SSC CGL Previous Paper (Held On: 9 August 2017 Shift 3) (Previous Year Paper)

In the case of two dices, we’ll write the face of dices in the anticlock wise direction starting from N,

Hence, we can say that face ‘Q’ will be opposite to face ‘B’.

Pearl Towers is taller than Sky Towers but shorter than Unity Towers,

Unity Towers > Pearl Towers > Sky Towers

Unity Towers and Cyber Towers are of the same height,

Unity Towers = Cyber Towers

Pearl Towers is shorter than Indus Towers,

Pearl Towers < Indus Towers

The possible final arrangement:

Cyber Towers = Unity Towers > Indus Tower > Pearl Towers > Sky Towers

Or

Indus Tower > Cyber Towers = Unity Towers > Pearl Towers > Sky Towers

Hence, in both cases, 'Pearl Towers' will be the second shortest.

Hence, answer is option 4.

Hence, the given question figure is embedded in option 4.

The pattern followed in 5: 130,

5³ + 5 = 130

The same pattern will be followed for 6,

6³ + 6 = 222

Hence, the answer is 222.

54 + 162 – 18 × 12 ÷ 6 = ?

On replacing symbols:

→ 54 ÷ 162 × 18 + 12 – 6

→${54} \over162$ × 18 + 12 – 6

→ 6 + 12 – 6

→ 12

Hence, answer is 12.

Pattern followed in JPC : GMZ,

J – 3 = G, P – 3 = M, Z – 3 = C

Same pattern will be followed for PUV,

P – 3 = M, U – 3 = R, V – 3 = S

Hence, answer is MRS.

1. 351 → 3 + 5 + 1 → 9

2. 345 → 3 + 4 + 5 → 12

3. 243 → 2 + 4 + 3 → 9

4. 432 → 4 + 3 + 2 → 9

Here, sum of digits of all numbers is 9, except 345.

Hence, the answer is 345.

The least possible Venn Diagram for the given statements is as follow,

(I). No cup is a shop → true.

(II). No shop is a plate → true.

Hence, both given conclusions follow.

1. ‘Quick’ and ‘Fast’ are synonyms.

2. ‘Lazy’ and ‘Slow’ are synonyms.

3. ‘Credible’, is an antonym of ‘Deceptive’.

4. ‘Exhaust’ and ‘Tired’ are synonyms.

Hence, the odd pair is ‘Credible : Deceptive’.

Pattern followed here is,

C + 2 → E + 2 →G,

I + 2 → K + 2 → M,

O + 2 → Q + 2 → S

Same pattern will be followed for next term,

1. U + 2 → W + 2 → Y

2. U + 4 → Y – 1 → X

3. U + 1 → V + 3 → Y

4. T + 3 → W + 2 → Y

 Hence, next letters in the series will be UWY.

The pattern followed here is,

Figure 1:

→ 3 × 4 + 2 × 5 = 22

Figure 2:

→ 2 × 1 + 7 × 6 = 44

Same will be followed for figure 3,

→ 7 × 8 + 5 × 2 = 66

 Hence, the missing number in the diagram is 66.

According to question,

People who speak only in Italian = 7

People who speak only in French = 14

So, Total number of people = 7 + 14 = 21

Hence, 21 people can speak in Italian and French.

Hence, the correct option is 1.

Hence, the unfolded figure will appear as option 2.

Dictionary order of the given words is as follows,

4. Gap
5. Glade
6. Glitch
7. Globe
8. Group

Hence, the dictionary order for the given 45312.

An ammeter (from Ampere Meter) is a measuring instrument used to measure the current in a circuit. 

Same way, an anemometer is a device used for measuring the speed of the wind.

Hence, the answer is Anemometer : Wind.

1. 42, 03, 89, 13 → S, Q, A, R.

2. 11, 40, 65, 02 → S, T, A, T.

3. 04, 32, 96, 32 → S, R, A, R.

4. 30, 21, 77, 44 → S, T, A, R.

Hence, STAR is represented by ’30, 21, 77, 44’.

The pattern followed here is,

7 × 2 + 5 → 19 × 2 + 4 → 42 × 2 + 3 → 87 × 2 + 2 → 176

Hence, the next term in the series will be 176.

The pattern followed here is,

(3)2 @ 1 * 7 = 98

→ (3)² × 10 + (1 + 7) = 90 + 8 = 98

(4)2 @ 2 * 16 = 178

→ (4)² × 10 + (2 + 16) = 160 + 18 = 178

Similarly,

(5)2 @ 3 * 9

→ (5)² × 10 + (3 + 9) = 250 + 12 = 262

Hence, the answer is ‘262’.

