Two charges, each equal to $q$ , are kept at $x = -a$ and $x\,=\,a$ on the x-axis. A particle of mass $m$ and charge
$q_{0} = - \frac{q}{2}$ is placed at the origin. If charge $q_{0}$ is given a small displacement $(y << a)$ along the y-axis, the net
force acting on the particle is proportional to :
a.
$\frac{1}{y}$
b.
$- \frac{1}{y}$
c.
$-y$
Correct Answer
d.
$y$
No explanation saved for this question yet.
Q2mcq
What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$
and radius $R$ in a circular orbit at an altitude of $2R$ ?
a.
$\frac{GmM}{2R}$
b.
$\frac{GmM}{3R}$
c.
$\frac{5GmM}{6R}$
Correct Answer
d.
$\frac{2GmM}{3R}$
No explanation saved for this question yet.
Q3mcq
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will
decrease to $\alpha$ times its original magnitude, where $\alpha$ equals :
a.
0.729
Correct Answer
b.
0.6
c.
0.7
d.
0.81
No explanation saved for this question yet.
Q4mcq
A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical,
from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium
position. The extension $x_{0}$ of the spring when it is in equilibrium is :
The supply voltage to a room is $120\, V$ . The resistance of the lead wires is $6\,\Omega$ . A $60\, W$ bulb is already
switched on. What is the decrease of voltage across the bulb, when a $240\, W$ heater is switched on in parallel
to the bulb?
a.
$13 .3 \,V$
b.
$10. 4\,V$
Correct Answer
c.
$zero \,V$
d.
$2 .9 \,V$
No explanation saved for this question yet.
Q6mcq
The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is
gradually changed. The plate current $I$ of the photocell varies as follows :
No explanation saved for this question yet.
Q7mcq
A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal
table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced
across the ends of the rod is:
a.
$\frac{4B\omega l^{2}}{2}$
b.
$\frac{5B\omega l^{2}}{2}$
Correct Answer
c.
$\frac{2B\omega l^{2}}{2}$
d.
$\frac{3B\omega l^{2}}{2}$
No explanation saved for this question yet.
Q8mcq
A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric
potential at the point O lying at a distance L from the end A is :
a.
$\frac{Q}{4\pi \in _{0}L\,ln\,2}$
b.
$\frac{Q\,ln\,2}{4\pi \in _{0}L}$
Correct Answer
c.
$\frac{Q}{8\pi \in _{0}L}$
d.
$\frac{3Q}{4\pi \in _{0}L}$
No explanation saved for this question yet.
Q9mcq
In an $LCR$ circuit as shown below both switches are open initially. Now switch $S_{1}$ is closed, $S_{2}$ kept open. ( $q$
is charge on the capacitor and $τ = RC$ is capacitive time constant). Which of the following statement is
correct?
a.
At $t = 2τ,\, q = CV\,(1 -e^{-2})$
Correct Answer
b.
At $t = \frac{τ}{2} ,\, q = CV\,(1 -e^{-1})$
c.
Work done by the battery is half of the energy
dissipated in the resistor
d.
$At t =τ,\, q = CV/2$
No explanation saved for this question yet.
Q10mcq
The $I -V$ characteristics of an $LED$ is:
No explanation saved for this question yet.
🎉 10 Free Sample Solutions Completed
Unlock All 90 Questions & Solutions
Sign up free in seconds to unlock step-by-step AI answers for the remaining 80 questions.
The above $P - V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal mono-
atomic gas. The amount of heat, extracted from the source in a single cycle, is:
a.
$(\frac{11}{2} )P_{0}V_{0}$
b.
$4P_{0}V_{0}$
c.
$P_{0}V_{0}$
d.
$(\frac{13}{2} )P_{0}V_{0}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Diameter of a plano - convex lens is $6\, cm$ and thickness at the centre is $3\, mm$ . If the speed of light in the
material of lens is $2 \times 10^{8}\,m\,s^{-1}$ , the focal length of the lens is:
a.
$30\, cm$
b.
$10\, cm$
c.
$15\, cm$
d.
$20\, cm$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A projectile is given an initial velocity of $(ˆi + 2ˆj)\,m\,s^{-1}$ , where $ˆi$ is along the ground and $ˆj$ is along the vertical
upward. If $g= 10\, m \,s^{-2}$ , the equation of its trajectory is :
a.
$4y= 2x-5x^{2}$
b.
$4y = 2x -25x^{2}$
c.
$y=x-5x^{2}$
d.
$y= 2x-5x^{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$ . The piston
and the cylinder have equal cross-sectional area $A$ . When the piston is in equilibrium, the volume of the gas is
$V_{0}$ and its pressure is $M_{0}$ . The piston is slightly displaced from the equilibrium position and released.
Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic
motion with frequency
[Assume the system is in space.]
In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another
with quantum number $(n -1)$ . If $n >> 1$ , the frequency of radiation emitted is proportional to :
a.
$\frac{1}{n^{3/2}}$
b.
$\frac{1}{n^{3}}$
c.
$\frac{1}{n}$
d.
$\frac{1}{n^{2}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A sonometer wire of length $1 .5 m$ is made of steel. The tension in it produces an elastic strain of $1%$ . What is
the fundamental frequency of steel if density and elasticity of steel are $7 .7 \times 10^{3}\, kg \,m^{-3}$ and
$2 .2 \times 10^{11}\,N\,m^{-2}$ respectively?
a.
$200 .5 \, Hz$
b.
$770\, Hz$
c.
$188 .5 \, Hz$
d.
$178 .2 \, Hz$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
This question has $Statement - I$ and $Statement - II$ of the four choices given after the Statements, choose the
one that best describes the two Statements.
$Statement - I:$ A point particle of mass $m$ moving with speed $ν$ collides with stationary point particle of mass
$M$ . If the maximum energy loss possible is given as
$f( \frac{1}{2}mν^{2})$ then $f =(\frac{m}{M+m} )$ .
$Statement - II:$ Maximum energy loss occurs when the particles get stuck together as a result of the collision.
a.
Statement- $I$ is true, Statement- $II$ is false.
b.
Statement- $I$ is false, Statement- $II$ is true.
c.
Statement- $I$ is true, Statement- $II$ is true,
Statement- $II$ is a correct explanation of
Statement- $I$ .
d.
Statement- $I$ is true, Statement- $II$ is true,
Statement- $II$ is not a correct explanation of
Statement- $I$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two capacitors $C_{1}$ and $C_{2}$ are charged to $120 V$ and $200 V$ respectively. It is found that by connecting them
together the potential on each one can be made zero. Then:
a.
$3C_{1}+ 5C_{2} = 0$
b.
$9C_{1} = 4C_{2}$
c.
$5C_{1} = 3C_{2}$
d.
$3C_{1} = 5C_{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A circular loop of radius $0. 3\, cm$ lies parallel to a much bigger circular loop of radius $20\, cm$ . The centre of the
small loop is on the axis of the bigger loop. The distance between their centres is $15 cm$ . If a current of $2. 0\,A$
flows through the smaller loop, then the flux linked with a bigger loop is:
a.
$3 .3 \times 10^{-11} weber$
b.
$6 .6 \times 10^{-9} weber$
c.
$9 .1 \times 10^{-11} weber$
d.
$6 \times 10^{-11} weber$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A beam of unpolarised light of intensity $I_{0}$ is passed through a polaroid $A$ and then through another polaroid $B$
which is oriented so that its principle plane makes an angle of $45^{o}$ relative to that of $A$ . The intensity of the
emergent light is:
a.
$\frac{I_{0}}{4}$
b.
$\frac{I_{0}}{8}$
c.
$I_{0}$
d.
$\frac{I_{0}}{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two coherent point sources $S_{1}$ and $S_{2}$ are separated by a small distance $d$ as shown in the figure. The fringes
obtained on the screen will be
a.
semi-circles
b.
concentric circles
c.
points
d.
straight lines
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta _{0}$ , the
graph between the temperature $T$ of the metal and time $t$ will be closest to :
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of
capacity 250 pico farad in parallel with a load resistance of 100 kilo ohm. Find the maximum modulated
frequency which could be detected by it.
a.
$5.31 MHz$
b.
$5.31 kHz$
c.
$10.62 MHz$
d.
$10.62 kHz$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains
unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is $T$ , the density of
the liquid is and $\rho$ $L$ is its latent heat of vaporisation.)
a.
$\frac{T}{$\rho$L}$
b.
$\frac{2T}{$\rho$L}$
c.
$\frac{$\rho$L}{T}$
d.
$\sqrt{\frac{T}{$\rho$L}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A hoop of radius $r$ and mass $m$ rotating with an angular velocity $\omega _{0}$ is placed on a rough horizontal surface. The
initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it
ceases to slip?
a.
$\frac{r\omega _{0}}{2}$
b.
$r\omega _{0}$
c.
$\frac{r\omega _{0}}{4}$
d.
$\frac{r\omega _{0}}{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
This question has $Statement I$ and $Statement\,II$ . Of the four choices given after the Statements, choose the
one that best describes the two Statements.
$Statement - I :$ Higher the range, greater is the resistance of ammeter.
$Statement - II :$ To increase the range of ammeter, additional shunt needs to be used across it.
a.
