List of practice Questions

A car covers the first half of the distance between two places at 40 km/h and another half at 50 km/h. The average speed of the car is
A and B together can complete a work in 12 days. A alone can do it in 20 days. In how many days can B alone complete the work?
If \( \begin{bmatrix} 1 & 3 \\ 4 & 5 \end{bmatrix} \begin{bmatrix} x \\ 2 \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix} \), then value of \( x \) is :
The letters of the word ``UDAYPUR'' are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word ``UDAYPUR'' is
Consider a function \(f(x)\) which has exactly two roots at \(x=a\). If \[ \lim_{x\rightarrow a}\left(\frac{\lambda f^{\prime}(x)}{f(x)}-\frac{1}{x-a}\right)=m \ (\ne0), \] then the value of \(\lambda\) is:
If \( A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix} \), then:
Which of the following is correctly matched?
The roots of the equation $\begin{vmatrix} 2 & -2 & 4 \\ -5 & x+2 & -10 \\ -1 & 1 & x+1 \end{vmatrix} = 0$, are
Let $A = \begin{bmatrix} 2 & x \\ 3 & 1 \end{bmatrix}, B = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$ and $C = \begin{bmatrix} 3x+2 & 10 \\ 14-x & 10 \end{bmatrix}$. If $B^T A^T = C$, then the value of $x$ is equal to
A system of equations is given in the matrix form as $\begin{bmatrix} \alpha & 2 & 3 \\ 2 & 3 & -\alpha \\ 3 & 5 & \alpha+1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}$ where $\alpha$ is an integer. If the system of equations does not have a unique solution, then the value of $\alpha$ is equal to
Lactose, the milk sugar is composed of
Hinsberg’s reagent is
Choose the correct decreasing order of basic strength of amines in aqueous solution:
Which of the following carboxylic acid has the highest $pK_a$ value?
The IUPAC name of mesityl oxide is
$p$-Bromophenol is the major product formed when phenol is treated with
Identify the allylic alcohol in the following.
Which of the following is an ambident nucleophile?
1-Chlorocyclohexene is an example of
The alkane that cannot be prepared in pure state by Kolbe’s electrolysis is
The number of C-C, C-H and C=C bonds in but-2-en-1-yne are, respectively
The complexes $[Co(NH_3)_6] [Cr(CN)_6]$ and $[Cr(NH_3)_6 ][Co(CN)_6]$ are examples of
Which of the following complex has the lowest molar conductivity?
Which of the following element of first transition series has the lowest atomization enthalpy?
The overall order of the following reaction is $KClO_3 + 6FeSO_4 + 3H_2SO_4 \rightarrow KCl + 3Fe_2(SO_4)_3 + 3H_2O$