The pressure of an ideal gas varies with volume as $P =\alpha V$ , where $\alpha$ is a constant. One mole of the gas is
allowed to undergo expansion such that its volume becomes ' $m$ ' times its initial volume. The work done by
the gas in the process is
a.
$\frac{\alpha V}{2} (m^{2}-1)$
b.
$\frac{\alpha ^{2}V^{2}}{2}(m^{2} -1)$
c.
$\frac{\alpha}{2} (m^{2}-1)$
d.
$\frac{\alpha V^{2}}{2}(m^{2}-1)$
Correct Answer
No explanation saved for this question yet.
Q2mcq
Ionisation energy of Li (Lithium) atom in ground state is $5.4eV$ . Binding energy of an electron in $Li^{+}$ ion in
ground state is $75.6eV$ . Energy required to remove all three electrons of Lithium (Li) atom is
a.
$81.0eV$
b.
$135.4eV$
c.
$203.4eV$
d.
$156.6eV$
Correct Answer
No explanation saved for this question yet.
Q3mcq
A coil of self inductance $L$ is connected at one end of two rails as shown in figure. A connector of length $l$ ,
mass $m$ can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction
$B$ going into the page. At an instant $t= 0$ an initial velocity $v_{0}$ is imparted to it and as a result of that it starts
moving along $x$ -axis. The displacement of the connector is represented by the figure.
No explanation saved for this question yet.
Q4mcq
An electromagnetic wave with frequency $\omega$ and wavelength $\lambda$ travels in the $+y$ direction. Its magnetic field is
along $+x$ -axis. The vector equation for the associated electric field (of amplitude $E_{0}$ ) is
A large number of droplets, each of radius, $r$ coalesce to form a bigger drop of radius, $R$ . An engineer designs a
machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of
the drop is ( $T =$ surface tension, $\rho =$ density)
A steel wire can sustain $100\,kg$ weight without breaking. If the wire is cut into two equal parts, each part can
sustain a weight of
a.
$50\,kg$
b.
$400\,kg$
c.
$100\,kg$
Correct Answer
d.
$200\,kg$
No explanation saved for this question yet.
Q7mcq
A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic
field perpendicular to the direction of the field. If the deuteron follows a path of radius $R$ , assuming the
neutron and proton masses are nearly equal, the radius of the proton's path will be
a.
$\sqrt{2}R$
b.
$\frac{R}{\sqrt{2}}$
Correct Answer
c.
$\frac{R}{2}$
d.
$R$
No explanation saved for this question yet.
Q8mcq
A generator has armature resistance of $0.1\Omega$ and develops an induced emf of $120\,V$ when driven at its rated
speed. Its terminal voltage when a current of $50\,A$ is being drawn is
a.
$120\,V$
b.
$5\,V$
c.
$115\,V$
Correct Answer
d.
$70\,V$
No explanation saved for this question yet.
Q9mcq
Two point masses of mass $m_{1} =fM$ and $m_{2} = (1 - f)M(f < 1)$ are in outer space (far from gravitational
influence of other objects) at a distance $R$ from each other. They move in circular orbits about their centre of
mass with angular velocities $\omega _{1}$ for $m_{1}$ and $\omega _{2}$ for $m_{2}$ . In that case
a.
$(1 - f)\omega _{1} =f\omega$
b.
$\omega _{1} =\omega _{2}$ and independent of $f$
Correct Answer
c.
$f\omega _{1} = (1 - f)\omega _{2}$
d.
$\omega _{1} =\omega _{2}$ and depend on $f$
No explanation saved for this question yet.
Q10mcq
The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric
field $\vec{E}$ is applied at an angle $\frac{\pi}{4}$ with the vertical direction. The electric flux through the curved surface of the
hemisphere is
a.
$\pi a^{2}E$
b.
$\frac{\pi a^{2}E}{\sqrt{2}}$
Correct Answer
c.
$\frac{\pi a^{2}E}{2\sqrt{2}}$
d.
$\frac{(\pi +2\pi \phi ^{2}E}{(2\sqrt{2}^{2})}$
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.
