SSC CGL Previous Paper (Held On: 13 June 2019 Shift 3) (Previous Year Paper)

The pattern follow here is,

Similarly for PASSENGER,

Hence, “REGNESSAP” is the correct answer.

The logical order would be,

State Capital > State > State location > Country > Continent

Jaipur > Rajasthan > North India > India > Asia

Hence, “3, 1, 4, 2, 5” is the correct answer.

According to given coding language,

Code for J = 10 × 2 = 20,

Code for BAT = 2 + 1 + 20 = 23 × 2 = 46,

Similarly code for CRICKET,

CRICKET = 3 + 18 + 9 + 3 + 11 + 5 + 20 = 69 × 2 = 138,

Hence, “138” is the correct answer.

Given equation :-20 ÷ 20 + 20 – 25 × 25 = 419

1. Interchanging + and -,

Equation will become :- 20 ÷ 20 - 20 + 25 × 25

= 1 – 20 + 625

≠ 419

2. Interchanging + and ÷

Equation will become :- 20 + 20 ÷ 20 – 25 × 25

20 + 1 – 625

≠ 419

3. Interchanging × and –

Equation will become :- 20 ÷ 20 + 20 × 25 - 25

= 1 + 500 - 25

≠ 419

4. Interchanging ÷ and ×

Equation will become :- 20 × 20 + 20 – 25 ÷ 25

= 400 + 20 – 1

= 419

Thus, interchanging “÷ and ×” we get the correct answer.

The pattern follow here is,

1³ – 1 = 0;

2³ – 1 = 7;

3³ – 1 = 26;

4³ – 1 = 63;

5³ – 1 = 124;

6³ – 1 = 215;

7³ – 1 = 342;

8³ – 1 = 511;

9³ – 1 = 728;

10³ – 1 = 999;

Hence, “999” is the correct answer.

Hence, “15” is the correct answer.

Hence, “Veena is Mother of Kavi”.

Here, the arrow moves two places and three places in clockwise direction alternatively.

Hence, the above figure will come next in the given series.

The pattern follow here is,

(x²) : x,

Checking each options,

1. 11² = 121 ≠ 123

2. 196 = 14²

3. 144 = 12²

4. 225 = 15²

Hence, 123 : 11 is the odd number pair.

The pattern follow here is,

11 + 2 = 13;

13 + 4 = 17;

17 + 6 = 23;

23 + 8 = 31;

31 + 10 = 41;

41 + 12 = 53;

53 + 14 = 67;

67 + 16 = 83;

83 + 18 = 101

Hence, “101” is the correct answer.

The pattern follow here is,

Similarly for PEACE,

Hence, “QDBBF” is the correct answer.

Apple comes in the category of Fruit.

But there is no relation between Fruit and vegetable.

Hence, “Option 4” is the correct answer.

In numbers 7 will appear 11 times in numbers 7,17,27,37,47,57,67,77,87,and 97(two times in 77) and 9 times in numbers 70,71,72,73,74,75,76,78 and 79. Hence it will appear in total 20 times in numbers 1 to 99.

Hence, “20” is the correct answer.

If a cube is coloured and cut into 27 small cubes of equal sizes, smaller cubes present in the middle of the edges are coloured in two colours, the cubes which are at the corners of the edges are coloured in three colours and cubes which are at the centre of each side is coloured in a single colour (as shown in the figure).

So there are 6 such small cubes whose one edge is coloured.

Hence, “6” is the correct answer.

The pattern follow here is,

In AFKP : BGLQ,

Similarly in GLQV,

Hence, “HMRW” is the correct answer.

If we look closely, figure is hidden in option figure 1 as shown below.

Hence, “Option 3” is the correct answer.

Hence, the above figure will be the final figure.

The pattern follow here is,

2 + 3 = 5;

5 + 5 = 10;

10 + 7 = 17;

17 + 9 = 26;

26 + 11 = 37;

37 + 13 = 50;

50 + 15 = 65;

65 + 17 = 82;

82 + 19 = 101;

Hence, “50” is the correct answer.

