List of practice Questions

Read the following statements – Assertion (A) and Reason (R). Choose the correct option given below:
Assertion (A): Full employment situation refers to the absence of involuntary unemployment.
Reason (R): Under full employment situation, all the willing and able-bodied people get employment at the prevailing wage rate.

(b) “In the current situation, Information Technology plays a vital role in achieving food security in a nation like India.”
Justify the given statement.

(a)(i) “Under the liberalisation measures taken by the Government of India, financial sector reforms were extremely crucial.”
Reject or support the given statement with valid arguments.

(a)(ii) Clarify how the Green Revolution enabled the government to procure sufficient food grains to build stocks to be used during times of food shortages.

(a)(ii) Worker–population ratio is an indicator, used for analyzing the employment situation in a nation.
State and elaborate whether the statement is true or false, with valid arguments.

(b)(i) Elaborate the need to promote women’s education in India.

(b) Discuss the impacts of Special Economic Zones (SEZs) on the economic growth of China.

“In India, National Education Policy 2020 has stressed a lot on in-service training of the teachers.”
(a) Identify the source of Human Capital Formation (HCF) indicated in the aforesaid statement.

(a) Elaborate the reasons owing to which the private sector was regulated under the Industrial Policy Resolution, 1956.

(b) “During the colonial period the agricultural sector showed massive stagnation.”
Do you agree with the given statement? Justify your answer with valid arguments.

Read the following statements carefully:
Statement 1: As per the National Sample Survey Organization (NSSO), unemployment is a situation in which all those who, owing to lack of work, are not working, but are seeking work from prospective employers. They express their willingness/availability to work under the prevailing conditions of work and remuneration.
Statement 2: Disguised Unemployment is generally a massive problem in a highly populated country like India.
In the light of the given statements, choose the correct option:

Identify from the following options the \textit{incorrect objectives of regulated agriculture market:}
(i) To make the marketing system efficient and effective for farmers to get the best price for their products.
(ii) To discourage improvement of marketing infrastructure for farmers.
(iii) To prevent exploitation of farmers.
(iv) To discourage farmers from improving quality and quantity of their produce.

Identify the correct equation from the following:

A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential growth model, the rate of growth of this sample of bacteria is calculated.

The differential equation representing the growth of bacteria is given as: \[ \frac{dP}{dt} = kP, \] where \( P \) is the population of bacteria at any time \( t \). bf{Based on the above information, answer the following questions:}
[(i)] Obtain the general solution of the given differential equation and express it as an exponential function of \( t \).
[(ii)] If the population of bacteria is 1000 at \( t = 0 \), and 2000 at \( t = 1 \), find the value of \( k \).

Find the equation of the line passing through the point of intersection of the lines: \[ \frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 2}{3}, \quad \frac{x - 1}{0} = \frac{y - 3}{-3} = \frac{z - 7}{2}, \] and perpendicular to these given lines.

Find the absolute maximum and absolute minimum values of the function \( f(x) = \frac{x}{2} + \frac{2}{x} \) on the interval \( [1, 2] \).

Find the intervals in which the function \( f(x) = \frac{\log x}{x} \) is strictly increasing or strictly decreasing.

Find the value of \( a \) and \( b \) so that the function \( f \) defined as: \[ f(x) = \begin{cases} \frac{x - 2}{|x - 2|} + a, & x < 2, \\ a + b, & x = 2, \\ \frac{x - 2}{|x - 2|} + b, & x > 2, \end{cases} \] is a continuous function.

Check the differentiability of \( f(x) \) at \( x = 1 \), where: \[ f(x) = \begin{cases} x^2 + 1, & 0 \leq x < 1, \\ 3 - x, & 1 \leq x \leq 2. \end{cases} \]

If \( x = e^{y^2} \), prove that \( \frac{dy}{dx} = \frac{\log x - 1}{(\log x)^2} \).