RRB NTPC CBT-I Official Paper (Held On: 30 Jan 2021 Shift 1) (Previous Year Paper)

The alphabets and their positions are:

The logic here is:

So, the WIRE is coded as SENA.

Similarly, the word REPORT is coded as NALKNP

Hence, the correct answer is 'option 4'.

Given:

Data arranged in ascending order 8, 10, 12, 15, x, x + 2, 20, 25, 30, 32 and its median is 17.

Formula used:

Median for arranged even number of terms = $\frac{\text{sum of the middle two numbers}}{2}$

Calculation:

median =  17 = $\frac{x+x+2}{2}$

Solving for x,

x = 17 - 1 = 16

∴ The value of x is 16.

The alphabets and their positions are:

The logic here is:

Hence, the correct answer is 'option 4'.

The correct answer is the Coral Sea.

Key Points

• The Great Barrier Reef is a site of remarkable variety and beauty.
• The reef is located off the coast of Queensland, Australia, in the Coral Sea.
• It contains the world’s largest collection of coral reefs, with 400 types of coral, 1,500 species of fish, and 4,000 types of mollusc.
• It also holds great scientific interest as the habitat of species such as the dugong (‘sea cow’) and the large green turtle, which are threatened with extinction.

Additional Information

• The Beaufort Sea- It is a marginal sea of the Arctic Ocean, located north of the Northwest Territories, the Yukon, and Alaska, and west of Canada's Arctic islands.
• The Celtic Sea- It is the area of the Atlantic Ocean off the south coast of Ireland.
• The Caspian Sea- It is the world's largest water body that is enclosed or bordered by land on all sides. Russia, Iran, Azerbaijan, Kazakhstan, and Turkmenistan touch the border of the sea.

The correct answer is Minimum Reserve System.

Key Points

• The Minimum Reserve System is the currency issue system followed by the RBI to issue currency notes at present.
• It was adopted in 1956. The Proportional Reserve system was used to issue notes before 1956.
• The Minimum Reserve System requires the RBI to keep a minimum reserve of Rs 200 crores comprising foreign currencies, gold coins, and gold bullion.
• Out of this 200 crore, a minimum of 115 crores rupee should be in the form of Gold or gold bullion, and the rest should be in the form of foreign currencies.
• There is no limit for the RBI to issue currencies by keeping this minimum reserve.

The correct answer is P. V. Narasimha Rao.

Key Points

• A Telugu Novel was translated into Hindi by India's 9^th Prime minister Sri PV Narasimha Rao, with the name Sahasra Phan.
• The original novel, Veyi Padagal, was written by Viswanath Satyanarayana.
• The Hindi translation, Sahasra Phan, was done in the year 1968.

Additional Information

• The novel was also translated from Hindi into Sanskrit with the same name by Prabhavati Devi.
• In 1976, Chandrakant Mehta and Mahendra Dhave translated this novel into Gujarati.
• Later, R.V.S. Sundaram translated the work into Kannada.
• In 1998, it was published in a Kannada newspaper as Nootana.

The correct answer is Saurashtra.

Key Points

• Saurashtra won the 86^th Ranji Trophy Title by defeating Bengal.
• It was played between 9 to 13 March 2020 in Saurashtra Cricket Association Stadium, Rajkot.
• The 2019–20 Ranji Trophy was the 86^th season of the Ranji Trophy, which took place between December 2019 and March 2020.

Additional Information

• The Ranji Trophy is a domestic first-class cricket championship played in India.
• The competition currently consists of 38 teams, with all 28 states in India and four of the eight union territories having at least one representation.
• The competition is named after the first Indian cricketer who played international cricket, Ranjitsinhji, who was also known as Ranji.
• The very first match of the competition was held on 4 November 1934 between Madras and Mysore at the Chepauk ground in Madras.

The correct answer is a volcanic mountain. 

Key Points

• Mount Kilimanjaro is a dormant volcano in Tanzania, Africa.
• It has three volcanic cones: Kibo, Mawenzi, and Shira.
• It is the highest mountain in Africa.

Additional Information

Important volcanoes around the world

The correct answer is Andhra Pradesh.

Key Points

• Indian Space Research Organization's Satish Dhawan Space Centre is located at Nellore District, Andhra Pradesh.
• Satish Dhawan Space Centre (SDSC), Sriharikota, the Spaceport of  India, is responsible for providing Launch Base Infrastructure for the Indian  Space Programme.

Additional Information

Given:

a + b + c = 10

ab + bc + ca = 31

Identity used:

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Calculation:

Using the mentioned identity

10² = a2 + b2 + c2 +2(31)

a2 + b2 + c2 = 100 - 62 = 38

∴ The value of a2 + b2 + c² is 38

Given:

5% more is gained by selling a cow for Rs. 1,010 than what is gained by selling it for Rs. 1,000.

Formula used:

Profit = $\frac{\text{selling price - cost price}}{\text{cost price}}\times 100$

Calculation:

Let the cost price be x.

Then,

$\frac{1010-x}{x}-\frac{1000-x}{x}=\frac{5}{100}$

Solving for x,

$\frac{10}{x}=0.05$

$x=\frac{10}{0.05}=200$

∴ The cost price (in Rs.) of the cow is 200.

Formula used:

Mean = $\frac{\text{sum of observations}}{\text{no. of observations}}$

Calculation:

Mean = $\frac{9+35+20+25+25+15+25}{7}=22$

Arranging the data in ascending order - 9, 15, 20, 25, 25, 25, 35.

Therefore, the median is 25.

Mode is the observation with highest frequency. Hence the mode of the given data is 25.

∴ The sum of the mean, median and mode of the given data is 22 + 25 + 25 = 72.

Given: Daman and Diu : Daman :: Andaman and Nicobar : ?

