List of practice Questions

This reaction mechanism is favored by \( 3^{\circ} \) substrates, low temperatures, polar solvents, and low concentrations of very weak bases.

Which of the following is a cytokine inhibitor used as anti-inflammatory?

Let $f: R \rightarrow R$ be a differentiable function such that its derivative $f^{\prime}$ is continuous and $f(\pi)=-6$. If $F$ : $[0$, $\pi] \rightarrow R$ is defined by $F(x)=\int\limits_{0}^{x} f(t) d t$, and if
$\int\limits_{0}^{\pi}\left(f^{\prime}(x)+F(x)\right) \cos x d x=2$
then the value of $f (0)$ is _____

A fruit vendor purchases two varieties of oranges at the rates of 12 oranges for ₹ 18 and 18 oranges for ₹ 12. He mixes the two varieties in the ratio of 2: 3 and sells the mixed stock at a price of ₹ 144 for 10 dozens. What percentage of profit or loss does he make ?

In which of the following molecule, the bond angle is 107°48'?

Identify the related word:
'Needle' is to 'Clock' as 'Wheel' is to

Identify the wrong statement with regard to Restriction Enzymes.

Consider two ideal diatomic gases $A$ and $B$ at some temperature $T$. Molecules of the gas A are rigid , and have an mass $m$. Molecules of the gas $B$ have an additional vibrational mode, and have a mass $\frac{m}{4}.$ The ratio of the specific heats $(C^{A}_{V}$ and $C^{B}_{V})$ of gas $A$ and $B$, respectively is :

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $4\, kg$. (The coordinates of the same are shown in figure) are :

The electronic configurations of bivalent europium and trivalent cerium are : (atomic number: $Xe = 54, Ce =58, Eu ??63$)

Taking into account of the significant figures, what is the value of $9.99 \,m - 0.0099 \,m$ ?

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $'a'$ and a concentric thin cylindrical shell of radius $'b'$ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R ,$ the maximum Joule heating in $R$ will take place for :

In a building there are $15$ bulbs of $45\, W, 15$ bulbs of $100\, W$, $15$ small fans of $10\, W$ and $2$ heaters of $1\, kW$. The voltage of electric main is $220\, V$. The minimum fuse capacity (rated value) of the building will be:

A vessel of depth $2\,h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$ The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ Ls carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{E_{A}}\right|}{\left|\overrightarrow{E_{B}}\right|}$ of magnitude of electric field $\overrightarrow{E_{A}}$ and $\overrightarrow{E}_{B}$ respectively, at points A and B due to the remaining portion is :

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4\, cm$ and $4.8\, cm$, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

If the potential energy between two molecules is given by $U = - \frac{ A }{ r ^{6}}+\frac{ B }{ r ^{12}},$ then at equilibrium, separation between molecules, and the potential energy are :

In finding the electric field using Gauss law the formula $\left|\overrightarrow{E}\right|= \frac{q_{enc}}{\epsilon_{0}\left|A\right|}$ is applicable. In the formula $\epsilon_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and $ q_{enc}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation ?

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

Let $\vec{a}=\hat{i}-2\,\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b}\times\vec{c}=\vec{b}\times\vec{a}$ and $\vec{c}\cdot\vec{a}=0,$ then $\vec{c} \cdot \vec{b}$ is equal to :

If the volume of a parallelepiped whose coterminous edges are $\vec{a}=\hat{i}+\hat{j}+2\,\hat{k}, \vec{b}=2\,\hat{i}+\lambda\,\hat{j}+\hat{k}$ and $\vec{c}=2\,\hat{i}+2\hat{j}+\lambda\hat{k}$ is 35 cu.m, then a value of $\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}-\vec{c}\cdot\vec{a}$ is :

The probability that a randomly chosen 5 -digit number is made from exactly two digits is :

Let the ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a > b,$ pass through the point (2, 3) and have eccentricity equal to $\frac{1}{2}$. Then equation of the normal to this ellipse at $(2,3)$ is :

Identify the cells represented as \(p, q, r\) and \(s\) in the schematic representation of Oogenesis, shown below and choose the correct option.