JEE Main 2013 Paper 1 April 7 Question Paper is available here with solutions PDF, the official paper PDF and detailed solutions for every question. CBSE conducted the pen-and-paper (offline) JEE Main 2013 Paper 1 (B.E./B.Tech) on April 7, 2013. The 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: multiple choice questions (MCQs) with 4 options, one correct answer
- Marking: +4 for a correct answer, -1 for an incorrect answer, 0 for an unattempted question
- Maximum marks: 360 (120 per subject)
JEE Main 2013 Paper 1 April 7 Question Paper with Solution PDF
| CBSE Official PDF | CD PDF | CD PDF with Solutions |
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JEE Main 2013 Paper 1 April 7 Questions with Solutions
Mathematics (Q1 - Q30)
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of \(A \times B\) having 3 or more elements is :
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of \(10\) to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
\(\displaystyle\lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\) is equal to
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers \(x\) is given by \(\frac{dP}{dx} = 100 - 12\sqrt{x}\). If the firm employs 25 more workers, then the new level of production of items is
The area (in square units) bounded by the curves \(y=\sqrt{x}\), \(2y-x+3=0\), \(x\)-axis, and lying in the first quadrant is :
Statement-1 : The value of the integral \(\displaystyle\int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}\) is equal to \(\pi/6\)
Statement-2 : \(\displaystyle\int_a^b f(x)\,dx=\int_a^b f(a+b-x)\,dx\).
If \(\displaystyle\int f(x)\,dx=\psi(x)\), then \(\displaystyle\int x^5 f(x^3)\,dx\) is equal to
If \(x,y,z\) are in A.P. and \(\tan^{-1}x,\tan^{-1}y\) and \(\tan^{-1}z\) are also in A.P., then :
The equation of the circle passing through the foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}=1\) and having centre at (0, 3) is
If \(y=\sec\left(\tan^{-1}x\right)\), then \(\dfrac{dy}{dx}\) at \(x=1\) is equal to :
If the lines \(\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}\) and \(\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}\) are coplanar, then \(k\) can have :
A ray of light along \(x + \sqrt{3}\,y = \sqrt{3}\) gets reflected upon reaching \(X\)-axis, the equation of the reflected ray is :
The \(x\)-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as \((0, 1), (1, 1)\) and \((1,0)\) is
The term independent of \(x\) in expansion of \(\bigg(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\bigg)^{10}\) is
Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \(T_{n+1}-T_n =10\) then the value of \(n\) is
The number of values of \(k\), for which the system of equations :
\((k + 1)x + 8y = 4k\)
\(kx + (k + 3)y = 3k - 1\)
has no solution, is
If the equations \(x^2+2x+3=0\) and \(ax^2+bx+c=0, a, b, c \in R\) have a common root, then \(a : b : c\) is
If \(z\) is a complex number of unit modulus and argument \(\theta ,\) then \( \, arg \left(\frac{1 + z}{1 + \bar{z}}\right)\) is equal to
The real number \(k\) for which the equation \(2x^3 + 3x + k = 0\) has two distinct real roots in \([0, 1]\)
The expression\(\frac{tan\, A}{1-cot\, A}+\frac{cot\, A}{1-tan \, A}\) can be written as
If the vectors \(\overrightarrow{AB} = 3\hat{i} + 4\hat{k}\) and \(\overrightarrow{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}\) are the sides of a triangle \(ABC\), then the length of the median through \(A\) is :
Distance between two parallel planes \(2x+ y + 2z = 8\) and \(4x + 2y + 4z + 5 = 0\) is
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :
The circle passing through \((1, -2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point :
Given : A circle, \(2x^2 + 2y^2 = 5\) and a parabola, \(y^2 = 4\sqrt{5}\,x\).
Statement-1 : An equation of a common tangent to these curves is \(y = x + \sqrt{5}\).
Statement-2 : If the line, \(y = mx + \frac{\sqrt{5}}{m}\;(m \ne 0)\) is their common tangent, then \(m\) satisfies \(m^4 - 3m^2 + 2 = 0\).
\(ABCD\) is a trapezium such that \(AB\) and \(CD\) are parallel and \(BC\) \(\perp\) \(CD\), if \(\angle \) \(ADB = \theta, BC = p\) and \(CD = q\), then \(AB\) is equal to
The intercepts on \(x\)-axis made by tangents to the curve,
\(y = \int_0^x |t|\,dt,\; x \in R,\)
which are parallel to the line \(y = 2x\), are equal to :
The sum of first \(20\) terms of the sequence \(0.7, 0.77, 0.777,....,\) is
If \(P=\begin{bmatrix}1&\alpha&3\\1&3&3\\2&4&4\end{bmatrix}\) is the adjoint of a \(3\times3\) matrix \(A\) and \(|A|=4\), then \(\alpha\) is equal to :
Consider :
Statement - I : \((p\wedge\sim q)\wedge(\sim p\wedge q)\) is a fallacy.
