SSC CGL Previous Paper (Held On: 9 August 2017 Shift 2) (Previous Year Paper)

According to the dictionary, the correct arrangement would be

1. Decollete
2. Decorous
3. Descrate
4. Desipicable
5. Destitute

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

Summing up the alphabetical positions of the letters,

ACOUSTIC → 1 + 3 + 15 + 21 + 19 + 20 + 9 + 3 = 91

Similarly,

RENOUNCE → 18 + 5 + 14 + 15 + 21 + 14 + 3 + 5 = 95.

Hence, the answer is ‘95’.

1. A + 2 = C; C + 3 = F; F + 4 = J

2. R + 2 = T; T + 3 = W; W + 4 = A

3. N + 2 = P; P + 3 = S; S + 3 = V

4. H + 2 = J; J + 3 = M; M + 4 = Q

Hence, odd letters are ‘NPSV’.

Given equation:

8 × 3 ÷ 4 + 9 – 5 = 16

On interchanging,

1. 3 and 4 → 8 × 4 ÷ 3 + 9 – 5 → 14.67 ≠ 16

2. 4 and 8 → 4 × 3 ÷ 8 + 9 – 5 → 5.5 ≠ 16

3. 5 and 3 → 8 × 5 ÷ 4 + 9 – 3 → 16 = 16

4. 5 and 9 → 8 × 3 ÷ 4 + 5 – 9 → 2 ≠ 16

Hence, on interchanging ‘5 and 3’ we’ll get the correct answer.

The pattern followed here is,

(2)# * 4 = 2

→ (2)³/4 → 8/4 = 2

(4)# * 4 = 16

→ (4)³/ 4 → 64/4 = 16

Similarly,

(6)# * A = 18

→ (6)³/A = 18

→ 216/A = 18

→ 12 = A

Therefore, the correct answer is 12.

Hence, there are 12 triangles in the given question figure.

The pattern followed here is,

1357 → (12)³ + 1357 → (13)³ + 3085 → (14)³ + 5282 → (15)³ + 8026 → 11401

Thus, the next term in the series will be ‘11401’.

Just as in a calendar we find dates, similarly in an index we find the content.

Hence, the correct answer is ‘Content’.

5 year hence, let the ages of A and B be 7x and 5x.

And, differences between their ages will be 4 years → 7x – 5x = 4

→ x = 2

Present ages of A and B would be (7x – 5) and (5x – 5) respectively.

Therefore, A’s age = 9 and B’s age = 5.

Summing up the alphabetical positions of the letters of the word,

RAIN → 18 + 1 + 9 + 14 = 42

OHBQ → 15 + 8 + 2 + 17 = 42

Similarly,

SUMMER → 19 + 21 + 13 + 13 + 5 + 18 = 89

Hence, ‘SUMMER’ will be coded as ‘89’.

1. It cannot be formed as ‘B’ is opposite to ‘O’.

2. It can be formed.

3. It cannot be formed as ‘Y’ is opposite to ‘I’.

4. It cannot be formed as ‘G’ is opposite to ‘R’.

Hence, dice (option) 2 can be formed.

1. acbddb → a a b c c a b b c d a b c d d a d c d b

2. adbcbd → a a bc d a b b c d a b c c d a b c d d

The sequence which follows is alphabetical order 2 times.

aabcd → abbcd → abccd → abcdd

3. cabddc → a c b c a a b b c d a b c d d a d c d c

4. ddcbbc → a d b c d a c b c d a b c b d a b c d c

The pattern followed here is, ‘a → a b c d → d’.

Hence, the answer is ‘adbcbd’.

First image:

(1 × 2 × 5 × 3) + (1 + 2 + 5 + 3) → 30 + 11 → 41

Second image:

(4 × 3 × 6 × 2) + (4 + 3 + 6 + 2) → 144 + 15 → 159

Similarly,

Third image:

(5 × 7 × 3 × 2) + (5 + 7 + 3 + 2) → 210 + 17 → 227

Hence, the missing number in the diagram is ‘227’.

The least possible Venn Diagram for the given statements will be as follows,

Conclusions:

I. Some wickets are rackets → True

II. All wickets are rackets → False as it is possible but not definite.

Thus, only conclusion I follows.

After looking at the picture, we can assume that the upper circle is the part of its diagonal circle where extra cross lines have been brought. So, the missing part will be the square where the cross line has been added.

Hence, option 3 will complete the given question figure.

​

Hence, the unfolded figure will be similar to option 3.

1. 10, 79, 23, 32, 42 → CREEC

2. 24, 55, 14, 41, 12 → CREEX

3. 33, 86, 32, 13, 43 → CRETP

4. 42, 98, 41, 00, 34 → CREEP

Hence, ‘CREEP’ will be represented by ‘42, 98, 41, 00, 34’.

The logic is:

First number + (1st digit × 2nd digit × 3rd digit)2 = Second number

243 + (2 × 4 × 3)2 

= 243 + (24)2 

= 243 + 576

= 819

Similarly,

163 + (1 × 6 × 3)2 

= 163 + (18)2 

= 163 + 324

= 487

Hence 487 is the correct answer.