Triangles in the given figure as follow,

→ AGB, BFG, GFC, ABC, CGH, HEG, DEG, DGC, ECG, DGH, ADG, ABD, BCD,BGC,ACD

Alternate solution:

Hence, there are 15 triangles in the given figure.

Hence, the mirror image of the given figure will be as option 3.

The code followed for MATCH and BOARD is as follow,

The same pattern will be followed to write “PRINT”,

Hence, PRINT will be coded as QPLJY.

1. Raise → LEGISLATOR → can be formed.

2. Gist → LEGISLATOR → can be formed.

3. Legal → LEGISLATOR → can be formed.

4. Greater → LEGISLATOR → cannot be formed as there is no letter "E,R".

Hence, Greater cannot be formed.

1. C + 1 = D

2. P + 2 = R

3. S + 1 = T

4. W + 1 = X

Hence, the odd pair is PR.

Present age of A = 2B (twice of B, given)

If C celebrated his fifth birthday 9 years ago, (given)

→ Present age of C = 9 + 5 = 14 years

(B + 8) = 4 × 14 (present age of C)

→ B + 8 = 56

→ B = 48 years

Present age of A = 2 × 48 = 96 years

Hence, the present age od A is 96 years.

Sidi Bashir Mosque in Ahmedabad, Gujarat is a former mosque which is also known as the Jhulta Minar or Shaking Minarets. Surviving remains consist of the central gateway and two minarets.

This mosque is believed to be built by either Sidi Bashir (a slave of Ahmed Shah) or by Malik Sarang (a noble in the court of Mahmud Begada) in 1452.

The SI unit of frequency is Hertz (Hz), named in the memory of the 19^th –century German physicist Heinrich Hertz. One hertz means that an event repeats once per second.

Sanjeev Kapoor was awarded Padma Shri 2017 for his culinary contributions. However, the Padma award lists don’t include a separate category for food. So, Sanjeev Kapoor is listed under the Others-Culinary category.

Japan has launched a spy satellite due to North Korea’s increased missile and nuclear programs. A spy satellite, the Radar 5 unit was carried into space on Japan’s mainstay H-IIA rocket. This spy satellite replaced the existing satellite which is approaching the end of its mission.

The correct answer is ​President.

Key Points

Indian Armed Forces:

• The military forces of the Republic of India.
• It consists of three professional uniformed services: the Indian Army, Indian Navy, and Indian Air Force.
• Supported by the Indian Coast Guard and paramilitary organizations (Assam Rifles, and Special Frontier Force) and various inter-service commands and institutions such as the Strategic Forces Command, the Andaman and Nicobar Command, and the Integrated Defence Staff.
• The President of India is the Supreme Commander of the Indian Armed Forces. So, Option 1 is correct.
• Under the management of the Ministry of Defence (MoD).

• ‘The World Outside My Window’ is written by Ruskin Bond, an Indian author of British descent.
• In this book, Ruskin Bond writes about some of the most interesting insects, birds, trees, and flowers he has observed.
• Ruskin Bond was awarded the Sahitya Akademi Award in 1992 for ‘Our Trees Still Grow in Dehra’ in English.
• He was awarded the Padma Shri in 1999 and Padma Bhushan in 2014.

India’s electronics good import is the third largest import item for the country and to tackle this situation, the central government launched Modified Special Incentive Package Scheme (M-SIPS) in 2012. This scheme is launched to encourage investment and production in the domestic electronic goods sector.

This scheme was modified in 2015, 2016 and 2017.

Banaras Hindu University was established by the ‘B.H.U. Act 1915’ in 1916. Madan Mohan Malaviya was the founder of Banaras Hindu University. He was also the Vice-Chancellor of BHU from 1919-1938.

The correct answer is China.

Key PointsChina and India have a land dispute near Tawang in which China especially claims Tawang and other 8 to 10 disputed “hotspot” areas along the Arunachal Pradesh Border.

Some of the disputed areas in Tawang are Namka Chu river valley, Sumdorong Chu, Yangste, and Khizemane.

• The cells of connective tissue are separated from each other and the space between the cells contain matrix. Connective tissues join and support various parts of the body. Cartilage, Bone, and Blood tissues are examples of connective tissues.
• Skin is an example of epithelial tissue.

When a chemical element is present in one or more forms in the same physical state then it is known as allotrope. Swedish scientist Jons Jakob Berzelium proposed the concept of allotropes in 1841.

Ozone (O₃) is an allotrope of oxygen. It is more soluble than oxygen in the water.

Ozone is used for air purification at the crowded places. It is also used in sterilizing drinking water as it oxidizes all germs and bacteria.

An inert gas is a gas that has extremely low reactivity with other substances. The term inert means non-reactive.

Inert gases are also known as noble gases which are placed in group 18 of the periodic table. Inert gases are Helium, Neon, Argon, Krypton, Radon, and Xenon.

• Pedalfer soil is composed of aluminium and iron oxides. This type of soil is usually found in humid areas.
• Pedalfers have three subdivisions of which one is Lateritic soils.

• Bilateral monopoly is a market structure where there is only one buyer (monopsony) and one seller of a product (monopoly).
• When a labor union (monopoly in the supply of labor) faces a single large employer in an industrial town (a monopsonist), it would be an example of a bilateral monopoly.

Clarence Birdseye invented a quick-freezing method in 1924 which is responsible for the modern frozen-food industry. This freezing method produces the type of frozen foods that we know today.

Convex mirror is also known as the diverging mirror and the image of the object formed by this mirror is always virtual. The image formed by the mirror is smaller than the size of the object.

Convex mirror is used in sunglasses, as a rear view mirror in vehicles, magnifying glasses, and in telescopes.

Red Data Book is a public document which contains the data of endangered and rare species including animals, plants, fungi as well as some local subspecies present in the country.

It was published by the International Union for Conservation of Nature. This book is responsible for the evaluation of the total number of wild animals present, identification of all animals and birds and their extinct species.

Regional Rural Banks were established under the provisions of RRB Act 1976. These banks were established to provide sufficient banking and credit facility for agriculture and other rural sectors.

Regional Rural Banks are sponsored by any commercial bank, PSU or private bank. The central government, sponsor bank, and state government have share capital in the ration of 50:35:15.

• The second Battle of Tarain was fought between the army of Mohammed Ghori and Rajput army of Prithviraj Chauhan in 1192 CE. Prithviraj Chauhan was defeated by Mohammed Ghori.
• This battle is regarded as the turning point in India’s history which finally led to the foundation of Delhi Sultanate in 1206 CE.

Explanation:

• Red rot is the disease of sugarcane. It is one of the most severe of the known diseases of sugarcane. It was first described from Java by Went in 1893.
• Pathogen: Colletotrichum falcatum Went
• Host: Saccharum officinarum Sugarcane
• Symptoms:

1. Fruit - extensive mould, lesions: black or brown
2. Leaves - abnormal colours, abnormal patterns, necrotic areas
3. Stems - canker on the woody stem, dieback, discoloration of bark

Additional Information

Modifier keys are those which are used to enter keyboard shortcuts. When another key is pressed with a modifier key, it modifies the action. Shift, Alt, Control, Command, Function, and Option are the common modifier keys.

• Anti-defection law was introduced by the 52^nd Amendment in 1985 during the tenure of Rajiv Gandhi. It is given in the Tenth Schedule of the Constitution.
• This law enables the disqualification of legislators on the ground of defection which finally provides a stronger grip to the political parties on their members.

To simplify the expression : {1/[(1/cosA) + (sinA/cosA)]}²

⇒ [cosA/(1 + sinA)]²

⇒ cos²A/(1 + sinA)²

⇒ 1 - sin²A/(1 + sinA)²

⇒ (1 – sinA)(1 + sinA)/(1 + sinA)²

⇒ (1 – sinA)/(1 + sinA)

Given: The speed of 2 trains = 43 km/hr and 51 km/hr

Relative velocity of one train w.r.t. another = (51 - 43)km/hr = 8 km/hr

Relative velocity in m/s = 8 × (5/18) m/s

⇒ Distance covered by the train in 72 sec = 8 × (5/18) × 72 = 160

Since, this is the distance covered in crossing the man

Hence, the length of faster train = 160 m

In ∆ABC

⇒ ∠ABC + ∠BAP + ∠BCP = 180°

⇒ 90° + 50° + ∠BCP = 180°

⇒ ∠BCP = 40°

Now, in ∆BPC

⇒ ∠PBC + ∠BCP + ∠CPB = 180°

⇒ ∠PBC + 40° + 90° = 180°

⇒ ∠PBC = 180° – 130° = 50°

∴ the correct option is 3)

Volume of the cone = (1/3) π r² h = (1/3) π (8)² (24)

Volume of solid cylinder = π r² h = π (6)² (6)

