SSC CGL Previous Paper (Held On: 5 August 2017 Shift 1) (Previous Year Paper)

In Power : Watt,

Watt is SI unit of Power. Similarly, Joule is SI unit of Work.

Hence, “Work : Joule” is correct combination.

In NPBG : OQCH

→ N + 1 = O

→ P + 1 = Q

→ B + 1 = D

→ G + 1 = H

Similarly,

In AJOT : ?

→ A + 1 = B

→ J + 1 = K

→ O + 1 = P

→ T + 1 = U

Hence, “BKPU” is the related number.

In 101 : 10201

→ 101² = 10201

Similarly,

→ 107² = 11449

Hence, “11449” is related number.

Lion, Leopard and Tiger are mammal whereas Snake is an reptile.

Hence, “Snake” is odd word among given alternatives.

1. NPR ⇒ N + 2 = P; P + 2 = R

2. TVX ⇒ T + 2 = V; V + 2 = X

3. FHJ ⇒ F + 2 = H; H + 2 = J

4) OMK ⇒ O – 2 = M; M – 2 = K                      

Hence, “OMK” is the odd letters from the given alternatives.

59, 61 and 53 are prime numbers whereas 69 is a composite number.

Therefore, “69” is an odd number from the given alternatives.

On arranging given words as per dictionary,

4. Road
5. Roasted
6. Roller
7. Ropped
8. Roster

Hence, “43512” is correct order as per dictionary.

The pattern followed here is,

→ B + 1 = C; C + 1 = D; D + 1 = E

→ C + 1 = D; D + 1 = E; E + 1 = F

→ F + 1 = G; G + 1 = H; H + 1 = I

Hence, “EFI” is a term that will complete the series.

The pattern followed here is, 

→ (2 × 2) + 1 = 4 + 1 = 5

→ (5 × 2) + 2 = 10 + 2 = 12

→ (12 × 2) + 3 = 24 + 3 = 27

Similarly,

→ (27 × 2) + 4 = 54 + 4 = 58

Hence, “58” is a term that will complete the series.

Based on information given,

Using the following symbol:

In J3L9N3O5K

→ J is daughter of L

→ L is sister of N

→ N is daughter of O

→ O is father of K

Hence, “J” is Niece of “K”.

Let Rakhi present age = N years.

Rakhi got engaged 10 years ago → Rakhi Age at the time of engagement = N – 10 years

Rakhi's present age is 5/3 of her age at the time of engagement.

⇒ N = 5/3 × (N – 10)

⇒ 3N = 5N – 50

⇒ 2N = 50

⇒ N = 25

Therefore, present age of Rakhi = N = 25 Years.

If the present age of Rakhi's mother is twice that of present age of Rakhi

Present age of Rakhi’s Mother = 2N

Rakh’s Mother age at the time of Rakhi’s Engagement = 2N – 10 = 2 × 25 – 10 = 40 years.

Hence, “40” years is correct option.

1. SENSE ⇒ Can be formed from the letter of word SUSPENSEFULNESS

2. FUELS ⇒ Can be formed from the letter of word SUSPENSEFULNESS

3. USEFUL ⇒ Can be formed from the letter of word SUSPENSEFULNESS

4. FULLNESS ⇒ Can’t be formed from the letter of word SUSPENSEFULNESS as there is only one ‘L’ in SUSPENSEFULNESS but we need two ‘L’ for form word “FULLNESS”.

"BAD" is written as "7" and "SAP" is written as "9"

With reference to English alphabet,

B = 2; A = 1; D = 4

⇒ BAD = B + A + D = 2 + 1 + 4 = 7

S = 19; A = 1; P = 16

⇒ SAP = S + A + P = 19 + 1 + 16 = 36 = 3 + 6 = 9

Similarly,

B = 2; A = 1; N = 14

⇒ BAN = B + A + N = 2 + 1 + 14 = 17 = 1 + 7 = 8

In the given code language BAN is coded as 8.

Given Equation ⇒ 9 × 3 + 8 ÷ 4 – 7 = 28

After interchanging,

1) × and –

⇒ 9 – 3 + 8 ÷ 4 × 7 = 28

⇒ 5 + 2 × 7 = 28

→ 19 = 28 (LHS ≠ RHS) (False)

2) + and –

⇒ 9 × 3 – 8 ÷ 4 + 7 = 28

⇒ 27 – 2 + 7 = 28

→ 33 = 28 (LHS ≠ RHS) (False)

3) ÷ and +

⇒ 9 × 3 ÷ 8 + 4 – 7 = 28

⇒ 3.375 – 3 = 28

→ 0.375 = 28 (LHS ≠ RHS) (False)

4) × and ÷

⇒ 9 ÷ 3 + 8 × 4 – 7 = 28

⇒ 3 + 32 – 7 = 28

⇒ 28 = 28 (True)

Logic: Multiply operation in place of * but power operation in place of %

4 * 5 % 3 = 8000

⇒ 4 * 5 % 3 = (4 × 5)³ = 20³ = 8000

2 * 3 % 2 = 36

⇒ 2 * 3 % 2 = (2 × 3)² = 6² = 36

Then,

4 * 3 % 3 = ?

