SSC CGL 2023 Tier-I Official Paper (Held on: 14 Jul 2023 Shift 2) (Previous Year Paper)

1. PONSMPNO → MN PO S / M N PO S / M N P OS / M N P O S
2. PNOSMPNO → MN PN S / M O PO S / M N P OS / M N P O S
3. PONMSPNO → MN PO S / M N PO M / S N P OS / M N P O S
4. PONSNOMP → MN PO S / M N PO S / N N O OS / M M P B S

• In option 1, MNPOS is repeated.

Hence, ‘PONSMPNO’ is the correct answer.

The image embedded in given figure is as shown below:

Hence, 'option 1' is the correct answer.

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols are moved as shown below.

From Figure (2) to (3):

The symbols are moved as shown below.

From Figure (3) to (4):

The symbols are moved as shown below.

From Figure (4) to Answer Figure (5):

The symbols are moved as shown below.

Hence, the correct answer is "Option (4)".

The logic followed here is:

Hence, '84' is the correct answer.

The logic followed here is:

Logic: (First number + Third number) × 4 = Second number 

• (8, 44, 3) → (8 + 3) × 4 = 11 × 4 = 44
• (12, 60, 3) → (12 + 3) × 4 = 15 × 4 = 60

Similarly,

• (12, 68, 5) → → (12 + 5) × 4 = 17 × 4 = 68

Hence, '(12, 68, 5)' is the correct answer.

The logic followed here is:

Hence, '155' is the correct answer.

The paper when unfolded will appear as shown below:

Hence, 'option 2' is the correct answer.

1. ÷, +, −, ×, =

150 ÷ 3 + 10 - 2 × 7 = 46

⇒ 50 + 10 - 14 = 46

⇒ 60 - 14 = 46

⇒ 46 = 46

2. −, ×, +, ÷, =

150 - 3 × 10 + 2 ÷ 7 = 46

⇒ 150 - 30 + 0.28 = 46

⇒ 150.28 - 30 = 46

⇒ 120.28 ≠ 46

3. +, −, ÷, ×, =

150 + 3 - 10 ÷ 2 × 7 = 46

⇒ 150 + 3 - 5 × 7 = 46

⇒ 150 + 3 - 35 = 46

⇒ 153 - 35 = 46

⇒ 118 ≠ 46

4. ×, +, ÷, −, =

150 × 3 + 10 ÷ 2 - 7 = 46

⇒ 450 + 5 - 7 = 46

⇒ 455 - 7 = 46

⇒ 448 ≠ 46

Hence, '÷, +, −, ×, =' is the correct answer.

The logic followed here is:

Logic: First number + 16 = Second number; Second number - 12 = Third number

• (31, 47, 35) → 31 + 16 = 47; 47 - 12 = 35
• (51, 67, 55) → 51 + 16 = 67; 67 - 12 = 55

Similarly,

• (13, 29, 17) → 13 + 16 = 29; 29 - 12 = 17

Hence, '(13, 29, 17)' is the correct answer.

The correct mirror image of the given combination when the mirror is placed at MN is shown below:

Hence, 'option 1' is the correct answer.

The logic followed here is:

Logic: First one is an expert physician of the second one.

• Orthopaedic : Bone → Orthopaedic surgeons are devoted to the prevention, diagnosis, and treatment of disorders of the bones.

Similarly,

• Cardiologist : ? → A cardiologist is a physician who's an expert in the care of your heart

Hence, 'Heart' is the correct answer.

1. A V K R W M R → A V J R W B V K R W B V L R W B V M R W
2. A W K R X N R → A V J R W B W K R W B V L R X B V N R W
3. B V K R W M R → B V J R W / B V K R W / B V L R W / B V M R W
4. B W K R W M R → B V J R W B W K R W B V L R W B V M R W

• In option 3, a pattern is repeated.
• When the series is divided into four equal parts, we observe that first two and last two letters are same. And the middle most letter follows the pattern shown below.
• J + 1 = K; K + 1 = L; L + 1 = M

Hence, 'B V K R W M R' is the correct answer.

The least possible Venn diagram is:          

Conclusions:

I. Some knives are mixers. → Does not follow (There is no definite relation between knives and scissors. Hence, false)

II. Some scissors are coolers. → Does not follow (There is no definite relation between coolers and scissors. Hence, false)

III. Some knives are coolers. → Does not follow (There is no definite relation between knives and coolers. Hence, false)

IV. No knife is a mixer. → Does not follow (There is no definite relation between knives and mixer. Hence, false)

Hence, ‘None of the conclusions follow’ is the correct answer.

The logic followed here is:

Similarly,

Hence, 'WJV' is the correct answer.

1. 1076 → 1076 is completely divisible by 4.
2. 1675 → 1675 is not completely divisible by 4.
3. 1354 → 1354 is not completely divisible by 4.
4. 1998 → 1998 is not completely divisible by 4.

Therefore, 1076 is a leap year.

Hence, ‘1076’ is the correct answer.

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

Brother of the son of my wife → My wife's son's brother is my son.

Daughter of the brother of the son of my wife → My son's daughter is my granddaughter.

Therefore, Suresha is granddaughter of the person 'I'.

Hence, ‘Grandfather’ is the correct answer.

As 1 and 3 are the common faces on both the dice, the remaining faces 5 and 4 are opposite to each other.

Hence, '5' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'PUJUCCQY' is the correct answer.

The logic followed here is:

Logic: (Second number - Third number)² = First number

1. 36 ∶ 13 ∶ 7 → (13 - 7)2 = 62 = 36
2. 16 ∶ 9 ∶ 5 → (9 - 5)2 = 42 = 16
3. 72 ∶ 16 ∶ 8 → (16 - 8)2 = 82 = 64 ≠ 72
4. 1 ∶ 3 ∶ 2 → (3 - 2)2 = 12 = 1

Hence, '72 ∶ 16 ∶ 8' is the correct answer.

1. + and ÷

294 ÷ 14 × 4 + 16 - 67 = 33

⇒ 21 × 4 + 16 - 67 = 33

⇒ 84 + 16 - 67 = 33

⇒ 100 - 67 = 33

⇒ 33 = 33

2. × and ÷

294 + 14 ÷ 4 × 16 - 67 = 33

⇒ 294 + 3.5 × 16 - 67 = 33

⇒ 294 + 56 - 67 = 33

⇒ 350 - 67 = 33

⇒ 283 ≠ 33

3. + and -

294 - 14 × 4 ÷ 16 + 67 = 33

⇒ 294 - 14 × 0.25 + 67 = 33

⇒ 294 - 3.5 + 67 = 33

⇒ 361 - 3.5 = 33

⇒ 357.5 ≠ 33

4. - and ÷

294 + 14 × 4 - 16 ÷ 67 = 33

⇒ 294 + 56 - 0.23 = 33

⇒ 350 - 0.23 = 33

⇒ 349.77 ≠ 33

Hence, ‘+ and ÷’ is the correct answer.

The logic followed here is:

Logic: First letter is exactly opposite of second letter and First letter - 3 = Third letter

1. KPH → K ↔ P; K - 3 = H
2. GTD → G ↔ T; G - 3 = D
3. DWA → D ↔ W; D - 3 = A
4. EVC → E ↔ V; E - 3 = B ≠ C

Hence, 'EVC' is the correct answer.

The logic followed here is:

Logic: (Second number ÷ First number) ÷ 3 = Third number

• (14, 378, 9) → (378 ÷ 14) ÷ 3 = 27 ÷ 3 = 9
• (18, 432, 8) → (432 ÷ 18) ÷ 3 = 24 ÷ 3 = 8

Similarly,

• (15, 405, 9) → (405 ÷ 15) ÷ 3 = 27 ÷ 3 = 9

Hence, '(15, 405, 9)' is the correct answer.