Material wasted = Volume of the cone - Volume of solid cylinder

⇒ Material wasted = (1/3) π (8)² (24) - π (6)² (6)

⇒ % of Material wasted = {[(1/3) π (8)² (24) - π (6)² (6)] / (1/3) π (8)² (24)} × 100

⇒ [π (8)³ - π (6)²] / π (8)³] × 100

⇒ [(512 – 216) / 512] × 100

⇒ 57.8%

∴ the correct option is 3)

For second show,

Number of audience in screen 3 = 7 × 100 = 700      ……..(i)

Number of audience in screen 1 = 3 × 100 = 300      ……..(ii)

⇒ required value = (i) – (ii) = 700 – 300 = 400

∴ the correct option is 3)

Given:

Sandy and Mandy do (8/13)^th part of a work.

The rest of the work was completed by Andy.

Sandy, Mandy and Andy take the same work for Rs 2600.

Formula used:

W = E × T     Where, W = Work, E = Efficiency, and T = Time

Calculation:

Let the amount of total work be a

Work done by Sandy and Mandy = 8a/13

Work done by Andy = a – 8a/13 = 5a/13

Total amount of money taken by the 3 people = Rs. 2600

⇒ Andy’s share = 2600 × [(5a/13)/a]

⇒ Andy’s share = Rs. 1000

∴ The share (in Rs) of Andy is 1000.

Given : (x² – 9) is a factor of the given expression

⇒ x = 3, - 3

Putting values of x = 3, -3 in the given expression

We get,

⇒ p(3)³ – 2(3)² – q(3) + 18 = 0 and p(-3)³ – 2( -3)² – q(-3) + 18 = 0

⇒ 27p – 3q – 18 + 18 = 0 and -27p – 18 + 3q + 18 = 0

⇒ 27p = 3q

⇒ p/q = 1/9

∴ the correct option is 1)

Here, every 3 digit number would need 3 presses and every 4 digit number would need 4 presses

⇒ 3 digit numbers from 121 to 999 = 999 – 121 + 1 = 879

⇒ 4 digit numbers from 1000 to 1346 = 1346 – 1000 + 1 = 347

So, total number of presses = (879) × 3 + 347 × 4 = 2637 + 1388

⇒ 4025

∴ the correct option is 4)

In ∆BCE

⇒ ∠CBE + ∠BEC + ∠ECB = 180°

⇒ ∠ECB = 180° – 2(84°) [ISOSCELES ∆]

⇒ ∠ECB = 12°

Now, we know that

⇒ ∠ADC + ∠DCB = 180° [ANGLES BETWEEN PARALLEL LINES]

⇒ ∠DCB = 180° - 78°

⇒ ∠DCB = 102°

So, ∠DCE = ∠ECB + ∠DCB

⇒ ∠DCE = 12° + 102°

⇒ ∠DCE = 114°

Since, BC = CE = DC [SIDES OF RHOMBUS ARE EQUAL]

In ∆DCE

⇒ ∠DCE + ∠CED + ∠EDC = 180°

⇒ ∠CED + ∠EDC = 180° - 114°

⇒ 2(∠DEC) = 66°

⇒ ∠DEC = 33°

∴ the correct option is 3)

To simplify the expression: (cosec⁴A – cot²A) – (cot⁴A + cosec²A)

[Identity used: 1 + cot²A = cosec²A]

⇒ cosec⁴A – cot⁴A – cot²A – cosec²A

Since, cosec⁴A = 1 + cot⁴A + 2 cot²A, we have

⇒ 1 + cot⁴A + 2 cot²A – cot⁴A – cot²A – cosec²A

⇒ 1 + cot²A – cosec²A

⇒ cosec²A - cosec²A

⇒ 0

∴ the correct option is 1)

Total number of people in second show = (3 + 4.5 + 7) × 100 = 14.5 × 100 = 1450

Total number of people in third show = (6 + 4 + 7.5) × 100 = 17.5 × 100 = 1750

Percentage increase = (1750 – 1450)/1450

⇒ 300/1450 = 20.69

∴ the correct option is 1)

Number of audience in Screen 1 from second show = 3 × 100 = 300

Number of audience in Screen 1 from third show = 6 × 100 = 600

Percentage increase = [(600 – 300) / 300] × 100 = 100%

∴ the correct option is 2)

Average of 11 numbers = 7

⇒ Sum of all the numbers = 11 × 7 = 77

⇒ If every number is doubled, the total sum will also double

⇒ Sum of all the new numbers = 77 × 2 = 154

Average of new numbers = 154/11 = 14

∴ the correct option is 4)