Given the electric field of a complete amplitude modulated wave as
$\vec{E} = \hat{i}E_{c}(1 + \frac{E_{m}}{E}cos\omega _{m}t)cos\omega _{c}t$
$c$
Where the subscript c stands for the carrier wave and $m$ for the modulating signal. The frequencies present in
the modulated wave are
a.
$\omega _{c}$ and $\sqrt{\omega ^{2}+\omega ^{2}}_{c}_{m}$
b.
$\omega _{c},\omega _{c}+\omega _{m}$ and $\omega _{c}- \omega _{m}$
c.
$\omega _{c}$ and $\omega _{m}$
d.
$\omega _{c}$ and $\sqrt{\omega _{c}\omega _{m}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A block of weight $W$ rests on a horizontal floor with coefficient of static friction $\mu$ . It is desired to make the
block move by applying minimum amount of force. The angle $\theta$ from the horizontal at which the force should
be applied and magnitude of the force $F$ are respectively.
A glass prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$ ) as shown in figure. A light
beam incident normally on the face $AB$ is
$\,totally reflected to reach the face\,BC, if\,$
a.
$sin\theta > \frac{5}{9}$
b.
$sin\theta > \frac{2}{3}$
c.
$sin\theta > \frac{8}{9}$
d.
$sin\theta > \frac{1}{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A $6.0$ volt battery is connected to two light bulbs as shown in figure. Light bulb 1 has resistance 3 ohm while
light bulb 2 has resistance $6ohm$ . Battery has negligible internal resistance. Which bulb will glow brighter?
a.
Bulb 1 will glow more first and then its
brightness will become less than bulb 2
b.
Bulb 1
c.
Bulb 2
d.
Both glow equally
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$N$ divisions on the main scale of a vernier calliper coincide with $(N + 1)$ divisions of the vernier scale. If each
division of main scale is ' $a$ ' units, then the least count of the instrument is
a.
$a$
b.
$\frac{a}{N}$
c.
$\frac{N}{N+1} \times a$
d.
$\frac{a}{N+1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A uniform tube of length $60.5\,cm$ is held vertically with its lower end dipped in water. A sound source of
frequency $500\,Hz$ sends sound waves into the tube. When the length of tube above water is $16\,cm$ and again
when it is $50\,cm$ , the tube resonates with the source of sound. Two lowest frequencies (in $Hz$ ), to which tube
will resonate when it is taken out of water, are (approximately).
a.
281,562
b.
281,843
c.
276,552
d.
272,544
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $( \frac{L}{2})$ each.
The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100^{\circ }C$
and that of steel at $0^{\circ }C$ then the temperature of junction is (Thermal conductivity of copper is 9 times that of
steel)
a.
$90^{\circ }C$
b.
$50^{\circ }C$
c.
$10^{\circ }C$
d.
$67^{\circ }C$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Sand is being dropped on a conveyer belt at the rate of $2\,kg$ per second. The force necessary to keep the belt
moving with a constant speed of $3\,ms^{-1}$ will be
a.
$12\,N$
b.
$6\,N$
c.
zero
d.
$18\,N$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R(R>r$ ) such
that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: A metallic surface is irradiated by a monochromatic light
of frequency $v>v_{0}$ (the threshold frequency). If the incident frequency is now doubled, the photocurrent and
the maximum kinetic energy are also doubled. Statement 2: The maximum kinetic energy of photoelectrons
emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends
only on the intensity of the incident light.
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is false.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A moving particle of mass $m$ , makes a head on elastic collision with another particle of mass $2m$ , which is
initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
a.
$33%$
b.
$67%$
c.
$90%$
d.
$10%$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two coherent plane light waves of equal amplitude makes a small angle $\alpha (<< 1)$ with each other. They fall
almost normally on a screen. If $\lambda$ is the wavelength of light waves, the fringe width $\Delta x$ of interference patterns
of the two sets of waves on the screen is
a.
$\frac{2\lambda}{\alpha}$
b.
$\frac{\lambda}{\alpha}$
c.
$\frac{\lambda}{(2\alpha )}$
d.
