JEE Main 2019 · 11 Jan 2019 · Shift 1

Q1.A body is projected at $t=0$ with a velocity $10{\mathrm{ms}}^{-1}$ at an angle of $60^0$ with the horizontal. The radius of curvature of its trajectory at $t=1\mathrm{s}$ is R. Neglecting air resistance and taking acceleration due to gravity $g=10{\mathrm{ms}}^{-2}$, the rad …

Q2.A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980\mathring{A}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be:
($hc=12500\mathrm{eV}$ - Å)

Q3.In the given circuit the current through Zener Diode is close to:

Q4.There are two long co-axial solenoids of same length l. The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

Q5.A satellite is revolving in a circular orbit at a height h from the earth surface, such that $\mathrm{h}\ll \mathrm{R}$ where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the sa …

Q6.The force of interaction between two atoms is given by $F=\alpha \beta \exp \left(-\frac{x^2}{\alpha \mathrm{kt}}\right)$; where $x$ is the distance, k is the Boltzmann constant and T is temperature and $\alpha$ and $\beta$ are two constants. The dimension of $\beta$ …

Q7.In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $1/8^{\text{th }}$ of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:

Q8.In the circuit shown,

The switch ${\mathrm{S}}_1$ is close at time $\mathrm{t}=0$ and the switch $S_2$ is kept open. At some later time ( $t_0$ ), the switch $S_1$ is opened and $S_2$ is closed. The behaviour of the current I as a function of time ' t ' is gi …

Q9.Three charges $\mathrm{Q},+\mathrm{q}$ and +q are placed at the vertices of a right - angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of $Q$ is:

Q10.The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following, graph is the correct one, if ${\mathrm{D}}_{\mathrm{m}}$ is the angle of minimum deviation?

Q11.The equilateral triangle $ABC$ is cut from a thin solid sheet of wood. (See figure) D, E and F are the mid points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of …

Q12.A slab is subjected to the two forces ${\vec{F}}_1$ and ${\vec{F}}_2$ of same magnitude $F$ as shown in the figure. Force ${\vec{F}}_2$ is in $XY$ - plane while force $F_1$ acts along $z-$ axis at the point $(2\vec{i}+3\vec{j})$. The moment of these forces ab …

Q13.Ice at $-20^{\circ }\mathrm{C}$ is added to 50 g of water at $40^{\circ }\mathrm{C}$. When the temperature of the mixture reaches $0^{\circ }\mathrm{C}$, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of wate …

Q14.A particle is moving along a circular path with a constant speed of $10{\mathrm{ms}}^{-1}$. What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{\circ +}$ around the centre of the circle?

Q15.An object is at a distance of 20 m from a convex lens of focal length 0.3 m . The lens forms an image of the object. If the object moves away from the lens at a speed of 5 $\mathrm{m}/\mathrm{s}$, the speed and direction of the image will be:

Q16.A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T . Considering only translational and rotational modes, the total internal energy of the system is:

Q17.Two equal resistances when connected in series to a battery, consume electric power of 60 W . If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be.

Q18.The resistance of the meter bridge AB in given figure is $4\Omega$. With a cell of emf $\epsilon =0.5\mathrm{V}$ and rheostat resistance ${\mathrm{R}}_{\mathrm{h}}=2\Omega$ the null point is obtained at some point J . When the cell is replaced by another one of emf …

Q19.An electromagnetic wave of intensity $50{\mathrm{Wm}}^{-2}$ enters in a medium of refractive index' ${\mathrm{n}}^{\prime }$ without any loss . The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering …

Q20.In the figure shown below, the charge on the left plate of the $10\mu \mathrm{F}$ capacitor is $-30\mu \mathrm{C}$. The charge on the right plate of the $6\mu \mathrm{F}$ capacitor is:

Q21.A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The rational between temperature and volume for the process is TV ${}^{\mathrm{x}}=$ constant, then x is:

Q22.A liquid of density $\rho$ is coming out of a hose pipe of radius a with horizontal speed $v$ and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mes …

Q23.If the deBroglie wavelength of an electron is equal to $10^{-3}$ times the wavelength of a photon of frequency $6\times 10^{14}\mathrm{Hz}$, then the speed of electron is equal to: (Speed of light = $3\times 10^8\mathrm{m}/\mathrm{s}$; Planck's constant …

Q24.The give graph shown variation (with distance r from centre) of:

Q25.Equation of travelling wave on a stretched string of linear density $5\mathrm{g}/\mathrm{m}$ is $y=0.03\sin (450\mathrm{t}-9\mathrm{x})$ where distance and time are measured in SI united. The tension in the string is:

Q26.In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V . Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron $=1.6\times 10^{-19}\mathrm{C}$ Mass of the electron …

Q27.In a Wheatstone bridge (see figure) Resistance $P$ and $Q$ are approximately equal. When $\mathrm{R}=400\Omega$, the bridge is balanced. On interchanging P and Q , the value of R , for balance is $405\Omega$. The value of X is close to:

Q1.Among the following compounds, which one is found in RNA?

Q2.The correct match between items I and II is:

Item - I (Mixture)
(a) $\mathrm{H}{}_2\mathrm{O}$ : Sugar
(b) $\mathrm{H}{}_2\mathrm{O}$ : Aniline
(c) $\mathrm{H}{}_2\mathrm{O}$ : Toluene

Item - II (Separation method)
p. Sublimation
q. Recrystallization
r. Stem distillation
s. Differential extraction

Q3.Which compounds out of the following is/are not aromatic?
(a) (see structure)
(b) (see structure)
(c) (see structure)
(d) (see structure)

Q4.A solid having density of $9\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$ forms face centred cubic crystale of edge length $200\sqrt{2}\mathrm{pm}$. What is the molar mass of the solid?
[Avogadro constant $\cong 6\times 10^{23}$ and ${\mathrm{mol}}^{-1},\pi \cong 3$ ]

Q5.For the cell $\mathrm{Zn}(\mathrm{s})\left|{\mathrm{Zn}}^{2+}(\mathrm{aq})\right|\left|{\mathrm{M}}^{\mathrm{x}}+(\mathrm{aq})\right|\mathrm{M}(\mathrm{s})$, different half cells and their standard electrode potentials are given below:

| …

Q6.The correct match between item I and item II is:

Item - I
a. Norethindrone
b. Ofloxacin
c. Equanil

Item - II
p. Anti - biotic
q. Anti - fertility
r. Hypertention
s. Analgesics

Q7.The polymer obtained from the following reactions is:
(see reaction scheme)

Q8.NaH is an example of:

Q9.The element the usually does NOT show variable oxidation states is:

Q10.An example of solid sol is:

Q11.The concentration of dissolved oxygen (DO) is cold water can go upto:

Q12.The correct statements among (a) to (d) regarding ${\mathrm{H}}_2$ as a fuel are:
(a) it produces less pollutants than petrol
(b) A cylinder of compressed dihydrogen weighs $\sim 30$ times more than a petrol tank producing the same amount of energy.
(c) Dihydrogen is stored in ta …

Q13.The freezing point of diluted milk sample is found to be $-0.2^0\mathrm{C}$, while it should have been $-0.5^{\circ }\mathrm{C}$ for pure milk. How much water been added to pure milk to make the diluted sample?

