A cylindrical plastic bottle of negligible mass is filled with $310ml$ of water and left floating in a pond with
still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular
frequency $\omega .$ If the radius of the bottle is $2.5cm$ then $\omega$ is close to: $($ density of water $= 10^{3}kg/m^{3})$
a.
5.00 rad $sec^{-1}$
b.
$2.50\,rad\,sec^{-1}$
c.
$7.9 rad\,sec^{-1}$
Correct Answer
d.
$3.75\,rad\,sec^{-1}$
No explanation saved for this question yet.
Q2mcq
Consider a Young's double slit experiment as shown in figure. What should be the slit separation $d$ in terms of
wavelength $\lambda$ such that the first minima occurs directly in front of the slit $(S_{1})$ ?
a.
$\frac{\lambda}{(5-\sqrt{2})}$
b.
$\frac{\lambda}{2(\sqrt{5}-2)}$
c.
$\frac{\lambda}{2(5-\sqrt{2})}$
Correct Answer
d.
$\frac{\lambda}{\sqrt{5}-2}$
No explanation saved for this question yet.
Q3mcq
Consider the nuclear fission, $Ne^{20} \rightarrow 2 He\rightarrow^{4} + C^{12}$ . Given that the binding energy/nucleon of $Ne^{20}, \, He^{4}$ and
$C^{12}$ are $8.03 MeV, \,7.86\, MeV$ , respectively. Identify the correct statement:
a.
Energy of $12. 4\, MeV$ will be supplied.
b.
Energy of $9. 72\, MeV$ has to be supplied.
Correct Answer
c.
Energy of $3. 6\, MeV$ will be released.
d.
$8. 3\, MeV$ energy will be released.
No explanation saved for this question yet.
Q4mcq
A metal plate of area $1 \times 10^{-4} m^{2}$ is illuminated by a radiation of intensity $16\, \frac{milliW}{m^{2}}$ . The work function of
the metal is $5\,eV.$ The energy of the incident photons is $10\,eV$ and only $10%$ of it produces photo
electrons. The number of emitted photo electron per second and their maximum energy, respectively, will be:
$[1eV = 1.6 \times 10^{-19}J]$
a.
$10^{14}$ and $10eV$
b.
$10^{12}$ and $5eV$
c.
$10^{11}$ and $5eV$
Correct Answer
d.
$10^{10}$ and $5eV$
No explanation saved for this question yet.
Q5mcq
Four equal point charges $Q$ each are placed in the $xy$ plane at $(0, 2), (4, 2), (4, -2)$ and $(0, -2)$ . The work
required to put a fifth charge $Q$ at the origin of the coordinate system will be:
Two forces $P$ and $Q$ , of magnitude $2F$ and $3F$ , respectively, are at an angle $\theta$ with each other. If the force $Q$ is
doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:
a.
$120^{^{\circ}}$
Correct Answer
b.
$60^{^{\circ}}$
c.
$30^{^{\circ}}$
d.
$90^{^{\circ}}$
No explanation saved for this question yet.
Q7mcq
Half mole of an ideal monoatomic gas is heated at a constant pressure of $1 atm$ from $20^{\circ}\,C$ to $90^{\circ}\,C$ . Work
done by the gas is $($ Gas constant, $R= 8.21\,J\, mol^{-1} \,K^{-1}$ )
a.
$73 J$
b.
$581 J$
c.
$291 J$
Correct Answer
d.
$146 J$
No explanation saved for this question yet.
Q8mcq
An unknown metal of mass $192g$ heated to a temperature of $100^{\circ}C$ was immersed into a brass calorimeter of
mass $128\,g$ containing $240g$ of water at a temperature of $8.4^{o}C.$ Calculate the specific heat of the unknown
metal if water temperature stabilizes at $21.5^{o}C. ($ Specific heat of brass is $394J kg^{-1}K^{-1})$
a.
$916\,J kg^{-1}K^{-1}$
Correct Answer
b.
$458\,J kg^{-1}K^{-1}$
c.
$654\,J kg^{-1}K^{-1}$
d.
$1232\,J kg^{-1}K^{-1}$
No explanation saved for this question yet.
Q9mcq
Two stars of masses $3 \times 10^{31}\, kg$ each, and at distance $2 \times 10^{11}\,m$ rotate in a plane about their common centre
of mass $O.$ A meteorite passes through $O$ moving perpendicular to the stars,s rotation plane. In order to escape
from the gravitational field of this double star, the minimum speed that meteorite should have at $O$ is ( Take
Gravitational constant $G= 6.67 \times 10^{-11}\,N\,m^{2}\, kg^{-2}$ )
a.
