SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 1) (Previous Year Paper)

According to the English alphabets & their positional values:

The pattern followed in the given options is:

Option 1) 

Option 2) 

Option 3) 

Option 4) 

So, LEB does not belong to the group.

Hence, the correct answer is "Option 1".

According to the English alphabet & their positional values:

The pattern followed in the given series is:

First alphabet is placed as same,

Second alphabet is decreased by - 9,

Third alphabet is increased by + 8,

Fourth alphabet is decreased by - 10.

So, PCXR will complete the series.

Hence, the correct answer is "Option 3".

The pattern followed in the given series is:

The difference between the numbers is double of the previous difference.

So, 165 will complete the series.

Hence, the correct answer is "Option 2".

We apply the options to the given equation & solve it by using BODMAS rule:

Given Equation: 11 * 3 * 11 * 2 * 9 = 10

Now, replacing the * signs with the mathematical operator:

Option 1) ×, ÷, −, +

11 × 3 ÷ 11 - 2 + 9 = 10

11 × 0.27 - 2 + 9 = 10

3 - 2 + 9 = 10

12 - 2 = 10

10 = 10

LHS = RHS.

Option 2) ÷, ×, −, +

11 ÷ 3 × 11 - 2 + 9 = 10

3.6 × 11 - 2 + 9 = 10

40.3 - 2 + 9 = 10

49.3 - 2 = 10

47.3 ≠ 10.

LHS ≠ RHS.

Option 3) ÷, +, −, ×

11 ÷ 3 + 11 - 2 × 9 = 10

3.6 + 11 - 2 × 9 = 10

3.6 + 11 - 18 = 10

14.6 - 18 = 10

-3.4 ≠ 10.

LHS ≠ RHS.

Option 4) ×, ÷, +, −

11 × 3 ÷ 11 + 2 - 9 = 10

11 × 0.27 + 2 - 9 = 10

3 + 2 - 9 = 10

5 - 9 = 10

-4 ≠ 10.

LHS ≠ RHS.

Hence, the correct answer is "Option 1".

We apply the options to the given equation & solve it by using BODMAS rule:

Given Equation: 264 + 24 × 9 ÷ 60 – 4 = 630.

Now, Interchanging the numbers and sign:

Option 1) 264 and 9, ÷ and −

9 + 24 × 264 - 60 ÷ 4 = 630

9 + 24 × 264 - 15 = 630

9 + 6336 - 15 = 630

6345 - 15 = 630

6330 ≠ 630

LHS ≠ RHS.

Option 2) 264 and 9, + and –

9 - 24 × 264 ÷ 60 + 4 = 630

9 - 24 × 4.4 + 4 = 630

9 - 105.6 + 4 = 630

13 - 105.6 = 630 

-92.6 ≠ 630

LHS ≠ RHS.

Option 3) 4 and 24, ÷ and +

264 ÷ 4 × 9 + 60 – 24 = 630

66 × 9 + 60 – 24 = 630

594 + 60 – 24 = 630

654 – 24 = 630

630 = 630

LHS = RHS.

Option 4) 4 and 9, − and ×

264 + 24 - 4 ÷ 60 × 9 = 630

264 + 24 - 0.06 × 9 = 630

264 + 24 - 0.59 = 630

288 - 0.59 = 630

287.41 ≠ 630

LHS ≠ RHS.

Hence, the correct answer is "Option 3".

The pattern followed in the given series is:

Logic: (Second term + 2) ÷ 3 = First term

Now we apply the pattern to the given series:

For, 11 : 31

(31 + 2) ÷ 3 = 11

33 ÷ 3 = 11

11 = 11

For, 14 : 40

(40 + 2) ÷ 3 = 14

42 ÷ 3 = 14

14 = 14

Similarly, For, ? : 25

(25 + 2) ÷ 3 = ?

27 ÷ 3 = ?

9 = Answer

Hence, the correct answer is "Option 4".

The pattern followed in the given series is:

Each pattern repeats itself in an alternative step.

Next step:

The pattern in the second step will repeat itself in the fourth step.

       

Now we consider the given options:

Option 1) 

The figures are interchanged & the circle is hollow also the triangle is shaded.

Option 2) 

The circle is hollow.

Option 3) 

The pattern is correct.

Option 4) 

The figures are interchanged & the circle is hollow.

Hence, the correct answer is "Option 3".

The pattern followed in the given series is:

'FACES’ is written as 'AFCSE'

'JEANS' is written as 'EJASN'

Similarly, for 'HANGS'

So, 'HANGS' will be written as 'AHNSG'.

Hence, the correct answer is "Option 4".

Family Chart:

Given :

 

By using the symbols in the table given below, we can draw the following family tree:

Find:- R is the brother of P?

Let's check each option one by one.

Option 1) P ÷ R - Q

P is the sister of R, R is the father of Q.

Here, R is the Brother of P.(Correct)

Option 2) P × R - Q

P is the mother of R, R is the father of Q.

Here, R is the son of P. (Incorrect)

Option 3) P ÷ Q - R

P is the sister of Q, Q is the father of R.

Here, R is the Niece/Nephew of P. (Incorrect)

Option 4)  P ÷ R × Q

P is the sister of R, R is the mother of Q.

Here, R is the sister of P. (Incorrect)

Hence, the correct answer is "Option 1".

The correct order according to the English dictionary is:

3. Ageism
4. Ageist
5. Agency
6. Agenda
7. Agentry

From the arrangement, we can see that Agenda comes in fourth position.

Hence, the correct answer is "Option 2".

According to the English alphabets & their positional values:

The pattern followed in the given codes is:

The alphabets are increased by + 2

First and last alphabets are interchanged.

‘FANCY’ is written as ‘ACPEH’

‘TRACTOR’ is written as ‘TTCEVQV’

Similarly, for ‘CARROT’

So, ‘CARROT’ will be coded as 'VCTTQE'.

Hence, the correct answer is "Option 4".

The option figure in which image is embedded is:

Hence, the correct answer is "Option 2".

Statements:

All reds are pinks.

All whites are pinks.

All pinks are oranges.

Venn diagram:

Conclusions:

I. All whites are oranges → Follow → Since 'all whites are pinks' & 'all pinks are oranges' thus the conclusion follows.

II. All oranges are reds → Does not follow → From the diagram we can see that all reds are oranges but all oranges are not red therefore the conclusion does not follow.

III. Some oranges are whites → Follow → We have 'all whites are pink' and 'all pinks are oranges' so some oranges will be definitely whites.

So, only conclusions I and III follow.

Hence, the correct answer is "Option 1".

The pattern followed in the given options is:

Logic: First term² + 10 = Second term

Now we consider the given options:

Option 1) 14 - 208

14²  + 10 = 208

196 + 10 = 208

206 ≠ 208

Option 2) 18 - 334

182  + 10 = 334

324 + 10 = 334

334 = 334

Option 3) 12 - 154

122  + 10 = 154

144 + 10 = 154

154 = 154

Option 4) 16 - 266

162  + 10 = 266

256 + 10 = 266

266 = 266

So, 14 - 208 is the odd one.

Hence, the correct answer is "Option 1".

Family Chart:

Given:

<br>

Now we substitute the values in the given equation:

A & B # C & D @ E % F + G becomes A is the wife of B, B is the father of C, C is the wife of D, D is the son E, E is the husband of F, F is the mother of G.       

From the chart we can see that, A is mother-in-law of D.

Hence, the correct answer is "Option 2".

