SSC CGL Previous Paper (Held On: 5 August 2017 Shift 3) (Previous Year Paper)

Group of Players constitutes a Team, group of Ministers constitutes a Council.

So, Player : Team :: Minister : Council.

Hence, answer is Council.

T + 2 = V, R + 2 = T, A + 2 = C, C + 2 = E, K + 2 = M

VTCEM reversed = MECTV

Same pattern will be followed for POND,

P + 2 = R, O + 2 = Q, N + 2 = P, D + 2 = F

RQPF reversed is FPQR.

So, TRACK : MECTV ∷ POND : FPQR.

Hence, answer is FPQR.

Here, 8 + 5 + 0 = 13.

850 + 13 = 863.

Same pattern will be followed for 430,

4 + 3 + 0 = 7.

430 + 7 = 437

Hence, answer is 437.

Since, Mustard, Peas, Sesame are food crops and cotton is a fibre crop.

Hence, cotton is odd word.

Here, addition of first two letters is 27 and if we add 3 in second letter, we get third letter.

CXA → C + X = 3 + 24 = 27, X + 3 = A

MNQ → M + N = 13 + 14 = 27, N + 3 = Q

PKN → P + K = 16 + 11 = 27, K + 3 = N

HSU → H + S = 8 + 19 = 27, S + 3 = V ≠ U

Except HSU, all other pair of letters give third letter when we add 3 in second letter.

Hence, HSU are odd letters.

1. (6 × 4) = 24, Square of 24 = 576

2. (1 × 7) = 7, Square of 7 = 49 ≠ 343

3. (2 × 7) = 14, Square of 14 = 196

4. (3 × 2) = 6, Square of 6 = 36

Hence, 17 – 343 is odd number pair.

2. Yakking
3.  Yakuzas
4. Yangtze
5. Yobbery
6. Yobbish

Hence, correct sequence is 23145.

Here,

A + K = 1 + 11 = 12

G + V = 7 + 22 = 29

L + F = 12 + 6 = 18

P + O = 15 + 16 = 31

Hence, answer is 31.

21, 26, 33, 42, 53, ?

Difference in 21 and 26 = 5

Difference in 26 and 33 = 7

Difference in 33 and 42 = 9

Difference in 42 and 53 = 11

Next odd number is 13.

Thus, 53 + 13 = 66.

Hence, answer is 66.

Let Present age of Pankaj = 5x

Present age of Punit = 6x

Sum of their ages,

5x + 6x = 33

11x = 33

x = 3

Present age of Pankaj = 5 × 3 = 15

Present age of Punit = 6 × 3 = 18

Difference in their ages = 18 - 15 = 3

Hence answer is 3 years.

The following diagram shows the displacement of Kritika,

Here she is 90 m away from her initial position.

Hence, answer is 90 m.

CONSOLE → CONSOLIDATE → can be formed.

ONSET → CONSOLIDATE → can be formed.

SALTY → CONSOLIDATE → cannot be formed as there is no Y.

SOLID → CONSOLIDATE → can be formed.

Hence, answer is SALTY.

Here,

Same pattern is to be followed for ‘SHIPPING’

Hence, answer is JITOOHOJ.

1. -, × and 4, 5 → 7 - 6 + 4 × 5 = 21 → 21 ≠ 33

2. ×, + and 4, 5 → 7 + 6 × 4 - 5 = 26 → 26 ≠ 33

3. +, - and 5, 6 → 7 × 5 - 6 + 4 = 33

4. ×, - and 5, 6 → 7 - 5 + 6 × 4 = 26 ≠ 33

Hence, we’ll interchange “+, - and 5, 6” to get the correct equation.

Logic:

3 @ 3 * 3 = 3 → 3 ÷ 3 × 3 = 3

48 @ 4 * 3 → 48 ÷ 4 × 3 = 36

Same pattern will be followed to find out the missing number:

91 @ 13 * 2 → 91 ÷ 13 × 2 = 14

Hence, answer is 14.

The method followed here is,

Number of the first column × number of second column = number of third column.

12 × 13 = 156

15 × 13 = 195

Same method will be followed to find out the missing number:

→ 14 × ? = 154

→ ? = 154/14 → 11

Hence, missing number is 11.

Triangles in the given figure: KLE, HEI, AFG, FEM, MEN, FEN, MJH, JIN, JGF, FCJ

Hence, there are 10 triangles in all.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. No leather is cloth → False (it may be possible but not definite).

II. Some leather are cloth → False (it may be possible but not definite).

III. Some leather are purses → True

The statements I and II make a complementary pair.

Hence,  Only conclusion III follows and either I or II follow.

If we observe the dice, we can see that 2, 4, 3 and 1 numbered sides are visible while 5 is not visible.

Clearly, 5 numbered face will come opposite to 6 numbered face.

A man can have both relation. Man can be brother or husband or can be a brother to someone at the same time can be husband to some other

Hence, the figure given in option 2 is correct..

User may get confused about the part that how a husband can be the brother, They view this relation from the angle of wife(women). Relationship of husband and brother with different person exists, just like a father is a son also but to different person.

Clearly, option 4 will complete the incomplete figure.

Hence, answer is option 4.

Clearly, the given question figure is hidden in the option 2.

Hence, answer is option 2.

Hence, mirror image of the given figure will be option 1.