⇒ 4 * 3 % 3 = (4 × 3)³ = 12³ = 1728

Logic: Middle number = multiplication of surroundings digit + 1

⇒ (3 × 5 × 2 × 1) + 1 = 31

⇒ (4 × 3 × 2 × 6) + 1 = 145

⇒ (2 × 7 × 5 × 1) + 1 = ?

⇒ 71 = ?

Hence, “71” is the correct answer.

As shown in above diagram there are total 22 triangles.

On drawing a Venn diagram of given statements, 

I. Some Pens are erasers. ⇒ True (as it is shown in above Venn diagram)

II. No pens are erasers. ⇒ False (as pens which are pencils are erasers)

III. Some erasers are pencils. ⇒ True (as it is shown in above Venn diagram) 

Therefore, only conclusion I and III follow.

From first dice we can see that ‘II’ and ‘IV’ are beside of ‘I’

From 2^nd Dice we can see that, ‘III’ and ‘V’ are beside of ‘I’.

Now we can say that ‘VI’ will come opposite to face containing ‘I’.

Pens which are only blue = 19. 

Hence, there are 19 pens which are only blue.

As we can see in the figure shown below, 

The figure of option 3) will complete the question figure.

As we can see in the figure shown below,

Question figure is hidden/embedded in figure 1)

When we open punched sheet of paper, it will appear as shown in below diagram,

Thus, the figure present in option 2) will be the correct answer.

The mirror image of given questions figure is,

Hence, the figure present in option 3) will be the correct mirror image of given question figure.

1. 10, 14, 00, 68, 79 ⇒ B, L, A, N, S

2. 31, 41, 33, 96, 86 ⇒ B, L, A, N, S

3. 44, 20, 42, 88, 59 ⇒ B, L, A, P, D

4) 23, 32, 24, 55, 66 ⇒ B, L, A, N, D

Hence, “**23, 32, 24, 55, 66 “**is the set for the word ‘BLAND’

• Movement along the supply curve takes place when all the factors affecting supply remain constant and only the price changes.
• Therefore, when price increases supply contracts and when price decreases supply expands.

The correct answer is 35 years.

• Trick: Minimum age required for the post of Vice President and President = 35. In Hindi, we call them as UpRashtrapati and Rashtrapati. 35 = Patis in Hindi.
• Articles 63-73 deal with the qualifications, election and removal of Vice-President of India.
• To hold that post one must be at least 35 years of age and not hold any office of profit.

As per Article 32 of Indian Constitution, following writs can be issued

The correct answer is option 1 i.e Bindusara

• Trick: Chandrabindu. A popular term in Hindi.
• Bindusara was the second Mauryan emperor of India.
• He was the son of the dynasty's founder Chandragupta, and the father of Ashoka.
• As per estimates, Bindusara ascended the throne around 297 BCE.
• Bindusara was also known by the name Amritghata.
• To the Greeks, he was known as Amitrochates.
• | Person | Dynasty | Year | | --- | --- | --- | | Chandragupta II | Gupta Empire | c. 375 – c. 415 CE | | Ashoka | Maurya dynasty | Born -304 BC,Died -232 BC | | Bimbisara | Haryanka dynasty | Born -558 BC,Died -491 BC |

The correct answer is The Sayyids.

• The Delhi Sultanate was an Islamic empire based in Delhi that stretched over large parts of the Indian subcontinent for 320 years (1206–1526).
• Five dynasties ruled over the Delhi Sultanate sequentially:
• Mamluk dynasty (1206–1290)
• Khalji dynasty (1290–1320)
• Tughlaq dynasty (1320–1414)
• Sayyid dynasty (1414–1451)
• Lodi dynasty (1451–1526)

Key Points

• The Sayyid dynasty was the fourth dynasty of the Delhi Sultanate, with four rulers ruling from 1414 to 1451.
• Founded by a former governor of Multan, Khizr Khan in 1414 they succeeded the Tughlaq dynasty and ruled the sultanate.
• They were displaced by the Lodi dynasty in 1451.