Logic = Islands : Capital city

As we know that, Daman is the capital city of the Daman and Diu islands.

Similarly the capital city of Andaman and Nicobar islands (a union territory of India in the Bay of Bengal) is 'Port Blair'.

Hence, the correct answer is 'option 4'.

The correct answer is Khetri Mahal at Jhunjhunu.

Key Points

• Hawa Mahal at Jaipur was inspired by Khetri Mahal or the Wind Palace in Jhunjhunu, Rajasthan.
• It was built by Maharaja Sawai Pratap Singh, the grandson of Maharaja Sawai Jai Singh, who was the founder of the city of Jaipur.
• It was built from red and pink sandstone.

Additional Information

Famous places in Rajasthan

Given:

Cost price of 15 notebooks = Selling price of 12 notebooks.

Formula used:

percentage change = $\frac{\text{selling price - cost price}}{\text{cost price}}\times 100=25\%$

Calculation:

Let the cost price of one notebook be Rs. 100.

Then, the cost price for 15 notebooks is 15 × 100 = Rs. 1500.

This means that the 12 notebooks are sold at Rs. 1500 when the cost price for 12 notebooks is Rs. 1200.

percentage change = $\frac{1500-1200}{1200}\times 100=25\%$

∴ There is a gain of 25%.

From given statements, we have the Venn diagram as:

Thus, combining both the statements, we get,

Next, we will check the conclusions as:

1. Some villas are expensive: Since, we have some expensive are villas and so some villas are expensive. This is true.
2. No flat is Villa: Since some flats are expensive and some expensive are villas. So, some flats are villas is possible. This is not true.
3. Some villas are flats: Since some flats are expensive and some expensive are villas. So, this is not true.
4. All villas are expensive: Since some expensive are villas and some villas are expensive but not all. This is not true.

Hence, only 'conclusion I' is true.

Given:

In a triangle the ratio of angles is 2 : 3 : 4. 

Concept used:

The sum of all three angles of a triangle is 180°.

Calculation:

Let the three angles be 2x, 3x and 4x.

Then, 2x + 3x + 4x = 180

Solving for x, 

$x=\frac{180}{9}=20^{\circ}$

∴ The  difference between the greatest and the smallest angle is (4×20 - 2×20) = 40°.

Calculation:

Let the numerator of the original fraction be x.

Then, the denominator is 'x+5'

Then, $\frac{x-2}{x+5+2}=\frac{2}{5}$

Solving for x,

5x -10 = 2x +14

$x=\frac{24}{3}=8$

∴ The original fraction is $\frac{8}{13}$.

The correct answer is mica.

Key Points

• Muscovite, pegmatite and biotite are ores of mica.
• Muscovite is a hydrated phyllosilicate mineral of aluminium and potassium with formula KAl2(AlSi3O10)(FOH)2, or (KF)2(Al2O3)3(SiO2)6(H2O).
• Pegmatite is an igneous rock and is composed of quartz, feldspar, and mica, having a similar silicic composition as granite.
• Biotite is a common group of phyllosilicate minerals with the approximate chemical formula K2AlSi3O10.

 Additional Information

• Minerals and their ores

From the given statements, we draw the Venn diagram as:

Thus, combining the statements, we get,

Next, we will check all the conclusions as:

1. All cats are dogs: Since some dogs are cats and so some cats are dogs but not all. This is not true.
2. Some rats are dogs: Since no cat is rat and some dogs are cats. So, no dog is a rat. This is not true.
3. All mosquitoes are dogs: Since all rats are mosquitoes and and no cat is a rat. This is not true.
4. No mosquito is a dog: Since no cat is rat and all rats are mosquitoes. So no mosquito is a cat and also no mosquito is a dog. This is true.

Hence, only 'conclusion 4' is true.

Given:

Length = 18 m 

 A road of width 3 m is constructed outside the square around it.

Formula used:

Area of a square = length × length 

Calculation:

Area of the park = 18 × 18 = 324 m2 

If the width of the road is 3 m then the length of the outer boundary of the road is 18 + 3 + 3 = 24 m.

Area within the outer boundary of the road =  24 × 24 = 576 m² 

∴ The area of the road is 576 - 324 = 252 m2

Given:

Lengths $3\frac{1}{2} \ m \ \text{and} \ 8 \frac{3}{4} \ m.$

Formula used:

HCF of the two fractions = $\frac{\text {HCF of the two numerators}}{\text {LCM of the two denominators}}$

Calculation:

Here,  $3\frac{1}{2} =\frac{7}{2} \ m \ \text{ and } \ 8 \frac{3}{4} = \frac{35}{4} \ m$

HCF of the numerators = HCF(7,35) =  7

LCM pf the denominators = LCM(2,4) = 4

HCF of the two fractions =  $\frac{7}{4}$

∴ The greatest possible length that can be used to exactly measure the lengths is $\frac{7}{4}$ m.

The correct answer is 700%.

Key Points

• The formula for the volume of a right circular cylinder πr²h;
• where π= 22/7,
• r= radius of the cylinder, and
• h= height.
• The volume of the original cylinder is πr²h.
• The volume of the new cylinder will be π(2r)²(2h)= π4r²2h= 8πr2h.
• Increment in volume =  8πr²h-  πr2h=  7πr2h.
• Percentage increase= (7πr2h/πr2h)x100 = 700 %

The correct answer is five.

Key Points

• The State Banks (Repeal and Amendment) Bill, 2017 seeks to repeal the State Bank of India (Subsidiary Banks) Act, 1959, the State Bank of Hyderabad Act, 1956.
• These Acts merged the following subsidiary banks of SBI-
• State Bank of Bikaner
• State Bank of Mysore
• State Bank of Patiala
• State Bank of Travancore
• State Bank of Hyderabad
• Source- https://prsindia.org/billtrack/the-state-banks-repeal-and-amendment-bill-2017

Additional Information

• About SBI- 
• Established- 1 July 1955
• Headquarters- Mumbai, Maharashtra
• Chairperson- Dinesh Kumar Khara (Feb 2022)

Given:

A 450 m long train travelling at the speed of 80 km/h crosses a platform of length 150 m.

Formula used:

Time taken = $\frac{\text{distance traveled}}{\text{speed}}$

Calculation:

Time taken =  $\frac{(450+150)\times60\times60}{80\times1000}=27s$ 

∴ The time taken by a 450 m long train travelling at the speed of 80 km/h to cross a platform of length 150 m is 72 seconds.

Given:

An inlet pipe can fill a tank in 4 h and an outlet pipe can empty the tank in 6 h.

Formula used:

If a task is finished in x hours, the in an hour $\frac{1}{x}$ of the task is finished.

Calculation:

The inlet pipe can filled $\frac{1}{4}$ of the volume of the tank in an hour and the outlet pipe can empty $\frac{1}{6}$ the tank in an hour.

Therefore, if both the pipes are open, then in one hour the tank filled upto $\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$ of the total volume.

∴ The number of hours in which the tank will be half-full is $\frac{12}{2}=6$ hours.

The correct answer is Weightlifter.

Key Points

• Saikhom Mirabai Chanu is an Indian weightlifter.
• She is the winner of the silver medal at the 2020 Tokyo Olympics in the Women's 49 kg category.
• She belongs to Nongpok Kakching village in Manipur's Imphal East district.

Additional Information

Given: Eight persons A, B, C, D, E, F, G and H are sitting a around a circular table facing towards the centre.

According to the given statement, we have:

1) B sits third to the right of A.

2. A is second to the right of C.

3. Only two persons sits between C and E.

4) F is not the neighbour of C or E.

5. H sits second to the left of D. 

Thus, the final sitting arrangement is:

Hence, 'D' is sitting third to the left of G.

The correct answer is a concave lens.

Key Points

• The concave lens is a type of lens that is thin in the middle but thick at its periphery.
• A concave lens is also called diverging lens meaning that it spreads out light rays that have been refracted through it.
• A concave lens is used to correct short-sightedness (myopia) and is also used in binoculars, telescopes, cameras, flashlights.

Additional Information

• Convex lens- 
• It is thick in the middle and thin at its periphery.
• It is also called converging lens meaning that it will focus all the rays of lights (coming from infinity) at its focus.
• A convex lens is used to correct farsightedness. It is also used as a simple reading lens.

Shortcut Trick 

let a = 1, b = 1, c = -2

So,

$\frac{(a^2 + b^2 + c^2)^2}{a^2 b^2 + b^2 c^2+c^2a^2}$

Numerator:

(a² + b² + c²)² = (1² + 1² + (-2)²)² = (1 + 1 + 4)² = 6² = 36

Denominator:

a²b² + b²c² + c²a²

= 1².1² + 1².(-2)² + (-2)².1²

= 1 × 1 + 1 × 4 + 4 × 1 = 1 + 4 + 4 = 9

So, required answer = 36/9 = 4

∴ The correct answer is option (3).

Alternate Method

Given:

a + b + c = 0

Concept Used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculation:

⇒ We have, a + b + c = 0

⇒ Squaring both the sides, we get

⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 0

⇒ a2 + b2 + c2 = –2(ab + bc + ca)             → (1)

⇒ Now to find the value, $\frac{(a^2 + b^2 + c^2)^2}{a^2 b^2 + b^2 c^2+c^2a^2}$

⇒ Putting the value of (1), we get

⇒ $\frac{(-2(ab+bc+ca))^2}{a^2b^2+b^2c^2+c^2a^2}$

⇒ $\frac{4(a^2b^2+b^2c^2+c^2a^2)}{a^2b^2+b^2c^2+c^2a^2}=4$

Therefore, the required value of $\frac{(a^2 + b^2 + c^2)^2}{a^2 b^2 + b^2 c^2+c^2a^2}$ is 4

Formula used:

Surface area of a cuboid =  2(l × b + b × h + l × h), where l, b and h are the length, breadth and height, respectively. 

Calculation:

Length, breadth and height of the cuboid formed are 16×3=48cm, 16cm and 16cm, respectively. 

Surface area of the cuboid = 2(48 × 16 + 48 × 16 + 16 × 16) = 3584 cm2 

∴ The surface area of the cuboid so formed is 3584 cm2

Given:

Lengths 7 m, 3 m 85 cm and 12 m 95 cm.

Concept used:

Highest common factor

Calculation:

Here, 7 m = 700 cm, 3 m 85 cm = 385 cm and 12 m 95 cm = 1295 cm

HCF of 700, 385 and 1295 = 35

∴ The greatest possible length that can be used to measure exactly the lengths 7 m, 3 m 85 cm and 12 m 95 cm is 35 cm.

The correct answer is Bihar. 

Key Points

• Valmiki National Park is a Tiger Reserve in the West Champaran District of Bihar, India.
• It is the only national park in Bihar.
• The national park is spread across Nepal as well and in Nepal, it is called Chitwan National Park.

Additional Information

Concept used:

For a given number to be divisible by 11, the difference between the sums of the first alternative digits and the second alternative digits must be divisible by 11.

Calculation:

Sum of first alternative digits = 6+8+3+2 = 19

Sum of second alternative digits = 7+4+A = 11 + A

Difference = 19 - (11 + A) = 8 -  A

Since difference must be divisible by 11 and A is a single digit whole number, A = 8.

∴ The value of A is 8.