Pedologyis the study of soils in their natural environment. Cardiology is the study of heart, Seismology is the study of earthquakes. Terminology is the term used for a list of terms used in a particular field.

Hence, Terminology is the odd among the given alternatives.

In 19 : 400,

→ 19 : (19 + 1)² = 19 : 400;

Similarly in 24 : ?

→ 24 : (24 + 1)² = 24 : 625;

Hence, “625” is the correct answer.

Statement I :No grass is a flower.

Statement II :All flowers are trees.

Conclusion I: Some trees are flowers → True

Conclusion II: Some trees are grasses → False(it is possible but not definite)

Conclusion III: No trees is a grass. → False(it is possible but not definite)

Here, Conclusion II and III makes complimentary pairs.

Hence, “Either conclusions II or III, and I follow” is the correct answer.

1) accbdb/cbcdac/aadbda → doesn't follow any pattern

2) ccdbdc/cbcdab/aadbda → doesn't follow any pattern

3) bcdbdb/cbcdac/abdbaa → doesn't follow any pattern

4) acdbda/cbcdab/acdbda → follows a pattern i.e. the term acdbda is repeated alternately.

Hence, None of these is the correct answer.

The word is flipped horizontally

Hence, “Option 1” is the correct answer.

Here all of them are vowels except “V”.

Hence “V” is odd one among the given options.

Student goes to college to receive knowledge. Similarly, a patient goes to hospital to receive Treatment. In other options the first element of the pair is workplace of second element where they provide their services.

• The 'Instrument of Surrender' which ended the Portuguese rule in India was signed on 19th December 1961.
• This ended 450 years of Portuguese in India.
• Francisco de Almeida was the first Viceroy of the Portuguese state and its headquarter was Cochin.
• The movement to end the Portuguese rule was called the Goa Liberation Movement.

• The East India Company sent Captain William Hawkins to the court of Emperor Jahangir in 1608 to seek permission to open a factory at Surat.
• He was well versed with Turkish and Jahangir also knew some of it since it was the native tongue of Mughal Emperor Babur.
• He was called 'English Khan' by Jahangir.
• William Hawkins was the commander of Hector, the first ship of the British East India Company to anchor at Surat in 1608.

• Team Vidarbha won the Ranji Trophy 2018-19.
• This was the 85th season of the trophy, where team Saurashtra and team Vidarbha competed in the finals.
• Team Saurashtra was defeated by 78 runs.
• This was the second successive Ranji Trophy title of Vidarbha.
• BCCI presented them a cash prize of Rs. 2 crore, while the Vidarbha Cricket Association presented Rs. 3 crore.

• The Khadi and village Industries Commission Act was passed in the year 1956.
• Through this Act, a statutory body was established- Khadi and Village Industries Commission.
• It works under the Ministry of MSME and aims to organise, promote and plan the development and establishment of khadi industries in the rural areas.

• By area, Mahe in Puducherry is the smallest district in India.
• The district is spread across an area of 9 sq km.
• As per 2001 census, it has a population of 36,000, while the population density is 4091 sq. km.
• Kutch in Gujarat is the largest district of India in terms of area.
• Leh is the second largest district of India.

• The movement of the local farmers of Bardoli in Gujarat against the British in 1928 was led by Vallabhbhai Patel.
• It was done against the unjust raising of taxes.
• It is considered as a major revolt of the Indian Independence Movement.
• Its success gave rise to Vallabhbhai Patel, thus making him one of the important leaders of the Indian freedom struggle.

• Sushmita Sen was the first Indian to win the Miss Universe title.
• She won the pageant in the year 1994.
• She was also crowned Miss India in the year 1994.
• Reita Faria was the first Indian and Asian to win the Miss World title in 1966.
• Madhu Sapre won the Miss India title in 1992.
• Persis Khambatta won the Miss India title in 1965.

• An adult human body has 206 bones.
• The internal framework of the human body forms the human skeleton.
• At the time of birth, there are around 300 bones present in the body.
• The human skeleton is divided into 2 parts, namely appendicular skeleton and axial skeleton.

