JEE Main 2017 · 02 Apr 2017 · Offline

Q1.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 :

Q2.The temperature of an open room of volume $30{\mathrm{m}}^3$ increases from $17^{\circ }\mathrm{C}$ to $27^{\circ }\mathrm{C}$ due to the sunshine. The atmospheric pressure in the room remains $1\times 10^5\mathrm{Pa}$. If ${\mathrm{n}}_i$ and ${\mathrm{n}}_f$ are the numb …

Q3.Which of the following statements is false ?
(1) A rheostat can be used as a potential divider.
(2) Kirchhoff's second law represents energy conservation.
(3) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.
(4) In a balanc …

Q4.The following observations were taken for determining surface tension T of water by capillary method :
diameter of capillary, $D=1.25\times 10^{-2}\mathrm{m}$
rise of water, $\mathrm{h}=1.45\times 10^{-2}\mathrm{m}$.

Using $\mathrm{g}=9.80\mathrm{m}/{\mathrm{s}}^2$ and …

Q5.In amplitude modulation, sinusoidal carrier frequency used is denoted by ${\omega }_{\mathrm{c}}$ and the signal frequency is denoted by ${\omega }_{\mathrm{m}}$. The bandwidth ( $\Delta {\omega }_{\mathrm{m}}$ ) of the signal is such that …

Q6.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 :

Q7.The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is I. What is the ratio $l/R$ such that the moment of inertia is minimum?

Q8.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 ${\lambda }_{\text{min }}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of …

Q9.A radioactive nucleus A with a half life T, decays into a nucleus B. At $t=0$, there is no nucleus B. At sometime $t$, the ratio of the number of B to that of A is 0.3. Then, $t$ is given by :

Q10.An electric dipole has a fixed dipole moment $\overrightarrow{\mathrm{p}}$, which makes angle $\theta$ with respect to $x$-axis. When subjected to an electric field ${\overrightarrow{\mathrm{E}}}_1=\mathrm{E}\hat{i}$, it experiences a torque …

Q11.In a common emitter amplifier circuit using an $\mathrm{n}-\mathrm{p}-\mathrm{n}$ transistor, the phase difference between the input and the output voltages will be :

Q12.$C_p$ 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:

Q13.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 $75^{\circ }C$. T is given by: (Given: room temperature …

Q14.A body of mass $m=10^{-2}$ kg is moving in a medium and experiences a frictional force $F=-k{v}^2$. Its initial speed is $v_0=10$ ms${}^{-1}$. If, after 10 s, its energy is $\frac{1}{8}m{v}_0^2$, the value of k will be:

Q15.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 a voltmeter of range 0-10 V is:

Q16.A slender uniform rod of mass M and length $l$ 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 m …

Q17.Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r={\lambda }_1/{\lambda }_2$, is given by:

Q18.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:

Q19.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:

Q20.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 …

Q21.A magnetic needle of magnetic moment $6.7\times 10^{-2}$ Am${}^2$ 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:

Q22.The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R=$ Earth's radius):

Q23.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:

Q24.An external pressure $P$ is applied on a cube at $0^{\circ }\mathrm{C}$ 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 b …

Q25.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 :

Q26.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 ?
(speed of light $=3\times 10^8{\mathrm{ms}}^{-1}$)

Q27.In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

Q28.A capacitance of $2\mu \mathrm{F}$ is required in an electrical circuit across a potential difference of 1.0 kV . A large number of $1\mu \mathrm{F}$ capacitors are available which can withstand a potential difference of not more than 300 V .

The minimum number of capacitors …

Q29.A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Q1.Which of the following compounds will form significant amount of meta product during mono-nitration reaction?

Q2.$\Delta \mathrm{U}$ is equal to :

Q3.The increasing order of the reactivity of the following halides for the ${\mathrm{S}}_{\mathrm{N}}1$ reaction

(I) (see structure)
(II) ${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{CH}}_2\mathrm{Cl}$
(III) …

Q4.The radius of the second Bohr orbit for hydrogen atom is :
(Planck's Const. $\mathrm{h}=6.6262\times 10^{-34}\mathrm{Js}$; mass of electron $=9.1091\times 10^{-31}\mathrm{kg}$; charge of electron $\mathrm{e}=1.60210\times 10^{-19}\mathrm{C}$; permittivity of vacuum …

Q5.$\mathrm{p}{K}_{\mathrm{a}}$ of a weak acid (HA) and $\mathrm{p}{K}_{\mathrm{b}}$ of a weak base $(\mathrm{BOH})$ are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :

Q6.The formation of which of the following polymers involves hydrolysis reaction?