1. 23, 76, 22, 77 → B, D, N, O

2. 11, 67, 40, 95 → B, A, S, D

3) 00, 55, 03, 59 → B, A, N, D

4. 44, 89, 30, 87 → B, P, N, D

Hence, BAND will be represented by 00, 55, 03, 59.

Law of Demand says that when the price increases of a comodity demand decreases of that commodity and when price decreases of commodity demand increases of commodity. However, in case of Giffen or inferior goods the relationship between price and demand becomes positive. 

In Inferior goods its depend on salary or income of a customer.

Inferior goods are those goods for example a soap and shower gel now when consumer income is low he will buy soap but when his income increases he will go for shower gel because now he can afford it and for him now soap is an inferior good.

• An oligopoly is a market form wherein a market or industry is dominated by a small number of large sellers. Oligopolies can result from various forms of collusion which reduce competition and lead to higher prices for consumers.
• Perfect competition is a market structure where competition is at its greatest possible level.Large number of buyers and sellers.
• It is the opposite of a monopoly, in which only a single firm supplies a good or service and that firm can charge whatever price it wants, since consumers have no alternatives and it is difficult for would-be competitors to enter the marketplace.
• There is a single seller in a certain market and there are no close substitutes for the product, then the market structure is that of a "pure monopoly".

The correct answer is option 2, i.e. six.

The Constitution guarantees six fundamental rights to Indian citizens as follows:

(i) Right to Equality

(ii) Right to Freedom

(iii) Right against Exploitation

(iv) Right to freedom of Religion

(v) Cultural and Educational Rights

(vi) Right to constitutional remedies

Note: Right to property was deleted by the 44th amendment act of 1978.

Article 20 prohibits the double jeopardy, ex-post facto laws, and unlawful detention, self-incrimination.

Article 21 declares that no person shall be deprived of his life or personal liberty except according to procedure established by law. This right is available to both citizens and non-citizens.

These two articles can’t be suspended even during an emergency because they are essential to human life and can’t be violated at all.

• Lord Canning was the Governor-General of India during the “First War of Independence of 1857”.
• Lord Canning served as Governor-General of India from 1856 to 1862.
• During his tenure, the Government of India Act, 1858 was passed which created the office of Viceroy to be held by the same person who was Governor-General of India.
• Thus, Lord Canning also served as first Viceroy of India.

The Nyaya Sutra is an ancient Indian Sanskrit text composed by Akṣapada Gautama and the foundational text of the Nyaya school of Hindu philosophy.

Vyasa - vedant sutra 

Kapila - sankhya sutra

Charaka - shushrut sanhita writer , Ayurved specialist

The Mariana Trench is the deepest part of the world's oceans. It is located in the western Pacific Ocean, an average of 200 kilometres (124 mi) to the east of the Mariana Islands, in the Western Pacific east of Philippines.

• Maasai are a Nilotic ethnic group inhabiting central and southern Kenya and northern Tanzania.
• They are among the best known local populations due to their residence near the many game parks of the African Great Lakes, and their distinctive customs and dress.

Pacemaker:

• A pacemaker is a small electrical device, fitted in the chest or abdomen.
• It's used to treat some abnormal heart rhythms (arrhythmias) that can cause your heart to either beat too slowly or miss beats.
• Some pacemakers can also help the chambers of your heart beat in time.

Key Points

Human Heart

• The human heart is one of the most important organs responsible for sustaining life.
• The human heart is a four-chambered muscular organ.
• The size of the heart is the size of about a clenched fist.
• It functions throughout a person’s lifespan and is one of the most robust and hardest working muscles in the human body.
• Its function is to maintain a constant flow of blood throughout the body. This replenishes oxygen and circulates nutrients among the cells and tissues.

Thus, the 'pacemaker' is associated with the heart.

Haemoglobin is the iron-containing oxygen-transport metalloproteinase in the red blood cells of all vertebrates. Haemoglobin is involved in the transport of other gases like respiratory carbon dioxide as carbaminohemoglobin and nitric oxide which is very important for human body.

The total distance covered by the sound from the point of generation to the reflecting surface and back should be at least 344 m/s (speed of sound) × 0.1 s = 34.4 m. Thus, for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be half of this distance. I.e., 34.4/2 = 17.2 m.

The board absorbs all light that falls on it so it appears as "Black", which is actually the absence of colour. However, no substance is a perfect black body so it will reflect some of the light incident on it whose intensity is so low that it cannot be noticed by the naked eye.

A motherboard is the main printed circuit board (PCB) in a computer. The motherboard is a computer’s central communications backbone connectivity point, through which all components and external peripherals connect.

Galvanization or galvanizing is the process of applying a protective zinc coating to steel or iron, to prevent rusting. The most common method is hot-dip galvanizing, in which the parts are submerged in a bath of molten zinc.

Dry Ice is the common name for solid carbon dioxide (CO2). It gets this name because it does not melt into a liquid when heated; instead, it changes directly into a gas. This process is known as sublimation. It is widely used as a refrigerant.

An ecosystem is a community made up of living organisms and non-living components such as air, water, and mineral soil.

Arogya Raksha Yojana is a comprehensive health insurance plan that offers people of rural India affordable access to high quality healthcare, provided by a network of renowned hospitals and clinics, supported by leading doctors and surgeons.

The correct answer is 7.

