question_answer1) A particle is executing simple harmonic motion with a time period T. AT time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer2) The temperature of an open room of volume \[30{{m}^{3}}\]increases from \[17{{\,}^{o}}C\]to\[27{{\,}^{o}}C\] due to sunshine. The atmospheric pressure in the room remains \[1\times {{10}^{5}}\,Pa.\] If \[{{n}_{i}}\]and \[{{n}_{f}}\] are the number of molecules in the room before and after heating, then \[{{n}_{f}}-{{n}_{i}}\]will be:- [JEE Main 2017]
A) \[2.5\times {{10}^{25}}\]
B) \[-2.5\times {{10}^{25}}\]
C) \[-1.61\times {{10}^{23}}\]
D) \[1.38\times {{10}^{23}}\]
View Answer play_arrowquestion_answer3) Which of the following statements is false?
A) A rheostat can be used as a potential divider
B) Kirchhoff's second law represents energy conservation
C) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.
D) In a balanced wheat stone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. [JEE Main 2017]
View Answer play_arrowquestion_answer4) The following observations were taken for determining surface tensiton T of water by capillary method : Diameter of capilary, \[D=1.25\times {{10}^{-2}}m\] rise of water, \[h=1.45\times {{10}^{-2}}m\]. Using \[g=9.80\,m/{{s}^{2}}\]and the simplified relation\[\text{T=}\frac{\text{rhg}}{\text{2}}\text{ }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\,\text{N/m,}\] the possible error in surface tension is closest to: [JEE Main 2017]
A) 2.4%
B) 10%
C) 0.15%
D) 1.5%
View Answer play_arrowquestion_answer5) In amplitude modulation, sinusoidal carrier frequency used is denoted by \[{{\omega }_{c}}\]and the signal frequency is denoted by\[{{\omega }_{m}}.\]The bandwidth \[(\Delta {{\omega }_{m}})\] of the signal is such that\[\Delta {{\omega }_{m}}<<{{\omega }_{c}}.\]Which of the following frequencies is not contained in the modulated wave? [JEE Main 2017]
A) \[{{\omega }_{m}}+{{\omega }_{c}}\]
B) \[{{\omega }_{c}}-{{\omega }_{m}}\]
C) \[{{\omega }_{m}}\]
D) \[{{\omega }_{c}}\]
View Answer play_arrowquestion_answer6) A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is:
A) real and at a distance of 40 cm from the divergent lens
B) real and at a distance of 6 cm from the convergent lens
C) real and at a distance of 40 cm from convergent lens
D) virtual and at a distance of 40 cm from convergent lens. [JEE Main 2017]
View Answer play_arrowquestion_answer7) The moment of inertia of a uniform cylinder of length\[\ell \]and radius R about its perpendicular bisector is I. What is the ratio \[\ell /R\]such that the moment of inertia is minimum? [JEE Main 2017]
A) 1
B) \[\frac{3}{\sqrt{2}}\]
C) \[\sqrt{\frac{3}{\sqrt{2}}}\]
D) \[\frac{\sqrt{3}}{2}\]
View Answer play_arrowquestion_answer8) An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If\[{{\lambda }_{\min }}\] is the smallest possible wavelength of X-ray in the spectrum, the variation of \[\log {{\lambda }_{\min }}\] with log V is correctly represented in: [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer9) A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by: [JEE Main 2017]
A) \[t=T\log (1.3)\]
B) \[t=\frac{T}{\log (1.3)}\]
C) \[t=\frac{T\log 2}{2\log 1.3}\]
D) \[t=T\frac{\log 1.3}{\log 2}\]
View Answer play_arrowquestion_answer10) An electric dipole has a fixed dipole moment\[\vec{p},\], which makes angle \[\theta \] with respect to x-axis. When subjected to an electric\[{{\vec{E}}_{1}}=E\hat{i},\] field It experiences a torque \[\vec{T}=\tau \hat{k}.\] When subjected to another electric field \[{{\vec{E}}_{2}}=\sqrt{3}{{E}_{1}}\hat{j}\] it experiences torque\[{{\vec{T}}_{2}}=-{{\vec{T}}_{1}}.\] The angle \[\theta \] is: [JEE Main 2017]
