question_answer1) If\[{{(27)}^{999}}\]is divided by 7, then the remainder is: [JEE Online 08-04-2017]
A) 3
B) 1
C) 6
D) 2
View Answer play_arrowquestion_answer2) If\[S=\left\{ x\in [0,2\pi ]:\left| \begin{matrix} 0 & \cos x & -\sin x \\ \sin x & 0 & \cos x \\ \cos x & \sin x & 0 \\ \end{matrix} \right|=0 \right\},\] Then \[\sum\limits_{x\in S}^{{}}{\tan }\left( \frac{\pi }{3}+x \right)\] [JEE Online 08-04-2017]
A) \[4+2\sqrt{3}\]
B) \[-2-\sqrt{3}\]
C) \[-2+\sqrt{3}\]
D) \[-4-2\sqrt{3}\]
View Answer play_arrowquestion_answer3) Let A be any \[3\times 3\]invertible matrix. Then which one of the following is not Always true? [JEE Online 08-04-2017]
A) \[adj(adj(1))=|A{{|}^{2}}.{{(adj(1))}^{-1}}\]
B) \[adj(adj(1))=|A|.{{(adj(1))}^{-1}}\]
C) \[adj(adj(1))=|A|.A\]
D) \[adj(1)=|A|.{{A}^{-1}}\]
View Answer play_arrowquestion_answer4) The value of \[{{\tan }^{-1}}\left[ \frac{\sqrt{1+{{x}^{2}}}+\sqrt{1-{{x}^{2}}}}{\sqrt{1+{{x}^{2}}}-\sqrt{1-{{x}^{2}}}} \right],|x|<\frac{1}{2},x\ne 0,\]is equal to: [JEE Online 08-04-2017]
A) \[\frac{\pi }{4}+\frac{1}{2}{{\cos }^{-1}}{{x}^{2}}\]
B) \[\frac{\pi }{4}-{{\cos }^{-1}}{{x}^{2}}\]
C) \[\frac{\pi }{4}-\frac{1}{2}{{\cos }^{-1}}{{x}^{2}}\]
D) \[\frac{\pi }{4}+{{\cos }^{-1}}{{x}^{2}}\]
View Answer play_arrowquestion_answer5) The area (in sq. units) of the parallelogram whooshed diagonals are along the vectors \[8\hat{i}-6\hat{j}\]and\[3\hat{i}+4\hat{j}-12\hat{k},\]is: [JEE Online 08-04-2017]
A) 20
B) 65
C) 52
D) 26
View Answer play_arrowquestion_answer6) The integral\[\int\limits_{\frac{\pi }{12}}^{\frac{\pi }{4}}{\frac{8\cos 2x}{{{(tanx+cosx)}^{3}}}}dx\]equals: [JEE Online 08-04-2017]
A) \[\frac{13}{256}\]
B) \[\frac{15}{64}\]
C) \[\frac{13}{32}\]
D) \[\frac{15}{128}\]
View Answer play_arrowquestion_answer7) Let\[z\in C,\]the set of complex numbers. Then the equation, \[2|z+3i|-|z-i|=0\]a circle with radius\[\frac{8}{3}.\] [JEE Online 08-04-2017]
A) a circle with radius\[\frac{8}{3}\]
B) an ellipse with length of minor axis\[\frac{16}{9}\]
C) an ellipse with length of major axis\[\frac{16}{3}\]
D) a circle with diameter\[\frac{10}{3}\]
View Answer play_arrowquestion_answer8) If the um of the first n terms of the series\[\sqrt{3}+\sqrt{75}+\sqrt{243}+\sqrt{507}+........\]is\[435\sqrt{3},\]then n equals. [JEE Online 08-04-2017]
A) 13
B) 15
C) 29
D) 18
View Answer play_arrowquestion_answer9) The tangent at the point (2,-2) to the curve\[{{x}^{2}}{{y}^{2}}-2x=4(1-y)\]does not pass through the point: [JEE Online 08-04-2017]
A) (-2,-7)
B) (8, 5)
C) (-4,-9)
D) \[\left( 4,\frac{1}{3} \right)\]
View Answer play_arrowquestion_answer10) Let \[f(x)={{2}^{10}}dx+1\]and\[g(x)={{3}^{10}}x-1.\]If\[(fog)(x)=x,\]then x is equal to: [JEE Online 08-04-2017]
A) \[\frac{{{2}^{10}}-1}{{{2}^{10}}-{{3}^{-10}}}\]
B) \[\frac{1-{{2}^{-10}}}{{{3}^{10}}-{{2}^{-10}}}\]
C) \[\frac{{{3}^{10}}-1}{{{3}^{10}}-{{2}^{-10}}}\]
D) \[\frac{1-{{3}^{-10}}}{{{2}^{10}}-{{3}^{-10}}}\]
View Answer play_arrowquestion_answer11) The proposition\[(\tilde{\ }p)V(p\wedge \tilde{\ }q)\]is equivalent to: [JEE Online 08-04-2017]
A) \[P\to \tilde{\ }q\]
B) \[P\wedge \tilde{\ }q\]
C) \[q\to p\]
D) \[P\vee \tilde{\ }q\]
View Answer play_arrowquestion_answer12) If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is: [JEE Online 08-04-2017]
A) 47th
B) 45th
C) 46th
D) 44th
View Answer play_arrowquestion_answer13) The curve satisfying the differential equation, \[ydx-(x+3{{y}^{2}})dy=9\]and passing through the point (1,1), also passes through the point: [JEE Online 08-04-2017]
A) \[\left( \frac{1}{4},-\frac{1}{2} \right)\]
B) \[\left( -\frac{1}{3},\frac{1}{3} \right)\]
C) \[\left( \frac{1}{4},\frac{1}{2} \right)\]
D) \[\left( \frac{1}{3},-\frac{1}{3} \right)\]
View Answer play_arrowquestion_answer14) An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tails is: [JEE Online 08-04-2017]
A) \[\frac{127}{128}\]
B) \[\frac{63}{64}\]
C) \[\frac{255}{256}\]
D) \[\frac{1}{2}\]
View Answer play_arrowquestion_answer15) If the arithmetic mean of two numbers and b,a, > b > 0. Is five times their geometric mean, then\[\frac{a+b}{a-b}\]is equal to: [JEE Online 08-04-2017]
