Latest Current Affairs 07 February 2022

NATIONAL NEWS

Legendary singer Lata Mangeshkar passes away

Legendary singer Lata Mangeshkar has passed away at the age of 92 after suffering a multi-organ failure. The Bharat Ratna awardee was admitted to the hospital after being diagnosed with pneumonia and tested positive for the coronavirus disease in January. She is survived by her 3 sisters – Usha Mangeshkar, Asha Bhosle, Meena Khadikar and brother Hridaynath Mangeshkar. She began her career as a singer back in 1942 and never looked back. She recorded innumerable songs in over 36 Indian and foreign languages. She gave us musical gems such as Aye Mere Watan Ke Logo, Lag Jaa Gale, Yeh Kahan Aage Hain Hum and Pyar Kiya To Darna Kya, among others. Having led an eventful and rich life of several milestones, Lata Mangeshkar was conferred with the Dadasaheb Phalke Award in 1990. For her contribution to Indian music, she also was bestowed with Padma Bhushan in 1969 and Bharat Ratna in 2001.

Kotak General Ins. Partners CARS24 to offer Motor Insurance for used cars

Kotak Mahindra General Insurance Company has signed an agreement with Cars24 Financial Services Private Limited (CARS24 Financial Services) to provide motor insurance services to used car buyers. Under the partnership, used car buyers from Cars24 will be directly provided with Kotak General Insurance’s comprehensive motor insurance plans. The partnership will provide a trustworthy and faster way to avail of motor insurance with a fully digital insurance process. Customers can also avail of cashless claims servicing at Kotak General Insurance’s platform of garages and enable convenient claim settlement services.

LIC tie-up with Policybazaar for digital distribution of life insurance

Life Insurance Corporation (LIC) has tied up with Policybazaar to digitally offer a wide range of Life Insurance and investment products to its customers across India. This is LIC’s first association with a private insurance aggregator, which has mainly relied on its 1.33 million agents for distributing products. To facilitate seamless digital distribution of life insurance products and boost financial inclusion across India. The benefit of the tie-up: The alliance will provide insurance services in smaller cities to ensure financial inclusion and social security. It will increase its penetration digitally in rural and remote areas and offer a wide range of term and investment products to the customers.

India records win in 1000th ODI

India beat West Indies by six wickets at Narendra Modi stadium in Ahmedabad, Gujarat on February 6, 2022. This was India’s 1000th ODI match. Skipper Rohit Sharma, who is back after recovering from an injury, scored 60 runs off 51 balls helping India achieve the target of 177 runs in just 28 overs. The visitors were bowled out for 176 in 43.5 overs with Yuzvendra Chahal taking four wickets and Washington Sundar grabbing three wickets. India is now one up in the three-match ODI series.

Powerthon 2022 launched for enabling advanced technology in Power Distribution

Union Power Minister RK Singh launched Powerthon 2022 to enable participants to find innovative solutions based on advanced emerging technologies to solve the complex problems in power distribution and ensure quality and reliable power supply. The hackathon will see participation from startups, Technology Solution Providers (TSPs), educational and research institutions, equipment manufacturers and state power utilities and other power entities. The participants will be briefed on the current challenges faced across the power distribution sector and then invited to participate and showcase their technology-driven solutions to solve complex problems.

INTERNATIONAL NEWS 

Sri Lankan foreign minister on 3-day visit to India

Sri Lankan Foreign Minister G.L Peiris arrived in Delhi, India on February 7, 2022 for a 3-day visit. India’s Foreign Secretary Harshvardhan Shringla is expected to call on the Sri Lankan Foreign Minister. India’s External Affairs Minister Dr. S Jaishankar will also hold a meeting with the visiting Sri Lankan foreign minister in the evening.

Bangladesh signs deal to purchase 420 broad-gauge railway wagons from India

Bangladesh signed an agreement with India on February 6, 2022 for the procurement of 420 broad-gauge wagons. The agreement was signed in Dhaka between the Bangladesh Railways project director Mizanur Rahman and India’s Hindustan Engineering and Industries Limited. The agreement is worth Tk. 231 crore and it will be implemented within 27 months of the contract’s signing. It will be implemented with the joint funding of the Bangladesh Government and Asian Development Bank (ADB) under the Rolling Stock Operation Improvement Project.  

 

Latest Current Affairs 06 February 2022

NATIONAL NEWS 

PM Modi inaugurates 50th Anniversary Celebrations of Hyderabad-based ICRISAT

Prime Minister Narendra Modi has inaugurated the 50th Anniversary celebrations of the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) in Patancheru, Hyderabad. During the occasion, PM also inaugurated two research facilities of ICRISAT, which were Climate Change Research Facility on Plant Protection and Rapid Generation Advancement Facility. These two facilities are dedicated to the smallholder farmers of Asia and sub-Saharan Africa. Prime Minister also unveiled a specially designed logo of ICRISAT and launched a commemorative stamp issued on the occasion. Its objective is to conduct agricultural research for rural development, in Asia & sub-Saharan Africa.

West Bengal launch open-air classroom programme ‘Paray Shikshalaya

West Bengal government has launched an open-air classroom programme Paray Shikshalaya (Neighbourhood Schools) for primary and pre-primary students. Under the ‘Paray Shikshalaya’ project, primary and pre-primary students of government schools will be taught in open spaces. The state government will also provide mid-day meals to the students of ‘Paray Shikshalaya’. The para teachers and primary school teachers would be part of this project. They will provide elementary education to children of Class 1-5.

GoI approved the renaming of three places in Madhya Pradesh

The government of India (GoI) has approved the renaming of 3 places in Madhya Pradesh, Hoshangabad Nagar as “Narmadapuram”, Shivpuri as “Kundeshwar Dham” and Babai as “Makhan Nagar”. In 2021, the government of MP led by Shivraj Singh Chouhan has proposed the renaming of the 3 places in Madhya Pradesh. The approval for the renaming was granted by the Ministry of Home Affairs (MHA). The Hoshangabad Nagar named after Hoshang Shah, the first formally appointed Sultan of the Malwa Sultanate of Central India was renamed as Narmadapuram. Babai has been renamed after the renowned journalist and poet Makhanlal Chaturvedi. Makhanlal Chaturvedi was born in Babai, MP. The government has named a national university of journalism and communication at Bhopal after Makhanlal in 1992.

Professor Dinesh Prasad Saklani named as new NCERT director

Professor Dinesh Prasad Saklani has been appointed as the new Director of the National Council of Educational Research and Training (NCERT). He has replaced Hrushikesh Senapaty, who finished his term a year ago. The new director has been appointed for a period of five years with effect from the date of assumption of charge of the post, or till he attains the age of 65 years, or until further orders, whichever is earlier. Professor Saklani has been awarded with Distinguished Academy Award by Punjab Kala and Sahitya Academy, Jalandhar for Historical writing in 2005. The new director is a member of the Academic Council of Uttarakhand Open University, Haldwani. Professor Saklani is also a life member in the Indian History Congress; Uttarakhand History and Culture Association and of Book Club IIAS Shimla.

INTERNATIONAL NEWS 

International Day of Zero Tolerance to Female Genital Mutilation

International Day of Zero Tolerance for Female is observed on 6th February globally. This day is sponsored by the United Nations for their efforts to eradicate female genital mutilation. It was first introduced in 2003. This year theme of International Day of Zero Tolerance for Female: Accelerating Investment to End Female Genital Mutilation. Female genital mutilation (FGM) comprises all procedures that involve altering or injuring the female genitalia for non-medical reasons and is recognized internationally as a violation of the human rights, the health and the integrity of girls and women.