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols are moved as shown below.

From Figure (2) to (3):

The symbols are moved as shown below.

From Figure (3) to (4):

The symbols are moved as shown below.

From Figure (4) to Answer Figure (5):

The symbols are moved as shown below.

Hence, the correct answer is "Option (2)".

The least possible Venn diagram is:

Conclusions:

I. All rice are edibles. → Follows (As, All rice are grains and All grains are edibles)

II. All pulses are edibles. → Follows (As, All pulses are grains and All grains are edibles)

III. Some edibles are grains. → Follows (As, All grains are edibles)

Hence, 'All conclusions follow' is the correct answer.

The option that represents the correct order of the given words as they would appear in an English dictionary is:

3. Shirking
4. Spawn
5. Spider
6. Strident
7. Student
8. Stuffy

Hence, '3, 6, 5, 1, 2, 4' is the correct answer.

The correct option is Sarangi. 

Key Points

• Sarangi:-
• It is a bowed string instrument that is a staple of Indian classical music.
• It is a long, hollow wooden body with a skin covering. It has three strings, which are attached to a bow.
• The bow is played with a bow.
• Shakoor Khan and Pandit Ram Narayan were both renowned musicians who played the sarangi, a stringed instrument that is popular in Indian classical music.

Additional Information

• Shehnai:-
• It​ is a wind instrument that is commonly played in North Indian weddings and other auspicious occasions.
• Guitar:-
• It is a western instrument that is not typically associated with Indian classical music.
• Veena:-
• It is a plucked stringed instrument that is popular in South Indian classical music.

The correct option is 3rd.

Key Points

• Indian Brand Equity Foundation:-
• It is a government of India initiative that works to promote the brand image and prestige of India.
• IBEF was formed in 2003 and is headquartered in New Delhi.
• The mission of IBEF is to develop India as a global brand. It works to promote India's diversity, richness, and culture.
• IBEF also works to raise awareness of India and attract foreign investment.
• According to IBEF 2021, the Indian pharmaceutical industry ranks 3rd in the world on the basis of volume.

Additional Information

• Indian pharmaceutical industry:-
• It is the largest provider of generic drugs globally and accounts for 20% of the world's generic drug exports.
• India is also one of the world's largest producers of vaccines, supplying more than 60% of vaccines globally.
• The Indian pharmaceutical industry is expected to grow at a CAGR of 11% to reach USD 130 billion by 2030.

The correct answer is 1954.

Key Points

• Linus Carl Pauling:-
• He was an American chemist, biochemist, chemical engineer, peace activist, author, and educator.
• He published more than 1,200 papers and books, of which about 850 dealt with scientific topics.
• Linus Carl Pauling received the Nobel Prize in Chemistry in 1954.
• He received the prize for his research into the nature of the chemical bond and its applications to the elucidation of the structure of complex substances.

Additional Information

• Pauling's work on chemical bonding led to the development of the concept of electronegativity, which is a measure of the ability of an atom to attract electrons towards itself.
• In addition to his work in chemistry, Pauling was also a peace activist and received the Nobel Peace Prize in 1962 for his efforts in promoting nuclear disarmament.

The correct option is Odisha.

Key Points

• Daskathia:-
• It is a tribal dance form that originated in Odisha and is performed by two males.
• The dance form depicts historic and Puranic events through facial expressions, hand gestures, and body movements.
• The performers wear traditional attire and use various musical instruments like mridanga, dhol, and flute.
• The dance form is an integral part of the Odia culture and is performed during festivals and important occasions.

Additional Information

• Uttar Pradesh:
• The state is known for its rich cultural heritage and is home to various dance forms like Kathak, and Charkula.
• Gujarat:
• The state is famous for Garba, a dance form performed during Navratri.
• Dandiya Raas is another popular dance form of Gujarat.
• Goa:
• The state is known for its Portuguese influence and is famous for its music and dance forms like Fugdi and Dekhni.

The correct option is Article 21.

• KA Najeeb Vs Union of India:-
• It​ case deals with the violation of the right to life and personal liberty under Article 21 of the Indian Constitution.
• Article 21 is a fundamental right that protects the life and personal liberty of every person.
• It has been interpreted by the Indian judiciary to include a wide range of rights such as the right to live with dignity, the right to privacy, the right to health, the right to clean environment, the right to education, and the right to speedy trial.
• Article 16:-
• It deals with the right to equality of opportunity in matters of public employment.
• It prohibits discrimination based on religion, race, caste, sex, descent, or place of birth when it comes to government jobs

Article 14:-

• It​ deals with the right to equality before the law and equal protection of the law.
• It essentially states that everyone is equal in the eyes of the law, regardless of factors like religion, race, caste, sex, or place of birth.
• Article 19:-
• It deals with the six freedoms of speech and expression, assembly, association, movement, residence, and profession or occupation.
• These are subject to reasonable restrictions imposed by the state in the interest of sovereignty and integrity of India, security of the state, friendly relations with foreign states, public order, decency, or morality, or in relation to contempt of court, defamation, or incitement to an offense.

The correct answer is Rhodophyceae.

Key Points

• Red algae:-
• It is a type of marine algae that are predominantly red in color due to the presence of pigments such as phycoerythrins and phycocyanins.
• They are found in both tropical and temperate waters and play an important role in marine ecosystems as primary producers and as a food source for herbivorous marine animals.
• Some species of red algae are also used by humans for various purposes such as food, medicine, and cosmetics.
• Red algae are known for their ability to survive in extreme environments such as deep-sea hydrothermal vents and polar regions.

Additional Information

• Chlorophyceae:
• This is a class of green algae that are mostly freshwater species and are commonly found in ponds, lakes, and streams.
• Liverwort:
• This is a type of non-vascular plant that grows in damp habitats such as forests, bogs, and riverbanks.
• They are commonly found in temperate and tropical regions and play an important role in soil formation and nutrient cycling.
• Phaeophyceae:
• This is a class of brown algae that are predominantly marine and are commonly found in temperate and cold waters.
• They are important primary producers in coastal ecosystems and are also used by humans for food and other purposes.

The correct answer is 9.

Key Points

• Element X:-
• The element X placed in period 2 and group 17 is a halogen.
• Halogens are highly reactive non-metals and have 7 valence electrons in their outermost shell.
• Since the element X is placed in group 17, it means it has 7 valence electrons.
• The atomic number of an element is equal to the number of protons in its nucleus.
• Therefore, the atomic number of element X will be 9 as it has 9 protons in its nucleus.

Additional Information

• The atomic number of oxygen is 8, which is the element placed in period 2 and group 16.
• Nitrogen is the element placed in period 2 and group 15 with an atomic number of 7.
• The element with atomic number 10 is neon, which is placed in period 2 and group 18.

The correct answer is 2021 and 2022.

Key Points

• Republic Day:-
• It​ is celebrated in India on 26th January every year to commemorate the day on which the Constitution of India came into effect in 1950.
• The event is marked by a grand parade in the national capital, New Delhi, which is attended by the President of India, who is also the Commander-in-Chief of the Indian Armed Forces.
• However, in some years, there may not be a chief guest, who is usually a foreign dignitary invited to attend the celebrations as a guest of honor.
• In 2021 and 2022, there were no chief guests at the Republic Day celebrations due to the COVID-19 pandemic and the resulting travel restrictions.

Additional Information

• In 2019, the chief guest was Cyril Ramaphosa, the President of South Africa.
• In 2020, the chief guest was Jair Bolsonaro, the President of Brazil.
• In 2018, the chief guest was Nguyen Phu Trong, the General Secretary of the Communist Party of Vietnam.

