question_answer2) The system of linear equations \[x+\lambda y-z=0\] \[\lambda x-y-z=0\] \[x+y-\lambda z=0\] has a non-trivial solution for :
[JEE Main Solved Paper-2016 ]
question_answer3) A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then :
[JEE Main Solved Paper-2016 ]
question_answer4) A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is \[30{}^\circ \]. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is \[60{}^\circ \]. Then the time taken (in minutes) by him, form B to reach the pillar, is :
[JEE Main Solved Paper-2016 ]
question_answer5) Let two fair six-faced dice A and B be thrown simultaneously. If \[{{E}_{1}}\] is the event that die A shows up four, \[{{E}_{2}}\]is the event that die B shows up two and \[{{E}_{3}}\] is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ?
[JEE Main Solved Paper-2016 ]
question_answer8) The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is :
[JEE Main Solved Paper-2016 ]
question_answer9) The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :
[JEE Main Solved Paper-2016 ]
question_answer10) Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the center C of the circle, \[{{x}^{2}}+{{(y+6)}^{2}}=1\]. Then the equation of the circle, passing through C and having its centre at P is :
[JEE Main Solved Paper-2016 ]
question_answer12) Consider \[f(x)={{\tan }^{-1}}\left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right),x\in \left( 0,\frac{\pi }{2} \right).\] A normal to \[y=f(x)at\,x=\frac{\pi }{6}\]also passes through the point :
[JEE Main Solved Paper-2016 ]
question_answer13) Two sides of a rhombus are along the lines, \[x-v+1=0\]and \[\text{7x}\text{y}\text{5}=0.\] If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus ?
[JEE Main Solved Paper-2016 ]
question_answer14) If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, \[y(1+xy)dx=xdy,\]then \[f\left( -\frac{1}{2} \right)\] is equal to :
[JEE Main Solved Paper-2016 ]
question_answer15) If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :
[JEE Main Solved Paper-2016 ]
question_answer16) If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :-
[JEE Main Solved Paper-2016 ]
question_answer17) If the number of terms in the expansion of \[{{\left( 1-\frac{2}{x}+\frac{4}{{{x}^{2}}} \right)}^{n}},x\ne 0,\] , is 28, then the sum of the coefficients of all the terms in this expansion, is :-
[JEE Main Solved Paper-2016 ]
question_answer18) If the sum of the first ten terms of the series \[{{\left( 1\frac{3}{5} \right)}^{2}}+{{\left( 2\frac{2}{5} \right)}^{2}}+{{\left( 3\frac{1}{5} \right)}^{2}}+....,\]is\[\frac{16}{5}m,\]then m is equal to :-
[JEE Main Solved Paper-2016 ]
question_answer19) If the line,\[\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}\]lies in the plane, \[1x+my-z=9,\]then\[{{1}^{2}}{{+}^{2}}\] is equal to :-
[JEE Main Solved Paper-2016 ]
question_answer22) If one of the diameters of the circle, given by the equation, \[\text{x2}+\text{y2}\text{4x}+\text{6y}\text{12}=0,\]is a chord of a circle S, whose centre is at (-3, 2), then the radius of S is :-
[JEE Main Solved Paper-2016 ]
question_answer24) The centres of those circles which touch the circle, \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}\text{8x}\text{8y}\text{4}=0,\]externally and also touch the x-axis, lie on :-
[JEE Main Solved Paper-2016 ]
question_answer25) Let\[\overrightarrow{a},\overrightarrow{b}\]\[\overrightarrow{c}\]be three unit vectors such that\[\overrightarrow{a}\times \left( \overrightarrow{b}\times \overrightarrow{c} \right)=\frac{\sqrt{3}}{2}\left( \overrightarrow{b}+\overrightarrow{c} \right).\]If \[\overrightarrow{b}\]is not parallel to \[\overrightarrow{c}\], then the angle between \[\overrightarrow{a}\]and\[\overrightarrow{b}\]is :-
[JEE Main Solved Paper-2016 ]
question_answer26) Let\[p=\underset{x\to 0+}{\mathop{\lim }}\,{{\left( 1+{{\tan }^{2}}\sqrt{x} \right)}^{\frac{1}{2x}}}\] then log p is equal to :-
[JEE Main Solved Paper-2016 ]
question_answer27) If \[0\le x<2\pi ,\]then the number of real values of x, which satisfy the equation \[\cos x+\cos 2x+\cos 3x+\cos 4x=0,\]is :-
[JEE Main Solved Paper-2016 ]
question_answer28) The sum of all real values of x satisfying the equation \[{{\left( {{x}^{2}}-5x+5 \right)}^{{{x}^{2}}+4x-60}}=1\]is :-
[JEE Main Solved Paper-2016 ]
question_answer29) The area (in sq. units) of the region \[\{(x,y):{{y}^{2}}\ge 2x\]and\[{{x}^{2}}+{{y}^{2}}\le 4x,x\ge 0,y\ge 0\]\[\}\] is :-
[JEE Main Solved Paper-2016 ]
question_answer31) A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the \[4\mu F\] and \[9\mu F\]capacitors), at a point 30 m from it , would equal:
[JEE Main Solved Paper-2016 ]
question_answer32) An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears :
[JEE Main Solved Paper-2016 ]
question_answer33) Hysteresis loops for two magnetic materials A and B are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use;
[JEE Main Solved Paper-2016 ]
A)
B for electromagnets and transformers.
