SSC CGL Previous Paper (Held On: 10 August 2017 Shift 2) (Previous Year Paper)

Just as we use barometer to measure pressure, similarly odometer is used to measure distance.

Hence, answer is Distance.

Additional Information

• The hygrometer is an instrument used to measure humidity to find the quantity of water vapor in the air, in soil, or in enclosed spaces.
• A vernier caliper is a high-precision measurement tool that can be used in multiple types of measurements. It can measure thickness, diameter and even inside diameter for pipes.
• An anemometer is an instrument that measures wind speed and wind pressure.

A + 13 = N; E + 13 = R; D + 13 = Q; M + 13 = Z

Now NRQZ is written in reverse order that is ZQRN.

Similarly, F + 13 = S; L + 13 = Y; M + 13 = Z; O + 13 = B

SYZB is written in reverse order, that is BZYS.

Hence, answer is BZYS.

2 × 4 × 3 = 24

(24)² = 576

576 + 2 = 578

Similarly,

1 × 6 × 3 = 18

(18)² = 324

324 + 2 = 326

Hence, answer is 326.

Flowers, fruit and leaves grow above the ground whereas roots grow under the ground.

Clearly, odd word is Root.

1. CEAC → C + 2 = E; E – 4 = A; A + 2 = C

2. FHDF → F + 2 = H; H – 4 = D; D + 2 = F

3. PRMP → P + 2 = R; R – 5 = M; M + 3 = P

4. TVRT → T + 2 = V; V – 4 = R; R + 2 = T

Therefore, PRMP is the odd one out.

1. 2132 - 161 → (2 × 1 × 3 × 2) = 12 not 161

2. 2678 - 672 → (2 × 6 × 7 × 8) = 672

3. 4325 - 120 → (4 × 3 × 2 × 5) = 120

4. 6931 - 162 → (6 × 9 × 3 × 1) = 162

Therefore, 2132 - 161 is the odd one out.

Dictionary order arrangement would be,

4. Dilled
5. Dillydallied
6. Dillydallies
7. Dillydally
8. Dillydallying

Hence, the dictionary order for given words is “42531”.

1. molnon → l m m o o n m l l n n o n n m l

2. nolmoo → l m n o o n m l l m n o o n m l

3. nomloo → l m n o o n m m l l n o o n m l

4. noolmm → l m n o o n m o l l n m m n m l

The series starts from ‘lmno’ and then the same letters are written in reverse alphabetical order ‘onml’. Again same letters are written in correct alphabetical order and then again reverse alphabetical order and so on.

Hence, ‘nolmoo’ will complete the given series.

21 + (2)² = 25

25 + (3)³ = 52

52 + (4)² = 68

68 + (5)³ = 193

193 + (6)² = 229

Hence, next number in the series will be 229.

As clear from the diagram, Kamal is 10 km in North direction from his home.

Given,

P > Q

R does not have least marks.

S > T, T > P

⇒ S > T > P > Q

⇒ Q has the least marks.

1. PROCEED → RECIPROCATE → cannot be formed as there is no letter D.

2. RACE → RECIPROCATE → can be formed.

3. REPEAT → RECIPROCATE → can be formed.

4. TEAR → RECIPROCATE → can be formed.

The word ‘Proceed’ cannot be formed by using the letters of the word ‘Reciprocate’ because the letter ‘D’ is missing in the given letter.

The letters are represented by their respective alphabetical positions starting from the left.

Similarly,

Hence, CITIZEN will be coded as ‘3920926514’.

On interchanging,

1. × and ÷ → 6 × 17 ÷ 51 + 6 – 12 = -4

2. • and ÷ → 6 + 17 × 51 ÷ 6 - 12 = 138.5
3. • and - → 6 ÷ 17 × 51 - 6 + 12 = 24

4. – and ÷ → 6 - 17 × 51 + 6 ÷ 12 = -861.5

Hence, × and ÷ should be interchange.

Logic,

(6 × 9) + 4 = 58

(3 × 9) + 7 = 34

Therefore,

(A × 4) + 9 = 91

⇒ A = 20.5

Sum of surrounding number = product of digits of central number

5 + 6 + 7 + 9 = 27 = 9 × 3 

8 + 9 + 7 + 6 = 30 = 6 × 5 

Similarly,

x + 3 + 6 + 5 = 6 × 3 = 18

⇒ × + 14 = 18

⇒ × = 4

Hence, missing number is 4.

Triangles in the given figure,

ADE, BFH, CIJ, KLE, MNE, OGH.

There are total of 6 triangles in the given figure.

Conclusions:

I. Some staplers are markers → True.

II. All markers are pins → False.

Thus, only conclusion I follows.

The four sides adjacent to face containing ‘5’ are ‘4’, ‘2’, ‘1’, ‘6’. Also ‘4’ and ‘2’ & ‘6’ and ‘1’ are adjacent.

