Q JEE Advanced 2016

Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of...

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Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of...

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Let $F_1\left(x_1, 0\right)$ and $F_2\left(x_2, 0\right)$, for $x_10$, be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$. Suppose a parabola having vertex...

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Q JEE Advance2016

Let $F_1\left(x_1, 0\right)$ and $F_2\left(x_2, 0\right)$, for $x_10$, be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$. Suppose a parabola having vertex...

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Let $\hat{u}=u_1 \hat{i}+u_2 \hat{j}+u_3 \hat{k}$ be a unit vector in $R^3$ and $\hat{w}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2 \hat{k})$. Given that there exists a vector...

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Let $\alpha, \lambda, \mu \in \mathrm{R}$. Consider the system of linear equations $$ \begin{aligned} & a x+2 y=\lambda \\ &...

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Let $P$ be the point on the parabola $y^2=4 x$ which is at the shortest distance from the centre $S$...

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Let $a, b \in R$ and $a^2+b^2 \neq 0$. Suppose $...

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let $f:\left[-\frac{1}{2}, 2\right] \rightarrow R$ and $g:\left[-\frac{1}{2}, 2\right] \rightarrow R$ be functions defined by $f(x)=\left[x^2-3\right]$ and $...

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Let $f: \mathrm{R} \rightarrow(0, \infty)$ and $\mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$ be twice differentiable function such that $\mathrm{f}^{\prime \prime}$ and g...

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Let $\mathrm{a}, \mathrm{b} \in \mathrm{R}$ and $f: \mathrm{R} \rightarrow \mathrm{R}$ be defined by $\mathrm{f}(\mathrm{x})=\mathrm{a} \cos \left(\left|\mathrm{x}^3-\mathrm{x}\right|\right)+\mathrm{b}|\mathrm{x}| \sin \left(\left|\mathrm{x}^3+\mathrm{x}\right|\right)$. Then f...

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Q JEE Advance2016

Let $f(x)=\lim _{n \rightarrow \infty}\left(\frac{n^n(x+n)\left(x+\frac{n}{2}\right) \ldots\left(x+\frac{n}{n}\right)}{n!\left(x^2+n^2\right)\left(x^2+\frac{n^2}{4}\right) \ldots\left(x^2+\frac{n^2}{n^2}\right)}\right)^{\frac{x}{n}}$, for all $x>0$. Then

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Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the...

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Area of the region $\left\{(x, y) \in R^2: y \geq \sqrt{|x+3|}, 5 y \leq x+9 \leq 15\right\}$ is equal to

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The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+e^x} d x$ is equal to

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The value of $\sum_{k=1}^{13} \frac{1}{\sin \left(\frac{\pi}{4}+\frac{(k-1) \pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{k \pi}{6}\right)}$ is equa ito

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Let $b_i>1$ for $i=1,2, \ldots, 101$. Suppose $\log _e b_1, \log _e b_2, \ldots, \log _e b_{101}$ are in Arithmetic...

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Let $P=\left[\begin{array}{ccc}1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1\end{array}\right]$ and $I$...

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Treatment of compound $\mathbf{O}$ with $\mathrm{KMnO}_4 / \mathrm{H}^{+}$gave $\mathbf{P}$, which on heating with ammonia gave $\mathbf{Q}$. The compound $\mathbf{Q}$ on...

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Q JEE Advance 2016

Treatment of compound $\mathbf{O}$ with $\mathrm{KMnO}_4 / \mathrm{H}^{+}$gave $\mathbf{P}$, which on heating with ammonia gave $\mathbf{Q}$. The compound $\mathbf{Q}$ on...

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Thermal decomposition of gaseous $\mathrm{X}_2$ to gaseous X at 298 K takes place according to the following equation : $$...

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Q JEE Advance2016

Thermal decomposition of gaseous $\mathrm{X}_2$ to gaseous X at 298 K takes place according to the following equation : $$...

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Q JEE Advance2016

Among the following, reaction(s) which gives(give) tert-butyl benzene as the major product is (are)

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Q JEE Advance 2016

Reagent(s) which can be used to bring about the followng transformation is (are)

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For 'invert sugar' the correct statement(s) is(are) (Given: specific rotations of (+)-sucrose, (+)-maltose, L-(-)-glucose and L-(+)-fructose in aqueous solution are...