Statement- $I$ is true, Statement- $II$ is false.
b.
Statement- $I$ is false, Statement- $II$ is true.
c.
Statement- $I$ is true, Statement- $II$ is true,
Statement- $II$ is the correct explanation of
Statement- $I$ .
d.
Statement- $I$ is true, Statement- $II$ is true,
Statement- $II$ is not the correct explanation of
Statement- $I$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two short bar magnets of length $1 cm$ each have magnetic moments $1 .20 \,A\,m^{2}$ and $1 .00 \,A\,m^{2}$ respectively.
They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the south. They
have a common magnetic equator and are separated by a distance of $20 .0 \, cm$ . The value of the resultant
horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to
( Horizontal component of earth's magnetic induction is $3 .6 \times 10^{-5}\,\, Wb \,m^{-2}$ )
a.
$3 .50 \times 10^{-4}\, Wb \,m^{-2}$
b.
$5 .80 \times 10^{-4}\,\, Wb \,m^{-2}$
c.
$3 .6 \times 10^{-5}\,\, Wb \,m^{-2}$
d.
$2 .56 \times 10^{-4}\, Wb \,m^{-2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An organic compound A upon reacting with $NH_{3}$ gives B. On heating, B gives C. C in presence of KOH reacts
with Br to give CH CH NH . A is :
2 3 2 2
b.
$CH_{3}CH_{2}COOH$
c.
$CH_{3}COOH$
d.
$CH_{3}CH_{2}CH_{2}COOH$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A compound with molecular mass $180$ is acylated with $CH_{3}COCl$ to get a compound with molecular mass
$390$ . The number of amino groups presents per molecule of the former compound is
a.
$4$
b.
$6$
c.
$2$
d.
$5$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant
temperature of $37. 0^{\circ }C$ . As it does so, it absorbs 208 J of heat. The values of q and w for the process will be
(R = 8.314 J/mol K) (ln7.5 = 2.01)
a.
$q = -208 J, w\, = +208 J$
b.
$q = +208 J, w = +208 J$
c.
$q = +208 J, w = -208 J$
d.
$q = -208 J, w = -208 J$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Experimentally it was found that a metal oxide has formula $M_{0.98}O$ . Metal M, is present as $M^{2+}$ and $M^{3+}$ in
its oxide. Fraction of the metal which exists as $M^{3+}$ would be:
a.
$6. 05%$
b.
$5. 08%$
c.
$7. 01%$
d.
$4. 08%$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The rate of a reaction doubles when its temperature changes from $300K\, to \,310K$ . Activation energy of such a
reaction will be:
$(R = 8.314 JK^{-1} mol^{-1} \, and \, log 2= 0.301)$
a.
$58. 5\, kJ \, mol^{\,-1}$
b.
$60. 5\, kJ \, mol^{\,-1}$
c.
$53. 6\, kJ \, mol \,^{-1}$
d.
$48. 6\, kJ \, mol^{\,-1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given
$E^{o}_{Cr^{3+}/Cr} = -0. 74\,V;\,\,E^{o}_{MnO^{-}_{4}}_{/Mn^{2+}} = 1. 51 V$
$E^{o}_{Cr_{2}O^{2-}_{7}}_{/Cr^{3+}} = 1.33\,V;\,\,\,E^{o}_{Cl_{2}}_{Cl^{-}} = 1. 36 V$
Based on the data given above, strongest oxidising agent will be:
a.
$Mn^{2+}$
b.
$MnO^{-}_{4}$
c.
$Cl^{-}$
d.
$Cr^{3+}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$|$
Compound (A), $C H Cl$ , gives a white precipitate when warmed with alcoholic $AgNO$ Oxidation of (A)
$8 9 3$ .
gives an acid (B), $C_{8}H_{6}O_{4}$ . (B) easily forms anhydride on heating. Identify the compound (A).
a.
b.
c.
d.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$-_{For gaseous state, if most probable speed is denoted byC}*_{, average speed byCand root mean square speed}$
by $C$ , then for many molecules, what is the ratios of these speeds?
Energy of an electron is given by $E = -2.178 \times 10^{-18}( \frac{Z^{2}}{n^{2}})\,J$ . Wavelength of light required to excite an
electron in a hydrogen atom from level n=1 to n=2 will be :
$(h = 6.62 \times 10^{-34}\,Js\,and\,c = 3.0 \times 10^{8}\,ms^{-1})$
a.
$6.500 \times 10^{-7} m$
b.
$8.500 \times 10^{-7} m$
c.
$1.214 \times 10^{-7} m$
d.