Therefore, the face opposite to ‘4’ would be ‘1’.

All mangos are fruits. Some mangos are green.

Hence option 2 correctly describes the relationship between mango, fruit and green.

Option figure 4 will complete the question figure.

The question figure is hidden in option figure 2.

After unfolding, the paper would look like option figure 2.

The mirror image of the question figure would be option figure 3.

1. 00, 68, 95, 58, 04 → GUILE

2. 14, 75, 88, 87, 40 → GUIUE

3. 23, 99, 76, 78, 31 → GUIDE

4. 41, 87, 57, 66, 12 → GUIDR

Hence, “23, 99, 76, 78, 31”is the correct set.

• Oligopoly is a situation in which a few firms make a cartel and dominates the industry.
• By the term “Oligopoly” we mean a state of limited competition.
• Features of Oligopoly:
• Small number of Large firms
• Barriers to new entry
• Interdependence
• Advertising
• Group policies

The correct answer is Public Debt

• Public Debt (Government Debt) is the debt owed by the government.
• Whereas monetary policy is framed, devised, and implemented by the RBI.
• Public Debt does not fall in the ambit of RBI and can never be a part of monetary policy.
• Public debt includes the total liabilities of the Union government that have to be paid from the Consolidated Fund of India. Sometimes, the term is also used to refer to the overall liabilities of the central and state governments. However, the Union government clearly distinguishes its debt liabilities from those of the states. It calls the overall liabilities of both the Union government and states as General Government Debt (GGD) or Consolidated General Government Debt.
• Since the Union government relies heavily on market borrowing to meet its operational and developmental expenditure, the study of public debt becomes key to understand the financial health of the government. The study of public debt involves the study of various factors such as debt-to-GDP ratio, and sustainability, and sources of government debt. The fact that almost a fourth of the government expenditure goes into interest payment explains the magnitude of the liabilities of the Union government.

• A president is not a member of any house of the parliament as:
• To be a member of LokSabha a person must be elected through Universal Adult Franchise and
• To be a member of Rajya Sabha person must be elected by elected members of only legislative assemblies of state.
• Whereas, he is elected by an electoral college consisting of elected members from both the houses of parliament.
• Further Vice President is the ex-officio chairman of RajyaSabha (aka Upper House) and is responsible for the conduct of business.

• There are three types of emergencies mentioned in our constitution which can be declared by a president.
• National Emergency - Article 352
• State Emergency – Article 356
• Financial Emergency – Article 360
• Learning Tip: The articles of emergency have a gap of +4 starting from 352.

• Bardoli Satyagraha was started in 1928 in the state of Gujarat during the period of British Raj lead by SardarVallabhBhaipatel
• The movement was started to reduce the taxes for the year in face of the calamities. Patel then instructed all the farmers of Bardolitaluka to refuse payment of their taxes.
• Above all, Patel instructed the farmers to remain completely non-violent, and not respond physically to any incitements or aggressive actions from officials.
• He directed them that the struggle would not end only by the cancellation of all taxes for the year, but when all the seized property and lands were returned to their rightful owners.

The correct answer is Bal Gangadhar Tilak.

Key Points 

• Bal Gangadhar Tilak raised the slogan, “Swaraj is my birthright and I shall have it!”.
• The word Swarajya was first coined by Bal Gangadhar Tilak.
• Bal Gangadhar Tilak was also known as Lokmanya Tilak.
• He established a prominent organization Deccan Education Society to promote modern learning.
• He also established Fergusson College at Pune.
• He along with Annie Besant played an important role during Home Rule Movement(1916-18).
• Kesari and Mahratta were the two newspapers started by Bal Gangadhar Tilak.

Important Points

• Sardar Vallabhbhai Patel popularly known as Sardar Patel was an Indian statesman.
• He served as the First Deputy Prime Minister of India.
• He was an Indian barrister and a senior leader of the Indian National Congress who played a leading role in the country's struggle for independence and guided its integration into a united, independent nation.
• His commitment to national integration in the newly independent country was total and uncompromising, earning him the sobriquet "Iron Man of India".
• Subhash Chandra Bose, a Freedom Fighter addressed Mahatma Gandhi as "Father of the Nation" for the 1st time.
• Mahatma Gandhiji is revered in India as the Father of the Nation.
• Much before the Constitution of Free India conferred the title of the Father of the Nation upon the Mahatma, it was Bose who first addressed him as such in his condolence message to the Mahatma on the demise of Kasturba Gandhi.

• Western Ghats, also known as Sahyadri ranges, are home to tropical evergreen forests, which include deciduous forests and montane rain forests in both the North-Western and South Western Ghats.
• Western Ghats is also a UNESCO world heritage site.

The correct answer is Magnetopause.