The correct answer is MV = PT.

Key Points

• Fisher's quantity theory:-
• It​ is a monetary theory that explains the relationship between money supply, velocity of money, price level, and output.
• The famous equation given by Fisher is MV = PT, where M is the money supply, V is the velocity of money, P is the price level, and T is the level of transactions.
• The equation suggests that an increase in the money supply (M) will lead to an increase in the price level (P), assuming that the velocity of money (V) and the level of transactions (T) are constant.
• The theory also implies that changes in the money supply have a direct impact on inflation, as an increase in the money supply leads to an increase in the price level, which in turn reduces the purchasing power of money.

Additional Information

• The quantity theory of money has been subject to criticism over the years, with some economists arguing that it oversimplifies the complex dynamics of the economy.
• One of the criticisms is that the velocity of money is not constant and can vary significantly over time, making it difficult to predict the impact of changes in the money supply on the price level.
• Another criticism is that the theory assumes that the level of transactions is fixed, which is not always the case as it can be influenced by a variety of factors such as technology, demographics, and government policies.

The correct answer is cotton and silk fabrics.

Key Points

• Before the rise of the modern industrial system, Indian exports consisted chiefly of manufactures like cotton and silk fabrics.
• Cotton and silk fabrics were the major exports from India before the modern industrial system.
• India has a rich history of textile manufacturing, and fabrics were in high demand in the international market.
• The textile industry was the backbone of the Indian economy during the pre-industrialization period.
• The demand for Indian fabrics was so high that it led to the establishment of the East India Company in India.

Additional Information

• Electricals:
• Electricals were not manufactured in India during the pre-industrialization period.
• It was only after the British introduced the electric power system in India that the manufacturing of electricals began.
• Chemicals:
• Chemicals were not a major export from India during the pre-industrialization period.
• It was only after the establishment of the chemical industry in India that it became a major export.
• Light Machinery:
• Light machinery was not manufactured in India during the pre-industrialization period.
• It was only after the introduction of the modern industrial system in India that the manufacturing of machinery began.

The correct answer is Darjeeling and Sikkim Himalayas.

Key Points

• Kanchenjunga:-
• ​It is the third-highest mountain peak in the world and is located in the eastern Himalayas, specifically between Nepal and Sikkim, India.
• Darjeeling and Sikkim Himalayas are part of the Eastern Himalayan range, which is known for its rich biodiversity and cultural heritage.

Additional Information

• Kashmir Himalayas:-
• These​ are located in the western part of the Himalayan range and are known for their scenic beauty and adventure sports opportunities.
• Himachal and Uttaranchal Himalayas:-
• These​ are located in the central part of the Himalayan range and are known for their hill stations, trekking trails, and religious sites.
• Arunachal Himalayas:-
• These are located in the easternmost part of the Himalayan range and are known for their **rugged terrain, diverse wildlife, and tribal culture.**​

​

The correct answer is Manipuri.

Key Points

• Guru Bipin Singh:-
• He​ was a renowned dance exponent and teacher from Manipur, India.
• He was instrumental in promoting and popularizing the Manipuri dance form across the country and the world.
• He trained several students and established the Manipuri Nartanalaya in New Delhi to impart training in the dance form.
• Guru Bipin Singh received several prestigious awards for his contributions to the field of dance, including the Nrityacharya, Sangeet Natak Akademi, and Kalidas Samman awards.

Additional Information

• Kuchipudi
• It is a classical dance form from Andhra Pradesh, India.
• It is known for its intricate footwork, graceful movements, and expressive storytelling.
• Odissi:-
• It is a classical dance form from Odisha, India.
• It is characterized by fluid movements, intricate hand gestures, and elaborate costumes.
• Kathak:-
• It​ is a classical dance form from northern India, known for its rhythmic footwork, intricate hand movements, and storytelling through dance.

The correct option is The President of India.

Key Points

• President of India:-
• The President of India holds the authority of transferring judges from one High Court to another High Court.
• The president is elected by an electoral college consisting of the elected members of both houses of parliament and the elected members of the legislative assemblies of the states and union territories.
• The president serves a five-year term and can be re-elected .
• The President of India is the head of the executive branch of the government of India and is also the Commander-in-Chief of the Indian Armed Forces.

Additional Information

• The senior most judge of Supreme Court is responsible for the appointment of judges to the Supreme Court.
• The Chief Justice of India is responsible for the administration of the Supreme Court and the High Courts.
• The Law Minister of India is responsible for the formulation and implementation of laws and policies related to the legal system of India.

The correct answer is Rancidification.

Key Points

• Rancidification:-
• It is a process of spoilage of fats and oils when exposed to air, light, moisture, or bacterial action.
• The oxidation process breaks down the fatty acids and produces unpleasant odors and flavors in the food.
• Rancidification can be prevented by storing food in airtight containers, refrigeration, or adding antioxidants.

Additional Information

• Hydrogenation:-
• It is a process of adding hydrogen to unsaturated fats to make them solid at room temperature, which is used to make margarine and shortening.
• Auto-oxidation:-
• It is a chemical reaction that occurs when oxygen reacts with unsaturated fatty acids, leading to the formation of free radicals and lipid peroxides.
• Auto-reduction:-
• It is a process of reducing a chemical compound without the addition of external agents, which is not related to the spoilage of food.

The correct answer is Tripuri.

Key Points

• Tripuri:-
• It is a Tibeto-Burmese language spoken in the Indian state of Tripura and parts of Bangladesh.
• Tibeto-Burmese languages are a branch of the Sino-Tibetan language family and are spoken in parts of China, India, Myanmar, Nepal, Bhutan, and Bangladesh.

Additional Information

• Odia:-
• It​ is also known as Oriya, is an Indo-Aryan language spoken in the Indian state of Odisha.
• Assamese:-
• It is also an Indo-Aryan language spoken in the Indian state of Assam and parts of Bangladesh.
• Tulu:-
• It​ is a Dravidian language spoken in the Indian state of Karnataka and parts of Kerala.

The correct answer is Shudraka.

Key Points

• Mrichchhakatika:-
• It is a Sanskrit play, also known as 'The Little Clay Cart'.
• It is believed to have been written by Shudraka, a playwright who lived in ancient India in the 5th century CE.
• The play is a romantic comedy that tells the story of a poor Brahmin named Charudatta and his love for a courtesan named Vasantasena.
• Shudraka is considered one of the greatest playwrights of ancient India, along with Kalidasa and Bhasa.

Additional Information

• Kalidasa:-
• He is known for his plays like 'Abhijnanasakuntalam', 'Vikramorvasiyam', and 'Malavikagnimitram'.
• Amarasimha:-
• He was a Sanskrit grammarian and lexicographer.
• Bhasa:-
• He was another famous playwright who wrote plays like 'Swapnavasavadattam', 'Pratijna Yaugandharayana', and 'Madhyamavyayoga'.

The correct answer is Baikal rocks are formed from the dissolved materials that precipitate from the solution.

Key Points

• Baikal rocks are actually formed from the solidification of magma or lava, not from dissolved materials that precipitate from the solution. -
• Sedimentary rocks are indeed formed by the deposition and subsequent cementation of material within bodies of water and at the surface of the earth.
• Metamorphic rocks are formed by the alteration of existing rock types through heat, pressure, or chemically active fluids.
• Igneous rocks are indeed formed through the cooling and solidification of magma or lava.

