SSC CGL Previous Paper (Held On: 6 June 2019 Shift 3) (Previous Year Paper)

7 + 4 = 11

11 + 8 = 19

19 + 12 = 31

31 + 16 = 47

47 + 20 = 67

Hence, 47 is the correct answer.

The most appropriate venn diagram that illustrate relationship between Women, Entrepreneurs and Engineers is:

Hence, the figure in option 1 is the correct answer.

The logic followed here is:

V – 1 = U

E – 1 = D

R – 1 = Q

Y – 1 = X

Similarly,

U – 1 = T

R – 1 = Q

G – 1 = F

E – 1 = D

N – 1 = M

T – 1 = S

Hence, URGENT is coded as TQFDMS.

Each figure has three elements with three symbols. In each consecutive figure, the bottom most element moves to topmost position. Also, in each consecutive figure three symbols move from left side to right side or vice versa.

Hence, the final figure will be as given in the above diagram.

Hence, the mirror image will be figure 1

1. GKRV → ((R (18) + V (22)) – (G(7) + K(11)) → 22

2. BFMQ → (M (13) + Q (17)) – (B (2) + F(6)) → 22

3. EHPS → (P (16) + S (19)) – (E (5) + H (8)) → 22

4. DGKL → (K (11) + L(12)) – (D (4) + G (7)) → 12

Hence, as we can see the difference between the sum of positional value of first two alphabets and the sum of positional value of last two alphabets is 22 in all the options, except DGKL. Hence, DGKL is the odd one out.

The correct logical order here will be:

Low Pressure → Cloud → Rain → Rainbow → Flood → Devastation

Hence, ‘5, 1, 4, 2, 6, 3’ is the correct order.

Concept:

• The first step in solving a number series question usually is calculating the difference between the consecutive terms.
• If the first set of differences are not adequate to identify a pattern, one should calculate the second set of differences

Explanation:

The pattern followed here is:

Hence, the number that will complete the series is 57.

Alternate Method 

• There are multiple ways of solving the given question.
• Two more methods are shown below:

Method I:

Each term of the given series can be expressed as "a × (a + 1) + 1" as shown below:

Among the given options, only 57 can satisfy this condition.

Hence, the missing number is 57.

Method II:

Each term of the given series can be expressed as "a² - (a - 1)" as shown below:

• Here, 2, 4, 6, 8, and 10 are consecutive even numbers in ascending order.
• Similarly, 1, 3, 5, 7, and 9 are consecutive odd numbers in ascending order.

Among the given options, only 57 can satisfy this condition.

Hence, the missing number is 57.

Here, each alphabet is coded as the alphabet which has same positional value as the alphabet in reverse alphabetical order.

i.e., CX, DW, AZ, FU are reverse pairs.

Similarly, DW, EV, FU and CX are reverse pairs.

Hence, WVUX is the correct answer.

1. abcadbabcadbabcadb → abc / adb/abc / adb / abc / adb → form a pattern

2. abcacbabdadbabcadb → does not form a pattern

3. abcadbabcadaabcbdb → does not form a pattern

4. abcadbabdadaabccdb → does not form a pattern

Hence, ‘bdcba’ is the correct answer.

Hence, when the paper will be folded and cut as given in the question, the answer figure will be as given above.

Concept Used:

 $Triangles = n× 2$

Where, 

n= number of small triangles

→ In, □ABCD:

n= number of small triangles = 8

$Triangles = 8× 2 = 16$

Hence, Total triangles in □ABCD = 16

→ In, □PQST:

n = 8

$Triangles = 8× 2 = 16$

Hence, Total triangles in □PQST = 16

→ Now Adding all the ∆s:

Total ∆s = 16 + 16 = 32

Hence, there are 32 triangles in the given figure.

1. EFST → E + 1 = F; S + 1 = T.

2. ABOP → A + 1 = B; O + 1 = P.

3. CDQR → C + 1 = D; Q + 1 = R.

4) GHTV → G + 1 = H; T + 1 = U ≠ V.

Hence, GHTV is the odd one out.

The least possible venn diagram is as follows:

I. Some ponds are not wells → False (It is possible but not definite)

II. Some wells are pools → True (Some wells are ponds and all ponds are pools)

III. All pools are wells → False (It is possible but not definite)

Hence, only conclusion II follows.

An author creates a book.

Similarly, spider creates web.

Hence, ‘Spider : Web’ is the correct answer.

Table lamp is found in Study room, Frying pan is found in Kitchen, Shower is found in Bathroom whereas Ladle is found in kitchen and not in the Garden.