• As of 2018, India is the leading milk producing country in the world, accounting for approximately 19% of the global market share.
• This data was released by the Dairy and Milk Processing Market in India (2018-2023).
• The industry is expected to expand at an annual rate of 14.8% between FY 2018-2023.
• Gujarat, Rajasthan, and Uttar Pradesh are the major milk producing states of India.
• UP is the largest milk producing state and also has the highest buffalo population.

• Venus is the hottest planet in the solar system.
• The temperature on Venus reaches around 465 degrees Celsius, which is hot enough to melt lead.
• It is the second planet from the sun and is named after a Roman Goddess.
• Earth and Venus are called twins since they are the same in size, density, and mass.
• The coldest planet of the solar system is Uranus.

• Vaishno Devi is not a part of the 'Char Dham Yatra' in North India.
• The temple is located in Katra in Jammu.
• Char Dham comprise of 4 pilgrimage sites in North India, in the state of Uttarakhand.
• These are Gangotri, Yamunotri, Kedarnath, and Badrinath.
• Char Dham of India are Rameswaram, Puri, Dwarka, and Badrinath.

• The approximate diameter of the sun is 109 times the diameter of Earth.
• The sun contains 99.86% of all the mass of the solar system.
• The weight of the sun is 333,000 times as much as Earth.
• It is 864,400 miles across.

• Kolkata Port is the oldest operating port in India built by the British East India Company.
• There are a total of 12 major ports in India.
• Chennai Port is the third oldest and second largest port of India.
• Mumbai port is owned by the Government of India.
• The second largest port by volume of cargo handled is the Vishakapatnam Port.

• Pragjyotishpur was the historical name of the city of Guwahati.
• Under the Kamarupa kingdom, it used to be the capital of Assam.
• Durjaya was the ancient name for North Guwahati.
• Guwahati lies on the foothills of the Shillong plateau and between the banks of the river Brahmaputra.
• It is one of the largest cities of Assam.

The correct answer is 40.

Key Points

• Pradhan Mantri Shram Yogi Mandhan Yojana
• It was introduced mainly for the poor laborers of the unorganised sector.
• The minimum age for eligibility is 18 years.
• People above the age of 40 years are not eligible for the Pradhan Mantri Shram Yogi Mandhan Yojana.
• The scheme was launched by Piyush Goyal on 15 February 2019.
• It offers a regular pension to every individual after they attain an age of 60 years.

• Indore was named the cleanest city in the 'Swachh Survekshan Survey 2019'.
• Bhopal has been declared as the cleanest capital in the 'Swachh Survekshan Survey 2019'.
• Ambikapur in Chattisgarh was acknowledged as the second India's Cleanest City followed by Mysuru as the third cleanest city.
• Gujarat’s Ahmedabad was named as the Cleanest Big City in the population category of more than 10 lakh people.

• The Micro, Small and Medium Enterprises Development Act was passed in the year 2006.
• It regulates and classifies enterprises as small, medium, and micro enterprises.
• It classifies MSMEs on the basis of investment in equipment and plant and machinery.
• Nitin Gadkari is the Minister of MSME currently.

• Diksha Dagar is a hearing-impaired Indian golfer who won her first professional title at the age of 18.
• In March 2019, she became the second Indian golfer to win on the 'Ladies European Tour'.
• In November 2015, she became number 1 amateur female golfer of India.
• She also represented India at the Summer Deaflympics 2017.

• Pradhan Mantri Shram Yogi Maandhan is a voluntary and contributory Pension Scheme for Unorganized Workers for entry age of 18 to 40 years with monthly income of Rs. 15000 or less.
• Under this scheme, each subscriber will receive an assured pension of minimum Rs.3000 every month upon reaching the age of 60 years.
• People from the unorganized sector can contribute between Rs.55 to Rs.200 monthly to be eligible for the scheme.

• The Ayushman Bharat Scheme introduced by the Government of India provides medical coverage of upto Rs.5 lakh per family per year.
• It is a national health insurance scheme.
• It is the world's largest government-funded healthcare scheme.
• It was renamed as PM Jan Arogya Yojana and is targeted at poor rural families.