The logic followed here is:

Lethargy : Alertness → Lethargy is the antonym of the word Alertness.

Similarly.

Harsh is the antonym of the word Gentle.

Hence, the correct answer is "Option 4".

The pattern followed in the given sets is:

Logic: (First term ÷ 2) + Second term = Third term

Now we apply the pattern on the given sets:

(24, 9, 21)

(24 ÷ 2) + 9 = 21

12 + 9 = 21

21 = 21

(34, 16, 33)

(34 ÷ 2) + 16 = 33

17 + 16 = 33

33 = 33

Now we apply the pattern on the given options:

Option 1) (34, 8, 28)

(34 ÷ 2) + 8 = 28

17 + 8 = 28

25 ≠ 28

Option 2) (53, 6, 34)

(53 ÷ 2) + 6 = 34

26.5 + 6 = 34

32.5 ≠ 34

Option 3) (43, 17, 41)

(43 ÷ 2) + 17 = 41

21.5 + 17 = 41

38.5 ≠ 41

Option 4) (42, 9, 30)

(42 ÷ 2) + 9 = 30

21 + 9 = 30

30 = 30

So, (42, 9, 30) follows the same pattern as the given sets.

Hence, the correct answer is "Option 4".

The option figure in which image is embedded is:

Hence, the correct answer is "Option 2".

Statements:

I. All R are M.

II. All L are M.

Venn diagram:

Conclusions:

I. Some M are not R → Does not follow →(There is no negative relation given between R and M, so It can be possible not definite, Hence it is false)

II. Some L are R → Does not follow → (There is definite relation given between L and R, so it can be possible but not possible hence, it is false)

III. Some M are L → Follow → ( As all M are L so it is obvious that Some M will be L, Hence it is definitely true)

So, only conclusion III follows.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (2nd number + 8) × 4 = 1st number.

Now, 

For 76 : 11

⇒ (11 + 8) × 4 

⇒ 19 × 4 = 76.

For, 68 : 9

⇒ (9 + 8) × 4 

⇒ 17 × 4 = 68.

Similarly, for 88 : ?

⇒ (14 + 8) × 4 

⇒ 22 × 4 = 88.

Hence, the correct answer is "14".

We compare figures 1 and 3:

When the faces '6' and '5' are visible in both the cases, we get '3' on the left and '4' on the right.

So, '3' is the face opposite '4'.

Hence, the correct answer is "Option 2".

We interchange the signs & numbers in the given equations and solve them by using BODMAS rule:

By interchanging: - and ÷, 8 and 2

I. 5 + 7 - 8 × 4 ÷ 2 = 9

⇒ 5 + 7 ÷ 2 × 4 - 8 = 9

⇒ 5 + 3.5 × 4 - 8 = 9

⇒ 5 + 14 - 8 = 9

⇒ 19 - 8 = 9

⇒ 11 ≠ 9

II. 3 + 8 × 4 - 2 ÷ 1 = 3

⇒ 3 + 2 × 4 ÷ 8 - 1 = 3

⇒ 3 + 2 × 0.5 - 1 = 3

⇒ 3 + 1 - 1 = 3

⇒ 4 - 1 = 3

⇒ 3 = 3

So, only equation I is not correct.

Hence, the correct answer is "Option 4".

The pattern followed in the given series is:

The line moves in anticlockwise direction leaving +1 space from the previous step.

Triangle moves in clockwise direction leaving 1 and 2 spaces in alternate step.

Next step:

The line will leave 3 + 1 spaces in the next step to reach center of the right side.

The triangle will leave 1 space in the next step to reach top right.

Now we consider the given options:

Option 1) 

Both the triangle and line are placed incorrectly.

Option 2) 

The line is placed incorrectly.

Option 3) 

The pattern is correct.

Option 4) 

The line is positioned incorrectly.

Hence, the correct answer is "Option 3".

According to the English alphabets & their positional values:

The pattern followed in the given series is:

First alphabet is increased by +3

Second is increased by +2

Third & fourth alphabets are increased by +1.

So, IPRO will complete the series.

Hence, the correct answer is "Option 1".

The logic followed here is:

Lake : Land → A Lake is surrounded by the land.

Similarly,

A Island is surrounded by the water.

Hence, the correct answer is "Option 2".

The correct answer is Red.

Key Points

• Acid
• ​Acid changes the colour of blue litmus to Red.
• A Brnsted-Lowry acid or Lewis acid is a molecule or ion that can either donate a proton (the hydrogen ion, H+) or establish a covalent bond with an electron pair. Proton donors, also known as Brnsted-Lowry acids, are the first class of acids.
• Proton donors, also referred to as Arrhenius acids, generate the hydronium ion H3O+ under the unique situation of aqueous solutions.
• The Arrhenius theory was expanded upon by Brnsted and Lowry to take non-aqueous solvents into account.
• A hydrogen atom is typically bound to a chemical structure in a Brnsted or Arrhenius acid that is still energetically advantageous after the loss of H+.

Additional Information

• Aqueous Arrhenius acids have distinguishing characteristics that serve as a useful definition of an acid. Acids can turn blue litmus red, produce aqueous solutions with a sour taste, and react with bases and some metals (like calcium) to generate salts.
• The Latin word acidus, which means "sour," is where the word acid comes from. While the technical definition solely refers to the solute, an aqueous solution of an acid with a pH lower than 7 is sometimes commonly referred to as "acid" (as in "dissolved in acid"..
• Higher acidity and, thus, a higher concentration of positive hydrogen ions in the solution are indicative of a lower pH.

The correct answer is Javadi hills - Eastern ghats

Key Points

• Javadi Hills
• ​The Javadhu Hills, also known as Jawadhi or Jawadhu Hills, are an extension of the Eastern Ghats that are scattered across portions of Tirupattur (formerly part of Vellore District) and Tiruvannamalai districts in the northern section of Tamil Nadu state in southeastern India.
• Tirupattur and Tiruvannamalai districts are divided by this mountain.
• The districts of Tirupattur and Tiruvannamalai are located on opposite sides of this mountain range, respectively.
• On the northwestern side are the cities of Tirupattur, Vaniyambadi, and Ambur from the Tirupattur district, and on the south-eastern side are Chengam and Polur from the Tiruvannamalai district.

Additional Information

• The mountains are made of bluish-gray granite with peaks that are 3,800–4,000 feet high (1,300–1,350 m).
• The Cheyyar and Agaram rivers, tributaries of the Palar, divide them into eastern and western sections, with each being around 50 miles (80 km) wide and 20 miles (32 km) long.
• "The Jawadhi range, in contrast to the Barahmahal hills to the west, is covered in vegetation all the way up to its highest point. As dusk falls, the entire range takes on a purple hue resembling a heather bloom.
• A silvery cascade that shines brightly in the evening sun may be seen beyond Bommaikuppam when looking from Tirupatur.

The correct answer is President.

Key Points

• President
• The head of state of the Republic of India is the president.
• The president serves as the titular leader of the executive branch, the nation's first citizen, and the supreme commander of the Indian Armed Forces.
• The 15th and current president is Droupadi Murmu, who took office on July 25, 2022.
• The position of president was established on January 26, 1950, when India became a republic after obtaining independence on August 15, 1947, when its constitution took effect.

Additional Information

• The legislative assemblies of each of India's states and territories, as well as both chambers of the Indian Parliament, which were all chosen directly by the people, are used to elect the president in an indirect manner.
• With a few exceptions, Article 53 of the Indian Constitution states that the president may exercise their powers directly or through a subordinate authority.
• In practise, however, the prime minister a subordinate authority exercises all of the president's executive powers while receiving advice from the Cabinet Ministers.

