List of practice Questions

A uniformly tapering conical wire is made from a material of Young?s modulus $Y$ and has a normal, unextended length $L$. The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R$, respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :

The following statements concern elements in the periodic table. Which of the following is true ?

An observer looks at a distant tree of height $10\, m$ with a telescope of magnifying power of $20$. To the observer the tree appears :

An aqueous solution of a salt $MX_2$ at certain temperature has a van?t Hoff factor of 2. The degree of dissociation for this solution of the salt is :

An arc lamp requires a direct current of $10\, A$ at $80 \,V$ to function. If it is connected to a $220 \,V \,(rms)$, $50 \,Hz\, AC$ supply, the series inductor needed for it to work is close to :

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the six trials of this experiment is :

An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% sulphur is : (atomic weight of S=32 amu)

At $300 \,K$ and $1 \,atm , 15\, mL$ of a gaseous hydrocarbon requires $375\, mL$ air containing $20 \% O _{2}$ by volume for complete combustion. After combustion the gases occupy $330\, mL$. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is :

Rayon is a semisynthetic polymer whose properties are better than natural cotton. Mechanical and aesthetic properties of cellulose can be improved by acetylation.

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r (r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$. Then :

Bromination of cyclohexene under conditions given below yields :

Bouveault-Blanc reduction reaction involves :

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

Consider the following sequence for aspartic acid : The pI (isoelectric point) of aspartic acid is :

Decomposition of $H_2O_2$ follows a first order reaction. In fifty minutes the concentration of $H_2O_2$ decreases from $0.5$ to $0.125 \,M$ in one such decomposition. When the concentration of $H_2O_2$ reaches $0.05 \,M$, the rate of formation of $O_2$ will be :

Extraction of copper by smelting uses silica as an additive to remove :

Figure shows elliptical path abcd of a planet around the sun $S$ such that the area of triangle $csa$ is $\frac{1}{4}$ the area of the ellipse. (See figure) With $db$ as the $semimajor$ axis, and $ca$ as the $semiminor$ axis. If $t_1$ is the time taken for planet to go over path $abc$ and $t_2$ for path taken over $cda$ then :

Galvanization is applying a coating of :

Gold numbers of some colloids are : Gelatin : 0.005 - 0.01, Gum Arabic : 0.15 - 0.25; Oleate : 0.04 - 1.0; Starch : 15 - 25. Which among these is a better protective colloid ?

Half-lives of two radioactive elements $A$ and $B$ are $20\, $ minutes and $40\,$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80\,$ minutes, the ratio of decayed numbers of $A$ and $B$ nuclei will be :

Hysteresis loops for two magnetic materials $A$ and $B$ are given below : These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

Identify the incorrect statement regarding heavy water :