Formula used:

n^th term of an A.P. with common difference d and first term a = $a+(n-1)d$

Calculation:

First number between 1000 and 3000 that is divisible by 7 is 1001 and the last number in the same range, divisible by 7 is 2996.

The numbers divisible by 7, from 1001 to 2996 are in an arithmetic progression with common difference as 7.

Therefore, the last nth term can be written as $2996=1001+(n-1)7$ 

Solving for n, 

$2996=1001+7n-7$

$n=\frac{2002}{7}=286$

∴ The number of numbers between 1000 and 3000 that are completely divisible by 7 is 286

The correct answer is 1906.

Key Points

• The All-India Muslim League was a political party established in 1906 in British India.
• The All-India Muslim League is popularly called the Muslim League.
• It was founded by Nawab Khwaja Salimullah on 30 December 1906 at Dacca, British India (now Dhaka, Bangladesh)
• The party was primarily formed due to the need for the political representation of Muslims in British India.

Formula used:

tan θ = cot (90 - θ)

tan θ × cot θ = 1

Calculation:

tan 1° . tan 2° . tan 3° ......... tan 89°

⇒ tan 1° × tan 2° ....... tan 45° .........tan 88° × tan 89°

⇒ tan (90 - 89) × tan (90 - 88)......tan 45°......tan 88° × tan 89°

⇒ cot 89° × cot 88°......tan 45°......tan 88° × tan 89°

⇒ 1

∴ The correct answer is option (2).

Given:

1216 - 32D

Concept used:

For a number to be divisible by 8, the last three digits must be divisible by 8.

Calculation:

If DDD is divisible by 8, then D = 8.

∴ The value of D is 8.

The correct answer is the Third Schedule.

Key Points

• Forms of Oaths or Affirmations for Ministers, Ministers of State, Members of Parliament, and Candidates and other important officeholders of the country are contained in the Third Schedule.

Additional Information

• There are a total of twelve schedules in the Indian constitution that deals with different subjects as given below-

Given:

$\frac{2\sqrt 2+ \sqrt 7}{2\sqrt 2 - \sqrt 7} = x+ y \sqrt {14}$

Concept used:

Rationalizing the denominator

Calculation:

Rationalizing the left hand side of the equation,

$\frac{(2\sqrt 2+ \sqrt 7)\times ({2\sqrt 2 + \sqrt 7})}{(2\sqrt 2 - \sqrt 7) \times ({2\sqrt 2 + \sqrt 7})} = \frac{8+7+4\sqrt{14}}{8-7}=15+4\sqrt{14}$

∴ The value of y is 4.

Given statement: In the modern era, lack of water availability is a major problem especially in summer times.

According to the statement, there is lack of water availability in major problem, but they not mentioned that the animal death is the main cause. So, conclusion I does not follow. Also, there is shortage of water in summer times, but not mentioned anything about winter. So, conclusion II does not follow.

Thus, 'neither conclusion I nor II' follows.

Hence, the correct answer is 'option 3'.

Given:

Mona was residing at a place 'X' from 17 February 2012 to 27 April 2012.

Concept used:

In a leap year, February consists of 29 days. 

Calculation:

2012 is a leap year, so February will have 29 days. Therefore, number of days she stayed in February is 29 -17 + 1 = 13

In March, 31 days.

In April, 27 days.

∴ The number of days Mona was residing at place 'X' is 13 + 31 + 27 = 71.

The correct answer is Guru Shikhar.

Key Points

• Guru Shikhar is the highest peak in the Aravalli Range at 5650 feet (1722 meters) in Mount Abu of Rajasthan.
• It is lies near the south-western extremity of the Central Aravalli range, close to the border with Gujarat state.
• About Aravalli:
• The Aravalli's of Northwestern India, one of the oldest fold mountains of the world, now form residual mountains with an elevation of 300m to 900m.
• They stretch for a distance of 800 km. from Himmatnagar in Gujarat to Delhi, spanning Haryana, Rajasthan, Gujarat, and Delhi, the 692 kilometers (km).
• The mountains are divided into two main ranges, the Sambhar Sirohi Range and the Sambhar Khetri Range in Rajasthan, where their extension is about 560 km.
• These are fold mountains of which rocks are formed primarily of the folded crust when two convergent plates move towards each other by the process called orogenic movement.
• The Aravallis act as a barrier between the fertile plains in the east and the sandy desert in the west.
• Historically, it is said that the Aravalli range checked the spread of the Thar desert towards the Indo-Gangetic plains, serving as a catchment of rivers and plains.

Additional Information

• Om Parvat:
• The ancient peak Om Parvat is situated in the Himalayan Mountain Range that is located in western Nepal's Darchula District.
• It is clipped on the border of India and Nepal.
• The massively fascinating impression of Om Parvat is that it is witnessed as the one being formed naturally as soon as the deposition of the snow commences with the backdrop of the mountain that is black in color.
• Om Parvat is situated nearby Nabhi Dhang camp (Nepal) and this majestic peak does not fall in our Kailash Yatra route.
• Kamet Peak:
• Kamet Peak is the highest point in the Zanskar range located at an altitude of 7756 meters.
• Zaskar Range also called Zanskar, group of mountains in the Himalayas, of northern India and the western Tibet Autonomous Region of China.
• They extend southeastward for some 640 km from the Karcha River to the upper Karnali River.
• The most important passes are Shipki, Lipu Lekh, and Mana.
• Zaskar is drained by the Zaskar River which flows northward, joining the Indus River below Leh.

From the given statements, we draw the Venn diagram as:

Thus, combining all the statements we get,

Next, we will check all the conclusions as:

1. No men is animal: Since some animal are men and so men are animal. This is not true.
2. All animals are birds: Since all birds are animals and so some animals are birds but not all. This is not true.
3. Some men are animals: Since some animals are men and so some men are animals. This is true. 
4. Some men are birds: Since all birds are animals and so some animals are men. So men are birds is not possible. This is not true.

