List of top Questions asked in JEE Advanced- 2018

For a first order reaction ${A(g) \to 2B(g) + C(g)}$ at constant volume and $300\, K$, the total pressure at the beginning $(t = 0)$ and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only $A$ is present with concentration $[A]0$, and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and [ The relation between [

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y$. If the errors in $x ,y $ and $z$ are $\Delta x, \Delta y$ and $\Delta z$, respectively, then $z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y} \left( 1 \pm \frac{\Delta x}{x} \right) \left( 1 \pm \frac{\Delta y}{y} \right)^{-1}$. The series expansion for $\left( 1 \pm \frac{\Delta y}{y} \right)^{-1}$, to first power in $\Delta y/y $. is $1 \mp (\Delta y / y )$. The relative errors in independent variables are always added. So the error in $z$ will be $\Delta z = z \left( \frac{\Delta x}{x} + \frac{\Delta y}{y} \right)$ . The above derivation makes the assumption that $\Delta powers of these quantities are neglected. Consider the ratio $r = \frac{(1-a)}{(1+a)}$ to be determined by measuring a dimensionless quantity $a$. If the error in the measurement of $a$ is $\Delta a (\Delta a/a ??1)$ , then what is the error $\Delta r$ in determining $r$?

Two infinitely long straight wires lie in the $xy$-plane along the lines $x = \pm R$. The wire located at $x = + R$ carries a constant current $I_1$ and the wire located at $x = - R $ carries a constant current $I_2$. A circular loop of radius

The correct option(s) regarding the complex ${[Co(en)(NH3)3(H2O)]^{3+} (en = H2NCH2CH2NH2)}$ is (are)

The correct option(s) to distinguish nitrate salts of ${Mn^{2+}}$ and ${Cu^{2+}}$ taken separately is (are)

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\in_0$. Which of the following statements is (are) true?

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $\theta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y$. If the errors in $x ,y $ and $z$ are $\Delta x, \Delta y$ and $\Delta z$, respectively, then $z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y} \left( 1 \pm \frac{\Delta x}{x} \right) \left( 1 \pm \frac{\Delta y}{y} \right)^{-1}$. The series expansion for $\left( 1 \pm \frac{\Delta y}{y} \right)^{-1}$, to first power in $\Delta y/y $. is $1 \mp (\Delta y / y )$. The relative errors in independent variables are always added. So the error in $z$ will be $\Delta z = z \left( \frac{\Delta x}{x} + \frac{\Delta y}{y} \right)$ . The above derivation makes the assumption that $\Delta powers of these quantities are neglected. In an experiment the initial number of radioactive nuclei is $3000$. It is found that $1000 \pm 40 $ nuclei decayed in the first 1.0 s. For $|x| < < 1$, ln $(1 + x) = x$ up to first power in $x$. The error $\Delta \lambda$, in the determination of the decay constant $\lambda$, in $s^{-1}$, is

In a radioactive decay chain, $^{232}_{90}Th$ nucleus decays to $^{212}_{92}Pb$ nucleus. Let $N_{\alpha}$ and $N_{\beta}$ be the number of $alpha$ and $\beta^{-}$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500 \, Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $50.7 \, cm $ and $83.9 \, cm$. Which of the following statements is (are) true?

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and [ The relation between $[\varepsilon_0]$ and $[\mu_0]$ is

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt = \gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)