the surface is $cm$ .
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A $600\, pF$ capacitor is charged by $200\,V$ supply. It is then disconnected from the supply and is connected to
another uncharged $600\, pF$ capacitor. Electrostatic energy lost in the process is _____ $\mu$ $J$ .
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For a given transistor amplifier circuit in CE configuration $V_{CC} = 1\,V,R_{C} = 1\,k\Omega ,R_{b} = 100\,k\Omega$ and
$\beta = 100$ . Value of base current $I_{b}$ is
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A radio active material is reduced to $\frac{1}{8}$ of its original amount in $3$ days. If $8 \times 10^{-3}\, kg$ of the material is left
after $5$ days the initial amount of the material is
a.
$40\,g$
b.
$32\,g$
c.
$64\,g$
d.
$256\,g$
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Given below are two statements:
Statement I:Area under velocity-time graph gives the distance travelled by the body in a given time.
Statement II:Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given 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 correct but Statement II is false
d.
Statement I is incorrect but Statement II is true
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The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$
from the centre of coil on its axis is $\sqrt{x}: 1$ . The value of $x$ is _____.
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Match List I with List II
List I List II
A. Torque I. $M\,L^{-2}\,T^{-2}$
B. Stress II. $M\,L^{2}\,T^{-2}$
C. Pressure gradient III. $M\,L^{-1}\,T^{-1}$
Coefficient of
D. IV. $M\,L^{-1}\,T^{-2}$
viscosity
Choose the correct answer from the options given below :
a.
A-II, B-I, C-IV, D-III
b.
A-IV, B-II, C-III, D-I
c.
A-II, B-IV, C-I, D-III
d.
A-III, B-IV, C-I, D-II
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A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\,m\,s^{-1}$ (as shown
in figure). Maximum height with respect to the initial position covered by it will be _____ $cm$
(take, $g= 10\,m\,s^{-2}$ )
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Electric potential at a point $P$ due to a point charge of $5 \times 10^{-9}\,C$ is $50\,V$ . The distance of $P$ from the point
charge is:
(Assume, $\frac{1}{4\pi \epsilon _{0}} = 9 \times 10^{9}\,N\,m^{2}\,C^{-2}$ )
a.
$9\, cm$
b.
$3\, cm$
c.
$0. 9\, cm$
d.
$90\, cm$
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A bullet of mass $0. 1\, kg$ moving horizontally with speed $400\,m\,s^{-1}$ hits a wooden block of mass $3. 9\, kg$ kept on
a horizontal rough surface. The bullet gets embedded into the block and moves $20\,m$ before coming to rest. The
coefficient of friction between the block and the surface is _______.
a.
$\,0. 90$
b.
$0. 50$
c.
$0. 65$
d.
$0. 25$
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A body of mass $5\, kg$ is moving with a momentum of $10\, kg \,m\,s^{-1}$ . Now a force of $2\,N$ acts on the body in the
direction of its motion for $5\,s$ . The increase in the Kinetic energy of the body is _____ $J$ .
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A steel rod of length $1\,m$ and cross-sectional area $10^{-4}\,m^{2}$ is heated from $0^{\circ}C$ to $200^{\circ}C$ without being
allowed to extend or bend. The compressive tension produced in the rod is _____ $\times 10^{4}\,N$ . (Given Young's
modulus of steel $= 2 \times 10^{11}\,N\,m^{-2}$ , coefficient of linear expansion $= 10^{-5}\,K^{-1}$ )
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The number density of free electrons in copper is nearly $8 \times 10^{28}\,m^{-3}$ . A copper wire has its area of cross-
section $= 2 \times 10^{-6}\,m^{2}$ and is carrying a current of $3. 2\,A$ . The drift speed of the electrons is _____
$\times 10^{-6}\,m\,s^{-1}$ .
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Which of the following have same number of significant figures?
(A) $0. 00253$
(B) $1. 0003$
(C) $15. 0$
(D) $163$
Choose the correct answer from the options given below
a.
A, B and C only
b.
C and D only
c.
B and C only
d.
A, C and D only
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A compound $'X'$ when treated with phthalic anhydride in presence of concentrated $H_{2}SO_{4}$ yields $'Y'$ . $'Y'$ is
used as an acid/base indicator. $'X'$ and $'Y'$ are respectively
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For complete combustion of ethene,
$C_{2}H_{4}(\,g) + 3O_{2}(\,g) \rightarrow 2 CO\rightarrow_{2}(\,g) + 2H_{2}O(l)$
the amount of heat produced as measured in bomb calorimeter is $1406\, kJ \, mol^{-1}$ at $300\,K$ . The minimum
value of $T\Delta S$ needed to reach equilibrium is $(-) kJ$ . (Nearest integer)
Given: $R = 8. 3\,J\,K^{-1}\, mol^{-1}$
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Arrange the following gases in increasing order of van der Waals constant $'a'$
(A) $Ar$
(B) $CH_{4}$
(C) $H_{2}O$
(D) $C_{6}H_{6}$
Choose the correct option from the following.
a.
D, C, B and A
b.
B, C, D and A
c.
C, D, B and A
d.
A, B, C and D
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The statement/s which are true about antagonists from the following is/are:
A. They bind to the receptor site.
B. Get transferred inside the cell for their action.
C. Inhibit the natural communication of the body.
D. Mimic the natural messenger.
Choose the correct answer from the options given below:
a.
B only
b.
A, C and D
c.
A and C
d.
A and B
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The solubility product of $BaSO_{4}$ is $1 \times 10^{-10}$ at $298\,K$ . The solubility of $BaSO_{4}$ in $0. 1M\,K_{2}SO_{4}(aq)$
solution is ------ $\times 10^{-9}\,g\,L^{-1}$ (nearest integer).
Given: Molar mass of $BaSO_{4}$ is $233\,g\, mol^{-1}$
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Given below are two statements:
Statement-I :Methyl orange is a weak acid.
Statement-II : The benzenoid form of methyl orange is more intense/deeply coloured than the quinonoid
form.
In the light of the above statement, choose the most appropriate answer from the options given below:
(1) Both Statement-Iand Statement-IIare incorrect(2)Statement-Iis incorrect but Statement-IIis
correct
(3) Both Statement-Iand Statement-IIare correct (4)Statement-I is correct but Statement-II is
incorrect
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The number of species trom the following carrying a single lone pair on central atom Xenon is
$XeF^{+}_{5} , XeO_{3}, XeO_{2}\,F_{2}, XeF^{-}_{5} , XeO_{3}\,F_{2}, XeOF_{4}, XeF_{4}$
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The descending order of acidity for the following carboxylic acid is-
(A) $CH_{3}COOH$
(B) $F_{3}C -COOH$
(C) $ClCH_{2}-COOH$
(D) $FCH_{2}-COOH$
(E) $BrCH_{2}-COOH$
Choose the correct answer from the options given below:
a.
$B > C > D > E > A$
b.
$E > D > B > A > C$
c.
$B > D > C > E > A$
d.
$D > B > A > E > C$
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Coagulating value of the electrolytes $AlCl_{3}$ and $NaCl$ tor $As_{2}\,S_{3}$ are $0. 09$ and $50. 04$ respectively. The
coagulating power of $AlCl_{3}$ is $x$ times the coagulating power of $NaCl$ . The value of $x$ is
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Given below are two statements:
Statement I:In redox titration, the indicators used are sensitive to change in $pH$ of the solution.
Statement II:In acid-base titration, the indicators used are sensitive to change in oxidation potential.
In the light of the above statements, choose the most appropriateanswer from the options given below
a.
Statement Iis correct but Statement IIis
incorrect
b.
Both Statement Iand Statement IIare incorrect
c.
Statement Iis incorrect but Statement IIis
correct
d.
Both Statement Iand Statement IIare correct
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If the boiling points of two solvents $X$ and $Y$ (having same molecular weights) are in the ratio $2:\,1$ and their
enthalpy of vaporizations are in the ratio $1 : \,2$ , then the boiling point elevation constant of $X$ is $m$ times the
boiling point elevation constant of $Y$ . The value of $m$ is (nearest integer).
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Match List I with List II
List II
List I
One Letter
Natural amino acid
Code
(A) Glutamic acid (I) $Q$
(B) Glutamine (II) $W$
(C) Tyrosine (III) $E$
(D) Tryptophan (IV) $Y$
Choose the correct answer from the options given below:
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The correct order of reactivity of following haloarenes towards nucleophilic substitution with aqueous $NaOH$
is:
Choose the correct answer from the options given below:
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Match List-I with List-II
LIST-I
LIST-II
Coordination
Number of unpaired electrons
Complex
A. $[Cr(CN)_{6}]^{3-}$ I. 0
B. $[Fe (H_{2}O)_{6}]^{2+}$ II. 3
C. $[Co (NH_{3})_{6}]^{3+}$ III. 2
D. $[Ni (NH_{3})_{6}]^{2+}$ IV. 4
Choose the correct answer from the options given below:
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Given below are two statements: One is labelled as
Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ : Sodium is about $30$ times as abundant as potassium in the oceans.
Reason $R$ : Potassium is bigger in size than sodium.
In the light of the above statements, choose the correct answer from the options given below
a.
Both $A$ and $R$ are true and $R$ is the correct
explanation of $A$
b.
$A$ is true but $R$ is false
c.
Both $A$ and $R$ are true but $R$ is NOT the correct
explanation of $A$
d.
Both $A$ and $R$ are false
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The incorrect statements from the following is:
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction
Gibbs energy.
B. $E^{\circ }_{cell}$ is dependent on the pressure.
$^{\circ}$
C. $\frac{dE_{cell}}{dT} = \frac{\Delta _{r}S^{^{\circ}}}{nF}$
D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential
difference.
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Henry Moseley studied characteristic $X$ -ray spectra of elements. The graph which represents his observation
correctly is
Given $v =$ Frequency of X-ray emitted
$Z =$ Atomic number
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The ordinates of the points $P$ and $Q$ on the parabola with focus $(3, 0)$ and directrix $x= -3$ are in the ratio
$3 : 1$ . If $R(\alpha ,\beta )$ is the point of intersection of the tangents to the parabola at $P$ and $Q$ , then $\frac{\beta ^{2}}{\alpha}$ is equal to
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Let $S$ be the set of all values of $\theta \in [-\pi ,\pi ]$ for which the system of linear equations
$x+y+ \sqrt{3}z= 0$
$-x+(tan\theta )y+ \sqrt{7}z= 0$
$x+y+ (tan\theta )z= 0$
has non-trivial solution.Then $\frac{120}{\pi} \sum _{0\in S} \theta$ is equal to
a.
$20$
b.
$40$
c.
$30$
d.
$10$
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If domain of the function $log_{e}(\frac{6x^{2}+5x+1}{2x-1})+ cos^{-1}(\frac{2x^{2}-3x+4}{3x-5})$ is $(\alpha ,\beta ) \cup (\gamma ,\delta )$ , then $18(\alpha ^{2} +\beta ^{2} +\gamma ^{2} +\delta ^{2})$
is equal to
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If $\alpha >\beta > 0$ are the roots of the equation $ax^{2} +bx+ 1 = 0$ , and
$\frac{1}{2}$
$lim (\frac{1-cos(x^{2}+bx+a)}{2(1-\alpha x)^{2}} ) = \frac{1}{k}(\frac{1}{\beta} - \frac{1}{\alpha} )$ , then $k$ is equal to
$x\rightarrow \rightarrow\frac{1}{\alpha}$
a.
$2\beta$
b.
$\alpha$
c.
$2\alpha$
d.
$\beta$
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Let the area enclosed by the lines $x+y= 2, \,y= 0$ , $x= 0$ and the curve $f(x)= min{x^{2} + \frac{3}{4} , 1 +[x]}$
where $[x]$ denotes the greatest integer $\leq x$ , be $A$ . Then the value of $12A$ is
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$---$
Let the vectors $\vec{u}_{1} = ˆi+ ˆj+aˆk, \,\vec{u}_{2} = ˆi+bˆj+ ˆk,$ and $\vec{u}_{3} =cˆi+ ˆj+ ˆk$ be coplanar. If the vectors
$--$
$\vec{v}_{1} = (a+b)ˆi+cˆj+cˆk, \,\vec{v}_{2} =aˆi+ (b+c)ˆj+aˆk$ and $\vec{v}_{3} =bˆi+bˆj+ (c+a)ˆk$ are also coplanar, then
$6(a+b+c)$ is equal to
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Let $a_{n}$ be $n^{th}$ term of the series $5 + 8 + 14 + 23 + 35 + 50+. . . . . . .$ and $S_{n} =\sum ^{n}_{k=1} a_{k}$ . Then $S_{30}- a_{40}$ is
equal to
a.
$11310$
b.
$11260$
c.
$11290$
d.
$11280$
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Let $R= {a,b,c,d,e}$ and $S = {1, 2, 3, 4}$ . Total number of onto functions $f :R\rightarrow \rightarrow S$ such that $f(a) \neq 1$ , is
equal to ________.
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Let $O$ be the origin and $OP$ and $OQ$ be the tangents to the circle $x^{2} +y^{2} -6x+ 4y+ 8 = 0$ at the points $P$
and $Q$ on it. If the circumcircle of the triangle $OPQ$ passes through the point $($ $\alpha$ $, \frac{1}{2})$ , then a value of $\alpha$ is
a.
$\frac{3}{2}$
b.
$- \frac{1}{2}$
c.
$\frac{5}{2}$
d.
$1$
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Let the solution curve $x=x(y), 0 <y< \frac{\pi}{2}$ , of the differential equation
$(log_{e}(cosy))^{2} cosy dx-(1 + 3xlog_{e}(cosy)) siny dy= 0$ satisfy $x(\frac{\pi}{3})= \frac{1}{2 log_{e}2}$ . If $x(\frac{\pi}{6})= \frac{1}{log_{e}m-log_{e}n}$ ,
where $m$ and $n$ are coprime, then $mn$ is equal to
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Let $m$ and $n$ be the numbers of real roots of the quadratic equations $x^{2} -12x+[x]+ 31 = 0$ and
$x^{2} -5 x+ 2 -4 = 0$ respectively, where $[x]$ denotes the greatest integer $\leq x$ . Then $m^{2} +mn+n^{2}$ is equal
to
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$||$
Let $A(0, 1), \,B(1, 1)$ and $C(1, 0)$ be the mid-points of the sides of a triangle with incentre at the point $D$ . If the
focus of the parabola $y^{2} = 4ax$ passing through $D$ is $(\alpha +\beta \sqrt{2}, 0)$ , where $\alpha$ and $\beta$ are rational numbers, then
$\frac{\alpha}{\beta ^{2}}$ is equal to
a.
$8$
b.
$12$
c.
$6$
d.
$\frac{9}{2}$
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Let $P_{1}$ be the plane $3x- y-7z= 11$ and $P_{2}$ be the plane passing through the points $(2, -1, 0)$ , $(2, 0, -1)$ ,
and $(5, 1, 1)$ . If the foot of the perpendicular drawn from the point $(7, 4, -1)$ on the line of intersection of the
planes $P_{1}$ and $P_{2}$ is $(\alpha ,\beta ,\gamma )$ , then $\alpha +\beta +\gamma$ is equal to
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If the probability that the random variable $X$ takes values $x$ is given by $P(X =x) =k(x+ 1)3^{-x}$ ,
$x= 0, 1, 2, 3, … …$ , where $k$ is a constant, then $P(X \geq 2)$ is equal to
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If the number of words, with or without meaning. which can be made using all the letters of the word
MATHEMATICS in which $C$ and $S$ do not come together, is $(6!)k$ then $k$ is equal to
a.
$2835$
b.
$5670$
c.
$1890$
d.
$945$
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Let the mean and variance of $12$ observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two
observations were considered as $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $\frac{m}{n}$ , where
$m$ and $n$ are coprime, then $m+n$ are coprime, then $m+n$ is equal to
a.
$315$
b.
$316$
c.
$314$
d.
$317$
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Let $[t]$ denote the greatest integer function. If
$\int _{0}^{2.4}[x^{2}]dx=\alpha +\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}, then\,\alpha +\beta +\gamma +\delta$ is equal to
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For $a,b\in Z$ and $|a- b| \leq 10$ , let the angle between the plane $P : \,a x+y- z=b$ and the line
$L: \,x-1 =a- y=z+ 1$ be $cos^{-1}(\frac{1}{3})$ If the distance of the point $(6, -6, 4)$ from the plane $P$ is $3\sqrt{6}$ , then
$a^{4} +b^{2}$ is equal to
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Let $0 <z<y<x$ be three real numbers such that $\frac{1}{x}, \frac{1}{y} , \frac{1}{z}$ are in an arithmetic progression and $x, \sqrt{2}y,z$ are
in a geometric progression. If $xy+yz+zx= \frac{3}{\sqrt{2}}xyz$ , then $3(x+y+z)^{2}$ is equal to
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$3x^{2}+k\sqrt{x+ 1}, 0 <x< 1$
Let $k$ and $m$ be positive real numbers such that the function $f(x) ={$
$mx^{2} +k^{2}, x\geq 1$
is differentiable for all $x> 0$ . Then $\frac{8f^{'}(8)}{f^{'}(^{1})}$ is equal to
$8$
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Let $P$ be the plane passing through the line $\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$ and the point $(2, 4, -3)$ . If the image of the
point $(-1, 3, 4)$ in the plane $P$ is $(\alpha ,\beta ,\gamma )$ , then $\alpha +\beta +\gamma$ is equal to
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