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Q JEE Advanced 2016

The total number of distinct $x \in R$ for which $...

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Let $\alpha, \beta \in R$ be such that $\lim _{x \rightarrow 0} \frac{x^2 \sin (\beta x)}{\alpha x-\sin x}=1$. Then $6(\alpha+\beta)$...

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Let $z=\frac{-1+\sqrt{3} i}{2}$, where $i=\sqrt{-1}$, and $r, s \in[1,2,3]$. Let $P=\left[\begin{array}{cc}(-z)^r & z^{2 s} \\ z^{2 s} & z^r\end{array}\right]$ and...

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Q JEE Advanced 2016

Let $m$ be the smallest positive integer such the coefficient of $x^2$ in the expansion $(1+x)^2+(1+ x)^3+\ldots .+(1+x)^{49}+(1+m x)^{50}$ is...

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Q JEE Advanced 2016

The total number of distinct $x \in[0,1]$ for which $\int_0^x \frac{t^2}{1+t^4} d t=2 x-1$ is

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The circle $C_1: x^2+y^2=3$, with centre at $O$, intersects the parabola $x^2=2 y$ at the point $P$ in the first...

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Q JEE Advanced 2016

Let $P=\left[\begin{array}{ccc}3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0\end{array}\right]$, where $...

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Let $f:(0, \infty) \rightarrow R$ be a differentiable function such that $f^{\prime}(x)=2-\frac{f(x)}{x}$ for all $x \in(0, \infty)$ and $...

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Q JEE Advance2016

The nitrogen containing compound produced in the reaction of $\mathrm{HNO}_3$ with $\mathrm{P}_4 \mathrm{O}_{10}$

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Let $f: R \rightarrow R, g: R \rightarrow R$ and $h: R \rightarrow R$ be differentiable functions such that $...

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Let $R S$ be the diameter of the circle $x^2+y^2=1$, where $S$ is the point $(1,0)$. Let $P$ be a...

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Extraction of copper from copper pyrite $\left(\mathrm{CuFeS}_2\right)$ involves

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Consider a pyramid OPQRS located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$...

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The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)

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Mixture(s) showing positive deviation from Raoult's law at $35^{\circ} \mathrm{C}$ is(are)

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A solution curve of the differential equation $\left(x^2+x y+4 x+2 y+4\right) \frac{d y}{d x}-y^2=, x>0$ passes through the point $(1,3)$....

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Q JEE Advance2016

According to Molecular Orbital Theory,

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The major product of the following reaction sequence is

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The correct order of acidity for the following compounds is

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The geometries of the ammonia complexes of $\mathrm{Ni}^{2+}, \mathrm{Pt}^{2+}$ and $\mathrm{Zn}^{2+}$, respectively, are

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In a triangle $X Y Z$, let $x, y, z$ be the lengths of sides opposite to the angle $...

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In the following reaction sequence in aqueous solution, the species $\mathrm{X}, \mathrm{Y}$ and Z , respectively, are

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THe qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three...

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For the following electrochemical cell at 298 K , $$ \begin{aligned} & \operatorname{Pt}(\mathrm{s}) \mid \mathrm{H}_2(\mathrm{~g}, 1 \text { bar })\left|\mathrm{H}^{+}(\mathrm{aq},...

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Q JEE Advanced 2016

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from...

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Let $-\frac{\pi}{6}\beta_2$, then $\alpha_1+\beta_2$ equals

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Let $S=\left\{x \in(-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}$, The sum of all distinct solutions of the equation $...

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Q JEE Advanced 2016

The least value of $\alpha \in R$ for which $4 \alpha x^2+\frac{1}{x} \geq 1$ for all $x>0$, is

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A computer producing factory has only two plants $T_1$ and $T_2$ produces $20 \%$ and plant $T_2$ produces $80 \%$...

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Consider an evacuted cylindrical chamber of height $h$ having rigid conducting plates at the end and an insulting curved surface...

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Consider an evacuted cylindrical chamber of height $h$ having rigid conducting plates at the end and an insulting curved surface...

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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame...

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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame...

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A rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$...

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In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of...

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The mole fraction of a solute in a solution is 0.1 . At 298 K , molarity of this solution...

