List of top Questions asked in JEE Main- 2015

Gaseous $N_2O_4$ dissociates into gaseous $NO_2$ according to the reaction $N _{2} O _{4}( g ) \rightleftharpoons 2 NO _{2}( g )$ At $300\, K$ and $1\, atm$ pressure, the degree of dissociation of $N_2O_4$ is $0.2.$ If one mole of $N_2O_4$ gas is contained in a vessel, then the density of the equilibrium mixture is :

In Carius method of estimation of halogens $250\, mg$ of an organic compound gave $141\, mg$ of $AgBr$. The percentage of bromine in the compound is (atomic mass $Ag\, =\, 108, Br \,= \,80$)

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R << L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is $T$ and its distance from the galaxy's axis is $r$, then :

Monochromatic light is incident on a glass prism of angle $A$. If the refractive index of the material of the prism is $u$, a ray incident at an angle $\theta$, on the face $AB$ would get transmitted through the face $AC$ of the prism provided

If A = $ \begin {bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end {bmatrix}$ is a matrix satisfying the equation $AA^T =9 I,$ where, $I$ is $3 \times 3$ identity matrix, then the ordered pair $(a, b)$ is equal to

A vector \(\vec{A}\) is rotated by a small angle \(\Delta\theta\) radians \(\left(\Delta\theta<<1\right)\) to get a new vector \(\vec{B}.\) In that case \(\left|\vec{B}-\vec{A}\right|\) is :

Given in the figure are two blocks $A$ and $B$ of weight $20\,N$ and $100\,N$, respectively. These are being pressed against a wall by a force $F$ as shown in figure. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall in block $B$ is

The current voltage relation of diode is given by $I=\left(e^{1000 V / T}-1\right) mA$, where the applied voltage $V$ is in volt and the temperature $T$ is in kelvin. If a student makes an error measuring $\pm 0.01\, V$ while measuring the current of

The following reaction is performed at $298\, K ?$ $2 NO ( g )+ O _{2}( g ) \rightleftharpoons 2 NO _{2}( g )$ The standard free energy of formation of $NO ( g )$ is $86.6 \,kJ /\, mol$ at $298 \,K .$ What is the standard free energy of formation of $NO _{2}( g )$ at $298 \,K ?\left( K _{n}=1.6 \times 10^{12}\right)$

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (molecular weight = $206$). What would be the maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin

The AC voltage across a resistance can be measured using a :

Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $'\theta'$ with the vertical. If wires have mass $\lambda$ per unit length then, the value of $I$ is : ( $g =$ gravitational acceleration)

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}}$. Measured value of $L$ is $20.0\, cm$ known to $1\, mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\, s$ using a wrist watch of $1\, s$ resolution. The accuracy in the determination of $g$ is

A $25\, cm$ long solenoid has radius $2\, cm$ and $500$ total number of turns. It carries a current of $15\, A$. If it is equivalent to a magnet of the same size and magnetization $|\bar{M}|$ (magnetic moment/volume), then $|\bar{M}|$ is :

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is

Let k be a non-zero real number. If $f(x) = \begin{cases} \frac{\left(e^x-1\right)^2}{sin\left(\frac{x}{k}\right)log\left(1+\frac{x}{4}\right)}, & \text{x $\ne$ 0} \\[2ex] 12, & \text{x = 0} \end{cases}$ is a continuous function, then the value of $k$ is :

The de - Broglie wavelength associated with the electron in the $n = 4$ level is :

The value of $ \displaystyle \sum^{30}_{r = 16} (r + 2)(r - 3)$ is equal to :

A complex number $z$ is the said to be unimodular if $|z|=1 .$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z_{1}-2 z_{2}}{2-z_{1} z_{2}}$ is unimodular and $z _{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

The solution of the differential equation $ydx - (x + 2y^2)dy = 0$ is $x = f(y)$. If $f(- 1) = 1$, then $f(1)$ is equal to :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :

The term independent of $x$ in the binomial expansion of $\left(1-\frac{1}{x}+3x^{5}\right)\left(2x^{2}-\frac{1}{x}\right)^{8}$ is :

The mean of the data set comprising of $16$ observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is