• In 2015, aircraft make Boeing developed a metal called Microlattice, which is lighter than air and strong than steel.
• It was developed by a research team of HRL laboratories in 2011.
• It was designed as the structural component in aerospace engineering.
• Although it is light in weight, but it displays good strength.

• During the Sao Joao festivities, Goans present fruits to each other.
• The Sao Joao festival is celebrated in Goa to pay tribute to St. John the Baptist.
• It is held at the beginning of monsoon, on June 24.
• St. John was the relative of Mother Mary.

• Wilson's disease is an inherited disorder in which excessive amount of copper accumulates in the body.
• It accumulated majorly in brain and liver.
• Some of its symptoms include fatigue, eye discoloration, yellowing of the skin, etc.
• If it is untreated, the disease can become fatal too.

• Sukumar Sen was the first Chief Election Commissioner of India, who served from 1950-1958.
• The CEC is appointed by the President of India.
• He has a tenure of up to 65 years or 6 years.
• He is usually a member of the IAS or Indian Civil Service.
• The current Chief Election Commissioner (CEC) of India is Sh. Rajiv Kumar, who took office on 15th May 2022.

• Guhar Moti is the westernmost point of India.
• It is a small village located in the Kutch district of Gujarat.
• The northernmost point of India is located in the eastern Karakoram range in the Himalayas, near Indira Col, Siachen Glacier.
• The easternmost point is Kibithu in Arunachal Pradesh.
• Indira Point in Great Nicobar Island is the southernmost point.

Shortcut Trick

For an algebraic expression of the form x + 1/x = k, the value of x³ + 1/x³ is calculated as k³ − 3k.

Given that x + 1/x = 5, we have k = 5.

⇒ Value = 5³ − 3 × 5

⇒ Value = 125 − 15 = 110.

∴ The correct answer is 110.

Alternate Method

Given:

x + 1/x = 5

Formula Used:

The algebraic identity for the cube of a binomial: (a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

Cubing both sides of the given equation:

⇒ (x + 1/x)³ = 5³

⇒ x³ + (1/x)³ + 3 × x × (1/x) × (x + 1/x) = 125

⇒ x³ + 1/x³ + 3 × 1 × (x + 1/x) = 125

Substituting the value of (x + 1/x) = 5:

⇒ x³ + 1/x³ + 3(5) = 125

⇒ x³ + 1/x³ + 15 = 125

⇒ x³ + 1/x³ = 125 − 15

⇒ x³ + 1/x³ = 110

Therefore, the correct option is 3.

∴ The correct answer is 110.

Additional Information

Square Identity

If x + 1/x = k, then x² + 1/x² = k² − 2.

Negative Sign Identity (Cube)

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Negative Sign Identity (Square)

If x − 1/x = k, then x² + 1/x² = k² + 2.

Higher Powers

To find x⁴ + 1/x⁴, square the result of x² + 1/x² and subtract 2.

⇒ (x – 5)³ + (x – 6)³ + (x – 7)³ = 3 (x – 5) (x – 6) (x – 7)

As we know, if x³ + y³ + z³ – 3xyz = 0, then x + y + z = 0

⇒ (x – 5)³ + (x – 6)³ + (x – 7)³ = 3 (x – 5) (x – 6) (x –7)

⇒ (x – 5)³ + (x – 6)³ + (x – 7)³ – 3(x – 5) (x – 6) (x – 7) = 0

⇒ (x – 5) + (x – 6) + (x – 7) = 0

⇒ 3x – 18 = 0

⇒ x = 6

Total expenditure on interest over the years = 23.4 + 32.5 + 41.6 + 36.4 + 49.4 = 183.3 lakhs

Required average = 183.3/5 = 36.66 lakhs

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:   

\(9\frac{3}{4} \div \left[ {2\frac{1}{6} \div \left{ {4\frac{1}{3} - \left( {2\frac{1}{2}; + ;\frac{3}{4}} \right)} \right}} \right]\)

