RRB NTPC CBT-I Official Paper (Held On: 29 Jan 2021 Shift 1) (Previous Year Paper)

The correct answer is high rate of interest.

Key Points

• Dear money policy refers to a monetary policy by the central bank.
• The central bank sets high-interest rates so that credit is not easily available to the general public in order to decrease the rate of inflation in the economy by curbing demand.
• Dear money refers to money that is hard to obtain (e.g. by borrowing) because of abnormally high-interest rates.
• This is because people prefer to save when interest rates are high and spend or borrow when rates are low.

Additional Information

• A dear money policy would cause RBI to release less amount of money to the public which can only happen if the borrowing rates are increased for the public.
• The 4 different types of money as classified by the economists are commercial money, fiduciary money, fiat money, and commodity money.
• Money whose value comes from a commodity of which it is made is known as commodity money.

The correct answer is Alexander Cunningham.

Key Points

• Archeological Survey of India:
• It was founded by Alexander Cunningham in 1861.
• He also became its first Director-General.
• Sir Alexander Cunningham was a British army engineer with the Bengal Engineer Group.
• Alexander Cunningham was appointed to the newly created position of archaeological surveyor by the government of India in 1861.
• The (ASI) Archaeological Survey of India is an Indian government agency attached to the Ministry of Culture.
• ASI is responsible for archaeological research and the conservation and preservation of cultural monuments in our country.

Additional Information

• Saurabh Kumar is an Indian cricketer who plays for Uttar Pradesh.
• Jayanti Patnaik M.A. is an Indian Parliamentarian and renowned social worker. She was the first Chairperson of the National Commission for Women.
• Girish Kumar Taurani is an Indian actor working in the Hindi film industry.​

The correct answer is Rohit Jain.

Key Points

• Rohit Jain
• Rohit Jain has been appointed as Executive Director of RBI with effect from December 11, 2020.
• Prior to being promoted to ED, he was serving as Chief General Manager-in-Charge, of the Department of Supervision.
• As Executive Director, Shri Jain will look after the Department of Supervision (Risk, Analytics, and Vulnerability Assessment).
• Shri Jain holds a Master’s degree in Commerce and a Master’s in Business Administration besides having earned professional qualifications including an International Certificate in Banking Risk and Regulation (ICBRR), a Certified Associate of the Indian Institute of Banking and Finance (CAIIB), and Certified Bank Trainer.
• Reserve Bank of India
• The Reserve Bank of India is India's central bank and regulatory body responsible for the regulation of the Indian banking system.
• It is under the ownership of the Ministry of Finance, Government of India.
• It is responsible for the control, issuing, and maintaining of the supply of the Indian rupee.

Additional Information

• N. S. Vishwanathan
• N. S. Vishwanathan was the deputy governor of the Reserve Bank of India. He was appointed on 28 June 2016, by the Appointments Committee of the Cabinet of the Government of India.
• Usha Sharma
• Usha Sharma served as the Director General of the Archaeological Survey of India from 2017 - 2020.

The correct answer is Mahananda.

Key Points

• Mechi River
• The Mechi River is a transboundary river flowing through Nepal and India.
• It is a tributary of the Mahananda River.
• The Kosi-Mechi river interlinking project has been recently approved by the center, providing a major lease of life in the Seemanchal region of Bihar.
• The project is worth 4900 crores.
• This project is a green project.
• Its environmental approval note states the project involves no displacement of population and there is no acquisition of any forest land.
• This project not only relieves north Bihar from the menace of recurring floods but also provides irrigation for over 2.14 lakh hectares.
• It is the second major river interlinking project after Ken-Betwa of MP.

Additional Information

• The important tributaries of Ganga are the Yamuna, the Ramaganga, the Gomti, the Ghagra, the Son, the Gandak, the Burhi Gandak, the Kosi and the Mahananda.
• Teesta and Meghna are the tributaries of the Brahmaputra river which joins the basin.
• Hooghly river has two tributaries: the Rupnarayan River and Damodar River. Hooghly also reaches Bay of Bengal at Nurpur and then empties into the sea.

The correct answer is Valency.

Key Points

• Valency
• Valency is the combining power of an element.
• Elements in the same group of the periodic table have the same valency.
• The valency of an element is related to how many electrons are in the outer shell.
• On moving down a group, the number of valence electrons remains the same.
• All the elements in a group exhibit the same valency.
• For example, all the elements of group 1 have a valency equal to 1.

Additional Information

• Metallic character
• The metallic character is the tendency of an element to lose electrons and form positive ions or cations.
• The metallic nature increases moving down the group because electron shielding causes the atomic radius to increase.
• Atomic size
• The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. The atomic size of an atom increases across the period and decreases down the group.
• Number of shells
• This shell can contain a maximum of two electrons. The second shell can hold a maximum of eight electrons.

Explanation:

Table of English alphabet positional value

Similarly 

Hence, Sdurjr is the correct answer.

Given:

Point of triangle are A=(1, 0), B=(-1, 0), C=(0, 1).

Formula Used:

Area of isosceles triangle=$\frac{b\times h}{2}$

where b= Base of the triangle

h=Height of the triangle

d=$\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$

where d= Distance from one point to other

(x₁, y₁)=Coordinates of one point

(x2, y2)= Coordinates of another point

Pythagorean theorem,  h² = a² - b²

Calculation:

Distance between A and B=$\sqrt{(x_2+x_1)^2-(y_2+y_1)^2}=\sqrt{((-1)-1)^2+(0-0)^2}= \sqrt{(-2)^2+(0)^2}=\sqrt{4+0}=2$ sq. unit

Distance between B and C=$\sqrt{(x_2+x_1)^2-(y_2+y_1)^2}=\sqrt{(0-(-1))^2+(1-0)^2}= \sqrt{(1)^2+(1)^2}=\sqrt{1+1}=\sqrt2$ sq. unit

Distance between C and A=$\sqrt{(x_2+x_1)^2-(y_2+y_1)^2}=\sqrt{(0-1)^2+(1-0)^2}= \sqrt{(-1)^2+(1)^2}=\sqrt{1+1}=\sqrt2$ sq. unit

here, The two sides of the triangle are equal which means it is an isosceles triangle

Using the Pythagorean theorem,

Height of the triangle=$a^2=h^2+(\frac{b}{2})^2$

⇒ $h^2=a^2-(\frac{b}{2})^2=a^2-(\frac{b}{2})^2=(\sqrt2)^2-(\frac{2}{2})^2=2-1=1$

⇒ h=$\sqrt1=1$

Area of the isosceles triangle=$\frac{b\times h}{2}=\frac{2\times 1}{2}=1$

The area of the triangle is 1 sq. unit.

The correct answer is Ministry of Defence.

Key Points

• The Border Roads Organisation (BRO) is a road construction executive force in India.
• It provides support to and is now a part of the Indian Armed Forces.
• BRO develops and maintains road networks in India's border areas and friendly neighboring countries.
• Earlier Border Roads Organization was functioning under the Ministry of Road Transport & Highways.
• Now it is completely controlled by the Ministry of Defence.
• Border roads are important because they have improved accessibility in areas of difficult terrain.

Additional Information

• Ministry of Communications is a union ministerial agency under the Government of India responsible for telecommunications and postal service.
• The Ministry of Commerce and Industry administers two departments, the Department of Commerce and the Department for Promotion of Industry & Internal Trade. The head of the Ministry is a Minister of Cabinet rank.
• The Ministry of Consumer Affairs, Food, and Public Distribution is a government ministry of India. The Ministry is headed by a Cabinet rank minister.

The correct answer is Kerala.

Key Points

• The Indian electronic voting machine (EVM) was developed in 1989 by the Election Commission of India in collaboration with Bharat Electronics Limited and Electronics Corporation of India Limited.
• Electronic voting was first used in Estonia during the October 2005 local elections.
• Estonia became the first country to have legally binding general elections using the Internet as a means of casting the vote.
• The EVMs were first used in 1982 in the by-election to North Paravur Assembly Constituency in Kerala for a limited number of polling stations.

Additional Information

• EVM was introduced in Indian elections between 1998 and 2001, in a phased manner.
• An electronic Voting Machine ( EVM ) is an electronic device for recording votes.
• An Electronic Voting Machine consists of two Units – a Control Unit and a Balloting Unit – joined by a five-meter cable

Given:

$x+\frac{1}{x} = 5$

Calculation:

⇒ $x+\frac{1}{x} = 5$

⇒ $\frac{x^2+1}{x} = 5$

⇒ $x^2+1 = 5x$

⇒ $x^2-5x+1 =0$

According to the question,

⇒ $\frac{3x}{2x^2 + 2-5x}=\frac{3x}{2x^2-10x + 2-5x+10x}=\frac{3x}{2(x^2-5x+ 1)+5x}=\frac{3x}{2(0)+5x}=\frac{3x}{5x}=\frac{3}{5}$

Hence, The value of $\frac{3x}{2x^2 + 2-5x}$ is $\frac{3}{5}$.

Given:

Exterior angle - interior angle = 60°

The Interior angle(I) is greater than the exterior angle(E)

Formula Used:

Number of sides  = $\frac{360}{exterior \space angle}$

Calculation:

According to the question

⇒ I - E = 60º 

we know that I + E = 180º

On solving to we get,

⇒ 2I = 240º

⇒ I = 120º so E = 60º

Number of sides = $\frac{360}{exterior \space angle}=\frac{360}{60}=6$

The number of sides of the regular polygon is 6.

The correct answer is 2001.

Key Points

• The United Nations and its Secretary-General Kofi Annan have been awarded the Nobel Peace Prize “for their work for a better organized and more peaceful world.
• In 2001, the United Nations, as an organization, and Kofi Annan, as Secretary-General, won the Nobel Peace Prize.
• The United Nations is an intergovernmental organization.
• Its stated purposes are to maintain international peace and security, develop friendly relations among nations, achieve international cooperation, and be a center for harmonizing the actions of nations.

Additional Information

• The Nobel Committee declared that “everyone has understood the language of UNICEF, and even the most reluctant person is bound to admit that in action UNICEF has proved that compassion knows no national boundaries"

Explanation:

Madhu's ranks 11th from the top in the class of 29 students.

 Madhu's rank from bottom = 29 - 11 + 1 = 19

So, her rank from bottom is 19th.

Hence, 19 is the correct answer.

Explanation: Given the length of the room = 750 cm

Breadth of the room = 525 cm

Concept: The number of square tiles = Area of floor / Area of 1 square tile

To find the size of the square tile we need to find the HCF of the length and breadth of a room.

Calculation:

H.C.F of 750cm and 525cm is 75

therefore number of tiles = ( 750 × 525 ) / (75 × 75 ) = 393750/5625 = 70

Note: For this question, the discrepancy is found in the question/answer. So, We have update the Options.

Given:

x=$\frac{7^{\frac{1}{5}}}{7^\frac{1}{3}}$

Concept Used:

If a number is raised to the power and the base is the same then simply perform the action in power(when power comes from denominator to numerator then power gets subtract) 

Calculation:

x=$\frac{7^{\frac{1}{5}}}{7^\frac{1}{3}}=7^{\frac{1}{5}-{\frac{1}{3}}}=7^\frac{3-5}{15}=7^\frac{-2}{15}$

⇒ Hence, The value of x is $7^\frac{-2}{15}$

Explanation:

The pattern followed is:

Hence, 97 is the correct answer.