Alternate Method

Summing up the digit of the number,

2 + 4 + 3 = 9; 8 + 1 + 9 = 18 → 18 – 9 = 9 

Similarly,

1 + 6 + 3 = 10

Required sum = 10 + 9 = 19

Given options,

1. 487 → 4 + 8 + 7 = 19

2. 563 → 5 + 6 + 3 = 14

3. 572 → 5 + 7 + 2 = 14

 4) 593 → 5 + 9 + 3 = 17

Hence 487 is the correct answer.

Hence, the question figure is hidden in option 1.

Hence, the mirror image of the question figure will be similar to option 1.

The following diagram shows the displacement of Lokesh,

Hence, Lokesh is to the west with respect to his starting point.

The pattern followed here is,

1. (4, 16, 48) → (4)² = 16 × 3 → 48

2. (6, 36, 90) → (6)² = 36 × 2.5 → 90

3. (8, 64, 160) → (8)² = 64 × 2.5 → 160

4. (12, 144, 360) → (12)² = 144 × 2.5 → 360

Hence, the odd pair is ‘(4, 16, 48)’.

Hence, the answer is option 3.

Table tennis is completely indoor while football, cricket and hockey are completely outdoor games.

Hence, ‘Table Tennis’ is the correct answer.

1. CONE → ENCYCLOPEDIA → can be formed.

2. CYCLE → ENCYCLOPEDIA → can be formed.

3. NOISY → ENCYCLOPEDIA → cannot be formed as there is no ‘S’.

4. PEACE → ENCYCLOPEDIA → can be formed.

Hence, word ‘NOISY’ cannot be formed.

Plant tissues are of three types: dermal, ground, and vascular.

There are three constituents of Indian Parliament: The President of India, Lok Sabha and Rajya Sabha.

• The Forest Research Institute of India is located in Dehradun, the capital city of the northern Indian state of Uttarakhand.
• The institute was established in 1906 and is one of the oldest and most prestigious institutions in India dedicated to forestry research, education, and training.
• It is spread over 450 hectares and includes a museum, herbarium, arboretum, and several research centers and laboratories.
• The Forest Research Institute of India is a leading center for forestry research and education in the country and plays a crucial role in the conservation and sustainable management of India's forest resources.

A software bug is an error in a computer program or system which can cause an incorrect and unexpected result. Through debugging, bugs can be fixed.

• Sun Temple of Konark was built by King Narasimhadeva I of the Eastern Ganga Dynasty about 1250 CE. This temple is dedicated to the Hindu god Surya and located 35 km northeast from Puri.
• The temple complex consists of a 100-foot high chariot with immense wheels and horses which is mainly in ruins.
• This temple complex was declared a UNESCO World Heritage Site in 1984.

Antonie Van Leeuwenhoek discovered bacteria. He was a Dutch scientist and commonly known as “the father of Microbiology”. He is best known for his pioneering work in microscopy and for his contribution toward the establishment of microbiology as a scientific discipline.

A microscope is an instrument used to see very small objects which can’t be seen by the naked eye. It was invented by Zacharias Janssen in 1590.

Akash Chopra has written the book titled ‘Numbers Do Lie: 61 Hidden Cricket Stories’ along with Impact statistical system.

This book has facts about the cricket which challenge and enrich conventional knowledge. The book has the data of 7 years of Impact Index’s work.

India has 15106.7 Km of land border in which it has longest border with Bangladesh and the shortest border with Afghanistan.

• Electromagnetic waves consist of both electric and magnetic field waves. Light waves and Radio waves are the examples of electromagnetic waves.
• Electromagnetic waves show the phenomenon of interference and diffraction. Other three properties are correct.

Iris Mittenaere of France has won the ‘Miss Universe 2016’ title which was the 65^th Miss Universe pageant.

It was held at the Mall of Asia Arena, Pasay, Philippines on January 30, 2017.

• Western Ghats is also known as Sahyadri range which is a mountain range runs parallel to the western coast of the Indian peninsula.
• Sometimes it is also called as the Great Escarpment of India. Western Ghats is a UNESCO World Heritage Site and is one of the 8 “hottest hot-spots” of biological diversity in the world.
• Anamudi (2,695 m) is the highest peak of the Western Ghats which is located in Kerala.

pH measures the hydrogen-ion concentration of any solution. Human blood has the pH range of 7.35 – 7.45 which is slightly basic.

The ideal pH for blood is 7.4.

In Badminton, shuttlecock is used in spite of ball. Rests of the games are played using ball.

Singles (one player per side) and doubles (two players per side) are the common forms of the game. Formally, it is an indoor game.

• Lord Warren Hastings was the first Governor General of Bengal. After the charter act of 1833, Governor General of Bengal was considered as the Governor-General of India.
• After the Revolt of 1857, Act for the Good Government of India was introduced by the British government in India in 1858 by which the post of Governor General of India was changed to the Viceroy of India.

• Monopoly refers to that market structure where there is only one seller in the market who controls the entire market supply and no substitute of the product is available in the market.
• Maximizing profits, lack of economic competition, a lack of visible substitute goods, and the high monopoly price are the characteristics of Monopolies.

• Half life of any radioactive substance is the amount of time required for the decay of substance to the half of its initial value.
• After one half life, we will have ½ of the substance remaining. After another half life, we will have ¼ of the substance remaining. It means 3/4^th of the substance will decay after two half lives.

