RRB NTPC CBT-I Official Paper (Held On: 8 Feb 2021 Shift 2) (Previous Year Paper)

GIVEN:

Base of a cylinder = base of a cone 

Height of the cylinder = Height of the cone 

FORMULA USED:₁

Base of a cylinder = $\pi$ r²

Base of a cone = $\pi$ r²  

Volume of the cylinder = $\pi$  r² h 

Volume of the cone = 1/3 $\pi$ r² h

CALCULATION:

Here, let radius of cylinder and radius of cone be r₁ and r₂ respectively

Also, height of the cylinder and cone be h₁ and h2  respectively

As, base of a cylinder = base of a cone

⇒ $\pi$ r₁² = $\pi$ r₂²  ⇔ r₁² = r₂²

⇒ r₁ = r₂

Also, it is given height is same. So, h₁ = h_2.

⇒  Volume of the cylinder = $\pi$ r₁² h₁ 

_{⇒ Volume of the cone = 1/3 \(\pi\)} r₂² h₂ 

⇒ Ratio of volume of the cylinder and volume of the cone = $\pi$ r₁² h₁ : 1/3 $\pi$ r₁² h₁ = 1 :1/3 = 3 :1.

Hence, the ratio of volume of the cylinder and  volume of the cone = 3 :1.

GIVEN:

Ratio of A's salary to B's salary = 4:5 

A''s salary increased by 10%

B's salary increased by 20%

CALCULATION:

Let the salary of A and B  be 400 and 500 respectively 

 Now, as A's salary increased by 10% 

⇒ New salary = 400 + 10 % 400 = ( 400 + 40 ) = 440 .

Also, B's salary increased by 20% 

⇒ New salary = 500 + 20% of 500 = ( 500  + 100 ) = 600.

Ratio of new salary of A : Ratio of new salary of B = 440 : 600 =  11 : 15.

Hence, the Ratio of new salary of A and B is 11 : 15.

Correct answer is Nylon.

Key Points

• Nylon, the first synthetic fiber in the "fully synthetic" feeling of that word, was developed by Wallace Carothers, an American researcher at the chemical firm DuPont in the 1930s.
• Nylon is a generic designation for a family of synthetic polymers composed of polyamides.
• Nylon is a silk-like thermoplastic, usually made from petroleum, that can be melt-processed into fibers, films, or shapes.
• Nylon is the first fully processed synthetic fibre, made from coal, water and air.

Additional Information

• Spandex is a synthetic fabric that is prized for its elasticity.​
• Acrylic fiber fabrics are made from a synthetic polymer called acrylonitrile.
• Silicones are a durable alternative to conventional plastics that preserves our environment.

Correct answer is Aam Aadmi Bima Yojana.

Key Points

• The Aam Aadmi Bima Yojana covers natural death/accidental death, permanent total disability, and partial permanent disability.
• The scheme gives coverage to individuals residing in rural areas and individuals who are below the poverty line.
• “Aam Admi Bima Yojana” has come into effect from 01.01. 2013.
• One member of the family who is the householder is eligible for coverage.
• 

Additional Information

• Janashree Bima Yojana is a government life insurance scheme that was started together with the LIC.
• Rashtriya Swasthya Bima Yojana has been started by Ministry of Labour and Employment, Government of India to provide health insurance coverage for Below Poverty Line (BPL) families. ​
• LIC's Jeevan Umang plan offers a combination of income and protection to your family.

GIVEN:

A alone can complete a work = 12 days

B alone can complete a work = 18 days

FORMULA USED:

Efficiency = Total work / No. of days

CALCULATION:

Let us assume total work done to be 36 unit.

( You can assume any number but for the sake of calculation it is advised to take the L.C.M of the given numbers. Here L.C.M of the given numbers is 36)

Efficiency of A = Total work / No. of days  = 36/ 12   = 3 unit /day 

Efficiency of B = Total work/ No. of days = 36/18 = 2 unit/day 

⇒ Total Efficiency = ( 3 + 2 ) = 5 unit/day.

According, to the given  Question they work together for 3 days 

⇒ Total work done in 3 days = 5 × 3 = 15 unit 

⇒ Remaining work = ( 36 - 15 ) =  21 unit.

Also, A left after 3 days.So, B does the  remaining work alone

⇒ No. of days taken by B = 21/2 = 10.5 days.

Hence, B alone takes 10.5 days to complete the work alone.

From the given options, when we observe closely we see that three of them are exactly the same but only one have a different character in it,

In option 3) the character is different whereas in other options in that place there is a M placed. So it is the odd one.

Hence the correct answer is option 3)

Correct answer is 1986.

Key Points

• In presence of this provision, the Government of India constituted the NARCOTICS CONTROL BUREAU on the 17^th of March, 1986.
• The Narcotics Control Bureau was created in March 1986 in words of Section 4 (3) of the Narcotic Drugs and Psychotropic Substances Act, 1985.
• The Narcotics Control Bureau (abbr. NCB) is an Indian central law enforcement and intelligence agency under the Ministry of Home Affairs, Government of India.
• The Narcotics Control Bureau is an agency incharge for fighting drug trafficking and the abuse of illicit substances.
• 

Additional Information

• ​National Crime Investigation Bureau is a name of Crime and Corruption killer team, operating over India with help of good officers and powerful legal team.
• The Department of Revenue is mostly responsible for the following functions: - All matters relating to levy and collection of Direct Taxes.
• The Department of Economic Affairs (DEA), Ministry of Finance, assists the Central Government.

Correct answer is The Morely-Minto Reforms.

Key Points

• The Minto-Morley Reforms of 1909 known for separate Muslim electorates.
• It was instituted to placate the Moderates (Congress) and establish separate electorates on the basis of religions.
• The Indian Councils Act, 1909 establish a few reforms in the legislative councils and the act increased the involvement of Indians in the governance of British India.
• So, Lord Minto came to be called as the Father of Communal Electorate in India.

Additional Information

• The Rowlatt  acts allowed certain political cases to be tried without juries and permitted internment of suspects without trial.​
• Ilbert Bill, in the history of India, a controversial measure proposed in 1883 that sought to allow senior Indian magistrates to preside over cases involving British subjects in India.
• Diarchy government shared by two rulers, powers, etc.

GIVEN:

M.P. = 25% above the Cost Price 

reduction = 12% on their bills 

FORMULA USED:

S.P. = ( 1 - d1/100 ) × M.P. 

Profit = S.P. - C.P. 

Profit% =( Profit/ C.P.) × 100

  Where,  C.P. = Cost Price ,S.P. = Selling Price, M.P = Marked Price  d1 = discount%

CALCULATION:

Let the Cost Price be 100 

⇒ M.P. = 100 + 25% × 100  = 100 + 25 = 125.

⇒ S.P. =  ( 1 - d1/100) × M.P.  = ( 1 - 12/100) × 125 

⇒ S.P. = 22/25 × 125 = 110.

⇒ Profit = S.P. - C.P. = ( 110 - 100 ) = 10

⇒ Profit% =( Profit/ C.P.) × 100 =( 10/100 )× 100  =  10%.

Hence, the Profit percentage is 10%.

From the given words:

Pamphlets, Newspapers, Radio 

Let's compare each option:

1. All are means of spreading information: Correct. 

2) All are means of print media: Incorrect, only pamphlets and newspapers are print media.

3) All are means of broadcast media: Incorrect, only radio is broadcast media.

4) All are means of global news: Incorrect, all of them are local means of news.

So, they all are means of spreading information.

Hence the correct answer is option 1)

GIVEN:

58 out of 100 students in a school are boys

CALCULATION:

Here, total students = 100

⇒ No. of boys = 58 

⇒ Part of the school that consists of boys =  58/100 

⇒ Part of the school of boys in decimal = 58/100 = 0.58.

The required value in decimal is 0.58.

GIVEN:

The total number of persons in a party = 20.

FORMULA USED:

Number of handshakes possible with various people saying "n"

can be solved by a formula $n \times ( n - 1) \over 2$ 

This is because each of the "n" numbers of people can shake hands with " ( n - 1)" people and they will not shake their own hands.

The handshake between two people cannot be counted twice.

CALCULATION:

As the total number of people in the party is 20.

⇒ The total number of handshakes when each one of the persons shakes had with other exactly once 

⇒ $20 \times ( 20 - 1) \over 2$ = 20 × 19 /2 =  190.

Hence, the total number of handshakes is 190.

Preparing the family tree using the following symbols:

From the given information:

Step 1: Fatima has only one sibling. She also has only one daughter Rushna. Rushna and Rameez are married to each other.

Step 2: Their maternal aunts are Maryam and Khadija, respectively.

Now Khajida's mother will be Rameez's mother's mother and Rushna is married to Rameez.

So, Khajida's mother is husband's mother's mother to Rushna (who is Maryam's niece).

Hence the correct answer is option 1)

GIVEN:

Speed = 45 km/h 

FORMULA USED:

Distance = Speed × Time 

CALCULATION:

Here, we have Speed  = 45 km/h  , Time =  64 seconds 

⇒ As,  3600 seconds  = 1hour

⇒ 64 seconds = 0.0177

⇒ Distance = 45 × 0.0177 = 0.8 k

The distance is 0.8 km.

Correct answer is Ajmer.

Key Points

• The Pushkar fair is the largest camel, horse and cattle fair in Ajmer.
• Aside from the trading of livestock, it is an important pilgrimage season for Hindus to the Pushkar lake.
• In 2022, Pushkar Fair will be celebrated from 11^th November 2022 to 19^th November 2022.
• The Pushkar Camel Fair in Pushkar is celebrated at the beginning of the Hindu month of Kartik.
• 

Additional Information

• Amer is now part of the Jaipur urban agglomeration.
• The Adventure festival is one of the most fascinating festivals of Rajasthan in Kota.​
• Kolayat fair is held in Bikaner, Rajasthan.

GIVEN:

x × y = x + y + $\sqrt{x y}$ 

CALCULATION:

Here, we have x + y = x + y + $\sqrt{x y}$ 

Now, x = 6 , y  = 24 

⇒ 6 × 24 = 6 + 24 + $\sqrt{ 6 \times 24}$  = 6 + 24 + 12 = 42.

Hence, the required value is 42.

GIVEN:

Numbers are 12 , 15 and 18

CONCEPT USED:

Largest four digits number are 9999

CALCULATION:

L.C.M of 12, 15 and 18 = 180 

Largest four digit number is 9999

To find the largest 4 digit number exactly divisible by 12,15 and 18 , we have to divide the 9999 by 180 and subtract the remainder  from 9999.

When we divide the 9999 by 180, the remainder is 99

Required number = 9999 - 99  = 9900.

Hence, the required number is 9900.

According to the English alphabets and their positional values: 

The pattern followed in the given code is:

 Alphabets at odd places are increased by 3 positional values.

 Alphabets at even places are decreased to 6 positional values.

Similarly,

Hence the correct answer is option 1)

Correct answer is Malaysia.

Key Points

• Malaysia is a country in Southeast Asia, it is not the part of SAARC.
• Malaysia is a federation of 13 states and three federal territories in Southeast Asia.
• It consists of two regions split up by the South China Sea and is bordered by Brunei, Indonesia, and Thailand.
• Malaysia has a strategic position along the Strait of Malacca and the southern South China Sea.

Additional Information

• The South Asian Association for Regional Cooperation (SAARC) was established on 8 December 1985.
• SAARC has eight member countries Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri-Lanka.​
• SAARC mainly aims to promote welfare of South Asians.

​

Correct answer is 1993.

Key Points

• The National Human Rights Commission (NHRC) was launched on October 12, 1993.
• Human rights are rights inherent to all human beings, regardless of race, sex, nationality, ethnicity, language, religion, or any other status.
• Human rights cover the right to life and liberty, freedom from slavery and torture, freedom of opinion and expression, the right to work and education e.t.c
• Human rights guarded by the International Covenant on Civil and Political Rights.

Additional Information

• Article 12 to 35 contained in Part III of the Constitution deal with Fundamental Rights.​
• Right to equality, including equality before law, prohibition of discrimination on grounds of religion, race, caste, sex or place of birth, and equality of opportunity in matters of employment are fundamental rights.

