List of practice Questions

In a constant head permeameter, having cross-sectional area of $20 \, \text{cm}^2$, when the flow was taking place under a hydraulic gradient of $0.5$, the amount of water collected is $1200 \, \text{cm}^3$ in $60 \, \text{sec}$. The permeability of the soil is:

The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation:

If $f(x) = x^2$, then the second order divided difference for the points $x_0, x_1, x_2$ will be:

In a Binomial distribution, the sum of its mean and variance is $1.8$. If the event was conducted $5$ times, then the probability of two successes is:

The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is:

The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:

For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:

The solution(s) of the ordinary differential equation $y'' + y = 0$, is:

(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:

Match the following organometallic compounds (List-I) with their Characteristics (List-II)\[\begin{array}{|c|c|} \hline \textbf{List-I (Organometallic Compounds)} & \textbf{List-II (Characteristics)} \\ \hline \text{(A) Fe(C$_5$H$_5$)$_2$} & \text{(III) Fluxionality} \\ \hline \text{(B) K$^+$[PtCl$_3$(C$_2$H$_4$)]} & \text{(I) dsp$^2$ hybridization} \\ \hline \text{(C) Mg(CH$_3$)$_2$} & \text{(IV) Polymeric in nature} \\ \hline \text{(D) (CH$_3$)$_2$AlF$_4$} & \text{(II) Tetramer structure} \\ \hline \end{array}\]

The biomedical applications of polyphosphazene polymers are: (A) As structural materials for the construction of heart valves and blood vessels.
(B) They are used in drug delivery systems.
(C) Biodegradable support for in vivo bone regeneration.

Find the ground state term symbol for Pr$^{3+}$ (Pr = 59).

For the second and third row of transition elements, which statement is not true?

Arrange the following ligands in their increasing d-orbital splitting: (A) NH$_3$
(B) C$_2$O$_4^{2-}$
(C) OH$^-$
(D) CN$^-$

The IUPAC name of the coordination compound is: \[ [\text{Rh}(CO)_2I_2]^- \]

The CFSE for the $ d^8 $ octahedral ion is:

The magnitude of CFSE depends on: (A) The nature of the ligand
(B) The charge on the metal ion
(C) Position of the metal ion in transition series
(D) Geometry of the complex

Match the xenon compounds (List-I) with structures (List-II)\[\begin{array}{|c|c|} \hline \textbf{List-I (Xenon compounds)} & \textbf{List-II (Structures)} \\ \hline \text{(A) XeF$_4$} & \text{(IV) Square planar} \\ \hline \text{(B) XeO$_3$} & \text{(III) Pyramidal} \\ \hline \text{(C) XeO$_2$F$_2$} & \text{(I) Trigonal bipyramidal} \\ \hline \text{(D) XeO$_4$} & \text{(II) Tetrahedral} \\ \hline \end{array}\]