List of practice Questions

The octahedral complex of a metal ion $M^{3+} $ with four monodentate ligands $L_1,L_2,L_3 \, and \, L_4 $ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is

The variance of first $50$ even natural numbers is

Van der Waal's equation for a gas is stated as, $p = \frac{nRT}{V-nb}-a\left(\frac{n}{V}\right)^{2}.$ This equation reduces to the perfect gas equation, $p = \frac{nRT}{V}$ when ,

When a rubber -band is stretched by a distance x, it exerts a restoring force of magnitude $ F = ax + bx^2$, where a and b are constants. The work done in stretching the unstretched rubber-band by $L$ is :

When the rms voltages $V _{ L }, V _{ C }$ and $V _{ R }$ are measured respectively across the inductor $L ,$ the capacitor $C$ and the resistor $R$ in a series LCR circuit connected to an AC source, it is found that the ratio $V _{ L }: V _{ C }: V _{ R }=1: 2: 3$. If the rms voltage of the AC sources is $100 \,V ,$ the $V _{ R }$ is close to:

Which one of the following substituents at para-position is most effective in stabilizing the phenoxide ion ?

Which one of the following molecules is paramagnetic ?

Which one of the following compounds will not be soluble in sodium bicarbonate?

Which one of the following acids does not exhibit optical isomerism?

Which of the following will not show mutarotation?

Three rods of copper , brass and steel are welded together to form a Y-shaped structure .Area of cross -section of each rod is $4cm^2$.End of copper rod is maintained at $100^{\circ}C$ whereas ends of brass and steel are kept at $0^{\circ C}$ Lengths of the copper, brass and steel rods are 46,13 and 12 cm respectively The rods are thermally insulated from surroundings except at ends.Thermal conductivities of copper , brass and steel are 092 , 0.26 and 0.12 in CGS units , respectively .Rate of heat flow throught cooper rod is

On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius r with the bottom of the vessel. If $r << R$, and the surface tension of water is T, value of r just before bubbles detatch is (density of water is $\rho_{w}$ )

Steel ruptures when a shear of $ 3.5 \times 10^8 \,Nm^{-2}$ is applied. The force needed to punch a $1\, cm$ diameter hole in a steel sheet $0.3\, cm$ thick is nearly :

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

The angular frequency of the damped oscillator is given by, $\omega = \sqrt{\left(\frac{k}{m} - \frac{r^{2}}{4m^{2}}\right)}$ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^{2}}{mk}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as follows :

The coefficient of $x^{1012}$ in the expansion of $(1 + x^n + x^{253})^{10}$, (where n $\le$ 22 is any positive integer), is :-

The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x (1 + x)^{999} + x^2(1 + x)^{998} + .... + x^{1000}$ is:

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

The gap between the plates of a parallel plate capacitor of area A and distance between plates $d$, is filled with a dielectric whose permittivity varies linearly from $\epsilon_{1}$ at one plate to $\epsilon_{2}$ at the other. The capacitance of capacitor is :

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x - y + z+ 3 = 0$ is the line.

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :

The least positive integer n such that $1-\frac{2}{3}-\frac{2}{3^{2}}-.......-\frac{2}{3^{n-1}} < \frac{1}{100},$ is :

The ratio mass of oxygen and nitrogen of a particular gaseous mixture is $1 : 4$ The ratio of number of their molecule is

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation : $K\left(x\right)=K_{0}+\lambda x\left(\lambda=a\,\text{constant}\right)$ The capacitance $C$, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :

The total number of octahedral void(s) per atom present in a cubic close packec structure is :-