China locks down city of 3.5 million near Vietnam border

China locked down a city of 3.5 million near the Vietnam border on February 7, 2022 after over 70 coronavirus cases were detected in the past three days. China is the only major world economy that is still sticking to a staunch zero-Covid policy. The nation is on a high alert for any outbreaks as it hosts the Beijing Winter Olympics. The officials in the southern Guangxi region announced that no one would be allowed to leave the city and residents in some districts will be confined to their homes.

Latest Current Affairs 05 February 2022

NATIONAL NEWS 

UP best state tableau in Republic Day Parade 2022

The Uttar Pradesh state tableau was selected as the best state tableau, while Maharashtra tableau was selected as best in popular choice category. The UP tableau showcased the glorious history of the Kashi Vishwanath Dham, while Maharashtra tableau showcased the five state components including state bird, state animal, state tree and state flower. 

ISRO targets to launch Chandrayaan 3 in August 2022

The Indian Space Research Organisation (ISRO) is targeting to launch Chandrayaan 3 mission in August 2022. Similar to Chandrayaan 2 mission, the mission will include a modified lander and a rover. It will not include an orbiter and as it will use Chandrayaan 2 orbiter to communicate with the Earth.  

India nominates Hoysala temples for World Heritage Sites

India has nominated Karnataka’s Hoysala Temples for World Heritage Sites List for 2022-23. According to Tourism Minister G Kishan Reddy, these temples represent one of the highest points of human creative genius and stand testimony to the rich historical and cultural heritage of our country.

PR Sreejesh named World Games Athlete

PR Sreejesh, Indian men’s hockey goalkeeper, has been named World Games Athlete of the Year 2021. He has become the second Indian to win World Games Athlete after Indian women’s hockey captain Rani Rampal. PR Sreejesh had played a crucial role in India winning bronze at the Tokyo Olympics 2020.

Indian Olympic champion Neeraj Chopra nominated for Laureus World Breakthrough

Indian Olympic Gold medalist Neeraj Chopra has been nominated for Laureus World Breakthrough of the Year Award 2022. He has been nominated for the award along with six others including Daniil Medvedev, Pedri, Emma Raducanu, Ariarne Titmus and Yulimar Rojas. He is the third Indian to be nominated for the award after Vinesh Phogat and Sachin Tendulkar. 

India’s GDP growth projected at 8-8.5 percent in FY23

  Economic Survey 2021-22 has projected India’s GDP growth at 8-8.5 percent in Fiscal Year 2022-23. The survey Survey 2022 was tabled by Union Finance Minister Nirmala Sitharaman in the Lok Sabha.  The survey has also estimated the GDP growth for the ongoing financial year 2021-22 at 9.2 percent.

INTERNATIONAL NEWS

Queen Elizabeth II to become Britain’s first ruler to reign for 70 years.

Queen Elizabeth II, the world’s longest-reigning living monarch, will be Britain’s first monarch to rule for 70 years on February 6, 2022. She was born as Elizabeth Alexandra Mary Windsor and not the direct heir to the throne but became the next heir after her uncle King Edward VIII abdicated the throne to marry an American divorcee. She was crowned the Queen of England in 1952 after the passing of her father King George VI. 

Australia to reopen borders to foreign tourists on February 21, after almost 2 years

Australia will reopen its borders for foreign tourists on February 21st after a hiatus of almost two years.  The nation had shut its borders for international tourists in March 2020, at the very beginning of the Covid-19 pandemic. Now, fully vaccinated tourists will be allowed to travel to Australia.

 

GATE 2021 Statistics Previous Year Paper

GATE 2021 Statistics Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1 The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Q.2 p and q are positive integers and pq+qp=3then, P2/q2 +q2/P2
(A) 3
(B) 7
(C) 9
(D) 11
Q.3

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is  _______.
(A) 4
(B) 3
(C) 6
(D) 7
Q.4 Nostalgia is to anticipation as_________is to__________Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Q.5 Consider the following sentences:I woke up from sleep.I woked up from sleep.I was woken up from sleep.I was wokened up from sleep.Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6 Given below are two statements and two conclusions. Statement 1: All purple are green.Statement 2: All black are green. Conclusion I: Some black are purple. Conclusion II: No black is purple.Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only conclusion II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Q.7 Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.Which of the following can be deduced from the above passage?Nowadays, computers are present in almost all places.Computers cannot be used for solving problems in engineering.For humans, there are both positive and negative effects of using computers.Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Q.8 Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is 
(A) 𝜋/3
(B) 2𝜋/3
(C) 3𝜋/2
(D) 3π
Q.9

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Q.10

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

 
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6
Statistics 
Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
Q.1 Let 𝑿 be a non-constant positive random variable such that (𝑿) = 𝟗. Then which one of the following statements is true?
(A)
(B)
(C )
(D)
Q.2 Let {(𝒕)}𝒕≥𝟎 be a standard Brownian motion. Then the variance of𝑾(𝟏)𝑾(𝟐) equals
(A) 1
(B) 2
(C) 3
(D) 4
Q.3

Let 𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏 be a random sample of size 𝒏 (≥ 𝟐) from a distribution having the probability density function

where 𝜃 ∈ (0, ∞). Then the method of moments estimator of 𝜃 equals
(A)
(B)
(C)
(D)
Q.4

Let {𝒙𝟏, 𝒙𝟐, … , 𝒙𝒏} be a realization of a random sample of size 𝒏 (≥ 𝟐) from a 𝑵(𝝁, 𝝈𝟐) distribution, where −∞ < 𝝁 < ∞ and  𝝈 > 𝟎. Which of the following statements is/are true?

P: 95% confidence interval of 𝜇 based on {𝑥1, 𝑥2, … , 𝑥𝑛} is unique when𝜎 is known

Q.: 95% confidence interval of 𝜇 based on {𝑥1, 𝑥2, … , 𝑥𝑛} is NOT unique when 𝜎 is unknown.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Q.5
(A) 𝑆 has a monotone likelihood ratio in 𝑇1 and 𝐻0 is rejected if 𝑇1 > Xn,𝛼2
(B) 𝑆 has a monotone likelihood ratio in 𝑇1 and 𝐻0 is rejected if 𝑇1 > Xn,1-𝛼2
(C) 𝑆 has a monotone likelihood ratio in 𝑇2 and 𝐻0 is rejected if 𝑇2 > Xn,𝛼2
(D) 𝑆 has a monotone likelihood ratio in 𝑇2 and 𝐻0 is rejected if 𝑇2 > Xn,1- 𝛼2
Q.6
(A) Under 𝐻0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 20/3
(B) Under 𝐻0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 20/3
(C) Under 𝐻0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 16/3
(D) Under 𝐻0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 16/3
 
Q.7
(A) 4Φ𝜌(0,0) − 1
(B) 4Φ𝜌(0,0)
(C) 4Φ𝜌(0,0) + 1
(D) Φ𝜌(0,0)
Q.8
(A)
(B)
(C)
(D)
 
Q.9
(A) 𝑍 follows 𝑊4(7, 𝐼4) distribution
(B) 𝑍 follows 𝑊4(4, 𝐼4) distribution
(C) 𝑍 follows 𝑊7(4, 𝐼7) distribution
(D) 𝑍 follows 𝑊7(7, 𝐼7) distribution

Q.10 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.10
   
Q.11

Let

Then the value of 𝒆𝑰+𝝅 equals (round off to 𝟐 decimal places).
   