A) \[{{60}^{o}}\]
B) \[{{90}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{45}^{o}}\]
View Answer play_arrowquestion_answer11) In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be: [JEE Main 2017]
A) \[{{135}^{o}}\]
B) \[{{180}^{o}}\]
C) \[{{45}^{o}}\]
D) \[{{90}^{o}}\]
View Answer play_arrowquestion_answer12) \[{{C}_{p}}\]and\[{{C}_{v}}\]are specific heats at constant pressure and constant volume respectively. It is observed that \[{{C}_{p}}-{{C}_{v}}=a\]for hydrogen gas \[{{C}_{p}}-{{C}_{v}}=b\]for nitrogen gas The correct relation between a and b is: [JEE Main 2017]
A) \[a=14\,b\]
B) \[a=28\,b\]
C) \[a=\frac{1}{14}b\]
D) \[a=b\]
View Answer play_arrowquestion_answer13) A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be \[75{{\,}^{o}}C.\] T is given by: (Given : room temperature\[=30{{\,}^{o}}C,\]specific heat of copper\[\text{=}\,\text{0}\text{.1}\,\text{cal/gm}{{\,}^{\text{o}}}\text{C}\][JEE Main 2017]
A) \[\text{1250}{{\,}^{o}}\text{C}\]
B) \[825{{\,}^{o}}\text{C}\]
C) \[800{{\,}^{o}}\text{C}\]
D) \[885{{\,}^{o}}\text{C}\]
View Answer play_arrowquestion_answer14) A body of mass \[m={{10}^{-2}}kg\]is moving in a medium and experiences a frictional force \[m={{10}^{-2}}kg\]Its intial speed is \[{{v}_{0}}=10m{{s}^{-1}}.\]If, after 10 s, its energy is\[\frac{1}{8}mv_{0}^{2},\] [JEE Main 2017]
A) \[{{10}^{-4}}kg\,{{m}^{-1}}\]
B) \[{{10}^{-1}}kg\,{{m}^{-1}}{{S}^{-1}}\]
C) \[{{10}^{-3}}kg\,{{m}^{-1}}\]
D) \[{{10}^{-3}}kg\,{{s}^{-1}}\]
View Answer play_arrowquestion_answer15) When a current of 5 mA is passed through a galvanometer having a coil of resistance \[15\,\Omega ,\] it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into to voltmeter of range 0 - 10 V is: [JEE Main 2017]
A) \[2.535\times {{10}^{3}}\Omega \]
B) \[4.005\times {{10}^{3}}\Omega \]
C) \[1.985\times {{10}^{3}}\Omega \]
D) \[2.045\times {{10}^{3}}\Omega \]
View Answer play_arrowquestion_answer16) A slender uniform rod of mass M and length \[\ell \] is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle\[\theta \] with the vertical is: [JEE Main 2017]
A) \[\frac{3g}{2\ell }\cos \theta \]
B) \[\frac{2g}{3\ell }\cos \theta \]
C) \[\frac{3g}{2\ell }\sin \theta \]
D) \[\frac{2g}{3\ell }\sin \theta \]
View Answer play_arrowquestion_answer17) Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths \[r={{\lambda }_{1}}/{{\lambda }_{2}},\]is given by: [JEE Main 2017]
A) \[r=\frac{3}{4}\]
B) \[r=\frac{1}{3}\]
C) \[r=\frac{4}{3}\]
D) \[r=\frac{2}{3}\]
View Answer play_arrowquestion_answer18) A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of : [JEE Main 2017]
A) 81
B) \[\frac{1}{81}\]
C) 9
D) \[\frac{1}{9}\]
View Answer play_arrowquestion_answer19) In a coil of resistance \[100\,\Omega ,\] a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: [JEE Main 2017]
A) 250 Wb
B) 275 Wb
C) 200 Wb
D) 225 Wb
View Answer play_arrowquestion_answer20) In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is: [JEE Main 2017]
A) 9.75 mm
B) 15.6 mm
C) 1.56 mm
D) 7.8 mm
View Answer play_arrowquestion_answer21) A magnetic needle of magnetic moment \[6.7\times {{10}^{-2}}\,A{{m}^{2}}\]and moment of inertia \[7.5\times {{10}^{-6}}\,kg\,{{m}^{2}}\]is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is: [JEE Main 2017]
A) 6.98 s
B) 8.76 s
C) 6.65 s
D) 8.89 s
View Answer play_arrowquestion_answer22) The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth's radius): [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer23) In the above circuit the current in each resistance is: [JEE Main 2017]
A) 0.5
B) 0 A
C) 1 A
D) 0.25 A