• The final boundary between the Earth and the outer space (magnetosphere) is called the magnetopause.
• As per planetary science, it is the boundary between the solar wind and the planet’s magnetic field.
• The magnetopause is a Regions of the Earth’s Magnetosphere.
• The boundary between the Earth and the outer space dominated by the planet's magnetic field

Extra Information

• In May 2020, The Indian Institute of Geomagnetism (IIG) has developed a one-dimensional fluid simulation code.
• It is capable of studying electric field structures in the earth’s magnetosphere.

Indian Institute of Geomagnetism

• Establishment year-1971
• It is an autonomous institution functioning directly under the Department of Science and Technology.
• Headquarter- Panvel, Navi Mumbai,
• The Ministry of Science and Technology-Dr. Harsh Vardhan

Thymosin is the hormone produced by the thymus gland. It is responsible for stimulating the development of disease fighting T cells. Thymus gland is active only till puberty, post which it slowly shrinks and gets replaced by fat.

Photosynthesis is a process by which green plants synthesize nutrients from water and carbon dioxide in the presence of chlorophyll and sunlight and give out oxygen as a by-product.

AB+ is the blood group which is a universal acceptor since it has both kinds of antigens, which are Antigen A and Antigen B. People having a blood group of AB+ can accept blood from any person of any blood group.

A concave mirror is used when the object appears enlarged and inverted in a rear view mirror. A concave mirror is curved inward in the middle.

• A soap bubble attains spherical shape because of surface tension.
• As per the surface tension phenomenon, the fluid has the tendency to acquire least possible surface area, but when it is not on any surface it takes a spherical shape in order to acquire the minimum possible surface area.

CAD or Computer Aided Design is a software used in the computer systems by engineers, architects, drafters, artists and others to create, analyze, optimize and modify a design or even create 2D and 3D technical illustrations.

• An exothermic reaction is a chemical reaction which is responsible for releasing energy in the form of heat or light.
• ‘Exo’ means 'releases' and ‘thermic’ means 'heat'.
• The reaction in which there is a release of heat, with or without light is an exothermic reaction.

The chemical formula for sodium chloride (salt) is NaCl. Sodium chloride is a common sodium salt used to season food. It is a metal halide composed of sodium (Na) and Chloride (Cl).

Carbon dioxide is the gas that contributes maximum to the phenomena of global warming. Carbon dioxide is generated as a by product of cellular respiration as well as combustion of fossil fuels. It is also generated by human industries which leads to the global warming of the planet.

Gram Sabha selects the Social Audit Committee under MGNREGA scheme. As per the 73^rd Amendment of the Constitution, the Gram Sabha conducts Social Audits along with some other functions as well including examining audit reports, inspecting all public documents and more.

The correct answer is Safety Lamp.

Key Points

• Safety Lamp was invented by Sir Humphry Davy in the year 1815.
• It was created to be used in the coal mines and consisted of wick lamp along with a flame enclosed inside a mesh screen.

Additional Information

• Safety pin
• The safety pin was invented by Walter Hunt.
• American mechanic Walter Hunt is regarded as the inventor of the safety pin.
• Steam Engine
• Steam Engine was invented by James Watt in 1776.
• He was a Scottish inventor and mechanical engineer
• X-rays
• X-rays w ere discovered in 1895 by German physicist Wilhelm Roentgen.
• Roentgen was a recipient of the first Nobel Prize for Physics, in 1901, for his  discovery of X-ras.

The correct answer is Stan Wawrinka

Key Points

• Stan Wawrinka from Switzerland won the 2016 Men Single title at US Open,in the final match with Novak Djokovic. He won by 6-7 (1), 6-4, 7-5, 6-3 after 3 hours and 55 minutes.
• Carlos Alcaraz defeated Casper Ruud in the final, 6–4, 2–6, 7–6, 6–3 to win the men's singles tennis title at the 2022 US Open.

Raja and Radha Reddy are a Kuchipudi dancing couple, choreographers and guru. Padma Subrahmanyam is an Indian classical Bharatanatyam dancer. Sitara Devi was an eminent Indian Kathak dancer.

The President of Colombia Juan Manuel Santos is the recipient of the 2016 Nobel Peace Prize for his resolute efforts in order to bring the country’s 50 year long civil war to an end. The war had displaced around 6 million people and had costed lives of 220,000 Colombians.

The correct answer is An Era of Darkness.

Key Points

• Shashi Tharoor
• Shashi Tharoor, an Indian politician, author, and member of the Congress party has won the Sahitya Akademi Award for 2019.
• The honourable prize was given to the Lok Sabha member from Thiruvananthapuram for his book' An Era of Darkness: The British Empire in India.'
• In 2016, the book was released.
• The Sahitya Akademi published a press release in 23 languages on December 18, 2019, announcing the winners of the annual Sahitya Akademi Awards.
• One of the list's winners was Shashi Tharoor.
• He received the award for his English-language creative non-fiction work.
• The impact of British colonial rule in India and how the colonists abused the nation are discussed in Shashi Tharoor's book.

Additional Information 

• Shashi Tharoor has also held the positions of Minister of State for External Affairs and Under-Secretary-General for Communications and Public Information at the UN.
• He is well-known for having a perfect command of the English language and for having a vocabulary that went viral online.
• Since 1981, Tharoor has written 23 books, both fiction and nonfiction, with a focus on India and its history, culture, film, politics, society, and other relevant topics.
• He was born in London and earned his degree from Delhi's St. Stephen's College in 1975.
• He earned his doctorate in international relations and affairs from the Tufts University Fletcher School of Law and Diplomacy in 1978.
• It's not about you is Ratna Vira's second novel.
• Invisible People is written by Alex Tizon.
• democrats and dissenters is written by Ramachandra Guha.

India has recently decided to partner with United Arab Emirates for the strategic storage of crude oil in southern India. The deal allows the Gulf OPEC country to store 6 million barrels of crude oil at Mangalore, Karnataka.

Bhutan is the neighbouring country of India which is also referred to as ‘Druk Yul’. The Druk, which means thunder dragon is the national symbol of Bhutan and appears on its flag as well. Bhutan is called Druk Yul, which means ‘Land of Druk’ and the leaders of Bhutan are called Druk Gyalpo, which means ‘Thunder Dragon KIngs’.

Since we know that 1^st number divisible by 3 is 3 × 1 = 3

Last number divisible by 3 but less than 200 is 3 × 66 = 198

⇒ Total numbers = 66 – 1 + 1 = 66 numbers

But this includes the number which is divisible by 7 also

Since we know that LM of 3 and 7 is 21

So, the first 1^st number divisible by 21 is 21 × 1 = 21

Last number divisible by 21 but less than 200 is 21 × 9 = 189

⇒ Total numbers = 9 – 1 + 1 = 9 numbers

⇒ numbers are there between 1 to 200 which are divisible by 3 but not by 7 = 66 – 9

∴ 57 numbers are there between 1 to 200 which are divisible by 3 but not by 7

Work done by 1 women in 1 day is 1/10 × 1/6 = 1/60

Work done by 1 men in 1 day is 1/6 × 1/5 = 1/30

Work done by 1 children in 1 day is 1/8 × 1/10 = 1/80

⇒ Ratio of their efficiencies is 1/60 : 1/30 : 1/80

Now, to make it a simple ratio we have to take LCM of 60, 30, and 80 and dividing the L.C.M by each denominator get, (240 ÷ 60) : (240 ÷ 30) : (240 ÷ 80) = 4 : 8 : 3

∴ their efficiencies are in ratio 4 : 8 : 3

Volume of the cylinder can be written as 7y and 3y

Height of the cylinder can be written as 7h and 9h

Since we know that the Volume of cylinder is Area of base × height

⇒ Volume of second cylinder = 154 × 9h

Let the radius of first cylinder be r

⇒ base area of first cylinder = πr²

Volume of first cylinder = πr² × 7h

their Ratios can be written as

⇒ 154 × 9h/ (πr² × 7h) = 3/7 put π = 22/7

⇒ r² = 7 × 7 × 3

⇒ r = 7√3

∴ radius is 7√3 cm

Let the marked price be Rs. 100

Kanchan bought it for 100 × (1 - 25/100)

She bought it for Rs. 75

She sold it for gain of 75%

she sold it for = 75 × (1 + 75/100)

⇒ she sold it for = Rs. 131.25

Profit = Rs 131.25 – 100 = 31.25

∴ profit percentage will be 31.25 %

From the given ratio 6 : 8 : 7

Amount A will get = 6 × 8400 / (6 + 8 + 7)

⇒ A will get = Rs. 2400

Amount B will get = 8 × 8400 / (6 + 8 + 7)

⇒ A will get = Rs. 3200

Amount C will get = 7 × 8400/(6 + 8 + 7)

⇒ A will get = Rs. 2800

Let the amount saved by A, B and C is 3y, 2y and 4y

Given 2y = 400

⇒ y = 200

⇒ Amount save by A = 3 × 200 = Rs. 600

⇒ Amount save by B = 2 × 200 = Rs. 400

⇒ Amount save by C = 4 × 200 = Rs. 800

Their expenditure can be given as

⇒ A’s expenditure = 2400 – 600 = 1800

⇒ B’s expenditure = 3200 – 400 = 2800

⇒ C’s expenditure = 2800 – 800 = 2000

⇒ Ratio of their expenditure = 1800 : 2800 : 2000

∴ the ratio is 9 : 14 : 10

While considering the age of 1 student as 14 the average can be given as

⇒ (sum of age of other 23 students + 14)/24 = 12

⇒ sum of age of other 23 students = 12 × 24 – 14

⇒ sum of age of other 23 students = 274

Correct average age can be given as

⇒ (sum of age of other 23 students + 8)/24

⇒ (274 + 8)/24

⇒ 11.75

∴ The average age is 11.75 years

Average of 24 student age is 12 years

Sum of the 24 student age 

⇒ 24 × 12 = 288

According to the question,

⇒ (288 - 14 + 8)/24

⇒ 282/24

⇒ 11.75 years.