The correct answer is Padma Shri

Key Points

• Sitara Devi
• ​Sitara Devi, also known as Dhanlakshmi, was an Indian actress, singer, and traditional Kathak dancer.
• She performed at a number of prestigious venues in India and overseas, including the Carnegie Hall in New York (1967) and the Royal Albert Hall in London.
• She was the recipient of numerous honours and prizes (1976). Devi first met Rabindranath Tagore when she was a young girl, and he inspired her to bring back Indian performing arts like Kathak.
• After witnessing her performance when she was only sixteen years old, Rabindranath Tagore referred to her as Nritya Samragni, which translates to "the empress of dance." She is regarded by some as the Kathak queen.

Additional Information

• Padma Shri
• ​The Padma Shri, which is often spelled Padma Shree, is India's fourth-highest civilian honour, behind the Bharat Ratna, Padma Vibhushan, and Padma Bhushan.
• Awarded for "distinguished achievement in different realms of life, including the arts, education, industry, literature, research, acting, medicine, social service, and public affairs," the award was established on January 2, 1954.
• Every year on India's Republic Day, the Indian government presents it to the recipient.

The correct answer is Article 21 A.

Key Points

• Article 21 A
• Article 21-A, which states that all children between the ages of six and fourteen have the fundamental right to free and compulsory education, was added to the Indian Constitution by the Constitution (Eighty-sixth Amendment) Act of 2002.
• Every child has the right to a full-time elementary education of satisfactory and equitable quality in a formal school that complies with certain fundamental norms and standards.
• According to the Right of Children to Free and Compulsory Education (RTE) Act, 2009, which represents the consequential legislation anticipated under Article 21-A.

Additional Information

• The RTE Act and Article 21-A both went into force on April 1, 2010.
• The words "free and compulsory" are part of the RTE Act's title. Under the definition of "free education," no child aside from a child whose parents have allowed him or her to enrol in a school that is not financially supported by the relevant government shall be required to pay any kind of fee, charge, or expense that might prevent them from pursuing and completing elementary education.

The correct answer is Declined

Key Points

• In India, the share of agriculture in the country's GDP decreased dramatically between 1950 and 1990 (from 67.5% to 64.9%), but not the population that depended on it.
• ​A monetary indicator of the market worth of all the final goods and services produced and sold (not resold) in a certain time period by nations is the gross domestic product (GDP).
• This measurement is frequently reviewed before being regarded as a valid indicator due to its subjective and complicated character. While nominal GDP is more useful for comparing national economies on the global market.
• GDP (nominal) per capita does not account for variations in the cost of living and inflation rates of the various nations.
• The contribution made by each industry or sector of the economy can also be calculated as a percentage of the total GDP.

Additional Information

• Many national and international economic groups keep track of GDP definitions.
• The GDP is defined by the Organisation for Economic Co-operation and Development (OECD) as "an aggregate measure of production equal to the sum of the gross values added of all resident and institutional units engaged in production and services (plus any taxes, and minus any subsidies on products not included in the value of their outputs)".
• According to an IMF report, "GDP represents the monetary value of final goods and services that are purchased by the final user produced in a country in a certain period of time (say, a quarter or a year)."

The correct answer is Calcium hydrogen carbonate

Key Points

• Calcium hydrogen carbonate
• ​Ca(HCO3)2 is the chemical formula for calcium bicarbonate, often known as calcium hydrogencarbonate.
• It only exists in aqueous solutions containing calcium (Ca2+), bicarbonate ions, and dissolved carbon dioxide; the word does not refer to a known solid substance (CO2).
• The pH affects the relative quantities of these carbon-containing species, with bicarbonate predominating in fresh water between 6.36 and 10.25.

Additional Information

• The majority of natural waters that are drawn from streams, lakes, and especially wells can be thought of as diluted solutions of these bicarbonates because all waters that come into contact with the atmosphere absorb carbon dioxide.
• As these waters interact with rocks and sediments they pick up metal ions, most frequently calcium and magnesium.
• These hard fluids often result in carbonate scale building up in boilers and pipes, and when they interact with soap, they create an unfavourable scum.

The correct answer is Bengal.

Key Points

• Fa Xian boarded a ship owned by some merchants to start his voyage back home from Bengal.
• ​Faxian was a Chinese Buddhist monk and translator who walked on foot from China to India in search of Buddhist literature.
• He was also known by the names Fa-Hien, Fa-hsien, and Sehi.
• Between 399 and 412 CE, he began his gruelling journey at the age of roughly 60, visiting holy Buddhist places in Central, South, and Southeast Asia, with 10 of those years spent in India.

Additional Information

• Bihar
• ​Eastern India contains the state of Bihar.
• It is the second most populous state in terms of people in 2019, has the 12th-largest size (94,163 km2) and the 14th-largest GDP in 2021.
• Bihar shares borders with Jharkhand to the south, Uttar Pradesh to the west, Nepal to the north, and the northern portion of West Bengal to the east.
• The Ganges River, which runs from west to east, divides the Bihar plain.
• Maharashtra
• ​Maharashtra is a state in western India's peninsula that takes up a sizable chunk of the Deccan Plateau. Maharashtra is the second-most populous country subdivision in the world as well as the second-most populous state in India.
• The bilingual Bombay State, which had been in existence since 1956, was divided on May 1 to create the majority-Marathi-speaking Maharashtra and the majority-Gujarati-speaking Gujarat.
• Odisha
• Eastern India is home to the Indian state of Odisha. By area, it is the eighth-largest state, and by population, it is the eleventh-largest. The number of scheduled tribes in the state is the third highest in all of India.
• It shares borders with the states of Andhra Pradesh to the south, Jharkhand to the north, West Bengal to the northeast, and Chhattisgarh to the west. Odisha's coastline stretches for 485 kilometres (301 mi) along the Indian Ocean's Bay of Bengal.

The correct answer is Gross fiscal deficit - Net interest liabilities

Key Points

• Primary Deficit
• ​​The difference between the fiscal deficit for the current fiscal year and the interest payment required for the prior fiscal year is referred to as the primary deficit.
• It is one of the three crucial metrics for calculating the federal deficit.
• It displays the government's borrowing needs but does not include interest of any kind. In addition to the interest payment.
• It draws attention to the total amount of government spending that must be covered by borrowing.

Additional Information

• Primary deficit is the difference between total government borrowings and interest payments, or fiscal deficit, and total government borrowings only.
• In most cases, when a loan is raised by the government, the interest payment amount is also included.
• When the principal loan amount is removed from this sum, the primary deficit is shown.

The correct answer is Newsprint Control Order, 2004.

Key Points

• The 1955 Essential Commodities Act covered newsprint. The Newsprint Control Order of 1962 controlled its production and trade.
• The Newsprint Control Order was revoked in 2004 and Newsprint was removed from the list of essential goods.
• The Newsprint Control Order 2004 was then published in its place. This enables the mills that produce newspapers to register with Schedule I. Subject to the actual user condition, mills registered under the schedule are exempt from excise duty.