View Answer play_arrowquestion_answer24) A particle A of mass m and initial velocity v collides with a particle B of mass\[\frac{m}{2}\]which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths \[{{\lambda }_{A}}\]to \[{{\lambda }_{B}}\] after the collision is: [JEE Main 2017]
A) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{2}{3}\]
B) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]
C) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]
D) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{_{B}}}}=2\]
View Answer play_arrowquestion_answer25) An external pressure P is applied on a cube at \[0{{\,}^{o}}C\]so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and\[\alpha \]is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by: [JEE Main 2017]
A) \[\frac{3\alpha }{PK}\]
B) \[3PK\alpha \]
C) \[\frac{P}{3\alpha K}\]
D) \[\frac{P}{\alpha K}\]
View Answer play_arrowquestion_answer26) A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be: [JEE Main 2017]
A) 9 J
B) 18 J
C) 4.5 J
D) 22 J
View Answer play_arrowquestion_answer27) An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? [JEE Main 2017] (speed of light\[=3\times {{10}^{8}}\,m{{s}^{-1}}\])
A) 17.3 GHz
B) 15.3 GHz
C) 10.1 GHz
D) 12.1 GHz
View Answer play_arrowquestion_answer28) In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: [JEE Main 2017]
A) \[CE\frac{{{r}_{2}}}{(r+{{r}_{2}})}\]
B) \[CE\frac{{{r}_{1}}}{({{r}_{1}}+r)}\]
C) CE
D) \[CE\frac{{{r}_{1}}}{({{r}_{2}}+r)}\]
View Answer play_arrowquestion_answer29) A capacitance of \[2\mu F\]is required in an electrical circuit across a potential difference of 1.0 kV. A large number of\[1\mu F\]capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is: [JEE Main 2017]
A) 24
B) 32
C) 2
D) 16
View Answer play_arrowquestion_answer30) A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer31) Let k be an integer such that triangle with vertices \[(k,-3k),(5,k)\] and (-k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point: [JEE Main 2017]
A) \[\left( 2,\frac{1}{2} \right)\]
B) \[\left( 2,-\frac{1}{2} \right)\]
C) \[\left( 1,\frac{3}{4} \right)\]
D) \[\left( 1,-\frac{3}{4} \right)\]
View Answer play_arrowquestion_answer32) If, for a positive integer n, the quadratic equation, \[x(x+1)+(x+1)(x+2)+.....\] \[+(x+\overline{n-1})(x+n)=10n\] has two consecutive integral solutions, then n is equal to: [JEE Main 2017]
A) 11
B) 12
C) 9
D) 10
View Answer play_arrowquestion_answer33) The function \[f:R\to \left[ -\frac{1}{2},\frac{1}{2} \right]\]defined as \[f(x)=\frac{x}{1+{{x}^{2}}},\]is: [JEE Main 2017]
A) neither injective nor surjective.
B) invertible.
C) injective but not surjective.
D) surjective but not injective
View Answer play_arrowquestion_answer34) The following statement \[(p\to q)\to [(\tilde{\ }p\to q)\to q]\]is: [JEE Main 2017]
A) a fallacy
B) a tautology
C) equivalent to \[\tilde{\ }p\to q\]
D) equivalent to \[p\to -q\]
View Answer play_arrowquestion_answer35) If S is the set of distinct values of 'b' for which the following system of linear equations \[x+y+z=1\] \[x+ay+z=1\] \[ax+by+z=0\] has no solution, then S is : [JEE Main 2017]
A) a singleton
B) an empty set
C) an infinite set
D) a finite set containing two or more elements
View Answer play_arrowquestion_answer36) The area (in sq. units) of the region \[\{(x,y)\}:x\ge 0,x+y\le 3,{{x}^{2}}\le 4y\]and \[y\le 1+\sqrt{x}\}\]is: [JEE Main 2017]
A) \[\frac{5}{2}\]
B) \[\frac{59}{12}\]
C) \[\frac{3}{2}\]
D) \[\frac{7}{3}\]
View Answer play_arrowquestion_answer37) For any three positive real numbers a, b and c, \[9(25{{a}^{2}}+{{b}^{2}})+25({{c}^{2}}-3ac)=15b(3a+c).\] Then: [JEE Main 2017]
A) a, b and c are in G.P.
B) b, c and a are in G.P.
C) b, c and a are in A.P.
D) a, b and c are in A.P.