Additional Information

• Rulers of the Sayyid dynasty
• Khizr Khan (1414-1421 AD)
• Mubarak Khan (1421-1434 AD)
• Muhammad Shah (1434-1445 AD)
• Ala-ud-din Shah (1445-1451 AD)

• Pluto is a dwarf planet in the Kuiper belt, a ring of bodies beyond Neptune. In 2005, Eris, a dwarf planet in the scattered disc which is 27% more massive than Pluto, was discovered.
• This led the International Astronomical Union (IAU) to define the term "planet" formally in 2006, which excluded Pluto from the category of the planet.

The correct answer is Sedimentary Rock.

Key Points

• Calcareous rock: 
• ​Composed primarily of calcium carbonate
• Often formed from the accumulation of marine organisms such as coral and shellfish
• Examples include limestone and marble
• Igneous rock:
• Formed from the solidification of molten magma or lava
• Can be classified as intrusive (formed underground) or extrusive (formed on the surface)
• Examples include granite, basalt, and obsidia
• Metamorphic rock:
• ​​​​Formed from the alteration of existing rock through heat, pressure, or chemical processes
• Often have a layered or banded appearance
• Examples include marble, slate, and gneiss
• Sedimentary rock:
• ​​Formed from the accumulation and compression of sediment such as sand, mud, and organic material
• Often contain fossils and other evidence of past environments
• Examples include sandstone, shale, and limestone

Herb

Key Points

• Herbs are small, non-woody plants.
• They usually have a green and tender stem and may not grow very tall. Herbs are annuals, biennials, or perennials without a significant woody stem above the ground.
• Wheat falls into this category as it is a grass widely cultivated for its seed, a cereal grain which is a worldwide staple food.
• Herbs are known for their culinary, medicinal, and in some cases, aromatic qualities. Wheat being an herb means it's cultivated for the grain it produces
• Botanically, based on the size, plants are classified into 3 types: herbs, shrubs and trees.
• Wheat (Triticum aestivum) belongs to the family Grasses (Poaceae) but falls under the category called Herbs.

Additional Information

 Creepers

• they are plants with thin, long, and tender stems that cannot stand upright on their own.
• They spread horizontally along the soil. In some cases, they may use other structures for support to climb.
• Examples of creepers include watermelon and pumpkin plants.

Shrub

• Shrubs are medium-sized, woody plants taller than herbs and generally smaller than a tree.
• They often have multiple stems and can grow up to 15-20 feet tall.
• Shrubs can be evergreen or deciduous and are commonly seen in gardens and landscapes for decorative purposes.
• Examples include rose plants and lilacs.

Tree

• Trees are large plants with a single woody stem or trunk, capable of growing to a considerable height and size.
• Trees are perennial, meaning they live for several years.
• They have a distinct elevated stem, or trunk, which supports branches and leaves.
• Examples include oak, maple, and pine trees.

• Reptiles are tetrapod animals in the class Reptilia, comprising today's turtles, crocodilians, snakes, amphisbaenians, lizards, tuatara, and their extinct relatives.
• The study of these traditional reptile orders, historically combined with that of modern amphibians, is called herpetology.

The correct answer is Newton.

Key Points

• The SI unit of both weight and force is Newton.
• The SI unit of force is the newton, symbol N. The base units relevant to force are:

Additional Information

• Pascal:
• Pascal (Pa), unit of pressure and stress in the meter-kilogram-second system.
• A Pascal is a pressure of one newton per square meter, or, in SI base units, a kilogram per second square.
• Watt:
• Watt (W) is a unit of power.
• It is defined as a derivative unit of 1 joule per second and is used to determine the rate of energy transfer.
• Joule:
• The SI unit for work and energy is the joule (J), which is equal to the force of a newton exhaled through a distance of one meter (m).

The correct answer is Glass.

• Glass resists the passage of heat through it and is, therefore, an insulator not just of heat but of electricity as well.
• The thermal conductivity of glass is 0.8 W/mK.
• Other examples of thermal insulators are wood, rubber, wax, etc.

Important Points

• The thermal conductivity of a material is a measure of its ability to conduct heat.
• Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity.
• It is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’.
• The reciprocal of this quantity is known as thermal resistivity.

Additional Information

• The thermal conductivity of Aluminium is 205 W/mK.
• The thermal conductivity of Copper is 385W/mK.
• The thermal conductivity of Silver is 429 W/mK.

• ROM (Read Only Memory) is memory containing hardwired and permanent instructions that the computer uses when it boots up, before the system software loads.
• In PCs, the instructions are read from a small program in the ROM, called the BIOS.

The correct answer is Oxidation.

• Rusting is an oxidation reaction.
• The iron reacts with water and oxygen to form hydrated iron oxide, which we see as rust.

iron + water + oxygen → hydrated iron oxide

• The ion that has the positive charge is called a cation eg. Copper ion
• the ion which has the negative charge on it is called as an anion. eg. Sulphate ion
• Secondly, the cation which is positively charged always gets attracted to the cathode (negative electrode), and the anion which is negatively charged get attract towards the anode (positive electrode).
• Al³⁺
• Cu²⁺
• SO₄^2--
• Zn²⁺

• Smog is a kind of air pollution, originally named for the mixture of smoke and fog in the air.
• Classic smog results from large amounts of coal burning in an area and is caused by a mixture of smoke and sulfur dioxide.
• Smog does not contain Chlorine oxide.

Trick: Niti means Planning

The NITI Aayog or National Institution for Transforming India, is a policy think tank of the Government of India, established with the aim to achieve Sustainable Development Goals and to enhance cooperative federalism in India.

• The term "laser" originated as an acronym for "Light Amplification by Stimulated Emission of Radiation".

• Saurashtra Cricket Association Stadium, also known as the Khandheri Cricket Stadium, is a cricket stadium in Rajkot, India.
• It is Gujarat's first solar-powered stadium and hosted its first match on 9^th November 2016.

The correct answer is Virat Kohli.

Key Points

• Polly Umrigar was an Indian cricketer who mostly played first-class cricket.
• It is an annual award given by BCCI.
• The modern-day legend Virat Kohli holds the record for winning the Polly Umrigar award most times in history.
• The former India captain has won the prize record five times - 2011-12, 2014-15, 2015-16, 2017-18, 2018-19.

• The book was published in 2015
• It’s a satire revolving around issues like slavery and legal system of USA
• Paul Beatty is an American author and an associate professor of writing at Columbia University

• This was announced in the India-US joint statement issued at the close of Carter’s (US Secretary of Defense) visit to New Delhi in 2016.
• This means that India and US will work together closely in matters of defense and defense technology sharing.

• The aim of the EKUVERIN exercise was to conduct military training between armies of both countries with emphasis on counterinsurgency, counterterrorism operations.
• The exercise saw its 8^th Edition happen in 2017.

Shortcut Trick

For a number to be divisible by 80, it must be divisible by both 8 and 10.

Divisibility by 10 ⇒ Last digit Y = 0.

Divisibility by 8 ⇒ Last three digits 7X0 must be divisible by 8.

For 7X0, if X = 2, then 720 ÷ 8 = 90 (perfectly divisible).

Minimum X + Y = 2 + 0 = 2.

∴ The correct answer is 2.

Alternate Method

Given: The number is 347XY and it is divisible by 80.

Formula: A number is divisible by 80 if it is divisible by 8 and 10 (where 80 = 8 × 10).

Step 1: Determine Y

⇒ For 347XY to be divisible by 10, the unit digit must be 0.

⇒ Y = 0.

Step 2: Determine X

⇒ The number is now 347X0. For divisibility by 8, the last three digits 7X0 must be divisible by 8.

⇒ Possible values for 7X0: 700, 710, 720, 730, 740, 750, 760, 770, 780, 790.

⇒ 720 ÷ 8 = 90 (Divisible, so X = 2)

⇒ 760 ÷ 8 = 95 (Divisible, so X = 6)

Step 3: Minimum Value

⇒ For minimum X + Y, we take X = 2 and Y = 0.

⇒ X + Y = 2 + 0 = 2.

∴ The correct answer is 2.

Additional Information

Divisibility Rule of 8

A number is divisible by 8 if its last three digits are divisible by 8 or if the last three digits are 000.

Divisibility Rule of 10

A number is divisible by 10 if its units digit is 0.

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, then it is also divisible by their product a × b.

Given:

Time is taken by A to complete a work = 20 days 

Time is taken by B to complete a work = 24 days 

Time is taken by C to complete a work = 30 days 

Formula Used:

Total work = Efficiency × Total time taken

Calculation:

 The  LCM for 20, 24, 30 is (120)

Total work = 120 units

The efficiency of A = 120/20 ⇒ 6 units/day

The efficiency of B = 120/24 ⇒ 5 units/day

The efficiency of C = 120/30 ⇒ 4 units/day

The efficiency of A + B + C = 6 + 5 + 4 ⇒ 15 units/day

The efficiency of B + C = 5 + 4 ⇒ 9 units/day

A, B, C work together for first 4 days = 15 × 4 = 60 units

Remaining work = 120 - 60 ⇒ 60 units

B left the work 6 days before completion

so,C completed the remaining work in last 6 days = 4 × 6 = 24 unit

Middle work = Total work - First work - last work

The B and C complete the work in middle days = 120 - 60 - 24 = 36 units

Time taken by B and C to do the middle days work = 36/9 ⇒ 4 days

Total Time taken to complete the work = 4 + 4 + 6 ⇒ 14 days

∴ In 14 days  the total work completed was completed

Radius of the sphere is 17.5/2 = 8.75

When the sphere is cut into two halves, the curved surface area will stay the same and two additional surfaces will be created which are circular with radius equal to the area of the sphere.

