The aperture of the objective is $24. 4\, cm$ . The resolving power of this telescope, if a light of wavelength
$2440\,A^{\circ }$ is used to see the object will be
a.
$8. 1 \times 10^{6}$
b.
$10. 0 \times 10^{7}$
c.
$8. 2 \times 10^{5}$
Correct Answer
d.
$1. 0 \times 10^{-8}$
No explanation saved for this question yet.
Q2mcq
The refracting angle of a prism is $A$ and refractive index of the material of the prism is $cot(\frac{A}{2})$ . Then the
angle of minimum deviation will be
a.
$180^{\circ}-2A$
Correct Answer
b.
$90^{\circ}-A$
c.
$180^{\circ}+2A$
d.
$180^{\circ}-3A$
No explanation saved for this question yet.
Q3nat
An AC source is connected to an inductance of $100\, mH$ , a capacitance of $100\,\mu F$ and a resistance of $120\,\Omega$ as
shown in figure. The time in which the resistance having a thermal capacity $2\,J\,^{\circ }C^{-1}$ will get heated by $16^{\circ}C$
is _____ $s$ .
✓ Accepted Answer:15
No explanation saved for this question yet.
Q4mcq
An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface.
Choose the correct representation of magnetic field $(B)$ as a function of radial distance $(r)$ from the axis of
cylinder.
No explanation saved for this question yet.
Q5mcq
Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the
charge may increase if the charge is positive.
Statement-II :An electric dipole is placed in a uniform electric field. The net electric force on the dipole will
not be zero.
a.
Both statement-I and statement-II are true.
b.
Both statement-I and statement-II are false.
c.
Statement-I is true but statement-II is false.
Correct Answer
d.
Statement-I is false but statement-II is true.
No explanation saved for this question yet.
Q6nat
A pendulum is suspended by a string of length $250\, cm$ . The mass of the bob of the pendulum is $200\,g$ . The
bob is pulled aside until the string is at $60^{\circ}$ with vertical as shown in the figure. After releasing the bob, the
maximum velocity attained by the bob will be _____ $m\,s^{-1}$ . (if $g= 10\,m\,s^{-2}$ )
✓ Accepted Answer:5
No explanation saved for this question yet.
Q7mcq
Match List-I with List-II
List-I List-II
(A) Television signal I. $03 KHz$
(B) Radio signal II. $20 KHz$
(C) High Quality Music III. $02 MHz$
(D) Human speech IV. $06 MHz$
a.
$A -I, B -II, C -III, D -IV$
b.
$A -IV, B -III, C -I, D -II$
c.
$A -IV, B -III, C -II, D -I$
Correct Answer
d.
$A -I, B -II, C -IV, D -III$
No explanation saved for this question yet.
Q8nat
The total internal energy of two mole monoatomic ideal gas at temperature $T = 300\,K$ will be _____ $J$ . (Given
$R= 8. 31\,J\, mol^{-1} \cdot K$ )
✓ Accepted Answer:7479
No explanation saved for this question yet.
Q9mcq
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_{c}$ is
varying with time $t$ as $a_{c} =k^{2}rt^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting
on it is -
a.
Zero
b.
$2mk^{2}r^{2}t$
c.
$mk^{2}r^{2}t$
Correct Answer
d.
$2mk^{2}rt$
No explanation saved for this question yet.
Q10mcq
Assertion A:Product of Pressure $(P)$ and time $(t)$ has the same dimension as that of coefficient of viscosity.
Reason:Coefficient of viscosity $= \frac{\, Force \,}{\, Velocity \, gradient \,}$
a.
Both A and R true, and R is correct explanation of
A.
b.
Both A and R are true but R is NOT the correct
explanation of A.
c.
A is true but R is false.
Correct Answer
d.
A is false but R is true.
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.
Statement - I :When $\mu$ amount of an ideal gas undergoes adiabatic change from state $(P_{1},V_{1},T_{1})$ to state
$(P_{2},V_{2},T_{2})$ , then work done is $W = \frac{\mu R(T_{2}-T_{1})}{1-\gamma}$ , where $\gamma = \frac{C_{P}}{C_{V}}$ and $R=$ universal gas constant.
Statement - II :In the above case, when work is done on the gas, the temperature of the gas would rise.
a.
Both statement-I and statement-II are true.
b.
Both statement-I and statement-II are false.
c.
Statement-I is true but statement-II is false.
d.