Q.12
   
Q.13
   
Q.14 Let 𝑨 and 𝑩 be two events such that (𝑩) = ¾ and 𝑷(𝑨 𝖴 𝑩𝒄) = ½. If 𝑨 and 𝑩 are independent, then 𝑷(𝑨) equals_________(round off to𝟐 decimal places).
Q.15 A fair die is rolled twice independently. Let 𝑿 and 𝒀 denote the outcomes of the first and second roll, respectively. Then 𝑬(𝑿 + 𝒀 | (𝑿 − 𝒀)𝟐 = 𝟏) equals  
Q.16
   
Q.17

If the marginal probability density function of the 𝒌𝒕𝒉 order statistic of a random sample of size 8 from a uniform distribution on [𝟎, 𝟐] is then 𝒌 equals  

 
   
Q.18
Q.19 Let {𝑿𝒏}≥𝟏 be a sequence of independent and identically distributed random variables each having uniform distribution on [𝟎, 𝟐]. For 𝒏 ≥ 𝟏, letZn=-logei = 1n(2-Xi)1nThen, as 𝒏 → ∞, the sequence {𝒁𝒏}𝒏≥𝟏 converges almost surely to ___________(round off to 𝟐 decimal places).
Q.20 Let {𝑿𝒏}𝒏≥𝟎 be a time-homogeneous discrete time Markov chain with state space {𝟎, 𝟏} and transition probability matrix
   
Q.21 Let {𝟎, 𝟐} be a realization of a random sample of size 𝟐 from a binomial distribution with parameters 𝟐 𝐚𝐧𝐝 𝒑, where 𝒑 ∈ (𝟎, 𝟏). To test 𝑯1 : 𝒑 = ½ against 𝑯0 : 𝒑 ≠ ½, the observed value of the likelihood ratio test statistic equals_________(round off to 𝟐 decimal places).
   
Q.22
Q.23
   
Q.24 Let 𝑿𝟏, 𝑿𝟐 and 𝑿𝟑 be a random sample from a bivariate normal distribution with unknown mean vector 𝝁 and unknown variance- covariance matrix 𝚺, which is a positive definite matrix. The 𝒑-value corresponding to the likelihood ratio test for testing 𝑯𝟎: 𝝁 = 𝟎  against 𝑯1: 𝝁 = 𝟎 based on the renzation 12, 4-2, -50 sample equals_________(round off to 𝟐 decimal places).
Q.25

Let 𝒀𝒊 = + 𝒙𝒊 + 𝝐𝒊, 𝒊 = 𝟏, 𝟐, 𝟑, where 𝒙𝒊’s are fixed covariates, 𝑎 and are unknown parameters and 𝝐𝒊’s are independent and identically distributed random variables with mean zero and finite variance. Let and be the ordinary least squares estimators of and , respectively. Given the following observations. 

the value of  +   equals__________(round off to  𝟐  decimal places).

Q.26 – Q.43 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26
(A) 𝑓 is not continuous at 0
(B) 𝑓 is not differentiable at 0
(C) 𝑓 is differentiable at 0 and the derivative of 𝑓 at 0 equals 0
(D) 𝑓 is differentiable at 0 and the derivative of 𝑓 at 0 equals 1
Q.27 Let 𝒇: [𝟎, ∞) → ℝ be a function, where ℝ denotes the set of all real numbers. Then which one of the following statements is true?
(A) If 𝑓 is bounded and continuous, then  𝑓 is uniformly continuous
(B) If 𝑓 is uniformly continuous, then 𝑥∞ 𝑓(𝑥) exists
(C) If 𝑓 is uniformly continuous, then the function 𝑔(𝑥) = 𝑓(𝑥) sin 𝑥 is also uniformly continuous
(D) If 𝑓 is continuous and 𝑥∞ 𝑓(𝑥) is finite, then 𝑓 is uniformly continuous
Q.28 Let 𝒇: ℝ → ℝ  be a differentiable function such that    𝒇(𝟎) = 𝟎    and 𝒇′(𝒙) + 𝟐𝒇(𝒙) > 𝟎 for all 𝒙 ∈ ℝ, where 𝒇′ denotes the derivative of 𝒇 and ℝ denotes the set of all real numbers. Then which one of the following statements is true?
(A) 𝑓(𝑥) > 0, for all 𝑥 > 0 and 𝑓(𝑥) < 0, for all 𝑥 < 0
(B) 𝑓(𝑥) < 0, for all 𝑥 ≠ 0
(C) 𝑓(𝑥) > 0, for all 𝑥 ≠ 0
(D) 𝑓(𝑥) < 0, for all 𝑥 > 0 and 𝑓(𝑥) > 0, for all 𝑥 < 0
Q.29

Let 𝑴 be the collection of all   × 𝟑 real symmetric positive definite matrices. Consider the set

where 𝟎 denotes the 𝟑 × 𝟑 zero matrix. Then the number of elements in𝑺 equals
(A) 0
(B) 1
(C) 8
(D) ∞
Q.30 Let   𝑨   be a   𝟑 × 𝟑   real matrix such that 𝑰𝟑 + 𝑨 is invertible and let 𝑩 = (𝑰𝟑 + 𝑨)−𝟏(𝑰𝟑 − 𝑨), where 𝑰𝟑 denotes the 𝟑 × 𝟑 identity matrix. Then which one of the following statements is true?
(A) If 𝐵 is orthogonal, then 𝐴 is invertible
(B) If 𝐵 is orthogonal, then all the eigenvalues of 𝐴 are real
(C) If 𝐵 is skew-symmetric, then 𝐴 is orthogonal
(D) If 𝐵 is skew-symmetric, then the determinant of 𝐴 equals −1
Q.31 Let 𝑿 be a random variable having Poisson distribution such that 𝑬(𝑿𝟐) = 𝟏𝟏𝟎. Then which one of the following statements is NOT true?
(A) 𝐸(𝑋𝑛) = 10 𝐸[(𝑋 + 1)𝑛−1], for all 𝑛 = 1, 2, 3, …
(B) 𝑃(𝑋 is even) = ¼ (1 + 𝑒−20)
(C) 𝑃(𝑋 = 𝑘) < 𝑃(𝑋 = 𝑘 + 1), for 𝑘 = 0, 1, … , 8
(D) 𝑃(𝑋 = 𝑘) > 𝑃(𝑋 = 𝑘 + 1), for 𝑘 = 10, 11, …
Q.32 Let 𝑿   be a random variable having uniform distribution on –2, 2 Then which one of the following statements is NOT true?
(A) 𝑌 = cot 𝑋 follows standard Cauchy distribution
(B) 𝑌 = tan 𝑋 follows standard Cauchy distribution
(C)
(D)
Q.33 Let 𝛀 = {𝟏, 𝟐, 𝟑, … } represent the collection of all possible outcomes of a random experiment with probabilities 𝑷({𝒏}) = 𝑎𝒏 for 𝒏 ∈ 𝛀. Then which one of the following statements is NOT true?
(A) nan=0
(B)
(C)
(D)
Q.34