Additional Information

• Newsprint 
• ​Newspapers, other periodicals, and advertising materials are most frequently printed on newsprint, a cheap, non-archival paper made primarily of wood pulp.
• It was created in 1844 by Charles Fenerty in Nova Scotia, Canada, and often has an off-white cast.
• It is made to be used in printing presses that use large webs of paper rather than single sheets of paper, such as web offset, letterpress, and flexographic.
• Publishers and printers prefer newsprint because it is relatively inexpensive (in comparison to paper grades used for glossy magazines and sales brochures), sturdy (enough to run through contemporary high-speed web printing presses), and can accept four-color printing at qualities suitable for standard newspapers.

The correct answer is Gallium.

Key Points

• Gallium
• ​The chemical element gallium has the atomic number 31 and the symbol Ga.
• Gallium is a metal in group 13 of the periodic table and was first discovered by the French chemist Paul-Émile Lecoq de Boisbaudran in 1875. (aluminium, indium, and thallium).
• Gallium is an element that is soft and silvery at ordinary pressure and temperature.
• It turns silvery white when it's liquid. Gallium may fracture conchoidally if excessive force is used.
• Gallium has been commonly utilised to create alloys with low melting points ever since it was discovered in 1875.

Additional Information

• Chemical element aluminium has the atomic number 13 and the symbol Al. Aluminum has a density that is around one third that of steel, which is lower than that of most common metals.
• Chemical element boron has the atomic number 5 and the letter B in its symbol. It is an amorphous brown powder and a brittle, black, glossy metalloid in its crystalline form.
• The chemical element thalium has the atomic number 81 and the letter Tl assigned to it. It is a post-transition grey metal that is not naturally occurring in free form. while segregated.

The correct answer is Coordination isomerism.

Key Points

• Coordination isomerism
• ​A type of structural isomerism known as coordination isomerism occurs when the coordination **complex ion'**s makeup changes.
• The overall ligand to metal ratio in a coordination isomer doesn't vary, but the ligands bound to a particular metal ion do.
• Instances of a whole series of coordination isomers call for two or even more metal ions.
• The exchange of one or more ligands between the cationic complex ion and the anionic complex ion is known as coordination isomerism, and it happens in compounds that have complex anionic and cationic components.

Additional Information

• Two or more coordination compounds having a difference in composition within the coordination sphere are said to be coordination isomers.
• This kind of isomerism is caused by the exchange of ligands between anionic and cationic entities of various metal ions that are present in the complex.
• Coordination isomerism, which can be thought of as an exchange of some ligands from the cation to the anion, occurs in compounds that contain complex cationic and anionic components.
• As a result, two complicated chemicals that have opposite charges one negative and the other positive are linked together.

The correct answer is Pakistan.

Key Points

• The Radcliffe Line served as the dividing line between British India's Punjab Province and Bengal Presidency in India and Pakistan.
• It was named after Cyril Radcliffe, who had the final responsibility for dividing 175,000 square miles (450,000 km2) of land with 88 million inhabitants as the joint head of the two border commissioners for the two provinces.
• Following the partition of British India on August 17, 1947, the demarcation line was made public.
• Nowadays, the line's western side forms part of the border between India and Pakistan, while the eastern side forms the border between Bangladesh and India.

Additional Information

The correct answer is Granite.

Key Points

• On all continents, granitic rocks can be found close to or past plate borders.
• They developed as magma cooled thousands of kilometres below the surface of the Earth.
• Then, as the volcanic mountains above them eroded away, the granitic rocks were elevated to the surface.
• Granitic rocks, which were cooled from rock melted during the subduction process that also created the Franciscan Complex's rocks, make up the Sierra Nevada's core in California.

Additional Information

• Magma
• All igneous rocks are formed from magma, which is a naturally occurring substance that is molten or semi-molten.
• The Earth possesses magma beneath its surface, and other terrestrial planets and several naturally occurring satellites have also been confirmed to have magmatic activity.
• Magma may also include gas bubbles and suspended crystals in addition to molten rock.
• In a variety of tectonic settings on Earth, including as subduction zones, continental rift zones, mid-ocean ridges, and hotspots, the mantle or the crust melts to produce magma.
• Mantle and crustal melts are assumed to be stored in magma chambers or trans-crustal crystal-rich mush zones as they move upward through the crust.

The correct answer is R K Gupta.

Key Points

• According to a Personnel Ministry order, senior bureaucrat R K Gupta has been named the deputy election commissioner.
• He steps in for T. Sreekanth.
• Gupta, a member of the Central Secretariat Service (CSS), will hold the position of deputy election commissioner (Joint Secretary level) until his retirement on February 28 of the next year.

Additional Information

• Election Commission 
• The Indian Constitution established the Election Commission as a permanent and autonomous entity.
• On January 25, 1950, the Election Commission of India was established.
• The Election Commission is required by Article 324 of the Indian Constitution to hold elections for the State Legislatures and the Parliament.
• There is a Chief Election Commissioner and two other Election Commissioners that make up the Election Commission.
• The 25th Chief Election Commissioner of India is Shri Rajiv Kumar.

The correct answer is Prerna Shrimali.

Key Points

• Senior Kathak dancer of the Jaipur Gharana is Prerana Shrimali.
• Shrimati Prerana Shrimali, who was born in Banswara, Rajasthan, was trained in Kathak dancing by Guru Shri Kundan lal Gangani in Jaipur. Subsequently, she received instruction in the art from the same Guru, late Shri Kundan Lal Gangani of the Jaipur gharana, at Kathak Kendra in New Delhi.
• She has also taken part in numerous international dance seminars and conferences and created a number of performances.
• Also, she has trained young dancers at Shriram Bharatiya Kala Kendra and Gandharva Mahavidyalaya.

Additional Information

• Kathak dance
• ​One of the eight primary styles of Indian classical dance is kathak.
• It is an Uttar Pradesh classical dancing style. The storytellers or itinerant bards known as Kathakars in ancient northern India are often credited as the creators of Kathak.
• The Vedic Sanskrit words Katha, which means "story," and Kathakar, which means "the one who tells a story" or "to do with stories," are the roots of the word Kathak.
• Traveling Kathakars used dance, songs, and music to transmit tales from the great epics and ancient mythology. Kathak dancers use intricate footwork, flexible body movements, and, most importantly, expressive face expressions to convey a variety of stories.

The correct answer is Nidhi Chibber.

Key Points

• Nidhi Chibber, a senior IAS officer, was appointed to lead the Central Board of Secondary Education in May 2022 (CBSE).
• A member of the Indian Administrative Service is Nidhi Chhibber.
• Nidhi Chibber, an Indian Administrative Service officer from the 1994 batch assigned to the Chhattisgarh cadre, has been appointed as the new head of the Central Board of Secondary Education.

Additional Information

• Central Board of Secondary Education
• The Central Board of Secondary Education (CBSE) is the government of India's national board of secondary education for both public and private schools.
• The Board was a government-instituted experiment in interstate integration and collaboration in secondary education that was established in 1929.
• The CBSE is associated with more than 27,000 schools in India and 240 schools in 28 other countries.
• The NCERT curriculum is utilised by all CBSE-affiliated institutions, particularly in grades 9 through 12.
• Nidhi Chibber, an IAS, is the CBSE's current chairwoman.

The correct answer is Jaipur-Atrauli.

Key Points

• Kishori Amonkar was an inventive representative of the Jaipur Gharana and one of the greatest singers in the Indian classical vocal heritage.
• Indian classical dancer, choreographer, and teacher Mrinalini Vikram Sarabhai.
• Indian classical vocalist Mogubai Kurdikar, who lived from July 15, 1904, until February 10, 2001, was a well-known member of the Jaipur-Atrauli Gharana.
• Madurai Shanmukhavadivu Subbulakshmi, often known as MS Subbulakshmi, was a Tamil Nadu-born Indian Carnatic singer. She was the first musician ever to receive India's highest civilian distinction, the Bharat Ratna.

Additional Information

• Jaipur Gharana
• ​The Jaipur-Atrauli Gharana developed from the family of Alladiya Khan, who came from Atrauli and settled in Jaipur.
• Alladiya Khan (1855–1946), a pioneer of Hindustani music, developed the Jaipur–Atrauli Gharana.
• The raga repertory, vocal aesthetics, and technical prowess of the Gharana are well renowned.
• Alladiya Khan, Mallikarjun Mansur, Kesarbhai Kerkar, Kishori Amonkar, Shruti Sadolikar, Padma Talwalkar, and Ashwini Bhide Deshpande are the leading representatives of the Jaipur Gharana.

The correct answer is Rabindranath Tagore.

Key Points

• At Santiniketan, West Bengal, India, it is a public research university and an Institute of National Importance.
• Rabindranath Tagore formed it in 1921 and gave it the name Visva-Bharati, which translates to "the communion of the world with India."
• It was a college up till independence.

Additional Information

• Rabindranath Tagore
• Gurudev Rabindranath Tagore, a Bengali polymath who was a poet, playwright, novelist, composer, philosopher, social reformer, and painter, lived from 7 May 1861 to 7 August 1941.
• In the late 19th and early 20th centuries, he used contextual modernism to transform Indian art, Bengali literature, and music.
• Gitanjali, whose poetry has been described as "profoundly sensitive, fresh, and lovely," was the first non-European and lyricist to win the Nobel Prize in Literature in 1913.
• Tagore's "beautiful prose and mystical poetry" are largely unknown outside of Bengal, despite the fact that his poetic songs were considered to be spiritual and mercurial. He was a Royal Asiatic Society fellow.
• Tagore was referred regarded as "the Bard of Bengal" and went by the nicknames Gurudeb, Kobiguru, and Biswokobi.

The correct answer is Assam.

Key Points

• The Mission Bhumiputra Portal was recently introduced by Assam Chief Minister Himanta Biswa Sarma.
• This portal's goal is to give pupils access to digitalized caste certificates within a month.
• In October 2021, the state government also started Mission Basundhara with the goal of resolving issues relating to land.

Additional Information

• Mission Bhumiputra
• ​For both students and Assamese citizens, a caste certificate is a necessary document. Prior to now, obtaining a caste certificate required individuals to go to the appropriate government office.
• Mission Bhumiputra is a new platform that the Hon. Chief Minister of Assam, Dr Himanta Biswa Sharma, has introduced for the online application of caste certificates in Assam.
• An online platform called Assam Mission Bhumiputra was created to make it easier and quicker for residents to get caste certificates directly.
• When applying for certain government employment, government programmes, or admittance to schools and colleges, these cast certifications could be necessary.
• The entire procedure for applying for a caste certificate online through the Mission Bhumiputra portal is outlined here.

The correct answer is Salt Satyagraha.

Key Points

• Indian political activist, feminist, and poet Sarojini Naidu (13 February 1879 – 2 March 1949) was born in India.
• She played a significant role in India's fight for independence from colonial control as a supporter of civil rights, women's emancipation, and anti-imperialist beliefs.
• Mahatma Gandhi was convinced by Sarojini Naidu to permit women to participate in the Dandi March.
• She was also the first Indian woman to be selected as governor of an Indian state and to serve as president of the Indian National Congress (United Provinces).

Additional Information

• Salt Satyagraha
• ​Mahatma Gandhi led the nonviolent civil disobedience movement known as the Salt March, sometimes referred to as the Salt Satyagraha, the Dandi March, and the Dandi Satyagraha, in colonial India.
• The 24-day march, which served as a direct-action campaign of tax resistance and peaceful protest against the British salt monopoly, took place from March 12 to April 6, 1930.
• The Civil Disobedience Movement need a powerful inauguration to encourage more people to follow Gandhi's example, which was another motivation for this march.
• Gandhi led 78 of his dependable volunteers at the beginning of this march.
• The march covered a distance of 387 km (240 mi), from Sabarmati Ashram to Dandi, which was then known as Navsari (now in the state of Gujarat).

The correct answer is Dubai.

Key Points

• The World Para Athletics Grand Prix got underway on March 21 and last until March 24, 2022. This occasion took place in Dubai.
• There will be 450 competitors competing from 43 different nations.
• The competitors competing in this event aim to qualify for both the Birmingham 2022 Commonwealth Games and the Hangzhou 2022 Asian Para Games.
• Over 100 para-athletes, including Indian participants, have the chance to get classified in this event.

Additional Information

• World Para Athletics Championship
• ​The International Paralympic Committee's World Para Athletics subcommittee hosts the biennial World Para Athletics Championships, formerly known as the IPC Athletics World Championships before 2017 (IPC).
• Athletes with intellectual and physical limitations compete in sporting competitions.
• Berlin, Germany hosted the inaugural IPC Athletics World Championships in 1994.
• They serve as a Paralympic equivalent of the able-bodied competitors' World Athletics Championships.
• The IPC championships have been conducted in the same years as the IAAF championships since 2011 when they changed from a quadrennial to a biennial calendar. However, they are independent competitions, and they are not always held in the same host city.

The correct answer is Padma Shri.

Key Points

• Guru Singhajit Singh is well-known for his proficiency in the Manipuri dance style. He has also distinguished himself as a superb performer, choreographer, scholar, and artist with exceptional creative abilities.
• On May 1st, 1935, Rajkumar Singhajit Singh was born in Manipur.
• For his contributions to Manipuri dance, he received the Padma Shri in 1986 as well as the Sangeet Natak Akademi Award in 1984.

Additional Information 

The correct answer is K Srikanth.

Key Points

• Srikanth Kidambi is an Indian badminton player who was born on 7 February 1993.
• Kidambi, a former world number one, received the Arjuna award in 2015 and the Padma Shri, India's fourth-highest civilian honour, in 2018.
• He was the first Indian to play in the men's singles final of a World Championship in 2021.
• Kidambi was a member of the 2022 Indian men's Thomas Cup team. After defeating Indonesia 3-0 in the championship match, the team went on to win the Thomas Cup, with Kidambi triumphing over Jonatan Christie.

Additional Information

• Badminton
• Racquets are used in the racquet sport of badminton to hit a shuttlecock through a net.
• The most popular versions of the game are "singles" (with one player per side) and "doubles," however it can also be played with bigger teams (with two players per side).
• While formal matches are conducted on a rectangular indoor court, badminton is frequently played as a recreational outdoor pastime in a yard or on a beach.
• The shuttlecock must land in the half of the court belonging to the opposing team in order to score a point.​

The correct answer is 1801.

Key Points

• The Nawab of Awadh was forced to accept the Policy of Subsidiary Alliance by Wellesley in 1801.
• The first king to form a secondary alliance with the British following the Battle of Buxar was the Nawab of Awadh.
• The Nizam of Hyderabad was the first to consent to a carefully crafted subsidiary alliance, though.

Additional Information

• Subsidiary Alliance
• ​The Subsidiary Alliance was essentially a pact between the British East India Company and the princely states of India, through which the English gained control over the Indian kingdoms.
• It was also a significant factor in the development of the British Empire in India.
• Lord Wellesley, who served as the Governor-General of India from 1798 to 1805, drafted it.
• The Marquis Dupleix, the French Governor-General, really used it for the first time.