Q7.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 ${}^1\mathrm{H}$ atoms are replaced by …

Q8.Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolourize the colour of bromine?

Q9.In the following reactions, ZnO is respectively acting as a/an :
(a) $\mathrm{ZnO}+{\mathrm{Na}}_2\mathrm{O}\to {\mathrm{Na}}_2{\mathrm{ZnO}}_2$
(b) $\mathrm{ZnO}+{\mathrm{CO}}_2\to {\mathrm{ZnCO}}_3$

Q10.Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is :

Q11.3-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 :

Q12.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 :

Q13.Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by $10\mathrm{kJ}{\mathrm{mol}}^{-1}$. If ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are rate constants for reactions $R_1$ and $R_2$ …

Q14.The correct sequence of reagents for the following conversion will be :

Q15.The Tyndall effect is observed only when following conditions are satisfied :
(a) The diameter of the dispersed particles is much smaller than the wavelength of the light used.
(b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used.
( …

Q16.Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

Q17.Given
${\mathrm{C}}_{\text{(graphite) }}+{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g})$;
${\Delta }_{\mathrm{r}}{\mathrm{H}}^{\circ }=-393.5\mathrm{kJ}{\mathrm{mol}}^{-1}$ …

Q18.Which of the following reactions is an example of a redox reaction?

Q19.Which of the following species is not paramagnetic ?

Q20.The freezing point of benzene decreases by $0.45^{\circ }\mathrm{C}$ 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 :
$({\mathrm{K}}_{\mathrm{f}}$ for benzene …

Q21.Which of the following molecules is least resonance stabilized ?

Q22.On treatment of 100 mL of 0.1 M solution of ${\mathrm{CoCl}}_3\cdot 6{\mathrm{H}}_2\mathrm{O}$ with excess ${\mathrm{AgNO}}_3$; $1.2\times 10^{22}$ ions are precipitated. The complex is :

Q23.A water sample has ppm level concentration of following anions
${\mathrm{F}}^{-}=10;{\mathrm{SO}}_4^{2-}=100;{\mathrm{NO}}_3^{-}=50$

The anion/anions that make/makes the water sample unsuitable for drinking is/ are :

Q24.1 gram of a carbonate $({\mathrm{M}}_2{\mathrm{CO}}_3)$ on treatment with excess HCl produces 0.01186 mole of ${\mathrm{CO}}_2$. The molar mass of ${\mathrm{M}}_2{\mathrm{CO}}_3$ in $\mathrm{g}{\mathrm{mol}}^{-1}$ is :

Q25.Given
${\mathrm{E}}_{{\mathrm{Cl}}_2/{\mathrm{Cl}}^{-}}^{\circ }=1.36\mathrm{V},{\mathrm{E}}_{{\mathrm{Cr}}^{3+}/\mathrm{Cr}}^{\circ }=-0.74\mathrm{V}$ …

Q26.The group having isoelectronic species is :

Q27.The products obtained when chlorine gas reacts with hot and concentrated NaOH are:

Q28.Sodium salt of an organic acid 'X' reacts with aqueous CaCl₂ solution to give a white precipitate. The organic acid salt 'X' is:

Q29.The major product obtained in the following reaction is: [PhCHBr-CH₂Ph treated with tBuOK — structure in source]

Q1.Let k be an integer such that the triangle with vertices $(\mathrm{k},-3\mathrm{k}),(5,\mathrm{k})$ and $(-\mathrm{k},2)$ has area 28 sq. units. Then the orthocentre of this triangle is at the point :

Q2.If, for a positive integer n , the quadratic equation,
$x(x+1)+(x+1)(x+2)+\dots$.
$+(x+\overline{\mathrm{n}-1})(x+\mathrm{n})=10\mathrm{n}$
has two consecutive integral solutions, then n is equal to :

Q3.The function $f:\mathbf{R}\to \left[-\frac{1}{2},\frac{1}{2}\right]$ defined as $f(x)=\frac{x}{1+x^2}$, is :

Q4.The following statement
$(\mathrm{p}\to \mathrm{q})\to [(\sim \mathrm{p}\to \mathrm{q})\to \mathrm{q}]$ is :

Q5.If S is the set of distinct values of ' b ' for which the following system of linear equations

has no solution, then S is :

Q6.The area (in sq. units) of the region $\{(x,y):x⩾0,x+y\le 3,x^2\le 4y$ and $y\le 1+\sqrt{x}\}$ is :

Q7.For any three positive real numbers $\mathrm{a},\mathrm{b}$ and c ,
$9\left(25a^2+b^2\right)+25\left(c^2-3ac\right)=15b(3a+c)$.
Then :

