List of practice Questions

If $a,b,c$ are distinct positive numbers and the vectors $a\hat i+a\hat j+c\hat k,\ \hat i+\hat k$ and $c\hat i+c\hat j+b\hat k$ lie in a plane, then

Evaluate $\displaystyle \int_{-2}^{2} [x]\,dx$, where $[x]$ denotes the greatest integer function

If $\displaystyle \int \frac{x^2+1}{(x-3)(x-2)}\,dx = Px + Q\log|x-3| + R\log|x-2| + c$, where $c$ is constant of integration, then the values of $P,Q,R$ are respectively

The separate equations of the lines represented by $4x^2 - y^2 + 2x + y = 0$ are

The dual of the statement `Mangoes are delicious but expensive' is

If $AX = B$, where $A = \begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4 \end{bmatrix}$, $X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$ and $B = \begin{bmatrix} 12 \\ 15 \\ 13 \end{bmatrix}$, then $x^2 + y^2 + z^2 =$

The angle between the lines $\vec r = (2\hat i + \hat j - 3\hat k) + \lambda(\hat i - \hat j + \hat k)$ and $\dfrac{x-1}{1} = \dfrac{y+2}{3} = \dfrac{z-3}{2}$ is

Identify the reducing agent in the following reaction:
\[ \mathrm{CH_4(g) + O_2(g) \rightarrow CO_2(g) + 2H_2O(l)} \]

Which is an example of molecular hydride?

Which among the following amino acids has the lowest molecular mass?

If $Z = 10x + 25y$ subject to $0 \le x \le 3$, $0 \le y \le 3$, $x + y \le 5$, $x \ge 0$, $y \ge 0$, then $Z$ is maximum at the point

A problem in statistics is given to three students $P$, $Q$ and $R$. Their chances of solving the problem are $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently, then the probability that the problem is solved is

Which of the following groups increases the basic strength of substituted aniline?

Which among the following is an example of metal–sparingly soluble salt electrode?

How much part of an atom occupies each corner of a bcc unit cell?

Which of the following is reacted with benzaldehyde to obtain 1-phenylethanol?

Which of the following alcohols is least soluble in water?

Which among the following is an example of amorphous solid?

Which of the following is the formula of BHA?

\[ If 2\,\text{kJ of heat is released from the system and } 6\,\text{kJ of work is done on the system,} \] what is the enthalpy change of the system?

What is the highest oxidation state exhibited by any transition element among all?

Find the empirical formula of an organic compound if it contains
\[ 18.6%\,\mathrm{C},\ 1.55%\,\mathrm{H},\ 55.04%\,\mathrm{Cl} (atomic masses: C = 12, H = 1, Cl = 35.5, O = 16). \]

Which coordinate compound from the following has a net negative charge on the complex ion?

Benzene diazonium chloride on reaction with ethanol forms

Which of the following is a tricarboxylic acid?