$2.4 \times 10^{4\,}\,m\,s^{-1}$
b.
$3.8 \times 10^{4}\,m\,s^{-1}$
c.
$2.8 \times 10^{5}\,m\,s^{-1}$
Correct Answer
d.
$1.4 \times 10^{5}\,m\,s^{-1}$
No explanation saved for this question yet.
Q10mcq
At some location the horizontal component of earth's magnetic field is $18 \times 10^{-6}\,T.$ At this location,
magnetic needle of length $0.12\,m$ and pole strength $1.8\, Am$ is suspended from its mid-point using a thread, it
makes $45^{\circ}$ angles with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should
be applied at one of its ends is:
a.
$1.8 \times 10^{-5}\,N$
b.
$3.6 \times 10^{-5}\,N$
c.
$6. 5 \times 10^{-5}\,N$
Correct Answer
d.
$1.3 \times 10^{-5}\,N$
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.
A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted
at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular
acceleration will be
a.
$\frac{g}{2l}$
b.
$\frac{7g}{3l}$
c.
$\frac{g}{3l}$
d.
$\frac{g}{13l}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and
mass $M$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the
centre of the rod is
a.
$\frac{209}{15}MR^{2}$ .
b.
$\frac{152}{15}MR^{2}$ .
c.
$\frac{137}{15}MR^{2}$ .
d.
$\frac{17}{5}MR^{2}$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A closed organ pipe has a fundamental frequency of $1.5 kHz$ . The number of overtones that can be distinctly
heard by a person with this organ pipe will be $($ Assume that the highest frequency a person can hear is
$20,000 Hz$ ).
a.
$7$
b.
$4$
c.
$6$
d.
$5$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A particle starts from the origin at time $t= 0$ and moves along the positive $x-$ axis. The graph of velocity with
respect to time is shown in figure. What is the position of the particle at time $t= 5s?$
a.
10 $m$
b.
9 $m$
c.
$6m$
d.
$3m$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A particle which is experiencing a force, given by $\vec{F} = 3ˆi -12ˆj$ , undergoes a displacement of $\vec{d}= 4ˆi$ . If the
particle had a kinetic energy of $3\,J$ at the beginning of the displacement, what is its kinetic energy at the end of
the displacement?
a.
$9\,J$ .
b.
$15\,J$ .
c.
$12\,J$ .
d.
$10\,J$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The modulation frequency of an $AM$ radio station is $250kHz,$ which is $10%$ of the carrier wave. If another
$AM$ station approaches you for license what broadcast frequency will you allot?
a.
$2750kHz$
b.
$2000kHz$
c.
$2250kHz$
d.
$2900kHz$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of
the cornea $(7 .8 \, mm)$ . This surface separates two media of refractive indices $1$ and $1.34$ . Calculate the
distance from the refracting surface at which a parallel beam of light will come to focus.
a.
$4 .0 cm$
b.
$1 cm$
c.
$2\, cm$
d.
$3.07 cm$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two vectors and have equal magnitudes. The magnitude of $+$ is ' ' times the magnitude of
$\vec{A} \vec{B} (\vec{A} \vec{B}) n$
$(\vec{A}- \vec{B})$ . The angle between $\vec{A}$ and $\vec{B}$ is:
a.
$cos^{-1}[ \frac{n^{2}-1}{n^{2}+1}]$
b.
$sin^{-1}[\frac{n-1}{n+1}]$
c.
$cos^{-1}[ \frac{n-1}{n+1} ]$
d.
$sin^{-1}[\frac{n^{2}-1}{n^{2}+1} ]$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The self induced emf of a coil is $25$ volts. When the current in it is changed at uniform rate from $10A$ to $25A$
in $1s$ , the change in the energy of the inductance is:
a.
$637.5\,J$
b.
$740\,J$
c.
$437.5\,J$
d.
$540\,J$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The electric field of a plane polarized electromagnetic wave in free space at time $t= 0$ is given by the
expression $\vec{E}(x, y) = 10ˆjcos(6x+ 8z)$ . The magnetic field $\vec{B}(x, z, t)$ is given by ( $c$ is the velocity of light.)
a.
$\frac{1}{c}(6ˆk -8ˆi)cos(6x+ 8z+ 10ct)$
b.