\(\Rightarrow \frac{{39}}{4} \div \left[ {\frac{{13}}{6} \div \left{ {\frac{{13}}{3} - \left( {\frac{5}{2}; + ;\frac{3}{4}} \right)} \right}} \right]\)

\(\Rightarrow \frac{{39}}{4} \div \left[ {\frac{{13}}{6} \div \left{ {\frac{{13}}{3} - \frac{{13}}{4}} \right}} \right]\)

$\Rightarrow \frac{{39}}{4} \div \left[ {\frac{{13}}{6} \div \frac{{13}}{{12}}} \right]$

$\Rightarrow \frac{{39}}{4} \div \left[ {\frac{{13}}{6}{\rm{;}} \times {\rm{;}}\frac{{12}}{{13}}} \right]$

⇒ 39/4÷2

⇒ 39/8

Total expenditure on Royalty = 15%

Total expenditure on Printing = 20%

Required percentage = [(20 – 15)/20] × 100 = 25%

Total sales of books from branch B1 in 2000 and 2001 = 80 + 105 = 185

Total sales of books from branch B3 in 2000 and 2001 = 95 + 110 = 205

Total sales of books from branch B6 in 2000 and 2001 = 70 + 80 = 150

Total sales of books from branches B1, B3 and B6 for both years = 185 + 205 + 150 = 540

Given ABCD is a cyclic quadrilateral, and ∠ADC = 129°

As we know, the sum of the either pair of the opposite angles of a cyclic quadrilateral is 180°.

⇒ ∠ADC + ∠ABC = 180

⇒ ∠ABC = 180° – 129° = 51°

In ΔACB, if AB is diameter, then ∠ACB = 90°

⇒ ∠ACB + ∠ABC + ∠BAC = 180°

⇒ 90° + 51° + ∠BAC = 180°

⇒ ∠BAC = 180° – 90° – 51° = 39°

Speed of A = 4 km/h

Distance covered by A in 4 hours = 4 × 4 = 16 km

Speed of B = 10 km/h

Time taken by B to catch up with A = 16/(10 – 4) = 16/6 = 8/3 hr

Total distance covered by B in 8/3 hrs = 10 × 8/3 = 80/3 = 26.67 km

As we know, simple interest and compound interest of the first year are same.

Let the principal be Rs. 2,190 it will be in the next year Rs, 2,409

Principal = 2190 and time = 1 year and r = ?

Interest = 2409 – 2190 = 219

⇒ S.I = (P × r × t)/100

⇒ 219 = (2190 × r × 1)/100

⇒ r = 21900/2190 = 10%

A earns Rs. 180 per hour

Total earning of A if he works for 7 hours per day = 180 × 7 = 1260

B earns Rs. 160 per hour

Total earning of B if he works for 5 hours per day = 160 × 5 = 800

Ratio of the wages of A and B = 1260 : 800 = 63 : 40

Short trick:

Single Successive equivalent discount of 25% and 5%

⇒ 25 + 5 – [(25 × 5)/100] = (30 – 1.25)%

Required difference between a single discount of 30% and single discount equivalent to two successive discounts of 25% and 5% = 30% – (30 – 1.25)% = 30 – 30 + 1.25 = 1.25%

Required difference = Rs. 2000 × 1.25/100 = Rs. 25

Detailed solution:

Shopping price after discount = Rs. 2000 × 70/100 = 1400

Shopping price after two successive discounts of 25% and 5% = Rs. 2000 × 75/100 × 95/100 = 1425

Required difference = 1425 – 1400 = Rs. 25

The angle between the external bisectors of two angles of a triangle is difference between right angle and half of the third angle.