1 Half life = 6 months

2 Half lives = 12 months

• Underemployment is also regarded as Disguised unemployment. It results when a person contributes to less production than what he/she is capable. For example, an engineer working as a clerk is underemployed.
• It exists frequently in developing countries whose large populations create a surplus for the labor force.

The correct answer is Newton's third law

It is difficult to fix a nail on a freely suspended wooden frame. This is because of Newton's third law of motion. When we apply a force on the frame, It gets deflected due to the reaction of applied force. 

Concept:

Newton’s First law:

• A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state.
• If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate.
• Newton’s first law defines inertia and is rightly called the law of inertia.

Newton’s Second Law:

• The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.
• If a body of mass m moves with velocity $\vec v$then its linear momentum can be given by $\vec p = m\vec v$ and if force is applied on a body, then

$\therefore \vec F = m\vec a$

Where F = Force, m = mass  and a = acceleration

Newton’s Third Law:

• To every action, there is always an equal (in magnitude) and opposite (in direction) reaction.
• When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first.
• Forces in nature always occur in pairs. A single isolated force is not possible.

• A tissue is group of cells with similar structure and functions. The study of tissue is called histology.
• Plant tissues are of three types: dermal, ground, and vascular.
• Animal tissues are grouped into four categories: connective, muscle, nervous and epithelial.

MP government started its ambitious ‘DeenDayalRasoi Yojana’ on 6^th April 2017 under which subsidized meals will be available at only Rs 5.

Chief Minister Shivraj Singh Chouhan inaugurated this scheme at Gwalior.

• Amazon River in South America is the largest river by discharge volume of water in the world which flows through Brazil, Colombia, and Peru.
• About 20% of the global riverine discharged to the ocean is represented by the Amazon. The Amazon basin is also the largest drainage basin in the world.

• President of India is the executive head of state in India. Article 53 states that all the executive power of the union will be vested in the President. He can exercise his executive power through his office or officers subordinate to him in accordance with the Constitution of India.
• He is also the Supreme Commander of Indian Armed Forces.

Antonio Guterres has been appointed as the Secretary-General of the United Nations by the General Assembly on October 13, 2016. His term has started from January 2017. He is the 9^th Secretary-General of the United Nations.

Antonio Guterres is a Portuguese politician and diplomat. He was the Prime Minister of Portugal from 1995 to 2002.

Work done by A in 1 day 1/20^thof the total work

work done by B in 1 day is 1/25^thof the total work

⇒ Work done in 3 days = 3 × (1/25 + 1/20)

⇒ work done in 3 days = 27/100 of total work

Which is 27 × 100/100 percent

∴ 27% of the total work will be completed

Distance travelled by A from 9 am to 11 am .i.e. 2 hrs is

⇒ Distance = 25 × 2

⇒ 50 Kms

Now, remaining distance = (260 – 50)

⇒ 210 Kms is remaining distance between them

Relative speed = 25 + 10

⇒ relative speed = 35 km/hr

time taken by them to cover 210 Kms is

⇒ 210/35

⇒ 6 hours

∴ they will meet at 6 hours from 11 am i.e. at 5 pm

Given that B got 220 marks

⇒ A got 18% more that of B’s marks

⇒ A’s marks = 220 × (1 + 18/100)

⇒ A’s marks = 220 × 1.18

⇒ A’s marks = 259.6

Given that A’s marks are 12% less than that of C

⇒ A’s marks = 12% less than that of C

⇒ C’s marks × (1 – 12/100) = 259.6

⇒ C’s marks = 259.6/0.88

∴ C’s marks are 295

Given x⁴ + (1/x⁴) = 34

Adding 2 to both sides

⇒ x⁴ + (1/x⁴) + 2 = 34 + 2

⇒ {x² + (1/x²)}² = 6²

⇒ x² + (1/x²) = 6        ……(i)

Subtracting 2 from both sides

⇒ x² + (1/x²) – 2 = 6 – 2

⇒ (x – 1/x)² = 2²

⇒ x – 1/x = 2        ……(ii)

since we know that x³ – (1/x³) = (x – 1/x) (x² + 1/x² + 1) from (i) and (ii)

⇒ x³ – (1/x³) = (2)(6 + 1)

∴ x³ – (1/x³) = 14

Given:

AB = AC = 6 cm

Calculation:

Diagonals in the rhombus bisect each other at a right angle.

In ΔAOB

AO² + BO² = AB²

⇒ (6/2)² + BO2 = (6)2

⇒ 9 + BO2 = 36

⇒ BO2 = 27

⇒ BO = 3√ 3

So, Bigger diagonal = 2×  3√ 3 = 6√ 3

Hence, area of equilateral triangle

⇒√3/4 × side²

⇒ √3/4 × (6√3)2

⇒ 27√3 cm²

∴ The correct answer is option (2).

