List of practice Questions

The least number of squares to be added in the figure to make AB a line of symmetry is: \begin{center} \includegraphics[width=6cm]{10.png} \end{center}

Let \( f: \mathbb{R} \to \mathbb{R} \) be a function such that \( f(x) = \max\{x, x^3\ \), \( x \in \mathbb{R} \), where \( \mathbb{R} \) is the set of all real numbers. The set of all points where \( f(x) \) is NOT differentiable is:}

The product of all eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2 & 3
4 & 5 & 6
7 & 8 & 9 \end{bmatrix} is: \]

Consider the following sample of numbers: \[ 9, \, 18, \, 11, \, 14, \, 15, \, 17, \, 10, \, 69, \, 11, \, 13 \] The median of the sample is:

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.
Steve was advised to keep his head \_\_\_ (i) \_\_\_ before heading \_\_\_ (ii) \_\_\_ to bat; for, while he had a head \_\_\_ (iii) \_\_\_ batting, he could only do so with a cool head \_\_\_ (iv) \_\_\_ his shoulders.

A wooden plant accumulates $10 𝑚𝑔 𝑘𝑔^{−1}$ of $^{14}C$ during its life span. A fossil of this plant was discovered and contains $2.5 𝑚𝑔 𝑘𝑔^{−1}$ of $^{14}C$. The age of this fossil at the time of discovery is years (rounded off to the nearest integer).
(Use 5730 years as half-life of $^{14}C$)

Which one of the following organisms has axial filaments?

In a single pass cold rolling operation, a flat plate is reduced to a thickness of 3 mm. In this operation, two rolls of diameter 400 mm each are rotating in opposite direction at 300 RPM, and the elastic deflection of these rolls is negligible. The angle of bite is 10°. If the neutral point is present at an angle of 7° from the exit side, then the thickness of the plate (in mm) at the neutral point is _____ . (Rounded off to 1 decimal place)

If the collision occurs at time \( t_0 = \frac{\pi}{2\omega} \), then the value of \( \frac{4b^2}{a^2} \) will be:

In the following reaction sequence, the major product \(Q\) is:

Let the function \( f : [1, \infty) \to \mathbb{R} \) be defined by:
\[ f(t) = \begin{cases} (-1)^{n+1}2, & \text{if } t = 2n-1, \, n \in \mathbb{N}, \\ \frac{(2n+1-t)}{2}f(2n-1) + \frac{(t-(2n-1))}{2}f(2n+1), & \text{if } 2n-1 < t < 2n+1, \, n \in \mathbb{N}. \end{cases} \]
Define \( g(x) = \int_1^x f(t) \, dt, \, x \in (1, \infty). \) Let \( \alpha \) denote the number of solutions of the equation \( g(x) = 0 \) in the interval \( (1, 8] \) and \( \beta = \lim_{x \to 1^+} \frac{g(x)}{x-1}. \) Then the value of \( \alpha + \beta \) is .........

To form a complete monolayer of acetic acid on 1 g of charcoal, 100 mL of 0.5 M acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 mL of 1 M NaOH solution was required. If each molecule of acetic acid occupies \(P \times 10^{-23} \, m^2\) surface area on charcoal, the value of \(P\) is \_\_\_\_\_. \text{[Use given data: Surface area of charcoal} = 1.5 \times 10^{2} \text{ m}^{2}\text{g}^{-1}; \text{Avogadro's number (N}_{\text{A}}) = 6.0 \times 10^{23} \text{mol}^{-1}]

According to Bohr's model, the highest kinetic energy is associated with the electron in the:

The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are: