SSC CGL Previous Paper (Held On: 7 March 2020 Shift 1) (Previous Year Paper)

The logic is:

Hence, ‘qLx’ is the correct answer.

The option figure in which the given figure is embedded is option ‘3’.

Hence, option ‘3’ is the correct answer.

The logic is :

The pattern followed is :

→ 16 + 20 = 36 = 6²

→ 30 + 51 = 81 = 9²

→ 4 + 5 = 9 = 3²

→ 25 + 41 = 66 ≠ 8²

Hence, 25/41 : 8 is odd among given.

The words in the order in which they appear in an English dictionary is shown below:

4. Deceive
5. Decide
6. Decimal
7. Decipher
8. Decision
9. Decline

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

The logic is:

Column 1: (8 × 4) - 3 = 29

Column 2: (11 × 7) - 6 = 71

Similarly,

Column 3: (14 × ?) - 3 = 67

(14 × ?) = 70

=> ? = 5

Hence, ‘5’ is the correct answer.

The logic is:

Consonants are coded by the place value of their reverse letters and the vowels are numbered as shown below and then the code of CIRCULAR is obtained.

Similarly,

Hence, ‘5-4-9-7-3-24-5-15’ is the odd one out.

When the transparent sheet of paper is folded at the dotted line, it will appear as shown below:

Hence, option 2 is the correct answer.

A private taxi company charges a fixed charge along with a per kilometre charge based on the distance covered. For a journey of 24 km, the charges paid are Rs. 368 and for a journey of 32 km, the charges paid Rs. 464.

Let, the fixed charge be ‘a’ and charge per km be ‘b’.

According to question:

a + 24b = 368      ---- (I)

a + 32b = 464     ---- (II)

(II) - (I), we get:

32b - 24b = 96

8b = 96

b = 12

If we put the value of ‘b’ in equation (I), we get:

a + 24 × 12 = 368

a = 368 - 288

a = 80

For travelling a distance of 15 km, a person will have to pay Rs. (a + 15b) = Rs. (80 + 15 × 12) = Rs. (80 + 180) = Rs. 260.

Hence, ‘260’ is the correct answer.

The logic is :

6 : 16 → 6 : (6 - 2)²

11 : 81 → 11 : (11- 2)²

Similarly,

20 : ? → 20 : (20- 2)²

=> ? = 18² = 324

Hence, ‘324’ is the correct answer.

The meaning of the words are :

1. Scream - make a loud, high-pitched sound.

2. Shout - say something very loudly.

3. Mumble - say something indistinctly and quietly, making it difficult for others to hear.

4. Roar - a very loud, deep, prolonged sound made by something inanimate.

All words except ‘mumble’ are synonyms of each other.

Hence, ‘mumble’ is the odd one out.

When the box will be constructed, the following letters will be opposite to each other as shown below :

The dice in option ‘2’ has ‘e’ and ‘d’ appearing together which is not a possible case, as these two letters are opposite faces of each other.

Hence, option 2 dice cannot be formed.

W × Z + Y ÷ X → W is son of Z, Z is mother of Y, Y is daughter of X.

Hence, X is husband of Z.

The correct mirror image of the given figure when the mirror is placed on the right of the figure is shown below :

Hence, option 1 is the correct answer.

The least possible venn diagram is:

I. Some cars are scooters. → False (Possible but not Definite)

II. Some trucks are buses. → True

III. Some scooters are buses. → False (Possible but not Definite)

IV. All scooters are trucks. → False (Possible but not Definite)

Hence, only conclusion II follows

Given series: 17, 19, 22, 27, 34, 45, 58,?

The logic is:

where 2, 3, 5, 7, 11, 13, 17 are the consecutive prime numbers.

Hence, ‘75’ is the correct answer.

The relation is:

Bacteria : Illness → Bacteria can infect any area of the body. Pneumonia, meningitis, and food poisoning are just a few illnesses that may be caused by harmful bacteria.

The relation is that bacteria causes illness.

1. Painting : Painter → The job of a painter is to paint.

2. Disease : Doctor → A doctor treats different kinds of diseases.

3. Carelessness: Errors → Carelessness results in errors.

4. Appraisal: Performance → For a goof performance, one gets appraisal.

The relation between ‘Bacteria : Illness’, is same as the relation between ‘Carelessness: Errors’.

Hence, ‘Carelessness : Errors’ is the correct answer.

1. ÷, -, =, ×

Given equation: (14 * 9 * 6) * 15 * 8

After replacing the *’s by ‘’, we get :

=>(14 ÷ 9 - 6) = 15 × 8

=> -4.44 = 120

Not true

2. ×, -, ÷, =

Given equation: (14 * 9 * 6) * 15 * 8

After replacing the *’s by ‘’, we get :

=>(14 × 9 - 6) ÷ 15 = 8

=> (126 - 6) ÷ 15 = 8

=> 120 ÷ 15 = 8

=> 8 = 8

True

3. ×, =, ÷, - Given equation: (14 * 9 * 6) * 15 * 8

After replacing the *’s by ‘’, we get :

=> (14 × 9 = 6) ÷ 15 - 8

=> 126 = -7.6

Not true

4. -, ÷, ×, =

Given equation: (14 * 9 * 6) * 15 * 8

After replacing the *’s by ‘’, we get :

=>(14 - 9 ÷ 6) × 15 = 8

=> (14 - 1.5) × 15 = 8

=> 12.5 × 15 = 8

=> 187.5 = 8

Not true

Hence, ‘×, -, ÷, =’ is the correct answer.