Key Points

• Water polo is typically played in an all-deep pool seven feet (or two meters) deep.
• Special equipment for water polo includes a water polo ball, which floats on the water.
• Water Polo was originally called ‘Water Rugby’ and it used to be played in the rivers and lakes in England.
• William Wilson of the UK is credited for giving rules and regulations for the game of Water Polo during the late 19th century.
• The first time Water Polo was introduced in the Olympics was in 1990 and Women’s Water Polo was introduced ten years later.
• The size of the Water Polo ball is almost the same as a soccer ball or a volleyball.

The correct answer is Maharashtra.

Key Points

• Lavani is a famous folk dance form of Maharashtra State.
• Lavani is a combination of traditional song and dance, which is particularly performed to the beats of the Dholki, a percussion instrument.
• Lavani is noted for its powerful rhythm.
• Lavani has contributed substantially to the development of Marathi folk theatre.
• In Maharashtra and southern Madhya Pradesh, it is performed by female performers wearing nine-yard-long sarees.
• The songs are sung in a quick tempo.
• The lavani dance originated in Maharashtra in the 18th and 19th centuries.
• Lavani dancers were patronized by Maratha Lords and Kings.
• Lavani dance was generally performed by Dhangars or Shepherd living in Solapur, Maharashtra
• Traditionally, this genre of folk dance deals with different and varied subject matters such as society, religion, and politics.
• The songs in 'Lavani' are mostly erotic in sentiment and the dialogues tend to be pungent in socio-political satire.
• Originally, it was used as a form of entertainment and morale booster to the tired soldiers.

Vikram Harshad Patel FMedSci is an Indian psychiatrist and researcher best known for his work on child development and mental disability in low-resource settings.

The correct answer is Kailash Satyarthi.

Key Points

• Kailash Satyarthi is an Indian children's rights activist.
• He is a Nobel Peace Prize recipient and founder of BachpanBachaoAndolan (lit. Save Childhood Movement), the Kailash Satyarthi Children’s Foundation, Global March Against Child Labour, and GoodWeave International.
• He started a magazine, Sangharsh Jaari Rahega where he doubled up as owner cum a photo-journalist.
• He conceived and led the Global March Against Child Labor and its international advocacy body, the ICCLE.
• ICCLE: International Center on Child Labor and Education.

The mega annual cultural festival 'India by the Nile', organised to celebrate Indian culture and its diversity. The festival which provides audiences an Indian cultural experience and encourages artistic collaborations between India and Egypt will be held in several cities such as Cairo, Alexandria and Port Said.

Sheikh Hasina Wazed is the current Prime Minister of Bangladesh, in office since January 2009. Hasina's political career has spanned more than four decades.

[12/(√5 + √3)] + [18/(√5 - √3)]

⇒(12√5 - 12√3 + 18√5 + 18√3)/(√5 + √3)(√5 - √3)

⇒ (30√5 + 6√3)/(5 - 3)                                                [∵ (a + b)(a - b) = a² - b²)

⇒ 6(5√5 + v3)/2

⇒ 3(5√5 + √3)

S’s 1 day work = 1/40

T’s 1 day work = 1/48

U’s 1 day work = 1/60

Let the work be completed in ‘x’ days, such that S worked for all x days, T worked for (x - 2) days and U for (x - 5) days

⇒ x/40 + (x - 2)/48 + (x - 5)/60 = 1

⇒ 6x + 5(x - 2) + 4(x - 5) = 240

⇒ 6x + 5x - 10 + 4x - 20 = 240

⇒ 15x = 270

⇒ x = 270/15 = 18 days

Hence, ratio of their share = (18/40) ∶ (16/48) ∶ (13/60) = 27 ∶ 20 ∶ 13

Sum of ratios = 27 + 20 + 13 = 60

∴ S’s share = (27/60) × 10800 = Rs. 4860

Area of a trapezium = {(sum of its parallel sides) × (distance between parallel sides)}/2

Area of the farmer’s land = (2.56 + 3.44) × 1.44/2 = 4.32 sq. yards

∴ Amount spent to plough land = 4.32 × 1800 = Rs. 7776

Marked price - discount = Selling price

⇒ MP - 18% of MP = 1599

⇒ 82% of MP = 1599

⇒ MP = 1599/0.82 = Rs. 1950

∴ Marked price of book is Rs. 1950

Let the amount received by each son be Rs. ‘x’

Amount received by each daughter = 1.5x

Amount received by wife = x - 600

Total amount = 19000

⇒ 3x + 2(1.5x) + x - 600 = 19000

⇒ 7x = 19600

⇒ x = 19600/7 = Rs. 2800

∴ Amount received by the 3 sons together = 3(2800) = Rs. 8400

Let amount received by 3 sons be x

Then amount received by 2 daughters will be 1.5 times the amount received by each son=1.5x

and amount received by wife is 600 less than each son = x - 600

According to the question,

⇒ x + x + x + 1.5x + 1.5x + x - 600 = 19000

⇒ 3x + 3x + x - 600 = 19000

⇒ 7x - 600 = 19000

⇒ 7x = 19600

⇒ x = 2800

Amount received by three sons

⇒ 3x = 3 × 2800

⇒ Rs. 8400.

∴ The total amount (in Rs) received by the 3 sons together is Rs. 8400.

