Q JEE Advance2018

For every twice differentiable function $f: R \rightarrow[-2,2]$ with $(f(0))^2+\left(f^{\prime}(0)\right)^2=85$, which of the following statement(s) is (are) TRUE ?

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Q JEE Advanced 2018

Sunlight of intensity $1.3 \mathrm{kWm}^{-2}$ is incident normally on a thin convex lens of focal length 20 cm . Ignore...

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Q JEE Advance2018

There are five students $S_1, S_2, S_3, S_4$ and $S_5$ in a music class and for them there are five...

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Q JEE Advance2018

There are five students $S_1, S_2, S_3, S_4$ and $S_5$ in a music class and for them there are five...

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Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at...

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Let $E_1 E_2$ and $F_1 F_2$ be the chords of $S$ passing through the point $P_0(1,1)$ and parallel to the...

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A farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0), Q(1,1)$ and $R(2,0)$. From...

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Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three non-zero real numbers such that the equation $$ \sqrt{3} a \cos x+2 b \sin...

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Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a} \cdot \vec{b}=0$. For some $x, y \in R$, let...

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Q JEE Advance2018

For each positive integer n , let $$ y_n=\frac{1}{n}((n+1)(n+2) \ldots(n+n))^{1 / n} . $$ For $x \in R$, let $[x]$...

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Q JEE Advance2018

The number of real solutions of the equation $$ \sin ^{-1}\left(\sum_{i=1}^{\infty} x^{i+1}-x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^i\right)=\frac{\pi}{2}-\cos ^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^i-\sum_{i=1}^{\infty}(-x)^i\right) $$ lying in the interval $...

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Q JEE Advance2018

The number of 5 digit numbers which are divisible by 4 , with digits from the set $\{1,2,3,4,5\}$ and the...

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Q JEE Advance2018

The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is $\_\_\_\_$。

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Q JEE Advance2018

Let $f:[0, \infty) \rightarrow R$ be a continuous function such that $$ f(x)=1-2 x+\int_0^x e^{x-1} f(t) d t $$ for...

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Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be two non-constant differentiable functions. If $\mathrm{f}^{\prime}(\mathrm{x})=\left(\mathrm{e}^{(\mathrm{f}(\mathrm{x})-\mathrm{g}(\mathrm{x}))}\right) \mathrm{g}^{\prime}(\mathrm{x})$ for all...

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Q JEE Advance2018

Let $P_1: 2 x+y-z=3$ and $P_2: x+2 y+z=2$ be two planes. Then, which of the following statement(s) is (are) TRUE...

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In a triangle PQR , let $\angle \mathrm{PQR}=30^{\circ}$ and the sides PQ and QR have lengths $10 \sqrt{3}$ and 10...

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For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument with $-\pi

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An organic acid $\mathbf{P}\left(\mathrm{C}_{11} \mathrm{H}_{12} \mathrm{O}_2\right)$ can easily be oxidized to a dibasic acid which reacts with ethylene glycol to...

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Q JEE Advance2018

An organic acid $\mathbf{P}\left(\mathrm{C}_{11} \mathrm{H}_{12} \mathrm{O}_2\right)$ can easily be oxidized to a dibasic acid which reacts with ethylene glycol to...

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Q JEE Advance2018

Treatment of benzene with $\mathrm{CO} / \mathrm{HCl}$ in the presence of anhydrous $\mathrm{AlCl}_3 / \mathrm{CuCl}$ followed by reaction with $...

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Q JEE Advance2018

Treatment of benzene with $\mathrm{CO} / \mathrm{HCl}$ in the presence of anhydrous $\mathrm{AlCl}_3 / \mathrm{CuCl}$ followed by reaction with $...

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Q JEE Advanced 2018

Let $f_1: \mathrm{R} \rightarrow \mathrm{R}, f_2:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow \mathrm{R}, \mathrm{f}_3:\left(-1, \mathrm{e}^{\pi / 2}-2\right) \rightarrow \mathrm{R}$ and $\mathrm{f}_4: \mathrm{R} \rightarrow \mathrm{R}$...

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Q JEE Advanced 2018

Let H : $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a>b>0$, be a hyperbola in the xy-plane whose conjugate axis LM subtends an angle of...