View Answer play_arrowquestion_answer38) A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is : [JEE Main 2017]
A) 484
B) 485
C) 468
D) 469
View Answer play_arrowquestion_answer39) The normal to the curve\[y(x-2)(x-3)=x+6\] at the point where the curve intersects the y-axis passes through the point: [JEE Main 2017]
A) \[\left( \frac{1}{2},\frac{1}{3} \right)\]
B) \[\left( -\frac{1}{2},\frac{1}{2} \right)\]
C) \[\left( \frac{1}{2},\frac{1}{2} \right)\]
D) \[\left( \frac{1}{2},-\frac{1}{3} \right)\]
View Answer play_arrowquestion_answer40) A hyperbola passes through the point \[\text{P(}\sqrt{\text{2}}\text{,}\sqrt{\text{3}}\text{)}\]and has foci at \[(\pm \,2,0).\]Then the tangent to this hyperbola at P is also passes through the point: [JEE Main 2017]
A) \[\left( -\sqrt{2},-\sqrt{3} \right)\]
B) \[\left( 3\sqrt{2},2\sqrt{3} \right)\]
C) \[\left( 2\sqrt{2},3\sqrt{3} \right)\]
D) \[\left( \sqrt{3},\sqrt{2} \right)\]
View Answer play_arrowquestion_answer41) Let \[a,b,c\in R.\]If \[f(x)=a{{x}^{2}}+bx+c\]is such that \[a+b+c=3\]and \[f(x+y)=f(x)+f(y)+xy,\forall x,y\in R,\]then \[\sum\limits_{n=1}^{10}{f(n)}\]is equal to: [JEE Main 2017]
A) 225
B) 330
C) 165
D) 190
View Answer play_arrowquestion_answer42) Let \[\vec{a}=2\hat{i}+\hat{j}-2\hat{k}\]and \[\vec{b}=\hat{i}+\hat{j}.\]Let \[\vec{c}\]be a vector such that\[|\vec{c}-\vec{a}|=3,\left| (\vec{a}\times \vec{b})\times \vec{c} \right|=3\]and the angle between \[\vec{c}\]and \[\vec{a}\times \vec{b}\] be \[{{30}^{o}}.\] Then \[\vec{a}.\vec{c}\] is equal to: [JEE Main 2017]
A) \[\frac{1}{8}\]
B) \[\frac{25}{8}\]
C) 2
D) 5
View Answer play_arrowquestion_answer43) Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If \[\angle BPC=\beta ,\] then \[\text{tan}\,\beta \] is equal to :- [JEE Main 2017]
A) \[\frac{4}{9}\]
B) \[\frac{6}{7}\]
C) \[\frac{1}{4}\]
D) \[\frac{2}{9}\]
View Answer play_arrowquestion_answer44) Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower -bed, is :- [JEE Main 2017]
A) 30
B) 12.5
C) 10
D) 25
View Answer play_arrowquestion_answer45) The integral\[\int\limits_{\frac{\pi }{4}}^{\frac{3\pi }{4}}{\frac{dx}{1+cos\,x}}\]is equal to:- [JEE Main 2017]
A) -1
B) -2
C) 2
D) 4
View Answer play_arrowquestion_answer46) If \[(2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0\]and \[y(0)=1,\]then \[y\left( \frac{\pi }{2} \right)\]is equal to:- [JEE Main 2017]
A) \[\frac{4}{3}\]
B) \[\frac{1}{3}\]
C) \[-\frac{2}{3}\]
D) \[-\frac{1}{3}\]
View Answer play_arrowquestion_answer47) Let\[{{I}_{n}}=\int_{{}}^{{}}{{{\tan }^{n}}xdx,(n>1).{{I}_{4}}+{{I}_{6}}}\]\[=a{{\tan }^{5}}x+b{{x}^{5}}+C,\]where C is a constant of integration, then ordered pair (a, b) is equal to:- [JEE Main 2017]
A) \[\left( -\frac{1}{5},0 \right)\]
B) \[\left( -\frac{1}{5},1 \right)\]
C) \[\left( \frac{1}{5},0 \right)\]
D) \[\left( \frac{1}{5},-1 \right)\]
View Answer play_arrowquestion_answer48) Let \[\omega \]be a complex number such that \[2\omega +1=z\]where \[z=\sqrt{-3}.\]If \[\left| \begin{matrix} 1 & 1 & 1 \\ 1 & -{{\omega }^{2}}-1 & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & {{\omega }^{7}} \\ \end{matrix} \right|=3k,\] then k is equal to:- [JEE Main 2017]
A) 1
B) \[-z\]
C) z
D) -1
View Answer play_arrowquestion_answer49) The value of \[({{\,}^{21}}{{C}_{1}}-{{\,}^{10}}{{C}_{1}})+({{\,}^{21}}{{C}_{2}}-{{\,}^{10}}{{C}_{2}})+\] \[({{\,}^{21}}{{C}_{3}}-{{\,}^{10}}{{C}_{3}})+({{\,}^{21}}{{C}_{4}}-{{\,}^{10}}{{C}_{4}})+....+\] \[({{\,}^{21}}{{C}_{10}}-{{\,}^{10}}{{C}_{10}})\]is:- [JEE Main 2017]