$\frac{\lambda}{\sqrt{\alpha}}$
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 1 and Statement 2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: An inventor claims to have constructed an engine that has
an efficiency of $30%$ when operated between the boiling and freezing points of water. This is not possible.
Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating
between the same two temperatures.
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
b.
Statement 1 is true, Statement 2 is false.
c.
Statement 1 is false, Statement 2 is true.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side
of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$ . The middle
wagon of the train passes the pole with a velocity.
a.
$\frac{u+v}{2}$
b.
$\frac{1}{2} \sqrt{u2+v2}$
c.
$\sqrt{uv}$
d.
$\sqrt{\,} (\frac{u^{2}+v^{2}}{2})$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The decay constants of a radioactive substance for $\alpha$ and $\beta$ emission are $\lambda _{\alpha }$ and $\lambda _{\beta }$ respectively. If the
substance emits $\alpha$ and $\beta$ simultaneously, then the average half life of the material will be
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: Self inductance of a long solenoid of length $L$ , total
number of turns $N$ and radius $r$ is less than $\frac{\pi \mu _{0}N^{2}r^{2}}{L}$ . Statement 2: The magnetic induction in the solenoid in
Statement 1 carrying current $I$ is $\frac{\mu _{0}NI}{L}$ in the middle of the solenoid but becomes less as we move towards its
ends.
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
c.
Statement 1 is false, Statement 2 is true.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A ring is suspended from a point $S$ on its rim as shown in the figure. When displaced from equilibrium, it
oscillates with time period of 1 second. The radius of the ring is (take $g=\pi ^{2}$ )
a.
$0.15\,m$
b.
$1.5\,m$
c.
$1.0\,m$
d.
$0.5\,m$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The amount of heat produced in an electric circuit depends upon the current $(I)$ , resistance $(R)$ and time $(t)$ . If
the error made in the measurements of the above quantities are $2%, 1%$ and $1%$ respectively then the maximum
possible error in the total heat produced will be
a.
$1%$
b.
$2%$
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.
An open vessel at $300\,K$ is heated till $2/5^{th\,}$ of the air in it is expelled. Assuming that the volume of the vessel
remains constant, the temperature to which the vessel is heated, is
a.
$1500\,K$
b.
$400\,K$
c.
$500\,K$
d.
$750\,K$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The enthalpy of neutralisation of $NH_{4}OH$ with $HCl$ is $-51.46\,kJ\,mol^{-1}$ and the enthalpy of neutralisation of
$NaOH$ with $HCl$ is $-55.90\,kJ\,mol^{-1}$ . The enthalpy of ionisation of $NH_{4}OH$ is
a.
$-107.36\,kJ\,mol^{-1}$
b.
$-4.44\,kJ\,mol^{-1}$
c.
$+107.36\,kJ\,mol^{-1}$
d.
$+4.44\,kJ\,mol^{-1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Which of the following paramagnetic ions would exhibit a magnetic moment (spin only) of the order of $5BM$ ?
(At. Nos. $Mn = 25, Cr = 24, \,V = 23, Ti = 22$ )
a.
$Mn^{2+}$
b.
$Ti^{2+}$
c.
$V^{2+}$
d.
$Cr^{2+}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Liquids A and B form an ideal solution. At $30^{\circ }C$ , the total vapour pressure of a solution containing $1\,mol$ of A
and $2\,mol$ of B is $250\,mmHg$ . The total vapour pressure becomes $300\,mmHg$ when 1 more mol of $A$ is added
to the first solution. The vapour pressures of pure $A$ and $B$ at the same temperature are
a.
$150, 450mmHg$
b.
$125, 150\,mmHg$
c.
$450, 150\,mmHg$
d.
$250, 300\,mmHg$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The value of $K_{p}$ for the equilibrium reaction $N_{2}O_{4}(g)\rightleftharpoons 2NO_{2}(g)$ is 2 . The percentage dissociation of
$N_{2}O_{4}(g)$ at a pressure of $0.5\,atm$ is
a.
25
b.
88
c.
50
d.
71
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Ammonium chloride crystallizes in a body centred cubic lattice with edge length of unit cell of 390 $pm$ . If the
size of chloride ion is $180pm$ , the size of ammonium ion would be
a.