GIVEN:

Length of the tangent from (2,5) is $\sqrt{37}$ 

FORMULA USED:

If equation of the circle is in the form of x² + y² + 2gx + 2fy + c = 0

Where, center of the circle = ( - g , - f)  and radius(r) = $\sqrt{ g^2 + f^2 - c}$ 

CALCULATION:

Here, we have x² + y² - 5x + 4y + k = 0  which is in the form of x² + y² + 2gx + 2fy + c = 0 

Now, g = -5/2 , f = 2 , c= k

⇒ Center = ( 5/2, -2 )  and radius  (r)= $\sqrt{25/4 + 4 - k}$ 

As tangent is perpendicular to the radius, we apply Pythagoras theorem ( See the figure )

⇒ AO² = AP² + PO²

⇒ 1/4 + 49 = r² + 37 

⇒ 197/4 = 25/4 + 4 - k + 37 

⇒ k =  -2 .

Hence, the value of k is -2.

Correct answer is be free and impartial.

Key Points

• The press in democracy must- · be free and impartial.
• Be perform to the policies of the government.
• Media democracy provides people the right to take part in media.
• The backbone of any democracy is an independent, executive and responsible media.
• 

Additional Information

• ​Freedom of press or media mentions to the rights given by the Constitution of India under the freedom and expression of speech in Article 19(1)(a).
• The law of India forbid increasing or publishing fake news through social or mass media, and could guide to imprisonment of a journalist or newspaper ban.

Correct answer is Nitin Jairam Gadkari.

Key Points

• Current transport minister is Nitin Gadkari.
• He is also famous for his work as the Public Works Department Minister of the State of Maharashtra.
• Nitin Gadkari was born into a Marathi family in Nagpur, India to Jairam Gadkari and Bhanutai Gadkari on 27 May 1957.
• Through his teenage, he worked for the Bharatiya Janata Yuva Morcha and the student union Akhil Bharatiya Vidyarthi Parishad.
• 

Additional Information

• The current Finance Minister of India is Nirmala Sitharaman.​
• Sushma Swaraj was the first female Spokesperson of a national political party in India.
• Piyush Goyal is minister of Consumer Affairs, Food & Public Distribution (2020 – present).

Correct answer is Sandstone.

Key Points

• Common sedimentary rocks include sandstone, limestone, and shale.
• These rocks frequently start as sediments carried in rivers and deposited in lakes and oceans.
• When secreted, the sediments lose water and become cemented to form rock.
• Sandstone is a clastic sedimentary rock composed mainly of sand-sized (0.0625 to 2 mm) silicate grains.
• 

Additional Information

• ​Lignite, frequently mention to as brown coal, is a soft brown combustible sedimentary rock that is formed from naturally compressed peat.
• Slate is a metamorphic rock of sedimentary origin.
• Granite is a coarse-grained intrusive igneous rock composed mostly of quartz, alkali feldspar, and plagioclase.

GIVEN:

Line passes through (2,3)

Line is perpendicular to the line joining (-5,6) and (-6,5)

CONCEPT USED:

The equation of any straight line is y = mx + c 

Where m is its slope and c = y - intercept 

Slope of the line × Slope of the perpendicular line = -1.

CALCULATION:

Slope of the line joining through points ( x₁ , y₁ ) and ( x₂ , y₂ ) = ( y₂ - y₁ ) / ( x₂ - x₁ ) 

So, slope of the line joining  ( -5 , 6 ) , ( -6 , 5 ) = $- 6 + 5 \over 5 - 6$ = -1/-1 = 1.

Slope of the line perpendicular to this line = -1 

So, equation of the required line will be y = -x + c 

Since, this line passes through (2,3) in the equation we get 

 3 = -2 + c 

⇒ c = 3 + 2 = 5.

Hence, required equation of the line y = -x + 5 or x + y - 5 = 0.

Hence, required equation of the line is x + y - 5 = 0.

GIVEN:

Cost price of 120 g = Selling price of 150 g 

FORMULA USED:

Loss = C.P. - S.P. 

Loss% = ( Loss / C.P.) × 100 

Where, C.P. = Cost price, S.P. = Selling Price 

CALCULATION:

Let the Cost price of 1 g = Rs100

⇒ Cost price of 120 g = Rs12000.

According to the given Question, Cost Price of 120 g = Selling Price of 150 g

⇒ Selling Price of 150 g = Rs12000.

⇒ Selling Price of 120 g = Rs9,600.

⇒ Loss = C.P. - S.P.  = ( 12000 - 9600 ) = Rs2,400.

Loss% =( Loss / C.P.) × 100 =  (2400 / 12000 ) × 100 = 0.2 × 100 = 20%.

The percentage of loss is 20%.

Correct answer is Fox.

Key Points

• fox, many members of the dog family (Canidae).
• Look like small to medium-sized bushy-tailed dogs with long fur, pointed ears, and a narrow snout.
• Despite the fact that red foxes are part of the Canidae family along with dogs, they have more in common with cats.
• Here are some similarities: Like cats, red foxes are most active at night.
• 

Additional Information

• Lion, cat and tiger belong to a common family.
• The lion is a member of the **Felidae family, which is a big cat family.**​
• The leopard  is be a member five extant species in the genus Panthera, a member of the cat family, Felidae.

From the given information: 

Now we substitute the values in the given equation and solving it using BODMAS rule:

(5/2 × 2) + (3 - 1) 

(5 × 2 - 2) ÷ (3 + 1)

(10 - 2) ÷ 4

8 ÷ 4

2 = Answer

Hence the correct answer is option 4)

The correct answer is Article 32 and Article 226.

Key Points

• Article 32 of the Indian Constitution grants the right to individuals to move the Supreme Court directly in case of any violation of their fundamental rights.
• Article 226 provides the power to High Courts to issue certain writs for the enforcement of Fundamental Rights and for any other purpose.
• Judicial review refers to the power of the judiciary to review and determine the validity of a law or an order.
• Both Articles 32 and 226 play a crucial role in upholding the principle of judicial review in India.