Hence, Garden : Ladle is the odd one out.

Similarly,

Hence, PERSONAL will be coded as SOREPLAN.

Decoding the given equation

72 ÷ 9 × 3 + 8 - 2 = ?

Applying BODMAS rule:

8 × 3 + 8 - 2 = ?

24 + 8 - 2 = 32 - 2 = 30

Hence, 30 is the correct answer.

Ceiling is the top cover of a room. Similarly, Palate is the top cover of Mouth.

Hence, Palate is the correct answer.

Cessation, Valediction, Closure are words which indicate an end to something or some event. Intermission means an interval in the middle or between two events.

Hence, Intermission is the odd one among the given options.

• Here, 1, 4, 3, 2 are adjacent to 6.
• Also, by changing the second position with respect to 6, we get:
• 6 - 4 - 1
• 6 - 2 - 3
• This implies that the pairs of opposite faces should be (5, 6), (4, 2), and (1, 3)

Hence, 3 will be at the top if 1 is at the bottom of the dice.

Hence, the above figure is the answer figure.

The logic followed here is:

(n² - 1) : n

1. 85 : 9 → does not follow the rule as 9² – 1 = 80 ≠ 85

2. 120 : 11 → follow the rule as 11² – 1 = 120

3. 26 : 5 → does not follow the rule as 5² – 1 = 24 ≠ 26

4. 64 : 8 → does not follow the rule as 8² – 1 = 63 ≠ 64

Hence, 120 : 11 is the correct answer.

Similarly,

Hence, EAML will be the correct answer.

The logic followed here is:

Logic: (1st number × 1.5 = 2nd number)

(2nd number × 2 = 3rd number)

Now,

(6 × 1.5 = 9)

(9 × 2 = 18)

Similarly, for (14, 21, 42)

(14 × 1.5 = 21)

(21 × 2 = 42).

Hence, the correct answer is "Option 3".

Alternate Method

(n, n × 1.5, n × 3)

1. (18, 27, 56) → does not follow the rule as 18 × 3 = 54 ≠ 56

2. (8, 14, 24) → does not follow the rule as 8 × 1.5 = 12 ≠ 14

3. (14, 21, 42) → (14, 14 × 1.5 = 21, 14 × 3 = 42) and hence, follows the rule

4. (10, 15, 35) → does not follow the rule as 10 × 3 = 30 ≠ 35

Hence, (14, 21, 42) is the correct answer.

• Pakhawaj is not a vocal form of Hindustani classical music. It is a two-headed drum which is barrel-shaped, also known as mridang.
• Tarana, Drupad, Khyal, and Dhamar are major vocal forms of Hindustani classical music.
• Hindustani classical music originated in 12th century CE.
• The music has 7 basic notes and 5 interspersed half-notes, which result in a 12-note scale.

• Leila Seth was the first woman judge of the Delhi High Court.
• She was also the first woman to become Chief Justice of a High Court of a state on 5 August 1991.
• Anna Chandi was the first female judge of India.
• Sujata Manohar is a retired judge of the Supreme Court.
• Ruma Pal is a former Supreme Court judge in India.

• The Khajuraho Temples are located in the state of Madhya Pradesh, in Chhatarpur district.
• It is a UNESCO World Heritage Site.
• The Khajuraho temples were built by the Chandela dynasty in the year 950-1050.
• It was added in UNESCO sites in 1986.

• The Gandhi-Irwin Pact was an agreement signed between Lord Irwin and Mahatma Gandhi.
• It conditions were:
• Removal of salt tax; allowing to produce, trade and sell legally
• The Indian National Congress should stop the civil disobedience movement
• Participation in the Round Table Conference by the Indian National Congress
• Withdrawal of ordinances issued by the Indian government
• Release of prisoners who were  arrested for taking part in the Salt March

• The Simon Commission(1927) was a group of seven Members of Parliament from the United Kingdom, constituted to suggest constitutional reforms for British India.
• Sir John Simon was its chairman.
• A protest against it was led by nationalist Lala Lajpat Rai in Lahore, during which he died because of his injuries in 1928.
• The Sargent scheme was a 1944 memorandum prepared by the British-run Government of India. It outlined the future development of literacy and education in India.
• The McGovern–Fraser Commission was created by the Democratic National Committee (DNC) in response to the Democratic National Convention 1968.
• Hunter Commission,1882, was the first education commission in the history of modern India.