Hence, only conclusion 3 is true.

Concept used:

BODMAS rule :- Any mathematical expression must be simplified by using the following priority order-Brackets, order of power, division, multiplication, addition and then subtraction. 

Calculation:

$\frac{4}{11} \times \frac{121}{16}\times 24 (75^2 - 55^2) \times \frac{1}{100}$ = $\frac{11}{4}\times 24(5625-3025)\times \frac{1}{100}=\frac{11\times 6\times2600}{100}=1716$

∴ The value of the given expression is 1716.

Given:

Rs. 8,000 is compounded at 10% per annum half yearly for $1\frac{1}{2}$ years.

Formula used:

Amount after n years =  $P\left(1 + \frac{r}{100} \right)^n$, P is the principle amount, r is the interest rate per annum.

Calculation:

Here, P = 8000, r = 5, n = 3  

Amount after first year = $8000\left(1 + \frac{5}{100} \right)^3=9261$

∴ The interest (in Rs.) on Rs. 8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years is 1261.

The correct answer is 2 percent.

Key Points

• According to the Election Commission of India, a political party shall be eligible to be recognized as a national party only if it fulfils any one of the following three conditions:
• It wins at least 2% (11 seats) in the Lok Sabha and these members are elected from at least three different states.
• And It secures at least 6% of the total valid votes polled in any four or more states at a general election to the Lok Sabha or to the State Legislative Assembly. In addition,  it wins at least 4 seats in Lok Sabha from any State or states.
• A party gets recognition as State Party in four or more States.

Additional Information

• Lok Sabha is also known as a lower house or a temporary house.
• The total strength of the Lok Sabha is 552 .
• In January 2020 The seats reserved for Anglo Indians in Parliament and State Legislatures of India were discontinued by the 126^th Constitutional Amendment Bill of 2019 enacted as 104^th Constitutional Amendment Act 2019.
• The tenure of Lok Sabha is 5 years and it can be dissolved by the President of India before the expiration of tenure.
• The first male speaker of Lok Sabha is Ganesh Vasudeo Mavalankar and the first female speaker is Meira Kumar.
• At present, there are 543 Lok Sabha constituencies and this number has not changed since 1971.

Given:

A and B can finish a task in 18 days, B and C can finish the same task in 27 days. A, B and C together can finish it in 12 days.

Formula used:

If A and B alone finish a task in a and b days, then the reciprocal of the days taken for them to finish the task together is $\frac{1}{a}+\frac{1}{b}$

Calculation:

Here, $\frac{1}{a}+\frac{1}{b}=\frac{1}{18}$     ...(1)

$\frac{1}{b}+\frac{1}{c}=\frac{1}{27}$      ...(2)

$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{12}$     ...(3)

From (1) and (3), $\frac{1}{c}=\frac{1}{12}-\frac{1}{18}$

From (3) and (3), $\frac{1}{a}=\frac{1}{12}-\frac{1}{27}$

This means that $\frac{1}{a}\frac{1}{c}=\frac{2}{12}-\frac{1}{18}-\frac{1}{21}=\frac{2}{27}$

∴  A and C will finish the task in $\frac{27}{2}=13\frac{1}{2}$ days.

The correct answer is Sidhu and Kanhu.

Key Points

• Santhal uprising was led by Siddhu and Kanhu it took place during 1855-56.
• Santhal uprising was a rebellion of Santhal tribes settled in Rajmahal Hills in Bihar (Now in Jharkhand against British and zamindars).
• The tyrannical British revenue system, usury practices, and the zamindari system in India made Santhal peoples annoyed, and two Santhal brothers Sidhu and Kanhu Murmu organized 10,000 Santhals and proclaimed a rebellion against the British.
• The Santhals are the largest tribal group in India found in Jharkhand, West Bengal, and Odisha.

Additional Information

• Britishers invited the Santhals to come and settle in Jharkhand promising land and economic amenities.
• Thus Santhals from different states came to settle in today's Jharkhand.
• Later zamindars dominated these areas as they collected taxes and lent money at very high rates which the people could not generally pay and their lands were forcibly taken.
• This became the roots of the Santhal rebellion.
• In a fierce encounter, Santhals were defeated as they were fighting with bows and arrows while Britishers had modern weapons.
• Sidhu was caught in August 1855 and was hanged on a banyan tree at a place called Panchkathia.

Given: A team of 5 members is to be selected from 5 men M1, M2, M3, M4 and M5 and 6 women W1, W2, W3, W4, W5 and W6.

According to the given statements:

1) M5 cannot be selected with W4 or M4.

⇒This means option 1 (i.e. M2, W2, W4, M5, W6) is eliminated.

2. M2 must be selected with M5. Also, given that there are at least three women in the team

⇒This means option 2 (i.e. M2, W3, M5, M3, W2) is eliminated.

3) M1 cannot be selected with M3.

⇒This means option 4 (i.e. M1, W2, W4, W6, M3) is eliminated.

4) W6 cannot be selected with M2 or W1 or W2. W5 cannot be selected with W6 or W2 or M2.

⇒This means option 3 (i.e. M1, W5, W4, M4, W3) is true.

Hence, the correct answer is 'option 3'.

The alphabets and their positions are:

First we will check all the options as:

1. CF:

2. AD:

3. OR:

4. VX:

Thus, we see that all follow the same pattern except 'VX'. 

Hence, the odd one is 'VX'

The correct answer is Article 108.