doneclear
B)
A for electric generators and transformers.
doneclear
C)
A for electromagnets and B for electric transformers.
question_answer34) Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes , the ratio of decayed numbers of A and B nuclei will be :-
[JEE Main Solved Paper-2016 ]
question_answer35) A particle of mass m is moving along the side of a square of side 'a', with a uniform speed u in the x-y plane as shown in the figure : Which of the following statement is false for the angular momentum \[\vec{L}\] about the origin ?
[JEE Main Solved Paper-2016 ]
A)
\[\vec{L}=\frac{m\upsilon }{\sqrt{2}}R\hat{k}\]when the particle is moving from D to A
doneclear
B)
\[\vec{L}=-\frac{m\upsilon }{\sqrt{2}}R\hat{k}\] when the particle is moving from to B
doneclear
C)
\[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}-a \right]\hat{k}\]when the particle is moving from C to D
doneclear
D)
\[\vec{L}=m\upsilon \left[ \frac{R}{\sqrt{2}}+a \right]\hat{k}\]when the particle is moving from B to C
question_answer37) In an experiment for determination of refractive index of glass of a prism by \[i-\delta ,\] plot, it was found that a ray incident at angle \[35{}^\circ \], suffers a deviation of \[40{}^\circ \] and that it emerges at angle \[79{}^\circ \]. In that case which of the following is closest to the maximum possible value of the refractive index?
[JEE Main Solved Paper-2016 ]
question_answer38) 'n' moles of an ideal gas undergoes a process \[A\to B\]as shown in the figure. The maximum temperature of the gas during the process will be :
[JEE Main Solved Paper-2016 ]
question_answer39) Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If \[{{B}_{A}}\]and \[{{B}_{B}}\]are the values of magnetic field at the centres of the circle and square respectively, then the ratio \[\frac{{{B}_{A}}}{{{B}_{B}}}\]is:
[JEE Main Solved Paper-2016 ]
question_answer40) A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement , it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line ?
[JEE Main Solved Paper-2016 ]
question_answer41) For a common emitter configuration, if \[\alpha \]and \[\beta \]have their usual meanings, the incorrect relationship between\[\alpha \]and\[\beta \]is
[JEE Main Solved Paper-2016 ]
question_answer42) The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength\[\lambda \]the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say \[{{b}_{\min }}\]) when :-
[JEE Main Solved Paper-2016 ]
question_answer43) A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies \[\text{3}.\text{8}\times \text{1}0\text{7J}\]of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 \[m{{s}^{}}^{2}\]:-
[JEE Main Solved Paper-2016 ]
question_answer45) An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by \[\text{P}{{\text{V}}^{\text{n}}}=\]constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) :-
[JEE Main Solved Paper-2016 ]
question_answer46) A satellite is reolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R ; h << R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere).
[JEE Main Solved Paper-2016 ]
question_answer47) A galvanometer having a coil resistance of \[100\Omega \] gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10A, is :-
[JEE Main Solved Paper-2016 ]
question_answer48) Radiation of wavelength \[\lambda ,\]is incident on a photocell. The fastest emitted electron has speed v. If the wavelength of changed to\[\frac{3\lambda }{4},\] the speed of the fastest emitted electron will be :-
[JEE Main Solved Paper-2016 ]
question_answer49) If a, b, c, d are inputs to a gate and x is its output, then as per the following time graph, the gate is
[JEE Main Solved Paper-2016 ]
question_answer50) The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density \[\rho =\frac{A}{r},\]where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :-
[JEE Main Solved Paper-2016 ]
question_answer51) A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :-
question_answer52) The temperature dependence of resistances of Cu and un doped Si in the temperature range 300-400K, is best described by :-
[JEE Main Solved Paper-2016 ]
A)
Linear decrease for Cu, linear decrease for Si.
doneclear
B)
Linear increase for Cu, linear increase for Si.