$\frac{1}{c}(6ˆk + 8ˆi)cos(6x+ 8z-10ct)$
c.
$\frac{1}{c}(6ˆk + 8ˆi)cos(6x-8z+ 10ct)$
d.
$\frac{1}{c}(6ˆk -8ˆi)cos(6x+ 8z-10ct)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Charges $-q$ and $+q$ , located at $A$ and $B$ , respectively, constitute an electric dipole. Distance $AB= 2a$ , $O$ is
the mid point of the dipole and $OP$ is perpendicular to $AB$ . A charge $Q$ is placed at $P$ where $OP =y$ and
$y\gg 2a$ . The charge $Q$ experiences an electrostatic force $F$ . If $Q$ is now moved along the equatorial line to $P'$
such that $OP'=(\frac{y}{3})$ the force on $Q$ will be close to $(\frac{y}{3} \ll 2a)$
a.
$27F$ .
b.
$\frac{F}{3}$ .
c.
$3F$ .
d.
$9F$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A parallel plate capacitor having capacitance $12 pF$ is charged by a battery to a potential difference of $10 V$
between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant $6.5$ is
slipped between the plates. The work done by the capacitor on the slab is
a.
$\,560\, pJ$
b.
$600\, pJ$
c.
$508\, pJ$
d.
$692\, pJ$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their
respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform
magnetic field in such a manner that their magnetic moments make a small angle with the field. If the
oscillation periods of hoop and cylinder are $T_{h}$ and $T_{c}$ respectively, then:
a.
$T_{h} = 2T_{c}$
b.
$T_{h} =T_{c}$
c.
$T_{h} = 0.5T_{c}$
d.
$T_{h} = 1.5T_{c}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as $R_{1}$ has the
colour code (orange, red, brown). The resistors $R_{2}$ and $R_{4}$ are $80\,\Omega$ and $40\,\Omega$ , respectively. Assuming that the
colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as
$R_{3}$ , would be
a.
brown, blue, black.
b.
brown, blue, brown.
c.
grey, black, brown.
d.
red, green, brown.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1cm$ and $34.2 \pm 0.1cm$ ,
respectively. What will be the value of its volume in appropriate significant figures?
a.
$4264 \pm 81cm^{3}$
b.
$4264.4 \pm 81.0\,cm^{3}$
c.
$4260 \pm 80\,cm^{3}$
d.
$4300 \pm 80\,cm^{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$2\, kg$ of a monoatomic gas is at a pressure of $4 \times 10^{4}\,N\,m^{-2}$ . The density of the gas is $8 kg \,m^{-3}$ . What is the
order of energy of the gas due to its thermal motion?
a.
$10^{5}\,J$
b.
$10^{6}\,J$
c.
$10^{4}\,J$
d.
$10^{3}\,J$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A particle executes simple harmonic motion with an amplitude of $5\,cm$ . When the particle is at $4\,cm$ from the
mean position, the magnitude of its velocity in $SI$ units is equal to that of its acceleration. Then, its periodic
time in seconds is:
a.
$\frac{8\pi}{3}$
b.
$\frac{3}{8}\pi$
c.
$\frac{4\pi}{3}$
d.
$\frac{7}{3}\pi$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A current of $2 mA$ was passed through an unknown resistor which dissipated a power of $4.4\,W.$ Dissipated
power when an ideal power supply of $11 V$ is connected across it is:
a.
$11 \times 10^{5}\,W$
b.
$11 \times 10^{-3}\,W$
c.
$11 \times 10^{-5}\,W$
d.
$11 \times 10^{-4}\,W$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The actual value of resistance $R$ , shown in the figure is $30\Omega .$ This is measured in an experiment as shown
using the standard formula $R= \frac{V}{I}$ , where $V$ and $I$ are the readings of the voltmeter and ammeter,
respectively. If the measured value of $R$ is $5%$ less, then the internal resistance of the voltmeter is:
a.
$35\Omega$
b.
$600\Omega$
c.
$570\Omega$
d.
$350\Omega$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An ideal gas undergoes isothermal compression from $5\,m^{3}$ to $1\,m^{3}$ against a constant external pressure of
$4\,N\,m^{-2}$ . The heat released in this process is $24\,J\, mol^{-1} K^{-1}$ and is used to increase the pressure of $1$ mole
of $Al$ . The temperature of $Al$ increases by:
a.
$\frac{2}{3}\,K$
b.
$1\,K$
c.