Let (𝑿, 𝒀) have the joint probability density function

Then which one of the following statements is NOT true?
(A)
(B) 𝑃(𝑋 + 𝑌 > 4) = ¾ 
(C) 𝐸(𝑋 + 𝑌) = 4 log𝑒 2
(D) 𝐸(𝑌 | 𝑋 = 2) = 4
Q.35 Let 𝑿𝟏, 𝑿𝟐 and 𝑿𝟑 be three uncorrelated random variables with common variance 𝝈𝟐< ∞. Let 𝒀𝟏 = 𝟐𝑿𝟏 + 𝑿𝟐 + 𝑿𝟑, 𝒀𝟐 = 𝑿𝟏 + 𝟐𝑿𝟐 + 𝑿𝟑 and 𝒀𝟑 = 𝑿𝟏 + 𝑿𝟐 + 𝟐𝑿𝟑. Then which of the following statements is/are true?P : The sum of eigenvalues of the variance covariance matrix of (𝒀𝟏, 𝒀𝟐, 𝒀𝟑) is 𝟏𝟖𝝈𝟐.Q :  The correlation coefficient between 𝒀𝟏 𝐚𝐧𝐝 𝒀𝟐 equals that between 𝒀𝟐 𝐚𝐧𝐝 𝒀𝟑.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Q.36 Let {𝑿𝒏}≥𝟎 be a time-homogeneous discrete time Markov chain with either finite or countable state space 𝑺. Then which one of the following statements is true?
(A) There is at least one recurrent state
(B) If there is an absorbing state, then there exists at least one stationary distribution
(C) If all the states are positive recurrent, then there exists a unique stationary distribution
(D) If {𝑋𝑛}𝑛≥0 is irreducible, 𝑆 = {1, 2} and [𝜋1 𝜋2] is a stationary distribution, then lim 𝑃(𝑋𝑛 = 𝑖 | 𝑋0 = 𝑖) = 𝜋𝑖 for 𝑖 = 1, 2𝑛→∞
Q.37 Let customers arrive at a departmental store according to a Poisson process with rate 𝟏𝟎. Further, suppose that each arriving customer is either a male or a female with probability ½ each, independent of all other arrivals. Let (𝒕) denote the total number of customers who have arrived by time 𝒕.Then which one of the following statements is NOT true?
(A) If 𝑆2 denotes the time of arrival of the second female customer, then𝑃(𝑆 ≤ 1) = 25 ∫1 𝑠𝑒−5𝑠𝑑𝑠2 0
(B) If 𝑀(𝑡) denotes the number of male customers who have arrived by time 𝑡,then 𝑃 (𝑀 (⅓) = 0 | 𝑀(1) = 1) = ⅓ 
(C) 𝐸 [(𝑁(𝑡))2] = 100𝑡2 + 10𝑡
(D) 𝐸[𝑁(𝑡)𝑁(2𝑡)] = 200𝑡2 + 10𝑡
Q.38 Let 𝑿(𝟏) < 𝑿(𝟐) < 𝑿(𝟑) < 𝑿(𝟒) < 𝑿(𝟓) be the order statistics corresponding to a random sample of size 𝟓 from a uniform distribution on [𝟎, 𝜽], where𝜽 ∈ (𝟎, ∞). Then which of the following statements is/are true?P : 𝟑𝑿(𝟐) is an unbiased estimator of 𝜽.Q : The variance of 𝑬[𝟐𝑿(𝟑) | 𝑿(𝟓)] is less than or equal to the variance of 𝟐𝑿(𝟑).
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Q.39
(A) 𝑇/𝑛2
(B) T/n
(C) (𝑛 + 1)𝑇/2𝑛
(D) (𝑛 + 1)2𝑇/4𝑛2
Q.40 Let 𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏 be a random sample of size 𝒏 (≥ 𝟐) from a uniform distribution on [−𝜽, 𝜽], where 𝜽 ∈ (𝟎, ∞). Let 𝑿(𝟏) = 𝐦𝐢𝐧{ 𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏} and 𝑿(𝒏) = 𝐦𝐚𝐱{ 𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏}. Then which of the following statementsis/are true?P :   (𝑿(𝟏), 𝑿(𝒏))   is a complete statistic. Q : 𝑿(𝒏) − 𝑿(𝟏) is an ancillary statistic.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Q.41 Let {𝑿𝒏}≥𝟏 be a sequence of independent and identically distributed random variables having common distribution function 𝑭(⋅). Let 𝒂 < 𝒃 be two real numbers such that 𝑭(𝒙) = 𝟎 for all 𝒙 ≤ 𝒂, 𝟎 < 𝑭(𝒙) < 𝟏 for all𝒂 < 𝒙 < 𝒃 and (𝒙) = 𝟏 for all 𝒙 ≥ 𝒃. Let 𝑺(𝒙) be the empirical distribution function at 𝒙 based on 𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏, 𝒏 ≥ 𝟏. Then which one of the following statements is NOT true?
(A)
(B)
(C)
(D)
Q.42
(A)
(B)
(C)
(D)
Q.43 Let 𝒀 follow 𝑵(𝟎, 𝑰𝟖) distribution, where 𝑰𝟖 is the 𝟖 × 𝟖 identity matrix. Let 𝒀𝑻𝚺𝟏𝒀 and 𝒀𝑻𝚺𝟐𝒀 be independent and follow central chi-square distributions with 𝟑 and 𝟒 degrees of freedom, respectively, where 𝚺𝟏 and𝚺𝟐 are 𝟖 × 𝟖 matrices and 𝒀𝑻 denotes transpose of 𝒀. Then which of the following statements is/are true?P : 𝚺𝟏 and 𝚺𝟐 are idempotent.Q : 𝚺𝟏𝚺𝟐 = 𝟎, where 𝟎 is the 𝟖 × 𝟖   zero matrix.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q

Q.44 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.44 Let (𝑿, 𝒀) have a bivariate normal distribution with the joint probability density functionfX,Y(x,y)=1e (3/2xy – 25/32x2 – 2y2), -<x,y<Then 𝟖 𝑬(𝑿𝒀) equals  _________.
   
Q.45 Let 𝒇: ℝ × ℝ → ℝ be defined by (𝒙, 𝒚) = 𝟖𝒙𝟐 − 𝟐𝒚, where ℝ denotes the set of all real numbers. If 𝑴 and 𝒎 denote the maximum and minimum values of 𝒇, respectively, on the set {(𝒙, 𝒚) ∈ ℝ × ℝ ∶ 𝒙𝟐 + 𝒚𝟐 = 𝟏}, then𝑴 − 𝒎 equals_________(round off to 𝟐 decimal places).
   
Q.46 Let 𝑨 = [𝒂 𝒖𝟏 𝒖𝟐 𝒖𝟑], 𝑩 = [𝒃 𝒖𝟏 𝒖𝟐 𝒖𝟑] and 𝑪 = [𝒖𝟐 𝒖𝟑 𝒖𝟏 𝒂 + 𝒃] be three 𝟒 × 𝟒 real matrices, where 𝒂, 𝒃, 𝒖𝟏, 𝒖𝟐 𝐚𝐧𝐝 𝒖𝟑 are 𝟒 × 𝟏 real column vectors. Let 𝐝𝐞(𝑨), 𝐝𝐞𝐭(𝑩) and 𝐝𝐞𝐭(𝑪) denote the determinants of the matrices 𝑨, 𝑩 and 𝑪, respectively. If 𝐝𝐞𝐭(𝑨) = 𝟔 and 𝐝𝐞𝐭(𝑩) = 𝟐, then𝐝𝐞𝐭(𝑨 + 𝑩) − 𝐝𝐞𝐭(𝑪) equals ________
   
Q.47

Let 𝑿 be a random variable having the moment generating function

Then (𝑿 > 𝟏) equals_____(round off to 𝟐 decimal places).
   
Q.48

Let {𝑿𝒏}≥𝟏 be a sequence of independent and identically distributed random variables each having uniform distribution on [𝟎, 𝟑]. Let 𝒀 be a random variable, independent of {𝑿𝒏}𝒏≥𝟏, having probability mass function

Then 𝑷(𝐦𝐚𝐱{𝑿𝟏, 𝑿𝟐, … , 𝑿𝒀} ≤ 𝟏) equals (round off to decimal places).
Q.49 Let {𝑿𝒏}𝒏≥𝟏 be a sequence of independent and identically distributed random variables each having probability density functionLet (𝒏) = 𝐦𝐚𝐱{𝑿𝟏, 𝑿𝟐, … , 𝑿𝒏} for 𝒏 ≥ 𝟏. If 𝒁 is the random variable to which {𝑿(𝒏) − 𝐥𝐨𝐠𝒆 𝒏}𝒏≥𝟏    converges in distribution, as 𝒏 → ∞, then the median of 𝒁 equals ______________(round off to 𝟐 decimal places).
Q.50 Consider an amusement park where visitors are arriving according to a Poisson process with rate 𝟏. Upon arrival, a visitor spends a random amount of time in the park and then departs. The time spent by the visitors are independent of one another, as well as of the arrival process, and have common probability density functionIf at a given time point, there are 𝟏𝟎 visitors in the park and 𝒑 is the probability that there will be exactly two more arrivals before the next departure, then 1/p equals ________.
Q.51

Let {𝟎. 𝟗𝟎, 𝟎. 𝟓𝟎, 𝟎. 𝟎𝟏, 𝟎. 𝟗𝟓} be a realization of a random sample of size 4 from the probability density function3

where 𝟎. 𝟓 ≤ 𝜽 < 𝟏. Then the maximum likelihood estimate of 𝜽 based on the observed sample equals__________(round off to 𝟐 decimal places).
Q.52 Let a random sample of size 𝟏𝟎𝟎 from a normal population with unknown mean 𝝁 and variance 𝟗 give the sample mean 𝟓. 𝟔𝟎𝟖. Let (⋅) denote the distribution   function   of   the   standard   normal   random variable. If (𝟏. 𝟗𝟔) = 𝟎. 𝟗𝟕𝟓, 𝚽(𝟏. 𝟔𝟒) = 𝟎. 𝟗𝟓 and the uniformly most powerful unbiased test based on sample mean is used to test 𝑯𝟎: 𝝁 = 𝟓. 𝟎𝟐 against 𝑯𝟏: 𝝁 ≠ 𝟓. 𝟎𝟐, then the 𝒑-value equals____(round off to 𝟑 decimal places).
Q.52 Let a random sample of size 𝟏𝟎𝟎 from a normal population with unknown mean 𝝁 and variance 𝟗 give the sample mean 𝟓. 𝟔𝟎𝟖. Let (⋅) denote the distribution   function   of   the   standard   normal   random variable. If (𝟏. 𝟗𝟔) = 𝟎. 𝟗𝟕𝟓, 𝚽(𝟏. 𝟔𝟒) = 𝟎. 𝟗𝟓 and the uniformly most powerful unbiased test based on sample mean is used to test 𝑯𝟎: 𝝁 = 𝟓. 𝟎𝟐 against 𝑯𝟏: 𝝁 ≠ 𝟓. 𝟎𝟐, then the 𝒑-value equals____(round off to 𝟑 decimal places).
Q.54 Let 𝑿𝟏, 𝑿𝟐, … , 𝑿𝟏𝟎 be a random sample from a probability density function𝒇𝜽(𝒙) = 𝒇(𝒙 − 𝜽), −∞ < 𝒙 < ∞,where   −∞ < 𝜽 < ∞   and   𝒇(−𝒙) = 𝒇(𝒙)   for   −∞ < 𝒙 < ∞. For testing 𝑯𝟎: 𝜽 = 𝟏. 𝟐 against 𝑯𝟏: 𝜽 ≠ 𝟏. , let 𝑻+ denote the Wilcoxson Signed- rank test statistic. If 𝜼 denotes the probability of the event {𝑻+ < 𝟓𝟎} under 𝑯𝟎, then 𝟑𝟐 𝜼 equals____(round off to 2 decimal places).
Q.55 Consider the multiple linear regression model𝒀𝒊 = 𝖰𝟎 + 𝖰𝟏𝒙𝟏, + 𝖰𝟐𝒙𝟐,𝒊 + ⋯ + 𝖰𝟐𝟐𝒙𝟐𝟐,𝒊 + 𝝐𝒊, 𝒊 = 𝟏, 𝟐, … , 𝟏𝟐𝟑, where, for 𝒋 = 𝟎, 𝟏, 𝟐, … , 𝟐𝟐, 𝖰𝒋’s are unknown parameters and 𝝐𝒊’s are independent   and   identically   distributed 𝑵(𝟎, 𝝈𝟐), 𝝈 > 𝟎,random variables.If the sum of squares due to regression is 𝟑𝟑𝟖. 𝟗𝟐, the total sum of squares is 𝟓𝟐𝟐. 𝟑𝟎   and 𝑹𝟐 denotes the value of adjusted 𝑹𝟐, then 𝟏𝟎𝟎 𝑹𝟐 equal _____(round off to 𝟐 decimal places).

Answer Key 

Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans
1 C  1 A  11 33.50 to 34.50  21 0.98 to 1.00  31 B  41 C  51 0.50 to 0.50 
2 B  2 C  12 2 to 2  22 8.60 to 8.75  32 D  42 D  52 0.045 to 0.055 
3 C  3 A  13 1.70 to 1.75  23 0.14 to 0.18  33 B  43 C  53 0.20 to 0.22 
4 C  4 B  14 0.32 to 0.35  24 1.00 to 1.00  34 C  44 3 to 3  54 31.60 to 31.80 
5 B  5 A  15 7 to 7  25 6.31 to 6.35  35 C  45 10.10 to 10.15  55 57.00 to 57.40 
6 C  6 A  16 0.32 to 0.35  26 C  36 B  46 72 to 72     
7 D  7 A  17 7 to 7  27 D  37 B  47 0.60 to 0.66     
8 A  8 B  18 0.50 to 0.50  28 A  38 C  48 0.20 to 0.26     
9 C  9 A  19 0.27 to 0.35  29 B  39 A  49 0.32 to 0.42     
10 A  10 2 to 2  20 50 to 50  30 C  40 D  50 143 to 143     

GATE 2021 Production and Industrial Engineering Previous Year Paper

GATE 2021 Production and Industrial Engineering Previous Year Paper

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

Q.1 The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Q.2 p and q are positive integers and   
(A) 3
(B) 7
(C) 9
(D) 11
Q.3

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is_____________
 

 
(A) 4
(B) 3
(C) 6
(D) 7
Q.4 Nostalgia is to anticipation as   ________ is to__________ Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
 