Additional Information

• Judicial Review
• Judicial review is a process under which executive or legislative actions are subject to review by the judiciary.
• It is an essential function in a democracy as it ensures the supremacy of the Constitution.
• Writs Issued Under Articles 32 and 226
• Habeas Corpus: To ensure the release of a person unlawfully detained.
• Mandamus: To direct a public official or body to perform a public duty.
• Prohibition: To prevent a lower court from exceeding its jurisdiction.
• Certiorari: To transfer the matter from a lower court to a higher court for review.
• Quo Warranto: To challenge the legality of a person’s claim to a public office.
• Fundamental Rights
• These are a set of rights granted to the citizens of India, which are enshrined in Part III of the Constitution.
• They ensure civil liberties so that all Indians can lead their lives in peace and harmony as citizens of India.
• Supreme Court of India
• It is the highest judicial forum and final court of appeal under the Constitution of India.
• The Supreme Court has extensive jurisdiction and is a guardian of the Constitution.

Correct answer is Goiter.

Key Points

• A goitre is a lump or swelling at the front of the neck caused by a swollen thyroid.
• The thyroid is a small gland in our neck that makes hormones.
• Goitres are not generally serious but should be checked by a GP.
• The most general cause of goiters worldwide is a absence of iodine in the diet.
• 

Additional Information

• Dry eye disease is a common condition that occurs when your tears aren't able to provide adequate lubrication for your eyes. ​
• Cataracts are when the lens, a small transparent disc inside your eye, develops cloudy patches.
• Glaucoma is a group of eye conditions that damage the optic nerve.

Given:

$\sqrt {2 + \sqrt {2 + {2\cos 4\theta } } }$

Concept Used:

$cos4\theta=2cos^22\theta-1$

$cos2\theta=2cos^2\theta-1$

Calculation:

⇒ $\sqrt {2 + \sqrt {2 + {2\cos 4\theta } } }$

⇒ Putting the value in it, we get

⇒ $\sqrt {2 + \sqrt {2 + {2(2cos^22\theta-1)} } }$

⇒ $\sqrt {2 + \sqrt {2 + {4cos^22\theta-2} } }$

⇒ $\sqrt {2 + \sqrt {{4cos^22\theta} } }$

⇒ $\sqrt {2 + 2cos2\theta}$

⇒ Again, substituting the value, we get

⇒ $\sqrt {2 + 2(2cos^2\theta-1)}$

⇒ $\sqrt {2 + 4cos^2\theta-2)} =\sqrt{4cos^2\theta}=2cos\theta$

Therefore, the simplified value of $\sqrt {2 + \sqrt {2 + {2\cos 4\theta } } }$ is $2cos\theta$.

According to the English alphabets and their positional values: 

The pattern followed in the given code is:

 Alphabets at odd places are increased by 2 positional values.

 Alphabets at even places are increased by 4 positional values.

Similarly,

Hence the correct answer is option 3)

From the given words:

Peacock, Woodpecker, Parrot, Bat

1. Peacock: It is a bird who lay eggs.

2. Woodpecker: It is a bird who lay eggs.

3. Parrot: It is a bird who lay eggs.

4. Bat: It is a flying mammal 

So, Bat is the odd one.

Hence the correct answer is option 1)

Correct answer is Seventh Five-Year Plan.

Key Points

• In the Seventh Five Year Plan (1985 - 1990) private sector got the priority over public sector for the first time in the history of economic planning in India.
• Its main aim was poverty eradication and technological self dependency.
• The plan laid stress on improving the productivity level of industries by upgrading technology.
• The Seventh Plan aims at increasing the green revolution to new areas between its emphasis on raising the productivity of rice in the eastern region and in rainfed and dryland agriculture.

Additional Information

• The Second five year Plan focused on the development of the public sector and "rapid Industrialisation".​
• Tenth Five-Year Plan was to reduction of poverty rate by 5% by 2007.
• The Sixth Five-Year Plan marked the beginning of economic liberalisation.

Correct answer is Carolus Linnaeus.

Key Points

• Linnaeus came up with the binomial system of nomenclature, in which each species is recognized by a generic name (genus) and a specific name (species).
• This system amounts to a method for
• Carl Linnaeus is most known for creating a system of naming plants and animals—a system we still use today.
• Carolus Linnaeus was a Swedish botanist, zoologist, taxonomist, and physician.
• 

Additional Information

• Charles Robert Darwin was an English naturalist, geologist and biologist, best famous for his contributions to evolutionary biology.​
• Louis Pasteur was a French chemist and microbiologist.
• James Watson was an American geneticist and biophysicist who played a important role in the discovery of the molecular structure of deoxyribonucleic acid (DNA), the substance that is the basis of heredity.

GIVEN:

x² - 7x + 12 = 0 

CALCULATION:

We have, x² - 7x + 12 = 0 

⇒ x² -4x -3x + 12 = 0 

⇒ x ( x - 4) - 3 ( x - 4 ) = 0 

⇒ ( x - 3 ) ( x - 4 )  = 0 

⇒  x- 3 = 0  ⇔ x = 3.

⇒ ( x - 4 ) = 0 ⇔ x = 4.

Hence, roots of the given equation are 3 and 4.

Correct answer is Sarod.

Key Points

• Ustad Amjad Ali Khan is an Indian classical sarod player, best famous for his clear and fast ekhara taans.
• He was born into a classical musical family and has performed internationally since the 1960s.
• Sarod, stringed musical instrument of the lute family that is normally to the Hindustani music tradition of northern India.
• The modern classical sarod is about 100 cm (39 inches) long and has a slightly waisted wood body with a skin belly.
• 

Additional Information

• Santoor, also called santouri, stringed instrument of the hammered dulcimer, or struck zither.
• ​Shehnai, double-reed conical oboe of North India.
• A flute is a musical wind instrument consisting of a long tube with holes in it.

Shortcut Trick

The ratio of a to d can be found directly using the compound ratio multiplication method.

We know that a/d = (a/b) × (b/d).

Given a/b = 3/4 and d/b = 4/3 ⇒ b/d = 3/4.

Multiplying both ratios: a/d = (3/4) × (3/4) = 9/16.

∴ The correct answer is 9 : 16.

Alternate Method

Given:

⇒ a : b = 3 : 4

⇒ d : b = 4 : 3

Calculations:

⇒ To establish a continuous ratio between a, b, and d, the common term 'b' must be made equal in both ratio sets.

⇒ The LCM of the values representing b (4 and 3) is 12.

⇒ Multiply the first ratio by 3: a : b = (3 × 3) : (4 × 3) = 9 : 12

⇒ Multiply the second ratio by 4: d : b = (4 × 4) : (3 × 4) = 16 : 12

⇒ Reversing the second ratio to match b sequentially, we get b : d = 12 : 16

⇒ Combining them gives the continuous proportion a : b : d = 9 : 12 : 16

⇒ Therefore, extracting only a and d yields a : d = 9 : 16

∴ The correct answer is 9 : 16.

Additional Information

Compound Ratio

When two or more ratios are multiplied term by term, the resulting ratio is called a compound ratio. For a : b and c : d, the compound ratio is ac : bd.

Inverse Ratio (Invertendo)

If the antecedent and consequent of a ratio are interchanged, the new ratio is called its inverse. The inverse of a : b is b : a.

Combining Multiple Ratios

To combine the ratios a : b and b : c into a single continuous ratio a : b : c, you must find the LCM of the numerical values corresponding to the common term 'b' and adjust the other terms proportionally.

GIVEN:

First term = 5 

Common difference = 4

FORMULA USED:

an = a + ( n - 1 ) d

Where, an = 9^th term , a = first term , common difference = d ( second term - first term) 

CALCULATION:

Here, we have a = 5 , d = 4

⇒ a_{9  =} a + ( n - 1 ) d 

⇒ a₉ = 5 + (9 - 1 ) × 4 

⇒ a_{9 =} 5 + 32 = 37.

Hence, the ninth term is 37.

GIVEN:

$\sqrt{1 + x/144}$

CALCULATION:

Here , we have 

⇒ $\sqrt{1 + x/144}$ = 13/12

Now, on squaring , we have 

⇒ (^{\(\sqrt{ 1 +x/144}\)})² = (13/12)² 

⇒ 1 + x/144 = 169/144 

⇒ x/144 = (169/144) - 1

⇒ x/144 = 25/144 

⇒ x = 25.

Hence, the value of x = 25.

Correct answer is Albert Einstein.

Key Points

• According to scientific folklore, Albert Einstein formulated this equation in 1905.
• "Energy equals mass times the speed of light squared."
• Albert Einstein was a Theoretical Physicist of German origin.
• He is the one who developed a pillar of modern Physics, the Theory of Relativity.
• 

Additional Information

• Isaac Newton was an English physicist and mathematician, who was the culminating figure of the Scientific Revolution of the 17^th century.​
• Stephen Hawking was a famous cosmologist, physicist, and professor.
• Marie Curie was a physicist, chemist and pioneer in the study of radiation.

Correct answer is Sikkim.

Key Points

• Every year the northeastern state of Sikkim hosts the Red Panda Festival.
• The winter occasion features parades, live music and draws tourists and locals alike.
• It's a cheerful celebration named for Sikkim's historic state animal.
• It is the biggest tourism festival of the state and motives at promoting communal harmony and 'Unity in Diversity'.
• 

Additional Information

• The Pushkar Camel Fair (Rajasthan) is one of the largest in India and the only one of its type in the whole world.​
• In Tamil, the word "Mattu" means bull and this day of Pongal is for celebration of cattle.
• Hornbill Festival is one of the most popular festivals of Nagaland, celebrated every year from 1^st to 10^th December.

The Correct answer is C-DAC, Pune.

Key Points

• C-DAC have built multiple generations of the Supercomputer starting from PARAM with 1 GF in 1988 to our latest 54 TF Supercomputer PARAM Yuva in November 2008.
• This began a new chapter of developing Indigenous supercomputer and Professor Vijay Bhatkar developed India's first supercomputer PARAM 8000 which was the second-fastest computer in the world at that time.
• Param Shivay, the first supercomputer assembled indigenously, was installed in IIT (BHU), followed by Param Shakti and Param Brahma at IIT-Kharagpur and IISER, Pune, respectively.

Additional Information

• PARAM Siddhi-AI. PARAM Siddhi-AI is India's fastest supercomputer as of December 2020.
• A supercomputer is a computer with a high level of performance as compared to a general-purpose computer.
• The Centre for Development of Advanced Computing (C-DAC) and the Indian Institute of Technology, Gandhinagar have jointly unveiled a new supercomputer in phase two of the central government's National Supercomputing Mission (NSM).

Correct answer is Sikkim.

Key Points

• Sikkim is a State in Northeast India.
• It is be one of fastest growing, multiethnic and multilingual Indian state.
• It borders Tibet in the north and northeast, Bhutan in the east, Nepal in the west and West Bengal in the south.
• SIkkim is also situated near to India's Siliguri corridor near Bangladesh.

Additional Information

• The Seven Sister States is a famous word for the contiguous states of Arunachal Pradesh, Assam, Meghalaya, Manipur, Mizoram, Nagaland and Tripura.​
• Arunachal Pradesh is famous for its pristine beauty and the lush green forests.
• Nagaland is also popularly known as the 'land of festivals.
• Meghalaya, also famous as the Abode of Clouds, falls in one of the richest biodiversity areas in the world.
• 

The correct answer is Trygve Lie

Key Points

• Norwegian lawyer and politician Trygve Lie was the United Nations first Secretary-General.
• He held the post for seven years, from 1946 to 1953, and was a Norwegian politician, labour leader, government official and author.
• The United Nations is an intergovernmental organization whose stated purposes are to maintain international peace and security, develop friendly relations among nations.

Additional Information

• Dag  Hammarskjöld was a Swedish economist and diplomat who served as the second Secretary-General of the United Nations.
• U Thant, was a Burmese diplomat and the third secretary-general of the United Nations from 1961 to 1971, the first non-Scandinavian to hold the position.
• Kurt Josef Waldheim was an Austrian politician and diplomat. Waldheim was the fourth Secretary-General of the United Nations.

From the information given, we interchange:

• × and ÷
• 2 and 4

​Now we consider the options:

1) 12 × 4 ÷ 42 = 168

14 ÷ 2 × 24 = 168

7 × 24 = 168

168 = 168 

2) 2 ÷ 4 × 14 = 60

4 × 2 ÷ 12 = 60

4 × 0.1 = 60 

0.4 ≠ 60 

3) 12 ÷ 42 × 4 = 160

14 × 24 ÷ 2 = 160

14 × 12 = 160

168 ≠ 160

4) 42 × 12 ÷ 2 = 20

24 ÷ 14 × 4 = 20

1.7 × 4 = 20

6.8 ≠ 20

Hence the correct answer is option 1)

The answer is INS Arihant

Key Points

• INS Arihant is the first of the planned five in the class of submarines designed and constructed as a part of the Indian Navy's secretive Advanced Technology Vessel (ATV) project.
• The ATV project was set up in 1984, under Vice Admiral Mihir K. Roy as the first Director General.