∴ The new average age is 11.75 years.

Let the cost price be Rs. 100 and selling price be y

According to the question

⇒ 70 × 100/100 = 40y/100

⇒ y = 175

⇒ Profit = 175 – 100

⇒ Profit = Rs. 75

∴ net profit % is 75%

Given that,

a% of b + b% of a

= (a × b)/100 + (b × a)/100

= (2a/100) × b

= 2a% of b 

∴ a% of b + b% of a = 2a% of b

Let his usual speed be y and the distance to be travel is d

According to the question

⇒ d/y - d/(7y/6) = 15

⇒ d/y = usually time taken by him = 15 × 7 = 105 min

Formula used:-

Simple Interest = $\frac{Principal;\times ;rate ;\times ; time}{100}$

Calculation:-

Let the rate be r%

From the question,

Interest from B = (10000 × 3 × r)/100

Interest from C = (6000 × 4 × r)/100

ATQ,

⇒ 5400 = (10000 × 3 × r)/100 + (6000 × 4 × r)/100

⇒ r = 540000/(30000 + 24000)

⇒ r = 10

∴ the rate is 10%

Given:

x3 + 2x2 – 5x + k is divisible by x + 1

Calculation:

Using remainder theorem the given expression should be equal to zero when we

put x + 1 = 0, Or x = -1

⇒ x³ + 2x² – 5x + k = 0 when x = -1

⇒ (-1)³ + 2(-1)² – 5 (-1) + k = 0

⇒ -1 +  2 + 5 + k = 0

⇒ k = -6

∴ The value of k is - 6.

It can be written as 15x² + 1 = 35x

Adding 15x to both sides

⇒ 15x² + 1 + 15x = 35x + 15x

⇒ 15x² + 1 + 15x = 50x ….. (i)

Put this in the denominator 5x/(15x² + 15x + 1) …. Using (i)

⇒ The required value = 5x/50x

⇒ 1/10

∴ 5x/(15x² + 15x + 1) = 1/10

It can be written as 4x² + 1 = 10x and we can write 64x⁶ + 1 = (4x² + 1)(16x⁴ + 1 – 4x²)

⇒ (4x² + 1)(16x⁴ + 1 – 8x²)

⇒ (4x² + 1){ (4x² + 1)² - 8x² – 4x²}

⇒ (4x² + 1){ (4x² + 1)² - 12x²} .... using 4x² + 1 = 10x

⇒ 10x{(10x)² – 12x²}

⇒ 880x³ Using this

⇒ (64x⁶ + 1)/8x³

⇒ 880x³/8x³ = 110

∴ the value of (64x⁶ + 1)/8x³ is 110

Shortcut Trick x + [1/(4x)] = 5/2

2x + 1/2x = 5

Now, (64x6 + 1)/8x³ = ?

⇒ 8x³ + 1/8x³ = ?

⇒ 8x3 + 1/8x3 = ?

⇒ (2x)3 + 1/(2x)3 = (2x + 1/2x)³ - 3 × 2x × 1/2x(2x + 1/2x)

⇒ (2x)3 + 1/(2x)3 = 5³ - 3 × 5 = 125 - 15 = 110

We can write it as

⇒ [(x + 5) + {1/(x + 5)}]² = (x + 5)² + [1/(x + 5)²] + 2

⇒ (x + 5)² + [1/(x + 5)²] = [x + {1/(x + 5)} + 5]² – 2

⇒ (x + 5)² + [1/(x + 5)²] = [{(x² + 5x + 1)/(x + 5)} + 5]² – 2

⇒ (x + 5)² + [1/(x + 5)²] = [{(x² + x + 4x + 1)/(x + 5)} + 5]² – 2 

Using x2 + x = 19,

⇒ (x + 5)² + [1/(x + 5)²] = [{(19 + 4x + 1)/(x + 5)} + 5]² – 2

⇒ (x + 5)2 + [1/(x + 5)2] = [{(20 + 4x)/(x + 5)} + 5]2 – 2

⇒ (x + 5)² + [1/(x + 5)²] = [{4(x + 5)}/(x + 5) + 5]² – 2

⇒ (x + 5)² + [1/(x + 5)²] = (4 + 5 )² – 2 = 79

∴ (x + 5)² + [1/(x + 5)²] is 79

2nd Approach:

Let, x + 5 = a, then x = a - 5 

Now, we have to find a2 + 1/a² = ?

x² + x = 19

⇒ (a - 5)² + (a - 5) = 19

⇒ a² - 9a + 1 = 0

⇒ a2 + 1 =  9a 

⇒ a + 1/a = 9

⇒ a² + 1/a² + 2 = 81

∴ a2 + 1/a² = 79.