Key Points

• Article 108 of the Indian Constitution provides for a joint sitting of both Houses of Parliament. Accordingly, a joint session can be summoned when:
• If after a bill is passed by one House and transmitted to the other House.
• The other House rejects this bill, or
• The Houses do not agree on the amendments made to the bill, or
• More than six months elapsed with the bill being received by the other House without it being passed.
• Then, the President can summon a joint sitting unless the bill had elapsed because of the Lok Sabha's dissolution.

Additional Information 

The logic here is:

Hence, the next number is '288',

The correct answer is the Competition Commission of India.

Key Points

• Competition Commission of India:
• It is the chief national competition regulator in India.
• It is a statutory body within the Ministry of Corporate Affairs and is responsible for enforcing the Competition Act, 2002 in order to

promote competition and prevent activities that have an appreciable adverse effect on competition in India.

• CCI also approves combinations under the act so that two merging entities do not overtake the market.
• The commission was established on 14 October 2003.
• It became fully functional in May 2009 with Dhanendra Kumar as its first Chairman.

Additional Information

• Research and Analysis Wing:
• RAW (Research and Analysis wing) is India's External Intelligence agency.
• Headquartered in New Delhi.
• RAW came into being on September 21^st, 1968, after the Sino-Indian war of 1962 and the India-Pakistan war of 1965, which exposed gaps in intelligence gathering undertaken by the Intelligence Bureau.
• RAW's first director was Rameshwar Nath Kao.
• The head of RAW is called the "Secretary" (research) in the cabinet secretariat. The current chief of RAW is Samant Kumar Goel. (Feb 2021).
• RAW is only answerable to the Prime Minister of the country, and the Joint Intelligence Committee, Hence it is exempted from RTI Act .
• Intelligence Bureau:
• It is the internal intelligence agency of our country.
• IB shares intelligence with the other intelligence agencies and the police.
• IB director- Arvind Kumar (Oct 2021).

The correct answer is 249.

Key Points

• According to the Public Enterprises Survey 2018-19, 249 Central Public Sector Enterprises (CPSEs) were in operation in India as of 31^st March 2019.

Additional Information

• Economic Survey:
• The Economic Survey of India is an annual document released by the Ministry of Finance, Government of India.
• It contains the most authoritative and updated source of data on India's economy.
• India's estimated GDP growth rate for 2018-19 in the Economic Survey was 7% - 7.5%.
• It is a report that the government presents on the state of the economy in the past year, the key challenges it anticipates, and their possible solutions.
• The Economic Survey document is prepared by the Economics Division of the Department of Economic Affairs (DEA) under the guidance of the Chief Economic Advisor.
• It is usually presented a day before the Union Budget is presented in the Parliament.
• The first Economic Survey in India was presented in the year 1950- 51.
• Up to 1964, it was presented along with the Union Budget. From 1964 onwards, it has been delinked from the Budget.

The correct answer is World Bank.

Key Points

• The International Development Association (IDA) provides interest-free loans – called credits – and grants to governments of the poorest countries. Together, IBRD and IDA make up the World Bank.
• The International Bank of Reconstruction and Development (IBRD) is one of the two major institutions that make up the World Bank.
• The IDA is a financial institution dedicated to making developmental loans to the world's poorest countries.
• Together, IBRD and IDA make up the World Bank.

Additional Information

• ​The United Nations is an international organization founded in 1945.
• The International Labor Organization (ILO) is devoted to promoting social justice and internationally recognized human and labour rights, pursuing its founding mission that labour peace is essential to prosperity.
• The International Monetary Fund (IMF) works to achieve sustainable growth and prosperity for all of its 190 member countries.
• The World Bank is an international development organization owned by 187 countries.

Given:

Total students = 130

Likes both Maths and History = 15

Likes only Hindi = 25

Likes only English = 30

Likes both English and Hindi = 20

Likes only History = 15

Likes only Maths = 15

Total who like English = 60

Total who like Hindi = 55

Total who like Maths = 40

Total who like History = 40

Formula Used

Total in a group = Only + Sum of all pairwise intersections + Thrice all three intersections + 4 times all four intersections.

Calculation:

Likes only English and Hindi = 20

Total who like English = Only English + English and Hindi + All four subjects

⇒ 60 = 30 + 20 + All four subjects

⇒ 60 = 50 + All four subjects

⇒ All four subjects = 60 - 50 = 10

∴ The number of students who like all four subjects is 10.

The correct answer is Calcutta.

Key Points

• Mahatma Gandhi was in Calcutta on the day India got Independence.
• Champaran was the first initiative of Mahatma Gandhi as a nationalist in India.
• Mahatma Gandhi was the leader who guided India towards Independence. India was under British rule for over 250 years.
• Gandhi returned to India from South Africa in 1915 at the request of Gopal Krishna Gokhale.
• Mahatma Gandhi's famous contributions to the Indian freedom movement.
• Champaran Satyagraha (1917):
• The Champaran agitation in Bihar was Gandhi's first active involvement in Indian freedom politics.
• The Champaran farmers were being forced to grow Indigo and were being tortured if they protested.
• The farmers sought Gandhi's help and through a calculated non-violent protest, Gandhi managed to win concessions from the authority.

Given:

$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03}\times \frac{1}{0.003}$

Concept used:

Division

Calculation:

$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03}\times \frac{1}{0.003}$ = $9\times3\times3\times3=243$

∴ The value of the given expression is 243.

Given:

A kite is flying with a thread of length 296 m, making an angle of elevation measuring 30° at a point of hand of a person of height 2 m from the ground.

Formula used:

sin(30°) =  0.5

Calculation:

The height of the kite from the person's hand = 296sin(30°) = 296 × $\frac{1}{2}$ = 148m

∴ The height of the kite from the ground is 148 + 2 = 150 m

The correct answer is Graphic User Interface.