$174pm$
b.
$158pm$
c.
$142pm$
d.
$126pm$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
On addition of $1\,mL$ of $10%NaCl$ solution to 10 $mL$ gold sol in the presence of $0.025\,g$ of starch, the
coagulation is just prevented. Starch has gold number
a.
$2.5$
b.
25
c.
$0.25$
d.
$0.025$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
When $CO_{2(\,g)}$ is passed over red hot coke it partially gets reduced to $CO(g)$ . Upon passing $0.5\,L$ of $CO_{2}(g)$
over red hot coke, the total volume of the gases increased to $700\,mL$ . The composition of the gaseous mixture
at STP is
a.
$CO_{2} = 300\,mL; CO = 400\,mL$
b.
$CO_{2} = 0.0\,mL; CO = 700\,mL$
c.
$CO_{2} = 200\,mL; CO = 500\,mL$
d.
$CO_{2} = 350\,mL; CO = 350\,mL$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For a reaction $A\rightarrow \rightarrow$ Products, a plot of $logt_{1/2}$ versus $loga_{0}$ is shown in the figure. If the initial concentration
of $A$ is represented by $a_{0}$ , the order of the reaction is
a.
one
b.
zero
c.
two
d.
three
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The standard potentials of $Ag^{+}/Ag, Hg_{2}^{2+}/2Hg$ , $Cu^{2+}/Cu$ and $Mg^{2+}/Mg$ electrodes are $0.80, 0.79$ , $0.34$ and
$-2.37\,V$ , respectively. An aqueous solution which contains one mole per litre of the salts of each of the four
metals is electrolyzed. With increasing voltage, the correct sequence of deposition of the metals at the cathode
is
a.
$Ag, Hg, Cu, Mg$
b.
$Cu, Hg$ , Ag only
c.
Ag, Hg, Cu only
d.
$Mg, Cu, Hg, Ag$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of arrangements that can be formed from the letters $a,b,c,d,e,f$ taken 3 at a time without
repetition and each arrangement containing at least one vowel, is
a.
96
b.
128
c.
24
d.
72
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the foci of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1$ coincide with the foci of the hyperbola $\frac{x^{2}}{144} - \frac{y^{2}}{81} = \frac{1}{25}$ , then $b^{2}$ is equal
to
a.
8
b.
10
c.
7
d.
9
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If six students, including two particular students $A$ and $B$ , stand in a row, then the probability that $A$ and $B$ are
separated with one student in between them is
a.
$\frac{8}{15}$
b.
$\frac{4}{15}$
c.
$\frac{2}{15}$
d.
$\frac{1}{15}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f : [1, 3] \rightarrow \rightarrow R$ be a function satisfying $\frac{x}{[x]} \leq f(x) \leq \sqrt{6 -x}$ , for all $x\neq 2$ and $f(2) = 1$ , where $R$ is the
set of all real numbers and $[x]$ denotes the largest integer less than or equal to $x$ . Statement 1: $lim_{x\rightarrow 2\rightarrow }_{-} f(x)$
exists. Statement 2: $f$ is continuous at $x= 2$ .
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation for
Statement 1.
d.
Statement 1 is true, Statement 2 is false.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement 1: The shortest distance between the lines $\frac{x}{2} = \frac{y}{-1} = \frac{z}{2}$ and $\frac{x-1}{4} = \frac{y-1}{-2} = \frac{z-1}{4}$ is $\sqrt{2}$ . Statement 2:
The shortest distance between two parallel lines is the perpendicular distance from any point on one of the
lines to the other line.
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
c.
Statement 1 is false, Statement 2 is true.
d.
Statement 1 is true, Statement 2 is true, ,
Statement 2 is not a correct explanation for
Statement 1.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $Z$ and $W$ be complex numbers such that $|Z| = |W|$ , and $argZ$ denotes the principal argument of $Z$ .
Statement 1:If $argZ+ argW =\pi$ , then $Z = -W-$ . Statement 2: $|Z| = |W|$ , implies arg $Z-arg W- =\pi$ .
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation for
Statement 1.
d.