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The number of geometric isomers possible for the complex $\left[\mathrm{CoL}_2 \mathrm{Cl}_2\right]^{-}\left(\mathrm{L}=\mathrm{H}_2 \mathrm{NCH}_2 \mathrm{CH}_2 \mathrm{O}^{-}\right)$is.

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Q JEE Advanced 2016

In the following monobromination reaction, the number of possible chiral products is:

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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature...

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The product(s) of the following reaction sequence is(are):

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While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the...

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A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and...

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In the circuit shown below, the key is pressed at time $t=0$. Which of the following statement ( $s$ )...

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Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal of the galvanometers $R_c

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According to the Arrhenius equation

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In an experiment to determine the acceleration due to gravity g , the formula used for the time period of...

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The compound(s) with TWO lone pairs of electrons on the central atom is(are):

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Light of wavelength $\lambda_{\text {ph }}$ falls on a cathode plate inside a vacuum tube as shown in the figure....

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The crystalline form of borax has

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Two thin circular discs of mass $m$ and $4 m$, having radii of $a$ and $2 a$, respectively are rigidly...

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The correct statement(s) about the following reaction sequence is(are):

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Positive Tollen's test is observed for

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A plot of the number of neutrons (N) against the number of protons(P) of stable nucleus exhibits upward deviation from...

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The reagent(s) that can selectively precipitate $\mathrm{S}^{2-}$ from a mixture of $\mathrm{S}^{2-}$ and $\mathrm{SO}_4{ }^{2-}$ in aqueous solution is(are)

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Q JEE Advanced 2016

One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to...

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On complete hydrogenation, natural rubber produces

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Among $\left[\mathrm{Ni}(\mathrm{Co})_4\right],\left[\mathrm{NiCl}_4\right]^{2-},\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right] \mathrm{Cl}, \mathrm{Na}_2\left[\mathrm{CoF}_6\right]^{3+}, \mathrm{Na}_2 \mathrm{O}_2$ and $\mathrm{CsO}_2$, the total number of paramagnetic compounds is

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Q JEE Advanced 2016

The increasing order of atomic radii of the following group 13 elements is

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A hydrogen atom in its ground state is irradiated by light of wavelength $970 \AA$. Taking hc/e $...

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A metal is heated in a furnace where a sensor is kept above the metal surface to read the power...

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There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale....

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Consider two solid sphere P and Q each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters 1 cm and 0.5 cm...

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Two inductors $\mathrm{L}_1$ (inductance 1 mH , internal resistance $3 \Omega$ ) and $\mathrm{L}_2$ (inductance 2 ml internal resistance $...

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The ends Q and R of two thin wires, PQ and RS , are soldered (Joined) together. Initially each of...

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The isotope ${ }_5^{12} \mathrm{~B}$ having a mass 12.014 u undergoues $\beta$ - decay to ${ }_6^{12} \mathrm{C}_{16}^{12} \mathrm{C}$ has...

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A gas enclosed in a cylinder with movable frictionless piston. Its initial thermodynamic state at pressure $P_i=10^5 \mathrm{~m}^3$ and volume...

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The position vector $\vec{r}$ of a particle of mass $m$ is given by the following equation $...

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An accident in a nuclear laboratory resulted in depostion of a certain amount of radioactive material of half - life...

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The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $...

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An incandesecent bulb has a thin filament of tungstgen that is heated to high temperature by passing an electric current....

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A transparent slab of thickness $d$ has a refractive index $n(z)$ that increases with $z$. Here $z$ is the vertical...

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Highly excited states for hydrogen-like atoms (also called Rydberg states) with nucles charge Ze are defined by their principal quantum...

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A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm...

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Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz an 121 Hz...

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A length-scale $(\ell)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzman constant $\left(\mathrm{k}_{\mathrm{B}}\right)$, the absolute temperature (T), the...

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Q JEE Advanced 2016

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept, such that...

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A parallel beam of light is incident from air at angle $\alpha$ on the side PQ of a right angled...

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A uniform wooden stick of mass 1.6 kg and length $\ell$ rests in an inclined manner on a smooth, vertical...

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A water cooler of storage capacity 120 liters can cool water at a constant rate of P watts. In a...

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In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted...

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An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical...

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