Two fixed frictionless inclined plane making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown in the figure.
Two block $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to
$B$ ?
a.
$4.9\,ms^{-2}$ in horizontal direction
b.
$9.8\,ms^{-2}$ in vertical direction
c.
zero
d.
$4.9\,ms^{-2}$ in vertical direction
Correct Answer
No explanation saved for this question yet.
Q2mcq
If a source of power $4\,kW$ produces $10^{20}$ photons/second, the radiation belong to a part of the spectrum called
a.
X-rays
Correct Answer
b.
ultraviolet rays
c.
microwaves
d.
$\gamma$ -rays
No explanation saved for this question yet.
Q3mcq
The equation of a wave on a string of linear mass density $0.04\,kg\,m^{-1}$ is given by
$y= 0.02(\,m) sin[2\pi (\frac{t}{0.04(\,s)} - \frac{x}{0.50(\,m)})]$ . The tension in the string is
a.
$4.0\,N$
b.
$12.5\,N$
c.
$0.5\,N$
d.
$6.25\,N$
Correct Answer
No explanation saved for this question yet.
Q4mcq
The respective number of significant figures for the numbers $23.023, 0.0003$ and $2.1 \times 10$ are
a.
$5, 1, 2$
Correct Answer
b.
$5, 1, 5$
c.
$5, 5, 2$
d.
$4, 4, 2$
No explanation saved for this question yet.
Q5mcq
Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic
collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions. Of the four
choices given after the statements, choose the one that best describes the two statements. Of the four choices
given after the statements, choose the one that best describes the two statements.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
Correct Answer
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation of
Statement1
c.
Statement-1 is false, Statement-2 is true.
d.
Statement-1 is true, Statement-2 is false.
No explanation saved for this question yet.
Q6mcq
A particle is moving with velocity $\vec{v}= K(y\hat{i}+ x\hat{j})$ , where $K$ is a constant. The general equation for its path is
a.
$y=x^{2}+$ constant
b.
$y^{2} =x+$ constant
c.
$xy=$ constant
d.
$y^{2} =x^{2}+$ constant
Correct Answer
No explanation saved for this question yet.
Q7mcq
A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of
the cycle, volume of the gas increases from $V$ to $32\,V$ the efficiency of the engine is
a.
$0.5$
b.
$0.75$
Correct Answer
c.
$0.99$
d.
$0.25$
No explanation saved for this question yet.
Q8mcq
The combination of gates shown below yields
a.
OR gate
Correct Answer
b.
NOT gate
c.
XOR gate
d.
NAND gate
No explanation saved for this question yet.
Q9mcq
Two conductors have the same resistance at $0^{\circ }C$ but their temperature coefficients of resistance are $\alpha _{1}$ and $\alpha _{2}$ .
The respective temperature coefficients of their series and parallel combinations are nearly
A small particle of mass $m$ is projected at an angle $\theta$ with the $x$ -axis with an initial velocity $v_{0}$ in the $x -y$
plane as shown in the figure. At a time $t< \frac{v_{0}sin\theta}{g}$ , the angular momentum of the particle is where $\hat{i}, \hat{j}$ and $\hat{k}$ are
unit vectors along $x, y$ and $z$ -axis respectively.
An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I) =\mu _{0}+\mu _{2}I$ , where $\mu _{0}$ and
$\mu _{2}$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with
increasing radius. The initial shape of the wave front of the beam is
a.
convex
b.
concave
c.
convex near the axis and concave near the
periphery
d.
planar
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A rectangular loop has a sliding connector PQ of length $\ell$ and resistance $R\Omega$ and it is moving with a speed $v$ as
shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents
$I_{1},I_{2}$ and $I$ are
a.
$I_{1} = -I_{2} = \frac{B\ell v}{R}, I = \frac{2\,B\ell v}{R}$
A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of
light is $C$ . The speed of daughter nuclei is
a.
$c\frac{\Delta m}{M+\Delta m}$
b.
$c\sqrt{\frac{2\Delta m}{M}}$
c.
$c\sqrt{\frac{\Delta m}{M}}$
d.
$c\sqrt{\frac{\Delta m}{M+\Delta m}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A ball is made of a material of density $\rho$ where $\rho _{oil\,} <\rho <\rho _{water\,}$ with $\rho _{oil\,}$ and $\rho _{water\,}$ representing the
densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in
a mixture of this oil and water, which of the following pictures represents its equilibrium position?
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I) =\mu _{0}+\mu _{2}I$ , where $\mu _{0}$ and
$\mu _{2}$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with
increasing radius. The speed of light in the medium is
a.
minimum on the axis of the beam
b.
the same everywhere in the beam
c.
directly proportional to the intensity I
d.
maximum on the axis of the beam
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is $V_{0}$ and the maximum
kinetic energy of the photoelectrons is $K_{max}$ . When the ultraviolet light is replaced by $X-$ rays, both $V_{0}$ and
$K_{max}$ increase. Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value
because of the range of frequencies present in the incident light. Of the four choices given after the statements,
choose the one that best describes the two statements.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation of
Statement- 1.
c.
Statement-1 is false, Statement-2 is true.
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.
Let $C$ be the capacitance of a capacitor discharging through a resistor R. Suppose $t_{1}$ is the time taken for the
energy stored in the capacitor to reduce to half its initial value and $t_{2}$ is the time taken for the charge to reduce
to one-fourth its initial value. Then the ratio $t_{1}/t_{2}$ will be
a.
1
b.
$\frac{1}{2}$
c.
$\frac{1}{4}$
d.
2
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here $\theta$
is measured from the $x$ -axis)
An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I) =\mu _{0}+\mu _{2}I$ , where $\mu _{0}$ and
$\mu _{2}$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with
increasing radius. As the beam enters the medium, it will
a.
diverge
b.
converge
c.
diverge near the axis and converge near the
periphery
d.
travel as a cylindrical beam
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of
light is $c$ . 40. The binding energy per nucleon for the parent nucleus is $E_{1}$ and that for the daughter nuclei is
$E_{2}$ . Then
a.
$E_{2} = 2E_{1}$
b.
$E_{1} >E_{2}$
c.
$E_{2} >E_{1}$
d.
$E_{1} = 2E_{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Two long parallel wires are at a distance $2\,d$ apart. They carry steady equal current flowing out of the plane of
the paper as shown. The variation of the magnetic field along the line $XX$ ' is given by
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In a series LCR circuit $R= 200\Omega$ and the voltage and the frequency of the main supply is $220\,V$ and $50\,Hz$
respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$ . On
taking out the inductor from the circuit the current leads the voltage by $30^{\circ }$ . The power dissipated in the LCR
circuit is
a.
$305\,W$
b.
$210\,W$
c.
Zero W
d.
$242\,W$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' $P$ '
is such that it sweeps out a length $s=t^{3} + 5$ , where $s$ is in metres and $t$ is in seconds. The radius of the path is
$20\,m$ . The acceleration of ' $P$ ' when $t= 2\,s$ is nearly
a.
$13\,m/s^{2}$
b.
$12\,m/s^{2}$
c.
$7.2\,m/s^{2}$
d.
$14\,m/s^{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r) =\rho _{0}(\frac{5}{4} - \frac{r}{R})$
upto $r=R$ , and $\rho (r) = 0$ for $r>R$ , where $r$ is the distance from the origin. The electric field at a distance
$r(r<R)$ from the origin is given by
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$
with each other. When suspended in a liquid of density $0.8\,g\,cm^{-3}$ , the angle remains the same. If density of
the material of the sphere is $16\,g\,cm^{-3}$ , the dielectric constant of the liquid is
a.
4
b.
3
c.
2
d.
1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A radioactive nucleus (initial mass number $A$ and atomic number Z) emits $3\alpha$ -particles and 2 positrons. The
ratio of number of neutrons to that of protons in the final nucleus will be
a.
$\frac{A-Z-8}{Z-4}$
b.
$\frac{A-Z-4}{Z-8}$
c.
$\frac{A-Z-12}{Z-4}$
d.
$\frac{A-Z-4}{Z-2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The potential energy function for the force between two atoms in a diatomic molecule is approximately given
by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^{6}}$ , where a and $b$ are constants and $x$ is the distance between the atoms. If the dissociation
energy of the molecule is $D= [U(x= \infty ) - U_{at equilbrium\,}],D$ is
a.
$\frac{b^{2}}{2a}$
b.
$\frac{b^{2}}{12a}$
c.
$\frac{b^{2}}{4a}$
d.
$\frac{b^{2}}{6a}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the
change in freezing point of water $(\Delta T_{f})$ , when $0.01\,mol$ of sodium sulphate is dissolved in $1\,kg$ of water, is
$(K_{f} = 1.86\,K\,kg\,mol^{-1})$
a.
$0.0372\,K$
b.
$0.0558\,K$
c.
$0.0744\,K$
d.
$0.0186\,K$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Three reactions involving $H_{2}PO^{-}_{4}$ are given below : (i) $H_{3}PO_{4}+ H_{2}O \rightarrow H\rightarrow_{3}O^{+} + H_{2}PO^{-}_{4}$ (ii)
$H_{2}PO^{-}_{4} + H_{2}O \rightarrow HPO\rightarrow^{2-}_{4} + H_{3}O^{+}$ (iii) $H_{2}PO^{-}_{4} + OH^{-} \rightarrow H\rightarrow_{3}PO_{4}+ O^{2-}$ In which of the above does
$H_{2}PO^{-}_{4}$ act as an acid ?
a.
(ii) only
b.
(i) and (ii)
c.
(iii) only
d.
(i) only
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
If $10^{-4}dm^{3}$ of water is introduced into a $1.0dm^{3}$ flask to $300\,K$ , how many moles of water are in the vapour
phase when equilibrium is established? (Given : Vapour pressure of $H_{2}O$ at $300\,K$ is
$3170\,Pa; R = 8.314\,J\,K^{-1}\,mol^{-1}$ )
a.
$5.56 \times 10^{-3}\,mol$
b.
$1.53 \times 10^{-2}\,mol$
c.
$4.46 \times 10^{-2}\,mol$
d.
$1.27 \times 10^{-3}\,mol$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$29.5mg$ of an organic compound containing nitrogen was digested according to Kjeldahl's method and the
evolved ammonia was absorbed in $20\,mL$ of $0.1MHCl$ solution. The excess of the acid required $15\,mL$ of
$0.1MNaOH$ solution for complete neutralization. The percentage of nitrogen in the compound is
a.
$59.0$
b.
$47.4$
c.
$23.7$
d.
$29.5$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A solution containing $2.675\,g$ of $CoCl_{3}.6NH_{3}$ (molar mass $= 267.5\,g\,mol^{-1}$ ) is passed through a cation
exchanger. The chloride ions obtained in solution were treated with excess of $AgNO_{3}$ to give $4.78\,g$ of $AgCl$
(molar mass $= 143.5\,g\,mol^{-1}$ ). The formula of the complex is (At. Mass of $Ag = 108u$ )
a.
$[Co(NH_{3})_{6}]Cl_{3}$
b.
$[CoCl_{2}(NH_{3})_{4}]Cl$
c.
$[CoCl_{3}(NH_{3})_{3}]$
d.
$[CoCl(NH_{3})_{5}]Cl_{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The time for half life period of a certain reaction $A\rightarrow \rightarrow$ products is 1 hour. When the initial concentration of the
reactant ' $A$ ', is $2.0\,mol\,L^{-1}$ , how much time does it take for its concentration to come from $0.50$ to
$0.25\,mol\,L^{-1}$ if it is a zero order reaction?
a.
$4\,h$
b.
$0.5\,h$
c.
$0.25\,h$
d.
$1\,h$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
On mixing, heptane and octane form an ideal solution. At $373\,K$ , the vapour pressures of the two liquid
components (heptane and octane) are $105kPa$ and $45kPa$ respectively. Vapour pressure of the solution
obtained by mixing $25.0\,g$ of heptane and $35\,g$ of octane will be (molar mass of heptane $= 100\,g\,mol^{-1}$ an dof
octane $= 114\,g\,mol^{-1}$ ).
a.
$72.0kPa$
b.
$36.1kPa$
c.
$96.2kPa$
d.
$144.5kPa$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The energy required to break one mole of $Cl -Cl$ bonds in $Cl_{2}$ is $242\,kJ\,mol^{-1}$ . The longest wavelength of
light capable of breaking a single $Cl -Cl$ bond is $(c = 3 \times 10^{8}\,ms^{-1}$ and $N_{A} = 6.02 \times 10^{23}\,mol^{-1})$
a.
$594\,nm$
b.
$640\,nm$
c.
$700\,nm$
d.
$494\,nm$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For a particular reversible reaction at temperature $T, \Delta H$ and $\Delta S$ were found to be both $+ve$ . If $T_{e}$ is the
temperature at equilibrium, the reaction would be spontaneous when
a.
$T_{e} >T$
b.
$T > T_{e}$
c.
$T_{e}$ is 5 times $T$
d.
$T =T_{e}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The standard enthalpy of formation of $NH_{3}$ is $-46.0\,kJ\,mol^{-1}$ . If the enthalpy of formation of $H_{2}$ from its
atoms is $-436\,kJ\,mol^{-1}$ and that of $N_{2}$ is $-712\,kJ\,mol^{-1}$ , the average bond enthalpy of $N -H$ bond in $NH_{3}$
is
a.
$-964\,kJ\,mol^{-1}$
b.
$+352\,kJ\,mol^{-1}$
c.
$+1056\,kJ\,mol^{-1}$
d.
$-1102\,kJ\,mol^{-1}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
In aqueous solution the ionization constants for carbonic acid are $K_{1} = 4.2 \times 10^{-7}$ and $K_{2} = 4.8 \times 10^{-11}$
Select the correct statement for a saturated $0.034M$ solution of the carbonic acid.
a.
The concentration of $CO^{2-}_{3}$ is $0.034M$ .
b.
The concentration of $CO^{2-}_{3}$ is greater than that of
$HCO^{-}_{3}$ .
c.
The concentration of $H^{+}$ and $HCO^{-}_{3}$ are
approximately equal.
d.
The concentration of $H^{+}$ is double that of $CO^{2-}_{3}$ .
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
At $25^{\circ }C$ , the solubility product of $Mg(OH)_{2}$ is $1.0 \times 10^{-11}$ . At which $pH$ , will $Mg^{2+}$ ions start precipitating
in the form of $Mg(OH)_{2}$ from a solution of $0.001MMg^{2+}$ ions ?
a.
9
b.
10
c.
11
d.
8
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The Gibbs energy for the decomposition of $Al_{2}O_{3}$ at $500^{\circ }C$ is as follows :
$\rightarrow 4 -1$
$\frac{2}{3}Al O \rightarrow Al + O , \Delta G = +966\,kJ\,mol$
$^{2}^{3} 3 ^{2}^{r}$
The potential difference needed for electrolytic reduction of $Al_{2}O_{3}$ at $500^{\circ }C$ is at least
a.
$4.5\,V$
b.
$3.0\,V$
c.
$2.5\,V$
d.
$5.0\,V$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
The line $L$ given by $\frac{x}{5} + \frac{y}{b} = 1$ passes through the point $(13, 32)$ . The line $K$ is parallel to $L$ and has the
equation $\frac{x}{c} + \frac{y}{3} = 1$ . Then the distance between $L$ and $K$ is
a.
$\sqrt{17}$
b.
$\frac{17}{\sqrt{15}}$
c.
$\frac{23}{\sqrt{17}}$
d.
$\frac{23}{\sqrt{15}}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $p(x)$ be a function defined on $R$ such that $p'(x) =p'(1 - x)$ , for all $x\in [0, 1],p(0) = 1$ and $p(1) = 41$ .
Then $\int _{0}^{1} p(x)dx$ equals
a.
21
b.
41
c.
42
d.
$\sqrt{41}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Consider the following relations: $R= {(x,y) | x,y$ are real numbers and $x=$ wy for some rational number w
$}$ ; $S ={(\frac{m}{n} , \frac{p}{q})| m,n,p$ and $q$ are integers such that $n,q\neq 0$ and $qm=pn}$ . Then
a.
neither $R$ nor $S$ is an equivalence relation
b.
$S$ is an equivalence relation but $R$ is not an
equivalence relation
c.
$R$ and $S$ both are equivalence relations
d.
$R$ is an equivalence relation but $S$ is not an
equivalence relation
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$k-2x, \,if\,x\leq -1$
Let $f :R\rightarrow \rightarrow R$ be defined by $f(x) ={$ . If $f$ has a local minimum at $x= -1$ , then a
$2x+ 3, \,if\,x> -1$
possible value of $k$ is
a.
0
b.
$- \frac{1}{2}$
c.
$-1$
d.
1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $A$ be a $2 \times 2$ matrix with non-zero entries and let $A^{2} = 1$ , where 1 is $2 \times 2$ identity matrix. Define
$Tr(A) =$ sum of diagonal elements of $A$ and $|A| =$ determinant of matrix $A$ . Statement-1: $Tr(A) = 0$
Statement-2: $|A| = 1$
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation for
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 for
Statement-1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A line $AB$ in three-dimensional space makes angles $45^{\circ }$ and $120^{\circ }$ with the positive $x$ -axis and the positive $y$ -
axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$ -axis, then $\theta$ equals
a.
$45^{\circ }$
b.
$60^{\circ }$
c.
$75^{\circ }$
d.
$30^{\circ }$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given
to be 2 and 4 , respectively. The variance of the combined data set is
a.
$\frac{11}{2}$
b.
6
c.
$\frac{13}{2}$
d.
$\frac{5}{2}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $S$ be a non-empty subset of R. Consider the following statement: $P$ : There is a rational number $x \in S$ such
that $x > 0$ . Which of the following statements is the negation of the statement $P$ ?
a.
There is no rational number $x\in S$ such that
$x\leq 0$
b.
Every rational number $x\in S$ satisfies $x\leq 0$
c.
$x\in S$ and $x\leq 0 \Rightarrow x$ is not rational
d.
There is a rational number $x\in S$ such that $x\leq 0$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f :R\rightarrow \rightarrow R$ be a positive increasing function with $lim_{x\rightarrow \infty \rightarrow } \frac{f(3x)}{f(x)} = 1$ . Then $lim_{x\rightarrow \infty \rightarrow } \frac{f(2x)}{f(x)} =$
a.
$\frac{2}{3}$
b.
$\frac{3}{2}$
c.
3
d.
1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
$\rightarrow \rightarrow$
Let $a= \hat{j}- \hat{k}$ and $\vec{c}= \hat{i}- \hat{j}- \hat{k}$ . Then vector $\vec{b}$ satisfying $a\times \vec{b}+ c= 0$ and $a\cdot \vec{b}= 3$ is
a.
$2\hat{i}- \hat{j}+ 2\hat{k}$
b.
$\hat{i}- \hat{j}-2\hat{k}$
c.
$\hat{i}+ \hat{j}-2\hat{k}$
d.
$-\hat{i}+ \hat{j}-2\hat{k}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Four numbers are chosen at random (without replacement) from the set ${1, 2, 3, … . , 20}$ . Statement-1: The
probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$ . Statement-2: If the
four chosen numbers from an AP, then the set of all possible values of common difference is
${\pm 1, \pm 2, \pm 3, \pm 4, \pm 5}$ .
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation for
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 for
Statement-1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{th\,}$ minute. If
$a_{1} = a_{2} = … … = a_{10} = 150$ and $a_{10}, a_{11}, … …$ are in A.P. with common difference $-2$ , then the time taken
by him to count all notes is
a.
34 minutes
b.
125 minutes
c.
135 minutes
d.
24 minutes
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Statement-1: The point $A(3, 1, 6)$ is the mirror image of the point $B(1, 3, 4)$ in the plane $x- y+z= 5$ .
Statement-2: The plane $x- y+z= 5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4)$ .
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation for
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 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 $f : (-1, 1) \rightarrow \rightarrow R$ be a differentiable function with $f(0) = -1$ and $f'(0) = 1$ . Let $g(x) = [f(2f(x) + 2)]^{2}$ .
Then $g'(0) =$
a.
$-4$
b.
0
c.
$-2$
d.
4
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls
are taken out at random and then transferred to the other. The number of ways in which this can be done is
a.
36
b.
66
c.
108
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 vectors $\vec{a}= \hat{i}- \hat{j}+ 2\hat{k}, \vec{b}= 2\hat{i}+ 4\hat{j}+ \hat{k}$ and $\vec{c}=\lambda \hat{i}+ \hat{j}+\mu \hat{k}$ are mutually orthogonal, then $(\lambda ,\mu ) =$
a.
$(2, -3)$
b.
$(-2, 3)$
c.
$(3, -2)$
d.
$(-3, 2)$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at
random without replacement from the urn. The probability that the three balls have different colour is
a.
$\frac{2}{7}$
b.
$\frac{1}{21}$
c.
$\frac{2}{23}$
d.
$\frac{1}{3}$
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
Let $f :R\rightarrow \rightarrow R$ be a continuous function defined by $f(x) = \frac{1}{e^{x}+2e^{-}^{x}}$ . Statement-1: $f(c) = \frac{1}{3}$ , for some $c\in R$ .
Statement-2: $0 <f(x) \leq \frac{1}{2\sqrt{2}}$ , for all $x\in R$
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the correct explanation for
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 for
Statement-1
Correct Answer & Step-by-Step Solution Locked
Sign in free to reveal the correct answer and AI explanation for this question.