Statement 1 is false, Statement 2 is true.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The median of 100 observations grouped in classes of equal width is 25 . If the median class interval is 20-30
and the number of observations less than 20 is 45 , then the frequency of median class is
a.
10
b.
20
c.
15
d.
12
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If three distinct points $A,B,C$ are given in the 2dimensional coordinate plane such that the ratio of the
distance of each one of them from the point $(1, 0)$ to the distance from $(-1, 0)$ is equal to $\frac{1}{2}$ , then the
circumcentre of the triangle $ABC$ is at the point
a.
$(\frac{5}{3} , 0)$
b.
$(0, 0)$
c.
$(\frac{1}{3} , 0)$
d.
$(3, 0)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$| |$
The weight $W$ of a certain stock of fish is given by $W =nw$ , where $n$ is the size of stock and $w$ is the average
weight of a fish. If $n$ and $w$ change with time $t$ as $n= 2t^{2} + 3$ and $w=t^{2} - t+ 2$ , then the rate of change of
$W$ with respect to $t$ at $t= 1$ is
a.
1
b.
8
c.
13
d.
5
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $\vec{a}= \hat{i}-2\hat{j}+ 3\hat{k}, \vec{b}= 2\hat{i}+ 3\hat{j}- \hat{k}$ and $\vec{c}=r\hat{i}+ \hat{j}+ (2r-1\hat{k}$ are three vectors such that $\vec{c}$ is parallel to the
plane of $\vec{a}$ and $\vec{b}$ , then $r$ is equal to
a.
1
b.
$-1$
c.
0
d.
2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$0 0 a$
$[ ]$
If $A^{T}$ denotes the transpose of the matrix $A= 0 b c$ , where $a,b,c,d,e$ and $f$ are integers such that
$[ ]$
$d e f$
$abd\neq 0$ , then the number of such matrices for which $A^{-1} =A^{T}$ is
a.
2(3!)
b.
$3(2!)$
c.
$2^{3}$
d.
$3^{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Suppose $\theta$ and $\phi (\neq 0)$ are such that $sec(\theta +\phi )$ , sec $\theta$ and $sec(\theta - \phi )$ are in A.P. If $cos\theta =kcos(\frac{\phi}{2})$ for some
$k$ , then $k$ is equal to
a.
$\pm \sqrt{2}$
b.
$\pm 1$
c.
$\pm \frac{1}{\sqrt{2}}$
d.
$\pm 2$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider a quadratic equation $ax^{2} +bx+c= 0$ , where $2a+ 3b+ 6c= 0$ and let $g(x) =a\frac{x^{3}}{3} +b\frac{x^{2}}{2} +cx$ .
Statement 1: The quadratic equation has at least one root in the interval $(0, 1)$ . Statement 2: The Rolle's
theorem is applicable to function $g(x)$ on the interval $[0, 1]$ .
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is false.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation for
Statement 1.
d.
Statement 1 is true, Statement 2 is true, ,
Statement 2 is a correct explanation for
Statement 1.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $L$ be the line $y= 2x$ , in the two dimensional plane. Statement 1: The image of the point $(0, 1)$ in $L$ is the
point $(\frac{4}{5} , \frac{3}{5})$ Statement 2: The points $(0, 1)$ and $(\frac{4}{5}, \frac{3}{5} )$ lie on opposite sides of the line $L$ and are at equal
distance from it.
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation for
Statement 1.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
d.
Statement 1 is false, Statement 2 is true.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $p,q,r\in R$ and $r>p> 0$ . If the quadratic equation $px^{2} +qx+r= 0$ has two complex roots $\alpha$ and $\beta$ ,
then $|\alpha | + |\beta |$ is
a.
equal to 1
b.
less than 2 but not equal to 1
c.
greater than 2
d.
equal to 2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $a,b,c$ , are non zero complex numbers satisfying $a^{2} +b^{2} +c^{2} = 0$ and
$b^{2} +c^{2} ab ac$
$ab c^{2} +a^{2} bc =ka^{2}b^{2}c^{2}$ , then $k$ is equal to
$ac bc a^{2} +b^{2}$
a.
1
b.
3
c.
4
d.
2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
