List of top Questions asked in WBJEE- 2014

The Respiratory Quotient (RQ) of glucose is

A piece of wood from an' archaeological sample has $5.0$ counts $\min ^{-1}$ per gram of $C-14$, while a fresh sample of wood has a count of $15.0 \,min ^{-1} \,g ^{-1}$. If half-life of $C-14$ is $5770\, yr$, the age of the archaeological sample is

If $\sqrt{y}=cos^{-1}x,$ then it satisfies the differential equation $\left(1-x^{2}\right)-x \frac{dy}{dx}=c,$ where $c$ is equal to

Consider two concentric spherical metal shells of radii $r_1$ and $r_2 (r_2 > r_1)$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is

A fair six-faced die is rolled $12$ times. The probability that each face turns up twice is equal to

The protein component of a holoenzyme is known as

$\left(_{32}Ge^{76}, _{34}Se^{76}\right)$ and $\left(_{14}Si^{30}, _{16}S^{32}\right)$ are examples of

The volume of ethyl alcohol (density $1.15\, g/cc$) that has to be added to prepare $100\,cc$ of $0.5\, M$ ethyl alcohol solution in water is

The compressibility factor $(Z)$ of one mole of a van der Waals gas of negligible $�a�$ value is

An infinite sheet carrying a uniform surface charge density o lies on the $x y$-plane. The work done to carry a charge $q$ from the point $A =a(\hat{ i }+2 \hat{ j }+3 \hat{ k })$ to the point $B =a(\hat{ i }-2 \hat{ j }+6 \hat{ k })$ (where $a$ is a constant with the dimension of length and $\varepsilon_{0}$ is the permittivity of free space) is

The order of decreasing ease of abstraction of Hydrogen atoms in the following molecule is

Let $X_{n}=\left\{z=x+i y:|z|^{2} \leq \frac{1}{n}\right\}$ for all integers $n \geq 1$. Then, $\overset{\infty}{\underset{n=1}{\cap}}$ is

Among the following statements about the molecules $X $ and $Y$, the one (s) which is (are) correct is (are)

The formal potential of $Fe ^{3+} / Fe ^{2+}$ in a sulphuric acid and phosphoric acid mixture $\left(E^{\circ}=+0.61 \,V \right)$ is much lower than the standard potential $\left(E^{\circ}=+0.77 \,V \right) .$ This is due to

The $4^{th}$ higher homologue of ethane is

The disease that occurs in mature adult human being due to deficiency of calciferol is

The structure of $XeF_6$ is experimentally determined to be distorted octahedron. Its structure according to VSEPR theory is

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is

The hydrides of the first elements in groups $15 - 17$, namely $NH_3, H_2O$ and $HF$ respectively show abnormally high values for melting and boiling points. This is due to

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

To observe an elevation of boiling point of $0.05^?C$, the amount of solute (Mol. $Wt. = 100$) to be added to $100\, g$ of water $(K_b=0.5)$ is