Given: x² – x – 6 is a factor of the given expression

So, roots of x² – x – 6 will also be the roots of the expression

⇒ x² – x – 6 = x² – 3x + 2x – 6

⇒ x(x – 3) + 2(x – 3)

⇒ (x + 2) (x – 3)

So, x = - 2,3 are the roots of px³ – qx² – 7x – 6

Putting x = - 2,3 in the expression, we should get the value equal to 0

⇒ p( - 2)³ – q( - 2)² – 7( - 2) – 6 = 0 and p(3)³ – q(3)² – 7(3) – 6 = 0

⇒ - 8p - 4q + 14 – 6 = 0 and 27p – 9q – 21 - 6 = 0

⇒ 8p + 4q = 8 and 27p – 9q = 27

Solving both the equations, we get

⇒ p = 1, q = 0

∴ the correct option is 2)

Let the cost price of the article = Rs. a

⇒ So, the actual selling price = a + (20/100)a = Rs. 1.2a

If he bought the article at 60% less price

⇒ Cost price would have been = a – (60/100)a = Rs. 0.4a

⇒ Selling price that would have been = Rs. 1.2a – 90

⇒ Gain % would have been = 50%

⇒ [(1.2a – 90) – 0.4a] / (0.4a) = 50/100

⇒ (1.2a – 90) – 0.4a = 20a/100

⇒ 0.8a – 90 = 0.2a

⇒ 0.6a = 90

⇒ a = 150

∴ the correct option is 1)

Join OA where OA = 10 cm

Here, AO is perpendicular to AB

⇒ Area of ∆ABC = Area of ∆OAB + Area of ∆AOC

⇒ Area of ∆ABC = 1/2(OA)(AB) + 1/2(OC)(OA)sin(∠AOC)

⇒ Area of ∆ABC = 1/2(10)(24) + 1/2(10)(10) sin(∠AOC)

⇒ Area of ∆ABC = 120 + 50 sin(∠AOC)

In right angled ∆OAB

⇒ tan(∠AOB) = 24/10 = 12/5

⇒ ∠AOB = 67.38°

So, ∠AOC = 180° – 67.38° = 112.62°

Hence, Area of ∆ABC = 120 + 50 (0.93) = 120 + 46.15 = 166.15

∴ The area (in cm2) of triangle ABC is 166.15.

In the triangle Δ OAB, Δ OAB is right angled triangle

OA is perpendicular to the AB

⇒ SinB = OA/OB = 10/26

⇒ 5/13

In triangle Δ ABC

⇒ (1/2)× AB × BC SinB

⇒ (1/2)× 24 × 36 × (5/13)

⇒ 166.15

∴ The area (in cm2) of triangle ABC is 166.15.

Given: 4^{(x + y)} = 256

 ⇒ 4^{(x + y)} = 4⁴

Since, bases are equal we can equate powers

⇒ x + y = 4        ----(i)

Given: (256)^{(x - y)} = 4

⇒ (4⁴)^{(x - y)} = 4

⇒ 4(x – y) = 1       ----(ii)

Putting x = 4 - y in (ii)

⇒ 4(4 – y – y) = 1

⇒ 4(4 – 2y) = 1

⇒ 4 – 2y = 1/4

⇒ 2y = 4 – 1/4

⇒ 2y = 15/4

⇒ y = 15/8

Putting y = 15/8 in (i)

⇒ x = 4 – 15/8 = 17/8

∴ the correct option is 1)

Given,

(x + 1/x) = 5

Squaring both sides

⇒ (x + 1/x)² = 25

⇒ x² + 1/x² = 25 – 2 = 23       ----(i)

Again, doing cubes of both sides

⇒ (x + 1/x)³ = 125

⇒ x³ + 1/x³ = 125 – 3(5) = 110      ----(ii)

By (i) and (ii)

⇒ (x² + 1/x²)( x³ + 1/x³) = 23 × 110 = 2530

⇒ x⁵ + (x + 1/x) + 1/x⁵ = 2530

⇒ x⁵ + 1/x⁵ = 2530 – 5

Required value: x⁵ + 1/x⁵ = 2525

Trick: 

If x + 1/x = k then the value of x⁵ + 1/x⁵ will always be equal to (k⁵ – 5k³ + 5k)