The students who scored 85% and above in all the subjects is represented by the area that lies in the intersection of the circle, triangle, rectangle and square as shown below :

Hence, ‘5’ is the correct answer.

The relation is:

Amusing - causing laughter and providing entertainment.

Hilarious - extremely amusing.

Amusing and Hilarious are synonyms of each other.

Moisten -to make something slightly wet or to become slightly wet.

1. Soak - make or allow (something) to become thoroughly wet by immersing it in liquid.

2. Dry - free from moisture or liquid; not wet or moist.

3. Humid - marked by a relatively high level of water vapour in the atmosphere.

4. Water - a colourless, transparent, odourless liquid that forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms.

The synonym of moisten from the given options is ‘soak’.

Hence, ‘Soak’ is the correct answer.

The logic is:

17 : 102 ∷ 153 → 17 : (17 × 6) : (17 × 9)

1. 13 : 78 : 108 → 13 : (13 × 6) = 78 : (13 × 9) ≠ 108

2. 23 : 162 : 207 → 23 : (23 × 6) ≠ 162 : (23 × 9) = 207

3. 16 : 96 : 144 → 16 : (16 × 6) = 96 : (16 × 9) = 144

4. 18 : 104 : 171 → 18 : (18 × 6) ≠ 104 : (18 × 9) ≠ 171

Hence, ‘16 : 96 : 144’ is the correct answer.

Given series :

The series is following a shifting pattern, in which the first term becomes the last term in the next figure.

Following the above pattern, the line with squares at its corners, will be at the lowermost position in the ‘?’ figure.

Option 2, 3 and 4 has the same line at the lowermost position.

Next, the line with circles at its corners, will be at the top position in the ‘?’ figure, which can be found in option 2 and 4 only.

Again, the line with triangle at its corners will be at the 2^nd position from the top in the ‘?’ figure, which is present in option 4.

Hence, option 4 is the correct answer.

The logic is:

Similarly,

Hence, ‘ESUQNEEC’ is the correct answer.

The logic is:

1. XAD

2. SVY

3. FIK

4. NQT

Hence, ‘FIK’ is the odd one out.

The number of triangles in the given figure is shown below:

ADB, ADE, CDE, BCD, IKH, IKJ, LKJ, HKL, FHL, GHI, AEG, CEF - 12

ABC, AEC, GEF, GHF, IHL, IJL - 6

ABE, BEC, IHJ, HLJ - 4

GCL, AFI - 2

ACG, GIL - 2

GCF, GLF, AGF, GIF, ACF, FIL- 6

Total number of triangles = 12 + 6 + 4 + 2 + 2 + 6 = 32

Hence, the figure has total 32 triangles.

The logic is:

P_rsqrps_pqs_qr_qrps_p_s

Dividing the series in group of 4 letters :

(p_rs) (qrps) (_pqs) (qr) (qrps) (_p_s)

We can see that the 2^nd and 5^th terms are same in the series.

So, accordingly, 1^st and 4^th term, 2^nd and 5^th and 3^rd and 6^th terms must be same.

So, on comparing 1^st and 4^th terms, (p_rs) and (qr), we can easily recognise that the blank in 1^st term will have ‘q’ and the two blanks in 4^th term will be filled by ‘p’ and ‘s’ respectively.

Similarly,

3^rd and 6^th term, on comparison, (_pqs) and (_p_s), we find that the 2^nd blank in 6^th term will be filled by ‘q’ and the 1^st blank in both the terms will be filled by ‘r’, as each term is made up od using all the four terms p, q, r and s.

So, following the pattern, we find that ‘q, r, p, s, r, q’, when filled in the blanks, will complete the given series.

Pqrsqrpsrpqspqrsqrpsrpqs

Hence, ‘q, r, p, s, r, q’ is the correct answer.

The correct answer is architecture.

• Pritzker Prize is given in the field of Architecture.
• This award is held to honor architects whose built work demonstrates a combination of talent, vision, and commitment.
• It was established by the Pritzker family of Chicago through their Hyatt Foundation in 1979.
• It is also referred to as “Architecture’s Nobel”.
• Award-$100,000 (US) and a bronze medallion.
• Pritzker Prize 2020- Yvonne Farrell and Shelley McNamara: They are the only fourth and fifth women to get this its 41-year history

• ATM - Automated Teller Machine.
• It is an e-banking outlet so that an individual can do basic transactions without involving any representative from the bank.
• A debit or credit or card issued by the bank is required to do the transactions.
• Shepherd - Barron is the inventor of ATM. He was British.
• It was opened on June 27, 1967 at a branch of Barclays bank in Enfield, North London.
• HSBC introduced the first ATM in India in 1987.

The Council of Ministers during the time of Shivaji Maharaj was known as Ashta Pradhan.

Key Points

• The translation of Ashta Pradhan in English is "Council of Eight".
• It was an administrative and advisory council. It is said that this council contributed to the military attacks on the Muslim Mughal Empire by Chhatrapati Shivaji Maharaj.
• He is the founder of the Maratha kingdom of India.
• He found the oppression by Muslims and religious persecution of the Hindus was highly intolerable and not fair.
• He was crowned as Chhatrapati at Raigarh in AD 1674.
• The Maratha Kingdom rose with the fierce actions of Shivaji and his followers.