Number of literate people are 63% of 600000

⇒ 63 × 600000/100

⇒ 378000

∴ there are 378000 literate people in city 4

Number of literate people in city 6 are 58% of 200000

⇒ 58 × 200000/100

⇒ 116000 literate people

literate female is given as

⇒ 3 × 116000/(2 + 3)

⇒ 69600 females are literate

Number of literate people in city 2 are 85% of 220000

⇒ 85 × 220000/100

⇒ 187000 literate people

literate male is given as

⇒ 7 × 187000/(7 + 4)

⇒ 1190000 males are literate

⇒ Required ratio = 1190000/696000

∴ ratio is 595 : 348

Number of literate people in city 1 are 80% of 250000

⇒ 80 × 250000/100

⇒ 200000 literate people

Number of literate people in city 2 are 85% of 200000

⇒ 85 × 200000/100

⇒ 170000 literate people

Number of literate people in city 3 are 78% of 220000

⇒ 78 × 220000/100

⇒ 171600 literate people

Number of literate people in city 4 are 63% of 300000

⇒ 63 × 300000/100

⇒ 189000 literate people

Number of literate people in city 5 are 92% of 150000

⇒ 92 × 150000/100

⇒ 138000 literate people

Number of literate people in city 6 are 58% of 400000

⇒ 58 × 400000/100

⇒ 232000 literate people

∴ we can see that City 6 > City 1 > City 4 > City 3 > City 2 > City 5

Let rate be r%

According to the question

⇒ 2970.25 = 2500(1 + r/100)²

⇒ (1 + r/100)² = 297025/ 250000

⇒ (1 + r/100) = 545 / 500

⇒ r = 9%

∴ rate is 9%

It can be written as sec² A – cos² A now using sec² A = 1 + tan² A and cos² A = 1 - sin² A

⇒ put this in the equation

⇒ 1 + tan² A – (1 - sin² A)

∴ sin² A + tan²A

Shortcut Trick

Rewrite the given equations as x + y = 1 and x² + y² = 2.

Use the standard algebraic identity: (x + y)² = x² + y² + 2xy.

Substituting the values: 1² = 2 + 2xy ⇒ 1 = 2 + 2xy.

Therefore, 2xy = 1 − 2 = −1 ⇒ xy = −1/2.

∴ The correct answer is −1/2.

Alternate Method

Given:

Equation 1: x = 1 − y ⇒ x + y = 1

Equation 2: x² = 2 − y² ⇒ x² + y² = 2

Formula Used:

The square of a binomial: (a + b)² = a² + b² + 2ab

Calculations:

⇒ Square both sides of Equation 1: (x + y)² = (1)²

⇒ x² + y² + 2xy = 1

⇒ Substitute Equation 2 (x² + y² = 2) into this equation:

⇒ 2 + 2xy = 1

⇒ 2xy = 1 − 2

⇒ 2xy = −1

⇒ xy = −1/2

∴ The correct answer is −1/2.

Additional Information

Algebraic Identity for Square of Difference

The identity (x − y)² = x² + y² − 2xy can be used to find the difference of variables if the product and sum of squares are known.

Difference of Squares

The expression x² − y² factors into (x − y)(x + y), which is useful for simplifying quadratic relations.

Relation between (x+y) and (x-y)

(x + y)² − (x − y)² = 4xy. This identity directly links the sum, difference, and product of two numbers.

let us assume ST be a and SQ be y

Radius = 10/2 = 5cm

⇒ taking sin(Q) in triangles QST, QOM and QPR

⇒ sin(Q) = a/y = 5/ (5 + y) = 9/ (10 + y), using last 2 equations

⇒ 50 + 5y = 45 + 9y

⇒ y = 5/4

using this in the equation a/y = 5/ (5 + y)

⇒ 4a/5 = 5/ (5 + 5/4)

⇒ a = 1

∴ ST is 1 cm

Given:

Two parallel sides are a and 12, height = 8 and area is 100.

Formula used:

Area of trapezium = 1/2 × sum of parallel sides × height

Calculation:

Area of trapezium = 1/2 × sum of parallel sides × height

⇒ 100 = 1/2 × (A + 12) × 8

⇒ 100 ÷  4 = A + 12

⇒ 25 = A + 12

⇒ A = 13

∴ The value of A is 13 cm.

Let the initial price be Rs. 100

After 2 successive discounts

⇒ 100 × (1 – 50/100) × (1 – 10/100)

⇒ 100 × 0.5 × 0.9

⇒ Rs. 45

So, Rs. 100 object is to be sold at Rs. 45

⇒ overall discount is Rs. 55

∴ 55% effective discount is been offered

Since it is given that ∠RPQ is 38°

⇒ Since PQ is diameter

⇒ ∠QRP must be 90° (Angle subtended by the diameter)

⇒ In triangle PRQ

⇒ ∠RPQ + ∠PQR + ∠QRP = 180° using the above values

⇒ ∠PQR = 180 – 90 – 38

⇒ ∠PQR = 52°

Since it is cyclic quadrilateral

⇒ ∠PQR + ∠PSR = 180

⇒ ∠PSR = 180 – 52

∴ ∠PSR is 128°

It can be written as x² + 7x + 1 = 0

⇒ roots of this quadratic equation are (-7 ±√45 )/2

they can be approximated as (Since √45 = 6.7)

⇒ Roots are x = – 0.15 or-6.85

Put this in x – 1/(x + 7)

Put x = - 0.15

⇒ – 0.15 – 1/(7 – 0.15)

⇒ – 0.3 and the value of 3 √5 – 7 = 3 × 2.23 – 7 = – 0.3

∴ the answer is 3√5 – 7

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

Calculation:

x + [1/(x + 7)] = 0

Adding both side 7

⇒ x + 7 + 1/(x + 7) = 7

Squaring both side

⇒ (x + 7)² + 1/(x + 7)² + 2 = 49

⇒  (x + 7)2 + 1/(x + 7)2 = 47

Subtracting both side by 2

⇒ (x + 7)2 + 1/(x + 7)2 - 2 = 47 - 2

⇒ {(x + 7) - 1/(x + 7)}² = 45

⇒ x + 7 - 1/(x + 7) = √45

⇒ x - 1/(x + 7) = √45 - 7

∴ The value of x – [1/(x + 7)] is √45 - 7.