$2.816 \times 10^{-7} m$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the following reaction:
$x\, MnO^{-}_{4} + y\,C_{2}O^{2-}_{4} + zH^{+} \longrightarrow x\, Mn^{2+} + 2y\, CO_{2}+ \frac{z}{2}H_{2}O$
The values of x, y and z in the reaction are, respectively:
a.
$2, 5\, and \,16$
b.
$5, 2\, and \,8$
c.
$5, 2\, and \,16$
d.
$2, 5\, and \,8$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An unknown alcohol is treated with the "Lucas reagent" to determine whether the alcohol is primary,
secondary or tertiary. Which alcohol reacts fastest and by what mechanism:
a.
Secondary alcohol by S 2
N
b.
Tertiary alcohol by S 2
N
c.
Secondary alcohol by S 1
N
d.
Tertiary alcohol by S 1
N
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Four successive members of the first row of transition elements are listed below with atomic numbers. Which
one of them is expected to have the highest $E^{o}_{M^{3+}/M^{2+}}$ value?
a.
Fe (Z = 26)
b.
Co (Z = 27)
c.
Cr (Z = 24)
d.
Mn (Z = 25)
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement - I : $^{\pi /3}$
The value of the integral $\int \frac{dx}{1+\sqrt{tan \,x}}$ is equal to $\frac{\pi}{6}.$
$\pi /6$
$b b$
Statement - II : $\int f(x)dx= \int f(a+b- x)dx.$
$a a$
a.
Statement - $I$ is true; Statement - $II$ is false.
b.
Statement - $I$ is false; Statement - $II$ is true.
c.
Statement - $I$ true; Statement - $II$ is true;
Statement - $II$ is a correct explanation for
Statement - $I$ .
d.
Statement - $I$ is true; Statement - $II$ is true;
Statement - $II$ is not a correct explanation for
Statement - $I$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t.
additional number of workers $x$ is given by $\frac{dP}{dx} = 100 -12\sqrt{x}$ . If the firm employs $25$ more workers, then the
new level of production of items is
a.
$3500$
b.
$4500$
c.
$2500$
d.
$3000$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$--$
If the vectors $A\vec{B}= 3ˆi + 4ˆk$ and $A\vec{C}= 5ˆi -2ˆj + 4ˆk$ are the sides of a triangle $ABC,$ then the length of the
median through $A$ is:
a.
$\sqrt{33}$
b.
$\sqrt{45}$
c.
$\sqrt{18}$
d.
$\sqrt{72}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$x$
The intercepts on the $x$ -axis made by tangents to the curve, $y= \int |t|\,dt, \,x\in R,$ which are parallel to the line
$0$
$y= 2x$ , are equal to
a.
$\pm 3$
b.
$\pm 4$
c.
$\pm 1$
d.
$\pm 2$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given: A circle, $2x^{2} + 2y^{2} = 5$ and a parabola, $y^{2} = 4\sqrt{5}x$ .
Statement - I :An equation of a common tangent to these curves is $y=x+ \sqrt{5}$ .
Statement - II :If the line, $y=mx+ \frac{\sqrt{5}}{m} (m\neq 0)$ is their common tangent, then $m$ satisfies
$m^{4} -3m^{2} + 2 = 0$ .
a.
Statement - $I$ is true; Statement - $II$ is false.
b.
Statement - $I$ is false; Statement - $II$ is true.
c.
Statement - $I$ is true; Statement - $II$ is true;
Statement - $II$ is a correct explanation for
statement - $I$ .
d.
Statement - $I$ is true; Statement - $II$ is true;
Statement - $II$ is not a correct explanation for
statement - $I$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to
each of the students. Which of the following statistical measures will not change even after the grace marks
were given ?
a.
mode
b.
variance
c.
mean
d.
median
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an $n$ -sided regular polygon. If
$T_{n+1}- T_{n} = 10$ , then the value of $n$ is :
a.
$10$
b.
$8$
c.
$5$
d.
$7$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $x, \,y, \,z$ are positive numbers in $A. P.$ and $tan^{-1} x$ , $tan^{-1} y$ and $tan^{-1} z$ are also in $A. P.$ , then which of the
following is correct.
a.
$6x= 3y= 2z$
b.
$6x= 4y= 3z$
c.
$x=y=z$
d.
$2x= 3y= 6z$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $A$ and $B$ be two sets containing $2$ elements and $4$ elements respectively. The number of subsets of $A\times B$
having $3$ or more elements is :
a.
$219$
b.
$211$
c.
$256$
d.
$220$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A multiple choice examination has $5$ questions. Each question has three alternative answers out of which
exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :
a.
$\frac{11}{3^{5}}$
b.
$\frac{10}{3^{5}}$
c.
$\frac{17}{3^{5}}$
d.
$\frac{13}{3^{5}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