A) \[{{2}^{20}}-{{2}^{10}}\]
B) \[{{2}^{21}}-{{2}^{11}}\]
C) \[{{2}^{21}}-{{2}^{10}}\]
D) \[{{2}^{20}}-{{2}^{9}}\]
View Answer play_arrowquestion_answer50) \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\frac{\cot x-\cos x}{{{(\pi -2x)}^{3}}}\] [JEE Main 2017]
A) \[\frac{1}{4}\]
B) \[\frac{1}{24}\]
C) \[\frac{1}{16}\]
D) \[\frac{1}{8}\]
View Answer play_arrowquestion_answer51) \[5({{\tan }^{2}}x-{{\cos }^{2}}x)=2\cos 2x+9,\]then the value of \[\cos 4x\]is :- [JEE Main 2017]
A) \[-\frac{7}{9}\]
B) \[-\frac{3}{5}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{9}\]
View Answer play_arrowquestion_answer52) If the image of the point P(1,-2,3) in the plane, \[2x+3y-4z+22=0\]measured parallel to line, \[\frac{x}{1}=\frac{y}{4}=\frac{z}{5}\]is Q, then PQ is equal to:- [JEE Main 2017]
A) \[6\sqrt{5}\]
B) \[3\sqrt{5}\]
C) \[2\sqrt{42}\]
D) \[\sqrt{42}\]
View Answer play_arrowquestion_answer53) The distance of the point (1, 3, -7) from the plane passing through the point (1, -1, -1), having normal perpendicular to both the lines \[\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}\]and \[\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1},\]is:- [JEE Main 2017]
A) \[\frac{10}{\sqrt{74}}\]
B) \[\frac{20}{\sqrt{74}}\]
C) \[\frac{10}{\sqrt{83}}\]
D) \[\frac{5}{\sqrt{83}}\]
View Answer play_arrowquestion_answer54) If for \[x\in \left( 0,\frac{1}{4} \right),\]the derivative of \[{{\tan }^{-1}}\left( \frac{6x\sqrt{x}}{1-9{{x}^{3}}} \right)\]is \[\sqrt{x}.g(x),\]then \[g(x)\]equals:- [JEE Main 2017]
A) \[\frac{3}{1+9{{x}^{3}}}\]
B) \[\frac{9}{1+9{{x}^{3}}}\]
C) \[\frac{3x\sqrt{x}}{1-9{{x}^{3}}}\]
D) \[\frac{3x}{1-9{{x}^{3}}}\]
View Answer play_arrowquestion_answer55) The radius of a circle, having minimum area, which touches the curve \[y=4{{x}^{2}}\]and the lines,\[y=\,|x|\]:- [JEE Main 2017]
A) \[4\left( \sqrt{2}+1 \right)\]
B) \[2\left( \sqrt{2}+1 \right)\]
C) \[2\left( \sqrt{2}-1 \right)\]
D) \[4\left( \sqrt{2}-1 \right)\]
View Answer play_arrowquestion_answer56) A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :- [JEE Main 2017]
A) \[\frac{6}{25}\]
B) \[\frac{12}{5}\]
C) 6
D) 4
View Answer play_arrowquestion_answer57) The eccentricity of an ellipse whose centre is at the origin is \[\frac{1}{2}.\]If one of its directices is \[x=-4,\]then the equation of the normal to it at \[\left( 1,\frac{3}{2} \right)\]is:- [JEE Main 2017]
A) \[x+2y=4\]
B) \[2y-x=2\]
C) \[4x-2y=1\]
D) \[4x+2y=7\]
View Answer play_arrowquestion_answer58) If two different numbers are taken from the set {0, 1, 2, 3, ......., 10), then the probability that their sum as well as absolute difference are both multiple of 4, is :- [JEE Main 2017]
A) \[\frac{7}{55}\]
B) \[\frac{6}{55}\]
C) \[\frac{12}{55}\]
D) \[\frac{14}{45}\]
View Answer play_arrowquestion_answer59) For three events A, B and C, P(Exactly one of A or B occurs)= P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) \[=\frac{1}{4}\]and P(All the three events occur simultaneously) \[=\frac{1}{16}.\] Then the probability that at least one of the events occurs, is :- [JEE Main 2017]
A) \[\frac{3}{16}\]
B) \[\frac{7}{32}\]
C) \[\frac{7}{16}\]
D) \[\frac{7}{64}\]
View Answer play_arrowquestion_answer60) If \[A\left[ \begin{matrix} 2 & -3 \\ -4 & 1 \\ \end{matrix} \right],\]then adj \[(3{{A}^{2}}+12A)\]is equal to:- [JEE Main 2017]
A) \[\left[ \begin{matrix} 72 & -63 \\ -84 & 51 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 72 & -84 \\ -63 & 51 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 51 & 63 \\ 84 & 72 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 51 & 84 \\ 63 & 72 \\ \end{matrix} \right]\]
View Answer play_arrowquestion_answer61) Which of the following compounds will significant amont of meta product during mono-nitration reaction? [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer62) \[\text{ }\!\!\Delta\!\!\text{ U}\]is equal to [JEE Main 2017]
A) Isochoric work
B) Isobaric work
C) Adiabatic work
D) Isothermal work
View Answer play_arrowquestion_answer63) The increasing order of the reactivity of the following halides for the \[{{\text{S}}_{\text{N}}}\text{1}\]reaction is [JEE Main 2017] \[\text{C}{{\text{H}}_{\text{3}}}\underset{\text{Cl}}{\mathop{\underset{\text{ }\!\!|\!\!\text{ }}{\mathop{\text{C}}}\,}}\,\text{HC}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{3}}}\] \[\text{C}{{\text{H}}_{\text{3}}}\text{C}{{\text{H}}_{\text{2}}}\text{C}{{\text{H}}_{\text{2}}}\text{Cl}\] \[p-{{H}_{3}}CO-{{C}_{6}}{{H}_{4}}-C{{H}_{2}}Cl\]
A) (III) < (II) < (I)
B) (II) < (I) < (III)
C) < (III) < (II)
D) (II) < (III) < (I)
View Answer play_arrowquestion_answer64) The radius of the second Bohr orbit for hydrogen atom is: (Plank's const. \[\text{h}\,\text{=}\,\text{6}\text{.6262}\times \text{1}{{\text{0}}^{-34}}\,Js;\]mass of electron\[=9.1091\times {{10}^{-31}}\,kg;\]charge of electron \[e=1.60210\times {{10}^{-19}}C;\]permittivity of vaccum\[{{\in }_{0}}=8.854185\times {{10}^{-12}}\,k{{g}^{-1}}{{m}^{-3}}{{A}^{2}})\] [JEE Main 2017]
A) \[1.65\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[4.76\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[0.529\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[212\overset{\text{o}}{\mathop{\text{A}}}\,\]
View Answer play_arrowquestion_answer65) \[\text{p}{{\text{K}}_{\text{a}}}\]of a weak acid (HA) and \[\text{p}{{\text{K}}_{\text{b}}}\]of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is [JEE Main 2017]
A) 7.2
B) 6.9
C) 7.0
D) 1.0
View Answer play_arrowquestion_answer66) The formation of which of the following polymers involves hydrolysis reaction? [JEE Main 2017]
A) Nylon 6
B) Bakelite
C) Nylon 6, 6
D) Terylene
View Answer play_arrowquestion_answer67) The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all 1H atoms are replaced by\[{{\,}^{\text{2}}}\text{H}\] atoms is [JEE Main 2017]
A) 15 kg
B) 37.5 kg
C) 7.5 kg
D) 10 kg
View Answer play_arrowquestion_answer68) Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine? [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer69) In the following reactions, ZnO is respectively acting as a/an : [JEE Main 2017] \[ZnO+N{{a}_{2}}O\to N{{a}_{2}}Zn{{O}_{2}}\] \[ZnO+C{{O}_{2}}\to ZnC{{O}_{3}}\]
A) base and acid
B) base and base
C) acid and acid
D) acid and base
View Answer play_arrowquestion_answer70) Both lithium and magnesium display several similar properties due to the diagonal relationship ; however, the one which is incorrect is: [JEE Main 2017]
A) Both form basic carbonates
B) Both form soluble bicarbonates
C) Both form nitrides
D) Nitrates of both Li and Mg yield\[\text{N}{{\text{O}}_{\text{2}}}\] and \[{{\text{O}}_{\text{2}}}\]on heating