Given (1/x) + (1/y) + (1/z) = 0

⇒ (xy + yz + zx) /(xyz) = 0

⇒ xy + yz + zx = 0      ---- (1)

and x + y + z = 9, squaring both sides

⇒ (x + y + z)² = 81

⇒ x² + y² + z²+ 2xy + 2yz + 2zx = 81 Using (1)

⇒ x² + y² + z² = 81      ---- (2)

Since we know that x³ + y³ + z³ – 3xyz = (x + y + z)( x² + y² + z² – xy – yz - zx)

Using (1) and (2) and x + y + z = 9

⇒ x³ + y³ + z³ – 3xyz = 81 × 9

∴ x³ + y³ + z³ – 3xyz = 729

Total numbers between 700 and 950 = 950 – 700 + 1 = 251

1^st number just after 700 that is divisible by 3 = 3 × 234 = 702

Last number divisible by 3 but less than 950 = 3 × 316 = 948

⇒ numbers between them are 316 – 234 + 1 = 83 numbers

1^st number divisible by 7 is 7 × 100 = 700

Last number divisible by 7 but less than 950 is 7 × 135 = 945

⇒ numbers between them are 135 – 100 + 1 = 36 numbers

These numbers also include numbers that are divisible by 21

So in order to avoid double subtraction we add multiples of 21

⇒ 1^st number just after 700 divisible by 21 is 21 × 34 = 714

the last number divisible by 21 but less than 950 is 21 × 45 = 945

⇒ numbers between them are 45 – 34 + 1 = 12 numbers

⇒ The numbers not divisible by 3 or 7 are 251 – (83 + 36 – 12) = 144 numbers

∴ there are 144 numbers that are not divisible by either 7 or 3

Shortcut Trick

Let Cost Price (CP₁) = 100.

Profit = 190% of 100 = 190 ⇒ Selling Price (SP) = 100 + 190 = 290.

New Cost Price (CP₂) = 100 + 10% of 100 = 110.

New Profit = SP − CP₂ = 290 − 110 = 180.

Required % = (Profit ÷ SP) × 100 = (180 ÷ 290) × 100 ≈ 62%.

∴ The correct answer is 62%.

Alternate Method

Given: Initial Profit = 190% of CP, CP increase = 10%, SP is constant.

Formulas: SP = CP + Profit | Profit % of SP = (Profit ÷ SP) × 100

⇒ Let original CP = 100 units.

⇒ Profit = 190% of 100 = 190 units.

⇒ SP = CP + Profit = 100 + 190 = 290 units.

⇒ New CP = 100 + (10% of 100) = 110 units.

⇒ New Profit = SP − New CP = 290 − 110 = 180 units.

⇒ Profit percentage of SP = (180 ÷ 290) × 100 = 1800 ÷ 29 ≈ 62.06%.

∴ The correct answer is 62%.

Additional Information

Profit Calculation Base

Standard Profit % is always calculated on Cost Price (CP) unless stated otherwise. However, in this problem, the question specifically asks for profit as a percentage of the Selling Price (SP).

Approximate Values

When calculating percentages like 180/290, you can simplify to 18/29. Since 18/30 = 60%, and the denominator 29 is smaller than 30, the result must be slightly higher than 60%.

Given AD/DB = 5/3

⇒ DB/AD = 3/5, add 1 to both sides

⇒ (AD + DB)/AD = (5 + 3)/5

⇒ AB/AD = 8/5

⇒ AD/AB = 5/8

Since triangle ADE is similar to ABC                         [From AAA similarity]

⇒ DE/BC = AD/AB = 5/8

∴ DE/BC = 5/8

So, Let us take A = 30

⇒ [tan(30)/{1 – cot(30)}] + [cot(30)/{1 – tan(30)}] – {2/sin(2 × 30)}

⇒ [1/{√3(1 - √3)}] + {√3/(1 – 1/√3)} – 2 × (2/√3) after simplifying and rationalizing

⇒ -{(1 + √3)/2√3} + {3(√3 + 1)/2} – (4/√3)

⇒ (-1 - √3 + 9 + 3√3 - 8)/2√3

⇒ (2√3)/(2√3)

⇒ 1

∴ its simplified value is 1.