Hence the increase in area will be the increase due to these circular surfaces

Area of each circular surface will be given by = π × (radius)² = π × 8.75 × 8.75 = 240.625

∴ Total increase in area = 2 × 240.625 = 481.25 cm²

Discount = 34% of marketed price

Let marketed price be = M

Discount = 0.34 × M

Selling price = M - Discount = M - 0.34 × M = 0.66 × M

⇒ 0.66 × M = 3168

∴ M = Rs 4800

3P/7 = 4Q/11

By cross multiplication we get

P/Q = 28/33

∴ P : Q = 28 : 33

Average of all 17 results is = 60

Sum of all 17 results = 60 × 17 = 1020

Average of first 9 results = 57

Sum of first 9 results = 57 × 9 = 513

Average of last 9 results = 65

Sum of last 9 results = 65 × 9 = 585

Both sums I.e. of first 9 and last 9 digits include the 9 result

So if we add both sums it will have the 9^th result one extra time and we can subtract the actual sum from this addition to get the 9^th result

So sum of first and last 9 results = 513 + 585 = 1098

∴ The 9^th result will be = 1098 - 1020 = 78

Let cost pric be X

Profit will be = 1.7 × X

Selling price will be = X + 1.7 × X = 2.7 × X

If the cost price is increased by 20%, the new cost price will become = 1.2 × X

New profit will be = Selling price - New Cost price = 1.5 × X

∴ Profit percentage = (1.5 × X ) × 100/1.2 × X = 125%

Let the number be X,

Then 32% of the number is = 0.32 × X

17% of the number will be given as = 0.17 × X

The difference = 0.15 × X = 120

∴ X = 120/0.15 = 800

Let the speed of boat in still water be = B km/hr

Speed of stream = S km/hr

Speed of boat in upstream = B - S = X      ----(a)

Speed of boat in downstream = B + S = Y      ----(b)

Time = Distance / Speed

From condition one

15/ X + 21/2Y = 3 + (15/60) = 3.25 hrs     ----(1)

12/X + 14/Y = 3      ----(2)

Let 1/X = P and 1/Y = Q

Putting in (1) and (2)

15P + 21Q/2 = 3.25      ----(3)

12P + 14Q = 3      ----(4)

Solving (3) and (4)

P = 1/6 and Q = 1/14

Thus means X = 6 and Y = 14

Putting in (a) and (b) and solving for B gives

∴ B = 10

Let the sum lent be P

Simple interest after 15 years at 5% = P × 0.05 × 15 = 0.75 × P

This amount is less than P by Rs 250

Hence P - 0.75 × P = 0.25 × P = 250

∴ P = 1000

$\begin{array}{l} X = \frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }}\ \Rightarrow \frac{1}{X} = \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }}\ \Rightarrow X + \frac{1}{X} = \frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} \end{array}$

⇒ X + 1/X = (2+√3 )² + (2- √3)²

⇒ X + 1/X = 4 + 3 + 4 × √3 + 4 + 3 - 4 × √3

∴ X + 1/X = 14

x = 2 + √3

⇒ 2x = 4 + 2√3

⇒ 2x = 3 + 2√3 + 1 = (√3 + 1)²

⇒ √(2x) = √{(√3 + 1)2} = (1 + √3)

1/√(2x) = 1/√{(√3 + 1)2} = 1/(1 + √3)

Now,

[√(2x) + 1/√(2x)]

⇒ (1 + √3) + 1/[(1 + √3)]

⇒ [(1 + √3)² + 1]/(√3 + 1)

⇒ [1 + 3 + 2√3 + 1]/(√3 + 1)

⇒ (5 + 2√3)/(√3 + 1) × (√3 - 1)/(√3 - 1)

⇒ {5√3 - 5 + 2 × 3 - 2√3}/(3 - 1)

⇒ (3√3 + 1)/2

x + 1/x = 4      ----(1)

Squaring eq (1) both sides, we have

x² + 1/x² + 2 = 16

⇒ x² + 1/x² = 14      ----(2)

Now, again squaring eq (2) on both sides, we have

(x² + 1/x²)² = 14²

⇒ x⁴ + 1/x⁴ + 2 = 196

⇒ x⁴ + 1/x⁴ = 194      ----(3)