• The Father of Leander Paes has been a member of the Indian National Team of Hockey.
• His father was Vece Paes.
• He represented the Indian Hockey team in the 1972 Munich Olympics and he won the bronze medal at the event. He was a midfielder in the game.
• He is also a certified doctor of sports medicine.
• Leander Paes is the professional Lawn Tennis Player.
• He had won Arjuna Awards in 1990, Padma Shri in 2001 and Padma Bhushan in 2014.
• He has won eight career Grand Slam doubles titles and ten career Grand Slam mixed doubles championships.

• Rumtek monastery is located in Sikkim.
• It is also known as the Dharmachakra Centre.
• It is said to be originally built in the 18th century by 9th Karmapa-Wangchuk Dorje.
• However, it was damaged because of an earthquake and was rebuilt by the 16th Karmapa.
• The main temple has a four-story building and it is topped by a golden sculpture and decorated by Tibetan-style murals.
• The shrine hall is decorated with silk banner and thangkas, and it has numerous religious texts. It also has a ten-feet-high statue of Sakyamuni Buddha.
• Sikkim Capital - Gangtok

The correct answer is Sudha Murthy.

Key Points

• Sudha Murthy is the author of the book 'Wise and Otherwise: A Salute to Life'.
• This book is written as an inspiration to people’s struggles and how they try to overcome it.
• There are 51 stories included in this book and extensively talk about challenges in India through narrations.
• Sudha Murty is a social activist.
• She is the chairperson of the Infosys Foundation in India.
• Other books by her- Dollar Bahu, Grandma's Bag of stories, Mahashweta, etc.
• Books by Zoya Hasan-Transforming India: Social and Political Dynamics of Democracy, Forging Identities: Gender, Communities, And The State In India, etc.
• Books by Amrita Pritam-Pinjar, Rasidi Ticket, Kagaj te Canvas, etc.
• Books by Kiran Desai-The Inheritance of Loss, The Inheritance of Loss Hullabaloo in the Guava Orchard, etc.

• Canada balsam has its refractive index closest to that of crown glass among the given options.
• Refractive Index is equal to the ratio of the velocity of light in a vacuum to its velocity of the light in a specified medium we are comparing with.
• In other words, this index helps us understand how and how much light would bend in the specified medium.
• The index has no unit.
• Refractive Index of Crown Glass - 1.52-1.62
• Refractive Index of Canada balsam - 1.54
• Refractive Index of Sapphire - 1.76 – 1.77
• Refractive Index of Ruby - 1.76 – 1.77
• Refractive Index of Diamond - 2.417 – 2.419

• Vedanga is a Sanskrit word. It means limbs of the Veda.
• These are the treatises of Vedic Literature. They are - Shiksha, Kalpa, Vyakarana, Nirukta, Chandas, and Jyotisha.
• Shiksha - It includes the rules of phonetics – sounds of syllables, of pronunciation.
• Kalpa - It is called the arms of the Veda Purusha. It is for the proper application of the Vedic texts. The texts are clear, short and practical for ceremonies.
• Vyakarana - It talks about the formation of the word. It also discusses the root and suffix of a word to study its meaning.
• Nirukta - It gives the meaning of the usage of words.
• Chandas - It is designed for the purpose of securing the proper reading and reciting of Vedic texts.
• Jyotisha - It conveys the knowledge of the heavenly bodies. It also gives some rules for calculating and fixing time for sacrifices

• Ammonium is a cation.
• The cation is a positively charged ion. It has more protons than electrons.
• NH₃ forms a bond with an H+ using the N lone pair. Then, there is 1 more proton than electrons making it a cation.
• An anion is a negatively charged ion. It has more electrons than protons.
• Fluoride, Iodide, and Chloride are anions.

• Pradhan Mantri Jeevan Jyoti Bima Yojana offers a protection term insurance cover of Rs. 2 Lakh to the insurer.
• It was mentioned first time in 2015 Budget speech by Late Arun Jaitley (Former Finance Minister).
• However, it was formally launched by PM Narendra Modi in May in 2015.
• Age eligibility- 18 to 50 years
• Under this scheme, the premium of Rs. 330 per annum would be auto-debited in one installment from the bank account of subscriber.

The correct answer is Calcutta.

Key Points 

• The Indian National Congress session of September 1920 was held at Calcutta.
• Lala Lajpat Rai was the President of this session. It was a special session.
• A special session was held to pass the resolution of the Non-Cooperation Movement.
• However, this session is also associated with Gandhi wrongly predicting that if the Non-cooperation movement gets successful, Swaraj could be attained in a year.
• The Non-cooperation movement was launched in 1920 by Mahatma Gandhi with the aim of Swaraj (self-governance). However, the movement was not successful.

Additional InformationOther Important sessions of the Indian National Congress (INC): 

• The power of a lens is –2.0 D. Here 'D' stands for: Dioptre.
• It is the unit of measurement of the refractive power of an optical lens and curved mirror.
• A dioptre is equal to the reciprocal of focal length of the lens or mirror.
• Here, the power of the lens is negative (-2.0 D). It means that the focal length is negative which means that it is diverging lens.
• It is a concave lens.
• Power=1/f ⇒ f=-0.5m.
• The focal length of the concave lens is -0.5m in this case.

