List of practice Questions

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

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:

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:

In very high electric field \( E > 10^5 \), 

(A) Asymmetric affect disappears 
(B) Electrophoretic affect disappears 
(C) The ion moves so rapidly that it loses its ionic atmosphere. 
(D) The weak electrolyte is completely ionised at all dilutions. 
 

Arrange the following spectral ranges in order of their increasing wavelength. 

(A) Radio 
(B) Visible 
(C) Infrared 
(D) Ultraviolet 
 

Which of the following statement/s is/are correct with regards to the tangential force which is needed to keep the speeds of different layers of liquid constant? 

(A) It is directly proportional to the velocity difference between the two adjacent layers. 
(B) It is inversely proportional to the area of contact between the two adjacent layers. 
(C) It is inversely proportional to the distance between the two adjacent layers. 
(D) None of the above. 
 

The major product (A) is: 

Which of the following are aromatic? 

Identify A, B, and C in the following reaction: 

The reaction is carried out by: 

Arrange the following set of carbocations in order of decreasing stability. 

Choose the correct answer from the options given below:

Which of the following amino compound(s) CANNOT be prepared by Gabriel phthalimide synthesis? 

(A) n-Butylamine 
(B) Alanine 
(C) Aniline 
(D) t-Butylamine 
Choose the correct answer from the options given below:

The final product (D) in the above sequential reaction is: 

Which of the following is true for the stereochemical relationship of the given structures (A-D)? 

The major product (P) in the following transformation is: 

Above conversion is carried out using: 

The reaction steps shown are: 

The final product (P) is:

Find the ground state term symbol for Pr\(^{3+}\) (Pr = 59).
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.
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 CFSE for the \( d^8 \) octahedral ion is:
The IUPAC name of the coordination compound is: \[ [\text{Rh}(CO)_2I_2]^- \]
Arrange the following ligands in their increasing d-orbital splitting: (A) NH\(_3\)
(B) C\(_2\)O\(_4^{2-}\)
(C) OH\(^-\)
(D) CN\(^-\)
For the second and third row of transition elements, which statement is not true?
Match the xenon compounds (List-I) with structures (List-II)\[\begin{array}{|c|c|} \hline \textbf{List-I (Xenon compounds)} & \textbf{List-II (Structures)} \\ \hline \text{(A) XeF$_4$} & \text{(IV) Square planar} \\ \hline \text{(B) XeO$_3$} & \text{(III) Pyramidal} \\ \hline \text{(C) XeO$_2$F$_2$} & \text{(I) Trigonal bipyramidal} \\ \hline \text{(D) XeO$_4$} & \text{(II) Tetrahedral} \\ \hline \end{array}\]