Let us assume that the total population be x

⇒ literate people are 92% of x

⇒ 92x/100

female among them is given as

⇒ (92x/100) × 7/(7 + 9) = 259210

⇒ x = (259210 × 16 × 100)/(92 × 7)

∴ total population is 644000

Let the capacity be z litres

For bottle 1, 2 : 5 implies that milk is 2a and water is 5a

⇒ 2a + 5a = z

⇒ a = z/7        …..(i)

For bottle 2, 3 : 4 implies that milk is 3b and water is 4b

⇒ 3b + 4b = z

⇒ b = z/7        …..(ii)

For bottle 1, 4 : 5 implies that milk is 4c and water is 5c

⇒ 4c + 5c = z

⇒ c = z/9        …..(iii)

Total milk is = 2a + 3b + 4c Using (i), (ii) and (iii)

⇒ milk = 2 × z/7 + 3 × z/7 + 4 × z/9

Total water is 5a + 4b + 5c

⇒ water = 5 × z/7 + 4 × z/7 + 5 × z/9

Ratio of milk and water is given as

⇒ (2 × z/7 + 3 × z/7 + 4 × z/9) / ( 5 × z/7 + 4 × z/7 + 5 × z/9)

⇒ 73/116

∴ ratio is 73 : 116

Average age after adding the age of servant will be = 20 × (1 + 25/100)

⇒ average age after adding servants age = 25 years

Let servants age be x, from the questions statement

⇒ sum of age of all family members except servant/6 = 20

⇒ sum of age of all family members except servant = 120….(i)

Now,

Given that (sum of age of all family members except servant + x)/7 = 25

⇒ sum of age of all family members except servant + x = 7 × 25

From (i) we get

⇒ x = 7 × 25 – 120

⇒ x = 55

∴ servant’s age is 55 years

Putting the values

cot(A) = cos(A)/sin (A)

tan(A) = sin(A)/cos (A)

cosec(A) = 1/sin(A)

⇒ [(1/sin(A)/ {cos (A) /sin (A) + sin(A)/cos (A)}]²

Using sin²(A) + cos²(A) = 1

⇒ Cos²(A)

∴ simplified form is 1 – sin²(A)

The correct answer is option1, i.e. Dull.

The given word i.e. ‘Monotonous’ means ‘dull, tedious, and repetitious; lacking in variety and interest’ and is synonymous with the word ‘dull’. ‘Timid’ means ‘showing lack of courage’ and ‘unfriendly’ means something or someone that is not friendly and ‘lusty’ means ‘healthy and strong’. Since, all the options except 1 are out of context with the given word ‘monotonous’ thus, can be eliminated.

The correct answer is option 2, i.e. It being a pleasant evening.

The original sentence is grammatically correct, but it can be improved by adding a subject to the sentence.

Option 2 provides a subject "it" to the sentence which makes it more clear and concise.

The phrase "it being" acts as a subject in the sentence and makes the sentence more grammatically sound.

Option 1 is also grammatically correct, but it sounds a little awkward. Option 3 changes the meaning of the sentence and doesn't fit well in the context

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

In the given sentence the comma (,) after industries is misplaced and should be removed. Also, ‘industries’ must be replaced with ‘companies’ as the word industry is usually used for many companies that are into the same kind/area of business. For example, the steel industry, auto industry etc..

Hence, the statement can be correctly rewritten as, The Tata group owns many companies that are spread across the globe.

The correct answer is: Option 3.

Key Points

• The word "Colossal" means something extremely large or great. (विशालकाय)
• Example: The ancient pyramids are colossal structures that attract millions of tourists every year.
• "Teeny" refers to something very small or tiny. (बहुत छोटा)
• Example: The newborn kitten was so teeny that it could fit in the palm of my hand.
• Hence, we can infer that the opposite of 'Colossal' is 'Teeny'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Epic (महाकाव्य): A long narrative poem, often written about a hero or heroic events.
• Example: Homer's Iliad is an epic that has been studied for centuries.
• Rust (जंग): A reddish-brown coating formed on iron or steel by oxidation, especially in the presence of moisture.
• Example: The old bicycle was covered in rust after being left out in the rain for years.
• Vast (विशाल): Of very great extent or quantity; immense.
• Example: The Sahara Desert is a vast expanse of sand and dunes.

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

From the word itself, we get a hint that the meaning must be related to something ‘round’ as the given word can be broken into two parts ‘circum’ and ‘locution’. From, ‘circum’ we have another word as ‘circumference’, which is used in reference to circle. Thus, from the options and the given phrase, it is obvious that the most appropriate and correct answer choice is option 2.

The correct answer is option 1, i.e. Adulation.

Key Points

• The word "opprobrium" means harsh criticism or public disgrace, and the opposite of it is "adulation," which means excessive praise or admiration.
• Examples:
• The actor's performance was met with great adulation from the audience.
• The politician's decision to accept the bribe was met with public opprobrium.
• Option 2, "ignominy," is a synonym of "opprobrium" and means disgrace or dishonor. It is not the opposite of "opprobrium."
• Thus, the correct answer is Option 1.

Additional Information

• Option 3, "mystical," is unrelated to the meaning of "opprobrium" and means having a spiritual or mystical nature.
• Option 4, "preclude," means to prevent or make impossible, and is not the opposite of "opprobrium."
• Examples:
• The athlete suffered ignominy when she was caught using performance-enhancing drugs.
• The mystical atmosphere of the ancient temple filled the tourists with a sense of awe.
• The lack of funding will preclude the construction of the new library.
• Note that options 2, 3, and 4 are all unrelated to the meaning of "opprobrium."

The correct answer is 'distorting'.

Key Points

• In this context, 'distorting' is the most fitting word to complete the sentence "If so, English is perhaps the most _____ lens through which to see animals."
• The word 'distorting' refers to the act of twisting or altering something out of its true, natural, or original state.
• The context implies that the English language may create a skewed or misrepresented view of animals.
• Hence, the correct answer will be Option 1.

Additional Information

• 'Distorting' means giving a misleading or false account or impression of something. It fits the context best, as it suggests that the English language may change or warp the way animals are seen.
• Example sentence: The mirror was distorting his reflection.
• 'Disturbing' means causing distress or worry or upsetting. This doesn't fit into the context of the lens or perspective through which we see animals.
• Example sentence: It was a disturbing news report.
• 'Popular' means liked or admired by many people or by a particular person or group. This doesn't fit into the context of the sentence which implies a characteristic of the lens, not its popularity.
• Example sentence: She's a popular singer among teenagers.
• 'Useful' means able to be used for a practical purpose or in several ways. In this context, it doesn't fit as it doesn't imply any form of alteration or misrepresentation in the way animals are seen.
• Example sentence: This guidebook is very useful for new travelers.

The correct answer is option 3, i.e. perpetuated.

The answer to this blank is hidden in the line before it. From the line preceding the blank, we assume that English provides the most distorting view and provides a perpetuated (continued) idea of the animals. Thus, a proper understanding of the passage and proper elimination of option choices is very important. Hence, the correct answer is option 3.

Hence, the statement can be rewritten as, It has perpetuated a cross-eyed view of birds, beasts, fish, and fowl.

The correct answer is option 1, i.e. connote.

‘Connote’ means ‘(of a word) imply or suggest (an idea or feeling) in addition to the literal or primary meaning’. It logically fits the blank well and coveys the meaning of the sentence in the sense as the very word ‘animal’ can imply or suggest (connote) the brutish and the sensual. Other options are irrelevant and can be rejected.

Hence, the statement can be rewritten as, The very word "animal" can connote the brutish and the sensual.

The correct answer is option 4, i.e. Spinster.

‘Spinster’ is a one-word substitute for the given expression ‘an old unmarried woman’. Rest of the options such as ‘masochist’ mean ‘a person who enjoys an activity that appears to be painful or tedious’, ‘septuagenarian’ means ‘a person who is between 70 and 79 years old’ and ‘sniper’ means ‘a person who shoots from a hiding place’ are irrelevant and can be eliminated.

The given word can be used in a sentence as –

The sisters were to remain spinsters for the rest of their lives.

The correct answer is 'instincts'.

Key Points

• In the given context, 'instincts' would be the most fitting word to complete the sentence "Animal _____ imply baseness and vulgarity."
• The word 'instincts' is used to refer to inherent inclinations of a living organism towards a particular complex behavior.
• In reference to animals, it could mean behaviors driven by primal urges or natural tendencies.
• Hence, the correct answer will be Option 3.

Additional Information

• 'Breeding' refers to the reproduction and raising of animals, or more generally the cultivation of plants and animals. This doesn't fit into the context of implying baseness and vulgarity.
• Example sentence: The farmer has been breeding cattle for many years.
• 'Gestures' means the use of motions of the limbs or body as a means of expression, usually related to humans and not commonly used for animals.
• Example sentence: The politician's gestures were animated as he delivered his speech.
• 'Instincts' refers to an innate, typically fixed pattern of behavior in animals in response to certain stimuli. In the context of the sentence, this could imply baseness and vulgarity because it refers to the inherent, often unrefined behaviors of animals.
• Example sentence: Cats have an instinct to hunt.
• 'Species' refers to a group of living organisms consisting of similar individuals capable of exchanging genes or interbreeding. This does not fit into the context of implying baseness and vulgarity.
• Example sentence: The panda bear is an endangered species.

The correct answer is option 4, i.e. To speak frankly

Hence, it is clear that the correct answer choice is option 4. Rest of the options are irrelevant and can be eliminated.

The given phrase can be used in a sentence as –

Not to mince matters, some of these pundits are my charlatans.

Not to mince matters, I don't approve of my daughter going out with you because you are a married man.

The correct answer is option 1, i.e. Nobody told Rohan about the e-mail.

Option 2 can be rejected as it introduces ‘someone’ who has no role to play in the given sentence. Moreover, it gives the impression that someone didn’t tell him about the mail deliberately. Further, options 3 and 4 can also be rejected as 3 seems to be grammatically inappropriate and does not follow the flow of ideas whereas, 4 also unnecessarily introduces ‘nobody who could’ as we are not dealing with the tendency, to tell the truth. Option 1 captures the flow of the idea in the most appropriate manner and is both grammatically and contextually correct.

The correct answer is option 1, i.e. lens.

From the given options it is very clear that the word that most appropriately fit the blank will be something through which humans can perceive the world. Among the choices available, we need to select the most appropriate answer and option 1, i.e. ‘lens’ perfectly fits the blank and highlights the fact that Language is the lens via which humans can perceive the world. Rest of the options can thus, be rejected.

Hence, the statement can be rewritten as, Language, they say, is the lens through which human beings perceive the world

The correct answer is option 1, i.e. has advised. The given sentence is in simple present and since the doctor gave the advice, i.e. action has been done thus, ‘advice’ must be replaced with ‘advised’ which makes the above sentence grammatically correct.

Hence, the statement can be correctly rewritten as The doctor has advised him to take proper diet.

