JEE Main 2016 April 3 (Code F) Question Paper is available here with solutions PDF and detailed solutions for every question. CBSE conducted the pen-and-paper (offline) Paper 1 on April 3, 2016, in the morning session from 9:30 AM to 12:30 PM. This page covers Code F of the paper. The JEE Main 2016 Paper 1 (B.E./B.Tech) question paper includes the following:
- 90 questions in a 3-hour pen-and-paper (offline) paper: 30 each from Mathematics, Physics and Chemistry
- Question type: all multiple choice questions (MCQs) with a single correct option, 4 marks each
- Sections: Mathematics (30), Physics (30) and Chemistry (30), all questions compulsory
- Marking: +4 for a correct answer, -1 for an incorrect answer, 0 for an unattempted question
- Maximum marks: 360 (120 per subject)
JEE Main 2016 April 3 (Code F) Question Paper with Solution PDF
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JEE Main 2016 April 3 (Code F) Questions with Solutions
Mathematics (Q1 - Q30)
For \( x \epsilon R , f (x) = | \log 2 - \sin x|\) and \(g(x) = f(f(x))\), then :
Let \(p = \displaystyle\lim_{x \to 0^+ } ( 1 + \tan^2 \sqrt{x} )^{\frac{1}{2x}}\) then \(log \,p\) is equal to
If the standard deviation of the numbers \(-1,0,1,k\) is \(\sqrt5\) where \(k\gt0\), then \(k\) is equal to
A value of \(\theta\) for which \(\frac{2+3i\sin\theta}{1-2i\sin\theta}\) is purely imaginary, is :
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?
The area (in sq. units) of the region \(\{(x,y): y^2\ge 2x\ \text{and}\ x^2+y^2\le 4x,\ x\ge0,\ y\ge0\}\) is :
If a curve \(y = f(x)\) passes through the point \((1, -1)\) and satisfies the differential equation, \(y(1 + xy) dx = x \,dy\), then \(f \left( - \frac{1}{2} \right)\) is equal to :
The integral \(\int\frac{2x^{12}+5x^{9}}{(x^{5}+x^{3}+1)^{3}}\,dx\) is equal to :
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 :
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 :
If \(A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}\) and \(A\) adj \(A\) = \(AA^T\) , then \(5a + b\) is equal to :
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 :
If one of the diameters of the circle, given by the equation, \(x^2+y^2-4x+6y-12=0\), is a chord of a circle \(S\), whose centre is at \((-3,2)\), then the radius of \(S\) is :
Two sides of a rhombus are along the lines, \(x - y + 1 = 0\) and \(7x - y - 5 = 0\). If its diagonals intersect at \((-1, -2)\), then which one of the following is a vertex of this rhombus?
If the \(2^{nd}, 5^{th}\) and \(9^{th}\) terms of a non-constant \(A.P.\) are in \(G.P.\), then the common ratio of this \(G.P.\) is :
The sum of all real values of \(x\) satisfying the equation \((x^2 - 5x + 5)^{x^2 + 4x -60} = 1 \) is
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:
If \(f(x)+2f\left(\frac1x\right)=3x,\ x\ne0\), and \(S=\{x\in\mathbf{R}: f(x)=f(-x)\}\); then \(S\) :
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:
Let \(\vec a,\ \vec b\) and \(\vec c\) be three unit vectors such that \(\vec a\times(\vec b\times\vec c)=\frac{\sqrt3}{2}(\vec b+\vec c)\). If \(\vec b\) is not parallel to \(\vec c\), then the angle between \(\vec a\) and \(\vec b\) is:
If the sum of the first ten terms of the series \(\left(1 \frac{3}{5}\right)^{2} + \left(2 \frac{2}{5}\right)^{2} + \left(3 \frac{1}{5}\right)^{2} + 4^{2} + \left(4 \frac{4}{5}\right)^{2} + .... , \) is \(\frac{16}{5} m , \) then \(m\) is equal to :
If the number of terms in the expansion of \(\left( 1 - \frac{2}{x} + \frac{4}{x^2} \right)^n , x \neq 0\) , is \(28\) , then the sum of the coefficients of all the terms in this expansion, is :
\(\lim_{n\to\infty}\left(\frac{(n+1)(n+2)\dots3n}{n^{2n}}\right)^{\frac1n}\) is equal to:
The Boolean expression \(\sim(p \vee q) \vee (\sim p \wedge q)\) is equivalent to :
If the line, \(\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}\) lies in the planes, \(lx+my-z=9\), then \(l^2+m^2\) is equal to :
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, from B to reach the pillar, is :
The locus of the centres of the circles, which touch the circle, \(x^2+y^2=1\) externally, also touch the y-axis and lie in the first quadrant, is :
Let \(P\) be the point on the parabola, \(y^2=8x\) which is at a minimum distance from the centre \(C\) 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:
The distance of the point \((1,-5,9)\) from the plane \(x-y+z=5\) measured along the line \(x=y=z\) is :
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:
Physics (Q31 - Q60)
Radiation of wavelength \(\lambda\), is incident on a photocell. The fastest emitted electron has speed \(v\). If the wavelength is changed to \(\frac{3 \lambda}{4}\), the speed of the fastest emitted electron will be :
Identify the semiconductor devices whose characteristics are given below, in the order \((a), (b), (c), (d)\) :
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 :
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 \(79^{\circ}\). ?n that case which of the following is closest to the maximum possible value of the refractive index ?