Q14.If a reaction follows the Arrhenius equation, the plot Ink $\vee 1/(\mathrm{RT})$ gives straight line with a gradient ( -y ) unit. The energy required to activate the reactant is:

Q15.A 10 g effervescent tablet containing sodium bicarbonate and oxalic acid releases 25 mL of ${\mathrm{CO}}_2$ at $\mathrm{T}=298.15\mathrm{K}$ and $\mathrm{p}=1$ bar. If molar volume of ${\mathrm{CO}}_2$ is 25.0 L under such condition, what is the percentage of sodium bicarbonat …

Q16.The amphoteric hydroxide is:

Q17.Peroxyacetyl nitrate (PAN), an eye irritant is produced by:

Q18.The major product of the following reactions is:

Q19.An organic compound is estimated through Dumus method and was found to evolve 6 mole of ${\mathrm{CO}}_2$ 4 moles of ${\mathrm{H}}_2\mathrm{O}$ and 1 mole of nitrogen gas. The formula of the compound is:

Q20.Consider the reaction
${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\rightleftharpoons 2{\mathrm{NH}}_3(\mathrm{g})$
The equilibrium constant of the above reaction is ${\mathrm{K}}_3$. If pure ammonia is left to dissociate, the partial pressure of ammonia at equili …

Q21.Two blocks of the same metal having same mass and at temperature $T_1$ and $T_2$ respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, $\Delta \mathrm{S}$, for this process is:

Q22.Match the metal column I with the coordination compounds/enzymes column II

Column I
Metals
a. Co
b. Zn
c. Rh
d. Mg

Column II
Coordination compounds/enzymes
i. Wilkinson catalyst
ii. Chlorophyll
iii. Vitamin ${\mathrm{B}}_{12}$
iv. Carbonic anhydrase

Q23.For the chemical reaction $\mathrm{X}\rightleftharpoons \mathrm{Y}$, the standard reaction Gibbs energy depends on temperature T (in K) as
${\Delta }_{\mathrm{r}}{\mathrm{G}}^0({\mathrm{in}\mathrm{kJ}\mathrm{mol}}^{-1})=120-\frac{3}{8}\mathrm{T}$
The major component of the reaction mixture at T …

Q24.Match the ores (column A) with the metals (column B)

Q25.Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H-atom is suitable for this purpose? …

Q26.The chloride that CANNOT get hydrolysed is

Q27.The correct order of the atomic radii of $\mathrm{C},\mathrm{Cs},\mathrm{Al}$ and S is:

Q1.If the system of linear equations
$2x+2y+3z=a$
$3x-y+5z=b$
$x-3y+2z=c$
Where $\mathrm{a},\mathrm{b},\mathrm{c}$ are non zero real numbers, has more than one solution, then:

Q2.Let $f_k(x)=\frac{1}{k}\left({\sin }^{k}x+{\cos }^{k}x\right)$ for $k=1,2,3,\dots$ Then for all $x\in R$, the value of $f_4(x)-f_6(x)$ is equal to:

Q3.A square is inscribed in the circle $x^2+y^2-6x+8y-103=0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of the square which is nearest to the origin is:

Q4.If $q$ is false and $p\wedge q\leftrightarrow r$ is true, then which one of the following statements is a tautology?

Q5.The area (in sq. units) of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is:

Q6.The value of the integral ${\int }_{-2}^2\frac{{\sin }^{2}x}{\left[\frac{x}{\pi }\right]+\frac{1}{2}}dx$ (where $[x]$ denotes the greatest integer less than or equal to $x$) is:

Q7.The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2}-\mathrm{d}$ each, 10 items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2}+\mathrm{d}$ each. If the variance of this outcome data is $\frac{4}{3}$ then …

Q8.The plane containing the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z-1}{3}$ and also containing its projection on the plane $2x+3y-z=5$, contains which one of the following points?