⇒ ∠BOC = 90° – [∠A/2]

Given, ∠A = 50°

⇒ ∠BOC = 90° – 50/2

⇒ ∠BOC = 90° – 25° = 65°

⇒ tan x = cot (45° + 2x),

⇒ tan x = tan [90° – (45° + 2x)] [tan(90 – x) = cot x]

⇒ x = 90° – 45° – 2x

⇒ 3x = 45°  

⇒ x = 15°

$\left[ {\frac{{{\rm{si}}{{\rm{n}}^2}24^\circ {\rm{}} + {\rm{;si}}{{\rm{n}}^2}66^\circ }}{{{\rm{co}}{{\rm{s}}^2}24^\circ {\rm{}} + {\rm{;co}}{{\rm{s}}^2}66^\circ }}} \right]{\rm{}} + {\rm{;si}}{{\rm{n}}^2}61^\circ {\rm{}} + {\rm{cos}}61^\circ {\rm{;sin}}29^\circ$

As we know,

⇒ sin(90 – θ) = cosθ and cos(90 – θ) = sinθ

$\Rightarrow \frac{{{\rm{si}}{{\rm{n}}^2}24{\rm{;}} + {\rm{;si}}{{\rm{n}}^2}\left( {90{\rm{;}}-{\rm{;}}24} \right)}}{{{\rm{co}}{{\rm{s}}^2}\left( {90{\rm{;}}-{\rm{;}}66} \right){\rm{;}} + {\rm{;;co}}{{\rm{s}}^2}66}}{\rm{;}} + {\rm{;si}}{{\rm{n}}^2}61^\circ {\rm{;}} + {\rm{;cos}}61^\circ \sin \left( {90 - 61} \right)$

$\Rightarrow \frac{{{\rm{si}}{{\rm{n}}^2}24{\rm{;}} + {\rm{;co}}{{\rm{s}}^2}24}}{{{\rm{si}}{{\rm{n}}^2}66{\rm{;}} + {\rm{;co}}{{\rm{s}}^2}66}}{\rm{}} + {\rm{;si}}{{\rm{n}}^2}61^\circ {\rm{}} + {\rm{;cos}}61^\circ {\rm{;cos}}61^\circ$

As we know,

⇒ sin²θ + cos²θ = 1

⇒ 1 + sin²61 + cos²61

⇒ 1 + 1 = 2

Let the number be x.

According to the question

⇒ x × 85/100 + 75 = x

⇒ x – [17x/20] = 75

⇒ 3x/20 = 75

⇒ x = 500

3 men, 4 women and 6 boys together can complete a work in 6 days

According to the question

⇒ W = 3M

⇒ M : W = 1 : 3

⇒ B = M/2

⇒ M : B = 2 : 1

Efficiency of man, woman and boy (M : W : B) = 2 : 6 : 1

Total work = (3M + 4W + 6B) × 6

⇒ (3 × 2 + 4 × 6 + 6 × 1) × 6 = 216

Suppose x women alone can complete that work in 4 days, then

⇒ x × 6 × 4 = 216

⇒ x = 9 days

Given, ∠APB = 40°

As we know,

⇒ ∠AOB + ∠APB = 180°

⇒ ∠AOB = 180° – 40° = 140°

In ΔOAB

OA = OB radius of the circle

∴ ∠OAB = ∠OBA

⇒ ∠OAB + ∠OBA + ∠AOB = 180°

⇒ 2∠OAB = 180 – ∠AOB = 180° – 140° = 40°

⇒ ∠OAB = 20°

Let there are 26 numbers value of each number is 1 then we can say sum of all 26 numbers is 26 and another 27^th number whose value is (-26), then

⇒ Average of all 27 numbers = (26 – 26)/27 = 0

Now, we can say there are 26 numbers may be greater than zero.

As we know,

Radius of circum-circle is 2 times of the radius of in-circle of an equilateral triangle.

Radius of in-circle = 8/2 = 4 cm

When an integer n is divided by 8, then remainder is 3

Let the value of n be 11 which satisfied the condition.

According to the question

⇒ (6n – 1) ÷ 8

⇒ (6 × 11 – 1) ÷ 8

⇒ (66 – 1) ÷ 8

⇒ 65 ÷ 8

Remainder will be 1

Total number obtained by A in Physics = 120 × 90/100 = 108

Total number obtained by B in Physics = 120 × 80/100 = 96

Total number obtained by C in Physics = 120 × 70/100 = 84

Total number obtained by D in Physics = 120 × 80/100 = 96

Total number obtained by E in Physics = 120 × 85/100 = 102

Total number obtained by F in Physics = 120 × 65/100 = 78

Total number obtained by G in Physics = 120 × 50/100 = 60

Total number obtained by all seven students in Physics = 108 + 96 + 84 + 96 + 102 + 78 + 60 = 624

Required average = 624/7 = 89.14

As we know,

Volume of sphere = 4/3 π r³

Radius of bigger sphere R = 6 cm

and radius of smaller sphere = 2 cm

Suppose x small spheres made by the bigger sphere.

According to the question

⇒ 4/3 π r³ × x = 4/3 π R³

⇒ 4/3 × π × 2³ × x = 4/3 × π × 6³

⇒ x = 27

Given, selling price of 40 articles is equal to the cost price of 50 articles

According to the question

40 SP = 50 CP

SP/CP = 50/40

SP : CP = 5 : 4

Suppose SP = 5 unit and CP = 4 unit

Profit = SP – CP = 5 – 4 = 1

Profit percentage = 1/4 × 100 = 25%

As we know, sin²A + cos²A = 1

⇒ 3 cos² A + 7 sin² A = 4

⇒ 3 cos²A + 3 sin² A + 4 sin²A = 4

⇒ 3(cos²A + sin² A) + 4 sin²A = 4

⇒ 3 × 1 + 4 sin² A = 4

⇒ 4 sin²A = 4 – 3 = 1

⇒ sin²A = 1/4

⇒ sin A = 1/2

⇒ sin A = sin 30°

⇒ A = 30°

⇒ cot A = cot 30° = √3

⇒ a³– b³ = (a – b) [(a + b)² – ab]

Given, a³ – b³ = 208 and a – b = 4

⇒ 208 = 4 [(a + b)² – ab]

⇒ [(a + b)² – ab] = 208/4 = 52

The correct answer is option 4.

Illuminate means light up.

Erase means to wipe clean

Light means the natural agent that stimulates sight and makes things visible.

Darken means make or become dark or darker.

The correct answer is option 2.

Here we have used passive voice, he is fed balls by someone ( that someone is hidden).

The sentence gives a general statement about what is usually given for eating to the tusker. According to the sentence, fed is the most appropriate word. So, option 2 is correct.

The correct answer is option 4.

The correct spelling of the given word is  choose.

The correct answer is option 1.

The given part is missing the verb have which makes the sentence incorrect. Therefore, option 1 is correct.-- It should be -- "I have done a lot of work today," she said.

The correct answer is option 3.

Involve means have or include (something) as a necessary or integral part or result.

Enrage means make (someone) very angry.

Invigorate means give strength or energy to.

Interest means the feeling of wanting to know or learn about something.

The sentence should use invigorate to state that the colours can give strength as well as energy.

The correct answer is: Option 1 i.e. scramble.

Key Points

• The word "scramble" is correctly spelled. It means to move or act quickly to get something, often in a disordered or frantic way. (जल्दबाजी में करना / हाथ-पांव मारना)
• Example: There was a scramble for the best seats in the theater.

Therefore, the correct answer is: scramble.

Additional Information

Here are the other options with their correct spellings:

• Definition (परिभाषा): A statement that explains the meaning of a word or phrase.
• Incorrect Spelling: defnition
• Jewelry (आभूषण): Decorative objects worn on the body, such as rings, necklaces, and bracelets.
• Incorrect Spelling: jewlri
• Acceptance (स्वीकृति): The action of consenting to receive or undertake something offered.
• Incorrect Spelling: acceptence

The correct answer is option 2.

The given idiom means perfectly or exactly right. The given sentence states that the glasses look good on Vandana's face.

The correct answer is CDAB

Key Points

• The first should be C as it describes the start of an incident i.e. the bus inching through the evening life.
• Then it should be D as it states how after the traffic grew, there was no space on the road. Then we talk about a man riding on the pavement i.e A. Last, it should be B.

Hence, the correct answer is Option 1.

The correct answer is option 1.

The given sentence has Ananya as subject and fresh flowers as an object. So change in voice will reverse this. Also, the sentence is in the present tense. So, option 1 is correct.

Option 2 is in present participle tense.

Option 3 is incorrect.

Option 4 is in the past tense.

The correct answer is option 4.

With should be used as balls of ragi flour were accompanied by rice, green gram, salt, and jaggery.

Of is used to show the relation of belonging.

From is used to show something derived from others.

By indicates the agent performing an action. So, option 4 is correct.

The correct answer is option 3.

The sentence is talking about the exact time when he had gone out and the client came. Therefore, than should be replaced with when to make the sentence correct. Also, the word scarcely has been used and according to the formation of the sentence had should come before he.

The correct answer is option 4.

The sentence should use there to focus attention on the people that are present around. So, options 1,2 and 3 are incorrect.

The correct answer is option 3.

Among is used when we are talking about more than two things.

Between is used when we are talking about 2 things.

So, here between should be used. So, option 3 is correct.

The correct answer is option 2.

Attribute means a quality or feature regarded as a characteristic or inherent part of someone or something.

Speech means the expression of or the ability to express thoughts and feelings by articulate sounds.

Quality means a distinctive attribute or characteristic possessed by someone or something.

Praise means express warm approval or admiration of.

Respect means a feeling of deep admiration for someone or something elicited by their abilities, qualities, or achievements.

The correct answer is option 2.

The given sentence should use of to show that the person is relating or belonging to an organization.

On is used when something is placed above others.

Between is used while talking about two things.

Among is used while talking about more than two things. So, option 2 is correct.

The correct answer is option 2.

A deficit means the amount by which something, especially a sum of money, is too small.

Adhere means stick fast to (a surface or substance).

Surplus means an amount of something left over when requirements have been met; an excess of production or supply.

Credit means the ability of a customer to obtain goods or services before payment, based on the trust that payment will be made in the future.

Remove means take (something) away or off from the position occupied.

The correct answer is option 3.

Fuse means to join or blend to form a single entity.

Unused means not being, or never having been used.

Break means separate into pieces as a result of a blow, shock, or strain.

Combine means join or merge to form a single unit or substance.

Correct means free from error; in accordance with fact or truth.

The correct answer is option 2.

First should be B as it gives an introduction of what is being talked about i.e how opening a bank account is intimidating. Next should be D as it is the statement contradicting B and describes how banks follow a standardized process. After D, it should be C as it shows how the account can be opened and C should be followed by A.

The sequence is :BDCA.

The correct answer is option 2.

Legislature means laws, considered collectively.

Judiciary means the part of a country's government responsible for its legal system.

Executive means denoting or relating to the part of a political administration with responsibility for putting into effect laws drawn up by the legislature.

Police mean the civil force of a state, responsible for the prevention and detection of crime and the maintenance of public order.

The correct answer is option 3.

The given idiom means as much as he wanted to. The sentence means that the dog played in the pond as much as he wanted to.

The correct answer is option 1.

A barometer means an instrument measuring atmospheric pressure.

The thermometer means an instrument for measuring and indicating temperature.

Ammeter means an instrument for measuring electric current in amperes.

Altometer means a surveying instrument with a rotating telescope for measuring horizontal and vertical angles.

The correct answer is option 3.

Comply means act in accordance with a wish or command.

Cope means to deal effectively with something difficult.

Compete means take part in a contest.

Collide means hit by accident when moving.

Compete should be used to state that women were not allowed to take part in the Olympic games.

The correct answer is option 3.

Entering is in present continuous tense but the phrase had started is in past participle tense. So, option 3 contains an error. It should be --When  I entered.

The correct answer is option 2.

It is clear that the active form of the sentence will contain Dinesh's grandmother as the subject. Also, the given sentence is in the past tense so the active form will also be in the past tense. The only sentence in the past tense is option 2.

The correct answer is option 4.

The people working in a department are referred to as officials. So, the most appropriate word is option 4.