A particle of mass \(m\) is moving along the side of a square of side \(a\), with a uniform speed \(v\) in the \(x\)-\(y\) plane as shown in the figure :
Which of the following statements is false for the angular momentum \(\vec{L}\) about the origin ?
Arrange the following electromagnetic radiations per quantum in the order of increasing energy :
A : Blue light
B : Yellow light
C : X-ray
D : Radiowave.
An arc lamp requires a direct current of \(10\, A\) at \(80 \,V\) to function. If it is connected to a \(220 \,V \,(rms)\), \(50 \,Hz\, AC\) supply, the series inductor needed for it to work is close to :
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 :
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 :
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 :
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 :
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 \(10\, A\) is :
The temperature dependence of resistance of \(\mathrm{Cu}\) and undoped \(\mathrm{Si}\) in the temperature range \(300 - 400\ \mathrm{K}\), is best described by :
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 distant \(30\, m\) from it, would equal :
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 :
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 :
A uniform string of length \(20 \,m\) 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 \(g\, = \,10\,ms^{-2}\))
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 frequency of the air column is now :
\('n'\) 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 :
An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity Cremains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(PV^n =\) constant, then \(n\) is given by (Here \(C_P\) and \(C_V\) are molar specific heat at constant pressure and constant volume, respectively) :
A pendulum clock loses \(12\,s\) a day if the temperature is \(40^{\circ}C\) and gains \(4\,s\) a day if the temperature is \(20^{\circ}C\). The temperature at which the clock will show correct time, and the co-efficient of linear expansion \((\alpha)\) of the metal of the pendulum shaft are respectively :
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 :
A person trying to lose weight by burning at 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 \(3.8 \times 10^7 \, J\) of energy per kg which is converted to mechanical energy with a \(20\%\) efficiency rate. Take \(g = 9.8 \, ms^{-2}\) :
A point particle of mass \(m\), moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). 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 \(QR\), 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 \(\mu\) and the distance \(x(=QR)\), are, respectively close to :
A satellite is revolving 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.)
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 \(45^{th}\) 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 \(25^{th}\) division coincides with the main scale line ?
Choose the correct statement :
For a common emitter configuration, if \(\alpha\) and \(\beta\) have their usual meanings, the incorrect relationship between \(\alpha\) and \(\beta\) is :
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 :
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 :
Chemistry (Q61 - Q90)
The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :
Which of the following compounds is metallic and ferromagnetic ?
Decomposition of \(H_2O_2\) follows a first order reaction. In fifty minutes the concentration of \(H_2O_2\) decreases from \(0.5\) to \(0.125 \,M\) in one such decomposition. When the concentration of \(H_2O_2\) reaches \(0.05 \,M\), the rate of formation of \(O_2\) will be :
Galvanization is applying a coating of :
18 g glucose (\(\mathrm{C_6H_{12}O_6}\)) is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueous solution is :
The reaction of propene with HOCl (\(\mathrm{Cl_2 + H_2O}\)) proceeds through the intermediate:
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 :
The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :
The equilibrium constant at 298 K for a reaction \(\mathrm{A + B \rightleftharpoons C + D}\) is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in \(\mathrm{mol\ L^{-1}}\)) will be:
The heats of combustion of carbon and carbon monoxide are \(-393.5\) and \(-283.5 \, kJ \, mol^{-1}\), respectively. The heat of formation (in \(kJ\)) of carbon monoxide per mole is :
The absolute configuration of
is :
2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields:
In the Hofmann bromamide degradation reaction, the number of moles of NaOH and \(\mathrm{Br_2}\) used per mole of amine produced are:
Which one of the following complexes shows optical isomerism?
(en = ethylenediamine)
Thiol group is present in :
The pair having the same magnetic moment is :
[At. No.: Cr = 24, Mn = 25, Fe = 26, Co = 27]
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 :
The species in which the \(N\) atom is in a state of \(sp\) hybridization is :
Which of the following atoms has the highest first ionization energy?
The hottest region of Bunsen flame shown in the figure below is :
The pair in which phosphorous atoms have a formal oxidation state of +3 is :
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 :
Which of the following is an anionic detergent?
Which one of the following ores is best concentrated by froth-flotation method?
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 :
Which of the following statements about low density polythene is FALSE ?
The main oxides formed on combustion of \(Li, Na\) and \(K\) in excess of air are, respectively :
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)
Which one of the following statements about water is FALSE ?
JEE Main 2016 Exam Pattern and Marking Scheme
| Particulars | Details |
|---|---|
| Exam Mode | Offline (Pen and Paper) |
| Paper | B.E./B.Tech (Paper 1) |
| Duration | 3 hours (180 minutes) |
| Type of Questions | Multiple Choice Questions (MCQs) |
| Subjects | Mathematics, Physics, Chemistry |
| Total Questions | 90 questions |
| Total Marks | 360 marks |
| Marking Scheme | +4 for correct answer & -1 for incorrect answer; 0 for unattempted |
JEE Main 2016 April 3 (Code F) Difficulty Level
In terms of difficulty level, JEE Main 2016 (offline mode) was tougher than last year.
JEE Main B.E./B.Tech 2016 Paper Analysis
- Physics was the toughest section with a total of 30 questions.
- Chemistry was the easiest one with 30 questions.
For every correct answer, candidates got 4 marks and for each wrong attempt 1 mark was deducted.
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