Given:

sin Y = x

Formula used:

cos 2Y = 1 - 2sin² Y

Calculations:

According to the question,

⇒ cos 2Y = 1 - 2sin2 Y

⇒ cos 2Y = 1 - 2(sin Y)²

⇒ cos 2Y = 1 - 2(x)²

∴ The value of cos 2Y is 1 - 2(x)2.

Given:

The value of (a + b)2 - (a - b)2 

Concept used:

(a + b)2 = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculations:

According to the question,

(a + b)2 - (a - b)2 = (a2 + b2 + 2ab) - (a2 + b2 - 2ab)

⇒ a2 + b2 + 2ab - a2 - b2 + 2ab

⇒ a2 + b2 - a2 - b2 + 2ab + 2ab

⇒ 2ab + 2ab = 4ab

∴ The value of (a + b)2 - (a - b)2 is 4ab.

Given:

The table given below shows the number of monuments in 5 different cities.

 

Calculations:

According to the question,

The ratio of city B to that of D = 30/150

⇒ B/D = 1/5

⇒ B:D = 1:5

∴ The ratio of number of monuments in B to the number of monuments in D is 1:5.

Given:

The following table shows the production of different type of two wheelers from 1993 to 1998.

Number of two wheelers (in 1000s)

 

Concept used:

Relative change in percentage = [(X₂ - X₁)/X₁] × 100

Calculations:

According to the question,

Increase in percentage in 2 years = [(334 - 268)/268] × 100

⇒ (66/268) × 100 

⇒ 0.2462 × 100 = 24.62% ~ 25%

∴ The percentage increase in the total production of all types of two-wheelers is 25%.

Given:

Three circles of radius 7 cm are kept touching each other.

The string is tightly tied around these three circles

Concept used:

Circumference of circle = 2πr

Calculations:

According to the question,

<br>

The length of the string not in contact with the circle,

⇒ 2r + 2r + 2r = 6r

⇒ 6 × 7 = 42

By symmetry, the angles swiped by a string on one circle is 120.

Length of string touching circle,

⇒ (2πг/3) + (2πг/3) + (2πr/3) = 2πr

⇒ 2 × 7 × π = 14π

Total length = 42 + 14π.

∴ The length of the string is 42 + 14π.

Given:

A dealer marks his goods at 15% above the cost price and allows a discount of 5% for cash payment.

Formula used:

SP = MP(1 - D%)

P% = [(SP - CP)/CP] × 100

Calculations:

Let CP be x and MP be 1.15x

According to the question,

SP = 1.15x(1 - 5%)

⇒ SP = 1.15x(1 - 0.05)

⇒ SP = 1.15x(0.95) = 1.0925x

Now the Profit %,

P% = [(1.0925x - x)/x] × 100

⇒ P% = [0.0925x/x] × 100

⇒ P% = 0.0925 × 100 = 9.25%

∴ His profit percentage is 9.25%

 Shortcut Trick

A dealer marks his goods at 15% above the cost price CP : MP = 20 : 23

Then, allows a discount of 5%, MP : SP = 20 : 19

Now, CP : SP : MP = 400 : 437 : 460

So, profit% = 37/400 × 100 = 9.25%

Given:

A right circular cone with height 8 m and slant height 10 m

Concept used:

Curve surface area of cone = πrl

Radius of cone = √[(l)² - (h)²] 

Calculations:

According to the question,

Radius = √[(10)2 - (8)2] 

⇒ R = √[100 - 64]

⇒ R = √36 = 6 m

Now Curve surface area of cone

⇒ CSA = π × 6 × 10

⇒ CSA = 60π m² 

∴ The area of the curved surface of a right circular cone is 60π m2.

Given:

The given table shows the production of units of different products in different months.

<br>

Calculations:

According to the question,

Total production of product Y = March + June + September + December 

⇒ 18 + 13 + 17 + 8 = 56

Total production of product Z = March + June + September + December 

⇒ 15 + 18 + 12 + 19 = 64

Now,

⇒ P = 56/64 × 100

⇒ P = 0.875% × 100 = 87.5%

∴ Y's total production is 87.5% of Z's total production.

Shortcut Trick

Since PQ ∥ AC, ΔPBQ is similar to ΔABC.

We can use a direct ratio shortcut to find the lower segment AP:

⇒ AP / AB = (AC − PQ) / AC

⇒ AP / 26 = (10 − 7) / 10

⇒ AP = 26 × (3 / 10) = 26 × 0.3

⇒ AP = 7.8

∴ The correct answer is 7.8.

Alternate Method

Given:

AB = 26, PQ = 7, AC = 10, and PQ ∥ AC.

A B C P Q 7 10 AB = 26 AP = ?

Concept Used:

If a line is parallel to one side of a triangle and intersects the other two sides, the smaller triangle formed is similar to the original larger triangle (ΔPBQ ∼ ΔABC).

Calculations:

⇒ In ΔABC, since PQ ∥ AC, the corresponding angles are equal.

⇒ ∴ ΔPBQ ∼ ΔABC

⇒ The ratio of their corresponding sides must be proportional:

⇒ PB / AB = PQ / AC

⇒ PB / 26 = 7 / 10

⇒ PB = (26 × 7) ÷ 10

⇒ PB = 182 ÷ 10 = 18.2

⇒ Since point P lies on the line segment AB, the total length is the sum of its parts:

⇒ AP + PB = AB

⇒ AP = AB − PB

⇒ AP = 26 − 18.2 = 7.8

∴ The correct answer is 7.8.

Additional Information

Thales Theorem (Basic Proportionality Theorem)

If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides in the same ratio. ⇒ AP / PB = CQ / QB.

Areas of Similar Triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. ⇒ Area(ΔPBQ) ÷ Area(ΔABC) = (PQ / AC)².

Midpoint Theorem

If a line segment joins the midpoints of two sides of a triangle, it is unconditionally parallel to the third side and is exactly half of its length.

Given: 

A shopkeeper advertises for selling clothes at a 7% loss.

However, by using a false scale of length 1 meter he actually gains 24%

Concept used:

Selling Price = CP + Profit 

Calculations:

Let the length of scale be ‘x’ meters.

Let the cost price per meter of cloth be Rs. 100

CP of cloth with false scale Rs. 93/metre and gains 24% profit

CP of x meter length cloth = 100x

According to the question,

⇒ 100x + 24% of 100x = 93

⇒ 100x + 24x = 93

⇒ 124x = 93

⇒ x = 93/124 = 0.75 m

∴ The actual length he uses instead of 1 meter is 75 cm.

Given:

A 100 ml solution of H2SO4 having concentration of 20% is mixed with a 50% concentrated x ml mixture

Such that the net mixture is 30% concentrated

Concept used:

C₁V₁ + C₂V₂ = C₃V₃ 

Calculations:

According to the question,

(100 × 20) + (50 × x) = 30 × (100 + x) 

⇒ 2000 + 50x = 3000 + 30x 

⇒ 50x - 30x = 3000 - 2000

⇒ 20x = 1000

⇒ x = 1000/20 = 50 ml

∴ The value of x is 50 ml.

 Shortcut Trick

Here, 2 unit → 100 ml

Then 1unit → 100/2 = 50 ml

Given:

ABCD is a square. △MAB is an equilateral triangle

MC and MD are joined

Concept used:

Sum of all the angles of triangle = 180° 

Calculations:

According to the question,

ABCD is a square,

⇒ AB = BC = CD = DA

MAB is an equilateral triangle,

⇒ MA = AB = BM

square ABCD and equilateral triangle MAB have a common side AB. 