• Nathula Pass - It connects Sikkim and Tibet.
• Rohtang Pass - It connects the Kullu Valley and Spiti Valleys of Himachal Pradesh.
• Bomdila Pass - It connects Arunachal Pradesh with Lhasa (the capital city of Tibet).
• Lipulekh Pass - It connects the Kumaon region of Uttarakhand with Taklakot in Tibet. This pass is also called Qiangla or Tri-Corner as it is an International mountain pass between India, China and Nepal.

• Pravasi Bharatiya Divas is celebrated on 9th January.
• This day is observed and celebrated to mark the contribution of the Indian community living overseas towards the development of India.
• This day was particularly chosen because Gandhiji returned to India from South Africa in 1915.
• The conventions of Pravasi Bharatiya Divas are being held since 2003.
• The conventions provide a platform to the overseas Indian community to engage with the government and people of the land of their ancestors for mutually beneficial activities.

• In December 2019, the Rohtang passageway in Himachal Pradesh was renamed as Atal Tunnel.
• The name of the pass was changed to mark the 95th birth anniversary of former prime minister Atal Bihari Vajpayee.
• The pass is in Manali and it connects the Kullu Valley with Spiti Valleys of Himachal Pradesh.
• Himachal Pradesh Capital-Shimla

The correct answer is Padayani – Kerala.

Key Points

• Dance forms of Kerala - Theyyam, Thiruvathirakali, Chakyar Koothu Koodiyattam, Ottamthullal, Mohiniyattam, Kathakali, Padayani, etc.
• Dance forms of Karnataka - Kunitha, Yakshagana, Sannatas, Parijata, Doddatas, etc.
• Dance forms of Himachal Pradesh - Nati, Kayang Mala, Shand, Shabu, etc.
• Dance forms of Bihar - Jat Jatin, Jhumri, Bidesia, etc.
• Dalkhai is from Odisha.
• Kalbelia is from Rajasthan.
• Thang-Ta is from Manipur.

• Indian states that share boundaries with Bangladesh - Assam, West Bengal, Mizoram, Meghalaya, and Tripura.
• Manipur does not share with Bangladesh.
• Bangladesh Capital - Dhaka
• Currency - Taka

• K Srikanth won the BCCI CK Nayudu Lifetime Achievement Award for the year 2019.
• Krishnamachari Srikkanth is a former Indian captain of the Indian Cricket Team.
• He represented India between 1981 and 1992.
• He has played 43 Tests, scoring 2062 runs with two hundred and 12 half-centuries.
• He had retired in 1992 after the World Cup in Australia and New Zealand.
• He also served as the chairman of the national selection committee from 2009-12.
• Cottari Kanakaiya Nayudu was the first captain of the Indian cricket team in Test matches.

• Narmada forms the Dhuandhar waterfall near Jabalpur.
• The river originates from Amarkantak. It also rises at an elevation of about 3,500 feet in the Maikala Range of Madhya Pradesh.
• Narmada and Tapti are the rivers in India that drain into the Arabian Sea and not in the Bay of Bengal.
• Tributaries of Narmada River- Tawa, Sher, Shakkar, Lohar, Hiran, Barna, Choral, etc.
• Dams on Narmada River - Sardar Sarovar Dam, Indira Sagar Dam, Bargi Dam, Jobat Dam.

• Articles 25-28 of the Constitution of India guarantees the Right to Freedom of Religion.
• Article 14-Equality before the law or the equal protection of the laws within the territory of India
• Article 15-No citizen of India shall be discriminated on the basis of religion, race, caste, sex or place of birth
• Article 16-Equal opportunity to all citizens in matters related to employment in the public sector.
• Article 17-Abolition of Untouchability
• Article 18-Abolishment of titles
• Article 19-Freedom of Speech
• Article 20-Protection against Conviction
• Article 21-Liberty to live
• Article 22-Protection against arrest and detention in certain cases
• Article 23-Prohibits the traffic in human beings and forced labor
• Article 24-Prohibits the employment of children below the age of 14 years

• P.V. Sindhu was appointed as brand ambassador of Visa - the payment technology company in 2019.
• Visa Incorporation is a global payments technology company. It is headquartered in the U.S.
• It enables consumers, businesses, banks and governments to use digital currency.
• VISA CEO: Alfred F Kelly Jr.
• P.V Sindhu is an Indian Badminton player.
• She made her international debut at The Sub-Junior Asian Badminton Championships in 2009.
• She was also the first Indian to win two back-to-back medals in the BWF World Badminton Championships in 2014.
• She became youngest and the first female athlete from India to win a silver medal at Rio Olympics in 2016.

The correct answer is 1951.

• The first amendment to the Constitution of India was made in 1951. 
• The Constitution (First Amendment) Bill sought to make several consequential changes from exempting land reforms from scrutiny to providing protections for backward classes in the Constitution.
• Insert provisions fully securing the constitutional validity of zamindari abolition laws in general and certain specified State Acts in particular
• The First Amendment Act amended articles 15, 19, 85, 87, 174, 176, 341, 342, 372, and 376.
• Added Ninth Schedule to protect the land reforms and other laws included in it from judicial review. After Article 31, Articles 31A and 31B were inserted.

The Dharmaraja Ratha monument is located in Mahabalipuram, Tamil Nadu.

• It is a part of the five ‘Ratha’ structures and there are thirty-eight inscriptions on the Ratha.
• It has a monolith rock-cut. The porch has columns with lion bases and leads to the sanctuary.
• It is believed to be built during the end of the seventh century by Pallava King Narasimhavarman I.

The correct answer is Mercury.