Q9.Two integers are selected at random from the set $\{1,2,\dots ,11\}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

Q10.Two circles with equal radii intersecting at the points $(0,1)$ and $(0,-1)$. The tangent at the point $(0,1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:

Q11.The value of $r$ for which ${}^{20}{\mathrm{C}}_{\mathrm{r}}{}^{20}{\mathrm{C}}_0+{}^{20}{\mathrm{C}}_{\mathrm{r}-1}{}^{20}{\mathrm{C}}_1+{}^{20}{\mathrm{C}}_{\mathrm{r}-2}{}^{20}{\mathrm{C}}_2+\dots +{}^{20}{\mathrm{C}}_0{}^{20}{\mathrm{C}}_{\mathrm{r}}$ is maximum i …

Q12.If tangents are drawn to the ellipse $x^2+2y^2=2$ at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve:

Q13.Let $f(x)=\{\begin{array}{cc}-1,& -2\le x<0\\ x^2-1,& 0,\le x\le 2\end{array}$ and $g(x)=|f(x)|+f(|x|)$, Then, in the interval ( $-2,2)$, $g$ is:

Q14.If $x{\log }_e\left({\log }_{e}x\right)-x^2+y^2=4(y>0)$, then $\frac{dy}{dx}$ at $x=e$ is equal to:

Q15.If $\int \frac{\sqrt{1-x^2}}{x^4}dx=A(x){\left(\sqrt{1-x^2}\right)}^m+C$, for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant of integration, then $(A(x){)}^m$ equals:

Q16.Let $[\mathrm{x}]$ denote the greatest integer less than or equal to x . Then:
${\lim }_{x\to 0}\frac{\tan \left(\pi {\sin }^{2}x\right)+(|x|-\sin (x[x]){)}^2}{x^2}$

Q17.The maximum value of the function $f(x)=3x^3-18x^2+27x-40$ on the set $S=\left\{x\in R:x^2+30\le 11x\right\}$ is

Q18.Let $f:R\to R$ be defined by $f(x)=\frac{x}{1+x^2},x\in R$. Then the range of $f$ is:

Q19.The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is $\frac{27}{19}$. Then the common ratio of this series is:

Q20.The straight line $x+2y=1$ meets the coordinate axes at A and B. A circle is drawn through $\mathrm{A},\mathrm{B}$ and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is:

Q21.In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$. If $x^2-c^2=y$, where $c$ is the length of the third side of the triangle, then the circumradius of the triangle is:

Q22.Equation of a common tangent to the parabola ${\mathrm{y}}^2=4\mathrm{x}$ and the hyperbola $\mathrm{xy}=2$ is:

Q23.The sum of the real values of x for which the middle term in the binomial expansion of ${\left(\frac{x^3}{3}+\frac{3}{x}\right)}^8$ equals 5670 is:

Q24.Let $a_1,a_2,\dots ,a_{10}$ be a G.P. If $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals:

Q25.Let $A=\left(\begin{array}{ccc}0& 2q& r\\ p& q& -r\\ p& -q& r\end{array}\right)$. If $A{A}^{\top }=I_3$, then $|p|$ is:

Q26.If $y(x)$ is the solution of the differential equation $\frac{dy}{dx}+\left(\frac{2x+1}{x}\right)y=e^{-2x},x>0$ where $y(1)=\frac{1}{2}{\mathrm{e}}^{-2}$, then:

Q27.The direction ratios of normal to the plane through the points $(0,-1,0)$ and $(0,0,1)$ and making an angle $\frac{\pi }{4}$ with the plane $y-z+5=0$

Q28.Let $\vec{a}=\hat{i}+2\hat{j}+4\hat{k},\vec{b}=\hat{i}+\lambda \hat{j}+4\hat{k}$ and $\vec{c}=2\hat{i}+4\hat{j}+\left({\lambda }^2-1\right)\hat{k}$ be coplanar vectors. Then the non - zero vector $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}}$ is:

Q29.If one real root of the quadratic equation $81x^2+kx+256=0$ is cube of the other root, then a value of k is:

Q30.Let ${\left(-2-\frac{1}{3}\mathrm{i}\right)}^3=\frac{\mathrm{x}+\mathrm{iy}}{27}(\mathrm{i}=\sqrt{-1})$, where x and y are real numbers, then $\mathrm{y}-\mathrm{x}$ equals: