SSC CGL Previous Paper (Held On: 6 March 2020 Shift 3) (Previous Year Paper)

The logic is:

We are taking the opposite value of the first term and then we are adding 2 in the first term.

First term = ► Opposite place value of first term = second term.

First term + 2 = Third term

1. KPT

2. UFW

3. BYD

4. CXE

Hence, ‘KPT’ is the odd one out.

The logic followed here is:

(1st number)² + (Second number / 2)² = third number.

(14, 18, 277)

(14)² + (18 / 2)² = 196 + 81 = 277

Similarly,

(20, 22, 521)

(20)² + (22 / 2)² = 400 + 121 = 521

Hence, the correct answer is "Option (3)."

Logic: First two number is even number with only 2 as a common factor and last number is third number is a prime number

Except (20, 22, 521) combination no other option have third option is prime number. 

(20, 22, 521) → In first two numbers only 2 is common factor and third number is prime number. 

Hence, (20, 22, 521) is correct answer.

The logic is:

Column 1: (350 ÷ 50) × 8 = 56

Column 2: (192 ÷ 48) × 8 = 32

Similarly,

Column 3: (? ÷ 30) × 8 = 40

(? ÷ 30) = 5

? = 150

Hence, ‘150’ is the correct answer.

1. 4 and 28

Given equation: 28 + 49 – 35 ÷ 7 × 4 = 68

After interchanging ‘4 and 28’, we get:

L.H.S = 4 + 49 – 35 ÷ 7 × 28

= 4 + 49 – 140

= -87 ≠ R.H.S

2. 28 and 49

Given equation: 28 + 49 – 35 ÷ 7 × 4 = 68

After interchanging ‘28 and 49’, we get:

L.H.S = 49 + 28 – 35 ÷ 7 × 4

= 49 + 28 – 20

= 77 – 20

= 57 ≠ R.H.S

3. 28 and 35

Given equation: 28 + 49 – 35 ÷ 7 × 4 = 68

After interchanging ‘28 and 35’, we get:

L.H.S = 35 + 49 – 28 ÷ 7 × 4

= 35 + 49 – 16

= 84 – 16

68 = R.H.S

4. 49 and 35

Given equation: 28 + 49 – 35 ÷ 7 × 4 = 68

After interchanging ‘49 and 35’, we get:

L.H.S = 28 + 35 – 49 ÷ 7 × 4

= 28 + 35 – 28

= 35 ≠ R.H.S

Hence, ‘28 and 35’ is the correct answer.

The number ‘4’ is common in both the dice, it means that the numbers 3, 6, 2 and 1 are adjacent to 4 and the remaining number left is 5, which is opposite to 4.

So, number 4 will be on the face opposite to the one having ‘5’.

Hence, ‘4’ is the correct answer.

The Venn diagram that best illustrates the relationship between Spices, Cumin, Foodis shown below:

Cumin is a spice and all the spices are food.

Hence, option 2 is the correct answer.

W × R × J – S ÷ V + L → W is mother of R, R is mother of J, J is wife of S, S is son of V, V is husband of L.

1. W is the maternal grandmother of J. →True

2. V is the father- in law of J. → True

3. L is the wife of V. → True

4. L is the mother-in-law of S. → False

Hence, option 4 is incorrect.

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

Hence, the figure has total 22 triangles.

The option figure in which the given figure is embedded is option ‘1’.

Hence, option ‘1’ is the correct answer.

‘Size’ is related to ‘Medium’ → Medium comes under the category of size.

Similarly,

‘Shape’ is related to ‘______’ → Oval comes under the category of shape.

Hence, ‘oval’ is the correct answer.

Among 160 players in a tournament, 57 did not participate in any of the three games, i.e. Cricket, Hockey and Badminton.

No. of players who participated in the game = (160 – 57) = 103

10 players participated in both Cricket and Hockey but not in Badminton, 9 players participated in both Hockey and Badminton but not in Cricket, and 13 players participated in both Cricket and Badminton but not in Hockey.

Number of players who participated in two games only = (10 + 9 + 13) = 32

Number of players who participated in all the three games = 103 – (32 + 37) = 34

Hence, ‘34’ is the correct answer.

The logic is:

Consonants:  Reverse  alphabetical Values are used

Vowel: Actual alphabetical Values are used

BLINK - I is Vowel so no change in their value.

PURSE - U and E is the Vowels, so no change in U and E's value.

Similarly: FIRST - I is Vowel so no change in their value.

Hence, the correct answer is "54".

Given series:

IF we point out the changes in figures 3 with respect to figure 1, we can easily find out how the fourth figure will be like.

In 1^st figure the triangle is at the upside corner, in the 3^rd figure the triangle is at the downside corner. In 1^st figure, the arrow which is at the downside corner, shifts to middle position in the 3^rd figure.

Similarly, in 2^nd figure the arrow is at the upside corner, so in the fourth figure the arrow will be at the downside corner. In 2^nd figure, the square which is at the downside corner, shifts to middle position in the 4^th figure.

If we see each option, it is seen that option 4 satisfies the above conditions.

Hence, option 4 is the correct answer.

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

Hence, option 3 is the correct answer.

The logic is:

Hence, ‘Z’ is the correct answer.

The logic is:

Similarly,

Hence, ‘SBDUFQ’ is the correct answer.

The least possible venn diagram is:

I. Some objects are helmets. → True

II. Some vehicles are helmets. → True

III. Some vehicles are objects. → True

Hence, all conclusions I, II and III follow.

The relation is:

Ear : Tinnitus → Tinnitus is the perception of noise or ringing in the ears. A common problem, tinnitus affects about 15 to 20 percent of people. Tinnitus isn't a condition itself, it's a symptom of an underlying condition, such as age-related hearing loss, ear injury or a circulatory system disorder.

The relation here is (Organ – Organ related illness)

1. Nose : Nerve → the part projecting above the mouth on the face of a person or animal, containing the nostrils and used for breathing and smelling is called nose. The nervous system is a highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body.

2. Joints : Muscles → The area where two bones are attached for the purpose of permitting body parts to move. Muscles are a specialized body part that produces movement or locomotion in animals.

3. Eye : Ophthalmology →The human eye is an organ that reacts to light and allows vision. Ophthalmology is a branch of medicine and surgery which deals with the diagnosis and treatment of eye disorders. An ophthalmologist is a specialist in ophthalmology.

4. Skin :Acne → A skin condition characterized by red pimples on the skin, especially on the face, due to inflamed or infected sebaceous glands and prevalent chiefly among adolescents. It follows the same relation of (Organ – Organ related illness).

Hence, ‘Skin : Acne’ is the correct answer.

The logic is:

Number : (Number)²  + (Number)³ = Second Number

8 : 576 → 8 : (8)² + (8)³ = 64 + 512 = 576

Similarly,

4 : ? → 4 : (4)² + (4)³ = 16 + 64 = 80

Therefore, ? = 80

Hence, ‘80’ is the correct answer.

All options except ‘machine’ are names of different electronic devices.

Hence, ‘machine’ is the odd one out.

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

Hence, option 2 is the correct answer.

We take admission first, then class starts. After studying for a certain period, we appear for examination. Examination paper is checked and marks is given according to performance. After that result is declared. So, the logical sequence is:

2. Admission
3. Class
4. Examination
5. Marking
6. Result

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

Given series: 58, 73, 99, 138, 193, ?, 368

The logic is:

Hence, ‘268’ is the correct answer.

The logic is:

1. 41263 : 18 → 41263 : (4 + 1 + 2 + 6 + 3) ≠ 18

2. 77052 : 21 → 77052 : (7 + 7 + 0 + 5 + 2) = 21

3. 26584 : 25 → 26584 : (2 + 6 + 5 + 8 + 4) = 25

4. 85245 : 24 → 85245 : (8 + 5 + 2 + 4 + 5) = 24

Hence, ‘41263 : 18’ is the correct answer.

The logic is:

Hence, ‘PCCQ’ is the correct answer.

• Rohit Sharma laid the foundation of the Cricket Stadium and Training Centre at ‘Heartfulness Institute’s’ headquarters in Hyderabad.
• Training Centre is named as 'Rohit Sharma Cricket Stadium'
• Kamlesh Patel (commonly known as Daaji) is a spiritual master and the guide of Heartfulness.
• Global headquarters of Heartfulness Institute is located in Kanha Shantivanam at Chegur, Hyderabad.

About Heartfulness:

• Heartfulness is a Raja Yoga system of meditation.
• Alternatively known as Sahaj Marg or the Natural Path.
• This system of meditation began at the end of the 20th century.
• In 1945 it was formalised with the establishment of the Shri Ram Chandra Mission.

• Manganese dioxide is used to remove the green colour from the glass which caused by iron impurities.
• Naturally occurring manganese dioxide (MnO₂) is known as pyrolusite. It usually MnO₂ found in nature is a black-brown solid.
• Among all the manganese compounds, MnO₂ is most plentiful compound.
• Manganese dioxide is further used as a key component in battery making.

Additional information about other compounds:

The correct answer is Kamakhya temple.

Key Points

• Ambubasi / Ambubachi Fair celebrated every year in the month of June. It is one of the most important festivals which is celebrated in the Kamakhya temple.
• Kamakhya temple is dedicated to  Hindu deity, mother goddess - Kamakhya. It is also a Shakti Peeth.
• "Ambubachi" indicates spoken with water. Another meaning is that the rains expected during this month make the earth fertile and ready for procreation.
• Kamakhya temple was built in the seventeenth century.

Additional Information

The correct answer is Gujarat.

Key Points

• Khadi and Village Industries Commission (KVIC) opened its first Silk Processing Plant in the Surendranagar district of Gujarat.
• The objective of this plant is to reduce the cost of production of silk yarn and increase the availability of raw material used in the production of Gujarati Patola sarees.
• Khadi and Village Industries Commission (KVIC) was established as a statutory body in the year 1956.
• KVIC works under the administrative control of the Ministry of Micro, Small & Medium Enterprises.
• KVIC chairman: VK Saxena
• Minister of Micro, Small & Medium Enterprises: Nitin Jairam Gadkari

Atomic Mass of Common Elements:

Basic Concepts Related to Atoms:

• According to the Regulating Act of 1773, the Bengal Governor came to be known as the Governor-General. According to this act, Lord Warren Hastings became the Governor-General of India.
• 3^rd Anglo-Mysore war happened during the tenure of 2nd Earl Cornwallis.

List of Anglo- Mysore wars:

• The president of India appointed two additional Commissioners on 16 October 1989.
• The objective behind the appointment of two more commissioners was to cope with the increased work of the election commission due to the lowering of the voting age from 21 to 18 years.
• By the 61^st constitutional amendment act, the 1989 voting age from 21 was reduced to 18 years.
• In January 1990 additional 2 posts of the election, commissioners were abolished. In 1993 president of India appointed two more election commissioners since then Election Commission of India is a multi-member body.
• All the election commissioners have similar equal power and their salary structure is also the same.
• Sukumar Sen was the first election commissioner of India.

• Barack Obama has authored a book -‘Dreams From My Father’. This book is a diary of events that explores his early life.
• Mr. Obama was 44^th President of the United States of America and 1^st Afro-American to be elected as President of the USA.
• His Presidential term was from the year 2009 to 2017. He represented the Democratic Party of the USA.
• Currently, Joe Biden is serving as 46^th President of the USA.

• According to UNICEF, the UN's Children's Fund, India topped the ranking of countries that have most childbirths on the first day of the New Year of 2020.
• UNICEF projected 67,385 childbirths in India, followed by China with 46,299 and Nigeria in 3^rd place with 26,039.

Information about UNICEF:

Additional Information:

• Stephanie Louise Kwolek invented Kevlar. It is a highly heat resistant and strong synthetic fibre.
• Due to its high tensile strength-weight ratio, it is primarily used in bulletproof garments, jackets, helmets, etc.
• Kevlar has high tensile strength and stability at high temperature. Hence, it is widely used in the automotive industry and protective instruments.

• A prominent Orientalist and avid typographer Sir Charles Wilkins was a pioneer in the study of Sanskrit and he was first European to translate Bhagavad Gita into English.
• He was fluent in Bengali and Persian and therefore appointed as a translator of Bengali and Persian into English in the Revenue Department.
• Under the tutelage of Kalinath Bhattacharya of Benares Wilkins learnt the Sanskrit language.
• The French version of Gita was translated by a renowned French scholar, J.P. Parraud from the English version of Charles Wilkins.

• Gully Boy was nominated for 92^nd Oscar Awards.
• 92^nd Academy Awards (Commonly known as Oscar Awards) ceremony held at the Dolby Theatre in Hollywood, Los Angeles, California, USA.
• This awards conferred by Academy of Motion Picture Arts and Sciences to honour best films across the world.
• Awards were given in a total of 24 categories. South Korean Film Parasite won the award for the best picture.
• Some Indian Oscar Award Winners: Satyajit Ray, Bhanu Athaiya (Best Costume Design-Gandhi), A. R. Rahman (Slumdog Millionaire)

Additional information about options given in the question:

• Rani Rampal has been nominated for the ‘World Games Athlete of the Year’ Award, 2019 by the International Hockey Federation (FIH).
• 'World Games Athlete of the Year' award has been the first time won by a hockey player.
• Rani Rampal has received Padmashree award, one of the highest civilian awards of our country in 2020.

Additional related information:

• The first chief statistician of India, Pronab Sen was the head of the standing committee on economic statistics set up by the Ministry of Statistics and Programme Implementation (MOSPI).
• The objective of the committee is to think and develop methodologies for surveys on industry, services and employment.
• The 27 member committee consists of different 4 standing committees on labour force statistics, industrial statistics, services sector and unincorporated sector enterprises.

Additional information about MoSPI:

• The Hindustan Socialist Republican Association (HSRA) was founded in the year 1928.
• The young men influenced by socialist ideas decided to set up a nationwide revolutionary organization. Prominent among them were Chandrashekhar Azad, Bhagat Singh, Rajguru, Sukhdev, etc. In 1928 in the meeting held at Feroz Shah Kotla ground in Delhi, these young men established the organization called ‘Hindustan Socialist Republican Association’.
• The objective behind the establishment of this organization was to free India from British exploitation and to overthrow the unjust socio-economic system which exploited the farmers and workers.
• The work of gathering arms and execution of programmes was entrusted to a separate wing of the organization. This wing was called ‘Hindustan Socialist Republican Army’ and Chandrashekar Azad was the chief of this wing.

