Online JEE 2016 Test ( Advanced 2016 )

A plano-convex lens is made of material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is (are) true?

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n. where n >>1. Which of the following statement(s) is (are) true?

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays \log(P/P_{0}) where P₀ is a constant. When the metal surface is at a temperature of 487⁰C, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767⁰C?

An accident in a nuclear laboratory resulted in deposition of a certain amourt of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

 The correct order of acidity for the  following compounds

In the following reaction sequence in aqueous  solution, the species X, Y and Z, respectively are

$S_{2}O_3^{2-}\underrightarrow {Ag^{+}}$  $X (Clear. solution)$   $\underrightarrow {Ag^{+}}$  $Y (white. ppt)\underrightarrow {with.time}$  $Z (black.ppt)$

Treatment of compound O with  $KMnO_{4}/H^{+}$ gave P, which on heating with ammonia gave Q. The compound Q on treatment with  $Br_{2}/NaOH$ produced R on strong heating, Q gave S which on further treatment with  ethyl 2-bromopropanoate in the presence of KOH followed by acidification gave a compound T

The compound T is

Thermal decomposition of gaseous X₂, to gaseous X at 298 K takes place according to the following equation

$X_{2}(g)\rightleftharpoons2X(g)$

The standard reaction Gibbs energy, Δ_rG⁰, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of X formed is given by β. Thus, βequilibrium is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given, R = 0.083 L bar K^-1 mol^-1)

The incorrect  statement among the following reaction , is

Let  $\hat{u}=u_{1}\hat{i}+u_{2}\hat{j}+u_{3}\hat{k}$ be a unit vector  R³ and $\hat{w}=\frac{1}{\sqrt{6}}({}\hat{i}+\hat{j}+2\hat{k})$. Given that there exists vector  $\overrightarrow{v}$  in  $R^{3}$ , such  that  $|\hat{u}+\vec{v}|=1$ and  $\hat{w}.(\hat{u}+\vec{v})=1$   which of the following statement(s) is/are correct?

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

THe crystalline form of borax has 

The possible number of geometrical isomers for the complex   

 $[CoL_{2}Cl_{2}]^{-}(L=H_{2}NCH_{2}CH_{2}O^{-})$ is (are)

Let  $f:(0,\infty)\rightarrow R$ be a differentiable function such that   $f'(x)=2-\frac{f(x)}{x}$  for all  $x \epsilon (0,\infty)$  and $f(1)\neq 1$ Then

Let $z=\frac{-1+\sqrt{3}i}{2}$ , where   $i=\sqrt{-1}$  , and  $ r,s \epsilon (1,2,3)$. Let  $P=\begin{bmatrix}(-z)^{r} & z^{2s} \\z^{2s} & z^{r} \end{bmatrix}$  and  I be the identity matrix of  order2.Then, the total number of ordered pairs (r,s) for which   $p^{2}=-I$ is

The total number of distincts   $x \epsilon R$ for  which $\begin{bmatrix}x & x^{2} &1+x^{3} \\2x & 4x^{2}& 1+8x^{3} \\3x&9x^{2}&1+27x^{3} \end{bmatrix}=10 $  is