Statement-I is false but statement-II is true.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The position vector of $1\, kg$ object is $\vec{r}=(3Ëi -Ëj)\,m$ and its velocity $\vec{v}=(3Ëj +Ëk)\,m\,s^{-1}$ . The magnitude of
its angular momentum is $\sqrt{x}\,N\,m\,s$ , where $x$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A hanging mass $M$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in
the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $2 Mg$ force. In this situation,
tension in the string is $\frac{x}{5}Mg$ for $x=$ _____. Neglect mass of the string and friction of the block (bigger mass)
with ice slab.
(Given $g=$ acceleration due to gravity)
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A radar sends an electromagnetic signal of electric field $(E_{0}) = 2. 25\,V\,m^{-1}$ and magnetic field
$(B_{0}) = 1. 5 \times 10^{-8}\,T$ which strikes a target on line of sight at a distance of $3\, km$ in a medium. After that, a
part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was
transmitted at time $t= 0$ from radar, then after how much time echo will reach to the radar?
a.
$2. 0 \times 10^{-5}\,s$
b.
$4. 0 \times 10^{-5}\,s$
c.
$1. 0 \times 10^{-5}s$
d.
$8. 0 \times 10^{-5}s$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The de Broglie wavelengths for an electron and a photon are $\lambda _{e}$ and $\lambda _{p}$ respectively. For the same kinetic
energy of electron and photon, which of the following presents the correct relation between the de Broglie
wavelengths of two?
A singly ionized magnesium atom $(A= 24)$ ion is accelerated to kinetic energy $5 keV$ , and is projected
perpendicularly into a magnetic field $B$ of the magnitude $0. 5\,T$ . The radius of path formed will be _____ $cm.$
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A water drop of diameter $2\, cm$ is broken into $64$ equal droplets. The surface tension of water is $0. 075\,N\,m^{-1}$ .
In this process the gain in surface energy will be
a.
$2. 8 \times 10^{-4}\,J$
b.
$1. 5 \times 10^{-3}\,J$
c.
$1. 9 \times 10^{-4}\,J$
d.
$9. 4 \times 10^{-5}\,J$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A} = 2T_{B}$ .
These planets are revolving in the circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which out of the following
would be the correct relationship of their orbits?
Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : $n- p- n$ transistor permits more current than a $p- n- p$ transistor.
Reason R :Electrons have greater mobility as a charge carrier.
a.
Both A and R true, and R is correct explanation
of A.
b.
Both A and R are true but R is NOT the correct
explanation of A.
c.
A is true but R is false.
d.
A is false but R is true.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Motion of a particle in $x- y$ plane is described by a set of following equations $x= 4 sin(\frac{\pi}{2} - \omega t)\,m$ and
$y= 4 sin(\omega t)\,m$ . The path of the particle will be
a.
circular
b.
helical
c.
parabolic
d.
eliptical
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A telegraph line of length $100\, km$ has a capacity of $0. 01\,\mu F\, km^{-1}$ and it carries an alternating current at $0. 5$
kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be
introduced in series is _____ $mH$ . (If $\pi = \sqrt{10}$ )
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A man of $60\, kg$ is running on the road and suddenly jumps into a stationary trolly car of mass $120\, kg$ . Then
the trolly car starts moving with velocity $2\,m\,s^{-1}$ . The velocity of the running man was _____ $m\,s^{-1}$ , when he
jumps into the car.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $R$ using a given
resistor of $15\,\Omega$ . The galvanometer $(G)$ shows null defection when tapping key is at $43\, cm$ mark from end $A$ .
If the end correction for end $A$ is $2\, cm$ , then the determined value of $R$ will be $\Omega$ .
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The three charges $\frac{q}{2},q$ and $\frac{q}{2}$ are placed at the corners $A,D$ and $C$ of a square of side $a$ as shown in figure.
The magnitude of electric field $(E)$ at the corner $B$ of the square, is
Match List-I with List-II
List-I List-II
Moment of inertia of solid sphere
(A) (I) $\frac{5}{3}MR^{2}$
of radius $R$ about any tangent.
Moment of inertia of hollow sphere of radius
(B) (II) $\frac{7}{5}MR^{2}$
$(R)$ about any tangent.
Moment of inertia of circular ring of radius
(C) (III) $\frac{1}{4}MR^{2}$
$(R)$ about its diameter.
Moment of inertia of circular disc of radius
(D) (IV) $\frac{1}{2}MR^{2}$
$(R)$ about any diameter.
a.
$A -II, \,B -I, \,C -IV, \,D -III$
b.
$A -I, \,B -II, \,C -IV, \,D -III$
c.
$A -II, \,B -I, \,C -III, \,D -IV$
d.
$A -I, \,B -II, \,C -III, \,D -IV$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The vapour pressures of two volatile liquids $A$ and $B$ at $25\,^{\circ}C$ are $50$ Torr and $100$ Torr, respectively. If the
liquid mixture contains $0. 3$ mole fraction of $A$ , then the mole fraction of liquid $B$ in the vapour phase is $\frac{x}{17}$ .