Q8.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 …

Q9.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:

Q10.A hyperbola passes through the point $\mathrm{P}(\sqrt{2},\sqrt{3})$ and has foci at $(\pm 2,0)$. Then the tangent to this hyperbola at P also passes through the point :

Q11.Let $\mathrm{a},\mathrm{b},\mathrm{c}\in \mathbf{R}$. If $f(x)=\mathrm{a}{x}^2+\mathrm{b}x+\mathrm{c}$ is such that $\mathrm{a}+\mathrm{b}+\mathrm{c}=3$ and
$f(x+y)=f(x)+f(y)+xy,\forall x,y\in \mathbf{R}$, then ${\sum }_{\mathrm{n}=1}^{10}f(\mathrm{n})$ is equal …

Q12.Let $\overrightarrow{\mathrm{a}}=2\hat{i}+\hat{j}-2\hat{k}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+\hat{j}$. Let $\vec{c}$ be a vector such that $|\vec{c}-\vec{a}|=3$, $|(\vec{a}\times \vec{b})\times \vec{c}|=3$ and the angle between …

Q13.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 $\mathrm{AP}=2\mathrm{AB}$. If $\angle \mathrm{BPC}=\beta$, then $\tan \beta$ is equal to :

Q14.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 :

Q15.The integral ${\int }_{\frac{\pi }{4}}^{\frac{3\pi }{4}}\frac{\mathrm{d}x}{1+\cos x}$ is equal to :

Q16.If $(2+\sin x)\frac{\mathrm{d}y}{\mathrm{d}x}+(y+1)\cos x=0$ and $y(0)=1$, then $y\left(\frac{\pi }{2}\right)$ is equal to :

Q17.Let ${\mathrm{I}}_{\mathrm{n}}=\int {\tan }^{\mathrm{n}}x\mathrm{d}x,(\mathrm{n}>1).$ If ${\mathrm{I}}_4+{\mathrm{I}}_6=\mathrm{a}{\tan }^{5}x+\mathrm{b}{x}^5+\mathrm{C}$, where C is a constant of integration, then the ordered pair $(a,b)$ is equal to :

Q18.Let $\omega$ be a complex number such that $2\omega +1=z$ where $z=\sqrt{-3}$. If
$\left|\begin{array}{rrr}1& 1& 1\\ 1& -{\omega }^2-1& {\omega }^2\\ 1& {\omega }^2& {\omega }^7\end{array}\right|=3\mathrm{k}$,
then k is equal to :

Q19.The value of $\left({}^{21}{C}_1-{}^{10}{C}_1\right)+\left({}^{21}{C}_2-{}^{10}{C}_2\right)+\left({}^{21}{C}_3-{}^{10}{C}_3\right)+\left({}^{21}{C}_4-{}^{10}{C}_4\right)+\dots ..+\left({}^{21}{\mathrm{C}}_{10}-{}^{10}{\mathrm{C}}_{10}\right)$ is :

Q20.${\lim }_{x\to \frac{\pi }{2}}\frac{\cot x-\cos x}{(\pi -2x{)}^3}$ equals :

Q21.If $5\left({\tan }^{2}x-{\cos }^{2}x\right)=2\cos 2x+9$, then the value of $\cos 4x$ is :

Q22.If the image of the point $\mathrm{P}(1,-2,3)$ in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ is Q , then PQ is equal to :

Q23.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 :

Q24.If for $x\in \left(0,\frac{1}{4}\right)$, the derivative of ${\tan }^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right)$ is $\sqrt{x}\cdot \mathrm{g}(x)$, then $\mathrm{g}(x)$ equals :

Q25.The radius of a circle, having minimum area, which touches the curve $y=4-x^2$ and the lines, $y=|x|$ is :

Q26.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 :

Q27.The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$. If one of its directrices is $x=-4$, then the equation of the normal to it at $\left(1,\frac{3}{2}\right)$ is :

Q28.If two different numbers are taken from the set $\{0,1,2,3,\dots \dots ,10\}$; then the probability that their sum as well as absolute difference are both multiple of 4, is :

Q29.For three events $\mathrm{A},\mathrm{B}$ and C ,

P(Exactly one of A or B occurs)
$=\mathrm{P}($ Exactly one of B or C occurs $)$
$=\mathrm{P}($ Exactly one of C or A occurs $)=\frac{1}{4}$ and
P(All the three events occur simultaneously) $=\frac{1}{16}$.

Then the p …

Q30.If $A=\left[\begin{array}{rr}2& -3\\ -4& 1\end{array}\right]$, then $\mathrm{adj}\left(3A^2+12A\right)$ is equal to :