⇒ AB = BC = CD = DA = MA = MB

In △MAD,

⇒ MA = DA

∠ADM = ∠AMD = x

With ∠DAM

⇒ ∠DAM = ∠MAB + ∠DAB

⇒ ∠DAM = 90° + 60°

⇒ ∠DAM = 150°

Sum of angles of triangle MAD = 180°

⇒ ∠DAM + ∠AMD + ∠ADM = 180°

⇒ 150° + x + x = 180°

⇒ 2x = 180° - 150° 

⇒ x = 30°/2 = 15° 

Hence, ∠ADM = ∠BCM = 15° 

Now for ∠MDC,

⇒ ∠MDC = ∠ADC - ∠ADM

⇒ ∠MDC = 90° - 15° = 75°

∴ The degree measure of ∠MDC is 75°.

Given:

Ten men begin to do a work. But after some days, four of them left the job.

The job that could have been completed in 40 days is completed in 50 days.

Concept used:

M₁D₁ = M₂D₂ 

Calculations:

According to the question,

10 Men begin the work 

It could been done in 40 days.

Let 4 men left after x days.

Left days are 40 − x if they do not left and 50−x if they left.

(40 − x)10 = (50 − x)6

⇒ 400 − 10x = 300 − 6x

⇒ 400 - 300 = 10x - 6x

⇒ 4x = 100

⇒ x = 100/4 = 25 days.

∴ The four men left after 25 days.

Given:

A + B = C

Concept used:

tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)

Calculations:

According to the question,

A + B = C

Multiplying tan on both sides,

⇒ tan(A + B) = tanC

⇒ (tanA + tanB)/(1 - tanA.tanB) = tanC

⇒ tanA + tanB = tanC(1 - tanA.tanB)

⇒ tanA + tanB = tanC - tanC.tanA.tanB

⇒ tanC.tanA.tanB = tanC - (tanA + tanB)

⇒ tanC.tanA.tanB = tanC - tanA - tanB

∴ The value of tanC.tanA.tanB is tanC - tanA - tanB.

Given:

9m² + n² = 40

mn = 4

Calculations:

9m² + n² = 40

On adding 6mn both sides, we get:

9m² + n² + 6mn = 40 + 6mn

⇒(3m)² + n² + 2(3m)n = 40 + 6(4)

⇒(3m + n)² = 64

⇒ 3m + n = √64 = 8

Hence, The Required value is 8.

Calculations:

 x²+ 4y2 - 4xy + 4y - 2x - 8

= (x - 2y)² - 2(x - 2y) - 8

now, let (x - 2y) be A,

then, as we know,

A² - 2A - 8

= (A - 4)(A + 2)

= (x - 2y - 4)(x - 2y + 2)

Hence, The Required option is option (1).

Given:

105,335,465

Concept used:

HCF = Highest Common Factor

Calculations:

According to the question,

HCF(105,335,465)

⇒ 105 = 1 × 3 × 5 × 7

⇒ 335 = 1 × 5 × 67

⇒ 465 = 1 × 3 × 5 × 31

HCF = 5

∴ The HCF of three numbers 105, 335 and 465 will be 5.

Shortcut Trick Check if the first divisor (221) is divisible by the second divisor (13). Since 221 ÷ 13 = 17 (perfectly divisible), the required remainder is simply the remainder of (First Remainder ÷ Second Divisor). Required Remainder = 30 ÷ 13 30 = (13 × 2) + 4 ∴ The correct answer is 4. Alternate Method Given: First divisor = 221, First remainder = 30, Second divisor = 13. Formula Used: Number = (Divisor × Quotient) + Remainder

⇒ Let the number be N. According to the question, N = 221k + 30 (where k is the quotient). ⇒ We need to find the remainder when N is divided by 13. ⇒ N/13 = (221k + 30) / 13 ⇒ N/13 = (221k / 13) + (30 / 13) ⇒ Since 221 is 13 × 17, the term 221k is perfectly divisible by 13 (Remainder = 0). ⇒ Therefore, the final remainder depends only on 30 / 13. ⇒ 30 = 13 × 2 + 4 ∴ The correct answer is 4. Additional Information Division Algorithm For any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. Remainder Theorem Property If a divisor D1 is a multiple of divisor D2, then the remainder when a number is divided by D2 is the same as the remainder when the first remainder (R1) is divided by D2.

Given:

The given table shows the number of new employees who joined in different categories of employees in an organisation and also the number of employees from these categories who left the organisation every year since the foundation of the organisation in 2015. 

 

Calculations:

According to the question,

Total Accountants working = Total joined - Total left

Working = (35 + 26 + 15 + 20 + 14) - (16 + 5 + 38 + 24)

Working = 110 - 83 = 27

∴ The total number of accountants working in the organization in the year 2019 is 27.

Shortcut Trick

The winning candidate gets 76% of total votes, meaning the losing candidate gets (100 − 76)% = 24% of the votes.

The difference in vote percentage = 76% − 24% = 52%.

This 52% difference corresponds to the winning majority of 1480 votes.

Total votes = (1480 ÷ 52) × 100 = 2846.15

Considering the integral part only, the total votes polled is 2846.

∴ The correct answer is 2846 votes.

Alternate Method

Given:

Winning candidate vote percentage = 76%

Majority votes = 1480

Formula Used:

Total Votes = [Majority ÷ (Winner % − Loser %)] × 100

Total Votes = 100%

Winner (76%)

Loser (24%)

Majority Difference = 52% = 1480

100% = (1480 ÷ 52) × 100 ≈ 2846

Calculations:

⇒ Let the total number of polled votes be 100%.

⇒ Votes secured by the losing candidate = 100% − 76% = 24%

⇒ Difference in vote percentage = 76% − 24% = 52%

⇒ This 52% difference is equal to the winning majority of 1480 votes.

⇒ 52% of Total Votes = 1480

⇒ Total Votes = (1480 ÷ 52) × 100

⇒ Total Votes = 148000 ÷ 52

⇒ Total Votes ≈ 2846.15

⇒ Considering only the integral part, the total votes polled = 2846

∴ The correct answer is 2846 votes.

Additional Information

Election Base Percentage

Unless otherwise stated, the total voters on the voting list form the 100% base. If some votes are invalid, the valid votes become the new sub-base for calculating winner and loser percentages.

Majority Margin

A candidate's winning margin is strictly the difference in votes between the winning candidate and the nearest rival (second position). Margin % = Winner % − Loser %.

Direct Base Calculation

When values are computed based on fractions or percentages, the required base value (100%) can be found directly by dividing the given part by its respective percentage.