A) \[\frac{7\sqrt{3}}{12}\]
B) \[\frac{3\sqrt{2}}{4}\]
C) \[\frac{\sqrt{6}}{2}\]
D) \[\frac{5\sqrt{6}}{12}\]
View Answer play_arrowquestion_answer16) \[\underset{x\to 3}{\mathop{\lim }}\,\frac{\sqrt{3x}-3}{\sqrt{2x}-4-\sqrt{2}}\]is equal to: [JEE Online 08-04-2017]
A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{1}{2\sqrt{2}}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[\sqrt{3}\]
View Answer play_arrowquestion_answer17) The locus of the point of intersection of the straight lines,\[tx-2y-3t=0\]\[x-2ty+3=0\]\[(t\in R),\]is: [JEE Online 08-04-2017]
A) A hyperbola with the length of conjugate axis 3
B) a hyperbola with eccentricity\[\sqrt{5}\]
C) an ellipse with the length of major axis 6
D) an ellipse with eccentricity\[\frac{2}{\sqrt{5}}\]
View Answer play_arrowquestion_answer18) If\[y={{\left[ x+\sqrt{{{x}^{2}}-1} \right]}^{15}}+y{{\left[ x-\sqrt{{{x}^{2}}-1} \right]}^{15}},\]then\[({{x}^{2}}-1)\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}\]is equal to: [JEE Online 08-04-2017]
A) \[224{{y}^{2}}\]
B) \[125y\]
C) \[225y\]
D) \[225{{y}^{2}}\]
View Answer play_arrowquestion_answer19) The area (in sq. units) of the smaller portion enclosed between the curves, \[{{x}^{2}}+{{y}^{2}}=4\]and\[{{y}^{2}}=3x,\]is: [JEE Online 08-04-2017]
A) \[\frac{1}{\sqrt{3}}+\frac{4\pi }{3}\]
B) \[\frac{1}{\sqrt{3}}+\frac{2\pi }{3}\]
C) \[\frac{1}{2\sqrt{3}}-\frac{\pi }{3}\]
D) \[\frac{1}{2\sqrt{3}}+\frac{2\pi }{3}\]
View Answer play_arrowquestion_answer20) If the common tangents to the parabola \[{{x}^{2}}+4y\]and the circle,\[{{x}^{2}}+{{y}^{2}}=4\]intersect at the point P, then the distance of P from the origin, is: [JEE Online 08-04-2017]
A) \[2\left( \sqrt{2}+1 \right)\]
B) \[3+2\sqrt{2}\]
C) \[\sqrt{2}+1\]
D) \[2\left( 3+2\sqrt{2} \right)\]
View Answer play_arrowquestion_answer21) The line of intersection of the planes \[\vec{r}.\left( 3\hat{i}-\hat{j}+\hat{k} \right)=1\]and\[\vec{r}.\left( \hat{i}+4\hat{j}-2\hat{k} \right)=2,\]is: [JEE Online 08-04-2017]
A) \[\frac{x-\frac{6}{13}}{2}=\frac{y-\frac{5}{13}}{7}=\frac{z}{-13}\]
B) \[\frac{x-\frac{7}{7}}{2}=\frac{y}{-7}=\frac{z+\frac{5}{7}}{13}\]
C) \[\frac{x-\frac{6}{13}}{2}=\frac{y-\frac{5}{13}}{-7}=\frac{z}{-13}\]
D) \[\frac{x-\frac{4}{7}}{-2}=\frac{y}{7}=\frac{z-\frac{5}{7}}{13}\]
View Answer play_arrowquestion_answer22) If a point P has co-ordinates (0,-2) and Q is any point on the circle,\[{{x}^{2}}+{{y}^{2}}-5x-y+5=0,\]then the maximum value of\[{{(PQ)}^{2}}\]is: [JEE Online 08-04-2017]
A) \[8+5\sqrt{3}\]
B) \[\frac{47+10\sqrt{6}}{2}\]
C) \[14+5\sqrt{3}\]
D) \[\frac{25+\sqrt{6}}{2}\]
View Answer play_arrowquestion_answer23) The mean age of 25 teaches in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teachers is: [JEE Online 08-04-2017]
A) 35
B) 40
C) 25
D) 30
View Answer play_arrowquestion_answer24) Let p (x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remainder 6 when divided by x + 1, then: [JEE Online 08-04-2017]
A) \[p(-2)=19\]
B) \[p(2)=19\]
C) \[p(-2)=11\]
D) \[p(2)=11\]
View Answer play_arrowquestion_answer25) Consider an ellipse, whose centre is at the origin and its major axis is along the x - axis. if its eccentricity is \[\frac{3}{5}\]and the distance between its foci is 6, then the area ( in sq. units ) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is : [JEE Online 08-04-2017]
A) 32
B) 80
C) 40
D) 8
View Answer play_arrowquestion_answer26) If two parallel chords of the a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles \[{{\cos }^{-1}}\left( \frac{1}{7} \right)\]and\[{{\sec }^{-1}}(7)\]at the centre respectively, then the distance between these chords, is : [JEE Online 08-04-2017]
A) \[\frac{8}{\sqrt{7}}\]
B) \[\frac{16}{7}\]
C) \[\frac{4}{\sqrt{7}}\]
D) \[\frac{8}{7}\]
View Answer play_arrowquestion_answer27) The number of real values of \[\lambda \]for which the system of linear equations \[2x+4y-\lambda z=0\] \[4x+\lambda y+2z=0\] \[\lambda x+2y+2z=0\] has infinitely many solutions, is : [JEE Online 08-04-2017]