Let the 3 consecutive even numbers be x, (x + 2) and (x + 4)

Average of 3 even numbers = (x + x + 2 + x + 4)/3

⇒ A = (3x + 6)/3

⇒ A = x + 2

⇒ x = A - 2

Average of 8 consecutive even numbers

⇒ (x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 + x + 14)/8

⇒ (8x + 56)/ 8

⇒ x + 7

Substituting for x,

⇒ A - 2 + 7

⇒ A + 5

∴ Required average = A + 5

Selling price = Rs. 18450

∵ Cost price - loss = Selling price

⇒ CP - 50% of CP = 18450

⇒ 50% of CP = 18450

⇒ CP = 18450/0.5 = Rs. 36900

∵ Selling price = Cost price + profit

∴ To earn a profit of 50%, Selling price = 36900 + 50% of 36900 = Rs. 55350

When the population increases at a rate of R% per annum and the current population is P, then,

Population n years ago = P/[1 + R/100]ⁿ

When the current population is 26010 and increases at a rate of 2% p.a.,

∴ Population 2 years ago = 26010/(1 + 2/100)² = 26010/1.0404 = 25000

∵ Time taken to cross the train = sum of lengths of trains/their relative speed

Their relative speed = (100 + 150)/9 = 250/9 m/sec. = 250/9 × 18/5 = 100 km/hr

When two trains are running in opposite direction, their relative speed is the sum of their individual speeds

⇒ 100 = 40 + speed of other train

∴ Speed of other train = 100 - 40 = 60 km/hr.

On a sum of Rs. P at a rate of R% per annum, when the compound interest is compounded half-yearly,

Compound interest after n years = P[(1 + R/200)²ⁿ - 1]

Given, P = Rs. 20000, R = 40%, n = 1 year

∴ Compound interest = 20000[(1 + 40/200)² - 1] = 20000 × 0.44 = Rs. 8800

I. x² - 8x + 15 = 0

⇒ x² - 5x - 3x + 15 = 0

⇒ x(x - 5) - 3(x - 5) = 0

⇒ (x - 5)(x - 3) = 0

⇒ x = 3, 5

II. y² + 2y - 35 = 0

⇒ y² + 7y - 5y - 35 = 0

⇒ y(y + 7) - 5(y + 7) = 0

⇒ (y + 7)(y - 5) = 0

⇒ y = - 7, 5

Hence, common root = 5

∴ Required difference = 5³ - 5² = 125 - 25 = 100

Given, (x - 1/3)² + (y - 4)² = 0

To satisfy the equation, each squared term must be zero,

Hence, we have,

⇒ x - 1/3 = 0 ⇒ x = 1/3

⇒ y - 4 = 0 ⇒ y = 4

∴ (y + x)/(y - x) = (4 + 1/3)/(4 - 1/3) = (13/3)/(11/3) = 13/11

Given,

x² + (1/x²) - 6

Formula used: 

a2 - b2 = (a + b)(a - b)

Calculation:

= x² + (1/x²) - 2 - 4

= x² + (1/x²) - 2(x)(1/x) - 4

= (x - 1/x)² - 2²

= (x - 1/x + 2)(x - 1/x - 2)                               

Hint

Till here in the question, we have factorised the given polynomial and got two factors. By subtracting these we will get the difference.

∴ Difference of factors = x - 1/x + 2 - x + 1/x + 2 = 4

Given, x + (1/x) = √13

⇒ (x + 1/x)² = 13

⇒ x² + 1/x² + 2 = 13

⇒ (x² + 1/x²) = 11

Also,

⇒ x² + 1/x² - 2 = 11 - 2

⇒ (x - 1/x)² = 3²

⇒ (x - 1/x) = 3

Now,

(x - 1/x) (x² + 1/x²)(x² + 1/x²) = 3(11)(11)

⇒ (x³ + 1/x - x - 1/x³)(x² + 1/x²) = 363

⇒ [x³ - 1/x³ - (x - 1/x)](x² + 1/x²) = 363

⇒ [x³ - 1/x³ - 3](x² + 1/x²) = 363

⇒ [x⁵ + x - 1/x - 1/x⁵ - 3(x² + 1/x²)] = 363

⇒ [x⁵ + 3 - 1/x⁵ - 3(11)] = 363

⇒ (x⁵ - 1/x⁵) = 363 - 3 + 33

∴ (x⁵ - 1/x⁵) = 393

The given triangle is shown below,

Considering similar triangles ∆ABC and ∆ADE,

⇒ AB/AD = AC/AE

⇒ (AD + DB)/AD = (AE + EC)/AE

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

⇒ (2x - 3)/x = (2x + 1)/(x + 3)

⇒ (2x - 3)(x + 3) = x(2x + 1)

⇒ 2x² + 6x - 3x - 9 = 2x² + x

⇒ 2x = 9

∴ x = 9/2 = 4.5

According to the Heron’s formula, if u, v and w are the medians of a triangle, then,

Area of triangle = (4/3) × √[s(s - u)(s - v)(s - w)]

where s = (u + v + w)/2

Let, u = 18 cm, v = 24 cm, w = 30 cm

⇒ s = (18 + 24 + 30)/2 = 36

∴ Area of triangle = (4/3) × √(36 × 18 × 12 × 6) = (4/3) × √(46656) = (4/3) × 216 = 288 cm²

Shortcut Trick As 18 cm, 24 cm and 30 cm are Pythagorian triplets

⇒ The triangle made by medians is a right angled triangle

⇒ Area of the triangle made by medians = (1/2) × base × height = (1/2) × 18 × 24 = 216

⇒ Area of the original triangle = 4/3 (Area of Δ made by medians)

⇒ (4/3) × 216 = 288.