Key Points

• GUI (graphical user interface):
• It is a system of interactive visual components for computer software.
• A GUI displays objects that convey information, and represent actions that can be taken by the user.
• The objects change color, size, or visibility when the user interacts with them.
• It allows users to interact with electronic devices through graphical icons and an audio indicator such as primary notation, instead of text-based user interfaces, typed command labels, or text navigation.

The correct answer is Odisha.

Key Points

• Odisha contributes around 90% of the total production of chromite in the country.
• Chromite is the only economic ore of chromium which is an oxide of iron and chromium which is used in chrome plating and alloying for the production of various materials such as corrosion-resistant superalloys, nichrome, stainless steel, etc.
• It is used for the production of Disodium that is necessary for the production of stainless steel.
• Apart from Odisha, Maharashtra, Tamil Nadu, Jharkhand, and Karnataka also contribute to chromite production in the country.
• Karnataka is the second-largest producer of chromite.

The alphabets and their positions are:

The logic here is:

Hence, the next letter is 'X'.

The correct answer is David Malpass.

Key Points

• David R. Malpass was selected as 13^th President of the World Bank Group by its Board of Executive Directors on April 5, 2019.
• Mr. Malpass previously served as Under Secretary of the Treasury for International Affairs for the United States.
• He was a senior economic adviser to US President Donald Trump during his 2016 election campaign.
• Malpass succeeds Jim Yong-Kim, who stepped down on February 1 to join an investment firm.
• Mr. Malpass represented the United States in international settings, including the G-7 and G-20 Deputy Finance Ministerial, World Bank- IMF Spring and Annual Meetings, and meetings of the Financial Stability Board, the Organization for Economic Cooperation and Development, and the Overseas Private Investment Corporation.

Additional Information

The correct answer is White Vitriol.

Key Points

• Zinc Sulphate is the chemical compound name of the white vitriol.
• It is a compound and dietary supplement that is inorganic.
• Zinc sulphate is formed by treating nearly every zinc-containing substance (metal, rocks, oxides) with sulfuric acid.
• The reaction of a metal with aqueous sulphuric acid involves a specific reaction:
• Zn + H₂SO₄ + 7H₂0 - ZnSO₄.7H₂O + H₂
• It is used as a supplement to treat zinc deficiency and avoid the disease in high-risk patients.
• It has the formula of ZnSO4 as well as several of the three hydrates.
• It is used in medicine together with oral rehydration therapy (ORT) and astringent treatment.

We add each option to the given number and check the conditions:

1. 3500 + 22 = 3522 

Divisible by 42 = 3522 ÷ 42 = 83.8

Divisible by 49 = 3522 ÷ 49 = 71.8

Divisible by 56 = 3522 ÷ 56 = 62.8

Divisible by 63 = 3522 ÷ 63 = 55.9

2. 3500 + 28 = 3528

Divisible by 42 = 3528 ÷ 42 = 84

Divisible by 49 = 3528 ÷ 49 = 72

Divisible by 56 = 3528 ÷ 56 = 63

Divisible by 63 = 3528 ÷ 63 = 56

3. 3500 + 24 = 3524 

Divisible by 42 = 3524 ÷ 42 = 83.9

Divisible by 49 = 3524 ÷ 49 = 71.9

Divisible by 56 = 3524 ÷ 56 = 62.9

Divisible by 63 = 3524 ÷ 63 = 55.9

4. 3500 + 26 = 3526 

Divisible by 42 = 3526 ÷ 42 = 83.9

Divisible by 49 = 3526 ÷ 49 = 71.9

Divisible by 56 = 3526 ÷ 56 = 62.9

Divisible by 63 = 3526 ÷ 63 = 55.9

Hence the correct answer is option 2)

The correct answer is Rigveda.

Key Points

• Rig Veda' is the oldest of the Vedas and in any Indo-European language one of the oldest extant texts.
• The Rig Veda is a set of ancient Indian texts comprising 1028 Sanskrit Hymns from the Vedic period and 10,600 verses devoted to the Rigvedic deities.
• It is arranged in 10 volumes, known as mandalas.
• It is one of the four canonical Hindu holy texts collectively known as the Vedas.
• The "Rig Veda" outlines one of the oldest types of yoga and provides knowledge about yoga and other spiritual disciplines.

Additional Information

• Samaveda:
• known as the Veda of melodies and chants, Samaveda dates back to 1200-800 BCE. This Veda is related to public worship.
• There are 1549 verses (except 75 verses, all have been taken from Rigveda).
• There are two Upanishads embedded in Samaveda - Chandogya Upanishad and Kena Upanishad.
• The Samaveda is considered the root of Indian classical music and dance.
• It is considered as the storehouse of the melodious chants.
• Yajurveda:
• Stands to mean 'Worship Knowledge', Yajurveda dates back to 1100- 800 BCE; corresponding with Samaveda. It compiles ritual-offering mantras/chants. These chants were offered by the priest alongside a person who used to perform a ritual (in most cases yajna fire.)
• It has two types - Krishna (Black/Dark) & Shukla (White/Bright).
• Krishna Yajurveda has an un-arranged, unclear, motley collection of verses.
• Shukla Yajurveda has arranged and clear verses.
• Atharvaveda:
• Stands to mean a tatpurusha compound of Atharvan, an ancient sage, and knowledge (atharvan+knowledge), it dates back to 1000- 800 BCE.
• The daily procedures of life are very well enumerated in this Veda.
• It has 730 hymns/suktas, 6000 mantras, and 20 books.
• Paippalada and the Saunakiya are two surviving recensions of Atharvaveda.
• Called a Veda of magical formulas, it includes three primary
• Upanishads - Mundaka Upanishad, the Mandukya Upanishad, and the Prashna Upanishad.

The correct answer is Mangrove forests.

Key Points

• The Sundarbans is a cluster of low-lying islands in the Bay of Bengal, spread across India and Bangladesh, famous for its unique mangrove

forests.