Given:

5000 becomes 5900 in one year

Formula Used:

Amount = Principal + Interest

Interest = $\frac{P\times R\times T}{100}$

Calculation:

According to the formula

Amount = Principal-Interest

Interest = Principal - Amount = 5900 - 5000 = Rs. 900

Interest = $\frac{P\times R\times T}{100}$

⇒ 900 = $\frac{5000\times R\times 1}{100}=50R$

R = 18%

Interest earned on Rs. 8000 at 18% in 5 years will be

Interest = $\frac{P\times R\times T}{100}=\frac{8000\times 18\times5}{100}=Rs. 7200$

Amount = Principal + Interest = 8000 + 7200 = Rs. 15200

Hence, The amount after 5 years at 18% on 8000 will be Rs. 15200.

Given:

A number, when divided by 7, leaves the remainder 4

Formula Used:

Dividend=Divisor x Quotient+Remainder

Calculation:

According to the question

​⇒ Number=7k+4

​⇒ Let the value of k=1

​⇒ then, number = 7x1+4=7+4=11

​⇒ Square of the Number=11x11=121

The number is divided by 7

​⇒ $\frac{Number}{7}=\frac{121}{7}$ = 7 x 17 + 2

​⇒ Hence, When the square of the same number is divided by 7 then the remainder will be 2

The correct answer is Gaur - Chhattisgarh.

Key Points

• Gaur Maria dance is performed on the plateau of Bastar in Chhattisgarh.
• It is performed on the occasion of marriage and is believed that it is performed with more joy than other dances.
• Gaur dance is a popular folk dance of Madhya Pradesh dances.
• Gaur dance is popular in the Sing Marias or Tallaguda Marias of South Bastar.
• Men put headdresses with stringed 'cowries' and plumes of peacock feathers and make their way to the dancing ground.

Additional Information

• Raas or Dandiya Raas is the socio-religious folk dance originating from the Indian state of Gujarat and popularly performed during the festival of Navaratri. The dance is performed in the Marwar region of Rajasthan too.
• Lavani is a genre of music popular in Maharashtra, India. Lavani is a combination of traditional song and dance, which is particularly performed to the beats of Dholki, a percussion instrument.
• Ghoomar or ghumar is a traditional folk dance of Rajasthan. It was the Bhil tribe who performed it to worship Goddess Sarasvati which was later embraced by other Rajasthani communities. The dance is chiefly performed by veiled women who wear flowing dresses called Ghaghara.

Given:

The number are 6, 72 and 120 

Concept Used:

LCM is the method of finding the smallest possible multiple of two or more numbers.

Calculation:

The factor of 6 = 2 x 3

​The factor of 72 = 2 x 2 x 2 x 3 x 3

​The factor of 120 = 2 x 2 x 2 x 3 x 5

LCM of 6,72 and 120 = 2 x 2 x 2 x 3 x 3 x 5 = 360

Hence, The LCM of 6, 72 and 120 will be 360.

Given:

A number lies between the cubes of 11 and 12

The number is divisible by both 80 and 6

Concept Used:

LCM is the method of finding the smallest possible multiple of two and more numbers

Calculation:

⇒ Cube of 11 = 1331

⇒ Cube of 12 = 1728

The number lies between 1331 to 1728

The number is divisible by both 80 and 6

⇒ Factor of 80 = 2 x 2 x 2 x 2 x 5

⇒ Factor of 6 = 2 x 3

⇒ LCM of 80 and 6 = 2 x 2 x 2 x 2 x 3 x 5 = 240

Since, number is divisible by twice of 80 and 6 both.

So, required number = 2 × 240 = 480

i.e. the number is a multiple of 480 and bigger than 1331 and less than 1728.

⇒ The only possible number = 3 × 480 = 1440

⇒ Hence, The Number lies between cubes of 11 and 12 and is divisible by both 80 and 6 is 1440

Explanation:

The answer is 3 because only 3 people are there in the section where doctors, artists, and players are present.

Hence, 3 is the correct answer.

Given: 

100 ÷ 5 - 6 + 1 × 6

'×' stands for '+', '+' stands for '÷' '-' stands for '×' and '÷' stands for '-' 

Explanation :

BODMAS Table 

by putting these values in given equation 100 ÷ 5 - 6 + 1 × 6 we get,

= 100 - 5 × 6 ÷ 1 + 6

by BODMAS rule

= 100 - 5 × 6 + 6 

= 100 - 30 + 6 

= 70 + 6

= 76 

Hence, "76" is the correct answer.

The correct answer is Maldives.

Key Points

• A former vice president of the Maldives who was arrested after fleeing to neighboring India to avoid questioning over the alleged embezzlement of state funds has been taken to a Maldives detention center after being returned to the country.
• India had refused entry to former Vice President Ahmed Adeeb.
• Maldives police later confirmed that they had arrested him and returned him to the Indian Ocean nation.
• Adeeb was brought to Male, the Maldives' capital.
• He was taken to the Dhoonidhoo detention center.
• Adeeb had his passport confiscated by a court order because of pending court cases, according to police.
• He had recently been freed from a 33-year jail sentence over corruption and terrorism.

Additional Information  A place where people who have entered a country illegally are kept for a period of time. It is also called Jail or Prison.

Given:

The cost of a pair of roller skates is Rs 450

The tax charged was 5%

Concept Used:

A percentage is a number or ratio that can be expressed as a fraction of 100

Calculation:

Cost Price(CP) = Rs. 450

Tax charged = 5%

Bill amount = Cost Price + 5% of Cost Price = 450 + $\frac{450\times5}{100}=450+22.5=Rs.472.50$

Hence, The Bill amount after tax charged will be Rs. 472.50.

The correct answer is Vietnam.

Key Points

• Currency manipulator is a designation applied by United States government authorities.
• The authorities as the United States Department of the Treasury.
• Its aim is to countries that engage in unfair currency practices so that gives them a trade advantage.
• Such practices may be currency intervention or monetary policy.
• In this practice, a central bank buys or sells foreign currency in exchange for domestic currency.
• Their intention of influence the exchange rate and commercial policy.
• In December 2020, the Trump administration designated Switzerland and Vietnam as currency manipulator.

Additional Information

• Policymakers may have different reasons for currency intervention, such as controlling inflation, maintaining international competitiveness, or financial stability.
• Singapore, Switzerland, Taiwan, and Thailand have been regular manipulators in both recent years and during the earlier period, 2003–13. Singapore and Switzerland together accounted for more than half of total currency manipulation in 2020.

The correct answer is Muslim League.

Key Points

• On 16 August 1946, Muslim League called for a “Direct Action Day” under the leadership of Mohammad Ali Jinnah.
• The aim of Direct Action Day by the Muslim League was to get Pakistan through violent means if not by legal means.
• Mohammad Ali Jinnah proclaimed that we shall have “either a divided India or a destroyed India”.
• Direct Action Day, also known as the 1946 Calcutta Killings as this was a day of widespread communal rioting between Muslims and Hindus in Calcutta, Bengal province of British India.

Additional Information

• Central Sikh League was a political party of the Sikhs. It was founded in Amritsar on 19 December 1919. The First Leader/President was Sardar Bahadur Sardar.
• Christian League is a charitable foundation for social harmony, social justice, and social development.
• The Hindu Mahasabha, which was initially a special interest group within the Indian National Congress and later an independent party,

The correct answer is Swachh Bharat Abhiyan.

Key Points

• To give wings to this vision, the Government of India initiated a tax known as 'Swachh Bharat Cess' at 0.5% on all taxable services to fund Swachh Bharat initiatives.
• The service tax rate including the Swachh Bharat Cess stands at 14.50%
• Swachh Bharat Mission, Swachh Bharat Abhiyan, or Clean India Mission is a country-wide campaign initiated by the Government of India in 2014 to eliminate open defecation and improve solid waste management.
• It started to accelerate the efforts to achieve universal sanitation coverage and put the focus on sanitation.
• It was launched by the Prime Minister of India.

Additional Information

• Stand Up India Scheme facilitates bank loans between 10 lakh and 1 crore to at least one scheduled caste (SC) or Scehduled Tribe, borrower, and at least one woman per bank branch for setting up a greenfield enterprise.
• Kisan Vikas Patra is a saving certificate scheme that was first launched in 1988 by India Post. It was successful in the early months but afterward, the Government of India set up a committee under the supervision of Shyamala Gopinath.
• Make in India is an initiative by the Government of India to make and encourage companies to develop, manufacture and assemble products made in India and incentivize dedicated investments into manufacturing.

The correct answer is Radhakant Deb.

Key Points

• Dharma Sabha was formed in 1830 in Calcutta by Radhakanta Deb.
• The organization was established mainly to counter the ongoing social reform movements.
• That was led by protagonists such as Raja Ram Mohun Roy and Henry Derozio.
• Radhakanta Deb always showed a marked interest in promoting education, particularly English education among the Hindus.
• He also advocated female education.
• Radhakanta Deb was actively involved in the establishment and activities of the Calcutta School Book Society in 1817 and the Calcutta School Society in 1818.

Additional Information

• Debendranath Tagore was an Indian Hindu philosopher and religious reformer, active in the Brahmo Samaj. He joined Brahmo samaj in 1842. He was the founder in 1848 of the Brahmo religion.
• Pandit Tulsi Ram Sharma was an Indian politician who served as the speaker of the Himachal Pradesh Legislative Assembly in India. He was elected as MLA from Bharmour constituency on the ticket of Bharatiya Janata Party in 1990, 1998, and 2000.
• Raja Ram Mohan Roy the founder of the Brahmo Samaj (one of the first Indian socio-religious reform movements) was a great scholar and an independent thinker. He was a religious and social reformer and is known as the 'Father of Modern India' or 'Father of the Bengal Renaissance'.

The correct answer is Telangana.

Key Points

• Relieving the Farmers from the debt burden and not allowing them to fall into the debt trap again.
• Rythu Bandhu Scheme is proposed by the Government of Telangana.
• It provides Investment Support to Agriculture and Horticulture crops.
• It gives a grant of Rs. 5,000/- per acre per farmer each season for the purchase of inputs like Seeds.
• The “Agriculture Investment Support Scheme” (Rythu Bandhu), the first cash transfer scheme for farmers, was introduced by the Telangana State government in 2018-19. Rythu Bandhu literally means 'Friend of Farmer'.

Additional Information

• Scheme in Telangana:
• Pradhan Mantri Gramin Awaas Yojana.
• Pradhan Mantri Kaushal Vikas Yojana.
• Aasara pensions.
• Arogya Lakshmi.
• Haritha Haram.
• KCR Kit.
• Mission Kakathiya.

Given:

The angle of depression of two houses of the same height from the building are 45° and 30° towards the east

Two houses are 50m apart

Formula Used:

tan$\theta=\frac{height}{Base}$

Calculation:

⇒ Let the height of the building = h metre

⇒ and, BC = x metre

⇒ In $\bigtriangleup$ABC

⇒ tan45º = $\frac{AB}{BC}$

⇒ tan45º = $\frac{h}{x}$

⇒ 1 = $\frac{h}{x}$

⇒ h = x metre

⇒ In $\bigtriangleup$ADB

⇒ tan30º = $\frac{AB}{BD}=\frac{h}{50+h}$

⇒ $\frac{1}{\sqrt3}=\frac{h}{50+h}$

⇒ 50 + h = $\sqrt3$h

⇒ $(\sqrt3-1)$h = 50

⇒ h=$\frac{50}{\sqrt3-1}=\frac{50}{\sqrt3-1}\times\frac{\sqrt3+1}{\sqrt3+1}=\frac{50(\sqrt3+1)}{(\sqrt3)^2-1^2}=\frac{50(\sqrt3+1)}{3-1}=\frac{50(\sqrt3+1)}{2}=25(\sqrt3+1)$

⇒ Hence, The height of the building is $25(\sqrt3+1)$ m

Given:

A cube of side 3 cm is formed by melting the cuboid of a length of 9 cm, breadth of 6 cm, and height of 6 cm

Formula Used:

Volume of cube = $a^3$

Volume of cuboid = $l\times b\times h$

Calculation:

Volume of cuboid = $l\times b\times h=9\times6\times6=324cm^3$

Volume of Cube = $a^3=3\times3\times3=27cm^3$

Cuboid is melted to form Cube, then

⇒ n x Volume of cube = Volume of cuboid

⇒ n x 27 = 324

⇒ n = 12

⇒ Hence, The cube of side 3cm can be formed by melting cuboid is 12.