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Q JEE Advanced 2018

In a high school, a committee has to be formed from a group of 6 boys $...

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Let $E_1=\left\{x \in \mathrm{R}: x \neq 1\right.$ and $\left.\frac{x}{x-1}>0\right\}$ and $E_2=\left\{x \in \mathrm{E}_1: \sin ^{-1}\left(\log _{\mathrm{e}}\left(\frac{x}{x-1}\right)\right)\right.$ is a real number...

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Q JEE Advance2018

The plot given below shows $\mathrm{P}-\mathrm{T}$ curves (where $P$ is the pressure and $T$ is the temperature) for two solvents...

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Q JEE Advanced 2018

Let $ \mathrm{X}=\left({ }^{10} \mathrm{C}_1\right)^2+2\left({ }^{10} \mathrm{C}_2\right)^2+3\left({ }^{10} \mathrm{C}_3\right)^2+\ldots .+10\left({ }^{10} \mathrm{C}_{10}\right)^2, $ where $...

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Q JEE Advanced 2018

Consider the cube in the first octant with sides OP, OQ and OR of length 1 , along the $x$-axis,...

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The solubility of a salt of weak acid ( $\mathbf{A B}$ ) at pH 3 is $...

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Q JEE Advanced 2018

Let $P$ be a point in the first octant, whose image $Q$ in the plane $x+y=3$ (that is, the line...

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F or the electrochemical cell, $\mathrm{Mg}(\mathrm{s})\left|\mathrm{Mg}^{2+}(\mathrm{aq}, 1 \mathrm{M}) \| \mathrm{Cu}^{2+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{Cu}(\mathrm{s})$ the standard emf of the cell is...

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Q JEE Advanced 2018

Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a differentiable function with $f(0)=1$ and satisfying the equation $\mathrm{f}(x+y)=\mathrm{f}(x) \mathrm{f}^{\prime}(y)+f^{\prime}(x) f(y)$ for all...

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Consider an ionic solid $\mathbf{M X}$ with NaCl structure. Construct a new structure $(\mathbf{Z})$ whose unit cell constructed from the...

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Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the differential equation $...

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Q JEE Advanced 2018

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $\alpha$...

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The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by $\mathrm{NiCl}_2 \cdot 6 \mathrm{H}_2 \mathrm{O}$ to...

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Let P be a matrix of order 3 x 3 such that all the entries in P are from the...

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Among the species given below, the total number of diamagnetic species is $\_\_\_\_$ . H atom, $\mathrm{NO}_2$ monomer, $\mathrm{O}_2{ }^{-}$(superoxide),...

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Q JEE Advanced 2018

The value of the integral $\int_0^{1 / 2} \frac{1+\sqrt{3}}{\left((x+1)^2(1-x)^6\right)^{1 / 4}} d x$ is $\_\_\_\_$ .

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Q JEE Advanced 2018

Let $f:(0, \pi) \rightarrow \mathrm{R}$ be a twice differentiable function such that $...

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A reversible cyclic process for an ideal gas is shown below. Here, $P, V$, and $T$ are pressure, volume and...

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Let $s, t, r$ be non-zero complex numbers and L be the set of solutions $...

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Consider two straight lines, each of which is tangent to both the circle $x^2+y^2=\frac{1}{2}$ and the parabola $y^2=4 x$. Let...

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Q JEE Advance2018

The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is(are)

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Let T be the line passing through the points $\mathrm{P}(-2,7)$ and $\mathrm{Q}(2,-5)$. Let $\mathrm{F}_1$ be the set of all pairs...

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For any positive integer $n$, define $f_n:(0, \infty) \rightarrow R$ as $...

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In the following reaction sequence, the correct structure(s) of X is (are)

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Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on...

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LIST-I contains reactions and LIST-II contains major products. Match each reaction in LIST-I with one or more products in LIST-II...

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B ased on the compounds of group 15 elements, the correct statement(s) is (are)

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Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II. The correct option is

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Consider an electrochemical cell: $\mathrm{A}(\mathrm{s})\left|\mathrm{A}^{\mathrm{n}+}(\mathrm{aq}, 2 \mathrm{M}) \| \mathrm{B}^{2 \mathrm{n}^{+}}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{B}(\mathrm{s})$. The value of $\Delta \mathrm{H}^{\ominus}$ for the...