∴ The correct answer is 288.

The given figure can be drawn as,

Radius of bigger circle = 28/2 = 14 cm

Area of bigger circle = (22/7) × 14 × 14 = 616 cm²

Diameter of small circle = radius of bigger circle= 14 cm

Radius of small circle = 14/2 = 7 cm

Area of small circle = (22/7) × 7 × 7 = 154 cm²

∴ Area of bigger circle not enclosed by two smaller circles = 616 - 2(154) = 308 cm²

According to the angle bisector theorem, a line that bisects an angle of a triangle, divides the opposite side into segments that are proportional to the other two sides

Let AB = x, BC = y and AC = z

Considering ∆ACD and ∆BCD,

⇒ CO/OD = AC/AD = BC/DB = 3/2

⇒ AD = (2/3)AC

⇒ DB = (2/3)BC

⇒ AB = AD + DB = (2/3)(AC + BC)

⇒ x = (2/3)(y + z)

⇒ 3x = 2y + 2z      ----(1)

Similarly, considering ∆ACE and ∆ABE,

⇒ AO/OE = AC/EC = AB/BE = 5/4

⇒ EC = (4/5)AC

⇒ BE = (4/5)AB

⇒ BC = BE + EC = (4/5)(AB + AC)

⇒ y = (4/5)(x + z)

⇒ 5y = 4x + 4z

Substituting for z from (1),

⇒ 5y = 4x + 2(3x - 2y)

⇒ 5y = 4x + 6x - 4y

⇒ 9y = 10x

⇒ y = (10/9)x      ----(2)

Similarly, considering ∆ABF and ∆BCF,

⇒ BO/OF = AB/AF = BC/FC = s(let)

⇒ AF = AB/s

⇒ FC = BC/s

⇒ AC = AF + FC = (AB + BC)/s

⇒ z = (x + y)/s

⇒ sz = x + y

Substituting for z from (1),

⇒ s(3x - 2y)/2 = x + y

⇒ 3sx - 2sy = 2x + 2y

⇒ 3sx - 2x = 2sy + 2y

⇒ x(3s - 2) = y(2s + 2)

Substituting for y from (2),

⇒ x(3s - 2) = (10/9)x(2s + 2)

⇒ 9(3s - 2) = 10(2s + 2)

⇒ 27s - 18 = 20s + 20

⇒ 27s - 20s = 18 + 20

⇒ 7s = 38

⇒ s = 38/7

∴ BO/OF = 38/7

Alternate Method

Given:

O is the incenter of the triangle ABC.

AO/OE = 5/4

CO/OD = 3/2

Concept used:

If O is incentre of the ΔABC, then 

1.) AO/OE = (AB + AC)/BC 

2.) BO/OF = (AB + BC)/CA

3.) CO/OD = (AC + BC)/AB

Calculations:

O is the incenter of the triangle ABC. If AO/OE = 5/4 and CO/OD = 3/2, then what is the value of BO/OF?

AO/OE = 5/4 

⇒ (AB + AC)/BC = 5/4 

⇒ (AB + AC + BC)/BC = (5 + 4)/4 

⇒ (AB + AC + BC)/BC = 9/4     

⇒ BC/(AB + BC + CA) = 4/9     ----(1)

⇒ (AC + BC)/AB = 3/2 CO/OD = 3/2

⇒ (AC + BC + AB)/AB = (3 + 2)/2 

⇒ (AB + BC + CA)/AB = 5/2    ----(2)

From equation (1) and (2)

So,BC = 20

AB + BC + CA = 45 

AB = 18

Now, CA = (AB + BC + CA) - (AB + BC)

⇒ CA = 45 - (20 + 18)

⇒ CA = 7 

Now, BO/OF = (AB + BC)/CA

⇒ BO/OF = (18 + 20)/7

⇒ BO/OF = 38/7

∴ The correct answer is 38/7

As we know, sin 2x = 2 tan x/(1 + tan² x)

Putting x = θ/2,

⇒ sin θ = 2 tan (θ/2)/[1 + tan² (θ/2)]

⇒ (sin θ)/2 = tan (θ/2)/[1 + tan² (θ/2)]

Given, tan (θ/2) + cot (θ/2)

⇒ tan (θ/2) + 1/tan (θ/2)

⇒ [1 + tan² (θ/2)]/tan (θ/2)

⇒ 2/sin θ

⇒ 2 cosec θ

∴ The correct answer is 2 cosec θ

Given:

[(sec3x - tan3x)/(sec x - tan x)] - 2 tan2x - sec x tan x 

Formula used:

⇒ a³ - b³ = (a - b)(a² + ab + b²)

⇒ sec2 x - tan2x = 1

Calculation:

⇒ (sec³x - tan³x) = (sec x - tan x)(sec² x + sec x tan x + tan²x)

⇒ (sec³x - tan³x)/(sec x - tan x) = (sec² x + sec x tan x + tan²x)

Now,

⇒ [(sec³x - tan³x)/(sec x - tan x)] - 2 tan²x - sec x tan x

⇒ sec² x + sec x tan x + tan²x - 2 tan²x - sec x tan x

⇒ sec² x - tan²x = 1                                  [∵ sec² x - tan²x = 1]

∴ The correct answer is 1.