A) 3
B) 1
C) 2
D) 0
View Answer play_arrowquestion_answer28) The coordinates of the foot of the perpendicular from the point (1, - 2,1) on the plane containing the lines, \[\frac{x+1}{6}=\frac{y-1}{7}=\frac{z-3}{8}\]and \[\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-3}{7},\]is: [JEE Online 08-04-2017]
A) (2, - 4, 2)
B) (1, 1, 1)
C) (0, 0, 0)
D) (0, 0, 0)
View Answer play_arrowquestion_answer29) Three persong P, Q and R independently try to hit a target. If the probabilities of their hitting the target are \[\frac{3}{4},\frac{1}{2}\]and\[\frac{5}{8}\]respectively, then the probability that the target is hit by P or Q but not by R is : [JEE Online 08-04-2017]
A) \[\frac{39}{64}\]
B) \[\frac{21}{64}\]
C) \[\frac{9}{64}\]
D) \[\frac{15}{64}\]
View Answer play_arrowquestion_answer30) The integral\[\int_{{}}^{{}}{\sqrt{1+2\cot x(cosecx+cotx)}dx}\]\[\left( 0<x<\frac{x}{2} \right)\]is equal to : (where C is a constant of integration ) [JEE Online 08-04-2017]
A) \[2\log \left( \sin \frac{x}{2} \right)+C\]
B) \[4\log \left( \sin \frac{x}{2} \right)+C\]
C) \[4\log \left( \cos \frac{x}{2} \right)+C\]
D) \[2\log \left( \cos \frac{x}{2} \right)+C\]
View Answer play_arrowquestion_answer31) A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increases by \[\Delta T.\] The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and \[\alpha \] its coefficient of linear expansion. Then, F is equal to - [JEE Online 08-04-2017]
A) \[IAY\alpha \Delta T\]
B) \[AY\alpha \Delta T\]
C) \[\frac{AY}{\alpha \Delta T}\]
D) \[{{I}^{2}}Y\alpha \Delta T\]
View Answer play_arrowquestion_answer32) A potentiometer PQ is set up to comapre two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key \[{{K}_{3}}\] is open. The balance point is at a length \[{{l}_{1}}\]cm from P when two way key \[{{K}_{3}}\] is plugged in between 2 and 1, while the balance point is at a length \[{{l}_{2}}\] cm from P when key \[{{K}_{3}}\] is plugged in between 3 and 1. The ratio of the two resistance \[\frac{{{R}_{1}}}{{{R}_{2}}},\] is found to be - [JEE Online 08-04-2017]
A) \[\frac{{{l}_{1}}}{{{l}_{1}}-{{l}_{2}}}\]
B) \[\frac{{{l}_{2}}}{{{l}_{2}}-{{l}_{1}}}\]
C) \[\frac{{{l}_{1}}}{{{l}_{1}}+{{l}_{2}}}\]
D) \[\frac{{{l}_{1}}}{{{l}_{2}}-{{l}_{1}}}\]
View Answer play_arrowquestion_answer33) A signal of frequency 20 kHz and peak voltage of 5 volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 volts. Choose the correct statement. [JEE Online 08-04-2017]
A) Modulation index = 5, side frequency bands are at 1400 kHz and 1000 kHz
B) Modulation index = 0.8, side frequency bands are at 1180 kHz and 1220 kHz
C) Modulation index = 0.2, side frequency bands are at 1200 kHz and 1180 kHz
D) Modulation index = 5, side frequency bands are at 21/2 kHz and 18.8 kHz
View Answer play_arrowquestion_answer34) A single slit of width b is illuminated by a coherent monochromatic light of wavelength \[\lambda \].If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e., distance between first minimum on either side of the central maximum) [JEE Online 08-04-2017]
A) 4.5 cm
B) 1.5 cm
C) 6.0 cm
D) 3.0 cm
View Answer play_arrowquestion_answer35) A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is - [JEE Online 08-04-2017]
A) 2 Hz
B) \[\frac{1}{4}Hz\]
C) \[\frac{1}{2\sqrt{2}}Hz\]
D) \[\frac{1}{2}Hz\]
View Answer play_arrowquestion_answer36) A magentic dipole in a constant magnetic field has - [JEE Online 08-04-2017]
A) maximum potential energy when the torque is maximum
B) zero potential energy when the torque is maximum
C) zero potential energy when the torque is minimum
D) minimum potential energy when the torque is maximum
View Answer play_arrowquestion_answer37) If the earth has no rotational motion, the weight of a person on the equation is W. Detrmine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight\[\frac{3}{4}W.\]Radius of the earth is 6400 km and \[g=10m/{{s}^{2}}.\] [JEE Online 08-04-2017]
A) \[0.63\times {{10}^{-3}}rad/s\]
B) \[0.28\times {{10}^{-3}}rad/s\]
