List of practice Questions

For the thermal decomposition of reactant AB(g), the following plot is constructed.

The half life of the reaction is 'x' min.
x =_______} min. (Nearest integer)}

What is the equivalent gate for the following digital circuit?

If a random variable $ x $ has the probability distribution

then $ P(3<x \leq 6) $ is equal to

Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3, \ldots, 50$. The probability that their product $ab$ is divisible by $3$ is

Let $ A, B, C $ be three $ 2\times2 $ matrices with real entries such that \[ B=(I+A)^{-1} \quad \text{and} \quad A+C=I. \] If \[ BC=\begin{bmatrix}1 & -5 \\-1 & 2\end{bmatrix} \quad \text{and} \quad B\begin{bmatrix}x_1\\x_2\end{bmatrix} =\begin{bmatrix}12\\-6\end{bmatrix}, \] then $ x_1+x_2 $ is:

In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.

From the following, the least stable structure is:
(Assume standard resonance structures)

Consider two arrangements of wires. Find the ratio of magnetic field at the centre of the semi–circular part.

Two tuning forks $A$ and $B$ are sounded together giving rise to 8 beats in 2 s. When fork $A$ is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork $B$ is $380\ \text{Hz}$, find the original frequency of tuning fork $A$. Given: \[ f_B = 380\ \text{Hz} \]

Consider the following compounds. Arrange these compounds in a n increasing order of reactivity with nitrating mixture. The correct order is :

Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius $ R $ as shown in figure. The net electric field at the center of the circle is ___________. ($ \varepsilon_0 $ is permittivity of free space)

For the matrices $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} $ and $ B = \begin{bmatrix} -29 & 49 \\ -13 & 18 \end{bmatrix} $, if $ (A^{15} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0\\ 0 \end{bmatrix} $, then among the following which one is true?}

The point of inflection of the function $f(x)=x^3$ in the interval $[-1,1]$ is

A regular hexagon is formed by six wires each of resistance $ r \,\Omega $ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

Object is placed at $40 \text{ cm}$ from spherical surface whose radius of curvature is $20 \text{ cm}$. Find height of image formed.

When $1$ g of compound $(X)$ is subjected to Kjeldahl's method for estimation of nitrogen, $15$ mL of $1$ M $\mathrm{H_2SO_4}$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $(X)$ is:

$ABCD$ is a parallelogram such that $AF = 7 \text{ cm}$, $FB = 3 \text{ cm}$ and $EF = 4 \text{ cm}$, length $FD$ equals

Foot of perpendicular from origin on a line passing through $(1, 1, 1)$ having direction ratios $\langle 2, 3, 4 \rangle$, is:

Monascus purpureus is a yeast used commercially in the production of which one of the following?

A line through $(1, 1, 1)$ and perpendicular to both $\hat{i} + 2\hat{j} + 2\hat{k}$ and $2\hat{i} + 2\hat{j} + \hat{k}$, let $(a, b, c)$ be foot of perpendicular from origin then $34 (a + b + c)$ is:

If angular position of a particle is given by $\theta = \frac{t^4}{4} + t^2$. Find angular acceleration at $t = 1s$:

Sum of $ \frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots $ up to 8 terms is:

If $50 \left( \frac{2x}{1 + 3i} + \frac{y}{1 - 2i} \right) = 31 + 17i$ where $x, y \in R$ & $i = \sqrt{-1}$ then value of $10(x + 3y)$ is ________

Consider two AP's $S_1$ & $S_2$ such that $S_1 : \{ \text{First term} = 1, \text{Common difference} = 5, \text{no. of terms} = 101 \}$
$S_2 : \{ \text{First term} = 9, \text{Common difference} = 7, \text{no. of terms} = 71 \}$
Find the number of common terms in both AP's.

If domain of $f(x) = \sqrt{\log_{0.6} \frac{2x - 5}{x^2 - 4}}$ is $(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$ then the value of $(a + b + c + d + e)$ is :