Given:

The foot of the ladder is at a distance of 2.5m from the wall

The top reaches the base of the window 6m above the ground

Formula Used:

Pythagorean Theorem,   $height^2=perpendicular^2+base^2$

Calculation:

According to the formula

⇒ $height^2=perpendicular^2+base^2$ = 6² + (2.5)² 

= 36 + 6.25

= 42.25 m

⇒ height = $\sqrt{42.25}$ = 6.5 m

Hence, The height of the ladder is 6.5 m.

Given: Five friends Kapil, Ravi, Jatin, Hari, Shiva are working in a company.

Explanation:

Kapil, Shiva and Hari are intelligent.

Kapil, Ravi and Jitin are hard working.

Ravi, Hari and Jitin are honest.

According to above table, shiva is neither honest nor hardworking but is intelligent.

Hence, Option 1 is the correct answer.

Given:

$\cot^{-1} \left(\frac{-1}{\sqrt 3}\right)$

Concept Used:

The principal value of the trigonometric function is the value of the inverse function at a point, which falls in the range of the principal value's unit

Calculation:

⇒ Let $\cot^{-1} \left(\frac{-1}{\sqrt 3}\right)$ = y

⇒ cot y = $\frac{-1}{3}$

⇒ cot y= - cot$\frac{\pi}{3}$

⇒ cot y $=cot(\pi-\frac{\pi}{3})$

⇒ cot y$=cot\frac{2\pi}{3}$

⇒ y=$\frac{2\pi}{3}$

⇒ Hence, The Principal value of $\cot^{-1} \left(\frac{-1}{\sqrt 3}\right)$ is $\frac{2\pi}{3}$

Given:

The standard deviation of 12 values is 3

Each value is increased by 4

Formula Used:

Standard Deviation =  $\sqrt{variance}$

Variance = $\frac{\sum(x_i-mean)^2}{N}$

where,

x_i = Each term

Mean = Average of all numbers

N - Number of terms.

Calculation:

Each number is increased by 4

Mean is increased by 4, Total number remains same and $x_i$ also increased by 4

$x_i - mean$ will remain same

So, There will be no change in variance

⇒ Standard Deviation(S.D)= $\sqrt{variance}$

Variance=$(S.D)^2=3^2=9$

Hence, The variance of new set of value is 9.

Given:

On selling an article at 90% of the Marked Price, there is a loss of 7%

Formula Used:

Profit/loss% = $\frac{profit/loss}{CP}\times 100$

Calculation:

⇒ Let the Marked Price = Rs. 100

⇒ Selling Price= 90% of 100 = Rs. 90

⇒ Loss = CP - SP = CP - 90

⇒ Loss% = $\frac{loss}{CP}\times 100$

⇒ 7 = $\frac{CP-90}{CP}\times 100$

⇒ 7CP = 100CP - 9000

⇒ 93CP = 9000

⇒ CP = $\frac{9000}{93}$

⇒ Now article is sold at MP

⇒ Profit=SP - CP = 100 - $\frac{9000}{93}$ = $\frac{9300-9000}{93}=\frac{300}{93}$

⇒ Profit% = $\frac{profit}{CP}\times 100=\frac{\frac{300}{93}}{\frac{9000}{93}}\times 100=\frac{300}{9000}\times100=3.33$

⇒ Hence, The profit% on selling the article at a marked price is 3.33%

The correct answer is 1954.

Key Points

• Article 35A of the Indian Constitution was an article that empowered the Jammu and Kashmir state's legislature to define "permanent residents" of the state and provide special rights and privileges to them.
• It was added to the Constitution through a Presidential Order.
• The Constitution (Application to Jammu and Kashmir) Order, 1954 – issued by the President of India under Article 370.
• The state of Jammu and Kashmir defined these privileges to include the ability to purchase land and immovable property, the ability to vote and contest elections, seeking government employment, and availing of other state benefits such as higher education and health care.
• Non-permanent residents of the state, even Indian citizens, were not entitled to these 'privileges'.

Additional Information

• The Constitution of India is the supreme law of India.
• The document lays down the framework that demarcates the fundamental political code, structure, procedures, powers, and duties of government institutions and sets out fundamental rights, directive principles, and the duties of citizens.
• Prem Behari Narain Raizada (Saxena), the man who hand wrote the original Constitution of India.
• Dr. Bhimrao Ramji Ambedkar is known as the father of the Indian Constitution. He was the then Law Minister who introduced the final draft of the Constitution in the Constituent Assembly.
• Constitution of India which was adopted by the Constituent Assembly on 26th November, 1949 and came into force on 26th January, 1950.

GIVEN:

28 teachers teach mathematics or physics 

12 teachers teach only mathematics 

4 teachers teach both physics and mathematics

FORMULA USED:

n( A U B) = n( A)  + n ( B) - n ( A ∩ B) 

Where A and B are two sets 

n ( A ∩ B) = Number of elements present in both A and B 

n ( A U B) = Number of elements present in either A or B 

n(A) = Number of elements present in A 

n( B) = Number of elements present in B

CALCULATION:

Here set M = mathematics, set P = physics 

n(M) = n(maths only) + n(M and P) = 12 + 4 = 16

n(M U P) = n(M) + n(P) - n(m ∩ P)

⇒ 28 = 16 + n(P) - 4

⇒ 28 = 12 + n(P)

⇒ n(P) = 28 - 12 = 16

So, Only Physics = n(P) - n(m ∩ P) = 16 - 4 = 12

Hence, 12 teachers teach only physics.

The correct answer is egg, larva, pupa, imago.

Key Points

• The mosquito goes through four separate and distinct stages of its life cycle:
• Egg.
• Larva.
• Pupa.
• Adult.
• Each of these stages can be easily recognized by its special appearance.
• The life cycle typically takes up to two weeks, but depending on conditions, it can range from 4 days to as long as a month.
• Eggs are held one at a time or linked together to form the "rafts." They hang on the external of the water.

Additional Information

• Egg - hatches when exposed to water.
• Larva - "wriggler" lives in water; molts several times; most species surface to breathe air.
• Pupa - "tumbler" do not feed; stage just before emerging as adult.
• Adult - flies a short time after emerging and after its body parts have hardened

The correct answer is Stockholm conference.

Key Points

• The Stockholm Convention is a global treaty that aims to protect human health.
• To protect the environment from the effects of persistent organic pollutants (POPs).
• The Convention entered into force on May 17, 2004.
  

The United Nations Conference on the Human Environment was held in Stockholm, Sweden, from June 5–16 in 1972.

• The principal purpose was to serve as a practical means to encourage, and to provide guidelines to protect and improve the human environment and to remedy and prevent its effect.

Additional Information

• The Nairobi Declaration, adopted by African ministers and heads of delegations November 19, 2021, underlined the need to deliver commitments on the Programme of Action (PoA) for implementing the Sendai Framework in Africa.
• Earth Summit was created as a response for member states to cooperate together internationally on development issues after the Cold War.
• Vienna Convention on the Law of Treaties, an international agreement governing treaties between states that was drafted by the International Law Commission of the United Nations.

The correct answer is G Madhavan Nair.

Key Points

• G. Madhavan Nair is an Indian space scientist and a former Chairman of the Indian Space Research Organisation.
• He was the Secretary to the Department of Space, Government of India.
• He has also been the Chairman of the Space Commission and Chairman of the Governing Body of the Antrix Corporation, Bangalore.
• He was born on 31 October 1943 in Kulasekharam.
• G Madhavan Nair was the chairman of ISRO whebn Chandrayaan-1 was launched.

Additional Information

• Avul Pakir Jainulabdeen Abdul Kalam was an Indian aerospace scientist and statesman who served as the 11th President of India from 2002 to 2007.
• Mr. Umamaheswaran R. is currently Distinguished Scientist and Scientific Secretary, Indian Space Research Organisation (ISRO), Department of Space (DOS), Government of India.
• Chandrayaan-1 was the first Indian lunar probe under the Chandrayaan program.
• It was launched by the Indian Space Research Organisation in October 2008, and operated until August 2009.
• The mission included a lunar orbiter and an impactor

Explanation :

Vijay is taller than raju

Sam is taller than Vijay

Sam > Vijay > Raju

Vijay is shorter than Arun

Sam is shorter than Arun

Arun > Sam > Vijay >  Raju

Raju is shorter than Sam

James is taller than arun

James > Arun > Sam > Vijay > Raju

∴ Raju is shortest among all in the group.

Hence, Raju is the correct answer.

Explanation :

The table of english alphabet positional value

The pattern followed here is :

Hence, O is the correct answer.

The correct answer is It is the system of growing agricultural crops between rows of planted trees.

Key Points

• The taungya is a system whereby villagers and sometimes forest plantation workers are given the right to cultivate agricultural crops during the early stages of forest plantation establishment.
• Cultivation is often allowed to continue until trees shade crops due to canopy closure.
• The taungya is a Burmese word coined in Burma in 1850s. The taungya system was introduced into India by Brandis in 1890 and the first taungya plantations were raised in 1896 in North Bengal.
• Types of Taungya:
• Departmental Taungya: Under this, agricultural crops and plantations are raised by the forest department.
• Leased Taungya: The forest land is given on lease to the person who affects the highest money for raising Agril.
• Village Taungya: This is the most successful of all the three Taungya systems.

Additional Information

• Afforestation is the planting or adding of trees in an area where there was never a forest or plantation. This is a method to create a new forest.
• Agroforestry is a collective name for land-use systems and technologies where woody perennials (trees, shrubs, palms, bamboos, etc.) are deliberately used on the same land-management units as agricultural crops and/or animals, in some form of spatial arrangement or temporal sequence.
• Soil fertility can be further improved by incorporating cover crops that add organic matter to the soil, which leads to improved soil structure and promotes healthy, fertile soil.

The correct answer is 1996.

Key Points

• Hotmail (the capital H, T, M, and L are a homage to HTML) was a free online e-mail service started by Jack Smith and Sabeer Bhatia in 1995.
• It was later acquired by Microsoft in December 1997.
• By 2001, Hotmail had over 100 million users and had become one of the most popular webmail services available.
• A Microsoft account is a free account you use to access many Microsoft devices and services, such as the web-based email service Outlook.com.
• For example, username@hotmail.com, username@live.com, or username@outlook.com.

Additional Information

• There are four types of digital platforms:
• Social media platforms like Facebook, Twitter, Instagram, and LinkedIn.
• Knowledge platforms like StackOverflow, Quora, and Yahoo! Answers.
• Media sharing platforms like YouTube, Spotify, and Vimeo.
• Service-oriented platforms like Uber, Airbnb, and GrubHub.

Explanation :

Table of English alphabet positional value

 SMILE is coded as HNROV

According to above table

Similarly,

TEACH is coded as GVZXS

Hence, Option 1 is the correct answer.

The correct answer is Foxing.

Key Points

• Foxing is the result of both mold and metal contaminants in paper.
• Foxing appears as brown, yellow, or red stains on the paper, often in spidery spots or blotches.
• Foxing is an age-related process of deterioration that causes spots and browning on old paper documents such as books, postage stamps, old paper money and certificates.

Additional Information

• Browning is the process of food turning brown due to the chemical reactions that take place within. The process of browning is one of the chemical reactions that take place in food chemistry.
• Ageing results from the impact of the accumulation of a wide variety of molecular and cellular damage over time.
• Leaching is the process of a solute becoming detached or extracted from its carrier substance by way of a solvent. Leaching is a naturally occurring process which scientists have adapted for a variety of applications with a variety of methods.

The correct answer is Dilras Banu Begum.

Key Points

• Dilras Banu Begum was the first wife and chief consort of Emperor Aurangzeb, the sixth Mughal emperor.
• She is also known by her posthumous title, Rabia-ud-Daurani.
• The Bibi Ka Maqbara in Aurangabad, which bears a striking resemblance to the Taj Mahal, was commissioned by her husband to act as her final resting place.
• She was born in 1622 in Daulatabad Fort, Kesapuri Tanda and died on 8 October 1657 in Aurangabad.

Additional Information

• Asmat Begum was the wife of Mirza Ghias Beg, the Prime minister of the Mughal emperor Jahangir, and the mother of Mughal empress Nur Jahan, the power behind the emperor.
• Nur Jahan, born Mehr-un-Nissa was the chief wife and empress consort of the Mughal emperor Jahangir. She was the twentieth and last wife of Jahangir.
• Manavati Bai better known by her title, Jagat Gosain, was the second wife and the empress consort of the fourth Mughal emperor Jahangir and the mother of his successor, Shah Jahan.

The correct answer is Reserving electoral seats for depressed classes.

Key Points

• The Poona Pact was an agreement between Mahatma Gandhi and Dr. B. R. Ambedkar on behalf of Dalits, depressed classes, and upper caste Hindu leaders on the reservation of electoral seats for the depressed classes in the legislature of British India in 1932.

Shortcut Trick

The Effective Rate for 2 years at 8% per annum = 8 + 8 + (8 × 8)/100 = 16.64%.

Compound Interest = 16.64% of ₹20,000 = (16.64 ÷ 100) × 20,000 = ₹3,328.

Since the calculated interest matches the given interest exactly, the Time period is 2 years.

∴ The correct answer is 2 years.

Alternate Method

Given:

Principal (P) = ₹20,000

Compound Interest (CI) = ₹3,328

Rate (R) = 8% p.a.

Formula Used:

Amount (A) = P(1 + R/100)ⁿ, where n is the Time period.

⇒ Amount (A) = Principal + CI

⇒ A = 20,000 + 3,328 = 23,328

⇒ 23,328 = 20,000 × (1 + 8 ÷ 100)ⁿ

⇒ 23,328 ÷ 20,000 = (108 ÷ 100)ⁿ

⇒ 1.1664 = (1.08)ⁿ

⇒ (1.08)² = (1.08)ⁿ

⇒ n = 2

∴ The correct answer is 2 years.

Additional Information

Effective Rate of Interest

For two successive interest periods with rate r, the effective rate is R_eff = r + r + (r × r) ÷ 100.

CI and SI Difference

The difference between Compound Interest and Simple Interest for 2 years is D = P × (R ÷ 100)².

Rule of 72

To find the approximate time it takes for an investment to double at a fixed annual rate of interest, divide 72 by the rate: Time ≈ 72 ÷ Rate.

Explanation:

The least possible Venn diagram of the given statement will be :

Conclusion 1.All gamma are remote

False ( All gamma are not remote as shown in the above)

Conclusion 2.Some gamma are remote.

True ( as some gamma are remote given in the above statement)

Conclusion 3.No remote are gamma

False ( because there is not any direct relation between remote and gamma)

Conclusion 4.Some remote are not infrared. 

False (as shown above)

Hence, Only conclusion 2 follows is the correct answer.

Explanation :

Table of English alphabet positional value

The pattern followed here is :

Hence, D is the correct answer.

The correct answer is Brazil.

Key Points

• Brazil is, quite simply, the largest coffee producer in the world.
• For example, in 2016 it is thought that 2,595,000 metric tons of coffee beans were produced in Brazil alone.
• According to a story written down in 1671, coffee was first discovered by the 9th-century Ethiopian goat-herder Kaldi.
• The earliest credible evidence of the drinking of coffee in the form of the modern beverage appears in modern-day Yemen from the mid**-15th century** in Sufi shrines, where coffee seeds were first roasted and brewed in a manner similar to current methods.

Additional Information

• Peru is the leading producer of alpaca fiber in the world. It is also the country with the largest alpaca population in the world, with more than 3.6 million specimens.
• Argentina is the largest producer in the world of yerba mate, one of the 5 largest producers in the world of soy, maize, sunflower seed, lemon, and pear.
• India is the world's largest producer of milk, pulses and jute, and ranks as the second largest producer of rice, wheat, sugarcane, groundnut, vegetables, fruit and cotton.

Given:

P = Rs 10,000 

Rate = 15% per annum 

Formula used:

S.I. = ( P × R × T) /100 

Where, S.I. = Simple Interest, P = Principal, R = Rate of interest, T = Time in years

Calculation:

Here,  P = 10,000 , R = 15% , T = 2  years

⇒ S.I. = ( P × R × T) /100 = ( 10000 × 15 × 2 ) /100 = 3,000

Hence, interest to be paid at the end of 2 years are Rs 3,000.

The correct answer is Yeast.

 Key Points​

• Yeast is mostly used in the manufacturing of baked goods and alcoholic beverages.
• Yeast is used to produce fermentation and leavening in the production of food. As they consume sugars, the fungi release alcohol and carbon dioxide.
• Yeast cells range in size from 3 to 5 microns.