C) \[1.1\times {{10}^{-3}}rad/s\]
D) \[0.83\times {{10}^{-3}}rad/s\]
View Answer play_arrowquestion_answer38) An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as \[t\to \infty \]is - [JEE Online 08-04-2017]
A) 3h
B) \[\infty \]
C) \[\frac{5}{3}h\]
D) \[\frac{8}{3}h\]
View Answer play_arrowquestion_answer39) The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains \[4\mu C\] charge, its radius will be: [Take:\[\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N-{{m}^{2}}/{{C}^{2}}\]] [JEE Online 08-04-2017]
A) 32 mm
B) 16 mm
C) 28 mm
D) 20 mm
View Answer play_arrowquestion_answer40) A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is - [JEE Online 08-04-2017]
A) \[\frac{2Mg}{2m+M}\]
B) \[\frac{2Mg}{2M+m}\]
C) \[\frac{2mg}{2M+m}\]
D) \[\frac{2mg}{2m+M}\]
View Answer play_arrowquestion_answer41) An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is - (Take \[{{C}_{v}}=1.4R,\]where R is gas constant) [JEE Online 08-04-2017]
A) 0.24
B) 0.15
C) 0.32
D) 0.08
View Answer play_arrowquestion_answer42) Time (T), velocity (3) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be - [JEE Online 08-04-2017]
A) \[[M]=[{{T}^{-1}}{{C}^{-2}}h]\]
B) \[[M]=[T{{C}^{-2}}h]\]
C) \[[M]=[{{T}^{-1}}{{C}^{-2}}{{h}^{-1}}]\]
D) \[[M]=[{{T}^{-1}}{{C}^{2}}h]\]
View Answer play_arrowquestion_answer43) In an experiment a sphere of aluminium of mass 0.20 kg is heated upto\[{{150}^{o}}C\]. Immediately, it is put into water of volume \[150cc\] at \[{{27}^{o}}C\] kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is\[{{40}^{o}}C\]. The specific heat of aluminium is - (take 4.2 Joule = 1 calorie) [JEE Online 08-04-2017]
A) \[434J/k{{g}^{-o}}C\]
B) \[378J/k{{g}^{-o}}C\]
C) \[315J/k{{g}^{-o}}C\]
D) \[476J/k{{g}^{-o}}C\]
View Answer play_arrowquestion_answer44) There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between in limits 589.0V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of \[60{}^\circ \] with the direction of the field? [JEE Online 08-04-2017]
A) 589.4 V
B) 589.5 V
C) 589.2 V
D) 589.6 V
View Answer play_arrowquestion_answer45) Magnetic field in a plane electromagnetic wave is given by\[\vec{B}={{B}_{0}}\sin (kx+\omega t)\hat{j}T\] Expression for corresponding electric field will be [JEE Online 08-04-2017]
A) \[\vec{E}=-{{B}_{0}}c\sin (kx+\omega t)\hat{k}V/m\]
B) \[\vec{E}={{B}_{0}}c\sin (kx-\omega t)\hat{k}V/m\]
C) \[\vec{E}={{B}_{0}}c\sin (kx+\omega t)\hat{k}V/m\]
D) \[\vec{E}=\frac{{{B}_{0}}}{c}\sin \,(kx+\omega t)\hat{k}V/m\]
View Answer play_arrowquestion_answer46) According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the \[{{\text{n}}^{\text{th}}}\] orbit is proportional to : (n = principal quantum number) [JEE Online 08-04-2017]
A) \[{{\text{n}}^{-3}}\]
B) \[{{\text{n}}^{-2}}\]
C) \[{{\text{n}}^{-4}}\]
D) \[{{\text{n}}^{-5}}\]
View Answer play_arrowquestion_answer47) Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre and perpendicular to its plane is I0 as shown in the figure. A cavithy DEF is cut out from the lamina, where D,E,F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is [JEE Online 08-04-2017]
A) \[\frac{15}{16}{{I}_{0}}\]
B) \[\frac{3{{I}_{0}}}{4}\]
C) \[\frac{7}{8}{{I}_{0}}\]
D) \[\frac{31{{I}_{0}}}{32}\]
View Answer play_arrowquestion_answer48) The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be - [JEE Online 08-04-2017]
A) more than \[\sqrt{3}v\]
B) equal to \[\sqrt{3}v\]
C) \[v\]
D) less than \[\sqrt{3}v\]
View Answer play_arrowquestion_answer49) What is the conductivity of a semiconductor sample having electron concentration of \[5\times {{10}^{18}}{{m}^{-3}},\] hole concentration of \[5\times {{10}^{19}}{{m}^{-3}},\] electron mobility of \[2.0{{m}^{2}}{{V}^{-1}}{{s}^{-1}}\]and hole mobility of \[0.01{{m}^{2}}{{V}^{-1}}{{s}^{-1}}\] (Take charge of electron as \[1.6\times {{10}^{-19}}C\]) [JEE Online 08-04-2017]
A) \[1.83{{(\Omega -m)}^{-1}}\]
B) \[1.68{{(\Omega -m)}^{-1}}\]
C) \[1.20{{(\Omega -m)}^{-1}}\]
D) \[0.59{{(W-m)}^{-1}}\]
View Answer play_arrowquestion_answer50) The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is : [JEE Online 08-04-2017]
A) 100
B) 106
C) 10-6
D) 10
View Answer play_arrowquestion_answer51) Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity? [JEE Online 08-04-2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer52) A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current \[I={{I}_{0}}\cos (\omega t).\]The emf induced in the smaller inner loop is nearly? [JEE Online 08-04-2017]
A) \[\pi {{\mu }_{0}}{{I}_{0}}\frac{{{a}^{2}}}{b}\omega \sin (\omega t)\]
B) \[\frac{\pi {{\mu }_{0}}{{I}_{0}}}{2}.\frac{{{a}^{2}}}{b}\omega \cos (\omega t)\]
C) \[\frac{\pi {{\mu }_{0}}{{I}_{0}}{{b}^{2}}}{a}\omega \cos (\omega t)\]
D) \[\frac{\pi {{\mu }_{0}}{{I}_{0}}}{2}.\frac{{{a}^{2}}}{b}\omega \sin (\omega t)\]
View Answer play_arrowquestion_answer53) A 9 V battery with internal resistance of \[0.5\Omega \] is connected across an infinite network as shown in the figure. All ammeters A1, A2, A3 and voltmeter V are ideal. Choose correct statement. [JEE Online 08-04-2017]
A) Reading of \[{{A}_{1}}\] is 18 A
B) Reading of V is 9 V
C) Reading of V is 7 V
D) Reading of \[{{A}_{1}}\] is 2 A
View Answer play_arrowquestion_answer54) Let the refractive index of a denser medium with respect to a rarer medium be \[{{n}_{12}}\]and its c critical angle be \[{{\theta }_{C}}.\]At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is \[90{}^\circ \]. Angle A given by - [JEE Online 08-04-2017]
A) \[{{\tan }^{-1}}(\sin {{\theta }_{C}})\]
B) \[\frac{1}{{{\tan }^{-1}}(\sin {{\theta }_{C}})}\]
C) \[{{\cos }^{-1}}(\sin {{\theta }_{C}})\]
D) \[\frac{1}{{{\cos }^{-1}}(\sin {{\theta }_{C}})}\]
View Answer play_arrowquestion_answer55) The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is \[10{{s}^{-1}}.\] [JEE Online 08-04-2017] At, t = 0 the displacement is 5 m. What is the maximum acceleration? The initial phase is\[\frac{\pi }{4}.\]
A) \[500m/{{s}^{2}}\]
B) \[750\sqrt{2}m/{{s}^{2}}\]
C) \[750m/{{s}^{2}}\]
D) \[500\sqrt{2}m/{{s}^{2}}\]
View Answer play_arrowquestion_answer56) Two wires \[{{W}_{1}}\] and \[{{W}_{2}}\] have the same radius r and respective densities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] such that\[{{\rho }_{2}}=4{{\rho }_{1}}.\]. They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in \[{{W}_{1}}\]to \[{{W}_{2}}\] is - [JEE Online 08-04-2017]
A) 4 : 1
B) 1 : 2
C) 1 : 1
D) 1 : 3
View Answer play_arrowquestion_answer57) An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure \[({{C}_{P}})\] and at constant volume \[({{C}_{V}})\]is [JEE Online 08-04-2017]
A) \[\frac{7}{5}\]
B) 6
C) \[\frac{7}{2}\]
D) \[\frac{5}{2}\]
View Answer play_arrowquestion_answer58) Two deuterons udnergo nuclear fusion to form a Helium nucleus. Energy released in this process is : [JEE Online 08-04-2017] (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
A) 23.6 MeV
B) 25.8 MeV
C) 30.2 MeV
D) 32.4 MeV
View Answer play_arrowquestion_answer59) In a certain region static electric and magentic fields exist. The magnetic field is given by \[\vec{B}={{B}_{0}}\left( \hat{i}+2\hat{j}-4\hat{k} \right).\]If a test charge moving with a velocity \[\vec{\upsilon }={{\upsilon }_{0}}\left( 3\hat{i}-\hat{j}+2\hat{k} \right)\]experience no force in that region, then the electric field in the region, in SI units, is - [JEE Online 08-04-2017]
A) \[\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( \hat{i}+\hat{j}+7\hat{k} \right)\]
B) \[\vec{E}=-{{\upsilon }_{0}}{{B}_{0}}\left( 3\hat{i}-2\hat{j}-4\hat{k} \right)\]
C) \[\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{i}+7\hat{k} \right)\]
D) \[\vec{E}={{\upsilon }_{0}}{{B}_{0}}\left( 14\hat{j}+7\hat{k} \right)\]
View Answer play_arrowquestion_answer60) In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
A) Every object that is weighted using this balance appears lighter than its actual weight
B) Left arm is shorter than the right arm
C) Both the arms are of same length
D) Left arm is longer than the right arm