• This active delta region is among the largest in the world, measuring about 40,000 sq km.
• The Sundarbans are of universal importance for globally endangered species including the Royal Bengal Tiger, Ganges and Irawadi dolphins, estuarine crocodiles, and the critically endangered endemic river terrapin (Batagur Baska).
• It is the only mangrove habitat in the world for Panthera tigris Tigris species.
• A mangrove is a shrub or small tree that grows in coastal saline or brackish water.

The correct answer is Shipping Corporation of India.

Key Points

• The 'Maharatna' status is granted to Public Sector Enterprises (PSEs) in India based on performance and financial health.
• Currently, 'Shipping Corporation of India' is not classified as a Maharatna company.
• Maharatna status enables greater autonomy and the ability to make decisions regarding investments up to Rs. 5,000 crore without seeking government approval.
• The Maharatna status is granted to companies like Coal India Limited, Indian Oil Corporation, and National Thermal Power Corporation.

Additional Information

• Maharatna Companies
• Maharatna companies are empowered to make investments up to Rs. 5,000 crore without government approval, enhancing their operational flexibility.
• Examples of Maharatna companies include Indian Oil Corporation, Coal India, NTPC, and ONGC.
• These companies contribute significantly to India’s economy in sectors like energy, coal mining, and petroleum.
• Navratna and Miniratna Status
• Navratna and Miniratna statuses are given to PSEs in India to encourage their performance and empower them in decision-making.
• While Navratna companies can make investments up to Rs. 1,000 crore, Miniratna companies have limited autonomy and can invest up to Rs. 300 crore.
• Shipping Corporation of India (SCI)
• SCI is one of India's largest shipping companies, primarily owned by the government.
• Despite its large contribution to the Indian economy, SCI does not currently hold Maharatna status.

The correct answer is Blue.

Key Points

• The blue color is itself a primary color.
• The category of all colors with their description is as follows:

Additional Information

• Color Wheel:
• The colour wheel or colour circle is a basic visual device where colours are organized in a circular manner for understanding fundamental principles of colour classification, arrangements, and colour relationships.
• Following is the most popular twelve-colour wheel:

Formula used:

Profit = $\frac{\text{selling price - cost price}}{\text{cost price}}\times100$

Calculation:

Let the cost price of the first table be x.

Then, $25=\frac{400-x}{x}\times 100$

Solving for x, 

$x=\frac{400}{1.25}=320$

This means he made a profit of Rs. 80.

Hence, he lost Rs. 80 in the second sale.

Let the cost price of the second table be y.

Then, $10=\frac{80}{y}\times 100$

Solving for y,

$y=\frac{80\times100}{10}=800$

Therefore, the cost price of the second table is Rs. 800.

The alphabets and their positions are:

The logic here is:  

Charger = C + H + A + R + G + E + R = 3 + 8 + 1 + 18 + 7 + 5 + 18 = 60

Similarly for the word 

TOPPER = T + O + P + P + E + R = 20 + 15 + 16 + 16 + 5 + 18 = 90

Hence, the correct answer is 'option 4'.

Formula used:

Principle amount 'P' in 'n' years at 'r'% interest rate per annum = $P+\frac{P\times r \times n}{100}$

Calculation:

For 6 years, $2613=P+\frac{P\times 5 \times 6}{100}$

Solving for P,

$P=\frac{2613}{1.3}=2010$

Then, for the amount to become Rs. 3015,

$3015=2010+\frac{2010\times 5 \times n}{100}$

Solving for n, 

$n=\frac{(3015-2010)\times 100}{2010\times 5}=10$

∴ The sum of money will amount to Rs. 3015 in 10 years.

The correct answer is 1 Gigabyte.

Key Points

• One gigabyte in the memory context of data storage comprises 1024 MB (megabyte) or 1 million bytes.
• In Sl units, it is written as 109. This is the most commonly used unit of storage in modern times.
• 1 Gigabyte = 1024 Megabytes.
• 1 Terabyte = 1024 Gigabytes.

Additional Information

• Unit Conversion Table:
• 4 bit = 1 Nibble.
• 8 bit = 1 byte.
• 1 kB (kilobyte) = 1024 byte.
• 1 MB (megabyte) = 1024 KB.
• 1 GB (gigabyte) = 1024 MB.
• 1 TB (terabyte) = 1024 GB.
• 1 PB (petabyte) = 1024 TB.
• 1 XB (Exabyte) = 1024 PB.
• 1ZB (zettabyte) = 1024 XB.
• 1 YB (yottabyte) = 1024 ZB.

The correct answer is PSLV-C11.

Key Points

• Chandrayaan -1, India's first mission to the Moon was launched using PSLV-C11 from Sriharikota, Andhra Pradesh.
• It was the first Indian lunar probe launched by ISRO in 2008.
• The mission included only a lunar orbiter and no lander or rover.
• Was announced by former PM Shri Atal Bihari Vajpayee on 15^th August 2003.

Additional Information

• ISRO facts:-
• Established on 15^th august 1969 as INCOSPAR with the efforts of Vikram Sarabhai.
• The headquarters is in Bengaluru.
• S. Somnath is the current chairman of ISRO.
• Aryabhata was the first satellite to be launched in 1975.
• Launched Mars Orbiter Mission on 5^th November 2013 making
• India is the first country ever to succeed in its maiden attempt at Mars.
• On 15^th February 2017, ISRO made a world record by launching 104 satellites in a single rocket (PSLV-C37).

The correct answer is Manipur.

Key Points

• India shares a 4,096-km-long border with Bangladesh which touches Assam, Tripura, Mizoram, Meghalaya, and West Bengal.
• A map showing the boundaries shared with the Bangladesh: