Three capacitances, each of 3 $\mu F$ , are provided. These cannot be combined to provide the resultant capacitance
of :
a.
$2\mu F$
b.
$6\mu F$
Correct Answer
c.
$1.5\mu F$
d.
$1\mu F$
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Q2mcq
A transverse wave is represented by : $y = \frac{10}{\pi} sin(\frac{2\pi}{T} t - \frac{2\pi}{\lambda}x)$ For what value of the wavelength the wave
velocity is twice the maximum particle velocity?
a.
40 cm
Correct Answer
b.
60 cm
c.
10 cm
d.
20 cm
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Q3mcq
The magnitude of the average electric field normally present in the atmosphere just above the surface of the
Earth is about $150\,N/C$ , directed inward towards the center of the Earth. This gives the total net surface charge
carried by the Earth to be : [Given : $\in _{O}= 8.85 \times 10^{-12}\,\,C^{2}/N-m^{2},\,\,R_{E} = 6.37 \times 10^{6}m$ ]
a.
$-680\, kC$
Correct Answer
b.
$+\,670\,kC$
c.
$+\,680\, kC$
d.
$-\,670\, kC$
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Q4mcq
A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal
table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the
maximum force that can be applied on B for the blocks to move together will be :
a.
0 N
Correct Answer
b.
25 N
c.
48 N
d.
27 N
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Q5mcq
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the
earth at $E$ and meets Mars at $M$ . If the semi-major axis of Earth's orbit is $a_{e} = 1.5 \times 10^{11}m$ , that of Mar's orbit
$a_{m} = 2.28 \times 10^{11}m$ , taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.
a.
$220$ days.
b.
$500$ days.
c.
$260$ days.
Correct Answer
d.
$320$ days.
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Q6mcq
In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :
A cylinder of mass M and sphere of mass M are placed at points A and B of two inclines, respectively. (See
c s
figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio $\frac{sin\theta _{c}}{sin\theta _{s}}$
is :
a.
$\frac{8}{7}$
b.
$\sqrt{\frac{8}{7}}$
c.
$\sqrt{\frac{15}{14}}$
d.
$\frac{15}{14}$
Correct Answer
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Q8mcq
Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container
o o
loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27 C to 77 C ?
(Specific heat of water is 4.2 kJ/kg and that of the container is negligible).
a.
8 min 20 s
Correct Answer
b.
7 min
c.
14 min
d.
6 min 2 s
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Q9mcq
A transmitting antenna at the top of a tower has a height $32\,m$ and the height of the receiving antenna is $50\,m$ .
What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode?
a.
$45. 5\, km$
Correct Answer
b.
$54. 5\, km$
c.
$55. 4\, km$
d.
$455\, km$
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Q10mcq
Water is flowing at a speed of 1.5 m s-1 -2 2
through a horizontal tube of cross-sectional area 10 m and you are
trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the
3 -3
minimum force that you must exert should be (density of water = 10 kg m )
a.
33.7 N
b.
45 N
c.
15 N
d.
22.5 N
Correct Answer
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The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8
cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of
carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in
carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).
a.
231 s
b.
142 s
c.
208 s
d.
161 s
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When the rms voltages $V_{L}, V_{C}$ and $V_{R}$ are measured respectively across the inductor $L,$ the capacitor $C$ and
the resistor $R$ in a series $LCR$ circuit connected to an $AC$ source, it is found that the ratio
$V_{L} :V_{C} :V_{R} = 1 : 2 : 3.$ If the rms voltage of the $AC$ source is $100 V,$ then $V_{R}$ is close to :
a.
$50 V$
b.
$70 V$
c.
$100 V$
d.
$90 V$
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The equation of state for a gas is given by $PV = nRT +\alpha V$ , where n is the number of moles and $\alpha$ is a
positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T
0
and P respectively. The work done by the gas when its temperature doubles isobarically will be :
0
a.
$P_{0} T_{0} ln 2$
b.
$\frac{P_{0}T_{0}R}{P_{0}+\alpha}$
c.
$\frac{P_{0}T_{0}R}{P_{0}-\alpha}$
d.
$P_{0} T_{0}R$
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The mid points of two small magnetic dipoles of length $d$ in end-on positions, are separated by a distance $x$
$(x\gg d)$ . The magnitude of force between them is proportional to $x^{-n}$ where $n$ is :
a.
$3$
b.
$4$
c.
$2$
d.
$1$
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The focal lengths of objective lens and eye lens of a Galilean Telescope are respectively 30 cm and 3.0 cm.
Telescope produces virtual, erect image of an object situated far away from it at least distance of distinct vision
from the eye lens. In this condition the Magnifying Power of the Galilean Telescope should be :
a.