Additional Information

• Baikal rocks refer to the rocks found in the Baikal Rift Zone, a region of active tectonic activity in Russia.
• Sedimentary rocks are the most common type of rock on Earth and include types such as sandstone, limestone, and shale.
• Metamorphic rocks include types such as marble, slate, and gneiss and can be formed from sedimentary, igneous, or even other metamorphic rocks.
• Igneous rocks can be intrusive (formed from magma that cools slowly beneath the Earth's surface) or extrusive (formed from lava that cools quickly on the Earth's surface).

The correct option is Khan Abdul Ghaffar Khan.

Key Points

• Khan Abdul Ghaffar Khan:-
• He was also known as Bacha Khan.
• Khudai Khidmatgars was a non-violent movement founded by Khan Abdul Ghaffar Khan in 1929 in the North-West Frontier Province of British India (now Khyber Pakhtunkhwa province of Pakistan).
• The movement was aimed at promoting social reforms and political freedom through peaceful means.
• The members of the movement wore red shirts as a symbol of their unity and commitment to the cause.
• Khan Abdul Ghaffar Khan was a Pashtun nationalist, a devout Muslim, and a close associate of Mahatma Gandhi.
• He was also known as the "Frontier Gandhi" for his commitment to non-violence and his work towards Hindu-Muslim unity.

Additional Information

• Muhammad Ali:-
• He was a prominent leader of the Indian National Congress and a supporter of the Khilafat movement.
• MA Ansar:-
• He was a Muslim scholar and a leader of the Khilafat movement.
• Hasrat Mohan:-
• He was a poet and a political activist who was associated with the Indian National Congress and the Communist Party of India.

The correct answer is Gujarat.

Key Points

• National Games:-
• The National Games is a biennial multi-sport event that features athletes from all over India.
• The event is organized by the Indian Olympic Association (IOA) and is considered to be one of the biggest sporting events in the country.
• The 36th National Games were held in Gujarat from 29^th Sep 2022 to 12^th Oct 2022.
• New Delhi, and Kerala have also hosted the National Games in the past.

Additional Information

• Andhra Pradesh: The 32nd National Games were held in Andhra Pradesh in 2002.
• The event was held in the city of Hyderabad and featured 34 sports disciplines.
• New Delhi: The 26th National Games were held in New Delhi in 1985.
• Kerala: The 27th and 35th National Games were held in Kerala in 1987, and 2015 respectively.
• Kerala is known for its sports culture and has produced many top athletes in various sports.

The correct answer is Arya Samaj.

Key Points

• Arya Samaj:-
• It was established in Bombay.
• Arya Samaj is a Hindu reform movement founded by Swami Dayanand Saraswati in 1875.
• It aims to promote the Vedas as the only source of truth and to reject all forms of idol worship, caste system, and superstitions.
• The Arya Samaj played a significant role in the Indian independence movement and social reform movements such as the abolition of child marriage and dowry system.

Additional Information

• Satyashodhak Samaj:
• It was founded by Jyotirao Phule in 1873 in Maharashtra.
• It aimed to fight against caste discrimination and to provide education to the lower castes.
• Aligarh movement:
• It was founded by Sir Syed Ahmed Khan in 1875 in Aligarh, Uttar Pradesh.
• It aimed to promote modern education among Muslims and to create a class of educated Muslims who could work with the British government.
• Brahmo Samaj:
• It was founded by Raja Ram Mohan Roy in 1828 in Kolkata.
• It aimed to promote monotheism and to reject idol worship, caste system, and other superstitions.

The correct answer is Elected head.

Key Points

• Elected head:-
• It conveys the meaning of the word "Republic" in the Indian Constitution.
• A republic is a form of government in which the head of state is elected by the citizens or their representatives.
• In India, the President is the head of state and is elected by an electoral college consisting of members of both houses of Parliament and state legislatures.
• The President holds a largely ceremonial role and acts as a symbol of national unity.

Additional Information

• Nominated head:-
• It​ refers to a monarch or a person appointed by a monarch.
• Subordinate head:-
• It​ refers to a position lower in rank than the head.
• Hereditary head:-
• It​ refers to a monarch or a person who inherits the position of head of state.

The correct answer is Medini Rai.

Key Points

• Battle of Chanderi:-
• It was fought on January 20, 1528, between the Mughal forces of Babur and the Rajput forces of Medini Rai, the ruler of Malwa.
• The battle took place in the aftermath of the Battle of Khanwa, in which Babur had defeated a Rajput confederacy led by Rana Sanga.

Additional Information

• Babur was the founder of the Mughal Empire in India and ruled from 1526 to 1530.
• Shershah Suri was a ruler of the Sur dynasty who defeated Humayun, the son of Babur, and established the Sur Empire in India.
• Sikandar Lodi  was the most important ruler of the Lodi Dynasty, a part of India's Delhi Sultanate.
• He ascended Bahlul Lodi and was the dynasty's second ruler.
• In 1504 CE, he founded Agra city and made it his new Capital (earlier Delhi).
• Ibrahim Lodi was a ruler of the Lodi dynasty who ruled Delhi before Babur's invasion.

The correct answer is Tokyo.

Key Points

• Olympic Games:-
• These are international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a variety of competitions.
• Tokyo was awarded the 2020 Olympic Games in 2013, beating Istanbul and Madrid in the final selection process.
• Tokyo had previously hosted the Summer Olympics in 1964, making it the first Asian city to do so.

Additional Information

• Sydney: Hosted the 2000 Summer Olympics.
• It is the largest city in Australia and the state capital of New South Wales.
• Rio: Hosted the 2016 Summer Olympics.
• It is the second-largest city in Brazil and is known for its beaches, carnival, and Christ the Redeemer statue.
• Los Angeles: Set to host the 2028 Summer Olympics.
• It is the largest city in California and the second-largest city in the United States.
• It previously hosted the Summer Olympics in 1932 and 1984.

The correct answer is 11 October.

Key Points

• International Day of the Girl Child:-
• It is celebrated every year on October 11th to highlight the challenges that girls face and promote their empowerment.
• The first Day of the Girl Child was observed on October 11, 2012.
• The International Day of the Girl Child was established on October 11 by Resolution 66/170, which was approved by the UN General Assembly on December 19, 2011.

Additional Information

List of important days in October:

• International Day of the Older Person (October 1)
• International Coffee Day (October 1)
• World Vegetarian Day (October 1)
• Gandhi Jayanti (October 2)
• International Day of Non-Violence (October 2)
• World Habitat Day (October 4)
• World Animal Welfare Day (October 4)
• World Teachers' Day (October 5)
• Indian Air Force Day (October 8)
• World Postal Day (October 9)
• World Mental Health Day (October 10)
• World Food Day (October 16)
• World Polio Day (October 24)
• United Nations Day (October 24)

The correct answer is Odisha.

Key Points

• Bhima Bhoi Bhinnakhyama Samarthya Abhiyan (BBSA):-
• In January 2022, the Odisha government announced the extension of its Bhima Bhoi Bhinnakhyama Samarthya Abhiyan (BBSA) for the next five years.
• This initiative is aimed at empowering persons with disabilities (PwDs) in the state.
• The BBSA was launched in 2018 and has been successful in providing various benefits to PwDs, including financial assistance, skill development, and employment opportunities.
• The extension of BBSA for the next five years will help in reaching out to more PwDs and providing them with the necessary support and resources.
• Odisha is among the leading states in India when it comes to promoting the welfare and rights of PwDs.
• The state has various schemes and programs in place to ensure their inclusion in society.

Additional Information

• Manipur:
• The government of Manipur has launched various schemes and programs for the welfare of PwDs, including financial assistance, education, and employment opportunities.
• Jharkhand:
• The Jharkhand government has launched the Mukhyamantri Divyangjan Udyamita Vikas Abhiyan (MDUVA) to promote entrepreneurship among PwDs.
• West Bengal:
• The West Bengal government has launched various schemes and programs for the welfare of PwDs, including financial assistance, education, and employment opportunities.

Given:

Length of circular cycling track = 75 km

The speed of 2 cyclists is 30 kmph and 25 kmph respectively.

Formula:

Time = distance/speed

LCM of fractions = [LCM of numerators of fractions] / [HCF of denominators of fractions]

Calculation:

Time taken by each to cover one round = 75/30

Time taken by each to cover one round = 75/25 

∴ Required time = LCM(75, 75) / HCF(30, 25)

= 75/5  = 15 hours

They meet at the point from where they started their journey after 15 hours.

Given

P is two times as efficient as Q

P is able to complete a piece of work in 40 days less than Q.

Concept

Efficiency is inversely related to time.

Work done = efficiency × time

Calculation

P = 2Q

P:Q = 2:1

The ratio of time = 1:2

1 → 40

P's time = 40

Q's time = 80

Working together, the whole number of days taken by them to complete the work is:

⇒ (80 × 40)/120

⇒ 26.66 = 27 days

Working together, the whole number of days taken by them to complete the work is 27 days.

Shortcut Trick

Let Total Enrolled Voters be 100%.

A got 43% of the voter list.

Since 2% did not vote and 500 were invalid, B received: (100% − 2% − 43%) − 500 = 55% − 43% − 500 = 12% − 500.

Difference (A − B) = 43% − (55% − 43% − 500) = 43% − 12% + 500 = 31% + 500 = 200 (Impossible, hence B is (100% − 2% − 43%) − 500).

Let Total = x. 0.43x − (0.98x − 0.43x − 500) = 200 ⇒ 0.43x − 0.55x + 500 = 200 ⇒ 0.12x = 300 ⇒ x = 2500.

Total Casted Votes = 98% of 2500 = 2450.

∴ The correct answer is 2450.

Alternate Method

Given:

⇒ Non-participants = 2% of Enrolled

⇒ Invalid votes = 500

⇒ A's votes = 43% of Enrolled

⇒ Victory margin (A − B) = 200

Calculations:

⇒ Let Total Enrolled Voters = x

⇒ Total Casted Votes = 98% of x = 0.98x

⇒ Valid Votes = Casted Votes − Invalid = 0.98x − 500

⇒ A's votes = 0.43x

⇒ B's votes = Valid Votes − A's votes = (0.98x − 500) − 0.43x = 0.55x − 500

⇒ Margin = A − B = 0.43x − (0.55x − 500) = 200

⇒ 0.43x − 0.55x + 500 = 200

⇒ −0.12x = −300

⇒ x = 300 ÷ 0.12 = 2500

⇒ Total Casted Votes = 0.98 × 2500 = 2450

∴ The correct answer is 2450.

Additional Information

Election Vocabulary

Voter List refers to total enrolled voters. Casted votes include valid and invalid votes. Valid votes are those used to determine the winner/loser.

Percentage Base Change

Always identify if a percentage is based on the total enrollment or valid votes. Calculation error occurs when the wrong base is used.

Shortcut Trick

Convert 65° to its complementary angle.

⇒ sin 65° = cos(90° − 65°) = cos 25°

⇒ cos 65° = sin(90° − 65°) = sin 25°

Substitute these into the given expression:

⇒ sin 25° cos 25° − cos 25° sin 25° = 0

∴ The correct answer is 0.

Alternate Method

Given:

sin 25° sin 65° − cos 25° cos 65°

Formula Used:

cos(A + B) = cos A cos B − sin A sin B

Calculation:

⇒ Re-write the given expression by taking the negative sign common:

⇒ − (cos 25° cos 65° − sin 25° sin 65°)

⇒ Apply the formula taking A = 25° and B = 65°

⇒ − cos(25° + 65°)

⇒ − cos(90°)

⇒ Since cos(90°) = 0

⇒ 0

∴ The correct answer is 0.

Additional Information

Complementary Angles

sin(90° − θ) = cos θ | cos(90° − θ) = sin θ | tan(90° − θ) = cot θ

Trigonometric Sum & Difference Formulas

sin(A + B) = sin A cos B + cos A sin B | cos(A − B) = cos A cos B + sin A sin B

Double Angle Formulas

sin 2A = 2 sin A cos A | cos 2A = cos² A − sin² A

Calculation

The population of village D(8%) in 2020 = 10,500.

The population of village A in 2020 = 12%

⇒ 8% → 10500

⇒ 12% → 10500 × 12/8

= 5250 × 3 = 15750

The population of village A in 2020 is 15750.

Given

64x3 + 38x2y + 20xy2 + y3

x = 3 and  y = - 4

Formula used

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

64x3 + 38x2y + 20xy2 + y³ = (4x + y)³ - 10x²y + 8xy²

⇒ (4x + y)3 - 10x2y + 8xy² = (12 - 4)3 - 10(3)2(- 4) + 8(3)(- 4)2

⇒ 8³ + 360 + 384

⇒ 1256

The value is 1256.

Shortcut Trick

Total Work = LCM(9, 36) = 36 units.

Efficiency: X = 4, Y = 1. Total efficiency in 2 days = 4 + 1 = 5 units.

Work in 14 days (7 cycles) = 5 × 7 = 35 units. Remaining work = 36 − 35 = 1 unit.

X takes 1/4 day to finish 1 unit. Total time = 14 + 1/4 = 14 1/4 days.

∴ The correct answer is 14 1/4 days.

Alternate Method

Given: X completes work in 9 days, Y in 36 days. They work alternately starting with X.

⇒ Total work completed in one cycle (Day 1: X + Day 2: Y) = 4 + 1 = 5 units.

⇒ Number of complete cycles to reach 36 units = 36 ÷ 5 = 7 cycles (remains 1 unit).

⇒ Time for 7 cycles = 7 × 2 = 14 days. Work done = 35 units.

⇒ Remaining Work = 36 − 35 = 1 unit.

⇒ On 15th day, it is X's turn. Time taken by X = 1/4 day.

⇒ Total time = 14 + 1/4 = 14 1/4 days.

∴ The correct answer is 14 1/4 days.

Additional Information

Alternate Day Work

In alternate work, identify the cycle length and total efficiency per cycle. The sequence of who starts first (X or Y) significantly changes the total time if the remaining work is not zero.

Efficiency and Time Relation

Efficiency is inversely proportional to time. If X is twice as efficient as Y, X will take half the time of Y to complete the same work.

Total Work Calculation

Total work is always assumed as the Least Common Multiple (LCM) of the individual days taken by workers to simplify fractional calculations.

Shortcut Trick

Use the Successive Multiplication Factor method:

Weight Ratio (Profit from cheating) = 1000 / 940

Price Ratio (Stated profit) = 104 / 100

Total Ratio = (1000 / 940) × (104 / 100) = 1040 / 940 = 1.10638...

Actual Profit % = (1040 − 940) / 940 × 100 = 1000 / 94 = 10.638...

∴ The correct answer is 10.64%.

Alternate Method

Given:

Actual weight = 1 kg = 1000 gm

False weight used = 940 gm

Stated profit % = 4%

Calculations:

⇒ Let the cost price (CP) of 1 gm be ₹1.

⇒ Total CP for 1000 gm = ₹1000.

⇒ Shopkeeper sells it at 4% profit ⇒ Selling Price (SP) = 1000 × (104 / 100) = ₹1040.

⇒ However, the shopkeeper gives only 940 gm ⇒ Actual cost to shopkeeper = ₹940.

⇒ Profit = SP − Actual CP = 1040 − 940 = ₹100.

⇒ Actual Profit % = (Profit / Actual CP) × 100

⇒ Actual Profit % = (100 / 940) × 100 = 1000 / 94

⇒ Actual Profit % ≈ 10.638%

∴ The correct answer is 10.64%.

Additional Information

Dishonest Dealer Formula

Profit % = [(True Weight − False Weight) / False Weight] × 100. When sold at profit 'p%', overall profit = [{(100+p)/100 × (True/False)} − 1] × 100.

Successive Discounts

If two successive discounts d₁% and d₂% are given, the equivalent discount = (d₁ + d₂ − d₁d₂/100)%.

Marked Price and CP Relation

MP / CP = (100 + Profit%) / (100 − Discount%). This is useful for finding the markup percentage.

Concept: In a right-angle triangle, the length of the median is half the length of the hypotenuse.

Calculation:

In right-angled ∆ABC, 90° at A

BC² = AB² + AC² 

If, D is the midpoint of BC, then

AD = BD = CD = BC/2

Given:

We know that the cost of water = Rs. 0 per litre

Cost of milk = Rs. 32 per litre

Cost of mixture = Rs. 28 per litre

Formula used:

Cost of mixture = Total cost / Total quantity

Calculation:

Let the ratio of water and milk be "1 : a"

⇒ (1 × 0) + (a × 32) = (1 + a) × 28

⇒ 0 + 32a = 28 + 28a

⇒ 4a = 28

⇒ a = 7

Now, the ratio of water and milk is 1 : 7

Shortcut Trick

Now the ratio of water and milk is 1 : 7.

Shortcut Trick

Daily earning of 5 women + 9 girls = 18720 ÷ 9 = ₹2080

Daily earning of 9 women + 16 girls = 52080 ÷ 14 = ₹3720

Solving equations: 1 woman (W) = ₹200 and 1 girl (G) = ₹120

12 women + 7 girls for 1 day = (12 × 200) + (7 × 120) = 2400 + 840 = ₹3240

Total for 13 days = 3240 × 13 = ₹42120

∴ The correct answer is ₹42120.

Alternate Method

Given:

Case 1: (5W + 9G) × 9 = ₹18720

Case 2: (9W + 16G) × 14 = ₹52080

Calculations:

⇒ 5W + 9G = 18720 ÷ 9 = 2080 ... (i)

⇒ 9W + 16G = 52080 ÷ 14 = 3720 ... (ii)

⇒ Multiply (i) by 9 and (ii) by 5:

⇒ 45W + 81G = 18720

⇒ 45W + 80G = 18600

⇒ Subtracting these: 1G = 18720 − 18600 = ₹120

⇒ Substitute G in (i): 5W + 9(120) = 2080 ⇒ 5W + 1080 = 2080 ⇒ 5W = 1000 ⇒ 1W = ₹200

⇒ Required: (12W + 7G) × 13 days

⇒ [(12 × 200) + (7 × 120)] × 13

⇒ [2400 + 840] × 13 = 3240 × 13 = ₹42120

∴ The correct answer is ₹42120.

Additional Information

Work and Wages Principle

Wages are distributed based on the efficiency and the number of days worked. Total Earnings = (Number of persons × Efficiency × Days).

Linear Equations in Two Variables

For equations of the form a₁x + b₁y = c₁ and a₂x + b₂y = c₂, the elimination method is used to find the individual value of variables like Women and Girls.

Given: 

Discounts allowed by shopkeeper = 20 % and 25 %

Reward points = 2850 

Marked price = 72000

Formula used: 

Marked price = Selling price [100 / (100 – discount %)] × [100 / (100 - discount %)]

Calculation: 

Selling price = 72000 × [100 / (100 – 20%)] × [100 / (100 - 25%)]

⇒ 72000 × 80/100 × 75/100

⇒ 72 × 8 × 75

⇒ 43200

1 reward point → ₹0.10

2850 reward points → 285

Final S.P will be = 43200 - 285

⇒ 42915

The net selling price is 42915.

Shortcut Trick

Let us assume values for variables such that a + b + c = 0.

Let a = 1, b = 1, and c = −2.

Calculate a³ + b³ + c³ ⇒ (1)³ + (1)³ + (−2)³ = 1 + 1 − 8 = −6.

Check the option 3abc ⇒ 3 × 1 × 1 × (−2) = −6.

Since both values match, the correct expression is 3abc.

∴ The correct answer is 3abc.

Alternate Method

Given:

a + b + c = 0

Formula Used:

a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Calculation:

⇒ Substitute the given condition (a + b + c) = 0 into the standard identity.

⇒ a³ + b³ + c³ − 3abc = (0) × (a² + b² + c² − ab − bc − ca)

⇒ a³ + b³ + c³ − 3abc = 0

⇒ a³ + b³ + c³ = 3abc

∴ The correct answer is 3abc.

Additional Information

Important Algebraic Identity

a³ + b³ + c³ − 3abc = 1/2(a + b + c)[(a − b)² + (b − c)² + (c − a)²]

Sum of Squares Expansion

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

Special Case Equality

If a² + b² + c² − ab − bc − ca = 0, then it implies a = b = c.

Given:

cos (36° - A) cos (36° + A) + cos (54° - A) cos (54° + A)

Formula used:

cos (a - b) = cos a cos b + sin a sin b.

sin (90 - a) = cos a

Calculation:

⇒ sin[90 – (36 – A)]sin[90 – (36 + A)] + cos (54° – A) cos (54° + A)

⇒ sin(54^º + A)sin(54^º – A) + cos (54° – A)cos (54° + A)

⇒ Using the identity cos(A – B),

⇒ cos(54 + A – 54 + A) = cos(2A)

Therefore, the value of cos (36° - A) cos (36° + A) + cos (54° - A) cos (54° + A) is cos(2A).

Given:

Expenditure incurred on binding = 30%

Expenditure incurred on printing = 25%

Calculation:

From the pie chart,

Total expenses = 100%

Total Central angle of circle = 360°

⇒ 100% → 360°

The difference between the angle of the pie-chart showing the expenditure incurred on binding and printing = 30 - 25 = 5%

⇒ 5% ≡ (360/100) × 5 = 18°  

∴  The central angle corresponding to the difference between the angle of pie-chart showing the expenditure incurred on binding and printing is 18°.

Given:

The total surface area of a cube = 24 cm².

Formula used:

The total surface area of a cube = 6a²

The volume of a cube = a³

Calculation:

According to the question,

6a2 = 24

⇒ a² = 4

⇒ a = 2 cm

The volume of the cube = (2)³

⇒ 8 cm³

∴ The volume of the cube is 8 cm3.

Given :

$4 \frac{4}{5} ÷ \frac{3}{5}$ of $5+\frac{4}{5} × \frac{3}{10}-\frac{1}{5}$

BODMAS Rule:

Calculation :

24/5 ÷ 3/5 of 5 + 4/5 × 3/10 - 1/5

⇒ 24/5 ÷ 3 + 4/5 × ​3/10 - 1/5

⇒ 8/5 + 6/25 - 1/5

⇒ (40 + 6 - 5)/25

⇒ 41/25

⇒ $1 \frac{16}{25}$

∴ The answer is $1 \frac{16}{25}$.

Given:

ΔABC ~ ΔPQR 

PR = 5 cm and BC = 13 cm

Concept:

The ratio of the sides of two similar triangles is equal.

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure

Calculation

Since the triangles are congruent their corresponding angles and side will always be equal.

∴ The length of AB is 12 cm.

Given:

Mean proportional of 7 and 112

Formula used:

Mean proportional of p and q = √(pq)

Calculation:

Let the mean proportion of p and q be x.