Given:

∠ABC = 15^o, In triangle ABD.

D is a point on BC such that AD = BD.

Calculation:

According to the question,

So, AD = BD then, ∠ABD = ∠BAD 

⇒ Now in triangle ABD

⇒ ∠ADB + ∠DBA + ∠BAD = 180° 

⇒ ∠ADB = 180° - ∠DBA - ∠BAD

⇒ ∠ADB = 180° – 15° – 15°

⇒ ∠ADB = 150^o

We know that,

∠ADB + ∠ADC = 180 

⇒ ∠ADC = 180° - ∠ADB (∠ADB = 150°)

⇒ ∠ADC = 180 – 150 = 30

∴ ∠ADC = 30° 

∴ The measure of ∠ADC is 30°.

Calculation:

Area of triangle ABC = 156 cm²

AD, BE and CF are the medians intersecting at point G

Therefore, Area of triangle joining the points D, E and F would be 1/4^th of triangle ABC

Area of triangle DEF = (1/4) × 156 = 39 cm²

Now, G will also be the centroid of triangle.

Area of triangle FGE = Area of triangle DFG = Area of triangle DGE = (1/3) × Area of triangle DEF

∴ Area of triangle FGE = (1/3) × 39 = 13cm²

∴ The correct answer is option (1).

Given :

Length of diagonal = 9√2 cm

The Square is reshaped to form an equilateral triangle such that the perimeter remains the same.

Formula used :

Perimeter of square = 4a

Area of circle = πr²

Radius of largest incircle = side of equilateral triangle /2√3

Calculation :

Side of square is 9√2/√2 = 9 cm

Perimeter of Square = 4 × 9 = 36 cm

⇒ Side of equilateral triangle = perimeter/3

⇒ Side of equilateral triangle = 36/3

⇒ Side of equilateral triangle = 12 cm

Radius of largest incircle can be given as = side of equilateral triangle /2√3

⇒ Radius of largest incircle = 12/2√3 = 6/√3 cm

Area of circle is = πr²

⇒ Area = π × (6/√3)² = 12π

∴ The area of in circle is 12π.

Concept:

we know that the line joining the centres of two circle perpendicularly bisects the common chord

Calculation:

radius of 1^st circle(r1) = 15/2 and that of 2^nd (r2) = 13/2

length of common chord = AB = 12 cm

let c = length of common chord/2 = 12/2 = 6

We can use the formula to get the distance between the centres

⇒ √((r1)² - c²) + √((r2)² – c²)

⇒ √{(7.5)² - 6²} + √{(6.5)² – 6²}

⇒ √20.25 + √6.25

⇒ 4.5 + 2.5 = 7 cm

∴ the distance between their centres is 7 cm

Formula used :

sec²θ - tan²θ = 1

Calculation :

It can be written as

⇒ sec²θ (sec²θ – tan²θ)

Now using sec²θ = 1 + tan²θ

⇒ sec²θ (1 + tan²θ - tan²θ) = sec²θ

∴ The correct answer is sec²θ.

Calculation :

By Putting A = 45° 

⇒ (sin A – cosec A)(sec A – cos A) (tan A + cot A)

⇒ (sin 45° – cosec 45°)(sec 45° – cos 45°) (tan 45° + cot 45°)

⇒ (-1/√2) × (1/√2) × 2

⇒ -1

∴ The value of(sin A – cosec A)(sec A – cos A) (tan A + cot A) is –1.

Given :

(1/cosθ) - (1/cotθ) = 1/P

Calculation :

Put cot θ = cosθ/sin θ

⇒ 1/cos θ - sin θ/cos θ = 1/p

⇒ cosθ/p = 1 – sinθ

⇒ sinθ = 1 – cosθ/p

Now Squaring both sides,

⇒ sin²θ = 1 + (cosθ/p)² – 2cosθ/p

Now put sin²θ = 1 – cos²θ

⇒ 1 – cos²θ = 1 + (cosθ/p)² – 2cosθ/p

⇒ 2cosθ/p = cos²θ (1 + 1/p²)

⇒ cos θ = 2p/(p² + 1)

∴ cos θ = 2p/(p² + 1)

∴ The correct answer is 2p/(p² + 1).

