List of practice Questions

Aarti prepared a fixture of 11 teams to conduct the Kho-Kho tournament in her locality as shown below:
Aarti prepared a fixture of 11 teams to conduct the Kho-Kho tournament
Tarun’s physical education teacher gave him the responsibility of organizing a Kabaddi competition in school. Tarun along with his classmates formed several committees and prepared a knockout fixture of 17 teams for the Kabaddi tournament. He faced many challenges in organizing the match, but finally, he was successful.
Answer the following questions based on the above case and your prior knowledge:
During the Physical Education class, Vivek’s physical education teacher provided information about sports for children with special needs. He explained how they are catered for the Paralympics, Deaflympics and Special Olympics. Additionally, he advised them to motivate such children to participate in physical activities to improve their performance.
Answer the following questions based on the above case and your prior knowledge:
Diya went to a sports training center for the first time. Her coach informed her that participation in sports not only promotes physical growth but also has social and psychological benefits. He highlighted numerous physical benefits for muscles, heart, and respiratory systems. He advised her to continue daily practice to improve her health-related and skill-related fitness.
Answer the following questions based on the above case and your prior knowledge:
Given below are two statements: 
Statement (I): Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode.
Statement (II): The rate of corrosion is more in alkaline medium than in acidic medium.
 In the light of the above statements, choose the correct answer from the options given below:
Royal Glaze Ltd. continues to maintain its position as one of the largest consumer goods companies in the world. Its organisational structure is designed to facilitate the achievement of its objectives in alignment with its vision statement. The company maintains two distinct product divisions in its organisational structure- ’Foods’ and ’Home Care’. Looking ahead, the company is focusing on embracing changes so that it can continue to be the market leader. As part of its expansion plans, it is planning to venture into the electronics segment in the near future.
Let \(\vec{a} = i + j + k\), \(\vec{b} = 2i + 2j + k\) and \(\vec{d} = \vec{a} \times \vec{b}\). If \(\vec{c}\) is a vector such that \(\vec{a} \cdot \vec{c} = |\vec{c}|\), \(\|\vec{c} - 2\vec{d}\| = 8\) and the angle between \(\vec{d}\) and \(\vec{c}\) is \(\frac{\pi}{4}\), then \(\left|10 - 3\vec{b} \cdot \vec{c} + |\vec{d}|\right|^2\) is equal to:
Eigenvalue question: \[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]
Given the matrix equation: \[A = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{pmatrix} \quad A \cdot X = B\]
Where \( A \) is the matrix, \( X \) is the unknown vector, and \( B \) is a constant vector. Solve for \( X \).
Given the following conditions, determine the value of the 15-minute Peak Hourly Factor (PHF): Given:
- Vehicles in the peak hour come in 10-minute intervals
- Find the value of the 15-minute PHF
Runway length after elevation and temperature correction is 700 m. The effective gradient is 1%. Find the final corrected length.
Sequence of Reactions of Ethylene and Chlorine to form PVC:
Find the sum of the series: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \]
Given the random variable \( X \) which takes the values 0, 1, 2, 7, 11, and 12 with the following probabilities: \[ P(X = 0) = 0.4, \quad P(X = 1) = 0.3, \quad P(X = 2) = 0.1, \quad P(X = 7) = 0.1, \quad P(X = 11) = ? \]
Given that \( \lambda \) is an eigenvalue of matrix \( A \) with the corresponding eigenvector \( x \), and \( x \) is also an eigenvector of \( B = A - 2I \), find the relationship between \( \lambda \) and the eigenvalue of \( B \).
Find the maximum value of the function \( f(x) = -x^3 + 2x^2 \) in the interval \( [-1, 1.5] \).
Mean Residence Time Calculation for a given system: \[ t_m = \int_0^{\infty} t E(t) \, dt \] Where \( E(t) \) is the distribution function. For the given system, the distribution function is: \[ E(t) = 1 - 2t, \quad t \leq 0.5 \] \[ E(t) = 0, \quad t > 0.5 \]
Which of the following are characteristics of steady flow?
Classify the following diameters into the corresponding categories:
What is the first stage of production of paper from wood?
Given the following parameters for a fluid flow, calculate the appropriate quantities: \[ V_0 = 1 \, \text{m/s}, \quad P_r = 7.01, \quad \nu = 10^{-6} \, \text{m}^2/\text{s} \] \[ S_{hn} = \frac{4.91}{\sqrt{Re_x}}, \quad \Delta x = 0.01 \, \text{m} \]
Solve the cubic equation: \[ x^3 - \frac{15}{2} x^2 + 18x + 20 = 0 \]
Given the following values, calculate the required properties: \[ S = 0.67, \quad e = 0.6, \quad w = 0.15, \quad G = 2.67, \quad \gamma_w = 9.81 \, \text{kN/m}^3, \quad V = 5 \, \text{m}^3 \]
Solve the second-order differential equation: \[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]
Match the following processes to their corresponding descriptions: Sintering, Fouling , Positioning , Coking