Shortcut Trick

Given sin⁸ θ + cos⁸ θ = 1. Let k = sin² θ cos² θ.

Using the identity sin⁸ θ + cos⁸ θ = (1 − 2k)² − 2k²:

⇒ (1 − 2k)² − 2k² = 1

⇒ 1 + 4k² − 4k − 2k² = 1 ⇒ 2k² − 4k = 0

Since θ ≠ 0 or π/2, sin θ and cos θ are non-zero, so k ≠ 0 ⇒ k = 2.

∴ The correct answer is 2.

Alternate Method

Given: sin⁸ θ + cos⁸ θ − 1 = 0 where θ ≠ 0 or π/2

Formula Used: sin² θ + cos² θ = 1; a² + b² = (a + b)² − 2ab

θ cosθ sinθ Radius = 1 Trigonometric Identity Basis sin²θ + cos²θ = 1

⇒ sin⁸ θ + cos⁸ θ = 1

⇒ (sin⁴ θ + cos⁴ θ)² − 2 sin⁴ θ cos⁴ θ = 1

⇒ [(sin² θ + cos² θ)² − 2 sin² θ cos² θ]² − 2 sin⁴ θ cos⁴ θ = 1

⇒ (1 − 2 sin² θ cos² θ)² − 2 sin⁴ θ cos⁴ θ = 1

⇒ 1 + 4 sin⁴ θ cos⁴ θ − 4 sin² θ cos² θ − 2 sin⁴ θ cos⁴ θ = 1

⇒ 2 sin⁴ θ cos⁴ θ − 4 sin² θ cos² θ = 0

⇒ 2 sin² θ cos² θ (sin² θ cos² θ − 2) = 0

⇒ sin² θ cos² θ − 2 = 0 (as sin θ, cos θ ≠ 0)

⇒ sin² θ cos² θ = 2

∴ The correct answer is 2.

Additional Information

Fundamental Pythagorean Identity

For any real angle θ, sin² θ + cos² θ = 1.

Power Reductions

sin⁴ θ + cos⁴ θ = 1 − 2 sin² θ cos² θ and sin⁶ θ + cos⁶ θ = 1 − 3 sin² θ cos² θ.

Range of Product

The expression sin² θ cos² θ can be written as (1/4) sin²(2θ), which has a maximum real value of 0.25.

Total marks in English = 87 + 74 + 89 + 62 + 95 = 407

Total marks in Mathematics = 96 + 99 + 99 + 89 + 92 = 475

Total marks in Science = 90 + 94 + 99 + 96 + 92 = 471

Total marks in Hindi = 81 + 89 + 92 + 91 + 86 = 439

∴ Total marks of all students is highest in Mathematics

Total marks scored by Student 1 = 87 + 96 + 90 + 81 = 354

Total marks scored by Student 2 = 74 + 99 + 94 + 89 = 356

Total marks scored by Student 3 = 89 + 99 + 99 + 92 = 379

Total marks scored by Student 5 = 95 + 92 + 92 + 86 = 365

∴ Maximum marks were scored by student 3

Considering marks of highest 4 subjects,

Student 2 = 100 + 99 + 94 + 89 = 382

Student 3 = 100 + 99 + 99 + 92 = 390

Student 4 = 100 + 89 + 96 + 91 = 376

Student 5 = 100 + 95 + 92 + 92 = 379

∴ Student 2 will be at second place.

Total marks in English = 87 + 74 + 89 + 62 + 95 = 407

Average marks per student in English = 407/5 = 81.4

Total marks in Hindi = 81 + 89 + 92 + 91 + 86 = 439

Average marks per student in Hindi = 439/5 = 87.8

∴ Required percentage = (81.4/87.8) × 100 = 92.71%

Here the correct answer is 2.

Key Points

• The given sentence has an error in the second part.
• From the context of the sentence, it can be easily interpreted that the statement is for many people.
• Hence, 'lives' should be changed to 'live' as “sisters-in-law” are living in Kolkata which is plural.
• Hence, option 2 is the correct answer.

Correct Sentence: My sisters-in-law who live in Kolkata have come to stay with us.

Here the correct answer is 1.

Key Points

• From the context of the given statement, more than one cloth is being talked about.
• This means that the first part of the statement is faulty.
• The correct replacement should be ”These kinds of clothes” .
• The correct option should be option 1.

Correct Sentence: These kinds of clothes are rather expensive for me to buy.

The correct answer is Concede.

Key Points

• The correct answer for the given blank is "concede".
• The word "concede" means to admit or acknowledge the truth of something, often unwillingly.
• In the given sentence, the employee did not agree with the argument of the manager.
• Therefore, the correct word to fill in the blank is "concede".
• Example: He finally conceded that he had made a mistake.
• Thus, the correct answer is Option 3.

Additional Information

• Other words and their meanings are:
• Precede - to come before something or someone in order or time
• Example: The opening speech will precede the awards ceremony.
• Exceed - to be greater than a particular number or amount
• Example: The cost of the project exceeded our budget.
• Recede - to move back or away from a previous position
• Example: The floodwaters began to recede after a few days.