• International exhibition and conference on the civil aviation sector, ‘Wings India 2020’ was held at Begumpet Airport in Hyderabad.
• This event was organized by the Ministry of Civil Aviation along with the Airports Authority of India (AAI) and FICCI.
• The theme of ‘Wings India 2020’: ‘Flying For All’
• One of the key events of this conference was the release of 'UDAN 4.0+ knowledge paper on the changing landscape of the Indian aviation sector under the regional connectivity scheme'.
• UDAN (Ude Desh ka Aam Nagarik) is a regional connectivity and airport development scheme of the Ministry of Civil Aviation.

The correct answer is Mumbai Central.

Key Points

• Mumbai Central railway station has been certified by FSSAI as the country’s first ‘Eat Right Station’.
• Mumbai Central railway station of the Western Railway was certified with a 4-Star rating.
• FSSAI in 2018 launched the ‘Eat Right India’ movement. “Eat Right Station” initiative was launched by Indian Railways to help passengers to make healthy food choices.
• There are two broad pillars of ' Eat Right India': 1) Eat Healthy 2) Eat Safe
• Chairperson, FSSAI: Rajesh Bhushan
• Chief Executive Officer, FSSAI: Shri Arun Singhal

• 24.56% of the total geographical area of the country is covered by forests and trees as per the report by the Forest Survey of India(FSI),2019.
• Since 1987, Forest Survey of India (FSI) is undertaking a biennial assessment of the country’s forest resources and the 16th assessment report was launched in 2019.
• Forest Survey of India was established in June 1981 and it is located at Dehradun, Uttarakhand.

Important Persons:

• Scandium has 13 types of isotopes but the naturally occurring Scandium has one stable isotope.
• Cesium (Cs) has the maximum number of isotopes.
• Isotope: Atoms of the same element having the same atomic number but different atomic masses.
• Isobars: Atoms of different elements having different atomic numbers but the same mass number.

• Mizoram recorded the highest number of fire alerts according to a report by the Forest Survey of India(FSI),2019.
• Since 1987, Forest Survey of India (FSI) is undertaking a biennial assessment of the country’s forest resources and the 16^th assessment report was launched in 2019.
• Forest Survey of India was established in June 1981 and it is located at Dehradun, Uttarakhand.
• Forest Fire Alerts System of Forest Survey of India (FSI) was started in the year 2004. In the year 2019, FSI released the Forest Fire Alerts System version 3.0 (FAST 3.0).
• The Fire hotspots are detected by MODIS (Moderate Resolution Imaging Spectro-radiometer) and SNPP-VIIRS (Visible Infrared Imaging Radiometer Suite) sensors.

Important Persons:

Key Points

• The district having the maximum urban percentage in Uttar Pradesh is Ghaziabad.
• The district having the least urban percentage in Uttar Pradesh is Shravasti.
• The district having the least rural percentage in Uttar Pradesh is Gautam Buddh Nagar.
• The district having the maximum rural percentage in Uttar Pradesh is Prayagraj.
• Out of India's total rural population UP has 18.63% of the rural population which is the highest in India

After the end of the Second World War, the British rulers were in favor of granting freedom to India.

• In the British Parliament, British Prime Minister Attlee clarified the British policy regarding India. According to it, the right of Indian people to draft their own Constitution was recognized.
• The three-member mission visited India between March and June 1946. The delegation of British ministers included Lord Pethick-Lawrence, Sir Stafford Cripps and Mr. A.V. Alexander.

Key Proposals of the Cabinet Mission Plan:

1. Rejected the demand for a sovereign Pakistan.
2. Grouping of existing assemblies into 3 sections A, B, C.
3. Provincial autonomy and residual powers.
4. Three-tier executive and legislature at the province, princely states, and union level.
5. Union government will be in charge only of defense, foreign affairs, and communications.

• Lai Haraoba festival is widely celebrated in Manipur. It is an important festival of the Meitai tribe.
• Traditional folk dances of Manipur: Rakhal, Nat Rash, Maha Rash, Raukhat
• Lai Haraoba festival is celebrated in honour of Umang-Lais, the deity of forest and environment.
• In the Meitei society following types of Lai Haraoba are prevalent:

1. Kanglei Haraoba
2. Chakpa Haraoba
3. Moirang Haraoba
4. Kakching Haraoba

• Chief Minister of Manipur: Shri N. Biren Singh
• Governor of Manipur: Dr. Najma Heptulla

• Article 140 deals with the Ancillary powers of the Supreme Court.
• Supreme Court of India consists of the Chief Justice of India and a maximum of 34 judges.
• It was established in the year 1950.
• The seat of the Supreme Court is declared as Delhi by the Constitution of India.
• 65 years is the age of retirement for the judge of the supreme court.
• Harilal J. Kania was the first Chief Justice of India.
• The 52nd and present Chief Justice is Bhushan Gavai. Sworn in on 14 May, 2025, he became the first Buddhist to hold this post. He will have a 6-month term which is due to end on November 23, 2025.

• National Highway 66 (NH 66) was previously known as ​NH 17. It runs through 5 states: Maharashtra, Goa, Karnataka, Kerala and Tamil Nadu.
• It connects Panvel in Maharashtra to Kanyakumari in Tamil Nadu state.
• Average road length per lakh population (Census 2011): 402.03 Kms
• The longest NH in India is NH-44 ( Srinagar- Kanyakumari)
• Minister of Road Transport and Highway: Nitin Jairam Gadkari
• Minister of State: GEN. (DR) Vijay Kumar Singh

Organizations related to Ministry of Road Transport and Highways:

Shortcut Trick4 $\left[ {\frac{{{{\left( {1 - secA} \right)}^2}; + ;{{\left( {1; + ;secA} \right)}^2}}}{{1; + ;{\rm{se}}{{\rm{c}}^2}A}}} \right]$

Put A = 0°

⇒ 4 [(1 – sec0)² + (1 + sec0)²]/(1 + sec²0)

⇒ 4 [(1 – 1)² + (1 + 1)²]/(1 + 1²)

⇒ 4 × [4/2]

⇒ 4 × 2

⇒ 8

Alternate Method 

4 $\left[ {\frac{{{{\left( {1 - secA} \right)}^2}; + ;{{\left( {1; + ;secA} \right)}^2}}}{{1; + ;{\rm{se}}{{\rm{c}}^2}A}}} \right]$

⇒ 4 $\left[ {\frac{{1; + ;{{\sec }^2}A - 2\sec A; + ;1; + ;se{c^2}A; + ;2;secA}}{{1; + ;{\rm{se}}{{\rm{c}}^2}A}}} \right]$

⇒ 4 $\left[ {\frac{{2; + ;2se{c^2}A}}{{1; + ;{\rm{se}}{{\rm{c}}^2}A}}} \right]$

⇒ 4 [2 (1 + sec²A)/(1 + sec²A)]

⇒ 4 × 2

⇒ 8

Let cost price of the article be Rs. x, then

According to the question

120x/100 – 116x/100 = 36

⇒ (120x – 116x)/100 = 36

⇒ 4x/100 = 36

∴ x = 900

Short Trick:

Let cost price of the article be 100%

20% - 16% = 36

⇒ 4% = 36

⇒ 1% = 9

∴ 100% = 900

b + c = ax, c + a = by and a + b = cz

Put a = b = c = 1 and x = y = z = 2, then all condition satisfied.

Now,

1/9 [1/(x + 1) + 1/(y + 1) + 1/(z + 1)]

⇒ 1/9 [1/3 + 1/3 + 1/3]

⇒ 1/9 × 3/3

⇒ 1/9

Detailed Method :

b + c = ax, c + a = by and a + b = cz

x = (b + c)/a, y = (a + c)/b and z = (a + b)/c

$\Rightarrow {\rm{;}}\frac{1}{9}\left[ {\frac{1}{{\frac{{b; + ;c}}{a}; + ;1}} + \frac{1}{{\frac{{a; + ;c}}{b}; + ;1}} + \frac{1}{{\frac{{a; + ;b}}{c}; + ;1}}} \right]$

$\Rightarrow {\rm{;}}\frac{1}{9}\left[ {\frac{a}{{\left( {a; + ;b; + ;c} \right)}} + \frac{b}{{\left( {a; + ;b; + ;c} \right)}} + \frac{c}{{\left( {a; + ;b; + ;c} \right)}}} \right]$

⇒ 1/9 [(a + b + c)/(a + b + c)]

⇒ 1/9

LCM of 3, 7, and 18 is 126.

3 = 3 × 1

7 = 7 × 1

18 = 2 × 3 × 3

∴ LCM = 2 × 3 × 3 × 7 = 126

Shortcut Trick Given cos(A + B) = 24/25 ⇒ tan(A + B) = 7/24 (using 7, 24, 25 triplet). Given sin(A − B) = 15/17 ⇒ tan(A − B) = 15/8 (using 8, 15, 17 triplet). Apply tan 2A = tan((A + B) + (A − B)) = [tan(A + B) + tan(A − B)] / [1 − tan(A + B) × tan(A − B)]. tan 2A = [7/24 + 15/8] / [1 − (7/24 × 15/8)] = [7/24 + 45/24] / [1 − 105/192] = [52/24] / [87/192]. tan 2A = (52/24) × (192/87) = 52 × 8 / 87 = 416/87. ∴ The correct answer is 416/87. Alternate Method Given: 0 < A, B < 45°, cos (A + B) = 24/25 and sin (A − B) = 15/17. Formula Used: tan(X + Y) = (tan X + tan Y) / (1 − tan X tan Y)

⇒ tan(A + B) = √(252 − 242) / 24 = 7/24 ⇒ tan(A − B) = 15 / √(172 − 152) = 15/8 ⇒ tan 2A = tan((A + B) + (A − B)) ⇒ tan 2A = [tan(A + B) + tan(A − B)] / [1 − tan(A + B) × tan(A − B)] ⇒ tan 2A = [7/24 + 15/8] / [1 − (7/24 × 15/8)] ⇒ tan 2A = [(7 + 45)/24] / [1 − 105/192] ⇒ tan 2A = (52/24) / (87/192) = (13/6) × (192/87) ⇒ tan 2A = 13 × 32 / 87 = 416/87 ∴ The correct answer is 416/87. Additional Information Trigonometric Sum and Difference Formulas tan(A + B) = (tan A + tan B) / (1 − tan A × tan B) and tan(A − B) = (tan A − tan B) / (1 + tan A × tan B). Double Angle Identities tan 2A = (2 tan A) / (1 − tan2A). Also, 2A can be expressed as (A+B) + (A-B). Pythagorean Triplets Common triplets like (3,4,5), (5,12,13), (7,24,25), and (8,15,17) help in finding trig ratios quickly without square root calculations.

OA = 8 cm, O’B = 6 cm, OO’ = BC = 8 + 6 = 14, OC = O’B and AC = 8 – 6 = 2

In Δ ACB

BC² = AB² + AC²

⇒ 14² = AB² + 2²

⇒ AB² = 196 – 4

⇒ AB = √192

∴ AB = 13.86

(When we reach at this point, AB = √192, as we know, root 192 is nearest to 14, only one option is 13.86 nearest to root 196)

From the following figure

∠AOB = 80° and ∠AOC = 120°

∠OAB = ∠OBA [OB = OA = radius]

∠OAC = ∠OCA [OC = OA = radius]

In ΔAOB

∠OAB + ∠OBA + ∠AOB = 180°

⇒ 2∠OAB = 180° – 80° = 100°

⇒ ∠OAB = 100°/2 = 50°

In ΔAOC

∠OAC + ∠OCA + ∠AOC = 180°

⇒ 2∠OAC = 180° – 120° = 60°

⇒ ∠OAC = 60°/2 = 30°

∴ ∠BAC = ∠OAC + ∠OAB = 50° + 30° = 80°

As we know,

Sum of all three angles of a triangle = 180

Ratio of all three angles of a triangle = 3 : 5 : 4

3 + 5 + 4 = 12 unit

According to question, 12 unit = 180

⇒ 1 unit = 180/12 = 15

Hence, required difference = 5 – 3 = 2 unit

∴ 2 unit = 15 × 2 = 30

MP of the article = 342

SP of the article = 342 × (68/100)

∴ CP of the article = 342 × (68/100) × (100/114) = Rs. 204

Shortcut Trick

Spirit volume remains constant: 30% of 25 → 7.5 litres.

New total volume = 25 + 5 = 30 litres.

New percentage = (7.5 ÷ 30) × 100.

New percentage = 1/4 × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given: Initial volume = 25 litres, Spirit = 30%, Added Water = 5 litres.

⇒ Quantity of Spirit = 30% of 25 = (30 × 25) ÷ 100 = 7.5 litres.

⇒ Quantity of Water = 25 − 7.5 = 17.5 litres.

⇒ New total volume of mixture = 25 + 5 = 30 litres.

⇒ New percentage of Spirit = (Spirit ÷ New Total) × 100

⇒ (7.5 ÷ 30) × 100 = (1 ÷ 4) × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Mixture Dilution Rule

When a solvent (like water) is added, the quantity of the solute (like spirit) remains constant. C₁V₁ = C₂V₂ where C is concentration and V is volume.

Percentage Change in Mixture

If the total volume increases, the percentage of the fixed component decreases proportionally. New % = (Original % × Original Volume) ÷ New Volume.

Alligation Method

Can be used when two mixtures are mixed. For water addition, the spirit percentage in the added part is taken as 0%.

Shortcut Trick

Let the numbers be 1x, 2x, and 4x.

Sum of squares ⇒ (1x)² + (2x)² + (4x)² = 1029

⇒ 1x² + 4x² + 16x² = 1029 ⇒ 21x² = 1029 ⇒ x² = 49 ⇒ x = 7.

Difference between greatest (4x) and smallest (1x) = 3x = 3 × 7 = 21.

∴ The correct answer is 21.

Alternate Method

Given: Ratio of numbers = 1 : 2 : 4, Sum of squares = 1029.

Let the natural numbers be k, 2k, and 4k.

⇒ k² + (2k)² + (4k)² = 1029

⇒ k² + 4k² + 16k² = 1029

⇒ 21k² = 1029

⇒ k² = 1029 ÷ 21

⇒ k² = 49

⇒ k = √49 = 7

⇒ Smallest number = k = 7

⇒ Greatest number = 4k = 4 × 7 = 28

⇒ Difference = 28 − 7 = 21

∴ The correct answer is 21.

Additional Information

Ratio and Squares

When terms in a ratio are squared or multiplied, always include the variable (x) because the constant of proportionality also gets squared (x²).

Natural Numbers

Natural numbers are positive integers starting from 1 (1, 2, 3, ...). In square root problems, we only consider the positive root for natural numbers.

Difference in Ratio

Difference between terms a:b:c is simply (c−a) multiplied by the common factor x.

Total work = 240

Work done by A and B in 4 days = (12 + 15) × 4 = 108

Remaining work = 240 – 108 = 132

∴ Remaining work, C complete in = 132/8 = $16\frac{1}{2}$ days

Price of commodity D in 2016 = 75 /kg

Price of commodity D in 2019 = 85 /kg

Price increased by = 85 = 75 = 10

∴ Required percentage = (10/75) × 100 = 13.33%

Total amount spent on A in 2019 = 80 × 15

Total amount spent on D in 2019 = 40 × 85

Required ratio = (80 × 15) : (40 × 85) = 6 : 17

x² – 4x + 4 = 0

⇒ x² – 2 × x × 2 + 2² = 0

⇒ (x – 2)² = 0

⇒ x = 2

Now, 16 (x⁴ – 1/x⁴)

⇒ 16 (16 – 1/16)

⇒ 256 – 1

⇒ 255

From the following figure, we know that

AD/BD = AE/EC

⇒ a/(a + 4) = (2a + 3)/7a

Put a = 3 in the following option,

3/(3 + 4) = (6 + 3)/21

⇒ 3/7 = 9/21

⇒ 3/7 = 3/7 (satisfied)

Concept used:

Calculation:

$\frac{{\left[ {54 - \left( {5 \div 2} \right); \times ;8} \right]; + ;13}}{{48 - 4 \div 3; \times ;8 - 2}}$

$\Rightarrow {\rm{;}}\frac{{\left[ {54 - \frac{5}{2}; \times ;8} \right]; + ;13}}{{48 - \frac{4}{3}; \times ;8 - 2}}$

$\Rightarrow {\rm{;}}\frac{{\left[ {54 - 20} \right]; + ;13}}{{48 - \frac{{32}}{3} - 2}}$

$\Rightarrow {\rm{;}}\frac{{34; + ;13}}{{46 - \frac{{32}}{3}}}$

⇒ (47 × 3)/(138 – 32)

⇒ 141/106

20 tan A = 21

⇒ tan A = 21/20

Now,

$\Rightarrow {\rm{;}}\frac{{5sinA - 2cosA}}{{4cosA - \frac{5}{7}sinA}}$

Divided by cos A

$\Rightarrow {\rm{;}}\frac{{5tanA - 2}}{{4 - \frac{5}{7}tanA}}$

$\Rightarrow {\rm{;}}\frac{{5{\rm{;}} \times {\rm{;}}\frac{{21}}{{20}} - 2}}{{4 - \frac{5}{7}{\rm{;}} \times {\rm{;}}\frac{{21}}{{20}}}}$

$\Rightarrow {\rm{;}}\frac{{\frac{{21}}{4} - 2}}{{4 - \frac{3}{4}}}$

⇒ [13/4]/[13/4]

⇒ 1

Amount spent of commodity A in 2019 = 80 × 15 = 1200

Amount spent of commodity B in 2019 = 60 × 20 = 1200

Amount spent of commodity C in 2019 = 40 × 12 = 480

Amount spent of commodity D in 2019 = 85 × 40 = 3400

Amount spent of commodity E in 2019 = 72 × 8 = 576

Total amount spent on the five commodities by the family in the year 2019 = 1200 + 1200 + 480 + 3400 + 576 = 6856

Interest rate for first 4 years = 5%

Interest rate for next 3 years = 8%

Interest rate for next 3 years = 10%

Total simple interest for 10 years = Rs. 1850

As we know, SI = Prt/100

According to the question

(P × 5 × 4)/100 + (P × 8 × 3)/100 + (P × 10 × 3)/100 = 1850

⇒ 20P/100 + 24P/100 + 30P/100 = 1850

⇒ 74P = 185000

⇒ P = 185000/74

∴ P = Rs. 2500

Short Trick:

Let Principal be 100% and SI for 10 years = 1850

Total percentage of interest for 10 years = 4 × 5 + 3 × 8 + 3 × 10 = 74%

74% = 1850

⇒ 1% = 25

⇒ 100% = 2500

Average of 60 students’ results = 38

Sum of 60 students’ results = 38 × 60 = 2280

Average of first 22 students’ results = 36

Sum of first 22 students’ results = 36 × 22 = 792

Average of last 32 students’ results = 32

Sum of last 32 students’ results = 32 × 32 = 1024

Sum of remaining 6 student’s results = 2280 – 792 – 1024 = 464

∴ Average of remaining 6 students’ results = 464/6 = 77.33

Extra amount spent on commodity B in 2019 as compared to 2016 = 20 × (60 – 50) = 200

Extra amount spent on commodity C in 2019 as compared to 2016 = 12 × (40 – 35) = 60

∴ Total extra amount = 200 + 60 = 260

a³ + 1/a³ = 52

As we know,

(a + 1/a)³ = a³ + 1/a³ + 3 (a + 1/a)       ---(1)

From the option

2 (a + 1/a) = 8

(a + 1/a) = 4

From equation (1)

4³ = a³ + 1/a³ + 3 × 4

⇒ a³ + 1/a³ = 64 – 12 = 52 (satisfied)

Let the length of the train be x meter. And length of the platform is 180.

Speed of train = 72 × 5/18 = 20 m/sec

As we know,

Speed = Distance/Time

20 = (180 + x)/60

⇒ 1200 = 180 + x

⇒ x = 1200 – 180 = 1020

∴ Required time to cross poll by train = 1020/20 = 51 sec

Inner radius of circular track r = 23 m and Outer radius of circular track R = 29 m

As we know,

Area of circular track = π (R² – r²) = 22/7 (29² – 23²) = 22/7 × 6 × 52 m²

Cost of leveling 1 m² the track = Rs. 7

∴ Cost of leveling 22/7 × 6 × 52 m² = 22/7 × 6 × 52 × 7 = 6864

Short Trick :

Answer divisible by 11 only, one option 6864 divisible by 11.

The correct answer is Option 1.

All the options are demonstrative pronouns.

• 'This' (singular) and 'these' (plural) is used to refer to a nearby object.
• 'That' (singular) and 'those' (plural) refers to an object that is at a far distance.

A number of factors is talked about in the paragraph, hence we say, these.

Other options are therefore incorrect.

The correct answer is Option 3.

The sentence is an interrogative statement in Active Voice. Its structure is: Interrogative word + helping verb + Subject + adverb + object?

When it changes in Passive voice, the structure is: Interrogative word + helping verb + adverb + Object (Active Voice) + past tense of the verb + by + object (the subject of Active Voice)?

Thus the correct sentence will be: Why is so much money spent by you?

While converting from active to Passive, the sentence undergoes the following changes:

Rules of Conversion from Active to Passive Voice:

• Identify the subject, the verb, and the object: S+V+O
• Change the object into subject
• The active verb does not have an object. Therefore, the passive form should begin with you.
• Change the verb into past participle of the verb
• Change the subject into object
  

Given below are the rules of tense conversion from Active to Passive Voice and vice verse:

Other options are incorrect, as they do not follow the rules of conversion.

The correct answer is Option 2.

To paddle one's own canoe means to be independent and self-sufficient.

Eg: She plunged into work, she'd got to paddle her own canoe.

Other options do not match the idiom.

The correct answer is Option 1.

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

The given sentences talk about a soldier who died on the battlefield and the money allotted to his family,

• The subject of the paragraph is introduced in C 'a soldier' who died on the battlefield while fighting.
• B follows C. As the soldier died, a gallantry award and financial aid were announced for him by the district collector.
• D follows B. It connects with sentence B of the financial aspect. It mentions the money was promptly disbursed from the Prime Minister’s Relief Fund.
• The conclusion is drawn in sentence A. As the money was disbursed, it brought relief to the family of the deceased, while the gallantry award was an honour.
• Thus the correct order is CBDA.

The correct answer is Option 4.

• Liable: likely to do or to be something; accountable, answerable
• Audacious: showing a willingness to take surprisingly bold risks
• Reliable: consistently good in quality or performance, able to be trusted; dependable
• Suspicious: having or showing a cautious distrust of someone or something

No other option suits the blank more than liable.

The reckless young man was liable for the debts incurred by him.

The correct answer is Option 2.

• Prophet: a person regarded as an inspired teacher or proclaimer of the will of God.
• Volunteer: a person who freely offers to take part in an enterprise or undertake a task.
• Scholar: a specialist in a particular branch of study, especially the humanities.
• Atheist: a person who disbelieves or lacks belief in the existence of God

Thus other options are incorrect.

The correct answer is Option 3.

Like a dying duck in a thunderstorm means having a dejected or hopeless expression.

Eg: The team felt like a dying duck in a thunderstorm after they lost the match.

Other options do not match the idiom.

The correct answer is Option 3.

• Measures: a plan or course of action taken to achieve a particular purpose
• Programmes: a set of related measures or activities with a particular long-term aim
• Attempts: make an effort to achieve or complete
• Enticements: something used to attract or to tempt someone

'Measures' is the correct fit for the blank. No other option suits better.

The correct answer is Option 1.

• Moral: concerned with the principles of right and wrong behaviour
• Dubious: hesitating or doubting
• Urgent: requiring immediate action or attention
• Pious: devoutly religious

No other options fit in the blank.

....moral duty and we should