ESE (ME) Paper I Mock Test - 2 Free Online Test 2026

The basic rights of engineers include the right to live freely and pursue their legitimate interests as any human being, along with the right to be against racial or sexual discrimination, receiving one’s salary according to the work, choosing of political activities, etc., as other employees. Besides all of them, engineers have some special rights as professionals.

The rights that engineers have as professionals are called Professional Rights. These professional rights include −

• The basic right of professional conscience.
• The right of conscientious refusal.
• The right of professional recognition.

Given,

Let λ₁ and λ₂ be the Eigen value of matrix A
|A| = λ₁λ₂
|A| = 2k - 1
∵ λ₁ and λ₂ are positive i.e., λ₁λ₂ > 0
(2k - 1) > 0
∴ k > 1/2

The maximum proportion of defectives that can be considered satisfactory as a process average for the purpose of sampling inspection of the quality of production is called Acceptable Quality Level. It is a method widely used to define a production order sample to find whether or not the entire product order has met the customer's specifications. Based on the sampling data, the customer can make an informed decision to accept or reject the lot.At Acceptable Quality Level the probability of acceptance should be one means 100%. The probability of rejecting the lot at AQL represents the producer’s risk.

Hence the correct option is (A).

The equation of ellipse,

Ellipticity

Then,

...(i)

By the above formula

The length of major axis

The length of the chord of the directrix

Then, required ratio

Given,
The distance of the point (k + 2, 2k + 3) from the line x + 3y = 7 is .

Let P = (k + 2, 2k + 3) 
⇒ x₁ = k + 2 and y₁ = 2k + 3
Here,  a = 1 and b = 3
Now substitute x₁ = k + 2 and y₁ = 2k + 3 in the equation x + 3y - 7 = 0 we get,

As we know that, the perpendicular distance d from P (x₁, y₁) to the line ax + by + c = 0 is given by:

The fundamental characteristics of a profession:

• Great responsibility
• Accountability
• Based on specialized, theoretical knowledge
• Institutional preparation
• Autonomy
• Clients rather than customers
• Direct working relationships
• Ethical constraints
• Merit-based
• Capitalist morality

Given:
Cost of production of phone = Rs 900
The ratio of costs of material, labor, and overheads = 3 : 4 : 2 
The profit on labor's component = 20%
We know that the profit is calculated on the cost price of the component.
⇒ The cost of material = 3 x 900/9 = Rs 300
The cost of labor = 4 x 900/9 = Rs 400
The cost of overheads = 2 x 900/9 =  Rs 200
Now, the profit is on the labor component = 20% of Rs 400 = 20 x 400/100 = Rs 80 
There is no profit on other components, so the marked price will be = Cost of material+ cost of labor+ cost of overheads+ profit on labor
⇒ Marked price = 300 + 400 + 200 + 80 = Rs. 980 
∴ the marked price of the set is Rs 980

• India is on a mission to drill a 6-kilometer deep hole in Koyna, Maharashtra, aiming to uncover seismic insights. Scientific deep-drilling involves strategically digging boreholes to observe and analyze deeper parts of the earth’s crust. Hence, statement 1 is correct.
• Scientific deep-drilling helps to study earthquakes and enhances understanding of the planet’s history, rock types, energy resources, life forms, climate change patterns, and the evolution of life. Hence, statement 2 is correct.

Primary green house gases are methane, water vapour, nitrous oxide and ozone. Carbon dioxide makes up the vast majority of greenhouse gas emissions from the sector, but smaller amounts of methane and nitrous oxide are also emitted. These gases are released during the combustion of fossil fuels, such as coal, oil, and natural gas, to produce electricity. Water vapour is also an effective greenhouse gas, as it does absorb longwave radiation and radiates it back to the surface, thus contributing to warming. When compared to other greenhouse gases, water vapour stays in the atmosphere for a much shorter period of time.

Total mixture 80 litres
Milk is 25%
⇒ 25/100 x 80 = 20 litre
To make it 20% amount of water required to add

So, 20 litres water should be added to the mixture so that milk becomes 20% of the mixture.

Ankur Gupta, an assistant chemical and biological engineering professor at the University of Colorado Boulder, has unveiled a groundbreaking technology that can charge an electric vehicle (EV) in just 10 minutes and a laptop or phone in just a minute. His research, published in the Proceedings of the National Academy of Sciences journal, represents a significant advancement in charging technology, promising faster and more efficient charging solutions for various electronic devices.

Cauchy-Riemann equations:

In rectangular form:

to be analytic it needs to satisfy Cauchy Riemann equations.

In polar form,

and

and

Solid material chemical bonds are ionic, covalent bond and metallic bond.

The atoms and molecules are held together by strong mutual forces of attraction. These interatomic forces are electrostatic in nature and depend upon the electronic structure of the element. Binding forces between atoms and molecules are known as chemical bonds. 

lonic bond is the strong electrostatic attraction between cation and anion. Covalent bonds are one in which there is a sharing of one or more electrons from the adjacent atoms. A metallic bond is formed by the partial sharing of valence electrons by the neighbouring atoms. The atoms in metals and alloys are held together by such bonds.

Given: 

We have to find the value of 3^x.

So, 2^{3 x 2} = 2^2x 

2⁶ = 2^2x

By equating the exponents we get,

x = 6/2

x = 3

By substituting the value of x in 3^x we get,
3^x = 3³ = 27

So, the value of 3^x is 27 .

The United Nations Conference on Trade and Development (UNCTAD) published the report, COVID-19 and Tourism: Assessing the Economic Consequences stating that the World Tourism sector could lose around 1.2 trillion USD or 1.5% of the Global Gross Domestic Product (GDP) because of the 4 months lockdown due to global pandemic situation.

Frictional unemployment is a type of unemployment that arises when workers are searching for new jobs or are transitioning from one job to another. It is part of natural unemployment and hence is present even when the economy is considered at full employment. So, statement 1 is correct.

In a recession, frictional unemployment tends to fall as workers have less confidence to wait for a better job. They are more likely to stay in their current job or take the first job that comes along. So, statement 2 is correct.

Given:
Equation of line y = 3x - 1
General equation of line is y = m₁x + c
∴ m₁ = 3
If two lines are perpendicular, then m₁.m₂ = -1 
Slope of line perpendicular to y = 3x- 1  will be -1/3 (∵ 3.m₂= -1, m₂ = -1/3) 
Equation of line y = m₂x + c 
y = -1/3x+ c
3y + x = c 
This line passes through the point (1,2)
∴ 3(2) + 1 = c 
c = 7
Equation of line becomes  x + 3y = 7 
x + 3y - 7 = 0 

Equation of lines are: x + y - 3 = 0  and x - y + 3 = 0

∴ Slopes of the above lines are -1 and 1 respectively.

Since product of their slope is -1. 

∴ Angle between these lines is  90° ⇒ α​​​​​​​ = 90°

Also, angle between the lines: x - √​​​​​​​3y + 2√3 = 0  and √3x - y +1 = 0

The gain or profit from the sale of assets is classified as a capital gain. ​Short Term Capital Gains Tax (STCG) is the tax levied on profits generated from the sale of an asset which is held for a government-defined short period is called short-term capital gains tax. The short term period differs for various items - for example, it is 24 months or less in the case of immovable property such as land and building and 12 months or less for equity, bonds, government securities etc. So, statement 1 is not correct.

The Securities Transaction Tax (STT) is a type of direct tax which is levied at the time of purchase and sale of securities listed on stock exchanges in India. Securities are tradable investment instruments such as shares, bonds, debentures, equity-oriented mutual funds (MFs) and so on and are issued either by companies or by the Indian government. This tax was introduced in the Union Budget of 2004. The Securities Transaction Tax (STT) was introduced in India in the Budget of 2004 to curb tax avoidance on capital gains. On the other hand, Capital gains for securities are levied on the gains made from the sale of securities and not on the transaction as in the case of STT. However, both of them fall under the category of direct taxes. So, statement 2 is not correct.

Maharashtra was officially formed as a separate state on May 1st, 1960, which is celebrated annually as Maharashtra Day or Maharashtra Diwas. This date marks the division of the former Bombay Presidency into Maharashtra and Gujarat following the States Reorganisation Act of 1956, which aimed to create states based on linguistic boundaries. It holds immense cultural significance for the Marathi people, symbolizing their unity, resilience, and heritage.

The application of information is called as knowledge. Knowledge application is when available knowledge is used to make decisions and perform tasks through direction and routines. In an information system, Knowledge can be described as: “an awareness and understanding of a set of information and the ways that information can be used to support a specific task or reach a decision”.

Leontief paradox:

• Leontief paradox model was given by Wassily W Leontief in the year 1953. He suggested that the United States had an abundance of capital and the country should export more capital-intensive goods.
• Although, he noticed that the data showed that the United States was importing capital-intensive goods.
• Keeping in mind Heckscher-Ohlin's theory US should have imported labor-intensive goods instead of capital-intensive goods. His analysis was called Leontief paradox as his theory was the opposite of Heckscher-Ohlin's theory.

Token money is made of cheaper metal, it is limited legal tender, it is not subject to free coinage and its face value is greater than its intrinsic or metallic value. Token money consists of small coins. So, statement 1 is not correct.

Under the Minimum Reserve System, RBI can issue an unlimited amount of currency by keeping the reserve (without backing the total currency in circulation with the gold of equal value). But RBI follows some principle or rule for issuing new currencies based upon the economic growth and transaction needs of the people. So, statement 2 is not correct.

According to RBI rules, those who refuse to accept the Indian currency can be liable for action under section 124A (sedition) of IPC. RBI clarified the coin was valid and anyone refusing it was liable to face legal action. So, statement 3 is correct.

• Spam is any kind of unwanted, unsolicited digital communication, an email, that gets sent out in bulk.
• Spam is an issue about consent, not content.
• The content is irrelevant and if the message was sent unsolicited and in bulk then the message is spam.
• Spam is a scam or that doesn't contain an unsubscribe link.
• Internet service providers (ISP) carry and store the data.
• When hackers can’t steal data bandwidth from the ISPs, they steal it from individual users, hacking computers and enslaving them in a zombie botnet.
• Software providers invest resources creating email applications that try to filter most of the spam out.
• If there’s an inbox, spammers will find a way to clog it.
• Spam can also be found on Internet forums, text messages, blog comments, and social media.

Formula Used:

When two successive discounts of x% and Y% are offered on a product, total discount  = ((x+y-xy)/100)%

Also, when the price is marked p\% above cost price and sold at a discount of q%, profit % = ((p-q-pq)/100)%

Now,

Store A marked the price 50% above CP \& sold at successive discounts of 15% and 10%,

⇒ Total discount offered by store A = (15+10-150)/100 = 25-1.5 = 23.5%

⇒ Profit % of store A = (50-23.5 - 1175)/100 = 50- 35.25 = 14.75% 

Similarly,

Store B marked the price 60% above CP \& sold at successive discounts of 15% and 12%,

⇒ Total discount offered by store B = (15+12-180)/100 = 27-1.8 = 25.2%

⇒ Profit % of store B = (6-25.2 - 1512)/100  = 60-40.32 = 19.68%

But, the customer has to pay Rs. 986 more at store B,

⇒ Profit of store B - Profit of store A = 986

⇒ (19.68 - 14.75%) of Cost price of product =986

⇒ of Cost price of product = 986

⇒ Cost price of product  = 98600/4.93 = Rs 20000

∴ The stores bought the product from the company for Rs 20000.

The National Institute of Mental Health & Neuro Sciences (NIMHANS) in Bengaluru has been awarded the prestigious Nelson Mandela Award for Health Promotion for 2024 by the World Health Organization (WHO). This recognition highlights NIMHANS' exceptional dedication and contributions to promoting mental health and well-being. Established by WHO in 2019, the Nelson Mandela Award for Health Promotion acknowledges institutions that demonstrate outstanding efforts in advancing health promotion initiatives, reflecting NIMHANS' significant impact in the field of mental health advocacy and promotion.

The current account records exports and imports in goods and services and transfer payments. Trade-in services denoted as invisible trade includes both factor income (payment for inputs-investment income, that is, the interest, profits and dividends on our assets abroad minus the income foreigners earn on assets they own in India) and non-factor income (shipping, banking, insurance, tourism, software services, etc.).

• CAD rises/widens when the value of goods and services a country imports exceeds the value of goods and services it exports. Reducing export subsidy can hamper the growth of exports and thus widen the current account deficit. So, statement 2 is correct.
• One of the objectives of enforcing import quota is to reduce the balance of payments deficit by restricting imports. That portion of national income going into imports can be utilised for investment in the import substitution or export industries. The expansion in exports, coupled with the restriction of imports is likely to bring about improvement in the balance of payments position of the country. So, statement 3 is not correct.
• India is one of the biggest importers of crude oil. A rise in crude oil prices indicates rising imports and thus CAD widens. So, statement 1 is correct.
• ECBs are borrowings raised by permitted resident entities from recognized non-resident entities. Therefore, ECBs would lead to capital inflow which would in turn reduce CAD. So statement 4 is not correct.

Business Environment:

• The term ‘business environment’ means the sum total of all individuals, institutions, and other forces that are outside the control of a business enterprise but that may affect its performance. The economic, social, political, technological, and other forces, which operate outside the business enterprise are part of its environment.
• It is important for business organizations to understand their environment because of the following reasons:
• It Helps the Firm to Identify Threats and Early Warning Signals
• It Helps in Coping with Rapid Changes
• It Helps in Assisting in Planning and Policy Formulation

PhonePe, a prominent digital payments platform, has partnered with Star Health Insurance to provide the Star Comprehensive Insurance Policy on its app. 

Concept:

Some pairs of Laplace transforms are given below.

Given,

By applying inverse Laplace transform