Key Points

• Mercury is NOT an insulator.
• Insulators are material that does not conduct electricity.
• Examples - paper, plastic, rubber, glass, Ebonite, air, Styrofoam, etc.

Additional Information

• The Conductors are the material that conducts electricity.
• Examples - Metals, Aqueous solutions of salts ( ionic compounds dissolved in water),  Mercury, graphite.
• Please note that Mercury is a poor conductor of heat.
• Mercury forms weak bonds and is a liquid at room temperature.
• Atomic Number of Mercury-80,  Symbol-Hg

• The scientific study of a cell is called Cytology.
• It is a branch of pathology and deals with making diagnoses of diseases and conditions through the examination of tissue samples from the body.
• Histology - It is the study of the microanatomy of cells, tissues, and organs which are to be seen through a microscope.
• Physiology -  It is the branch of biology and it deals with the functions of living organisms and their parts.
• Taxonomy - It is the branch of science and deals with the classification of biological organisms. This is done on the basis of shared characteristics.

Short Trick:

$\frac{{1 - 2si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }} - 1$

Put θ = 0

⇒ 1/1 – 1

⇒ 1 – 1

⇒ 0

Detailed Method:

$\frac{{1 - 2si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }} - 1$

⇒ $\frac{{1 - 2si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }} - si{n^4}{\rm{\theta }} - co{s^4}}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }}$

$\Rightarrow {\rm{}}\frac{{1 - \left[ {2si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}; + ;{{(si{n^2}{\rm{\theta }})}^2}{\rm{;}} + {\rm{;}}{{(co{s^2}{\rm{\theta }})}^2}} \right]}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }}$

$\Rightarrow {\rm{}}\frac{{1 - \left[ {;{{(si{n^2}{\rm{\theta ;}} + {\rm{;}}co{s^2}{\rm{\theta }})}^2}} \right]}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }}$

$\Rightarrow {\rm{}}\frac{{1 - 1}}{{si{n^4}{\rm{\theta ;}} + {\rm{;}}co{s^4}\theta }}$

⇒ 0

The five consecutive odd number are 1, 3, 5, 7, 9

Average of five consecutive odd number = (1 + 3 + 5 + 7 + 9)/5 = 25/5 = 5

So m = 5

If next three odd number are included, then the average of 8 consecutive odd number

(25 + 11 + 13 + 15)/8

⇒ 64/8

⇒ 8

We can write 8 = 5 + 3 or m + 3

Number of students who appeared for the examination = 840

Number of students who got with distinction = 210

Required percentage = 210/840 × 100 = 25%

1 – 64x³ – 12x + px² = (1 – 4x)³

⇒ 1 – 64x³ – 12x + px² = 1 – 64x³ – 3 × 1 × 4x (1 – 4x)

⇒ 1 – 64x³ – 12x + px² = 1 – 64x³ – 12x + 48x²

⇒ px² = 48x²

⇒ p = 48

BC = 6 cm

BD = ½ × BC = 1/2 × 6 = 3 cm

AD = 4 cm

In right angled triangle

AB² = AD² + BD²

⇒ AB² = 4² + 3² = 16 + 9 = 25

⇒ AB = √25 = 5 cm

Shortcut Trick

Identify the sides of the Right-Angled Triangle relative to angle θ.

The side Adjacent to θ is 5 units and the Hypotenuse (longest side) is 13 units.

Apply the direct ratio: cosθ = Base / Hypotenuse.

cosθ = 5 / 13.

∴ The correct answer is 5/13.

Alternate Method

Given:

In the right-angled triangle:

Base (Adjacent to θ) = 5

Perpendicular (Opposite to θ) = 12

Hypotenuse (Side opposite to 90°) = 13

Formula Used:

cosθ = Base / Hypotenuse

Calculations:

⇒ cosθ = 5 / 13

∴ The correct answer is 5/13.

Additional Information

Trigonometric Ratios

sinθ = Perpendicular / Hypotenuse and tanθ = Perpendicular / Base.

Pythagoras Theorem

In a right-angled triangle, Hypotenuse² = Base² + Perpendicular². Here, 13² = 5² + 12² (169 = 25 + 144).

Reciprocal Ratios

secθ is the reciprocal of cosθ, so secθ = Hypotenuse / Base = 13 / 5.

Number of teachers of age less than 40 = 2 + 3 + 5 + 2 = 12

151² – 149²

⇒ (151 + 149) (151 – 149)

⇒ 300 × 2

⇒ 600

GIVEN:

Length of wall = 6 m

Breadth of wall = 4 m 

Height of wall = 4 m.

CONCEPT:

Lateral surface area of a cuboid.

FORMULA USED :

Area of four wall = 2 (l + b) × h

CALCULATION :

Area of four wall = 2 (6 + 4) × 4

= 2 × 10 × 4

= 80 m²

∴ The area of the four walls of a room is 80 m2

Speed of first cars = 40 km/hr

Speed of second cars = 50 km/hr

Relative speed, if same direction = 50 – 40 = 10 km/hr

Distance cover by first cars in 1/2 hr = 40 × 1/2 = 20 km

Time = distance/speed

Both cars be together in = 20/10 = 2 hr

Distance cover by second car in next 2 hr to meet first car = 50 × 2 = 100 km

Concept used:

Calculation:

sin30 + cos30 – tan 45

⇒ 1/2 + √3/2 – 1

⇒ (1 + √3 – 2)/2

⇒ (√3 – 1)/2

(2y – 5)³

⇒ (2y)³ – 5³ – 3 × 2y × 5 (2y – 5)

⇒ 8y³ – 125 – 60y² + 150y

Coefficient of y = 150.