View Answer play_arrowquestion_answer71) 3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :- [JEE Main 2017]
A) Six
B) Zero
C) Two
D) Four
View Answer play_arrowquestion_answer72) A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be :- [JEE Main 2017]
A) 2a
B) \[2\sqrt{2}a\]
C) \[\sqrt{2}a\]
D) \[\frac{a}{\sqrt{2}}\]
View Answer play_arrowquestion_answer73) Two reactions\[{{R}_{1}}\]and\[{{R}_{2}}\]have identical preexponential factors. Activation energy of \[{{R}_{1}}\]exceeds that of \[{{R}_{2}}\]by \[10\,kJ\,mo{{l}^{-1}}.\] If \[{{k}_{1}}\]and \[{{k}_{2}}\]are rate constants for reactions \[{{R}_{1}}\]and \[{{R}_{2}}\]respectively at 300 K, then ln \[({{k}_{2}}/{{k}_{1}})\] is equal to:- \[(R=8.314\,J\,mo{{l}^{-1}}{{K}^{-1}})\][JEE Main 2017]
A) 8
B) 12
C) 6
D) 4
View Answer play_arrowquestion_answer74) The correct sequence of reagents for the following conversion will be:- [JEE Main 2017]
A) \[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},{{H}^{+}}/C{{H}_{3}}OH,C{{H}_{3}}MgBr\]
B) \[C{{H}_{3}}MgBr,{{H}^{+}}/C{{H}_{3}}OH,{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}}\]
C) \[C{{H}_{3}}MgBr,{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},{{H}^{+}},C{{H}_{3}}OH\]
D) \[{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}O{{H}^{-}},C{{H}_{3}}C{{H}_{3}}MgBr,{{H}^{+}}/C{{H}_{3}}OH\]
View Answer play_arrowquestion_answer75) The Tyndall effect is observed only when following conditions are satisfied :- [JEE Main 2017] [a] The diameter of the dispersed particles is much smaller than the wavelength of the ligh used. [b] The diameter of the dispersed particle is not much smaller than the wavelength of the light used. [c] The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude. [d] The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.
A) [a] and [d]
B) [b] and [d]
C) [a] and [c]
D) [b] and [c]
View Answer play_arrowquestion_answer76) Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer77) Given \[{{C}_{(grahite)}}+{{O}_{2}}(g)\to C{{O}_{2}}(g);\] \[{{\Delta }_{r}}{{H}^{o}}=-393.5\,kJ\,mo{{l}^{-1}}\] \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}O(l);\] \[{{\Delta }_{r}}{{H}^{o}}=-285.8\,kJ\,mo{{l}^{-1}}\] \[C{{O}_{2}}(g)+2{{H}_{2}}O(l)\to C{{H}_{4}}(g)+2{{O}_{2}}(g);\] \[{{\Delta }_{r}}{{H}^{o}}=+890.3\,kJ\,mo{{l}^{-1}}\] Based on the above thermochemical equations, the value of \[{{\Delta }_{r}}{{H}^{o}}\]at 298 K for the reaction [JEE Main 2017] \[{{C}_{(grahite)}}+2{{H}_{2}}(g)\to C{{H}_{4}}(g)\]will be:-
A) \[+\,74.8\,kJ\,mo{{l}^{-1}}\]
B) \[+\,144.0\,\,kJ\,mo{{l}^{-1}}\]
C) \[-74.8\,\,kJ\,mo{{l}^{-1}}\]
D) \[-144.0\,kJ\,mo{{l}^{-1}}\]
View Answer play_arrowquestion_answer78) Which of the following reactions is an example of a redox reaction? [JEE Main 2017]
A) \[Xe{{F}_{4}}+{{O}_{2}}{{F}_{2}}\to Xe{{F}_{6}}+{{O}_{2}}\]
B) \[Xe{{F}_{2}}+P{{F}_{5}}\to {{[XeF]}^{+}}P{{F}_{6}}^{-}\]
C) \[Xe{{F}_{6}}+{{H}_{2}}O\to XeO{{F}_{4}}+2HF\]
D) \[Xe{{F}_{6}}+2{{H}_{2}}O\to Xe{{O}_{2}}{{F}_{2}}+4HF\]
View Answer play_arrowquestion_answer79) The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are:- [JEE Main 2017]
A) \[Cl{{O}^{-}}\]and \[ClO_{3}^{-}\]
B) \[ClO_{2}^{-}\]and \[ClO_{3}^{-}\]
C) \[C{{l}^{-}}\]and \[Cl{{O}^{-}}\]
D) \[C{{l}^{-}}\]and \[ClO_{2}^{-}\]
View Answer play_arrowquestion_answer80) The major product obtained in the following reaction is :- [JEE Main 2017]
