Q JEE Advance 2012

Let $f:(-1,1) \rightarrow \operatorname{IR}$ be such that $f(\cos 4 \theta)=\frac{2}{2-\sec ^2 \theta}$ for $\theta \in\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then the...

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Q JEE Advance 2012

If the adjoint of a $3 \times 3$ matrix $P$ is $...

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Q JEE Advance 2012

If the straight lines $\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar, then the plane(s) containing these two lines is(are)

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Q JEE Advance 2012

For every integer n, let $a_n$ and $b_n$ be real numbers. Let function $f: I R \rightarrow I R$ be...

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Q JEE Advance 2012

If $f(x)=\int_0^x e^{t^2}(t-2)(t-3) d t$ for all $x \in(0, \infty)$, then

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Q JEE Advance 2012

Let $X$ and $Y$ be two events such that $P(X \mid Y)=\frac{1}{2}, P(Y \mid X)=\frac{1}{3}$ and $P(X \cap Y)=\frac{1}{6}$. Which...

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Q JEE Advance 2012

A tangent PT is drawn to the circle $\mathrm{x}^2+\mathrm{y}^2=4$ at the point $\mathrm{P}(\sqrt{3}, 1)$. A straight line L , perpendicular...

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Q JEE Advance 2012

A tangent $P T$ is drawn to the circle $x^2+y^2=4$ at the point $P(\sqrt{3}, 1)$. A straight line $L$, perpendicular...

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Q JEE Advance 2012

Let $a_n$ denote the number of all $n$-digit positive integers formed by the digits 0,1 or both such that no...

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Q JEE Advance 2012

Let $\mathrm{a}_{\mathrm{n}}$ denote the number of all n -digit positive integers formed by the digits 0,1 or both such that...

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Q JEE Advance 2012

Let $f(x)=(1-x)^2 \sin ^2 x+x^2$ for all $x \in$ IR and let $g(x)=\int_1^x\left(\frac{2(t-1)}{t+1}-\ell\right.$ nt $) f(t) d t$ for all...

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Q JEE Advance 2012

Let $f(x)=(1-x)^2 \sin ^2 x+x^2$ for all $x \in$ IR and let $g(x)=\int_1^x\left(\frac{2(t-1)}{t+1}-\ell\right.$ nt $) f(t) d t$ for all...

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Q JEE Advance 2012

Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation $(\sqrt[3]{1+a}-1) x^2+(\sqrt{1+a}-1) x+(\sqrt[6]{1+a}-1)=0$ where $a>-1$. Then $...

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Q JEE Advance 2012

Let $a_1, a_2, a_3, \ldots$. be in harmonic progression with $a_1=5$ and $a_{20}=25$. The least positive integer $n$ for which...

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Q JEE Advance 2012

If P is a $3 \times 3$ matrix such that $\mathrm{P}^{\top}=2 \mathrm{P}+\mathrm{I}$, where $\mathrm{P}^{\top}$ is the transpose of P and...

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Q JEE Advance 2012

The value of the integral $\int_{-\pi / 2}^{\pi / 2}\left(x^2+\ell \ln \frac{\pi+x}{\pi-x}\right) \cos x d x$ is

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Q JEE Advance 2012

Four fair dice $\mathrm{D}_1, \mathrm{D}_2, \mathrm{D}_3$ and $\mathrm{D}_4$ each having six faces numbered $1,2,3,4,5$ and 6 are rolled simultaneously. The...

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Q JEE Advance 2012

Let $P Q R$ be a triangle of area $\triangle$ with $a=2, b=\frac{7}{2}$ and $c=\frac{5}{2}$, where $a, b$ and $c$...

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Q JEE Advance 2012

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}+\vec{b}|=\sqrt{29}$ and $\vec{a} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{b}$,...

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Q JEE Advance 2012

The equation of a plane passing through the line of intersection of the planes $x+2 y+3 z=2$ and $x-y+z=3$ and...