$\frac{3}{2}\,K$
d.
$2\,K$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An aromatic compound $'A'$ having molecular formula $C_{7}H_{6}O_{2}$ , on treating with aqueous ammonia and
heating forms compound $'B'$ . The compound $'B'$ on reaction with molecular bromine and potassium hydroxide
provides compound $'C'$ having molecular formula $C_{6}H_{7}N$ . The structure of $'A'$ is:
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The elevation in boiling point for $1$ molal solution of glucose is $2\,K$ . The depression in freezing point for $2$
molal solution of glucose in the same solvent is $2\,K.$ The relation between $K_{b}$ and $K_{f}$ is:
a.
$K_{b} = 2\,K_{f}$
b.
$K_{b} = 1 .5 K_{f}$
c.
$K_{b} = K_{f}$
d.
$K_{b} = 0 .5 K_{f}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In the cell, $Pt(s)|H_{2}(g, \,1 bar)|\, HCl \,(aq)|AgCl(s)| Ag(s)|Pt(s),$ the cell potential is $0 .92 \,V$ when a $10^{-6}$
molar $HCl$ solution is used. The standard electrode potential of $Ag AgCl Cl^{-}$ electrode is:
(Given, $\frac{2.303RT}{F} = 0 .06 \,V$ at $298\,K$ )
a.
$0 .76 \,V$
b.
$0 .20 \,V$
c.
$0 .40 \,V$
d.
$0 .94 \,V$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A compound of formula $A_{2}B_{3}$ has the HCP lattice. Which atom forms the HCP lattice and what fraction of
the tetrahedral voids are occupied by the other atoms?
$5 .1 \,g\, NH_{4}SH$ is introduced in $3 .0 \,L$ evacuated flask at $327^{o}C$ . $30%$ of the solid $NH_{4}SH$ is decomposed to
$NH_{3}$ and $H_{2}S$ as gases. The $K_{P}$ of the reaction at $327^{o}C$ is
$(R = 0 .082 \,L\, atm \, mol^{-1} K^{-1}, \, Molar \, mass \, of \,S = 32\,g\, mol^{-1}, \, Molar \, mass \, of \,N = 14\,g\, mol^{-1})$
a.
$0 .242 \, atm^{2}$
b.
$0 .242 \times 10^{-4}\, atm^{2}$
c.
$1 \times 10^{-4}\, atm^{2}$
d.
$4 .9 \times 10^{-3}\, atm^{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$||$
A reaction of cobalt $(III)$ chloride and ethylenediamine in a $1\, : \,2$ mole ratio generates two isomeric products
$A$ (violet-coloured) and $B$ (green-coloured). $A$ can show optical activity, but, $B$ is optically inactive. What type
of isomers do $A$ and $B$ represent?
a.
Coordination isomers
b.
Linkage isomers
c.
Ionisation isomers
d.
Geometrical isomers
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of values of $\theta \in (0, \,\pi )$ for which the system of linear equations
$x+ 3y+ 7z= 0$
$-x+ 4y+ 7z= 0$
$(sin 3\theta )x+ (cos 2\theta )y+ 2z= 0$
has a non-trivial solution, is:
a.
Two
b.
Three
c.
Four
d.
One
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$\rightarrow \rightarrow \rightarrow \rightarrow$
Let $\alpha = (\lambda -2)\,\vec{a}+ \vec{b}$ and $\beta = (4\lambda -2)\,\vec{a}+ 3\vec{b},$ be two given vectors where vectors $\vec{a}$ and $\vec{b}$ are non-collinear.
$\rightarrow \rightarrow \rightarrow \rightarrow$
The value of $\lambda$ for which vectors $\alpha$ and $\beta$ are collinear, is:
a.
$-4$
b.
$-3$
c.
$4$
d.
$3$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the probability of hitting a target by a shooter, in any shot is $\frac{1}{3},$ then the minimum number of independent
shots at the target required by him so that the probability of hitting the target at least once is greater than $\frac{5}{6},$ is:
a.
$4$
b.
$5$
c.
$6$
d.
$3$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f(x)$ be a differentiable function such that $f'(x) = 7 - \frac{3}{4} \frac{f(x)}{x}, \,(x> 0)$ and $f(1) \neq 4.$ Then $_{x}lim_{\rightarrow 0\rightarrow }_{+}x f(\frac{1}{x})$
a.
does not exist.
b.
exists and equals $4$ .
c.
exists and equals $\frac{4}{7}$ .
d.
exists and equals $0$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $N$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g:N \rightarrow \rightarrow N$ such that
$\frac{n+1}{2}, \,\,\,if n is odd$
$f(n) ={$
$\frac{n}{2}, \,\,\,\,if n is even$
and $g(n) =n-(-1)^{n}.$ Then $fog$ is:
a.
onto but not one-one
b.
Both one-one and onto
c.
One-one but not onto
d.
Neither one-one nor onto
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the mean and standard deviation of $5$ observations $x_{1}, \,x_{2}, \,x_{3}, \,x_{4}, \,x_{5}$ are $10$ and $3,$ respectively, then the
variance of $6$ observations $x_{1}, \,x_{2}, \, … , \,x_{5}$ and $-50$ is equal to
a.
$582.5$
b.
$507.5$
c.
$509.5$
d.
$586.5$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $a_{1}, \,a_{2}, \,a_{3}… ,a_{10}$ be in $G.P. \,$ with $a_{i} > 0\,$ for $i= 1, \,2, \, … , \,10$ and $S$ be the set of pairs
$(r, \,k), \,r, \,k\in N$ (the set of natural numbers) for which
$log_{e}a^{r}_{1} a^{k}_{2} log_{e}a^{r}_{2}a^{k}_{3} log_{e}a^{r}_{3}a^{k}_{4}$
$log_{e}a^{r}_{4} a^{k}_{5} log_{e}a^{r}_{5}a^{k}_{6} log_{e}a^{r}_{6}a^{k}_{7} = 0$
$log_{e}a^{r}_{7}a^{k}_{8} log_{e}a^{r}_{8}a^{k}_{9} log_{e}a^{r}_{9}a^{k}_{10}$
Then the number of elements in $S,$ is:
a.
Infinitely many
b.
$4$
c.
$10$
d.
$2$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $z=(\frac{\sqrt{3}}{2} + \frac{i}{2})^{5} +( \frac{\sqrt{3}}{2} - \frac{i}{2})^{5}.$ If $R(z)$ and $I(z)$ respectively denote the real and imaginary parts of $z,$
then
a.
$I(z) = 0$
b.
$R(z) < 0$ and $I(z) > 0$
c.
$R(z) > 0$ and $I(z) > 0$
d.
$R(z) = -3$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
With the usual notation in $\Delta ABC$ , if $\angle A+ \angle B= 120^{\circ}, \,a= + 1\sqrt{3}$ units and $b= -1\sqrt{3}$ units, then the
ratio $\angle A: \angle B$ is
a.
$7 : 1$
b.
$9 : 7$
c.
$3 : 1$
d.
$5 : 3$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f : (-1, \,1) \rightarrow \rightarrow R$ be a function defined by $f(x) =max{-|x|, \, - \sqrt{1 -x^{2}}}.$ If $K$ be the set of all points
at which $f$ is not differentiable, then $K$ has exactly
a.
two elements
b.
one element
c.
three elements
d.
five elements
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the following three statements:
$P : 5$ is a prime number
$Q: 7$ is a factor of $192$
$R: \, LCM$ of $5$ and $7$ is $35$
Then the truth value of which one of the following statements is true?
a.
$P \vee (~Q\wedge R)$
b.
$(P \wedge Q) \vee (~R)$
c.
$(~P) \vee (Q\wedge R)$
d.
$(~P) \wedge (~Q\wedge R)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A helicopter is flying along the curve given by $y- x\frac{3}{2} = 7, \,(x\geq 0).$ A soldier positioned at the point $(\frac{1}{2}, \,7)$
, who wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is:
a.
$\frac{1}{6}\sqrt{\frac{7}{3}}$
b.
$\frac{1}{2}$
c.
$\frac{1}{3}\sqrt{\frac{7}{3}}$
d.
$\frac{\sqrt{5}}{6}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The plane which bisects the line segment joining the points $(-3, \, -3, \,4)$ and $(3, \,7, \,6)$ at right angles, passes
through which one of the following points?
a.
$(2, \,1, \,3)$
b.
$(4, \,1, \, -2)$
c.
$(4, \, -1, \,7)$
d.
$(-2, \,3, \,5)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The value of $\lambda$ such that sum of the squares of the roots of the quadratic equation, $x^{2} + (3 - \lambda )\,x+ 2 =\lambda$ has
the least value is:
a.
$2$
b.
$\frac{4}{9}$
c.
$\frac{15}{8}$
d.
$1$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