A) \[(\pm )\,{{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}C{{H}_{6}}{{H}_{5}}\]
B) \[{{C}_{6}}{{H}_{5}}CH=CH{{C}_{6}}{{H}_{5}}\]
C) \[(+){{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}{{H}_{5}}\]
D) \[(-){{C}_{6}}{{H}_{5}}CH({{O}^{t}}Bu)C{{H}_{2}}{{C}_{6}}{{H}_{5}}\]
View Answer play_arrowquestion_answer81) Sodium salt of an organic acid 'X' produces effervescence with conc. \[{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}\]'X' reacts with the acidified aqueous \[\text{CaC}{{\text{l}}_{\text{2}}}\] solution to give a white precipitate which decolourises acidic solution of \[\text{KMn}{{\text{O}}_{4}}.\] 'X' is :- [JEE Main 2017]
A) \[{{C}_{6}}{{H}_{5}}COONa\]
B) \[HCOONa\]
C) \[CH3COONa\]
D) \[N{{a}_{2}}{{C}_{2}}{{O}_{4}}\]
View Answer play_arrowquestion_answer82) Which of the following species is not paramagnetic :- [JEE Main 2017]
A) NO
B) CO
C) \[{{O}_{2}}\]
D) \[{{B}_{2}}\]
View Answer play_arrowquestion_answer83) The freezing point of benzene decreases by \[0.45{{\,}^{o}}C\]when 0.2 g of acetic acid is added to 20 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be :- (\[{{K}_{f}}\]for benzene \[=5.12\,K\,kg\,mo{{l}^{-1}}\]) [JEE Main 2017]
A) 64.6%
B) 80.4%
C) 74.6%
D) 94.6%
View Answer play_arrowquestion_answer84) Which of the following molecules is least resonance stabilized? [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer85) On treatment of 100 mL of 0.1 M solution of \[CoC{{l}_{3}}.6{{H}_{2}}O\]with excess \[AgN{{O}_{3}};1.2\times {{10}^{22}}\]ions are precipitated. The complex is :- [JEE Main 2017]
A) \[AgN{{O}_{3}};1.2\times {{10}^{22}}\]
B) \[[Co{{({{H}_{2}}O)}_{3}}C{{l}_{3}}].3{{H}_{2}}O\]
C) \[[Co{{({{H}_{2}}O)}_{6}}]C{{l}_{3}}\]
D) \[[Co{{({{H}_{2}}O)}_{5}}Cl]C{{l}_{2}}.{{H}_{2}}O\]
View Answer play_arrowquestion_answer86) The major product obtained in the following reaction is :- [JEE Main 2017]
A)
B)
C)
D)
View Answer play_arrowquestion_answer87) A water sample has ppm level concentration of following anions \[{{F}^{-}}=10;\,SO_{4}^{2-}=100;\,NO_{3}^{-}=50\] the anion/anions that make / makes the water sample unsuitable for drinking is / are : [JEE Main 2017]
A) only\[NO_{3}^{-}\]
B) both \[SO_{4}^{2-}\]and \[NO_{3}^{-}\]
C) only\[F-\]
D) only \[SO_{4}^{2-}\]
View Answer play_arrowquestion_answer88) 1 gram of a carbonate \[({{M}_{2}}C{{O}_{3}})\] on treatment with excess HCl produces 0.01186 mole of \[C{{O}_{2}}.\]the molar mass of \[{{\text{M}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}\]in \[\text{g}\,\text{mo}{{\text{l}}^{-1}}\]is:- [JEE Main 2017]
A) 1186
B) 84.3
C) 118.6
D) 11.86
View Answer play_arrowquestion_answer89) Given \[E_{Cl{{ }_{2}}/C{{l}^{-}}}^{0}=13.6,E_{C{{r}^{3+}}/Cr}^{0}=-0.74\,V\] \[E_{C{{r}_{2}}O_{7}^{2-}/C{{r}^{3+}}}^{0}=1.33V,E_{MnO_{4}^{-}/M{{n}^{2+}}}^{0}=1.51\,V.\] Among the following, the strongest reducing agent is [JEE Main 2017]
A) Cr
B) \[M{{n}^{2+}}\]
C) \[C{{r}^{3+}}\]
D) \[C{{l}^{-}}\]
View Answer play_arrowquestion_answer90) The group having isoelectronic species is :- [JEE Main 2017]
A) \[{{\text{O}}^{2-}},{{F}^{-}},N{{a}^{+}},M{{g}^{2+}}\]
B) \[{{O}^{-}},{{F}^{-}},Na,M{{g}^{+}}\]
C) \[{{O}^{2-}},{{F}^{-}},Na,M{{g}^{2+}}\]
D) \[{{O}^{-}},{{F}^{-}},N{{a}^{+}},M{{g}^{2+}}\]
View Answer play_arrow
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