The correct answer is option 1, i.e. Baffling.

Key Points

• The word ‘Baffling’ means ‘impossible to understand’ and has a meaning close to the given word.
• ‘elusive’ means ‘’ difficult to remember’.

Though, the meanings are not exactly the same but are close to each other as compared to the other option choices.

Additional Information

• ‘Enticing’ means ‘attractive or tempting’.
• ‘directing’ means ‘to aim (something) in a particular direction or at a particular person’
• ‘soothing’ means ‘having a gently calming effect’.

The correct answer is SRQP.

Key Points

• The given sentence is an example of a Sentence Jumble.
• The first statement of a sentence jumbled question is usually an independent general statement, a noun, a universal fact, or the starting of an incident
• Part S will be the first sentence because it introduces the subject 'environment'.
• In some para jumbles, it is easier to identify the conclusion sentence. For this P should be the conclusive statement as it starts with 'however'. You use however when you are adding a comment which is surprising or which contrasts with what has just been said. R and Q only mention what the environment offers us. P is the contrasting one, so should be the conclusive statement.

Hence, the statements can be correctly rewritten as: An environment includes all the natural resources which surround us to help in a number of ways. It provides us with a better medium to grow and develop. It gives us all things which we need to live our life on this planet. However, our environment also needs some help from all of us to get maintained as usual to nourish our lives forever and to never ruin our lives.

The correct answer is option 4, i.e. Sponser

From the given options, it is clear that the word ‘Sponsor’ is misspelled as ‘sponser’ and must be corrected. ‘Sponsor’ refer to a person or organization that pays for or contributes to the costs involved in staging a sporting or artistic event in return for advertising. Thus, the correct answer is option 4.

The correct answer is option 4, i.e. toiling.

• Options 1, i.e. ‘continuing’ refers to persist in an activity or process.
• ‘Functioning’ means to work or operate in a proper or particular way.
• ‘Learning’ refers to the process of the acquisition of knowledge or skills through study, experience, or being taught.
• As we can see that all of these options are irrelevant to the context of the given sentence and thus, can be rejected.

The correct and most appropriate answer choice is option 4. It logically follows the same idea conveyed in the above sentence.

• Hence, the statement can be rewritten as He could excel in his board exams only after working very hard.

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

R introduces an independent idea about Social criticism. P logically follows the same direction as R and further Q follows P by introducing the concept of postmodernism. S sums up the entire paragraph, by considering the fact that social critics still consider the Critique of capitalism to be central.

Hence, the statement can be correctly rewritten as The starting points of social criticism can be very different and the different forms of socialism never have a monopoly on Social Criticism. The starting point can be the experience of a minority within society generally or even the experience of a group of people within a progressive social movement which does not live up to its progressive agenda in every respect. Within (or after) postmodernism a grand unifying theory no longer seems possible. This does not exclude the possibility or the necessity of dialogue. Nevertheless, most social critics still consider the Critique of capitalism to be central.

The correct answer is option 4, i.e. Ram told Rohan not to run so fast.

The given statement cannot be assumed as a advice, suggestion and a request. It is a simple statement where Ram is saying to Rohan to not run fast. Thus, all the options except 4 can be rejected.

The correct answer is option 3, i.e. 3.

‘Much late’ is grammatically incorrect and must be replaced with ‘of late’ which signifies the event or the actions which happened a short time ago or recently. For example, His life has changed of late.

Hence, the statement can be correctly rewritten as She has not been to the restaurant of late.

The correct answer is: Option 3 i.e. Reciept.

Key Points

• The word "Reciept" is incorrectly spelt.
• English Meaning: The word "reciept" is a misspelling and does not have a meaning. The correct spelling is "receipt".
• Hindi Meaning: गलत वर्तनी (गलत वर्तनी)
• Example: The word "reciept" is often mistakenly used instead of the correct spelling "receipt".
• The correct word is "Receipt".
• English Meaning: A piece of paper or electronic document acknowledging that a person has received money or goods. (रसीद)
• Hindi Meaning: रसीद
• Example: She kept the receipt as proof of purchase.

Therefore, the correct answer is: Option 3 i.e. Reciept.

Additional Information

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

• Autumn (पतझड़): The season between summer and winter, when leaves fall from trees.
• Example: Autumn is my favorite season because of the beautiful fall colors.
• Desperate (निराश): Feeling or showing a hopeless sense that a situation is so bad as to be impossible to deal with.
• Example: He was desperate to find a job after being unemployed for months.
• Traffic (यातायात): The movement of vehicles along roads, or the movement of aircraft, ships, or trains.
• Example: The traffic was heavy this morning, making me late for work.

The correct answer is option 1, i.e. laid.

The correct past form of ‘lay’ is ‘laid’. As the event has already occurred in the past thus, ‘laid’ will be used and all other option choices will be rejected.

Hence, the statement can be rewritten as He laid his camera on the table.

The correct answer is option 3, i.e. Amazed.

The phrase ‘All agog’ means ‘amazed or impressed’. From the meaning itself, it is clear that the correct answer choice is option 3, i.e. ‘amazed’. Rest of the options are vague and can be eliminated.

The given phrase can be used in a sentence as - He sat there, all agog, as the master of ceremonies read his name as the winner of the first prize’.