Statement - II : \((p\to q)\leftrightarrow(\sim q\to\sim p)\) is a tautology.
Physics (Q31 - Q60)
A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is
In a hydrogen like atom electron makes transition from an energy level with quantum number \(n\) to another with quantum number \((n - 1). If n > > 1\), the frequency of radiation emitted is proportional to
A diode detector is used to detect an amplitude modulated wave of \(60\%\) modulation by using a condenser of capacity \(250\) picofarad in parallel with a load resistance \(100\) \(\Omega\). Find the maximum modulated frequency which could be detected by it.
The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ nT\). The peak value of electric field strength is :
The anode voltage of a photocell is kept fixed. The wavelength \(\lambda\) of the light falling on the cathode is gradually changed. The plate current \(I\) of photocell varies as follows
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Two coherent point sources \(S_1\) and \(S_2\) are separated by a small distance \(d\) as shown. The fringes obtained on the screen will be
The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by
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In an \(LCR\) circuit as shown below both switches are open initially. Now switch \(S_1\) is closed, \(S_2\) kept open. (\(q\) is charge on the capacitor and \(\tau=RC\) is Capacitance time constant). Which of the following statement is correct ?
A metallic rod of length \(l\) is tied to a string of length \(2l\) and made to rotate with angular speed (\(\omega\) on a horizontal table with one end of the string fixed. If there is a vertical magnetic field \(B\) in the region, the emf induced across the ends of the rod is
Diameter of a plano-convex lens is \(6 \,cm\) and thickness at the centre is 3 mm. If speed of light in material of lens is \(2 \times 10^8\) m/s, the focal length of the lens is
A beam of unpolarized light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of 45\(^{\circ}\) relative to that of \(A\). The intensity of the emergent light is
Two short bar magnets of length \(1\, cm\) each have magnetic moments \(1.20 \,Am^2 \) and \(1.00 \,Am^2 \) respectively. They are placed on a horizontal table parallel to each other with their \(N\) poles pointing towards the south. They have a common magnetic equator and are separated by a distance of \(20.0\, cm\). The value of the resultant horizontal magnetic induction at the mid-point \(O\) of the line joining their centres is close to (Horizontal component of the earth's magnetic induction is \( 3.6 \times {10}^{-5} W b/m^2\)
The supply voltage in a room is \(120\, V\). The resistance of the lead wires is \(6 \, \Omega\). A \(60\, W\) bulb is already switched on. What is the decrease of voltage across the bulb, when a \(240\, W\) heater is switched on in parallel to the bulb?
This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Higher the range, greater is the resistance of ammeter. To increase the range of ammeter, additional shunt needs to be used across it.
Two charges, each equal to \(q\), are kept at \(x = - a\) and \(x = a\) on the \(x-axis\). A particle of mass m and charge \(q_0=\frac{q}{2}\) is placed at the origin. If charge \(q_0\) is given a small displacement \(y ( y << a)\) along the y-axis, the net force acting on the particle is proportional to
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass \(M\). The piston and the cylinder have equal cross-sectional area \(A\). When the piston is in equilibrium, the volume of the gas is \(V_0\) and its pressure is \(P_0\). The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
A sonometer wire of length \(1.5\ m\) is made of steel. The tension in it produces an elastic strain of \(1\%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7\times10^{3}\ kg/m^3\) and \(2.2\times10^{11}\ N/m^2\) respectively ?
Two capacitors \(C_1\) and \(C_2\) are charged to \(120\ V\) and \(200\ V\) respectively. It is found that connecting them together the potential on each one can be made zero. Then
A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is
The shown p- V diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is
Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is \(T\), density of liquid is \(\rho\) and \(L\) is its latent heat of vaporization.
What is the minimum energy required to launch a satellite of mass \(m\) from the surface of a planet of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2\,R\) ?
This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - I: A point particle of mass \(m\) moving with speed \(v\) collides with stationary point particle of mass \(M\). If the maximum energy loss possible is given as \(f\left(\frac{1}{2}mv^2\right)\), then \(f = \left(\frac{m}{M+m}\right)\).
Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
A uniform cylinder of length \(L\) and mass \(M\) having cross-sectional area \(A\) is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density \(\sigma\) at equilibrium position. The extension \(x_0\) of the spring when it is in equilibrium is:
A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?