Additional Information

• Nerpa(INS Chakra) is a 8,140-tonne Project 971 nuclear-powered attack submarine. The construction of the submarine was started in Russia in 1993.
• INS Khukri was a Type 14 frigate of the Indian Navy. This was the first warship sunk in action by a submarine since World War II.
• NS Kalvari (S21) is the first of the six indigenous Scorpene-class submarines currently in service with the Indian Navy. It is a diesel-electric attack submarine which is designed and was manufactured at Mazagon Dock Limited in Mumbai.

The correct answer is Chola Dynasty

Key Points

• The Chola Dynasty was a Tamil empire of southern India, one of the longest-ruling dynasties in world history.
• Their core area of the rule was the Kaveri delta, later known as Cholamandalam.
• Their capital was Uraiyur (near Tiruchirapalli town) and Puhar or Kaviripattinam was an alternative royal residence and chief port town.
• Tiger was their emblem. The Cholas also maintained an efficient navy.

Additional Information

• The Chaulukya dynasty, also Solanki dynasty, was a dynasty that ruled parts of what are now Gujarat and Rajasthan in north-western India.
• The Gupta Empire was an ancient Indian empire which existed from the early 4^th century CE to late 6^th century CE, it covered much of the Indian subcontinent.
• The Chera dynasty, IPA, also known as the Keralaputra, was one of the principal lineages in and before the Sangam period history of the state of Kerala and the Kongu Nadu region of Western Tamil Nadu in southern India.

The correct answer is 6

Key Points

• The United Nations (UN) has six main organs. They are — the General Assembly, the Security Council, the Economic and Social Council, the Trusteeship Council and the Secretariat — are based at UN Headquarters in New York.
• The United Nations is an international organization founded in 1945.
• The mission and work of the United Nations are guided by the purposes and principles contained in its founding Charter.
• There are six official languages of the UN

Additional Information

• It is currently composed of 193 Member States.
• The United Nations is an intergovernmental organization whose stated purposes are to maintain international peace and security.
• Dvelop friendly relations among nations, achieve international cooperation, and be a centre for harmonizing the actions of nations

FORMULA USED:

CALCULATION:

Here, we have 105 ÷ 5 × 3 + 39 - 46

⇒  21 × 3 + 39 - 46

⇒ 63 + 39 - 46 

⇒ 102 - 46 = 56.

Hence, the required value is 56.

GIVEN:

Cost price = Rs 550.

Selling price = Rs 580

FORMULA USED:

Profit = S.P. - C.P.

Profit% = (Profit /C.P.) × 100 

Where, S.P. = Selling Price, C.P. = Cost Price 

CALCULATION:

Here, we have C.P. = Rs550 , S.P. = Rs 580

⇒ Profit = (S.P. - C.P.) = (580 - 550) = Rs 30.

⇒  Profit% = (30 / 550 ) × 100 = 5.45%.

The correct answer is Amitav Ghosh

Key Points

• Amitav Ghosh is an Indian writer, best known for his English language historical fiction.
• He won the 54^th Jnanpith award in 2018, India’s highest literary honor.
• The Jnanpith Award is the oldest and the highest Indian literary award presented annually by the Bharatiya Jnanpith to an author for their "outstanding contribution towards literature".

Additional Information

• Sankha Ghosh was an Indian poet and literary critic.
• Krishna Sobti was an Indian Hindi-language fiction writer and essayist. She was awarded the Sahitya Akademi Award.
• Raghuveer Chaudhari is a novelist, poet and critic from Gujarat, India. He has also worked as a columnist for numerous newspapers.

The correct answer is CHOGM : Commonwealth Heads of Government Ministries 

Key Points

• Leaders of Commonwealth countries meet every two years for the Commonwealth Heads of Government Meeting (CHOGM).
• Hosted by different member countries on a rotating basis. Since 1971, a total of 25 meetings have been held, with the most recent being in the Rwanda in 2022.
• The Commonwealth is an association of countries across the world.
• Works to strengthen governance, build inclusive institutions and promote justice and human rights.

Additional Information

• CITES is a multilateral treaty to protect endangered plants and animals from the threats of international trade. It was drafted as a result of a resolution adopted in 1963 at a meeting of members of the International Union for Conservation of Nature.
• The Competition Commission of India is the chief national competition regulator in India. It is a statutory body within the Ministry of Corporate Affairs.
• The Centre for Development of Advanced Computing is an Indian autonomous scientific society, operating under the Ministry of Electronics and Information Technology.

According to the English alphabets and their positional values: 

The pattern followed in the given options is:

1) 

2) 

4) 

So, XSP is the odd one.

Hence the correct answer is option 1)

GIVEN:

2, 5 , 4, 1 , 8 

CONCEPT USED:

First, we have to arrange the given data as ascending number then we have to see how many number of data (n) are given 

If n is odd then, Median = (n +1 /2 )^th term

If n is even then, Median = [( n/2)^th term + {(n/2) + 1}^th term] /2  

CALCULATION:

First arranging the given data in ascending order we get

1,2,4,5,8.

Hence, total number of data(n) = 5, an odd number

Median = ( n+ 1 /2) ^th term  = ( 5 +1)/2 = 3^rd term

⇒  Median = 3^rd term = 4.

Hence, Median is 4.

According to the English alphabets and their positional values: 

The pattern followed in the given code is:

 Alphabets are increased by 3 positional values.

Similarly,

Hence the correct answer is option 4)

The correct answer is Child marriage

Key Points

• The Child Marriage Restraint Act 1929, approved by the Imperial Legislative Council of India on September 28, 1929.
• The act fixed the marriageable age for girls at 14 years and 18 years for boys.
• It is popularly known as the Sharda Act

Additional Information

• The** Indian custom of a wife immolating herself either on the funeral pyre of her dead husband or in some other fashion soon after his death**. Although never widely practiced, suttee was the ideal of womanly devotion held by certain Brahman and royal castes.
• Polygamy usually takes the form of polygyny – when a man marries multiple women.
• Infanticide (or infant homicide) is the intentional killing of infants or offsprings.