doneclear
C)
Linear increase for Cu, exponential increase for Si
doneclear
D)
Linear increase for Cu, exponential de crease for Si
question_answer53) Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c), (d) :-
[JEE Main Solved Paper-2016 ]
A)
Zener diode, Solar cell, Simple diode, Light dependent resistance
doneclear
B)
Simple diode, Zener diode, Solar cell, Light dependent resistance
doneclear
C)
Zener diode, Simple diode, Light dependent resistance, Solar cell
doneclear
D)
Solar cell, Light dependent resistance, Zener diode, Simple diode
question_answer54) A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to :-
[JEE Main Solved Paper-2016 ]
question_answer55) A pendulum clock loses 12s a day if the temperature is \[40{}^\circ C\] and gains 4s a day if the temperature is \[20{}^\circ C\]. The temperature at which the clock will show correct time, and the coefficient of linear expansion (a) of the metal of the pendulum shaft are respectively :-
[JEE Main Solved Paper-2016 ]
question_answer56) A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is :- (take\[\text{g}=\text{1}0\text{m}{{\text{s}}^{\text{2}}}\])
[JEE Main Solved Paper-2016 ]
question_answer57) A point particle of mass, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals m. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and PR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction m and the distance x(=QR) are, respecitvely close to :-
[JEE Main Solved Paper-2016 ]
question_answer58) A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequencty of the air column is now :-
[JEE Main Solved Paper-2016 ]
question_answer59) A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a distance\[\frac{2A}{3}\]from equilibrium position. The new amplitude of the motion is :-
[JEE Main Solved Paper-2016 ]
question_answer60) An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :-
[JEE Main Solved Paper-2016 ]
question_answer62) The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :-
[JEE Main Solved Paper-2016 ]
question_answer65) Two closed bulbs of equal volume(V) containing an ideal gas initially at pressure \[{{p}_{i}}\] and temperature \[{{T}_{1}}\]are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to \[{{T}_{2}}\]The final pressure \[{{p}_{f}}\] is :-
[JEE Main Solved Paper-2016 ]
question_answer66) The heats of combustion of carbon and carbon monoxide are -393.5 and -285.5 kJ \[\text{mo}{{\text{l}}^{\text{-1}}},\] respectively. The heat of formation (in kJ) of carbon monoxide per mole is :-
[JEE Main Solved Paper-2016 ]
question_answer67) At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% \[{{O}_{2}}\] by volume for complete combustion. After combustion the gases occupy 330 mL. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is :-
[JEE Main Solved Paper-2016 ]
question_answer68) Decomposition of \[{{H}_{2}}{{O}_{2}}\]follows a first order reaction. In fifty minutes the concentration of \[{{H}_{2}}{{O}_{2}}\]decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of \[{{H}_{2}}{{O}_{2}}\]reaches 0.05 M, the rate of formation of \[{{O}_{2}}\]will be :-
[JEE Main Solved Paper-2016 ]
question_answer69) The pair having the same magnetic moment is:- \[[\text{At}.\text{No}.:\text{Cr}=\text{24},\text{Mn}=\text{25},\text{Fe}=\text{26},\text{Co}=\text{27}]\]
[JEE Main Solved Paper-2016 ]
question_answer73) The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :
[JEE Main Solved Paper-2016 ]
question_answer76) In the Hofmann bromamide degradation reaction, the number of moles of NaOH and \[\text{B}{{\text{r}}_{\text{2}}}\]used per mole of amine produced are :
[JEE Main Solved Paper-2016 ]
A)
Four moles of NaOH and one mole of \[\text{B}{{\text{r}}_{\text{2}}}\]
doneclear
B)
One mole of NaOH and one mole of \[\text{B}{{\text{r}}_{\text{2}}}\]
doneclear
C)
Four moles of NaOH and two moles of \[\text{B}{{\text{r}}_{\text{2}}}\]
doneclear
D)
Two moles of NaOH and two moles of \[\text{B}{{\text{r}}_{\text{2}}}\]
question_answer80) A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron respectively, then the value of\[h/\lambda \](where \[\lambda \]is wavelength associated with electron wave) is given by :
[JEE Main Solved Paper-2016 ]
question_answer81) 18 g glucose \[({{C}_{6}}{{H}_{12}}{{O}_{6}})\]is added to 178.2 g water. The vapour pressure of water (in torr) for this aqueous solution is :
[JEE Main Solved Paper-2016 ]
question_answer87) For a linear plot of log(x/m) versus log p in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are constants)
[JEE Main Solved Paper-2016 ]
question_answer89) The equilibrium constants at 298 K for a reaction \[A+BC+D\]is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol\[{{L}^{-1}}\]) will be :
[JEE Main Solved Paper-2016 ]