A projectile is given an initial velocity of \((\hat{i} + 2\hat{j}) m/s\), where \(\hat{i}\) is along the ground and \(\hat{j}\) is along the vertical. If \(g = 10 m/s^2\), then the equation of its trajectory is
Let \([\varepsilon_0]\) denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
If a piece of metal is heated to temperature \(\theta\) and then allowed to cool in a room which is at temperature \(\theta_0\), the graph between the temperature \(T\) of the metal and time \(t\) will be closest to
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The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude is \(5\, s\). In another \(10\, s\) it will decrease to a times its original magnitude, where \(\alpha\) equals
Chemistry (Q61 - Q90)
A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of \(37.0^\circ\mathrm{C}\). As it does so, it absorbs 208 J of heat. The values of q and w for the process will be:
(R = 8.314 J/mol K) (\(\ln 7.5 = 2.01\))
How many litres of water must be added to 1 litre of an aqueous solution of \(\mathrm{HCl}\) with a pH of 1 to create an aqueous solution with pH of 2?
An unknown alcohol is treated with the "Lucas reagent" to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:
The order of stability of the following carbocations
An organic compound A upon reacting with \(\mathrm{NH_3}\) gives B. On heating B gives C. C in presence of KOH reacts with \(\mathrm{Br_2}\) to given \(\mathrm{CH_3CH_2NH_2}\)2. A is :
Arrange the following compounds in the order of decreasing acidity
Compound \(( A ), C_8H_9Br\) gives a white precipitate when warmed with alcoholic \(AgNO_3\). Oxidation of \((A)\) gives an acid \((B)\), \(C_8H_6O\) 4. \((B)\) easily forms anhydride on heating. Identify the compound \((A)\).
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The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:
Which of the following complex species is not expected to exhibit optical isomerism?
Synthesis of each molecule of glucose in photosynthesis involves:
A compound with molecular mass \(180\) is acylated with \(CH_3COCl\) to get a compound with molecular mass \(390\). The number of amino groups present per molecule of the former compound is
The rate of a reaction doubles when its temperature changes from \(300\, K\) to \(310\,K\). Activation energy of such a reaction will be \((R = 8.314 JK^{-1} \,mol^{-1}\) and \(log \,2 = 0.301)\)
Which of the following arrangements does not represent the correct order of the property stated against it?
Four successive members of the first row transition elements listed below with atomic numbers. Which one of them is expected to have the highest \(E_{m{^{3+}}/m{^{2+}}}^{\circ}\)value?
Given, \(E^\circ _{Cr ^{3+}/Cr} =-0.74\, V;E^\circ_{MnO^-_4/Mn^{2+}}=1.51\, V\) \(\, \, \, \, \, E^\circ _{Cr_2 O ^{2-}_7/Cr^{3+}} =-1.33\, V;E^\circ_{Cl/Cl^-}=1.36\, V\) Based on the data given above strongest oxidising agent will be
The molarity of a solution obtained by mixing \(750\, mL\) of \(0.5\, M \,HCl\) with \(250\, mL\) of \(2 \,M \,HCl\) will be
A solution of \((-) 1-chloro-1-\)phenylethane in toluene racemises slowly in the presence of a small amount of \(SbCl_5\), due to the formation of
Stability of the species \( Li_2 , Li_2^- , \, \, and \, \, Li_2^+ \) increases in the order of
In which of the following pairs of molecules/ions both the species are not likely to exist?
Which one of the following molecules is expected to exhibit diamagnetic behaviour?
Which of the following represents the correct order of increasing first ionisation enthalpy for \(Ca, Ba, S, Se\) and \(Ar\)?
The first ionisation potential of \(Na\) is \(5.1\, eV\). The value of electron gain enthalpy of \(Na^+\) will be
Energy of an electron is given by
\(E = -2.178 \times 10^{-18}\,\mathrm{J}\left(\frac{Z^2}{n^2}\right)\)
. Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be
(h = \(6.62 \times 10^{-34}\) Js and c = \(3.0 \times 10^{8}\) ms-1)
Consider the following reaction, \(xMnO_4^- + yC_2O_4^{2-}+zH^+ \rightarrow xMn^{2+}+2yCO_2 + \frac{z}{2}H_2O\) The values of x, y and z in the reaction are, respectively
Experimentally it was found that a metal oxide has formula \( M_{0.98}O. \) Metal \(M\), present as \( M^{2+} \) and \( M^{3+} \) in its oxide.Fraction of the metal which exists as \( M^{3+} \) would be
A gaseous hydrocarbon gives upon combustion \(0.72\, g\) of water and \(3.08\, g\) of \(CO_2\). The empirical formula of the hydrocarbon is
For gaseous state, if most probable speed is denoted by \(c *\), average speed by \(\overline{C}\) and root square speed by \(c\), then for a large number of molecules, the ratios of these speeds are
Which of the following exists as covalent crystals in the solid state?
The coagulating power of electrolytes having ions \(Na^+, Al^{3+}\) and \(Ba^{2+}\) for arsenic sulphide sol increases in the order
Which of the following is the wrong statement?
JEE Main 2013 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 (30 per subject) |
| Total Marks | 360 marks |
| Marking Scheme | +4 for correct answer & -1 for incorrect answer; 0 for unattempted |
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