Here k = 5

x⁵ + 1/x⁵ = k⁵ – 5k³ + 5k = 5⁵ - 5 × 5³ + 5 × 5 = 2525

∴ Answer is 2525

Let the Principal be P, rate of interest be R and time be T

After 2 years

⇒ A = P + (P × R × T)/100

⇒ 918 = P + (P × R × 2)/100

⇒ 91800 = P + (2PR)/100

⇒ 918 = P(1 + 2R/100)       …….(i)

After 3.5 years

⇒ A = P + (P × R × T)/100

⇒ 969 = P + (P × R × 3.5/100)

⇒ 969 = P(1 + 3.5R/100)       …….(ii)

Dividing (i) and (ii)

⇒ 969/918 = (1 + 3.5R/100)/ (1 + 2R/100)

⇒ 969 + 1938R/100 = 918 + 3213R/100

⇒ 51 = 1275R/100

⇒ R = 4

So, rate of interest = 4%

∴ the correct option is 1)

Number of audience in screen 1 = (5 + 3 + 6) × 100 = 1400

Number of audience in screen 2 = (6 + 4.5 + 4) × 100 = 1450

Number of audience in screen 3 = (6.5 + 7 + 7.5) × 100 = 2100

Total revenue of screen 1 = 350 × 1400 = Rs. 490000

Total revenue of screen 2 = 300 × 1450 = Rs. 435000

Total revenue of screen 3 = 250 × 2100 = Rs. 525000

⇒ Maximum total revenue is of screen 3

∴ the correct option is 4)

$\left( {\frac{2}{{cot\frac{A}{2}; + ;tan\frac{A}{2}}}} \right)$

⇒ {2/ [cos² (A/2) + sin²(A/2) / {(sin(A/2) cos(A/2)}]}

⇒ {2/ [1/ (sin(A/2) cos(A/2)]}

⇒ 2sin(A/2) cos(A/2)

⇒ sin A

∴ the correct option is 1)

Let the total amount of sugar be a kgs

⇒ So, total selling price = Rs. 42a

Since the profit here is 20%

⇒ Cost price = 42a / (1 + 20/100)

⇒ Cost price = Rs. 35a

Let the amount of Rs 30/kg sold be b

Then, the amount of Rs 45/kg sold be a – b

⇒ 30b + 45(a - b) = 35a

⇒ 30b + 45a – 45b = 35a

⇒ 10a = 15b

⇒ b = 2a/3

Required ratio = b/(a - b) = (2a/3) / (a/3) = 2/1

Given: 2 successive discounts of 20% and 30%

Let a be the Principal value

⇒ Amount after 1^st discount = a – (20/100)a = 0.8a

⇒ Amount after 2^nd discount = 0.8a - 0.8a × (30/100)a = 0.56a

So, net discount = a – 0.56a = 0.44a

⇒ % net discount = (0.44a / a) × 100 = 44%

∴ the correct option is 2)

Let the total income of Amit be Rs. a

⇒ Amount donated to school = a × (20/100) = 0.2a

⇒ Remaining amount left with Amit = a – 0.2 = Rs. 0.8a

⇒ Amount deposited in the bank = 0.8a × (20/100) = 0.16a

⇒ Total remaining amount left with Amit = 0.8a – 0.16a = 0.64a

Now, 0.64a = 12800

⇒ a = 20000

So, the total income of Amit is Rs. 20000

∴ the correct option is 2)

Shortcut Trick

We know that the excenter of the triangle is the location where the bisectors of one internal angle and bisectors of two exterior angle bisectors of the opposite side of the triangle connect.

Here, O is the excenter

So, 90° - 1/2 (Opposite Angle) = Excenter angle

⇒ 90° - 1/2 × ∠QPR = ∠QOR

⇒ 90° - 1/2 × ∠QPR = 50°

⇒ ∠QPR = 2 × (90° - 50°) = 2 × 40° = 80°

Alternate Method

In ∆PQR

⇒ ∠QPR + ∠PRQ + ∠RQP = 180°

Now,

⇒ ∠QPR + (180 – 2 × ∠OQR) + (180 – 2 × ∠ORQ) = 180°

⇒ ∠QPR + 180 – 2 × ∠OQR + 180 – 2 × ∠ORQ = 180° (i)

In ∆OQR

⇒ ∠OQR + ∠QRO + ∠ROQ = 180°

⇒ ∠OQR + ∠QRO° = 180 - 50° = 130°

Multiplying by 2

⇒ 2(∠OQR + ∠QRO°) = 260° (ii)

Substituting (ii) in (i)

⇒ ∠QPR + 360° – 260° = 180°

⇒ ∠QPR = 80°

∴ the correct option is 3)

The correct answer is ‘Nemesis’

Nemesis means ‘a downfall caused by an inescapable agent.’

Hence, it is the closest in meaning to the given phrase and is the correct one-word substitute.

The other options,

Dandy means ‘excellent’

Prodigy means ‘an outstanding example of a particular quality’

Wagon means ‘a vehicle used for transporting or another purpose’.

The correct answer is ‘Drowsy’.

Lethargy means ‘a lack of energy or enthusiasm’

Drowsy means ‘sleepy or lethargic’.

Hence, the two words have similar meanings.

The other options,

Activity means ‘busy or vigorous action or movement’

Modest means ‘humble’

Pleasure means ‘a feeling of happy satisfaction and enjoyment’.

The correct answer is ‘The old lady was being laughed at by the kids.’

Sentence 1 changes the meaning completely and is incorrect.

Sentence 3 removes ‘at’ and thus, the meaning changes, making the sentence incorrect in the Passive voice.

Sentence 4 changes the tense and removes the continuous part (laughing), making it incorrect.

Only Sentence 2 retains the meaning the sentence and accurately converts the Active voice to the Passive voice.

The correct answer is ‘minimal’.

Minimal means of a minimum amount or negligible.

It fits with the context of the sentence as it means that the executive needs to have the least interference in the appointment of judges as per the Supreme Court’s last advisory opinion.

Hence, it is the correct word for the given blank.

The correct answer is ‘welcomed’.

Welcome means react with pleasure or approval to an event.

It fits with the context of the sentence as it means that the opinion of the least interference is received with approval.

Hence, it is the correct word for the given blank.

The correct answer is ‘QSRP’

The first sentence is Q, as it introduces ‘courage’.

It is followed by S, as it follows on the ‘feedback’ chain.

Then comes by R, followed by P, which talk about the ‘comfort zone’ and ‘frame of mind’.

Hence, the correct combination is QSRP, as seen in Option 1.

The correct answer is ‘To have a selfish motive’

The phrase ‘an axe to grind’ means ‘To have a personal motivation or selfish reason for saying or doing something.’

Hence, Option 3 has the closest meaning to the given phrase and is the correct answer.

An example sentence is:

‘The manager had no axe to grind and wanted the best for his employees’.

The correct answer is ‘Calm’

Trepidation means ‘a feeling of fear or anxiety’

Calm means ‘not showing or feeling strong emotions’.

Hence, the two words have opposite meanings.

The other options,

Bawdy means 'humorously indecent'.

Fear means ‘unpleasant emotion caused by the threat of danger’

Violent means ‘brutal or hurtful’

The correct answer is ‘vital’.

Vital means absolutely necessary or essential.

It fits with the context of the sentence as it says that the process of appointing judges is of essential importance.

Hence, it is the correct word for the given blank.

The correct answer is ‘To die’.

The phrase ‘kick the bucket’ means ‘to die’.

Hence, Option 3 has the exact meaning as the given phrase.

An example sentence is:

‘He was too young to kick the bucket’.

The correct answer is Sustanence

Key Points

• The incorrectly spelt word is ‘Sustanence’
• The correct spelling is ‘Sustenance’, meaning ‘nourishment’; Food and drink regarded as a source of strength; nourishment.
• The rest options are correctly spelt.

Additional Information Let's look at the meaning of other given options-

• Secondary- coming after, less important than, or resulting from someone or something else that is primary.
• ​For e.g.- There are some secondary issues which must be taken into account as well.
• Sizeable- fairly large : considerable
• ​For e.g.- Educational level has a sizeable direct effect on income
• Succumb-  to lose the determination to oppose something, or to accept defeat​
• ​For e.g.- Even good leaders eventually succumb to the pressure of the ruling class.

The correct answer is ‘democratic’

Democratic means relating to democracy and its principles, which uphold the judiciary.

Hence, it is the correct word to fill in the given blank.

The correct answer is ‘My cousin asked me whether I wanted some more chocolates.’

Sentence 1 does not convert to the past tense in the reported speech and is incorrect.

Sentence 2 uses an incorrect reporting verb, ‘said to’, instead of ‘asked’.  

Sentence 3 is incorrect in structure (asked…that) and is rejected.

Only Sentence 4 uses the correct reporting verb and tense and is the correct conversion from Direct to Indirect speech.

The correct answer is ‘Defraud’.

Hoodwink means ‘deceive or trick’.

Defraud means ‘illegally obtain something by deception’.

Hence, the two words have similar meanings.

