List of practice Questions

A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_{1}$ on a particle placed at $P$ , distance $2 \, R$ from the centre O of the sphere. A spherical cavity of the radius $R/2$ is now made in the sphere as shown in the figure. The sphere with the cavity now applies a gravitational force $F_{2}$ on the same particle placed at $P$ . The ratio $F_{2}/F_{1}$ will be
The percentage by volume of C3H8 in a mixture of C3H8, CH4 and CO is 36.5. Calculate the volume of CO2 produced when 100 ml of the mixture is burnt in excess of O2.
A radioactive nucleus undergoes a series of decay according to the scheme $ {A ->[\alpha] A1}$$ { ->[\beta] A2}$$ { ->[\alpha] A3}$$ { ->[\gamma] A4}$ If the mass number and atomic number of A are 180 and 72 respectively, these numbers of $A_4$ are
The equivalent resistance of the circuit, across $AB$ is given by
A problem is given to 3 students. Their chances of solving it individually are $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ . The probability that the problem will be solved is
$E^{\circ}$ values of three metals are listed below. $Zn^{2+}_{\left(aq\right)}+2e^{-} \to Zn_{\left(s\right)};\quad E^{\circ}=-0.76\,V$ $Fe^{2+}_{\left(aq\right)}+2e^{-} \to2Fe_{\left(s\right)}; \quad E^{\circ}=-0.44\,V$ $Sn^{2+}_{\left(aq\right)}+2e^{-} \to Sn_{\left(s\right)}; \quad E^{\circ}=-0.14\,V$ Which of the following statements are correct on the basis of the above information? (i) Zinc will be corroded in preference to iron if zinc coating is broken on the surface. (ii) If iron is coated with tin and the coating is broken on the surface then iron will be corroded. (iii) Zinc is more reactive than iron but tin is less reactive than iron.

$E=-\frac{dV}{dr}$ here negative sign sigified that
Seven resistances are connected as shown in the given figure. The equivalent resistance between A and B is
Five equal resistances each of resistance $R$ are connected as shown in the figure. A battery of $V$ volts is connected between $A$ and $B$. The current flowing in $AFCEB$ will be
A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20 \, Vm^{-1} $ and 0.5 T at right angles to the direction of motion of the electrons. What is the velocity of the electrons?
The more positive the value of $E^{\circ}$, the greater is the tendency of the species to get reduced. Using the. standard electrode potential of redox couples given below find out which of the following is the strongest oxidising agent. $E^{\circ}$ values : $Fe^{3+}/Fe^{2+} = + 0.77; I_{2\left(s\right)}/I^- = + 0.54$; $Cu^{2+}/Cu = + 0.34$; $Ag^{+}/Ag = + 0.80\, V$
A positively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge
A satellite is revolving round the earth with orbital speed $v_0$. If it stops suddenly, the speed with which it will strike the surface of earth would be ($v_e= $ escape velocity of a body on earth's surface)
During osmosis, water moves through a membrane
If the sums of n terms of two arithmetic series are in the ratio 2n + 3 : 6n + 5, then the ratio between their 13th terms is
The solubility product of silver chromate is $4 \times 10^{-12}$. The molar solubility of the salt is
The line passing through the points \((2,1,0) , (5,0,1)\) and \( (4,1,1)\) intersects the \(x-\)axis at
During osmosis,flow of water through a semipermeable membrane is
The equations of the lines through the point (3, 2) which make an angle of 45o with the line x - 2y = 3 are
The signum function, $f$ : $R \to R$ is given by $f(x) = \begin{cases} 1, & \text{if } x > 0 \\ 0, & \text{if } x=0 \\ -1, & \text{if } x < 0 \end{cases} $ is
The molarity of 98% $H_2SO_4$ (d = 1.8 g/mL) by weight is
Which one of the following statements is correct ? The power set of the null set is
The modulus of the complex number $z=\frac{\left(1-i\sqrt{3}\right)\left(cos\,\theta+i\, sin\,\theta\right)}{2\left(1-i\right)\left(cos\,\theta-i\, sin\,\theta\right)}$ is
A polarizer and an analyzer are oriented so that the maximum amount of lights is transmitted. Fraction of its maximum value is the intensity of the transmitted light reduced when the analyzer is rotated through (intensity of incident light = $I_0$) a) 30$^\circ$ b)45$^\circ$ c)60$^\circ$
The second heart sound (dubb) is associated with the closure of