Correct Answer 6

Key Points:

3 – (9 – 3 × 8 ÷ 2)

⇒ 3 – (9 – 3 × 4)

⇒ 3 – (9 – 12)

⇒ 3 + 3

⇒ 6

Total number of students = 32 + 18 + 28 + 45 + 42 + 42 + 13 + 30 = 250

Number of girls = 18 + 45 + 42 + 30 = 135

Required percentage = (135/250) × 100 = 54%

Given:

∠A = 100° 

Concept Used:

The sum of the opposite angles of a cyclic quadrilateral is 180°.

The sum of interior angles of a triangle is 180°.

Calculation:

∠A = 100

As we know,

∠A + ∠C = 180 [opposite angles of cyclic quadrilateral]

⇒ 100 + ∠C = 180

⇒ ∠C = 180 – 100 = 80

∴ ∠C is 80°

Let, maximum marks be x

So, Passing marks = x × (31/100) + 16      ---- (1)

Passing marks = x × (40/100) – 56      ---- (2)

From equation (1) and equation (2),

31x/100 + 16 = 40x/100 – 56

⇒ 40x/100 – 31x/100 = 56 + 16

⇒ 9x/100 = 72

⇒ x = 72 × (100/9)

⇒ x = 800

Passing marks = 800 × 31/100 + 16 = 248 + 16 = 264

∴ Passing marks is 264.

Shortcut TrickLet, maximum marks = 100%

40% - 31% = (16 + 56)

⇒ 9% = 72

⇒ 1% = 8

⇒ 100% = 800

∴ Passing marks = 800 × 31/100 + 16 = 264

SP of 18 fans = 11664

CP of 18 fans = 11664 × (10/9) = 12960

Now, CP of 1 fans = 12960/18 = 720

New SP of 1 fans = 720 × 11/10 = 792

In Rs. 792, fan sold = 1

∴ In Rs. 17,424, fans sold = 1/792 × 17424 = 22

Let efficiency of 1 man and 1 woman be m and w respectively.

10m = 12w

⇒ m : w = 6 : 5

Total work = 10 × 6 × 10 = 600 units

Work done by 5 men and 2 women in 1 day = 5 × 6 + 2 × 5 = 40

∴ Number of days = 600/40 = 15 days

MP of the article = Rs. 5040

SP of the article = 5040 × (3/5) = 3024

CP of the article = 3024 × (5/6) = 2520

∴ Profit = 3024 – 2520 = 504

Shortcut Trick

Multiply the first ratio by the first term of the second ratio (2) and the second ratio by the last term of the first ratio (5) to equalize B.

A : B = 3 × 2 : 5 × 2 = 6 : 10

B : C = 2 × 5 : 3 × 5 = 10 : 15

Combining the terms gives A : B : C = 6 : 10 : 15.

∴ The correct answer is 6 : 10 : 15.

Alternate Method

Given:

Ratio 1: A : B = 3 : 5

Ratio 2: B : C = 2 : 3

Calculations:

⇒ To combine, B must be the same in both ratios. LCM of 5 and 2 is 10.

⇒ A : B = (3 × 2) : (5 × 2) = 6 : 10

⇒ B : C = (2 × 5) : (3 × 5) = 10 : 15

⇒ A : B : C = 6 : 10 : 15

∴ The correct answer is 6 : 10 : 15.

Additional Information

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd). It is obtained by multiplying the corresponding terms.

Continued Proportion

Three quantities a, b, c are in continued proportion if a : b = b : c, which implies b² = ac.

Duplicate Ratio

The duplicate ratio of a : b is a² : b². For example, duplicate ratio of 2 : 3 is 4 : 9.

Given,

MP = 15, NQ = 8, PA = 17, BQ = 10

In right angled ΔPMA

AP² = PM² + AM²

⇒ 17² = 15² + AM²

⇒ AM² = 289 – 225

⇒ AM = √64 = 8

In right angled ΔBNQ

BQ² = BN² + NQ²

⇒ 10² = BN² + 8²

⇒ BN² = 100 – 64

⇒ BN = √36 = 6

As we know,

AM = AC = 8 and BN = BC = 6 cm.

Now, AB = AC + BC

⇒ AB = 8 + 6 = 14

P = 50000, time = 2 years and SI = 4000

SI = P × r × t/100

4000 = 50000 × 2 × r/100

r = 4000/1000

r = 4%

As we know,

A = P (1 + r/100)^t

⇒ A = 50000 (1 + 4/100)²

⇒ A = 50000 × 26/25 × 26/25

⇒ A = 54080

⇒ CI = 54080 – 50000 = 4080

Short Trick:

SI for 2 years = 4000

SI for 1 year = 2000

Rate percentage = 2000/50000 × 100 = 4%

4% of 2000 = 80

CI for 2 years = 4000 + 80 = 4080

Divisibility law of 11: If the difference of the alternating sum of digits of the number is a multiple of 11 (e.g. 2343 is divisible by 11 because 2 - 3 + 4 - 3 = 0, which is a multiple of 11).

The number 925x85 is divisible by 11, then

9 – 2 + 5 – x + 8 – 5 = 11

⇒ ⇒ 15 – x = 11

⇒ x = 15 – 11

⇒ x = 4

Concept used:

Sum of two opposite angle is equal to external angle

Calculation:

AS we know,

∠ABC + ∠BAC = ∠ACD

⇒ 62 + ∠BAC = 110

⇒ ∠BAC = 110 – 62 = 48

Total number of students = 50

Number of students scoring 40 or more, but less than 70 = 46 – 22 = 24

Required percentage = 24/50 × 100 = 48%

Kindly note that number of total students can be calculated by using cumulative addition.

The correct answer is Option 3.

'were going off' is used incorrectly instead of 'went off'.

The sentence shows a longer action that was interrupted in the past. The interruption is usually a shorter action in the simple past.

The sentence is in the past continuous tense + simple past tense. 'were going off' must be replaced with 'went off'.

Thus the correct sentence would be: Mother was watching a movie when the lights went off.

The correct answer is Option 3.

Key Points 

• Across is wrongly spelled as Accross; It is a preposition that expresses position or orientation. (यह एक पूर्वसर्ग है जो स्थिति या अभिविन्यास को व्यक्त करता है।)
• Thus, the correct option is 3 and therefore the answer.

Let's look at the other options and their meaning-

• Alien: belonging to a foreign country; unfamiliar and disturbing (एक विदेशी देश से संबंधित; अपरिचित और परेशान करने वाला)
• Awful: very bad or unpleasant; used to emphasize the extent of something, especially something unpleasant or negative. (बहुत बुरा या अप्रिय; किसी चीज की सीमा पर जोर देना, विशेष रूप से कुछ अप्रिय या नकारात्मक।)
• Already: before or by now or the time in question.(पहले या अब तक या विचाराधीन समय।)

The correct answer is Option 4.

When we combine the sentences to form a paragraph, it is important to establish a connection between them.

• D is the beginning of the paragraph. It introduces to the subject 'Whales have highly developed maternal instincts'.
• A connects with sentence D illustrating further about maternal instincts. As an instance, it states that 'When a calf is born underwater, the mother must get it to the surface before it drowns'.
• C follows A. It states that another whale assists the mother and encourage the baby to swim.
• B follows C. The conclusion is drawn which states that for 15 years they stay with their parents.

Thus the correct order is DACB.

Whales have highly developed maternal instincts. When a calf is born underwater, the mother must get it to the surface before it drowns. Often another whale assists the mother nudging the baby gently and encouraging it to swim. The young ones remain with their parents for up to fifteen years or more.

The correct answer is Keep oneself updated

Key Points

• Keep abreast of means to stay updated.
• Eg: It is important to keep ourselves abreast of the latest information on Covid 19.
• Thus other options do not match the idiom.

The correct answer is assurance

Key Points

• Meaning of the words given in the options are:
• Assurance(noun): a positive declaration intended to give confidence; a promise; confidence or certainty in one's own abilities.
• Ambition(noun): a strong desire to do or achieve something.
• Admission(noun): a statement acknowledging the truth of something.
• Insurance(noun): a thing providing protection against a possible eventuality.
• No other option except 'assurance' fits best in the blank.

Thus the sentence with the correct option will be: The minister gave an assurance that strict action would be taken against the culprits.

The correct answer is Option 4.

• Sacred: connected with God; dedicated or to consecrated to God or to a religious purpose
• Holy: dedicated or consecrated to God or a religious purpose; sacred.
  

Holy is synonymous with Sacred.

• Valued: considered to be important or beneficial; cherished.
• Precious: of great value; not to be wasted or treated carelessly.
• Scarce: (especially of food, money, or some other resource) insufficient for the demand.

The correct answer is To consider someone inferior

Key Points

• Look down upon means to consider someone or something is lesser or inferior.
• Eg: Homeowners often look down upon beggars.
• Other phrases do not match the idiom.

The correct answer is Option 3 i.e. are being honoured

Key Points

• The error is in the phrase 'are being honoured'.
• The article 'the' used only once with the first subject i.e. famous author which is indicative that the actor also refers to the same person.
• If two singular nouns refer to the same person or thing, the verb must be singular.

​​

Important Points

• When two subjects are connected with the conjunction 'and' and article or possessive adjective is used with the first subject, it refers to the singular subject
• Thus, the singular verb 'is' must be used instead of a plural verb 'are' in the given sentence.

Thus the correct sentence will be: The famous author and actor is being honoured at a function today.

The answer is Option 1 i.e Foreign

 Explanation

Let's look at the meaning of the given word and the option:

• Native: a person born in a specified place or associated with a place by birth, whether subsequently residing there or not.
• Foreign: of, from, in, or characteristic of a country or language other than one's own.

Here we find that both Native and Foreign express different meanings.

Therefore both these words are Antonyms and Option 1 Foreign is the correct answer.

Let's look at the meaning of other words:

• Rustic: relating to the countryside; rural.
• Urban: in, relating to, or characteristic of a town or city.
• Rural: in, relating to, or characteristic of the countryside rather than the town.

The correct answer is Option 4.

Key Points

• Benevolence: the quality of being kind and helpful.
• Condolence: an expression of sympathy, especially on the occasion of the death of a person's relative or close friend.
• Malevolence: the quality of causing or wanting to cause harm or evil.
• Insolence: rude and disrespectful behaviour.
• According to the context, benevolence is the correct option.
  

The sentence thus would be: She was loved by her employees for her benevolence.

The correct answer is Option 1.