The value of $x$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In the estimation of bromine, $0. 5\,g$ of an organic compound gave $0. 40\,g$ of silver bromide. The percentage of
bromine in the given compound is $%$ (nearest integer)
(Relative atomic masses of $Ag$ and $Br$ are $108u$ and $80u$ , respectively).
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements :
Statement I: $[Ni (CN)_{4}]^{2-}$ is square planar and diamagnetic complex, with $dsp^{2}$ hybridization for $Ni$ but
$[Ni (CO)_{4}]$ is tetrahedral, paramagnetic and with $sp^{3}$ hybridication for $Ni$ .
Statement II : $[NiCl_{4}]^{2-}$ and $[Ni (CO)_{4}]$ both have same d-electron configuration, have same geometry and are
paramagnetic.
In light the above statements, choose the correct answer form the options given below
a.
Both Statement I and Statement II are true.
b.
Statement I is correct but statement II is false.
c.
Statement I is incorrect but statement II is true.
d.
Both Statement I and Statement II are false.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given below are two statements :
Statement I: The pentavalent oxide of group- $15$ element, $E_{2}O_{5}$ , is less acidic than trivalent oxide, $E_{2}O_{3}$ , of the
same element.
Statement II : The acidic character of trivalent oxide of group $15$ elements, $E_{2}O_{3}$ , decreases down the group.
In light of the above statements, choose most appropriate 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 false but statement II is true.
d.
Statement I true, but statement II is false.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A primary aliphatic amine on reaction with nitrous acid in cold $(273\,K)$ and there after raising temperature of
reaction mixture to room temperature $(298\,K)$ , gives a/an
a.
Alcohol
b.
nitrile
c.
diazonium salt
d.
secondary amine
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A $2. 0\,g$ sample containing $MnO_{2}$ is treated with $HCl$ liberating $Cl_{2}$ . The $Cl_{2}$ gas is passed into a solution of
$KI$ and $60. 0 mL$ of $0. 1 MNaS_{2}O_{3}$ is required to titrate the liberated iodine. The percentage of $MnO_{2}$ in the
sample is____. Nearest integer)
[Atomic masses (in $u$ ) $Mn = 55; Cl = 35. 5 : O = 16, I = 127, Na = 23, K = 39, S = 32$ ]
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$4. 0\,L$ of an ideal gas is allowed to expand isothermally into vacuum until the total volume is $20\,L$ . The amount
of heat absorbed in this expansion is $L$ atm.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Given are two statements one is labelled as Assertion and other is labelled as Reason.
Assertion: Magnesium can reduce $Al_{2}O_{3}$ at a temperature below $1350\,^{\circ}C$ , while above $1350\,^{\circ}C$ aluminium
can reduce $MgO$ .
Reason: The melting and boiling points of magnesium are lower than those of aluminium.
In light of the above statements, choose most appropriate answer from the options given below
a.
Both Assertion and Reason are correct, and
Reason is correct explanation of Assertion.
b.
Both Assertion and Reason are correct, but
Reason is NOT the correct explanation of
Assertion.
c.
Assertion is correct Reason is not correct.
d.
Assertion is not correct, Reason is correct.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The solubility product of a sparingly soluble salt $A_{2}X_{3}$ is $1. 1 \times 10^{-23}$ . If specific conductance of the solution
is $3 \times 10^{-5} Sm^{-1}$ , the limiting molar conductivity of the solution is $x \times 10^{-3}\,S\,m^{2}\, mol^{-1}$ . The value of $x$ is
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the work function of a metal is $6. 63 \times 10^{-19}\,J$ , the maximum wavelength of the photon required to remove
a photoelectron from the metal is____ $nm$ . Nearest integer)
[Given : $h = 6. 63 \times 10^{-34}\,J\,s$ , and $c = 3 \times 10^{8}\,m\,s^{-1}$ ]
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For a first order reaction $A \rightarrow B\rightarrow$ , the rate constant, $k = 5. 5 \times 10^{-14}\,s^{-1}$ . The time required for $67%$
completion of reaction is $x \times 10^{-1}$ times the half life of reaction. The value of $x$ is Nearest integer) (Given :
$log 3 = 0. 4771$ )
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Element " $E$ " belongs to the period $4$ and group $16$ of the periodic table. The valence shell electron
configuration of the element, which is just above " $E$ " in the group is
a.
$2s^{2}2p^{4}$
b.
$3d^{10}, 4s^{2}, 4p^{4}$
c.
$3s^{2}3p^{4}$
d.
$4d^{10}, 5s^{2}, 5p^{4}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$|$
If $\vec{a}= 2Ëi+ Ëj+ 3Ëk, \,\,\vec{b}= 3Ëi+ 3Ëj+ Ëk$ and $\vec{c}=c_{1}Ëi+c_{2}Ëj+c_{3}Ëk$ are coplanar vectors and $\vec{a}\cdot \vec{c}= 5, \vec{b}\perp \vec{c}$ , then
$122(c_{1}+c_{2}+c_{3})$ is equal to ______.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $AB$ and $PQ$ be two vertical poles, $160m$ apart from each other. Let $C$ be the middle point of $B$ and $Q$ ,
which are feet of these two poles. Let $\frac{\pi}{8}$ and $\theta$ be the angles of elevation from $C$ to $P$ and $A$ , respectively. If
the height of pole $PQ$ is twice the height of pole $AB$ , then $tan^{2} \theta$ is equal to
a.
$\frac{3-2\sqrt{2}}{2}$
b.
$\frac{3+\sqrt{2}}{2}$
c.
$\frac{3-2\sqrt{2}}{4}$
d.
$\frac{3-\sqrt{2}}{4}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the lines $y+ 2x= + 7\sqrt{11} \sqrt{7}$ and $2y+x= 2 + 6\sqrt{11} \sqrt{7}$ be normal to a circle
$C : (x- h)^{2} + (y- k)^{2} =r^{2}$ . If the line $\sqrt{11}y-3x= \frac{5\sqrt{77}}{3} + 11$ is tangent to the circle $C$ , then the value of
$(5h-8k)^{2} + 5r^{2}$ is equal to ______.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$[e^{x}], x< 0$
$[$
$ae^{x} + [x-1], 0 \leq x< 1$
Let $f :R\rightarrow \rightarrow R$ be defined as $f(x) =$
$b+ [sin(\pi x)], 1 \leq x< 2$
$[_{-x}$
$[e ] - c, x\geq 2$
where $a,b,c\in R$ and $[t]$ denotes greatest integer less than or equal to $t$ . Then, which of the following
statements is true?
a.
There exists $a,b,c\in R$ such that $f$ is continuous
of $R$ .
b.
If $f$ is discontinuous at exactly one point, then
$a+b+c= 1$
c.
If $f$ is discontinuous at exactly one point, then
$a+b+c\neq 1$ .
d.
$f$ is discontinuous at atleast two points, for any
values of $a,b$ and $c$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the eccentricity of the hyperbola $H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ be $\sqrt{\frac{5}{2}}$ and length of its latus rectum be $6\sqrt{2}$ . If
$y= 2x+c$ is a tangent to the hyperbola $H$ , then the value of $c^{2}$ is equal to
a.
$18$
b.
$20$
c.
$24$
d.
$32$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $\sum ^{31}_{k=1}(^{31}C_{k})(^{31}C_{k-1})- \sum ^{30}_{k=1}(^{30}C_{k})(^{30}C_{k-1})= \frac{\alpha (60!)}{(30!)(31!)}$ , where $\alpha \in R$ , then the value of $16\alpha$ is equal to
a.
$1411$
b.
$1320$
c.
$1615$
d.
$1855$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking it was
found that, in the observations, $20$ was misread as $5$ . Then, the correct variance is equal to _____.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If the tangents drawn at the point $O(0, 0)$ and $P(1 + \sqrt{5}, 2)$ on the circle $x^{2} +y^{2} -2x-4y= 0$ intersect at
the point $Q$ , then the area of the triangle $OPQ$ is equal to
a.
$\frac{3+\sqrt{5}}{2}$
b.
$\frac{4+2\sqrt{5}}{2}$
c.
$\frac{5+3\sqrt{5}}{2}$
d.
$\frac{7+3\sqrt{5}}{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $l$ be a line which is normal to the curve $y= 2x^{2} +x+ 2$ at a point $P$ on the curve. If the point $Q(6, 4)$ lies
on the line $l$ and $O$ is origin, then the area of the triangle $OPQ$ is equal to _____.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A ray of light passing through the point $P(2, 3)$ reflects on the $X$ -axis at point $A$ and the reflected ray passes
through the point $Q(5, 4)$ . Let $R$ be the point that divides the line segment $AQ$ internally into the ratio $2 : 1$ .
Let the co-ordinates of the foot of the perpendicular $M$ from $R$ on the bisector of the angle $PAQ$ be $(\alpha ,\beta )$ .
Then, the value of $7\alpha + 3\beta$ is equal to _____.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If two distinct point $Q, \,R$ lie on the line of intersection of the planes $-x+ 2y- z= 0$ and $3x-5y+ 2z= 0$
and $PQ=PR= \sqrt{18}$ where the point $P$ is $(1, -2, 3)$ , then the area of the triangle $PQR$ is equal to
a.
$\frac{2}{3}\sqrt{38}$
b.
$\frac{4}{3}$
c.
$\frac{8}{3}\sqrt{38}$
d.
$\frac{\sqrt{38}}{152}$
$\sqrt{\,} _{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the solution curve $y=y(x)$ of the differential equation, $[\frac{x}{\sqrt{x^{2}-y^{2}}} +e\frac{y}{x}]x\frac{dy}{dx} =x+[\frac{x}{\sqrt{x^{2}-y^{2}}} +e\frac{y}{x}]y$ pass
through the points $(1, 0)$ and $(2\alpha ,\alpha ),\alpha > 0$ . Then $\alpha$ is equal to
a.
$\frac{1}{2}exp( \frac{\pi}{6} + -1\sqrt{e} )$
b.
$\frac{1}{2}exp(\frac{\pi}{3} + \sqrt{e}-1)$
c.
$exp(\frac{\pi}{6} + + 1\sqrt{e} )$
d.
$2 exp(\frac{\pi}{3} + -1\sqrt{e} )$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $p,q,r$ be three logical statements. Consider the compound statements
$S_{1} : ((~p) \vee q) \vee ((~p) \vee r)$ and $S_{2} :p\rightarrow (\rightarrow q\vee r)$
Then, which of the following is NOT true?
a.
If $S_{2}$ is True, then $S_{1}$ is True
b.
If $S_{2}$ is False, then $S_{1}$ is False
c.
If $S_{2}$ is False, then $S_{1}$ is True
d.
If $S_{1}$ is False, then $S_{2}$ is False
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let the plane $P : \vec{r}\cdot \vec{a}=d$ contain the line of intersection of two planes $\vec{r}\cdot (Ëi+ 3Ëj- Ëk)= 6$ and
$2$
$\vec{r}\cdot (-6Ëi+ 5Ëj- Ëk)= 7$ . If the plane $P$ passes through the point $(2, 3, \frac{1}{2})$ , then the value of $\frac{13\vec{a}}{d^{2}}$ is equal to
a.
$90$
b.
$93$
c.
$95$
d.
$97$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $y=y(x)$ be the solution of the differential equation $x(1 - x^{2}) \frac{dy}{dx} +(3x^{2}y- y-4x^{3})= 0,x> 1$ with
$y(2) = -2$ . Then $y(3)$ is equal to
a.
$-18$
b.
$-12$
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 $R_{1}$ and $R_{2}$ be relations on the set ${1, 2, âĶ , 50}$ such that $R_{1} =$ { $(p,p^{n}) :p$ is a prime and $n\geq 0$ is an
integer} and $R_{2} =$ { $(p,p^{n}) :p$ is a prime and $n= 0$ or $1$ }. Then, the number of elements in $R_{1}- R_{2}$ is ____.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The number of positive integers $k$ such that the constant term in the binomial expansion of
$(2x^{3} + \frac{3}{x^{k}})^{12},x\neq 0$ is $2^{8} \cdot l$ , where $l$ is an odd integer, is ______.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $A= {1,a_{1},a_{2}âĶ âĶa_{18}, 77}$ be a set of integers with $1 <a_{1} <a_{2} < âĶ . . <a_{18} < 77$ . Let the set
$A+A= {x+y:x,y\in A}$ contain exactly $39$ elements. Then, the value of $a_{1}+a_{2}+ âĶ . . +a_{18}$ is equal to
______.
Numerical answer locked.
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The acute angle between the planes $P_{1}$ and $P_{2}$ , when $P_{1}$ and $P_{2}$ are the planes passing through the intersection
of the planes $5x+ 8y+ 13z-29 = 0$ and $8x-7y+z-20 = 0$ and the points $(2, 1, 3)$ and $(0, 1, 2)$ ,
respectively, is
a.
$\frac{\pi}{3}$
b.
$\frac{\pi}{4}$
c.
$\frac{\pi}{6}$
d.
$\frac{\pi}{12}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $A_{1},A_{2},A_{3}, âĶ âĶ$ be an increasing geometric progression of positive real numbers. If
$A_{1} A_{3} A_{5} A_{7} = \frac{1}{1296}$ and $A_{2}+A_{4} = \frac{7}{36}$ , then, the value of $A_{6}+A_{8}+A_{10}$ is equal to
a.
$43$
b.
$33$
c.
$37$
d.
$48$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