• Bariatric surgery makes changes to a person's digestive system.
• It is also known as gastric bypass surgery.
• It helps a person lose weight by changing how mall intestine and stomach handle the food one eats.
• Thoracotomy is a surgery for the lungs.
• Turbinectomy is a surgery for the nasal passage.
• Bypass surgery is a surgery for the heart.

• Majuli is the largest river island in the world.
• It is situated in Assam on the Brahmaputra river.
• It is spread across an area of 880 sq km and is inhabited by tribes such as Deori and Mising.
• The Guinness World Records has declared the Majuli island as the largest river island in the world, toppling Marajo in Brazil to clinch the record.

• Varkala, Chowara, Chavakkad and Nattika are beaches in the state of Kerala.
• Kerala is a popular tourist destination in India.
• Other famous places of Kerala include Ponmudi, Wayanad Wildlife Sanctuary, Idukki Dam, etc.

• The National Board for Micro, Small, and Medium Enterprises meets once every 6 months in a year.
• It was established on 15 May 2007, having 47 members.
• It is responsible for examining the factors affecting the development and promotion of MSMEs.
• It also gives advice to the Central government about the use of funds constituted in Section 12.

• Malic acid is found in apples.
• It is a dicarboxylic acid which is also present in grapes, wine, and rhubarb.
• It imparts a tart taste to a food.
• Formic acid is found in ants.

• Razia Sultan was the first and the only Muslim woman to ever sit on the throne of Delhi.
• She was appointed by Iltutmish.
• She served as the Sultan of Delhi from 10 October 1236- 14 October 1240.
• Shajar Al Durr was an Egyptian ruler.
• Gevher Nesibe was the princess of Sultanate of Rum.
• Fatima Al Fihri was an Arab Musli woman who founded the oldest existing educational institution in the world.

• The Banking Regulation Act was passed in India in the year 1949.
• The act regulates all the banking firms in India.
• It came into effect on 16 March 1949 and was applicable in Jammu and Kashmir from 1956.

• Indian ranked 140th in 2019 World Happiness Report, released in March 2019.
• Finland topped the ranking for the second consecutive year.
• India dropped down by 7 places. It was at 133rd position in 2018.
• Pakistan stood at 67th, while China at 93rd position.
• The report ranks countries on the basis of national happiness.

• The Pradhan Mantri Shram Yogi Mandhan Yojana was launched by Prime Minister Narendra Modi in March 2019 in Ahmedabad for unorganized sector workers.
• The scheme ensures old age protection with a monthly pension of Rs. 3000 for people aged 60 years and above.
• Workers whose monthly income is less than or equal to Rs.15000/month will benefit from this scheme.
• The maximum yearly contribution is Rs.2400, that is, Rs. 200 per month.

• Royal Calcutta Golf Club, Kolkata is the oldest golf course outside the United Kingdom.
• It was established in the year 1829.
• It is also the second-oldest club outside Scotland.
• The Royal Blackheath in London is the oldest one outside Scotland, which was established in the year 1776.

The correct answer is West Bengal.

Key Points

• The highest railway station in India is located in the state of West Bengal.
• Its name is Ghum railway station, situated at an altitude of 2,258 m.
• It is situated in the Darjeeling Himalayan hill region.
• It is the world's 14th highest railway station.
• Tanggula railway station of the Chinese Railways is the highest railway station in the world.

• Akbar succeeded the Mughal throne in the year 1556 after Humayun.
• He was the third ruler of the Mughal Emperor.
• He reigned from 1556 to 1605.
• Jahangir succeeded him in the year 1605 to become the 4th Mughal Emperor.

• Rickets is a disease associated with the deficiency of Vitamin D.
• | Diseases | Caused by a deficiency of | | --- | --- | | Night blindness | Vitamin A | | Anaemia | Vitamin B | | Scurvy | Vitamin C | | Rickets | Vitamin D |

• The Indian Passport was ranked 67th in the 'Global Passport Index Report 2019'.
• The ranking has improved in the last 5 years from 77 in 2015 to 67 in 2019.
• The UAE passport secured 1st rank in the index.
• A Henley Passport Index 2019 was also released, which ranked India at 86th position.

• Article 324 of the Indian Constitution gives the Election Commission the power to supervise elections to the Parliament and state legislatures.
• Article 342 deals with Scheduled Tribes in India.
• Article 314 has been repealed.
• Article 341 deals with Scheduled Castes of India.

The correct answer is Option 3 i.e.  Commission for Agricultural Costs and Prices (CACP).