The correct answer is A geo-portal of ISRO with 3D imaging capabilities.

Key Points

• Bhuvan, is the national Geo-portal developed and hosted by ISRO comprising of Geo Spatial Data, Services and Tools for Analysis.
• It has many versatile features, for Example
• Visualization of Satellite Imagery and Maps
• Analysis
• Free Data Download.
• Download Reports to name a few.

Additional Information

• Bhuvan, is an Indian web based utility which allows users to explore a set of map based content prepared by Indian Space Research Organisation.
• The content which the utility serves is mostly restricted to Indian boundaries and is offered in 4 regional languages.

Given:

The first 100 positive integers are divisible by 3 or 4 without a remainder

Concept used:

If a number must be divisible by 3 and 4 both, then it must be divisible by 3 × 4 = 12.

Calculation:

From the first 100 positive integers, the first and the last numbers divisible by 3 are 3 and 99.

Number of numbers divisible by 3 between 3 and 99, including 3 = $\frac{99-3}{3}+1=33$

From the first 100 positive integers, the first and the last numbers divisible by 4 are 4 and 100.

Number of numbers divisible by 4 between 4 and 100, including 4 = $\frac{100-4}{4}+1=25$

From the first 100 positive integers, the first and the last numbers divisible by 12 are 12 and 96.

Number of numbers divisible by 12 between 12 and 96, including 12 = $\frac{96-12}{12}+1=8$

∴ The number of numbers from the first 100 positive integers which are divisible by 3 or 4 without a remainder is 33 + 25 - 8 = 50.

The correct answer is Bharat Heavy Electricals Limited

Key Points

• Bharat Heavy Electricals Limited is an Indian government owned engineering and manufacturing enterprise based in New Delhi, India.
• It is under the ownership of Ministry of Heavy Industries, Government of India
• It was Established in 1956.

Additional Information

• BHEL is India's largest power generation equipment manufacturer.
• The BHEL is one of the Public Sector Company in India, an Indian government owned engineering and manufacturing enterprise.

Given:

Formula used:

Calculation:

Distance between the two points = $\sqrt{(2-5)^2+(2-(-2))^2}=\sqrt{9+16}=5$ units

The correct answer is The Satavahana Dynasty 

Key Points

• The Satavahanas, also referred to as the Andhras in the Puranas, were an ancient Indian dynasty based in the Deccan region.
• Simuka was the founder of the Satavahana Dynasty.
• The Satavahanas were the first native Indian kings to have issued their own coins which had the rulers' portraits on them.
• Gautamiputra Satakarni started this practice which he imbibed from the Western Satraps after vanquishing them.

Additional Information

• Rashtrakuta was a royal Indian dynasty ruling large parts of the Indian subcontinent between the sixth and 10^th century.
• The earliest known Rashtrakuta inscription is a 7^th-century copper plate grant detailing their rule from Manapura, a city in Central or West India.
• ​The foundation for the Pandya supremacy in south India was laid by Maravarman Sundara I early in the 13^th century.

Given:

Maddy reads three-fifth of a chapter consisting of 75 pages. 

Concept used:

(3/5) × 75 = 45 pages

To find out how many more pages Maddy needs to read to complete the chapter, we need to subtract the number of pages he has already read from the total number of pages in the chapter:

Total number of pages in the chapter = 75 pages

Number of pages Maddy has read = 45 pages

Therefore, the number of pages Maddy needs to read to complete the chapter is:

75 - 45 = 30 pages

Maddy needs to read 30 more pages to complete the chapter.

The correct answer is Banabhatta.

Key Points​​​​

• India's Banabhatta was a poet and prose writer in Sanskrit during the seventh century. He served as the Asthana Kavi in King Harsha Vardhana's court.
• One of the finest writers in Sanskrit prose, Banabhatta is best known for his chronicle, Harshacharita, which describes the life of the Buddhist ruler Harsha of northern India and his court.
• From 606 until 647 CE, northern India was ruled by the Indian ruler Harshavardhana.

Additional Information​​​​

• In India's 12^th century, Vallal, a wealthy velir, lived in Puduvai and Thiruvenainallur.
• Jayachandra was a ruler of northern India's Gahadavala dynasty.
• Ananda Bhatta was a Bengali Shaivaite commentator on Vedanta who lived in the 16^th or 17^th century.

The correct answer is India.

Key Points

• The distinctive physical property of micas, a type of silicate mineral, is their ease in splitting into incredibly thin elastic plates.
• Mica are dielectric, insulating, and heat-tolerant. They are utilized in electrical equipment as a result of these qualities.
• One of the world's top producers and exporters of mica is India. It is mostly produced in Rajasthan, Andhra Pradesh, Bihar, Jharkhand, and Maharashtra.

 Additional Information​

• India's major producer of mica is Andhra Pradesh. India had a monopoly on the manufacturing and export of sheet mica around the world for more than a century.
• The two countries that export sheet mica the most internationally are India and Madagascar, with the majority of the mica being mined in unauthorised mines.
• The Andhra Pradesh state's Nellore mica belt is the biggest and most significant producer in the nation.

The correct answer is Liverpool.

Key Points

• The 16^th iteration of the FIFA Club World Cup took place in 2019.
• A competition between the winners of the six continental confederations and the league champions of the host country, organised by FIFA.
• Liverpool won the FIFA Club World Cup for the first time after defeating Flamengo 1-0 in a thrilling game in Doha, Qatar, thanks to an extra-time goal from Roberto Firmino.

Additional Information​

• Sumitomo, like all other clubs, reconstituted as the Kashima Antlers after the J.League's establishment and removed the corporate identity from its moniker.
• Flamengo, a Brazilian team and the current Copa Libertadores champions, represents CONMEBOL.
• With a 2-1 victory against opponents on the road, Monterrey guaranteed their entry into the World Club Cup.

The correct answer is The principle of a federation and parliamentary system.