Now, again cubing both sides, we have

(x + 1/x)³ = 4³

⇒ x³ + 1/x³ + 3(1 + 1/x) = 64

⇒ x³ + 1/x³ + 3 × 4 = 64

⇒ x³ + 1/x³ = 64 - 12

⇒ x³ + 1/x³ = 52      ----(4)

Multiplying eq (1) and eq (3), we have

(x + 1/x)(x⁴ + 1/x⁴) = 4 × 194 = 776

⇒ x⁵ + 1/x³ + x³ + 1/x⁵ = 776

⇒ x⁵ + 1/x⁵ + 52 = 776

⇒ x⁵ + 1/x⁵ = 776 - 52

⇒ x⁵ + 1/x⁵ = 724

$\begin{array}{l} Y = ;\frac{{2 - X}}{{1 + X}}\ \Rightarrow Y; + ;1; = \frac{3}{{1; + ;X}}\ \Rightarrow \frac{1}{{Y + 1}} = \frac{{X + 1}}{3}; \end{array}$

Now, ${Y^2} = \frac{{\left( {4 + {X^2} - 4X} \right)}}{{1 + {X^2} + 2X}}$

$\Rightarrow {Y^2} - 1 = \frac{{3; - ;6X}}{{{{\left( {1 + X} \right)}^2}}}$

Again, $2Y + 1 = \frac{{4 - 2X}}{{1 + X}} + ;1 = \frac{{4 - 2X + 1 + X}}{{1 + X}} = \frac{{5 - X}}{{1 + X}}$

So, $\frac{{2Y + 1}}{{{Y^2} - 1}} = \frac{{\left( {5 - X} \right)\left( {1 + X} \right)}}{{3 - 6X}}$

$\begin{array}{l} \Rightarrow \frac{1}{{Y + 1}} + \frac{{2Y + 1}}{{{Y^2} - 1}} = \frac{{1 + X}}{3} + \frac{{\left( {5 - X} \right)\left( {1 + X} \right)}}{{3 - 6X}};\ \Rightarrow \frac{1}{{Y + 1}} + \frac{{2Y + 1}}{{{Y^2} - 1}} = \frac{{\left( {1 + X} \right)\left( {2 - X} \right)}}{{1 - 2X}} \end{array}$

There will be two triangles formed here namely ABC and BPC. For triangle ABC, the sum of angles is 180° and one angles is 50°

The sum of remaining two angles will be = 180° - 50 = 130°

Now the sum of all angles of triangle PBC is 180°

Two of these angles are halves of angles ABC and ACB so their sum will be half of angles ABC and ACB = 130/2 = 65°

∴ The third angle is BPC which is = 180 - 65 = 115°

The radius is the perpendicular bisector of the common chord.

The distance is 40 cm and if we join P and Q it will cut the common chord in half and the point of intersection assumed M.

A and B are centres of the two circles

APM and AQM will be two right triangles.

AP = AQ = radius

Using Pythagoras theorem AP² = PM² + AM² = 400 + 15² = 400 + 225 = 625

∴ AP = 25

Given:

∠QRN = 40°, ∠PQR = 46°

Concept Used:

Theorem: The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Calculation:

Using the above theorem,

⇒ ∠RPQ = ∠QRN, ∠PRM = ∠PQR

⇒ ∠X = 40°, ∠Y = 46°

In ΔPQR,

⇒ ∠X + ∠Z + 46° = 180°

⇒ 40° + ∠Z + 46° = 180°

⇒ ∠Z = 94°

∴ The value of ∠X, ∠Y, and ∠Z is 40° , 46° and 94° respectively.

Triangle PRT is formed and sum of its angles is 180 two of its angles PRT and TPR are 54 and 46 respectively so the third angle is 180 - 54 - 46 = 80 degrees.

Since PS = SQ and PST and QST angles are equal and ST is common side so triangles PST and QST are similar and hence all their angles are equal

Angle PTQ = 180 - 80 = 100

Angles PTS and STQ are equal and half of PTQ and = 50

∴ Angle PQR = 180 - 50 - 90 = 40

$\begin{array}{l} \frac{{cotA + tanB}}{{cotB + tanA}}\ \Rightarrow \frac{{\frac{{cosA}}{{sinA}} + \frac{{sinB}}{{cosB}}}}{{\frac{{cosB}}{{sinB}} + \frac{{sinA}}{{cosA}}}}\ \Rightarrow \frac{{cosA;cosB + sinA;sinB}}{{cosA;cosB + sinA;sinB}} \times \frac{{sinB;cosA}}{{sinA;cosB}} \end{array}$