• Minimum Support Price (MSP) is recommended by the Commission for Agricultural Costs and Prices (CACP).
• MSP is a price set by the Indian government at which it purchases crops directly from the farmer.
• It is an important part of the agricultural policy of India.
• Minimum Support Price (MSP) is a form of market intervention by the Government of India to insure agricultural producers against any sharp fall in farm prices.

• Lal Krishna Advani is the oldest member of the 16th Lok Sabha.
• He served as the 7th Deputy PM of India from 2002-2004.
• He was awarded the Padma Vibhushan in the year 2015.
• Farooq Abdullah is the former CM of Jammu and Kashmir.
• Ram Jethmalani is the former Union Law Minister of India.
• Murli Manohar Joshi is the former MP from Kanpur.

• Wilson's disease is a disorder which causes accumulation of copper in the brain, liver and other organs.
• Its symptoms include:
• Fluid build-up in the legs or abdomen
• Problems with speech, swallowing or physical coordination
• Uncontrolled movements or muscle stiffness
• Fatigue, lack of appetite
• Yellowing of skin

Night blindness is caused by the deficiency of Vitamin A. People having it experience poor vision at night.

• During photosynthesis, green plants use energy from sunlight to synthesise glucose from carbon dioxide and water.
• Photosynthesis is a process that plants and other organisms use to convert light energy into chemical energy.
• Glucose, fructose, sucrose and galactose are all forms of simple sugar.

• Aditi Ashok became the first Indian golfer to win on the 'Ladies European Tour' in 2016.
• She is an 18-year old golfer.
• She defeated Lee Anne Pace in the finals to claim the title.

Given, AB = BD = DC

And ∠BAD = 70°

In ΔABD,

⇒ ∠BAD = ∠BDA = 70° [∵ AB = BD]

⇒ ∠ABD + ∠BAD + ∠BDA = 180°

⇒ ∠ABD = 180° – 70° – 70° = 40°

⇒ ∠BDC = 180° – ∠BDA = 180° – 70° = 110°

In ΔBDC,

⇒ ∠DBC = ∠DCB [∵ BD = DC]

⇒ ∠DBC + ∠BDC + ∠DCB = 180°

⇒ 2∠DBC = 180° – 110° = 70°

⇒ ∠DBC = 35°

⇒ ∠ABC = ∠ABD + ∠DBC = 40° + 35° = 75°

Total production of type B cars during 2013 to 2016 = 47 + 55 + 58 + 54 = 214

Total production of cars in 2017 = 64 + 66 + 72 + 66 + 62 = 330

∴ Required percentage = [(330 – 214)/330] × 100 = 35% (approx)

Shortcut Trick

Relative Speed (Same direction) = 44 − 8 = 36 km/h = 10 m/s.

Length of Train = 10 × 15 = 150 m.

Relative Speed (Opposite direction) = 150 ÷ 10 = 15 m/s = 54 km/h.

Woman Speed = 54 − 44 = 10 km/h.

∴ The correct answer is 10 km/h.

Alternate Method

Given: Speed of Train (S_T) = 44 km/h, Speed of Man (S_M) = 8 km/h, Time to cross man (t₁) = 15 s, Time to cross Woman (t₂) = 10 s.

Formula Used: Distance = Relative Speed × Time; 1 km/h = 5/18 m/s.

⇒ Relative speed with man = 44 − 8 = 36 km/h

⇒ Speed in m/s = 36 × 5/18 = 10 m/s

⇒ Length of train (L) = Speed × Time = 10 × 15 = 150 m

⇒ Let the speed of woman be x km/h. Relative speed (opposite) = (44 + x) km/h

⇒ Length = Relative Speed × Time

⇒ 150 = (44 + x) × (5/18) × 10

⇒ 15 = (44 + x) × 5/18

⇒ 270 = 220 + 5x → No, simpler: 15 × 18 / 5 = 44 + x

⇒ 54 = 44 + x

⇒ x = 10 km/h

∴ The correct answer is 10 km/h.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is S₁ − S₂. In the opposite direction, it is S₁ + S₂.

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Crossing a Moving Object

The distance covered while crossing a person is equal to the length of the train itself, regardless of the person's speed.