⇒ x = √7 × 112

⇒ x  = √784

⇒ x  = 28

The mean proportion between 7 and 112 is 28.

Shortcut Trick

Efficiency ratio of Woman : Boy → 4W = 6B ⇒ W : B = 3 : 2.

Total Work = Efficiency of Boy × Time = 2 × 60 = 120 units.

Efficiency of 5 Women = 5 × 3 = 15 units.

Required Time = Total Work ÷ Efficiency = 120 ÷ 15 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given: 4 Women = 6 Boys ⇒ 1 Woman = 1.5 Boys.

⇒ If 1 Boy takes 60 days, then 1 Woman takes 60 ÷ 1.5 = 40 days.

⇒ Total Work = 60 × 2 = 120 units (assuming Boy efficiency is 2).

⇒ Efficiency of 1 Woman = 120 ÷ 40 = 3 units.

⇒ Efficiency of 5 Women = 5 × 3 = 15 units.

⇒ Time taken by 5 Women = 120 ÷ 15 = 8 days.

∴ The correct answer is 8 days.

Additional Information

Work Equivalence Formula

M₁D₁H₁ = M₂D₂H₂ where M is number of workers, D is days, and H is hours per day.

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken. If the ratio of efficiency is x : y, the ratio of time taken is y : x.

Work and Wages

Wages are always distributed in the ratio of the work done or the ratio of efficiencies when time worked is the same.

Given :

A 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord

Concept used :

The line is drawn from the centre of a circle towards a chord always divides the chord in two equal parts and also perpendicular to the chord. 

Calculations :

Let the centre of the circle be 'O' and 'AO' is the radius 

Let the chord be 'AB' where 'C' is the midpoint of the chord.

The length of chord AB is 40 cm so AC is equal to 40 cm

Now according to the question 

AO² = OC² + AC²

AO2 = 152 + 202

AO2 = 225 + 400

AO2 = 625

AO = 25 cm

The radius is 25 cm.

Shortcut Trick

Apply complementary angle rules: sec(90° − θ) = cosec θ and cot(90° − θ) = tan θ.

The expression simplifies to: (sec² 54° − tan² 54°) + (3/2)(sin² 37° × cosec² 37°) + (2/√3)(√3).

Using identities sec² θ − tan² θ = 1 and sin θ × cosec θ = 1:

Result = 1 + (3/2) × 1 + 2 = 3 + 1.5 = 4.5 = 9/2.

∴ The correct answer is 9/2.

Alternate Method

Given: sec² 54° − cot² 36° + (3/2) sin² 37° × sec² 53° + (2/√3) tan 60°

Formulas Used:

1. Complementary Angles: cot 36° = tan(90° − 36°) = tan 54° and sec 53° = cosec(90° − 53°) = cosec 37°
2. Identities: sec² θ − tan² θ = 1 and sin θ × cosec θ = 1
3. Standard Values: tan 60° = √3

Calculations:

⇒ First part: sec² 54° − tan² 54° = 1

⇒ Second part: (3/2) sin² 37° × cosec² 37° = (3/2) × (sin 37° × cosec 37°)² = (3/2) × 1² = 3/2

⇒ Third part: (2/√3) × √3 = 2

⇒ Adding all parts: 1 + 3/2 + 2 = 3 + 1.5 = 4.5

⇒ 4.5 = 9/2

⇒ This value matches Option (2).

∴ The correct answer is 9/2.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Complementary Angle Relationships

For two angles adding to 90°, sin A = cos B, tan A = cot B, and sec A = cosec B.

Reciprocal Identities

The products of reciprocals are always 1: sinθ × cosecθ = 1, cosθ × secθ = 1, and tanθ × cotθ = 1.

Shortcut Trick

Calculate the Total Effective Principal for 1 year: (500 × 4) + (700 × 2) = 2000 + 1400 = 3400.

Applying the Rate formula: Rate = (Total Interest × 100) ÷ Total Effective Principal.

Rate = (280 × 100) ÷ 3400 = 280 ÷ 34 = 140/17 %.

Rate = 8 (4)/(17) %.

∴ The correct answer is 8 (4)/(17) %.

Alternate Method

Given:

Principal 1 (P₁) = ₹500, Time 1 (T₁) = 4 years

Principal 2 (P₂) = ₹700, Time 2 (T₂) = 2 years

Total Simple Interest = ₹280

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ Total SI = SI₁ + SI₂

⇒ 280 = [(500 × R × 4) ÷ 100] + [(700 × R × 2) ÷ 100]

⇒ 280 = 20R + 14R

⇒ 280 = 34R

⇒ R = 280 ÷ 34

⇒ R = 140 ÷ 17

⇒ R = 8 (4)/(17) %

∴ The correct answer is 8 (4)/(17) %.

Additional Information

Simple Interest (SI)

It is the interest calculated only on the initial principal amount for every period of time. Formula: SI = (P × R × T) ÷ 100.

Total Amount

The total money paid back after the time period, which includes both the principal and the interest: Amount = Principal + SI.

Effective Principal for Multi-periods

When different principals are invested for different times at the same rate, the total interest is proportional to Σ(P_i × T_i).

Difference between SI and CI

For a period of 2 years, the difference between Compound Interest and Simple Interest is given by P(R ÷ 100)².

Given

A thief steals a van at 3 : 00 a.m. and drives it at a speed of 57 km/h.

Formula

Time = Distance/Speed

Calculation

Speed of the car of the thief = 57 km/h

Since the robbery was discovered at 4:00 am

Distance travelled by the thief in 1 hour (4 - 3) = speed × time = 57 × 1 = 57 km

Speed of the owner of the car = 76 km/h

So, relative speed of the owner = (76 - 57) km/h = 19 km/h

∴ time taken to cover 57 km by the owner = 57/19 h = 3 hour

Time by watch = 4:00 am + 3 h = 7 : 00 am

∴ The owner will overtake the thief at 7:00 am.

Shortcut Trick

Ratio of Rahim to Savita age: Present = 5 : 1, After 7 years = 3 : 1.

Make the ratio difference equal: Present (5:1, diff 4) → 5:1. After 7 yrs (3:1, diff 2) × 2 → 6:2.

Increase in ratio unit: 6 − 5 = 1 unit. Since 1 unit = 7 years.

Rahim's present age = 5 units = 5 × 7 = 35 years.

∴ The correct answer is 35 years.

Alternate Method

Given: Present ratio = 5:1. After 7 years ratio = 3:1.

Formula: Age after n years = Present age + n.

⇒ Let Savita's present age be x. Then Rahim's present age = 5x.

⇒ After 7 years: (5x + 7) = 3 × (x + 7)

⇒ 5x + 7 = 3x + 21

⇒ 5x − 3x = 21 − 7

⇒ 2x = 14

⇒ x = 7 years.

⇒ Rahim's present age = 5 × 7 = 35 years.

∴ The correct answer is 35 years.

Additional Information

Ratio Difference Method

To solve age problems quickly, ensure the numerical difference between ratio parts remains constant by multiplying with the cross-difference of the other ratio.

Age Invariance

The difference between the ages of two people always remains the same, regardless of how many years pass.

The correct answer is "want to win."

Key Points 

• The subject of the sentence is "the boys and the teacher," which is plural.
• Therefore, the verb should also be plural.
• "Want" is the correct verb form for the plural subject.
• "To win" is the correct infinitive phrase to express the desired action.
• Thus, the correct phrase to use in the blank would be "want to win."
• The sentence would be: The boys and the teacher want to win.

Hence, the correct answer is option 4.

The correct answer is "Dissuaded."