When taking some position, there generally is an oath session which people have to take. But to retire, there is no such session. So options 2 and 4 are eliminated by common knowledge. Option 3 makes the sentence grammatically incorrect. The correct filler which makes the sentence meaningful and correct is option 1.

’Cantankerous’ means someone who is quarrelsome or argumentative and uncooperative. From the given words, the 2nd option is perfectly matching the actual meaning of the given word. On the other hand, ‘humorous’ means ‘laughable’, while ‘remorseful’ is something to be felt bad about. ‘Dullness’ means an attitude of a person who is mostly non-reactive to other stimuli and very inactive.

Answer- Discerning Judge 

Important Points

• ‘Decisive' means ‘resolute’ or ‘settling’. (निर्णायक या अंतिम)
• Uncivilized means someone who lacks the proper manners to which agreeable to the people or society. (असभ्य)
• Discerning Judge is a person who has a great sense of better judgement. (किसी वस्‍तु को योग्य देख या पहचान पाना)
• Narrow-minded is a person who is generally stereotypical and not much open to grasp others thoughts whether relevant or not. (संकुचित विचार करनेवाला)
• Connoisseur means someone who has a great taste of something and can make the perfect judgement. (कला, स्‍वादिष्‍ट भोजन, संगीत आदि का विशेष जानकार)

From the above meanings, the similar word would be option 3.

Here the correct answer is Productive.

Key Points

• The word "nugatory" means of no value or importance, useless, ineffective, or futile.
• Here are example sentences:
• The committee's decision was nugatory and had no impact on the final outcome.
• The company's efforts to improve their image proved to be nugatory in the face of mounting criticism.
• The correct answer for the opposite of "nugatory" is option 4) productive, which means yielding good results, profitable, or useful.
• Example sentences for "productive" are:
• The company's new strategy was very productive and led to a significant increase in revenue.
• She spent the weekend working on her garden, and it turned out to be very productive with a variety of flowers and vegetables.

Additional Information

• Other options in the question are:
• Delusive: misleading, deceptive, or illusory.
• Example: The promise of overnight wealth from the get-rich-quick scheme turned out to be delusive, and many people lost their savings.
• Futile: useless, ineffective, or incapable of producing any result.
• Example: His efforts to revive the dying plant were futile, and it eventually withered away.
• Unreal: imaginary, not real, or lacking substance.
• Example: The vivid dream felt so real, but it was actually unreal, and she woke up feeling disoriented.

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

Key Points

• The word "naive" means someone who is innocent, inexperienced, or lacking in worldly wisdom. (भोला-भाला)
• Example: She was naive to believe that everyone she met had good intentions.
• "Artful" refers to someone who is clever or skillful, especially in achieving a goal through deceit or cunning. (चालाक)
• Example: The artful negotiator managed to secure a better deal for his company.
• Hence, we can infer that the opposite of 'naive' is 'artful'.

Therefore, the correct answer is: Option 1 i.e. Artful.

Additional Information

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

• Candid (स्पष्टवादी): Being straightforward and truthful.
• Example: He was candid about his mistakes, which earned him respect.
• Credulous (विश्वासी): Having or showing too great a readiness to believe things.
• Example: His credulous nature made him an easy target for scams.
• Sincere (ईमानदार): Free from pretense or deceit; genuine.
• Example: She gave a sincere apology for her mistake.

The correct answer is: Afraid to speak frankly.

Key Points

• The word "Mealy-mouthed" means someone who is hesitant to speak directly or openly; they avoid being straightforward. (मुंहफट नहीं होना)
• Example: The politician's mealy-mouthed responses left the audience frustrated.
• "Afraid to speak frankly" refers to someone who is unwilling or hesitant to speak openly and honestly. (स्पष्ट रूप से बोलने से डरना)
• Example: He was afraid to speak frankly about his feelings, fearing it might hurt her.
• Hence, we can infer that 'mealy-mouthed' is best expressed by 'afraid to speak frankly'.

Therefore, the correct answer is: Afraid to speak frankly.

Additional Information

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

• Ill-tempered (क्रोधी): Someone who is easily angered or irritable.
• Example: The ill-tempered manager yelled at his employees for minor mistakes.
• Enthusiastic (उत्साही): Showing intense and eager enjoyment, interest, or approval.
• Example: She was enthusiastic about her new job and couldn't wait to start.
• Depressed (उदास): In a state of unhappiness or low spirits.
• Example: He felt depressed after hearing the bad news.

The given expression means irregular bursts of activity. From the given options, option 4 is the correct meaning to the given expression.  In a sentence, the expression can be used as-“In a startup one can always expect fits and starts in initial times.”

The correct answer is helped her not only by

Key Points

• When using not only . . . but also in a sentence, parallelism should be the goal. It means that the words following both parts of this correlative conjunction (i.e., not only and but also) should belong to the same parts of speech. For example, if a verb follows not only, then a verb should also follow but also. Using different parts of speech after each part of not only . . . but also makes the sentence imbalanced and, frankly, just awkward.
• Consider the example below:
• He’s not only intelligent but also funny.
• the adjectives intelligent and funny follow not only and but also, ensuring that the sentence is parallel.
• ​Here, in the given sentence 'but also' is followed by preposition, so 'not only' should also be followed by preposition.

​Thus, the correct sentence is: I had helped him not only by giving hints but also with providing him links.