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Q JEE Advance 2012

Which of the given statement(s) about N, O, P and Q with respect to M is (are) correct ?

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Q JEE Advance 2012

With reference to the scheme given, which of the given statments(s) about T, U, V and W is (are) correct?

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Q JEE ADVANCE 2012

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors satisfying $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9$, then $|2 \vec{a}+5 \vec{b}+5 \vec{c}|$ is

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Q JEE ADVANCE 2012

The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots .}}}\right)$ is

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Q JEE ADVANCE 2012

Let $f: \operatorname{IR} \rightarrow \operatorname{IR}$ be defined as $f(x)=|x|+\left|x^2-1\right|$. The total number of points at which $f$ attains either a...

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Q JEE ADVANCE 2012

Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum...

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Q JEE Advance 2012

For the given aqueous reaction which of the statement(s) is (are) true ?

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Q JEE ADVANCE 2012

Let $S$ be the focus of the parabola $y^2=8 x$ and let $P Q$ be the common chord of the...

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Q JEE ADVANCE 2012

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contacts of the...

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Q JEE ADVANCE 2012

If S be the area of the region enclosed by $\mathrm{y}=\mathrm{e}^{-\mathrm{x}^2}, \mathrm{y}=0, \mathrm{x}=0$, and $\mathrm{x}=1$. Then

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Q JEE Advance 2012

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the...

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Let $\theta, \phi \in[0,2 \pi]$ be such that $...

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Q JEE ADVANCE 2012

If $y(x)$ satisfies the differential equation $y^{\prime}-y \tan x=2 x \sec x$ and $y(0)$, then

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Q JEE Advance 2012

The given graph / data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes...

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Q JEE ADVANCE 2012

The ellipse $E_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse...

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Q JEE Advance 2012

With respect to graphite and diamond, which of the statement(s) given below is (are) correct ?

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Q JEE ADVANCE 2012

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line...

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Q JEE Advance 2012

In the following reactions sequence, the compound J is an intermediate. $$ \text { I } \xrightarrow{\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O}} \text...

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Q JEE Advance 2012

In the following reactions sequence, the compound J is an intermediate. $$ \text { I } \xrightarrow{\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O}} \text...

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Q JEE ADVANCE 2012

If $\lim _{x \rightarrow \infty}\left(\frac{x^2+x+1}{x+1}-a x-b\right)=4$, then

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Q JEE ADVANCE 2012

The function $f:[0,3] \rightarrow[1,29]$, defined by $f(x)=2 x^3-15 x^2+36 x+1$, is

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Q JEE Advance 2012

Bleaching powder and bleach solution are produced on a large scale and used in several house hold products. The effectiveness...

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Q JEE Advance 2012

Bleaching powder and bleach solution are produced on a large scale and used in several house hold products. The effectiveness...

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Q JEE Advance 2012

The electrochemical cell shown below is a concentration cell. $\mathrm{M} \mid \mathrm{M}^{2+}$ (saturated solution of a sparingly soluble salt, $...

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Q JEE Advance 2012

The electrochemical cell shown below is a concentration cell. $\mathrm{M} \mid \mathrm{M}^{2+}$ (saturated solution of a sparingly soluble salt, $...

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Q JEE Advance 2012

For a dilute solution containing 2.5 g of a non- volatile non- electrolyte solute in 100 g of water, the...

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Q JEE Advance 2012

The major product H in the given reaction sequence is

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Q JEE ADVANCE 2012

The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that...

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Q JEE Advance 2012

The shape of $\mathrm{XeO}_2 \mathrm{~F}_2$ molecule is

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Q JEE ADVANCE 2012

Let $z$ be a complex number such that the imaginary part of $z$ is non zero and $a=z^2+z+1$ is real....

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Q JEE Advance 2012

Using the data provided, calculate the multiple bond energy $\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ of a $\mathrm{C} \equiv \mathrm{C}$ bond $\mathrm{C}_2 \mathrm{H}_2$. That...