Given:

x = 8(sin θ + cos θ)

y = 9(sin θ - cos θ)

Formula used:

sin² θ + cos² θ = 1

(a + b)² = a² + b² +2ab

Calculations:

⇒  x = 8(sin θ + cos θ)

⇒  x² = 8²(sin θ + cos θ)²

⇒  x² = 8²(sin2 θ + cos2 θ + 2sinθcosθ)

⇒  x2 = 82(1 + 2sinθcosθ)

similarly,

⇒  y = 9(sin θ - cos θ)

⇒ y2 = 92(sin θ - cos θ)2

⇒ y2 = 92(sin2 θ + cos2 θ - 2sinθcosθ)

⇒ y2 = 92(1 - 2sinθcosθ)

According to the question,

⇒ ${x^2 \over 8^2} + {y^2 \over 9^2}$

⇒ ${8^2(1 + 2sinθcosθ) \over 8^2} + {9^2(1 - 2sinθcosθ) \over 9^2}$

⇒ 1 + 2sinθcosθ + 1 - 2sinθcosθ

⇒ 2

⇒ Hence, The value of above equation is 2

Shortcut Trick

​If we put, θ = 0° we get x = 8 and y = 9, so

${x^2 \over 8^2} + {y^2 \over 9^2}$

⇒ 8²/8² + 9²/9²

⇒ 1 + 1

⇒ 2

Given:

AB is the diameter of a circle with centre O. If P be point on the circle such that ∠AOP = 110°

Formula used:

Sum of the angles of triangle = 180°

Calculations:

<br>

As from figure,

⇒ OA = OP = OB = radius

In ΔOPB

⇒ OP = OB

so, ΔOPB is an isosceles triangle

⇒ ∠OPB = ∠OBP = x

As, AB is an striaght line

⇒ ∠AOP + ∠POB = 180°

⇒ ∠POB = 180° - 110° = 70°

In ΔOPB,

⇒ ∠O + ∠P + ∠B = 180°

⇒ 70° + x + x = 180°

⇒ 2x = 180° - 70° = 110°

⇒ x = 55°

⇒ Hence, The measure of the ∠OBP is 55º

Hint:

To put in ratio the values must be of the same unit / same type

Here, jumps will be either for the A or the B.

speed = Distance/ time

∴ speed ∝ distance 

Calculations:

7 jumps of A→ 5 jumps of B

8 jumps of the A → ((5/7) × 8) jumps of the B

= 40/7 jumps of B

∴The required ratio is (40/7) : 6

= 20 : 21

∴ The ratio of the speed of A and B is 20 : 21.

Given:

Sum becomes 2 times at 5% p.a rate 

At same time time the same sum becomes 5 times.

Concept used:

S.I = P × R × T/100

Calculations:

According to question,

P × 5 × T/100 = P

⇒ T = 20 years

Now, P × R × T/100 = 4P

⇒ P × R × 20/100 = 4P

⇒ R = 4 × 5 = 20%

Hence, The Required value is 20%.

Shortcut Trick

Initial Ratio (Milk : Water) = 5 : 3

New Ratio (Milk : Water) = 1 : 2

Multiply New Ratio by 5 to make Milk constant → (1 × 5) : (2 × 5) = 5 : 10

Change in Water units = 10 − 3 = 7 units

Given 7 units = 7 litres ∴ 1 unit = 1 litre

Quantity of Milk = 5 units = 5 × 1 = 5 litres

∴ The correct answer is 5 litres.

Alternate Method

Given:

Initial Milk : Water = 5 : 3

Water added = 7 litres

Final Milk : Water = 1 : 2

Milk (5x) Water (3x) Initial Mixture (5 : 3) + 7 Litres Water Milk (5x) Water (3x + 7) Final Mixture (1 : 2)

Let the initial quantity of Milk be 5x and Water be 3x.

⇒ New quantity of Water = 3x + 7

⇒ New Ratio = 5x / (3x + 7) = 1 / 2

⇒ 2 × (5x) = 1 × (3x + 7)

⇒ 10x = 3x + 7

⇒ 10x − 3x = 7

⇒ 7x = 7

⇒ x = 1

⇒ Quantity of Milk = 5x = 5 × 1 = 5 litres

∴ The correct answer is 5 litres.

Additional Information

Alligation Rule

A rule used to find the ratio in which two or more ingredients at their respective prices/concentrations are mixed to produce a mixture at a given mean price/concentration.

Component Balance

When one component (like milk) is not added or removed, its absolute quantity remains constant even if the total mixture volume and ratios change.

Ratio Scaling

To compare or combine ratios, multiply terms by a common factor to equalize the parts of a shared component (e.g., matching milk units in two different ratios).

The correct answer is "questionaire".

Key Points

• The misspelled word in the above statement is ''questionaire''.
• The correct spelling is - Questionnaire.
• The word 'questionnaire' means a list of questions that are answered by many people.
• Example: I have surveyed this area with very detailed questions.

Additional Information

• Committee - A group of people that are chosen to decide something.
• Example: Mr. Sumeet is the chairman of the committee.
• Intervention - Getting involved in a difficult situation intentionally.
• Example: I don't need any intervention in my court case.
• Outcome - It refers to the result or outcome of something.
• Example: The outcome of my first semester exams was brilliant.

The correct answer is "Our country witnessed a terrible disaster".

Key Points

• While using the active voice, the subject is acting.
• The given question is in the past indefinite tense.
• Rule of the active voice of past indefinite tense: Subject+verb(past indefinite form)+object.

Correct sentence: Our country witnessed a terrible disaster.

The correct answer is "overlook".

Key Points

• The one-word substitute for fail to notice; ignore; condone is ''overlook''.
• The word 'overlook' means to fail to see or notice something.
• Example: She never overlook at her previous mistakes.

Additional Information

• Overlong - This is used to refer to something that is longer than usual.
• Example: The new song is amazing but overlong.
• Overlie - This means to lie on top of.
• Example: She sleeps by overlying on her dad.
• Overly - Means something excess.
• Example: She is such an overly possessive woman.

Hinglish

• Overlong - बहुत लंबा
• Overlie - ऊपर स्थित होना
• Overly - अत्यधिक रूप से
• Overlook - अनदेखी करना या नजरअंदाज करना

The erroneous part is: but to work hard.

Key Points

• 'no other' and 'than' are correlative conjunctions.
• Correlative conjunctions are pairs of words that work together to join two elements of equal importance within a sentence.
• In this case, "no other" and "than" are used as a correlative conjunction to express a comparison or contrast between two options.
• In the sentence, "no other" is used to emphasize that there are no alternative options available. It suggests that the person referred to in the sentence has exhausted all possibilities and has only one option left.
• "Than" is used to introduce the only remaining option, which is to work hard.
• The combination of "no other" and "than" acts as a correlative conjunction because they work together to join the elements of the sentence, indicating the limited choices and emphasizing the necessity to work hard.
• Hence, 'than' must replace 'but' to make the sentence grammatically correct.

Therefore, the correct answer is: He knows that he has no other option than to work hard.

The correct answer is "to think hard".

Key Points

• 'Cudgel' word means a short and thick stick that is used as a weapon.
• Cudgel one's brain means to give careful thought to anything; to think hard.
• Example: Muskan cudgeled her brain about why can't she join the meeting.

Additional Information

• Some examples of idioms:

The correct answer is "No substitution".

Key Points

• In the given sentence, some words are underlined and we need to substitute them in the given segment to make this small.
• The underlined word is "to provide for ".
• Among the given options, no one is correct as the substitution.
• So, no substitution is needed.

The correct answer is "The hippopotamus, also known as ‘river horse’, lives throughout sub-Saharan Africa".

Key Points

• Hippopotamus is a large semiaquatic mammal.
• Option 4 has all the correct spellings.
• The sentence means that the hippopotamus is called a river horse. It is found in sub-Saharan Africa.

Additional Information

• In option 1, the spelling of hippopotamus is incorrect and the rest of the spellings are correct.
• In option 2, the spelling of the hippopotamus is incorrect and the rest of the spellings are correct.
• In option 3, again the spelling of hippopotamus is incorrect and the rest of the words are having correct spellings.