Q.5 Consider the following sentences:I woke up from sleep.I woked up from sleep.I was woken up from sleep.I was wokened up from sleep.Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Q.6 Given below are two statements and two conclusions. Statement 1: All purple are green.Statement 2: All black are green. Conclusion I: Some black are purple. Conclusion II: No black is purple.Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only conclusion II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Q.7 Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.Which of the following can be deduced from the above passage?Nowadays, computers are present in almost all places.Computers cannot be used for solving problems in engineering.For humans, there are both positive and negative effects of using computers.Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Q.8 Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is___________
(A) 𝜋/3
(B) 2𝜋/3
(C) 3𝜋/2
(D) 3π
Q.9 The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
 
(A) 4
(B) 5
(C) 6
(D) 7
Q.10

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

 
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6

Production & Industrial Engineering (PI)

  1. – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
Q.1 A product has an exponential time-to-failure distribution with a constant failure rate of 0.00006 per hour. The reliability of the product after 4000 hours of operation is
(A) 0.5866
(B) 0.6866
(C) 0.7866
(D) 0.8866
Q.2 In a typical product development process under concurrent engineering approach, all elements of product life cycle from conception to disposal are considered at
(A) Product design stage
(B) Process design stage
(C) Manufacturing stage
(D) Disposal stage
Q.3 When acceptance number of a single sampling plan under attribute category is zero with sample size less than or equal to 10, the Operating Characteristic (OC) curve is
(A) A horizontal line
(B) A vertical line
(C) A convex function
(D) An inverted S-shaped curve
Q.4 Which one of the following is an improvement type heuristic algorithm for computerized layout design technique?
(A) Systematic layout planning (SLP)
(B) Computerized relative allocation of facilities technique (CRAFT)
(C) Computerized relationship layout planning (CORELAP)
(D) Plant layout analysis and evaluation technique (PLANET)
 
Q.5 Which one of the following is NOT a measure of forecast error?
(A) Mean absolute deviation (MAD)
(B) Mean squared error (MSE)
(C) Mean absolute percent error (MAPE)
(D) Mean sum product error (MSPE)
 
Q.6 Pearlite microstructure in an eutectoid steel consists of alternating layers of two phases, namely α ferrite and
(A) Martensite
(B) Austenite
(C) Cementite
(D) Bainite
Q.7 Which one of the following defects is NOT associated with welding processes?
(A) Angular distortion
(B) Hot tear
(C) Hydrogen embrittlement
(D) Earring
Q.8 Match the component with the corresponding manufacturing process in the table below. 
(A) P-3, Q-2, R-1, S-4
(B) P-3, Q-4, R-2, S-1
(C) P-2, Q-3, R-4, S-1
(D) P-1, Q-3, R-2, S-4
Q.9 In a turning operation, doubling the cutting speed (𝑽) reduces the tool life (𝑻) to 𝟏⁄𝟖th of the original tool life. The exponent 𝒏 in the Taylor’s tool life equation, 𝑽𝑻𝒏 = 𝑪 is
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/8
 
Q.10 Which one among the following mechanisms is NOT used for transforming rotation to translation in machine tools?
(A) Screw-nut system
(B) 4-bevel gear type differential mechanism
(C) Cam and cam follower system
(D) Whitworth mechanism
Q.11 Match the measuring feature with the corresponding measuring instrument in the table below. 
(A) P-4, Q-1, R-2, S-3
(B) P-1, Q-3, R-4, S-2
(C) P-2, Q-4, R-3, S-1
(D) P-4, Q-3, R-1, S-2
Q.12 The frequency of pulsing in a die-sinking electric discharge machine (EDM) is 10 kHz. The pulse off-time is set at 40 micro-seconds. The duty factor at this setting is
(A) 0.40
(B) 0.60
(C) 0.67
(D) 2.50
Q.13

A cantilever beam of length 0.3 m is subjected to a uniformly distributed load C = 10 kN/m, as shown in the figure. The bending (flexural) rigidity of the beam is 5000 Nm2. Neglecting the self-weight of the beam, the magnitude of beam curvature in m-1 at the fixed end is

 
(A) 1.10
(B) 0.02
(C) 0.09
(D) 0.05

Q.14

A circular rod of length l = 2 m is subjected to a compressive load P, as shown in the figure. The bending (flexural) rigidity of the rod is 2000 Nm2. If both ends are pinned, then the critical load Pcr in N (rounded to the nearest integer) at which the rod buckles elastically is

                         
(A) 4935
(B) 2000
(C) 5167
(D) 1238
Q.15 Two cylindrical parts of equal length l, as shown in the figure, made of steel having Young’s modulus E = 200 GPa and Poisson’s ratio ν = 0.33 are press fitted upon one another. If radial interference δ = 0.05 mm, and radii R = 25 mm and R0 = 40 mm, then the contact pressure P in MPa at the interface upon press fit is 
(A) 10.7
(B) 60.9
(C) 121.9
(D) 1005.3
 
Q.16 The dimensionless number defined by the ratio of inertial force to viscous force is called
(A) Mach number
(B) Froude number
(C) Weber number
(D) Reynolds number
Q.17 A small capillary tube of 3 mm inner diameter is inserted into a fluid having density 900 kg/m3, surface tension 0.1 N/m, and contact angle 30⁰. The rise in the height of fluid in the capillary tube due to surface tension is
(A) 111.4 mm
(B) 128.3 mm
(C) 89.1 mm
(D) 154.1 mm

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.18 A given steel has identical yield strength of 700 MPa in uni-axial tension and uni-axial compression. If the steel is subjected to pure shear stress such that the three principal stresses are σ1 = σ, σ2 = 0, σ3 = −σ with σ1 ≥ σ2 ≥ σ3, then the stress σ in MPa for the initiation of plastic yielding in the steel as per von Mises yield criterion is  _________. [round off to 2 decimal places]
   
Q.19 A cylindrical mild steel tensile test specimen of gauge length 50 mm and diameter 10 mm is extended in two stages at a deformation speed of 4 mm/min. The specimen is extended from 50 mm to 55 mm in the first stage, and from 55 mm to 60 mm in the second stage. Neglecting elastic deformation, the total longitudinal true strain is  _______________. [round off to 2 decimal places]
   
Q.20 A M30 bolt needs to be subjected to pretension Fi = 350 kN. If the torque coefficient K of the bolt is 0.2, then the torque in Nm needed to achieve this pretension is_____________ . [in integer]
Q.21 A 150 mm wide polyamide flat belt is transmitting 15 kW power through a belt-pulley system. The driving pulley of 150 mm pitch diameter is rotating at 200 RPM. If F1 is the belt tension on high tension side, and F2 is the belt tension on low tension side, then the difference in belt tensions ΔF = F1 – F2 in N is  ______. [round off to one decimal place]
   
Q.22 Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at 2 ⁰C. If the input power to the refrigerator is 2 kW, the coefficient of performance of the refrigerator is ___________.[round off to one decimal place]
   
Q.23 In an ideal Otto cycle, 800 kJ/kg is transferred to air during the constant volume heat addition process and 381 kJ/kg is removed during the constant volume heat rejection process. The thermal efficiency in % of the cycle is____________________.[round off to one decimal place]
   
Q.24 If (3i +1)x + (4i + 4)y + 5 = 0 with x, y being real and i = √−𝟏, then x =____________. [correct up to one decimal place]
   
Q.25 The minimum value of function f defined by𝒇(𝒙, 𝒚, 𝒛) = 𝒙𝟐 + 𝟓𝒚𝟐 + 𝟓𝒛𝟐 − 𝟒𝒙 + 𝟒𝟎𝒚 − 𝟒𝟎𝒛 + 𝟑𝟎𝟎is   ________. [in integer]

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

Q.26 For a given process control chart, there are four rules for determining out- of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is
(A) 0.101
(B) 0.201
(C) 0.001
(D) 0.301
Q.27 An in-control process has an estimated standard deviation of 2 mm. The specification limits of the component being processed are 120 ± 8 mm. When the process mean shifts to 118 mm, the values of the process capability indices, Cp and Cpk , respectively are,
(A) 1.000, 1.667
(B) 1.333, 1.667
(C) 1.333, 1.000
(D) 1.000, 1.000
Q.28 There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).
(A) 2
(B) 4
(C) 6
(D) 8
Q.29

A retail chain company has identified four sites A, B, C and D to open a new retail store. The company has selected four factors as the basis for evaluation of these sites. The factors, their weights, and the score for each site are given in the following table.

  

The site that should be selected to open the new retail store is
(A) Site A
(B) Site B
(C) Site C
(D) Site D
Q.30 In the classical economic order quantity (EOQ) model, let 𝑸 and 𝑪 denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as 𝑸′ = 𝟐𝑸, then the corresponding total annual cost 𝑪′ is
(A) 𝐶′ = 1.25𝐶
(B) 𝐶′ = 1.5𝐶
(C) 𝐶′ = 1.75𝐶
(D) 𝐶′ = 2𝐶
Q.31 The eigenvalues of matrix A = are 5 and 10. For matrix B = A + α I,where α is a constant and I is 2×2 identity matrix, its eigenvalues are
(A) 5, 10
(B) 5 + α, 10 + α
(C) 5 – α, 10 – α
(D) 5α, 10α
Q.32

A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.

  

The maximum profit the company can make is
(A) 45
(B) 48
(C) 42
(D) 54
Q.33 A tool of an NC machine has to move along a circular arc from (20,20) to (10,10), while performing an operation. The center of the arc is at (20,10). Which one of the following NC tool commands performs the above mentioned operation?
(A) N020 G03 X20 Y20 X10 Y10 R10
(B) N020 G02 X20 Y20 X10 Y10 R10
(C) N020 G02 X10 Y10 X20 Y20 R10
(D) N020 G01 X20 Y20 X10 Y10 R10
 
Q.34 In a shaft-hole assembly, the hole is specified as 30𝟎. 𝟎𝟎𝟎𝟎. 𝟎𝟒𝟎 mm. The matingshaft has a clearance fit with minimum clearance of 0.01 mm. The tolerance on the shaft is 0.03 mm. The maximum clearance in mm between the hole and the shaft is
(A) 0.04
(B) 0.05
(C) 0.08
(D) 0.10
 
Q.35 ‘GO’ and ‘NO GO’ snap gauges are to be designed for a shaft 36.000+𝟎. 𝟎𝟏𝟎+𝟎. 𝟎𝟕𝟎mm. Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respective sizes of ‘GO’ and ‘NO GO’ gauges are
(A) 36.013 mm and 36.067 mm
(B) 36.015 mm and 36.065 mm
(C) 36.018 mm and 36.062 mm
(D) 36.020 mm and 36.060 mm
Q.36 A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center of the tank bottom (take acceleration due to gravity g = 9.81 m/s2) is [round off to the nearest integer]
(A) 5005
(B) 1807
(C) 8097
(D) 3154

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.37 The probability mass function (𝒙) of a discrete random variable 𝑿 is given by 𝑷(𝒙) =1/𝟐𝒙 , where 𝒙 = 𝟏, 𝟐, ⋯ , ∞. The expected value of X is________.[in integer]
Q.38 The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is  __________. [round off to 3 decimal places]
Q.40 A time study is carried out for a spot welding operation which is being performed by an operator. The time taken (in seconds) for five observations are recorded as 40, 35, 45, 37 and 43, respectively. If the standard time and the allowance for this operation are 45 seconds and 9 seconds, respectively, then the performance rating (in percentage) of the operator is    ___________. [in integer]
Q.41 The initial cost of a machine is INR 10,00,000 and its salvage value after 10 years of use is INR 50,000. Using the straight line depreciation method, the book value in INR of the machine at the end of 7th year is   ___________. [in integer]
Q.43 A wire of 5 mm diameter is drawn into a wire of 4 mm diameter through a conical die at a constant pulling speed of 5 m/s. Neglecting the coefficient of friction and redundant work, the drawing stress (𝝈𝒅) in MPa for the above process is given by   𝝈   = 𝝈̅ 𝐥𝐧 , where 𝝈̅  is the mean flow strength of wire material in MPa, and 𝒓 is the ratio of decrease in area of cross-section to initial area of cross-section of the wire. If the mean flow strength of wire material is 600 MPa, then the power required in kW in the above wire drawing process is  _____________ .[round off to 2 decimal places]
   
Q.44 In an arc welding process, the DC power source characteristic is linear with an open circuit voltage of 60 V and short circuit current of 600 A. The heat required for melting a metal during the welding is 10 J/mm3, and the heat transfer and melting efficiencies are 80% and 25%, respectively. If the weld cross-sectional area of 20 mm2 is made using the maximum arc power, then the required welding speed in mm/s is  __________. [round off to one decimal place]
   
Q.45 A company is producing a disc-shaped product of 50 mm thickness and 1.0 m diameter using sand casting process. The solidification time of the above casting process is estimated by Chvorinov’s equation 𝒕 = 𝑩 [ 𝑽/A ]2 , where 𝑩𝑨 is the mold constant, and 𝑽 and 𝑨 are the volume and surface area of the casting, respectively. It is decided to modify both the thickness and diameter of the disc to 25 mm and 0.5 m, respectively, maintaining the same casting condition. The percentage reduction in solidification time of the modified disc as compared to that of the bigger disc is _____________.[round off to one decimal place]
   
Q.46 A single point cutting tool with 15⁰ orthogonal rake angle is used to machine a mild steel plate under orthogonal machining condition. The depth of cut (uncut thickness) is set at 0.9 mm. If the chip thickness is 1.8 mm, then the shear angle in degree is ____________________. [round off to one decimal place]
Q.47 The top layer of a flat 750 mm × 300 mm rectangular mild steel plate is to be machined with a single depth of cut using a shaping machine. The plate has been fixed by keeping 750 mm side along the tool travel direction. If the approach and the over-travel are 25 mm each, average cutting speed is 10 m/min, feed rate is 0.4 mm/stroke, and the ratio of return time to cutting time of the tool is 1:2, the time (in minutes) required to complete the machining operation is___________. [round off to one decimal place]
   
Q.48 A 3 mm thick steel sheet, kept at room temperature of 30 ⁰C, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density= 8000 kg/m3, specific heat = 500 J/kg.⁰C, melting temperature = 1530 ⁰C, and latent heat of fusion = 3×105 J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is  ___________.[round off to 3 decimal places]
   
Q.49

In a point-to-point open-loop NC drive, a stepper motor with 1.8⁰ step angle is coupled to a leadscrew through a gear reduction of 4:1 (4 rotations of the motor enables 1 rotation of leadscrew). The single-start leadscrew has a pitch of 4 mm. The worktable of the system is driven by the leadscrew. If the table moves at a uniform speed of 10 mm/s, the pulse frequency (in Hz) required to drive the stepper motor is_____________. [round off to one decimal place]

  
Q.50

A 30 kg smooth, solid sphere rests on two frictionless inclines as shown in the figure. The magnitude of contact force in N acting at the point A is (take acceleration due to gravity g = 9.81 m/s2 and consider both sphere and inclines to be rigid) ________. [round off to 2 decimal places]

            
Q.54 Temperature field inside a sphere of radius R = 1 m with origin at its center is T(x, y, z) = 100 – 70x + 51y – 80z – 10x2 – 20y2 – 20z2 . If thermal conductivity of the sphere material is K = 50 W/m.K and Fourier law of heat conduction is valid, net heat leaving the sphere per unit time in W is_____________.[round off to one decimal place]

Q.55 A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of friction at the sheet and roll interface is 0.08, and the elastic deflection of the rolls is negligible. If the mean flow strength of the sheet material is 400 MPa, then the minimum possible thickness (in mm) of sheet that can be produced in a single pass is_______.[round off to 2 decimal places]

Answer Key 

Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans Q. No. Ans
1 C  1 C  11 B OR D  21 9545.0 to 9555.0  31 B  41 335000 to 335000  51 -5773.7 to -5773.4 
2 B  2 A  12 B  22 2.4 to 2.6  32 B  42 5 to 5  52 5.0 to 5.2 
3 C  3 C  13 C  23 52.2 to 52.5  33 A  43 16.80 to 16.84  53 33.4 to 33.6 
4 C  4 B  14 A  24 2.4 to 2.6  34 C  44 8.8 to 9.2  54 20943.8 to  20944.1 
5 B  5 D  15 C  25 136 to 136  35 A  45 74.5 to 75.5  55 1.85 to 1.95 
6 C  6 C  16 D  26 A  36 A  46 28.0 to 30.0     
7 D  7 D  17 MTA  27 C  37 2 to 2  47 89.0 to 91.0     
8 A  8 B  18 404.00 to 405.00  28 B  38 0.365 to 0.370  48 0.193 to 0.203     
9 C  9 B  19 0.17 to 0.19  29 C  39 4 to 4  49 1999.0 to 2001.0     
10 A  10 B  20 2100 to 2100  30 A  40 90 to 90  50 147.00 to 147.30     

*MTA means Marks to All

Latest Current Affairs 04 February 2022

NATIONAL NEWS

US regains top spot as India’s trade partner in 2021.

The United States was India’s top trading partner in the calendar year 2021 with a trade of $112.3 billion. The US is followed by China on second. The value of trade between India and China was $110.4 billion. In 2020, China was India’s top trading partner and the US was in the second rank. In 2019 USA was India’s top trading partner and China was on second. India’s list of top ten trading partners also includes the UAE, Saudi Arab, Switzerland, Hong Kong, Singapore, Iraq, Indonesia and South Korea.

Senior scientist GA Srinivasa Murthy appointed director of DRDL Senior scientist GA Srinivasa Murthy has been appointed director of Defence Research and Development Laboratory (DRDL) of the Defence Research and Development Organisation (DRDO) in Hyderabad. He joined DRDL in the year 1987 and made significant contributions in the area of structural dynamics, ground resonance testing, electrical integration and checkout for various projects of the missile complex. G A Srinivasa Murthy completed his BE in Electronics and Communication Engineering from Andhra University in 1986 and pursued his ME in Digital Systems from Osmania University in Hyderabad.


Ravi Mittal named as new Chairman of Insolvency and Bankruptcy Board of India

The former secretary, Department of Sports, Ravi Mittal has been appointed as the Chairman of Insolvency and Bankruptcy Board of India (IBBI), as per the notification issued by the Ministry of Corporate Affairs. He is a 1986 batch IAS officer from Bihar cadre. He will serve as the Chairman of IBBI for a term of five years or till he attains 65 years of age, whichever is early. The Insolvency and Bankruptcy Board of India is the regulator for overseeing insolvency proceedings and entities like Insolvency Professional Agencies, Insolvency Professionals and Information Utilities in India.

SBI tie-up with Ministry of Culture for Development of Atmanirbhar Bharat Centre for Design

The State Bank of India (SBI) has signed a tripartite Memorandum of Understanding (MoU) with the Indira Gandhi Centre for the Arts (IGNCA) and National Culture Fund (NCF) of the Ministry of Culture, for Development of Atmanirbhar Bharat Centre for Design (ABCD) at L1 Barrack, Red Fort, in Delhi. The main objective of Project ABCD is to highlight, promote and celebrate the products that have the Geographical Indication sign to give a boost to Economic Value Addition to GI products from India. The ABCD project will be implemented by IGNCA, an autonomous organization under the Ministry of Culture through the ministry’s NCF fund. SBI will sponsor the project under CSR with a contribution of Rs. 10 crores for the implementation of the ABCD Project.

RBI cancels the licence of Nashik’s Independence Co-operative Bank Limited 

The Reserve Bank of India has cancelled the license of Independence Co-operative Bank Ltd., Nashik, Maharashtra w.e.f February 03, 2022. The major reason for the cancellation of the license by RBI is that bank does not have adequate capital and earning prospects. This means that it does not comply with the provisions of Section 11(1) and Section 22 (3) (d) read with Section 56 of the Banking Regulation Act, 1949. The bank has stopped operation from the close of business on February 3, putting depositors of the bank in trouble. They would however receive up to Rs five lakh from Deposit Insurance and Credit Guarantee Corporation (DICGC), after the bank’s liquidation. RBI has told the Commissioner for Cooperation and Registrar of Cooperative Societies in Maharashtra to issue an order for winding up the bank and appoint a liquidator. As per the data submitted by the bank, more than 99 per cent of the depositors are entitled to receive the full amount of their deposits from DICGC.

INTERNATIONAL NEWS

Winter Olympics host China welcomes Year of Tiger

China is celebrating the Spring Festival, it’s the most important annual festival as it entered the Lunar new “Year of the Tiger”. Last year was celebrated as the Lunar Year of the Ox. According to the Chinese Zodiac calendar, the Year of the Ox has ended and the Year of the Tiger has begun from February 1, 2022, and will end on January 21, 2023. In Chinese culture, the tiger symbolizes bravery, vigor and strength and it is believed that it can lift people from adversity and usher in final auspiciousness and peace. Each year is named after one of 12 signs of the Chinese zodiac in a repeating cycle. This year, Spring Festival celebrations coincide with the Beijing Winter Olympics.

Exim Bank extends a $500 million credit line to Sri Lanka

Export-Import Bank of India (Exim Bank) on behalf of the government of India, extended a line of credit of $500 million to the government of the socialist republic of Sri Lanka for financing the purchase of petroleum products. The fund will be used by the Island nation for the purchase of petroleum products. With the signing of this new LOC agreement, the total LOC extended by Exim Bank to Sri Lanka till date has reached 10, taking the total value of LOCs extended to USD 2.18 billion.

New Zealand’s Daryl Mitchell named the ICC Spirit of Cricket Award 2021

New Zealand cricketer, Daryl Mitchell has been named the winner of the International Cricket Council (ICC) Spirit of Cricket Award 2021. This award is given to him for his gesture of refusing to take a single in the high-pressure 2021 ICC Men’s T20 World Cup Semi-Finals against England as he felt he had “obstructed” the way of bowler Adil Rashid at the Sheikh Zayed Stadium in Abu Dhabi. He has become the 4th New Zealand player to win the award after Daniel Vettori, Brendon McCullum and Kane Williamson. The ICC Spirit of Cricket Award is annually awarded by the ICC to recognise the player most notable for “upholding the ‘Spirit of the Game’”.

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