⇒ tanB cotA

Cosec A + Cot A = (1 + Cos A) /sin A

⇒ 1/ (Cosec A + Cot A)² = (Sin A)² / (1 + Cos A)²      ----(1)

⇒ (Sin A)² = 1 - (CosA)² = (1 + Cos A)(1 - CosA)

Putting in (1) we get,

⇒ (1 - cos A) / (1 + cos A)

Given:

Cos2θ – Sin θ = 1/4

Formula Used:

Sin²θ + Cos²θ = 1

Calculation:

Sin2θ + Cos2θ = 1

⇒ Cos2θ = 1 – Sin2θ      ----(I)

Cos2θ – Sin θ = 1/4

⇒ Cos2θ = 1/4 + Sinθ      ----(II)

Comparign equation I and II,

⇒ 1 – Sin2θ =  1/4 + Sinθ 

⇒ 1 – 1/4 = Sin2θ + Sinθ  

⇒ 3/4 = Sin2θ + Sinθ

Let Sinθ be x,

⇒ x² + x = 3/4

⇒ x2 + x – 3/4 = 0

By using options, we get 

⇒ x = 1/2

⇒ Sinθ = 1/2

∴ The value of Sinθ is 1/2.

Shortcut TrickPut θ = 30^o

⇒ cos²30^o - sin 30^o

⇒ (√3/2)² - 1/2

⇒ 3/4 - 1/2

⇒ (3 - 2)/4

⇒ 1/4

⇒ Sin 30^o = 1/2

∴ The value of Sinθ is 1/2.

Key Points

Cos 30^o = √3/2

Sin 30^o = 1/2

So, in 2015 shows the maximum percentage increase in the total number of students in these 4 subjects over the previous year.

Total Number of Students in Arts = 338

Average number of Students in Arts = 67.6

Total number of students in Science = 662

Average students in Science = 132.5

∴ Ratio is 67.6 : 132.5 multiply both by 2.5 = 169 : 331 (Approx)

Total increase from 2012 to 2016 for business students = 48 - 32 = 16

Total percentage increase = 16 × 100/32 = 50%

∴ Annual increase = 50/4 = 12.5%

Common Mistake∶

The increase/decrease has been made in 4 years, not in 5 years.

Hence, the annual increase will be 50/4 = 12.5% not 50/5 = 10%

Total increase in number of commerce students from 2012 to 2016 = 168 - 148 = 20

∴ %age increase = 20 × 100/148 = 13.51%

The correct answer is quarrelling with one another

Key Points

• 'quarrelling with each other' should be there in place of 'quarrelling with one another'
• We use each other when discussing two people or things, and one another when discussing more than two people or things.
  

Examples: The twins told each other everything. 

                   The triplets told one another everything.

• Thus, the correct sentence is: The two men were quarrelling with each other claiming the same watch as their own.

The correct answer is of all other countries

Key Points

• 'of all countries in the world' should be there in place of 'of all other countries in the world'
• The superlative 'the most peaceful' is mentioned. The superlative degree of an adjective is used when we don't compare.
• So, when the sentence says, 'Bhutan is the most peaceful of all other countries in the world', then there is no comparison between 'Bhutan' and 'all other countries of the world'.
  

Correct Sentence must be: Everybody knows that Bhutan is the most peaceful of all countries in the world​.

The sentence takes place in the present and presents a conditional argument. Therefore, Options 1, 3 and 4 cannot be used because they are in past or past continuous tenses which will make the sentence meaningless. The correct option to the blank would be ‘becomes’ because 'it' is the third person pronoun and for third person pronoun the verb we should  use in the form of verb+s form.

Option 2 cannot be used because it does not make much sense to the sense. ‘Till’ cannot be used in the blank as  it is used to define an ending period and the statement clearly states a starting period and not the ending period. Now, since a definite time period is mentioned in the sentence, it would be more appropriate to use ‘since’ than ‘for’ in the blank. 

I’ve been working in a bank ever since I left school.

The correct answer is Option 3

‘Opulent’ means 'much costly and luxurious' which is a synonym of ‘rich’. 

The word ‘fake’ is not similar to opulent because it refers to something fraudulent or incorrect.

’Gloomy’ refers to something dark which is not relevant either.

’Selfish’ means lacking consideration for other people. Therefore, the correct option is ‘rich'.

The word ‘morose’ means sullen and ill-tempered.

‘Flatter’ means to attract someone's attention by lavishly praising them to further one's cause.

‘Savvy’ is referred to someone who possesses good knowledge and is practical.

Hence, the correct option is 2.

‘Irk’ means to irritate. The opposite of ‘irk’ then would be to ‘please’. Hence the correct option is ‘please’. ‘Irritate’ is synonymous to ‘irk’ while ‘discourage’ means to lower a person’s morale which is not the opposite of ‘irk’.

Grotesque means distortion or malformation. Free and Odd do not have any relation, whatsoever, to the word grotesque. ’Queer’ is also synonymous to odd and hence can be easily eliminated as an answer. The correct option, that is the option totally opposite to the word ‘grotesque’ is ‘plain’

The idiom “To  keep the wolf from the door” means to maintain oneself at a minimum level. From the given options, “Avoid starvation” is a condition where one keeps himself to a level just to avoid himself from starvation. Therefore, option 1 is correct. The rest of the options are totally different. 

In a sentence, it could be used as-’We have small amount of ration left at the ISS,hardly enough to keep the wolf at the door.’

The correct answer is Problems at the start of a new project

Key Points

• “Teething problems” literally means problems at the start of a new project just like when a baby faces a problem when it is teething.
• In a sentence, it could be used as- "The startup is going through teething problems”.
• Therefore, options 1, 3, and 4 are totally incorrect.

The correct answer is nor did I

Key Points

• So + auxiliary + subject is added to a positive statement to express agreement, and neither/nor + auxiliary + subject is added to a negative statement for the same purpose.
  

Examples:

• I suggested that he should take the job, and so did all his friends. (his friends also suggested that he should take the job)
• Everybody knows that, and so should you. (you should know that, too)
• "I love South Korean films." "Really? So do I." (I also love South Korean films)
• "I am not going to Andy's party tonight." "Neither/nor is Susan." (Susan isn't going either)
• "My family have never been on a holiday abroad." "Neither/nor have mine." (my family haven't been either)

​Thus, the correct sentence is: She did not like to have coffee nor did I.

The correct answer is 'a monument worth seeing'

Key Points

• According to grammar, 'worth' is an adjective, 'seeing' is a gerund, and 'monument' is a noun. In the given sentence, the main noun for which the adjective is used is 'seeing'.
• 'worth' is always followed by a gerund.
• Here article 'a' is placed before the blank, so monument should come before worth.
• Also, adjectives should be used in an attributive manner i.e. 'A/An + Adjective + Noun.'
• Let's see an example-
• We have got some players talented enough.

So the correct sentence is- Taj Mahal is a monument worth seeing in Agra.

The correct answer is Incorrigible

Key Points

• Impregnable means unable to be broken or defeated.
• Immolation means the sacrifice of someone or something.
• Incorrigible means something which cannot be corrected.
• Ineligible means someone who is not qualified.
• By the above definitions, the correct option is 3

The correct answer is Scapegoat

Key Points

• Bursar is a person who manages the financial affairs of a college or school.
• A captor is a person who catches others.
• Phlegmatic is the kind of person who is unemotional.
• A scapegoat is a person who is blamed for all the ill-doings of others.
• From the above definitions, the correct option is 4.

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

Key Points

• The word "Neice" is incorrectly spelt. The correct spelling is "Niece". (भतीजी या भांजी)
• Example: My niece is coming to visit us this weekend.
• "Niece" refers to a daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. (भतीजी या भांजी)
• Example: She bought a beautiful dress for her niece's birthday.

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

Additional Information

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

• Conceive (गर्भ धारण करना): Form or devise (a plan or idea) in the mind.
• Example: She was unable to conceive a child naturally.
• Leisure (अवकाश): Free time when one is not working or occupied; free time activities.
• Example: In her leisure time, she enjoys reading books.
• Reign (शासन): The period during which a sovereign rules.
• Example: The king's reign lasted for over 40 years.

The correct answer is option 1

Key Points

• Dictionary is the correct spelling of the first option which was misspelt as “Dictionory”. Rest all the provided options are correct in their spellings and have a meaning. 
• ​Dictionary: A dictionary is a book in which the words and phrases of a language are listed alphabetically, together with their meanings or their translations in another language.
• Irrelevant: If you describe something such as a fact or remark as irrelevant, you mean that it is not connected with what you are discussing or dealing with.
• Perishable: Goods such as food that are perishable go bad after quite a short length of time.
• Tangible: If something is tangible, it is clear enough or definite enough to be easily seen, felt, or noticed.

The correct answer is QSRP

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 Q will be the first sentence because the sentence 'One dull dark day in autumn​...' is the starting of an incident.
• Part S will be the next in sequence. It mentions the further incident.
• Part R will be the next in sequence as it mentions whose house was it.
• Part P will be the last in sequence. It mentions the last time they had seen each other.