The correct answer is finished

Key Points

• You always use the simple past when you say when something happened, so it is associated with certain past time expressions.
• A definite point in time: last week, when I was a child, yesterday, six weeks ago
  

Examples:

• We saw a good film last week.
• Yesterday, I arrived in Geneva.
• She finished her work at seven o'clock
• I went to the theatre last night

​Thus, the correct sentence is: We finished our lunch half an hour ago.

The correct answer is Option 2)

Explanation:

• Blasphemy: The act of speaking irreverently about sacred things
• An atheist is a person who does not believe in faith or god.
• Bellicose is the act of showing aggression or willingness to fight.
• Defection means to desert one’s country in opposition.

Thus, the correct answer is Blasphemy

The correct answer is: Option 4.

Key Points

• The word "Egoist" refers to a person who is selfish and self-centered. (स्वार्थी व्यक्ति)
• Example: John's egoist behavior often alienates his friends.
• "Egotist" refers to a person who talks excessively about themselves. (अहंकारी व्यक्ति)
• Example: Mary is an egotist; she always dominates the conversation with stories about her own life.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Elite (विशिष्ट): A select group that is superior in terms of ability or qualities to the rest of a group or society.
• Example: The elite members of the society often have access to exclusive events.
• Emetic (वमनकारक): A substance that causes vomiting.
• Example: The doctor prescribed an emetic to induce vomiting in the patient.

The correct answer is: Option 4.

Key Points

• The word "Soveriegnity" is incorrectly spelt. The correct spelling is "Sovereignty".
• Soveriegnity (Incorrect Spelling)
• Example: The Soveriegnity of the nation was recognized by all.
• Sovereignty (Correct Spelling) refers to supreme power or authority. (सार्वभौमिकता)
• Example: The sovereignty of the state was upheld by the constitution.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Entrepreneur (उद्यमी): A person who sets up a business or businesses, taking on financial risks in the hope of profit.
• Example: The entrepreneur launched a new tech startup in Silicon Valley.
• Remuneration (वेतन): Money paid for work or a service.
• Example: She received a generous remuneration for her consultancy services.
• Apprentice (शिक्षु): A person who is learning a trade from a skilled employer, having agreed to work for a fixed period at low wages.
• Example: The apprentice spent years learning the trade of carpentry.

The correct answer is: Option 2.

Key Points

• The word "Preseverance" is incorrectly spelt.
• English Meaning: The correct spelling is "Perseverance" which means persistence in doing something despite difficulty or delay in achieving success. (दृढ़ता)
• Example: Her perseverance in studying for the exams paid off when she topped the class.
• "Perseverance" refers to the quality of continuing to try to achieve a particular aim despite difficulties. (दृढ़ता)
• Example: His perseverance in the face of adversity is truly inspirational.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Tranquility (शांति): The quality or state of being calm and peaceful.
• Example: The tranquility of the countryside is a refreshing change from the hustle and bustle of the city.
• Resplendence (चमक): Attractive and impressive through being richly colorful or sumptuous.
• Example: The resplendence of the royal palace left the visitors in awe.
• Accommodation (आवास): A room, group of rooms, or building in which someone may live or stay.
• Example: The hotel provides comfortable accommodation for its guests.

In such questions, The correct order should be like a story or a well-presented fact.

The correct order here is RSQP.

R presents the topic.

S gives its effect.

Q further develops the topic by taking examples.

And lastly, P tells about the other possibility to the topic.

In such questions, The correct order should be like a story or a well-presented fact. The correct order here is RQPS. 

Here, the quality of a man is discussed. R starts the fact by making some qualities peculiar. Then Q adds on to the qualities in continuation. Then statement P continues the paragraph by developing about what was said in 2nd statement. Lastly, S completes the paragraph by mentioning the most important aspect-”life”.

On transition from the given Active voice to Passive voice, the correct Passive voice is option 3. The active voice is being said in Present form of tense. Then the passive voice must follow present tense. Since, Options 2 and 4 are past forms, therefore, they are to be eliminated. Option 1 is grammatically incorrect and hence eliminated too.

Generally when transitioning from direct to indirect form of speech,”that” is used. But here, ‘that’ is used in statement 2 which is incorrect and has completely changed meaning to the given direct speech. The meaning of the statement should never be changed in such transition. Similarly options 3 and 4 are also incorrect due to slight changes in meaning. The correct indirect speech would be option 1

The passage talks mainly about the changing of the world and its development. It is by common knowledge that one can easily state that there has been a lot of development and still growing. From this context the filler in the blank should be an adjective showing immense development. Since, ‘tremendous’ is the only  appropriate word to be used, therefore, the correct option would be 1.

Due to the enhancement of new technologies, the development in the given fields are maximum. People generally are unable to measure the growth before, and hence, its effect remain unprecedented. Hence, the correct option would be 2. Other options do not convey the meaning the context tries to convey.

Earlier, due to lack of scientific discoveries and evolution of science, people could not see the brighter side of the world. But now, due to the evolution of science, the future is not as bad as earlier people expected. So the correct filler would be bleak.

Since, the developing countries still have many portions not much developed, therefore, poverty and famine are still a problem. Hence, option 4 is correct.

As poverty and famine are still prevailing due to population, therefore, there are still diseases originating and vectoring. Hence, option 1 is correct. Option 3 cannot be used as filler as there is no one liable to a disease. Instead, disease may inadvertently catch anybody.