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Q JEE Advance 2012

The compound that undergoes decarboxlylation most readily under mild condition is

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Q JEE Advance 2012

In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are

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Q JEE Advance 2012

The reaction of white phosphorous with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the...

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Q JEE Advance 2012

$\mathrm{NiCl}_2\left\{\mathrm{P}_{\left(\mathrm{C}_2 \mathrm{H}_5\right)_2}\left(\mathrm{C}_6 \mathrm{H}_5\right)\right\}_2$ exhibits temperature dependent magnetic behaviour (paramagnetic/ diamagnetic). the coordination geometries of $\mathrm{Ni}^{2+}$ in the paramagnetic and diamagnetic...

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Q JEE Advance 2012

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a...

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Q JEE Advance 2012

Two spherical planets $P$ and $Q$ have the same unfirom density $\rho$, masses $M_P$ and $M_Q$, an surface areas $A$...

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Q JEE Advance 2012

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre O , as...

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Q JEE Advance 2012

In the given circuit, the AC source has $\omega=100 \mathrm{rad} / \mathrm{s}$. considering the inductor and capacitor to be ideal,...

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Q JEE Advance 2012

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The...

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Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane form...

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Q JEE ADVANCE 2012

The integral $\int \frac{\sec ^2 \mathrm{x}}{(\sec \mathrm{x}+\tan \mathrm{x})^{9 / 2}} \mathrm{dx}$ equals (for some arbitrary constant K )

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Q JEE ADVANCE 2012

The point P is the intersection of the straight line joining the points $\mathrm{Q}(2,3,5)$ and $\mathrm{R}(1,-1,4)$ with the plane $...

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Q JEE ADVANCE 2012

A circular wire loop of radius R is placed in the $\mathrm{x}-\mathrm{y}$ plane centered at the origin O . A...

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Q JEE Advance 2012

The general motion of a rigid body can be considered to be a combination of (i) a motioon --- centre...

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Q JEE ADVANCE 2012

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a shown in the figure. Both the cylinder...

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Q JEE Advance 2012

The general motion of a rigid body can be considered to be a combination of (i) a motioon --- centre...

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Q JEE ADVANCE 2012

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity...

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Q JEE ADVANCE 2012

A lamina is made by removing a small disc of diameter $2 R$ from a bigger disc of uniform mass...

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Q JEE ADVANCE 2012

A proton is fired from very far away towards a nucleus with charge $Q=120 e$, where $e$ is the electronic...

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Q JEE ADVANCE 2012

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields...

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Q JEE Advance 2012

Most materials have therefractive index, $n>1$. So, when a light ray from air enters a naturally occurring material, then by...

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Q JEE ADVANCE 2012

For the resistance network shown in the figure, choose the correct option(s).

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Q JEE Advance 2012

Most materials have therefractive index, $n>1$. So, when a light ray from air enters a naturally occurring material, then by...

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Q JEE ADVANCE 2012

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at...

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Q JEE Advance 2012

The $\beta$-decay process, discovered around 1900, is basically the decay of a neutron (n), In the laboratory, a proton (...

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Q JEE Advance 2012

The $\beta$-decay process, discovered around 1900, is basically the decay of a neutron (n), In the laboratory, a proton (...

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Q JEE ADVANCE 2012

A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle $\theta$...

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Q JEE ADVANCE 2012

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the...

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Q JEE ADVANCE 2012

Young's double slit experiment is carried out by using green, red and blue light, one color at time. The fringe...

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Q JEE Advance 2012

Two moles of ideal helium gas are in a rubber balloon at $30^{\circ} \mathrm{C}$. The balloon is fully expandable and...

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A small mass $m$ is attached to a massless string whose other end is fixed at $P$ as shown in...

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Q JEE ADVANCE 2012

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the...

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Q JEE Advance 2012

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular...

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Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density....

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Q JEE Advance 2012

In the given circuit, a charge of $+80 \mu \mathrm{C}$ is given to the upper plate of the $...

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In the determination of Young's modulus $\left(Y=\frac{4 \mathrm{MLg}}{\pi \mathrm{ld}^2}\right)$ by using Searle's method, a wire of length $\mathrm{L}=2 \mathrm{~m}$ and...

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Q JEE Advance 2012

A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm . The...

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A thin uniform rod, pivoted at O , is rotating in the horizontal plane with constant angular speed $\omega$, as...

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Q JEE Advance 2012

Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre O . The...

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Q JEE ADVANCE 2012

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal...

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Q JEE ADVANCE 2012

A small block is connected to one end of a massless spring of un-stretched length 4.9 m . The other...

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Q JEE Advance 2012

An infinitely long hollow conducting cylinder with inner radius $R / 2$ and outer radius $R$ carries a uniform current...

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Q JEE Advance 2012

A mixture of 2 moles of helium gas (atomic mass = 4 amu), and 1 mole of argon gas (atomic...

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Q JEE Advance 2012

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water...

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Q JEE Advance 2012

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source...

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Q JEE Advance 2012

A loop carrying current I lies in the x -y plane as shown in the figure. the unit vector $\hat{\mathrm{k}}$...

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Q JEE Advance 2012

$29.2 \%(\mathrm{w} / \mathrm{w}) \mathrm{HCl}$ stock solution has a density of $1.25 \mathrm{~g} \mathrm{~mL}^{-1}$. The molecular weight of HCl is...

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Q JEE Advance 2012

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding...

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Q JEE Advance 2012

The substituents $R_1$ and $R_2$ for nine peptides are listed in the table given below. How many of these peptides...

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Q JEE Advance 2012

When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is :

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Q JEE Advance 2012

An organic compound undergoes first-order decomposition. The time taken for its decomposition to $1 / 8$ and $1 /$ 10...

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Q JEE Advance 2012

Which of the following halides react(s) with $\mathrm{AgNO}_3(\mathrm{aq})$ to give a precipitate that dissolves in $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3(\mathrm{aq})$ ?

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Q JEE Advance 2012

Choose the correct reason(s) for the stability of the lyophobic colloidal particles.

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Q JEE Advance 2012

Which of the following molecules, in pure form, is (are) unstable at room temperature?

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Q JEE Advance 2012

For an ideal gas, consider only $\mathrm{P}-\mathrm{V}$ work in going from an initial state X to the final stat $Z$....

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Q JEE Advance 2012

The colour of light absorbed by an aqueous solution of $\mathrm{CuSO}_4$ is :

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Q JEE Advance 2012

The carboxyl functional group $(-\mathrm{COOH})$ is present in

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Q JEE Advance 2012

As per IUPAC nomenclature, the name of the complex $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_4\left(\mathrm{NH}_3\right)_2\right] \mathrm{Cl}_3$ is :

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Q JEE Advance 2012

The number of optically active products obtained from the complete ozonolysis of the given compound is:

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A compound $\mathrm{M}_{\mathrm{p}} \mathrm{X}_{\mathrm{q}}$ has cubic close packing (ccp) arrangement of X . Its unit cell structure is shown below....

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Q JEE Advance 2012

In allene $\left(\mathrm{C}_3 \mathrm{H}_4\right)$, the type(s) of hybridisation of the carbon atoms is (are) :

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Q JEE Advance 2012

For one mole of a van der Waals gas when $\mathrm{b}=0$ and $\mathrm{T}=300 \mathrm{~K}$, the PV vs. $1 / \mathrm{V}$...

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Q JEE Advance 2012

The number of aldol reaction (s) that occurs in the given transformation is :

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The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is $\left[\mathrm{a}_0\right.$ is Bohr radius...

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Q JEE Advance 2012

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

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