$+8. 8$
b.
$-11. 2$
c.
$+11. 2$
d.
$-8. 8$
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Using monochromatic light of wavelength $\lambda$ , an experimentalist sets up the Young's double slit experiment in
three ways as shown.
If she observes that $y=\beta '$ , the wavelength of light used is :
a.
520 nm
b.
580 nm
c.
540 nm
d.
560 nm
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Match List I(Wavelength range of electromagnetic spectrum) with List II (Method of production of these
waves) and select the correctoption from the options given below the lists.
List I List II
$700\, nm$ to
(a) (i) Vibration of atoms and molecules.
$1\, mm$
$1\, nm$ to Inner shell electrons in atoms moving from one
(b) (ii)
$400\, nm$ energy level to a lower level.
(c) $< \,10^{-3}\, nm$ (iii) Radioactive decay of the nucleus.
(d) $1\, mm$ to $0. 1\,m$ (iv) Magnetron valve.
a.
(a) - (iii), (b) - (iv), (c) - (i), (d) - (ii)
b.
(a) - (i), (b) - (ii), (c) - (iii), (d) - (iv)
c.
(a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)
d.
(a) - (ii), (b) - (iii), (c) - (iv), (d) - (i)
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An n-p-n transistor has three leads A, B and C. Connecting B and C by moist fingers, A to the positive lead of
an ammeter, and C to the negative lead of the ammeter, one finds large deflection. Then, A, B and C refer
respectively to :
a.
Base, emitter and collector
b.
Base, collector and emitter
c.
Emitter, base and collector
d.
Collector, emitter and base
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A capillary tube is immersed vertically in water and the height of the water column is $x$ . When this arrangement
is taken into a mine of depth d, the height of the water column is $y$ . If R is the radius of earth, the ratio $\frac{x}{y}$ is :
a.
$(\frac{R\,-\,d}{R\,+\,d})$
b.
$(\frac{R\,+\,d}{R\,-\,d})$
c.
$(1 - \frac{2d}{R} )$
d.
$(1 - \frac{d}{R})$
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An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of
length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and
the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is
20.0 cm. The error in the determination of g would be :
a.
4.4%
b.
2.27%
c.
1.7%
d.
2.7%
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A d.c. main supply of e.m.f. $220\,V$ is connected across a storage battery of e.m.f. $200\,V$ through a resistance of
$1\,\Omega$ . The battery terminals are connected to external resistance $R$ . The minimum value of $R$ , so that a current
passes through the battery to charge it is:
a.
$9\,\Omega$
b.
$7\,\Omega$
c.
$11\,\Omega$
d.
$0$
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A diver looking up through the water sees the outside world contained in a circular horizon. The refractive
index of water is $\frac{4}{3}$ , and the diver's eyes are $15\, cm$ below the surface of the water. Then the radius of the circle
is :
a.
$\frac{15\times \sqrt{7}}{3}\, cm$
b.
$\frac{15\times 3}{\sqrt{7}}\, cm$
c.
$15 \times 3\sqrt{7}\, cm$
d.
$15 \times 3 \times \sqrt{5}\, cm$
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The magnetic field of earth at the equator is approximately $4 \times 10^{-5}T$ . The radius of earth is $6.4 \times 10^{6}m$ .
Then the dipole moment of the earth will be nearly of the order of :
a.
1020 2
A m
b.
1016 2
A m
c.
1010 2
A m
d.
1023 2
A m
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The position of a projectile launched from the origin at t = 0 is given by $\vec{r}=(40\,ˆi+ 50\,ˆj)m$ at t = 2s. If the
-2
projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take g = 10 ms ).
a.
$tan^{-1} \frac{3}{2}$
b.
$tan^{-1} \frac{2}{3}$
c.
$tan^{-1} \frac{7}{4}$
d.
$tan^{-1} \frac{4}{5}$
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A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by;
$x=a_{1}cos\omega t$ and $y=a_{2}cos 2\omega t$ traces a curve given by :
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Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring, as shown in the figure. The smaller
mass executes simple harmonic motion of angular frequency $25\, rad \,s^{-1}$ , and amplitude $1. 6\, cm$ while the
bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take
$g\, = \,10\,m\,s^{-2}$ ).
a.
$20\,N$
b.
$60\,N$
c.
$40\,N$
d.
$10\,N$
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Modern vacuum pumps can evacuate a vessel down to a pressure of $4.0 \times 10^{-15}$ atm. at room temperature
-1 -1 5 $23 -1$
(300 K). Taking R = 8.3 JK mole , 1 atm = 10 Pa and $N_{Avogadro} = 6 \times 10 mole$ , the mean distance
between molecules of gas in an evacuated vessel will be of the order of :
a.
$0. 2\,$ $\mu$ $m$
b.
$0. 2\, mm$
c.
$0. 2\, cm$
d.
$0. 2\, nm$
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If the binding energy of the electron in a hydrogen atom is $13. 6\, eV$ , the energy required to remove the
electron from the first excited state of $Li^{++}$ is :
a.
$13. 6\, eV$
b.
$3. 4\, eV$
c.
$122. 4\, eV$
d.
$30. 6\, eV$
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Van der Waal's equation for a gas is stated as,
$P = \frac{nRT}{V-nb} -a(\frac{n}{V})^{2}$ .
This equation reduces to the perfect gas equation, $P = \frac{nRT}{V}$ When,
a.
temperature is sufficiently high and pressure is
low.
b.
both temperature and pressure are very low.
c.
both temperature and pressure are very high.
d.
temperature is sufficiently low and pressure is
high.
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$-^{In a nucleophilic substitution reaction :}R -Br + Cl^{-DMF}\rightarrow \rightarrow R -Cl + Br^{^{-}, which one of the following}$
undergoes complete inversion of configuration ?
a.
C H CHC H Br
6 5 6 5
b.
C H CCH C H Br
6 5 3 6 5
c.
C H CH Br
6 5 2
d.
C H CH CH Br
6 5 2 2
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In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If atom
B is missing from one of the face centered points, the formula of the ionic compound is :
a.
A B
2 3
b.
AB
2
c.
A B
5 2
d.
A B
2 5
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The standard enthalpy of formation of $\, NH_{3}$ is $-\,46. 0\, kJ / mol$ . If bond enthalpy of $H_{2}$ is $-436\, kJ / mol$ and
that of $N_{2}$ is $-712\, kJ / mol$ , the average bond enthalpy of $N -H$ bond in $NH_{3}$ is :
a.
$-\,964\, kJ / mol$
b.
$-\,1102\, kJ / mol$
c.
$+\,1056\, kJ / mol$
d.
$+\,352\, kJ / mol$
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The standard electrode potentials $(E^{o}_{M^{+}/M})$ of four metals $A, B, C$ and $D$ are $-1.2 V,0.6 V$ , $0.85 V$ and
$-0.76 V$ , respectively. The sequence of deposition of metals on applying potential is
a.
$B\, > \,D\, > \,C\, > \,A$
b.
$A\, > \,C\, > \,B\, > \,D$
c.
$C\, > \,B\, > \,D\, > \,A$
d.
$D\, > \,A\, > \,B\, > \,C$
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In the following sets of reactants which two sets best exhibit the amphoteric character of Al O . xH O ?
2 3 2
$Set I Al_{2}O_{3}\cdot xH_{2}O_{(s)}+ OH^{-}_{(aq)}$
$Set II Al_{2}O_{3}x \cdot H_{2}O_{(s)}+ H_{2}O_{(l)}$
$Set III Al_{2}O_{3}x \cdot H_{2}O_{(s)}+ H^{+}_{(aq)}$
$Set IV Al_{2}O_{3}\cdot xH_{2}O_{(s)}+ NH_{3(aq)}$
a.
2 and 4
b.
1 and 2
c.
1 and 3
d.
3 and 4
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The gas evolved on heating $CaF_{2}$ and $SiO_{2}$ with concentrated $H_{2}SO_{4}$ , on hydrolysis gives a white gelatinous
precipitate. The precipitate is:
a.
Silicic acid
b.
Calcium fluorosilicate
c.
Hydrofluorosilicic acid
d.
Silica gel
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A current of $10. 0\,A$ flows for $2. 00\,h$ through an electrolytic cell containing a molten salt of metal $X$ . This
results in the decomposition of $0. 250\, mol$ of metal $X$ at the cathode. The oxidation state of $X$ in the molten
salt is:
$(F = 96, 500\,C)$
a.
$1+$
b.
$4+$
c.
$3+$
d.
$2+$
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If $OB$ is the semi-minor axis of an ellipse, $F_{1}$ and $F_{2}$ are its focii and the angle between $F_{1}B$ and $F_{2}B$ is a
right angle, then the square of the eccentricity of the ellipse is
a.
$\frac{1}{4}$
b.
$\frac{1}{\sqrt{2}}$
c.
$\frac{1}{2}$
d.
$\frac{1}{2\sqrt{2}}$
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If the differential equation representing the family of all circles touching $x$ -axis at the origin is
$(x^{2} - y^{2})\frac{dy}{dx} =g(x)y$ , then $g(x)$ equals
a.
$\frac{1}{2}x^{2}$
b.
$2x$
c.
$\frac{1}{2}x$
d.