• Motive: a reason for doing something
• Emotion: a strong feeling deriving from one's circumstances, mood, or relationship with others
• Influence: the capacity to have an effect on the character, development, or behaviour of someone or something, or the effect itself.
• Feeling: an emotional state or reaction; showing emotion or sensitivity.

One's aim or reason for commercial advertising is to increase sales and earn more profit. Thus motive fits in blank 5.

Other options are incorrect.

The correct answer is Insatiable

Key Points

• Insatiable means that which cannot be satisfied
• The other words mean:
• Inapt: not suitable or appropriate in the circumstances
• Ingenuous: innocent and unsuspecting
• Insane: in a state of mind thats prevents normal perception, behaviour, or social interaction; seriously mentally ill.

The correct answer is The traveller asked the passerby if he could kindly help him find his way.

Key Points

The given sentence is an interrogative sentence in direct speech. It needs to be changed in Indirect speech.

When we convert the sentence from direct to indirect, the following changes take place:

i) Quotation marks and commas are omitted.

ii) The tense of the reporting verb (past tense) does not change.

iii) In the reporting questions, the verb asked is added.

iv) The modal auxiliary of the reporting speech can changes to could.

v) The personal pronoun 'you' changes to 'he' and 'my' changes to 'him'.

vi) 'Please' changes to 'kindly'.

vii) Upon conversion, interrogative statement changes to an assertive sentence.

Thus the correct sentence will be: The traveller asked the passerby if he could kindly help him find his way.

When we convert a sentence from direct to indirect speech, we make the following changes:

• Quotation marks are omitted and the sentence ends with a full stop.
• The tense of the verb, in the reported speech involving any order, request and instruction does not undergo any change during the conversion from direct to indirect mode. This is also true if the statement is a universal truth.
• If the reporting verb is in the present tense, it does not undergo any change.
• We add the word 'to' before the verb if the verb is in bare infinitive.
• When the reporting or principal verb is in the present tense, all present tenses of the direct are changed into the corresponding past tenses.
• Words expressing nearness in time or place are generally converted into words expressing distance. For eg. now becomes then, today becomes that day, yesterday becomes the previous day, this becomes that etc.
• In reporting commands and requests, the verb expressing command or request is added and the imperative is changed into the infinitive.
• In reporting questions the verbs like asked, inquired are added
• In reporting exclamations and wishes, the verbs expressing exclamation or wish are added.
• When we convert a sentence from the direct to the indirect mode (especially for a sentence ending with a mark of interrogation), we reverse the subject-verb placement.
• In direct sentences, we have the verb before the subject; while in indirect, the verb follows the subject.

The correct answer is Option 2.

Guarantee is incorrectly spelled as guarranty. It means provide a formal assurance, especially that certain conditions will be fulfilled relating to a product, service, or transaction.

Other words are spelled correctly and their meanings are:

• Guardian: a person who protects or defends something.
• Guilty: culpable of or responsible for a specified wrongdoing.
• Guidance: advice or information aimed at resolving a problem or difficulty, especially as given by someone in authority.

The correct answer is Option 3.

With is used to denote possession or association.

In the sentence, the use of 'with' is incorrect.

Thus the correct sentence will be: He married a rich heiress last year.

The correct answer is Option 2.

When we combine the sentences to form a paragraph, it is important to establish a connection between them.

• The subject of the paragraph is introduced in sentence B. It states that Ramesh was always worried about his sickness and weakness in old age.
• D follows B. It connects with A further illustrating about his fear of losing his eyes sight and become blind.
• C follows D. A relation is established between his fear of losing eyesight and how he would overcome. To try how he would cope with blindness, Ramesh started walking with his eyes closed.
• A follows C. When walking with his eyes closed 'he missed seeing a velvet purse full of gold coins lying on the road'.

Thus the correct order is BDCA.

Ramesh always worried about how he would become sick and weak in old age. He feared that he might even lose his sight and go blind. To try how he would cope with blindness, Ramesh started walking with his eyes closed. While he was doing this, he missed seeing a velvet purse full of gold coins lying on the road.

The correct answer is Option 2.

The sentence is in the present tense and thus 'being', present participle form of the verb is the correct usage.

• 'be' is the base form of the verb
• 'been' is the past participle form

It means that advertisements are sometimes being pushed on the audience with the view to sell products and services.

Other options are grammatically not fit in blank 4.

The correct answer is The National Anthem was sung with great enthusiasm by the children.

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice and 'The children' is the subject and 'The National Anthem' is the object.
• When we convert this sentence into passive voice, the subject 'The children' of the active voice becomes the object, the object 'The National Anthem' becomes the subject.
• The passive format "was + V3 (sung)" should be used.
• This is the active and passive voice rule for the past simple tense.
  

Hence, the correct answer is option 3.

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:
  

The answer is Attractive

Key Points

• Let's look at the meaning of the given word and the option:
• Repulsive: arousing intense distaste or disgust. (प्रतिकूल or कुरूप)
• Attractive: pleasing or appealing to the senses; having qualities or features that arouse interest. (आकर्षक)
• .​Here we find that both Repulsive and Attractive express different meanings.
• Therefore both these words are Antonyms and Option 3 Attractive is the correct answer.

​

Additional Information

• Let's look at the meaning of other words:
• Hideous: extremely ugly; unpleasant. (भयानक or बुरा)
• Revolting: causing intense disgust; disgusting. (घिनौना)
• Brilliant: very bright; exceptionally clever or talented. (चमकदार or अत्यधिक बुद्धिमान)