View Answer play_arrowquestion_answer61) If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of \[H{{e}^{+}}\] is : [JEE Online 08-04-2017]
A) \[\frac{5A}{9}\]
B) \[\frac{36A}{7}\]
C) \[\frac{36A}{5}\]
D) \[\frac{9A}{5}\]
View Answer play_arrowquestion_answer62) Among the following, the essential amino acid is : [JEE Online 08-04-2017]
A) Valine
B) Alanine
C) Serine
D) Aspartic acid
View Answer play_arrowquestion_answer63) Identify the pollutant gases largely responsible for the discoloured and lustreless nature of marble of the Taj Mahal. [JEE Online 08-04-2017]
A) \[\text{S}{{\text{O}}_{\text{2}}}\,\text{and}\,{{\text{O}}_{\text{3}}}\]
B) \[{{\text{O}}_{3}}\,\text{and}\,C{{\text{O}}_{2}}\]
C) \[\text{S}{{\text{O}}_{2}}\,\text{and}\,N{{\text{O}}_{2}}\]
D) \[\text{C}{{\text{O}}_{2}}\,\text{and}\,N{{\text{O}}_{2}}\]
View Answer play_arrowquestion_answer64) Which of the following compounds will not undergo Friedel Craft's reaction with benzene? [JEE Online 08-04-2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer65) Which of the following is paramagnetic? [JEE Online 08-04-2017]
A) CO
B) \[N{{O}^{+}}\]
C) \[O_{2}^{2-}\]
D) \[{{B}_{2}}\]
View Answer play_arrowquestion_answer66) The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A. [JEE Online 08-04-2017]
A) 4.92 K
B) 9.84 K
C) 19.67 K
D) 2.45 K
View Answer play_arrowquestion_answer67) A solution containing a group-IV cation gives a precipitate on passing, \[{{H}_{2}}S.\]. A solution of this precipitate in dil. HCl produces a white precipitate with NaOH solution and bluish-white precipitate with basic potassium ferrocyanide. The cation is : [JEE Online 08-04-2017]
A) \[M{{n}^{2+}}\]
B) \[Z{{n}^{2+}}\]
C) \[N{{i}^{2+}}\]
D) \[C{{o}^{2+}}\]
View Answer play_arrowquestion_answer68) Which of the following statements is not true about partition chromatography? [JEE Online 08-04-2017]
A) Stationary phase is a finely divided solid adsorbent
B) Separation depends upon equilibration of solute between a mobile and a stationary phase
C) Paper chromatography is an example of partition chromatography
D) Mobile phase can be a gas
View Answer play_arrowquestion_answer69) Excess of NaOH (aq) was added to 100 mL of \[FeC{{l}_{3}}\](aq) resulting into 2.14 g of \[Fe{{(OH)}_{3}}.\] The molarity of \[FeC{{l}_{3}}\](aq) is : (Given molar mass of \[Fe=56gmo{{l}^{-1}}\]and molar mass of \[Cl=35.5gmo{{l}^{-1}}\]) [JEE Online 08-04-2017]
A) 0.3 M
B) 0.2 M
C) 0.6 M
D) 1.8 M
View Answer play_arrowquestion_answer70) 5 g of\[N{{a}_{2}}S{{O}_{4}}\] was dissolved in x g of \[{{H}_{2}}O.\] The change in freezing point was found to be \[3.82{}^\circ C\]. If \[N{{a}_{2}}S{{O}_{4}}\] is 81.5% ionised, the value of x (\[{{K}_{f}}\] for \[water=1.86{}^\circ C\] kg \[\text{mo}{{\text{l}}^{\text{-1}}}\]) is approximately: (molar mass of S = 32 g \[\text{mo}{{\text{l}}^{\text{-1}}}\] and that of Na = 23 g\[\text{mo}{{\text{l}}^{\text{-1}}}\]) [JEE Online 08-04-2017]
A) 25 g
B) 65 g
C) 15 g
D) 45 g
View Answer play_arrowquestion_answer71) Consider the following standard electrode potentials (\[E{}^\circ \] in volts) in aqueous solution : \[\frac{\text{Element}}{\begin{align} & \text{Al} \\ & \text{TI} \\ \end{align}}\] \[\frac{{{\text{M}}^{\text{3+}}}\text{/M}}{\begin{align} & \text{-1}\text{.66} \\ & \text{+1}\text{.26} \\ \end{align}}\] \[\frac{{{\text{M}}^{\text{+}}}\text{/M}}{\begin{align} & \text{+0}\text{.55} \\ & \text{-0}\text{.34} \\ \end{align}}\] Based on these data, which of the following statements is correct? [JEE Online 08-04-2017]
A) \[T{{\ell }^{3+}}\] is more stable than \[A{{\ell }^{3+}}\]
B) \[A{{\ell }^{+}}\]is more stable than \[A{{\ell }^{3+}}\]
C) \[T{{\ell }^{3+}}\] is more stable than \[A{{\ell }^{3+}}\]
D) \[T{{\ell }^{+}}\]is more stable than \[A{{\ell }^{+}}\]
View Answer play_arrowquestion_answer72) The major product expected from the following reaction is : [JEE Online 08-04-2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer73) Among the following, the incorrect statement is : [JEE Online 08-04-2017]
A) At low pressure, real gases show ideal behaviour.