Key Points 

• Antonym means a word that has the opposite meaning of the given word.
• Let us understand the meaning of the given and the marked words:
• "Compelled" **means forced or pressured to do something.(**मजबूर)
• Example: Her family compelled her to take the job.
• "Dissuaded" means being discouraged or advised against doing something.(रोक)
• Example: He was finally dissuaded to ignore the matter.
• Therefore, it can be concluded that the word "dissuaded" is the antonym of "compelled."

Hence, the correct answer is option 4.

Additional Information

• Demur means to object or hesitate.(आपत्ति)
• Obscured means to make unclear or difficult to understand.(अस्पष्ट करना)
• Confessed means to admit or acknowledge a wrongdoing.(स्वीकार करना)

The correct answer is "To die."

Key Points 

• The idiom "to kick the bucket" means to die.
• This idiom is considered informal and is often used in casual conversations or humorous contexts.
• Some synonyms for "to kick the bucket" include "to pass away," "to expire," and "to depart this life."
• Example: Every one of us will kick the bucket someday.
• Thus, it is clear that option 4 explains the meaning of the given idiom.

Hence, the correct answer is option 4.

The erroneous word is: hossting.

Key Points

• In the given sentence:
• The word "hossting" is spelled incorrectly. The correct spelling is: 'hoisting'.
• It means to raise or lift something, in this case referring to the act of raising the flag**.**
• Example: Hoist your sail when the wind is fair.

Hence, the correct answer is option 4.

Additional Information

• Option 1: "floral" refers to flowers or plants.
• Option 2: "statue" is a three-dimensional representation of a person or object.
• Option 3: "tributes" are acts or statements of respect or admiration.

The correct answer is "Misconstruction."

Key Points 

• The question asks for an antonym of the underlined word.
• The underlined word is 'adage.'
• "Adage" means a saying that sets forth a general truth and that has gained credit through long use (एक पुरानी और प्रसिद्ध कहावत जो एक आम सच्चाई को व्यक्त करती है।).
• Example: He remembered the old adage, "Look before you leap."
• The word "misconstruction" means a false interpretation of evidence , facts, etc.
• Example: Any misconstruction of these terms could lead to errors of law.
• Thus, it can be concluded that the word "misconstruction" is the antonym of the word "adage."

Hence, the correct answer is option 1.

Additional Information

• Rebuke means to scold or criticize someone.
• Dare means to challenge someone to do something risky or difficult.
• Addiction means a strong dependence on a substance or activity.

Hinglish

• Misconstruction: ग़लतफ़हमी
• Rebuke: फटकार
• Dare: हिम्मत
• Addiction: लत

The correct answer is "have."

Key Points

• In the given question, the sentence uses the phrase "reminds me always."
• The phrase 'reminds me always' suggests a habitual action, which requires the present tense.
• Thus, the sentence is in present tense, indicating that the action is ongoing.
• Now, 'Have' is the correct present tense form of the verb 'to have'.
• Also, "have" is used with the pronouns I, you, we, and they. Has is used with he, she, and it.
• Thus, the correct sentence should be: 
• She reminds me always that I have to be a little more careful.

Hence, the correct answer is option 2.

The correct answer is "sympathetic."

Key Points

• Let us understand the meaning of the given words:
• The word "callous" means showing no concern for others' feelings or suffering. (दूसरों की भावनाओं या पीड़ा के प्रति कोई चिंता नहीं दिखाना।)
• Example: This isn't callous and soulless; it can be rich and exciting.
• The antonym of "callous" is "sympathetic (सहानुभूति)," which means showing compassion or understanding for others' emotions or experiences.​
• Example: He gave me a sympathetic tone.
• In the given sentence, Mr. Khanna is described as "quite callous" towards earthquake victims, indicating that he lacks sympathy for them.
• Therefore, the most appropriate antonym to fill in the blank would be "sympathetic," as it expresses the opposite meaning of "callous."

Hence, the correct answer is option 3.

Additional Information

• Option 1 (rationalistic) refers to a belief in using reason and logic to understand the world, and is not directly related to the concept of sympathy or callousness. (दुनिया को समझने के लिए कारण और तर्क का उपयोग करने में विश्वास, और सीधे तौर पर सहानुभूति या संवेदनहीनता की अवधारणा से संबंधित नहीं है।)
  
• Option 2 (unsympathetic) (सहानुभूतिहीन) is a synonym of "callous," and therefore cannot be the correct antonym.
• Option 4 (nondiplomatic) refers to a lack of tact or diplomacy in one's communication and is not directly related to the concept of sympathy or callousness. (किसी के संचार में चातुर्य या कूटनीति की कमी)

The correct answer is "P, Q, R, S."

Key Points 

• The paragraph is about the aims and content of newspapers, with a focus on informing and entertaining readers.
• The first sentence (S1) sets the context and purpose of the paragraph.
• The sentences (P) and (Q) explain how newspapers achieve their aims of informing and entertaining readers.
• The sentence (R) provides additional information about the daily publication of newspapers and the need for up-to-date news.
• The sentences (S) and (S6) highlight the importance of immediacy and authenticity in news reporting.
• Thus, it can be concluded that the correct chronology of the given sentences would be: PORS.

Hence, the correct answer is option 4.

The correct answer is 'Preparing'.

Key Points

• 'Ready' means prepared for an immediate activity or use. (तैयार)
• Among the given options, 'Preparing' comes closest to the meaning of 'ready' as it implies a state of readiness or being prepared. (तैयार करना)
• Listening, organised, and equipped don't suggest a state of readiness directly, but rather are associated actions or conditions.

Therefore, the correct answer is- 'Option 1'.

Additional Information

• Preparing: This action implies making something or oneself ready in advance. This is the closest synonym to 'ready' among the options. (तैयार करना)
• Listening: This is a verb indicating the action of paying attention to sound or hearing something. It doesn't directly relate to the state or action of being 'ready'. (सुनना)
• Organised: Being organized suggests a state of being arranged in a systematic way or being well-structured. While it can contribute to one being ready, it's not a direct synonym. (संगठित)
• Equipped: This signifies having the necessary items for a particular purpose. While being equipped can lead one to be ready, the words do not share a synonymous meaning. (सुसज्जित)

The correct answer is "Were the books not being read by the children?"

Key Points

• The formula for forming negative passive sentences is subject + auxiliary verb “to be” (am/is/are) + negative adverb (not) + past participle of the main verb
• Consider the following:
• Option 1 uses the correct passive voice structure but is asking if the books were being read, not if they weren't.
• Option 2  uses the negative form of the passive voice, "not being read' and appropriately asks the question.
• Thus, it will be the correct passive form to ask everyone if the children were not reading the books.
• Option 3 has a grammatical error with the subject-verb agreement. It should be "books" instead of "book."
• Option 4 is asking the opposite of what the question is asking. It is asking if the children were reading the books.

Hence, the correct answer is option 2.

The correct answer is "Unfriendly."

Key Points

• Let us understand the meaning of the given and the marked words:
• Hostile means unfriendly, aggressive, or antagonistic.
• Example: People are very hostile to the idea.
• Unfriendly is a synonym of hostile, and it means not kind or pleasant.
• Example: They exchanged a few unfriendly words and left.
• Grammatical point: Adjectives like hostile and unfriendly are used to describe a person or thing.
• Thus, it can be concluded that the word "unfriendly" is the correct synonym of the word "hostile."

Hence, the correct answer is option 4.

Additional Information

• Pleasant (Option 1) means enjoyable or agreeable, which is the opposite of hostile.
• Hospitable (Option 2) means friendly and welcoming to guests or strangers, which is also the opposite of hostile.
• Empathetic (Option 3) means understanding and sharing the feelings of others, which is not related to hostility.