 Additional Information

• Cheese is a dairy product made from the coagulation of milk protein casein. It comes in a broad variety of flavours, textures, and forms.
• The United States, India, and the Russian Federation are close behind China in terms of land area used for wheat farming.
• Most frequently, tomato ketchup is added as a condiment to foods that are frequently served hot, fried, or oily.

Given:

Number of cylindrical pillars = 24 

Radius of each pillar = 28 cm

Height = 4 m 

Formula used:

Curved Surface Area = $2 \pi r h$

Where, r = radius , h = height 

Calculation:

Here, radius = 28 cm = 28/100 = 0.28 m ,  height = 4 m 

Curved Surface Area of 1 cylindrical pillar =  $2\pi rh$ = 2 × 22/7 × 0.28 × 4  

Curved Surface Area of 24 cylindrical pillars = 2 × 22/7 × 0.28 × 4 × 24 $m^2$

Cost of painting curved surface area of 1m² =  8 

Cost of painting curved surface area of all pillars = 2 × 22/7 × 0.28 × 4 × 24 × 8 = Rs1351.68.

Hence, total cost of painting curved surface area of all pillars are Rs1351.68.

The correct answer is Manipur.

Key Points

• Lynch law is defined as the practise of punishing people for alleged crimes or misdeeds without a fair trial.
• There had been no reported kid abductions in the three months prior in almost all of the lynching locations.
• In 2018, the Supreme Court issued instructions for the Center and State governments to follow when drafting laws to address the crime of lynching, describing it as a "horrendous act of mobocracy."
• The Manipur Law follows the rules established by the Supreme Court.

Additional Information

• Mob lynching is a flagrant breach of the Universal Declaration of Human Rights, Article 21 of the Constitution, and human dignity.
• Lynchings are a particularly disturbing way for government to go astray.
• Politicians could also consider challenging the social norms that support mob violence.

Given:

H.C.F of two numbers  = 5 

L.C.M = 750

One number = 125 

Formula used:

H.C.F × L.C.M = X × Y 

Where, X  and Y are two numbers respectively

Calculation:

Here, H.C.F = 5 , L.C.M = 750 , X = 125

H.C.F × L.C.M = X × Y 

⇒ 5 × 750 = 125 × Y 

⇒ 3750/125 = Y 

⇒ Y = 30

Hence, the other number is 30.

Given:

H.C.F = 11

L.C.M = 330 

One number = 55

Formula used:

H.C.F × L.C.M = X × Y 

Where, X and Y are two numbers respectively

Calculation:

Here, we have  H.C.F = 11 , L.C.M = 330 , X = 55 

H.CF × LC.M =  X × Y  

⇒ 11 × 330 = 55 × Y 

⇒ Y = 66

Hence, the other number is 66.

The correct answer is Saraswati.

Key Points​

• The Bharatiya Jnanpith annually presents an author with the Jnanpith Award, the highest and oldest literary honour in India, in recognition of their "great contribution to literature."
• The Bhartiya Jnanpith organisation annually bestows Indian authors with the Jnanpith Award.
• The most recent Jnanpith prize winners in 2021 and 2020 were the Konkani novelist Damodar Mauzo and the Assamese poet Nilmani Phookan Jr.

Additional Information

• Amitav Ghosh received the Jnanpith award for the first time in 2018.
• Ashapurna Devi, a Bengali writer, received the Jnanpith prize as the first female recipient in 1976.
• Universities, numerous literary and linguistic organisations, instructors, reviewers, and other literary specialists all submit nominations for the award.

Explanation :

Table of english alphabet positional value

The pattern followed here is :

Middle numbers are prime numbers

Hence, ''F17V" is the correct answer.

The correct answer is Manipur.

• The Innaphi, a delicate muslin shawl wrapped over the upper body, the rigid cylindrical skirt, a shirt, a woven belt around the waist, and the Potloi are all included in the ensemble.
• A potloi is a garment consisting of heavy cloth embellished with sequins and mirrors.
• Meidingu Chinthang Khoma or Maharaja Bhagyachandra invented the potloi as a costume.
• The bride in Kerala must wear the renowned Kasavu saree, an all-white saree with a golden border.
• In Rajasthan, women typically don a Ghagra and a Choli, also known as a Kanchli.
• In Odisha, the bride dons a customary crimson saree.

The correct answer is Anodising.

Key Points​

• The process of anodizing involves employing aluminium as an anode in an electrolyte bath.
• when a cathode is placed inside the anodizing tank and the medium is delivered a current through it.
• The electrochemical process of anodizing transforms the metal surface into an attractive, long-lasting, corrosion-resistant anodic oxide finish.
• The anode is created using the components and a weak acid solution.

Additional Information​​​​​​​

• Roasting is a method of slow cooking that uses diffused, indirect heat to roast its contents.
• Applying a protective zinc coating to steel or iron to stop rusting is the process of galvanization.
• Calcination is the term for applying heat to a solid chemical substance.

Given:

Time = 15 years 

Formula used:

S.I. = (P × R × T )/100 

S.I. = Simple Interest, P = Principal, R = Rate of interest, T = Time in years 

Calculation:

 Here, Let the original sum be P then,

According to the Question given,

Amount after 15 years = 3P 

⇒ S.I.  =( A - P) = ( 3P - P) = 2P  , Time = 15 years

⇒ S.I. = ( P × R × T )/ 100 

⇒ 2P =( P × R × 15) /100 

⇒ 2× 20 /3 = R  

⇒ R = 40/3%

Now,  in 2nd condition given in the Question, Amount becomes 5P and Rate of interest remains same 

⇒ S.I. = ( A - P ) = ( 5P - P) = 4P , R = 40/3

⇒ S.I. = ( P × R × T) / 100 

⇒ 4P = ( P × 40 × T) / 3×100 

⇒ T = 30 years

Hence, the required years is 30.