Key Points​​​

• The 1935 Government of India Act was a piece of legislation modified by the British Parliament. It was first given royal approval in August 1935.
• It called for the creation of an All India federation with units made up of provinces and princely states. Three lists—the federal list, the provincial list, and the concurrent list—were used to distribute the powers between the centre and the units.
• It did away with dyarchy in the provinces and replaced it with "provincial autonomy."

Additional Information

• The 1858 act that constituted the Council of India was repealed. An advisory group was instead given to the secretary of state.
• The act called for the establishment of the Reserve Bank of India, the Federal Public Service Commission, and the Joint Public Service Commission.
• Separate electorates were also made available to the working class, ladies, and the depressed classes.

Given:

A bacterial population increases at the rate of 6% in the first 10 minutes and then 10% in the next 10 minutes.

Formula used:

value after x% increase in y = $\frac{100+x}{100}\times y$

Calculation:

Let the initial population be 100.

After the first 10 minutes the population is 106.

Then, in next 10 minutes the population is $\frac{110}{100}\times106=116.6$ 

∴ The overall percentage increase in the population at the end of 20 minutes is 16.6%.

Given:

The ratio of the radii of two spheres is 2 : 3.

Formula used:

The surface area of a sphere with radius r = $4\pi r^2$ 

Calculation:

Let the radii of the two spheres be a and b. 

Then, $\frac{a}{b}=\frac{2}{3}$ 

Ratio of their surface areas = $\frac{4\pi a^2}{4\pi b^2}=\left (\frac{a}{b}\right)^2=\left (\frac{2}{3}\right)^2=\frac{4}{9}$

∴ The ratio of the surface areas of the two spheres is 4 : 9.

From the given conditions:

I. If P, Q or R is chosen, U cannot be chosen.

II. Either T or U must be chosen.

III. S and Q cannot be chosen together.

Now if R is chosen:

According to I, we cannot choose U.

According to II, we have to choose between T or U but U can't be chosen so we get T.

According to III, we can choose either S or Q.

In the given options we have to find either TS or TQ:

So, option 2) has TS.

Hence the correct answer is option 2)

Given:

The sum of two numbers is 20 and their product is 96.

Formula used:

$(x+y)^2=x^2+ 2xy+y^2$

Calculation:

Let the two numbers be x and y. 

Then, xy = 96 and x+y = 20. 

Using $(x+y)^2=x^2+ 2xy+y^2$,

$x^2+y^2=20^2-2\times 96=400-192=208$

Using $(x-y)^2=x^2-2xy+y^2$

$(x-y)^2=208-2\times96=16$

$\implies(x-y)=\sqrt{16}=4$

∴ The difference between the two numbers is 4.

The correct answer is Force.

Key Points

• In the International System of Units, the unit of force is the newton. It is described as the force that accelerates a mass of one kilogramme by one metre per second per second, or 1 kg m/s2.
• F=ma, or force is equal to mass times acceleration, is the second of Newton's laws of motion.
• Force is the push or pull that an item experiences that result in a change in velocity.

Additional Information​

• The amount of force applied to a certain region is referred to as pressure. Therefore, you can either apply a large force or a force over a limited region to create a large amount of pressure.
• The quantity of energy moved or converted per unit of time is known as power.
• The obstruction to current flow in an electrical circuit is measured by resistance.

Given:

A can finish a work in 15 days and B can finish the same work in 20 days.

Concept used:

If A and B alone can finish a work in x and y days, respectively, then the reciprocal of the number of days taken by them to finish the  work while working together is $\frac{1}{x}+\frac{1}{y}$

Calculation:

Let A and B, together can finish the work in x days.

Then, $\frac{1}{x}=\frac{1}{15}+\frac{1}{20}$

Solving for x,

$x=\frac{15\times20}{15+20}=8.57$

∴ Working together, A and B can finish the same work in 8.57 days.

According to the English alphabets and their positional values: 

The pattern followed in the given options is:

1) 

2) 

4) 

So, HLG is the odd one.

Hence the correct answer is option 2)

The correct answer is 'Neil Armstrong'.

Key Points

• American astronaut and aeronautical engineer Neil Alden Armstrong became the first person to set foot on the moon.
• He also went on to become a navy pilot, check pilot, and professor.
• Armstrong was born and raised in Wapakoneta ,Ohio.
• He received numerous honours, including the Congressional Space Medal of Honor in 1978, the Presidential Medal of Freedom in 1969, and the Congressional Gold Medal in 2009.

Additional Information

• Buzz Aldrin is an American former astronaut, engineer and fighter pilot.
• As the commander of the 1966 Gemini 12 mission, he completed three spacewalks.
• Katherine Johnson was an American Mathematician, as a NASA employee her calculations of orbital mechanics were critical to the success of the first and subsequent U.S. crewed spaceflights.

Given:

$co{s^{ - 1}}\left( {\frac{1}{{\sqrt 2 }}} \right) + ;se{c^{ - 1}}\left( { - \sqrt 2 } \right)$

Formula used:

$co{s^{ - 1}}\left( {\frac{1}{{x }}} \right) + ;se{c^{ - 1}}\left( x \right)=\pi$

Calculation:

Using the identity $co{s^{ - 1}}\left( {\frac{1}{{x }}} \right) + ;se{c^{ - 1}}\left( x \right)=\pi$, 

$co{s^{ - 1}}\left( {\frac{1}{{\sqrt 2 }}} \right) + ;se{c^{ - 1}}\left( { - \sqrt 2 } \right)=1$

Therefore, the value of $co{s^{ - 1}}\left( {\frac{1}{{\sqrt 2 }}} \right) + ;se{c^{ - 1}}\left( { - \sqrt 2 } \right)$ is 1.

• The correct answer is 'Cytology'.

Key Points

• ​Cytology is generally used on samples of free cells or tissue fragments, in contrast to histopathology, which studies whole tissues.
• There is also the use of cytology to diagnose medical conditions in other tissues of the body, generally referred to as non-gynaecological or diagnostic cytology.
• Cell is the basic unit of life that is responsible for the living and functioning of organisms.
• It is also called as Cytopathology.

 Additional Information

• Serology is used for historically to confirm infections with bacteria, fungi, and viruses that are not easily detected**.**
• The cause of a disease or abnormal condition is known as 'Etiology'
• Cytoplasm is a thick solution that fills each cell and is enclosed by the cell membrane. .