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Consider the following reversible reaction, $ \mathrm{A}(\mathrm{~g})+\mathrm{B}(\mathrm{~g}) \rightleftharpoons \mathrm{AB}(\mathrm{~g}) $ The activation energy of the backward reaction exceeds that of...

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Q JEE Advanced 2018

The surface of copper gets tarnished by the formation of copper oxide. $\mathrm{N}_2$ gas was passed to prevent the oxide...

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Q JEE Advanced 2018

In the following reaction sequence, the amount of $\mathbf{D}$ (in g ) formed from 10 moles of acetophenone is $\_\_\_\_$...

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To measure the quantity of $\mathrm{MnCl}_2$ dissolved in an aqueous solution, it was completely converted to $\mathrm{KMnO}_4$ using the reaction,...

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Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of...

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The total number of compounds having at least one bridging oxo group among the molecules given below is $\_\_\_\_$ ....

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For a reaction, $\mathrm{A} \rightleftharpoons \mathrm{P}$, the plots of $[\mathrm{A}]$ and $[\mathrm{P}]$ with time at temperatures $T_1$ and $T_2$ are...

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For a first order reaction $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ at constant volume and 300 K , the total pressure at...

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The correct statement(s) regarding the binary transition metal carbonyl compounds is (are) (Atomic numbers: $\mathrm{Fe}=26, \mathrm{Ni}=28$ )

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The Fischer presentation of D-glucose is given below The correct structures(s) of -L-glucopyranose is(are)

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The compound(s) which generate(s) $\mathrm{N}_2$ gas upon thermal decomposition below $300^{\circ} \mathrm{C}$ is (are)

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Aniline reacts with mixed acid (conc. $\mathrm{HNO}_3$ and conc. $\mathrm{H}_2 \mathrm{SO}_4$ ) at 288 K to give $...

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The correct option(s) to distinguish nitrate salts of $\mathrm{Mn}^{2+}$ and $\mathrm{Cu}^{2+}$ taken separately is (are)

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The correct option(s) regarding the complex $\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_3\right)_3\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}$ (en $\left.=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{NH}_2\right)$ is (are)

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In the List-I below, four different paths of a particle are given as functions of time. In these functions, $\alpha$...

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One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PVdiagram below. Among these...

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A planet of mass $M$, has two natural satellites with masses $m_1$ and $m_2$. The radii of their circular orbits...

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The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the...

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Consider a hydrogen-like ionized atom with atomic number Z with a single electron. In the emission spectrum of this atom,...

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In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a perfectly...

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One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial...

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If the measurement errors in all the independent quantities are known, then it is possible to determine the error in...

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A steel wire of diameter 0.5 mm and Young's modulus $2 \times 10^{11} \mathrm{Nm}^{-2}$ carries a load of mass M...

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A moving coil galvanometer has 50 turns and each turn has an area $2 \times 10^{-4} \mathrm{~m}^2$. The magnetic field...

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If the measurement errors in all the independent quantities are known, then it is possible to determine the error in...

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A particle, of mass $10^{-3} \mathrm{~kg}$ and charge 1.0 C , is initially at rest. At time $\mathrm{t}=0$, the particle...

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A ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum...

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In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic...

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A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4 \mathrm{~kg}$ is...

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In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500...

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In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic...

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In a radioactive decay chain, ${ }_{90}^{232} \mathrm{Th}$ nucleus decays to ${ }_{82}^{212} \mathrm{~Pb}$ nucleus. Let $N_\alpha$ and $N_\beta$ be...

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Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures...

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A wire is bent in the shape of a right angled triangle and is placed in front of a concave...

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In the $x y$-plane, the region $y>0$ has a uniform magnetic field $B_1 \hat{k}$ and the region $y

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Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially....

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A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $...

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Two men are walking along a horizontal straight line in the same direction. The man in front walks at a...

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An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It...

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One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $\boldsymbol{V}$ is the...

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Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid...

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Two infinitely long straight wires lie in the $x y$-plane along the lines $x= \pm R$. The wire located at...

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A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts...

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In the figure below, the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow...

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A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises...

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Consider a body of mass 1.0 kg at rest at the origin at time $t=0$. A force $...

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The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given...

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