B) At very low temperature, real gases show ideal behaviour.
C) At Boyle's temperature, real gases show idela behaviour.
D) At very large volume, real gases show ideal behaviour.
View Answer play_arrowquestion_answer74) The pair of compounds having metals in their highest oxidation state is : [JEE Online 08-04-2017]
A) \[\text{Mn}{{\text{O}}_{\text{2}}}\text{andCr}{{\text{O}}_{\text{2}}}\text{C}{{\text{l}}_{\text{2}}}\]
B) \[{{\text{ }\!\![\!\!\text{ Fe(CN}{{\text{)}}_{\text{6}}}\text{ }\!\!]\!\!\text{ }}^{\text{3-}}}\text{and}\,{{\text{ }\!\![\!\!\text{ Cu(CN}{{\text{)}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }}^{\text{2-}}}\]
C) \[{{[NIC{{l}_{4}}]}^{2-}}and{{[CoC{{l}_{4}}]}^{2-}}\]
D) \[{{\text{ }\!\![\!\!\text{ FeC}{{\text{l}}_{\text{4}}}\text{ }\!\!]\!\!\text{ }}^{\text{-}}}\text{andC}{{\text{o}}_{\text{2}}}{{\text{O}}_{\text{3}}}\]
View Answer play_arrowquestion_answer75) The IUPAC name of the following compound is [JEE Online 08-04-2017]
A) 2-Ethyl-1, 1-dimethylcyclohexane
B) 1, 1-Dimethyl 1-2-ethylcyclohexane
C) 2, 2-Dimethyl-1-1-ethylcyclohexane
D) 1-Ethyl-2,2-dimethylcyclohexane
View Answer play_arrowquestion_answer76) A mixture containing the following four compounds is extracted with 1 M HCl. The compound that goes to aqueous layer is: [JEE Online 08-04-2017]
A) IV
B) II
C) I
D) III
View Answer play_arrowquestion_answer77) Consider the following ionization enthalpies of two elements 'A' and 'B'.
Element | Ionization enthalpy (kJ/mol) | ||
1st | 2nd | 3rd | |
A | 899 | 1757 | 14847 |
B | 737 | 1450 | 7731 |
A) Both 'A' and 'B' belong to group-1 where 'A' comes below 'B'.
B) Both 'A' and 'B' belong to group-2 where 'A' comes below 'B'.
C) Both 'A' and 'B' belong to group-1 where 'B' comes below 'A'.
D) Both 'A' and 'B' belong to group-2 where 'B' comes below 'A'.
View Answer play_arrowquestion_answer78) \[s{{p}^{3}}{{d}^{2}}\] hybridization is not displayed by : [JEE Online 08-04-2017]
A) \[S{{F}_{6}}\]
B) \[Br{{F}_{5}}\]
C) \[P{{F}_{5}}\]
D) \[{{[Cr{{F}_{6}}]}^{3-}}\]
View Answer play_arrowquestion_answer79) The number of S = O and S-OH bonds present in peroxodisulphuric acid and pyrosulphuric acid respectively are : [JEE Online 08-04-2017]
A) (2 and 4) and (2 and 4)
B) (4 and 2) and (4 and 2)
C) (4 and 2) and (2 and 4)
D) (2 and 2) and (2 and 2)
View Answer play_arrowquestion_answer80) Among the following, correct statement is : [JEE Online 08-04-2017]
A) Sols of metal sulphides are lyophilic.
B) Brownian movement is more pronounced for smaller particles than for bigger-particles
C) One would expect charcoal to adsorb chlorine more than hydrogen sulphide.
D) Hardy Schulze law states that bigger the size of the ion is, the greater is its coagulating power.