Surplus in year 2013 = production – sales

⇒ Surplus in year 2013 = 1671 – 1641 = 30

Surplus in year 2014 = production – sales

⇒ Surplus in year 2013 = 1103 – 1002 = 101

∴ total surplus = 101 + 30 = 131

⇒ Stock of 2011 = 7835 + 2035 – 2247 = 7623

⇒ stock of 2012 = 7623 + 1821 – 2018 = 7426

⇒ stock of 2013 = 7426 + 1937 – 2563 = 6800

⇒ stock of 2014 = 6800 + 3014 – 2988 = 6826

∴ Stock of C after 4 years is 6826

Average production in C can be given as

⇒ (2035 + 1821 + 1937 + 3014)/4

⇒ Average production = 2201.75 

Average sales in C can be given as

⇒ (2247 + 2018 + 2563 + 2988)/4

⇒ Average sales = 2454

⇒ Difference between them = 2201.75 – 2454 =  – 252.25

∴ difference in average production and average sales respectively of country C in the given four years is – 252.25

For B

⇒ Surplus in year 2011 = 1881 – 1798 = 83

⇒ Surplus in year 2012 = 2067 – 2389 = -322

⇒ Surplus in year 2013 = 1328 – 2063 = -735

⇒ Surplus in year 2014 = 1578 – 1239 = 339

⇒ Total surplus = 83 + (-322) + (-735) + 339 = - 635 

For D

⇒ Surplus in year 2011 = 3126 – 2417 = 709

⇒ Surplus in year 2012 = 2987 – 2911 = 76

⇒ Surplus in year 2013 = 2143 – 3188 = -1045

⇒ Surplus in year 2014 = 4126 – 3563 = 563

⇒ Total surplus = 709 + (76) + (-1045) + 563 = 303

∴ we can see that Surplus of D > Surplus of B

Correct Answer: 3

Sugar is an uncountable noun and therefore, does not have any plurals, i.e., ‘sugars’ is incorrect. The correct sentence is: 'In spite of the doctor’s stern warning, Latika continued taking sugar in her milk'.

Correct Answer: 1

‘Myself’ is a reflexive pronoun, i.e., it needs something to refer to. Since the sentence does not have an ‘I’, using ‘myself’ is incorrect. The correct sentence is: 'Roshni and I will take care of the event on Sunday'.

Correct Answer: Until

‘Until’ is used in situations where one event is dependent on another event. In this case, the ‘suspension’ was dependent on the ‘stopping of the rain’.

‘Unless’ is used in cases of exception, while ‘till’ can’t be used to begin a sentence. ‘While’ denotes continuity and changes the meaning of the sentence.

The correct answer is 'Option 4' i.e. 'Down'.

Key Points

• In this context, "down" is the appropriate preposition to use with the verb "tore" (past of "tear").
• "Tore down" is a phrasal verb which means to destroy or remove something in a forceful and often reckless manner.
• The sentence suggests that the elephant was in a state of stampede and was destructively running through the streets.

Therefore, the correct sentence is: 'The elephant stampeded and tore down the streets.'

Additional Information

• Here's the explanation for the other options:
• On - "Tore on" doesn't make sense in this context. "On" could be used with verbs like "ran" or "rushed" ("The elephant ran on the streets"), but not with "tore".
• Out - "Tore out" typically means to remove something quickly or violently, often from a book or a piece of paper. It doesn't fit well with the action of an elephant running through the streets.
• Off - "Tore off" means to remove something quickly or violently, like tearing off a piece of cloth. It also doesn't fit well in this context.

The correct answer is: Brazier.

Key Points

• The word "Scuttle" means to run hurriedly or furtively with short quick steps. (तेज़ी से भागना)
• Example: The mouse scuttled across the floor, trying to avoid being seen.
• "Brazier" refers to a portable heater consisting of a pan or stand for holding lighted coals. (अंगीठी)
• Example: They gathered around the brazier to keep warm during the cold night.

Therefore, the correct answer is: Brazier.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Solitary (अकेला): Existing alone; without companions.
• Example: He led a solitary life in the mountains.
• Superficial (ऊपरी): Existing or occurring at or on the surface.
• Example: Her injury was only superficial and didn't require stitches.
• Soothing (सुखदायक): Having a gently calming effect.
• Example: The soothing music helped her relax.

Correct Answer: Talkative

‘Loquacious’ means ‘tending to talk a great deal; talkative’. Therefore, the word ‘talkative’ has the same meaning and is the correct answer.

Foolishness denotes stupidity, graceful denotes elegance and entertainer is someone who entertains.

Correct Answer: Clarify

‘Obfuscate’ means ‘to make obscure or unclear; confuse’. ‘Clarify’, on the other hand, means ‘make less confusing and more comprehensible’. Hence, it is the correct answer.

Puzzle and haze both mean the same thing as obfuscate and envelop means to cover or surround completely.

The correct answer is: Option 2 i.e. Sorrow.

Key Points

• The word "Triumph" means a great victory or achievement. (विजय)
• Example: His triumph in the marathon was celebrated by everyone in the town.
• "Sorrow" refers to a feeling of deep distress caused by loss, disappointment, or other misfortune suffered by oneself or others. (दुःख)
• Example: She was filled with sorrow after hearing about the untimely demise of her friend.
• Hence, we can infer that the opposite of 'Triumph' is 'Sorrow'.

Therefore, the correct answer is: Option 2 i.e. Sorrow.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Establish (स्थापित करना): To set up on a firm or permanent basis.
• Example: The company plans to establish a new branch in the city.
• Disdain (तिरस्कार): The feeling that someone or something is unworthy of one's consideration or respect.
• Example: He looked at the messy room with disdain.
• Elation (उल्लास): Great happiness and exhilaration.
• Example: The team felt a sense of elation after winning the championship.

Key Points

• ‘Chicken-hearted’ is used to refer to a person who is timid or easily frightened, i.e., a coward.
• An example sentence is: 'Tom is too chicken-hearted to show up to the fight'.

Additional Information

• Origin: This term derives from the idiomatic meaning of the word chicken in English, which also refers to someone who is cowardly.

The Correct Answer is option 1: Coward

Correct Answer: Significant day

‘Red letter day’ means a day that is noteworthy or memorable, i.e., a significant day.

An example sentence is: ‘His college graduation was a red-letter day for him’

Correct Answer: was running

The correct answer is ‘was running’ since the sentence follows the past continuous tense, i.e., the action of ‘jump’ was performed while the train was in motion. The other options use the incorrect form of the verb.

Correct Answer: have not seen

‘Did not see’ implies that the activity of ‘seeing’ is completed and there is not further possibility of seeing, while ‘have not seen’ indicates continuity and the possibility that the situation might resolve. Therefore, the correct usage of ‘see’ is ‘have not seen’, due to the presence of ‘two years ago’.

Correct Answer: Tyro

‘Tyro’ means a beginner or a novice, i.e., somebody who is new to something. Nuance means a subtle difference, pun is a play on words and a vandal is a person who deliberately destroys property.

Correct Answer: Extempore

‘Extempore’ means spoken or done without preparation. Hence, it is the correct one-word substitute. Euphemism means a mild substitution, obituary means a notice of death and soliloquy is a monologue.

Correct Answer: Proprietry

‘Proprierty’ is the incorrectly spelt word. The correct spelling is ‘Proprietary’, meaning ownership.

Correct Answer: Acquaintence

‘Acquaintence’ is the incorrectly spelt word. The correct spelling is ‘acquaintance’, meaning 'knowledge or experience of something'.

Correct Answer: SQPR

The sentences talk about water conflicts and the threats they pose. Therefore, the opening sentence of the passage must introduce the concept of water conflicts, which is done only by Sentence S. Moreover, Sentence P begins with an ‘and’, and cannot start a passage. Hence, the correct answer is SQPR.

Correct Answer: RPSQ

The sentences talk about sales and outsourcer. Therefore, the opening sentence of the passage must introduce the concept of ‘outsourcer’.

When reading Sentence S, it consists of an ‘it’, which refers to something else and can’t be the opening sentence.

Sentence Q uses ‘this’, which is a reference.

Sentence P uses ‘for one’, as a reason for something and has a reference.

Therefore, only Sentence R is free of references and is the opening sentence. Hence, the correct answer is RPSQ.

Correct Answer: I was told by somebody that there had been a robbery in the jewellery exhibition.

Sentences 1 and 4 are incorrect because it is missing the speaker of the action, ‘somebody’, while Sentence 3 twists the meaning of the sentence and removes the information that the robbery was already conducted. Only Sentence 2 changes the active voice to the passive voice properly.

Correct Answer: Rohan wondered where he would be that time the following month.

The sentence, in the indirect speech, should use only past-tense and third-person. Sentence 4 changes I to ‘he’, ‘this’ to ‘that and ‘next month’ to ‘following month’. Hence, it is the correct answer.

Correct Answer: different

The passage elaborates on the distinctions of science and religion. Therefore, the correct word to fill in the blank is ‘different’.

Correct Answer: experience

The previous sentence used experience to define what religion is based on. Therefore, the correct word to fill in the blank here is ‘experience’. Moreover, the sentence talks about Christ or Ramakrishna, who had religious experiences that they shared with the world.

Correct Answer: subjective

‘Subjective’ means ‘based on feelings, experience and changes by the individual’. To say that religious experiences are subjective means that an experience differs from person to person and is not constant, which is true.

Correct Answer: tangible

‘Tangible’ means ‘perceptible by touch’. The passage talks about science and religion. The sentence says that all theoretical proofs need to have some practical or physical proof as well. Hence, ‘tangible’ is the correct answer.

Correct Answer: extended

‘Extended’ means ‘make larger or apply to’. The sentence says that science is not restricted only to knowledge, but is applied for actual use as well.