The other options,

Illicit means ‘forbidden by law or custom’

Secret means ‘confidential or undisclosed’

Stare means ‘gaze or gawk’.

The correct answer is ‘to’.

The word ‘hindrance’ means ‘an obstacle’ and it is followed by the preposition to, in order to show the blockage.

Hence, it is the appropriate word to be used in the given sentence.

The other options do not make meaningful sentences and are incorrect.

The error lies in Part 2 of the sentence.

‘Pass away’ means ‘to cease or die’.

The correct word to be used in the sentence is pass, which means ‘spend or live’.

Hence, the correct sentence is:

‘My brother finds it difficult to pass the time at our grandparent’s house.’

The correct answer is ‘Unless’.

‘Unless’ means ‘except if’, that is a case that will happen if the condition is not met.

Hence, it fits well with the context of the sentence and is the correct answer.

The other options,

If means ‘in the event that something happens, the other thing will happen’.

Till means ‘an informal way of saying until’

Until means ‘up to the point in time or event concerned’

The correct answer is ‘Simple’.

Multifaceted means ‘having different aspects or features’.

Simple means ‘plain or uncomplicated in form’.

Hence, the two words have opposite meanings.

The other options,

Adroit means ‘clever or skilful’

Handy means ‘convenient or useful’

Pliable means ‘easily bent or flexible’.

The correct answer is are looking forward to

Key Points

• ‘Look forward for’ is grammatically incorrect.
• Look forward to something means to be pleased or excited that it is going to happen.
• The 'to' in look forward to is a preposition, so we must follow it by a noun phrase or a verb in the -ing form.
• Example: I'm looking forward to the holidays.

Hence, the correct sentence is: ‘We are looking forward to a positive response from you.’

The error lies in Part 3 of the sentence.

The given sentence uses ‘when’ in place of ‘than’.

The correct structure is ‘no sooner……than’.

Hence, the correct sentence is:

‘No sooner had he finished his morning walk than it began to rain.’

go through the link given below to understand the concept of bare infinitives in a better way 

https://www.youtube.com/watch?v=VOf0VwtGrnQ

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, the starting of an incident, or it starts with 'most' or 'once'.
• Part Q will be the first sentence because it introduces the topic 'comfort'.
• Part S mentions how comfort is turning into a habit and states the reason for comfort as one of the reasons for its spread.
• Part R will be the next in sequence. Its mentions how comfort is turning valuable.
• Part P mentions discomfort is the real torture for those who have taken comfort as a habit​

Paragraph after rearranging the sentences: Comfort is now one of the causes of its own spread. It has now become a physical habit, a fashion, an ideal to be pursued for its own sake. The more comfort is brought into the world, the more it is likely to be valued. To those who have known comfort, discomfort is a real torture.

Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the paragraph.
• Try to identify the opening and closing sentences of the paragraph. The sentence independent of the other sentences and introduces the new characters is generally the opening sentence. For the last sentence, look out for the sentence which can conclude the paragraph.
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.
• Identify the pronouns which are connecting the sentences with each other.
• Sometimes it is not necessary to identify all the sentences, we can arrange the sentences by eliminating the irrelevant option one by one.

The correct answer is ‘role’.

Role means the function assumed or part played by a person or thing in a particular situation.

It fits with the context of the sentence as it says that the executive plays a function in the appointment of judges.

Hence, it is the correct word for the given blank.

The correct answer is: Option 2.

Key Points

• The word "Glamoros" is incorrectly spelt. The correct spelling is "Glamorous". (ग्लैमरस)
• Example: She looked glamorous in her evening gown at the party.
• "Glamoros" is not an English word and has no meaning.
• Example: There is no example since "Glamoros" is incorrectly spelt.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Continuous (निरंतर): Uninterrupted in time; without cessation.
• Example: The continuous noise from the construction site was very annoying.
• Meticulous (सूक्ष्म): Showing great attention to detail; very careful and precise.
• Example: She was meticulous in her research, ensuring every detail was correct.
• Vicious (क्रूर): Deliberately cruel or violent.
• Example: The vicious dog attacked anyone who entered the yard.

The correct answer is ‘No improvement’.

The sentence is grammatically correct and does not require any improvements.

The correct answer is ‘Vindictive’

Vindictive means ‘having or showing a strong or unreasoning desire for revenge.’

Hence, it is the closest in meaning to given phrase and is the correct one-word substitute.

The other options,

Enmity means ‘a state or feeling of active opposition’

Nigger means ‘a contemptuous term for a black or dark-skinned person.’

Pedantic means ‘excessively concerned with minor details’