View Answer play_arrowquestion_answer81) The major product of the following reaction is: [JEE Online 08-04-2017] \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{2}}-C{{H}_{3}}\xrightarrow[{{C}_{2}}{{H}_{5}}OH]{{{C}_{2}}{{H}_{5}}ONa}\]
A) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}=\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}C{{H}_{3}}\]
B) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,=CHC{{H}_{3}}\]
C) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ O{{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{2}}C{{H}_{3}}\]
D) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{2}}C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]
View Answer play_arrowquestion_answer82) What is the standard reduction potential \[(E{}^\circ )\] for \[F{{e}^{3+}}\to Fe\]? Given that: [JEE Online 08-04-2017] \[F{{e}^{2+}}+2{{e}^{-}}\to Fe;{{E}^{o}}_{F{{e}^{2+}}/Fe}=-0.47V\] \[F{{e}^{3+}}+{{e}^{-}}\to F{{e}^{2+}};{{E}^{o}}_{F{{e}^{3+}}/F{{e}^{2+}}}=+0.77V\]
A) -0.057 V
B) + 0.30 V
C) - 0.30 V
D) + 0.057 V
View Answer play_arrowquestion_answer83) The reason for "drug induced poisoning" is : [JEE Online 08-04-2017]
A) Binding irreversibly to the active site of the enzyme
B) Binding at the allosteric sites of the enzyme
C) Binding reversibly at the active site of the enzyme
D) Bringing conformational change in the binding site of enzyme
View Answer play_arrowquestion_answer84) The major product of the following reaction is: [JEE Online 08-04-2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer85) The major product of the following reaction is: \[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C}}\,C{{H}_{2}}C{{H}_{3}}\xrightarrow[heat]{KOH,C{{H}_{3}}OH}\] [JEE Online 08-04-2017]
A) \[C{{H}_{3}}CH=CH-CH=CHC{{H}_{3}}\]
B) \[C{{H}_{2}}=CHCH=CHC{{H}_{2}}C{{H}_{3}}\]
C) \[C{{H}_{2}}CH=C=CHC{{H}_{2}}C{{H}_{3}}\]
D) \[C{{H}_{2}}=CHC{{H}_{2}}CH=CHC{{H}_{3}}\]
View Answer play_arrowquestion_answer86) In which of the following reactions, hydrogen peroxide acts as an oxidizing agent? [JEE Online 08-04-2017]
A) \[HOCl+{{H}_{2}}{{O}_{2}}\to {{H}_{3}}{{O}^{+}}+C{{l}^{-}}+{{O}_{2}}\]
B) \[{{I}_{2}}+{{H}_{2}}{{O}_{2}}+2O{{H}^{-}}\to 2{{I}^{-}}+2{{H}_{2}}O+{{O}_{2}}\]
C) \[PbS+4{{H}_{2}}{{O}_{2}}\to PbS{{O}_{4}}+4{{H}_{2}}O\]
D) \[2MnO_{4}^{-}+3{{H}_{2}}{{O}_{2}}\to 2Mn{{O}_{2}}+3{{O}_{2}}+2{{H}_{2}}O+2O{{H}^{-}}\]
View Answer play_arrowquestion_answer87) For a reaction, \[A(g)\to A(\ell );\Delta H=-3RT.\] The correct statement for the reaction is: [JEE Online 08-04-2017]
A) \[\Delta H=\Delta U=0\]
B) \[|\Delta H|<|\Delta U|\]
C) \[|\Delta H|>|\Delta U|\]
D) \[\Delta H=\Delta U\ne 0\]
View Answer play_arrowquestion_answer88) The enthalpy change on freezing of 1 mol of water at \[5{}^\circ C\] to ice at \[-5{}^\circ C\] is : (Given \[{{\Delta }_{fus}}H=6kJ\,mo{{l}^{-1}}\]at \[0{}^\circ C\], \[{{C}_{p}}({{H}_{2}}O,\ell )=75.3J\,mo{{l}^{-1}}{{K}^{-1}},\] \[{{C}_{p}}({{H}_{2}}O,s)=36.8J\,mo{{l}^{-1}}{{K}^{-1}})\] [JEE Online 08-04-2017]
A) \[6.00\,\text{kJ}\,mo{{l}^{-1}}\]
B) \[5.81\,\text{kJ}\,mo{{l}^{-1}}\]
C) \[5.44\,\text{kJ}\,mo{{l}^{-1}}\]
D) \[6.56\,\text{kJ}\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer89) Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. If ionization constant of HA is 10-5, the ratio of salt to acid concentration in the buffer solution will be : [JEE Online 08-04-2017]
A) 10 : 1
B) 4 : 5
C) 5 : 4
D) 1 : 10
View Answer play_arrowquestion_answer90) A metal 'M' reacts with nitrogen gas to afford \['{{M}_{3}}N'.'{{M}_{3}}N'\] on heating at high temperature gives back 'M' and on reaction with water produces a gas 'B'. Gas 'B' reacts with aqueous solution of \[CuS{{O}_{4}}\]to form a deep blue compound. 'M' and 'B' respectively are : [JEE Online 08-04-2017]
A) Li and \[N{{H}_{3}}\]
B) Na and \[N{{H}_{3}}\]
C) Ba and \[{{N}_{2}}\]
D) Al and \[{{N}_{2}}\]
View Answer play_arrow
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