$2x^{2}$
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A line in the $3$ -dimensional space makes an angle $\theta (0 <\theta \leq \frac{\pi}{2})$ with both the $X$ and $Y-$ axes. Then, the set of
all values of $\theta$ is in the interval :
a.
$(\frac{\pi}{3},\,\frac{\pi}{2} ]$
b.
$(0,\,\frac{\pi}{4}]$
c.
$[ \frac{\pi}{4} ,\,\frac{\pi}{2}]$
d.
$[\frac{\pi}{6},\,\frac{\pi}{3} ]$
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Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less
than $220.$ If the second term in it is $12$ , then its $4^{th}$ term is :
a.
$8$
b.
$24$
c.
$20$
d.
$16$
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$|| || ||$
Equation of the plane which passes through the point of intersection of lines $\frac{x-1}{3} = \frac{y-2}{1} = \frac{z-3}{2}$ and
$\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ and has the largest distance from the origin is:
a.
$4x+ 3y+ 5z= 50$
b.
$3x+ 4y+ 5z= 49$
c.
$5x+ 4y+ 3z= 57$
d.
$7x+ 2y+ 4z= 54$
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If $a, \,b, \,c$ are non - zero real numbers and if the system of equations
$(a-1)x=y+z$
$(b-1)y=x+z$
$(c-1)z=x+y$
has a non - trivial solution, then $ab+bc+ca$ equals :
a.
$-1$
b.
$a+b+c$
c.
$abc$
d.
$1$
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Let $a$ and $b$ be any two numbers satisfying $\frac{1}{a^{2}} + \frac{1}{b^{2}} = \frac{1}{4}.$ Then, the foot of perpendicular from the origin on
the variable line $\frac{x}{a} + \frac{y}{b} = 1$ lies on :
a.
A circle of radius $= 2$
b.
A hyperbola with each semi-axis $= \sqrt{2}$ .
c.
A hyperbola with each semi-axis $= 2$
d.
A circle of radius $= \sqrt{2}$
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If the point $(1, \,4)$ lies inside the circle $x^{2} +y^{2} -6x+ 10y+p= 0$ and the circle does not touch or intersect
the coordinate axes, then the set of all possible values of $p$ is the interval
a.
$(25, \,39)$
b.
$(25, \,29)$
c.
$(0, \,25)$
d.
$(9, \,25)$
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In a set of $2n$ distinct observations, each of the observation below the median of all the observations is
increased by $5$ and each of the remaining observations is decreased by $3$ . Then, the mean of the new set of
observations :
a.
Increases by $2$ .
b.
Increases by $1$ .
c.
Decreases by $2$ .
d.
Decreases by $1$ .
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Let $w(Im w\neq 0)$ be a complex number. Then, the set of all complex numbers $z$ satisfying the equation
$w- wz=k(1 - z)$ , for some real number $k$ , is
a.
$\bar{{}z: \,z\neq 1}$
b.
${z: \,|z| = 1, \,z\neq 1}$
c.
${z: \,z=z}$
d.
$-{z: \,|z| = 1}$
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If the Rolle's theorem holds for the function $f(x) = 2x^{3} +ax^{2} +bx$ in the interval $[-1, 1]$ for the point $c= \frac{1}{2}$ ,
then the value of $2a+b$ is:
a.
$-1$
b.
$2$
c.
$1$
d.
$-2$
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Given three points $P,Q,R$ with $P(5, 3)$ and $R$ lies on the $x-$ axis. If the equation of $RQ$ is $x-2y= 2$ and
$PQ$ is parallel to the $x-$ axis, then the centroid of $\Delta PQR$ lies on the line
a.
$x-2y+ 1 = 0$
b.
$2x+y-9 = 0$
c.
$2x-5y= 0$
d.
$5x-2y= 0$
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If $\frac{1}{\sqrt{\alpha}} , \frac{1}{\sqrt{\beta}}$ are the roots of the equation $ax^{2} +bx+ 1 = 0, \,(a\neq 0, \,a,b\in R)$ , then the equation
$x(x+b^{3})+(a^{3} -3abx)= 0$ has roots:
a.
$\sqrt{\alpha \beta}$ and $\alpha \beta$
b.
$\alpha ^{-}\frac{3}{2}$ and $\beta ^{-}\frac{3}{2}$
c.
$\alpha \beta \frac{1}{2}$ and $\alpha \frac{1}{2}\beta$
d.
$\alpha \frac{3}{2}$ and $\beta \frac{3}{2}$
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If the sum $\frac{3}{1^{2}} + \frac{5}{1^{2}+2^{2}} + \frac{7}{1^{2}+2^{2}+3^{2}}+ .... .+$ up to $20$ terms is equal to $\frac{k}{21} ,$ then $k$ is equal to
a.
$240$
b.
$120$
c.
$60$
d.
$180$
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