Given: 

$\frac{1}{{\sin {\rm{θ }}}} - \frac{{{{\cot }^2}{\rm{θ }}}}{{1{\rm{;}} + {\rm{;cosec;θ }}}}$

Calculation:

$\frac{1}{{\sin {\rm{θ }}}} - \frac{{{{\cot }^2}{\rm{θ }}}}{{1{\rm{;}} + {\rm{;cosec;θ }}}}$

Now,

$\frac{{{{\cot }^2}{\rm{θ }}}}{{1{\rm{;}} + {\rm{;cosec;θ }}}}$ = (cosec²θ - 1)/1 + cosecθ 

⇒ (cosecθ -1)(cosecθ + 1)/(1 + cosecθ)

⇒ cosecθ - 1 ------ (1)

As we know,

1/sinθ = cosecθ ------ (2)

From equation (1) and (2)

$\frac{1}{{\sin {\rm{θ }}}} - \frac{{{{\cot }^2}{\rm{θ }}}}{{1{\rm{;}} + {\rm{;cosec;θ }}}}$

⇒ cosecθ - (cosecθ - 1)

⇒ cosecθ - cosecθ + 1

⇒ 1

Alternate Solution:

$\frac{1}{{\sin {\rm{θ }}}} - \frac{{{{\cot }^2}{\rm{θ }}}}{{1{\rm{;}} + {\rm{;cosec;θ }}}}$

Put θ = 30°

$⇒ \frac{1}{{\frac{1}{2}}} - \frac{{{{\left( {\sqrt 3 } \right)}^2}}}{{1{\rm{;}} + {\rm{;}}2}}$

⇒ 2 – [3/3]

⇒ 1

In ΔORN,

⇒ RS = 12 cm and RN = 6 cm and OR = 10 cm

By using Pythagoras Theorem

⇒ (OR)² = (ON)² + (RN)²

⇒ 10² = (ON)² + 6²

⇒ ON = 8 cm

⇒ NM = 14 cm

⇒ OM = NM – ON = 14 – 8 = 6 cm

In ΔPMO

By using Pythagoras Theorem

⇒ (OP)² = (OM)² + (MP)²

⇒ 10² = (6)² + (x/2)² [∵ PQ = x cm, ∴ MP = x/2 cm]

⇒ x/2 = 8

⇒ x = 16 cm

Total production of type B cars in 2015 and type C cars in 2013 = 58 + 52 = 110

Total production of type E cars in 2013 and 2014 = 43 + 47 = 90

∴ Required percentage = [(110 – 90)/90] × 100 = 22.2%

Total production of type A cars in 2017 and type D cars in 2015 = 64 + 56 = 120

Total production of type B and type E cars in 2013 = 47 + 43 = 90

∴ Required ratio = 120 : 90 = 4 : 3

Total Production of type D cars = 60 + 53 + 56 + 65 + 66 = 300 thousands

Production of type D cars in 2016 = 65 thousands

⇒ 300 thousands represents = 360°

⇒ 65 thousands will represents = 360°/300 × 65 = 78°

Shortcut Trick

For expressions of the form a³ + b³ + c³ − 3abc, use the direct formula:

Value = (a + b + c) ÷ 2 × [3(a² + b² + c²) − (a + b + c)²]

⇒ Value = (2 ÷ 2) × [3(26) − (2)²]

⇒ Value = 1 × [78 − 4] = 74

∴ The correct answer is 74.

Alternate Method

Given:

Sum of terms: a + b + c = 2

Sum of squares: a² + b² + c² = 26

Formula Used:

1. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
2. a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca))

Calculations:

First, find the value of (ab + bc + ca):

⇒ (2)² = 26 + 2(ab + bc + ca)

⇒ 4 = 26 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 4 − 26

⇒ 2(ab + bc + ca) = −22

⇒ ab + bc + ca = −11

Now, substitute the values into the cubic identity:

⇒ a³ + b³ + c³ − 3abc = 2 × [26 − (−11)]

⇒ a³ + b³ + c³ − 3abc = 2 × [26 + 11]

⇒ a³ + b³ + c³ − 3abc = 2 × 37

⇒ a³ + b³ + c³ − 3abc = 74

∴ The correct answer is 74.

Additional Information

Special Case (a + b + c = 0)

If the sum of the three variables is zero, then a³ + b³ + c³ = 3abc.

Alternative Form of Cubic Identity

a³ + b³ + c³ − 3abc = 1/2 × (a + b + c) × [(a − b)² + (b − c)² + (c − a)²].

Condition for Zero Result

The expression a³ + b³ + c³ − 3abc equals zero if either a + b + c = 0 or a = b = c.

16 ÷ 4 of 4 × [3 ÷ 4 of {4 × 3 ÷ (3 + 3)}] ÷ (2 ÷ 4 of 8)

⇒ 16 ÷ 16 × [3 ÷ 4 of {4 × 3 ÷ 6}] ÷ (2 ÷ 32)

⇒ 1 × [3 ÷ 4 of 2] ÷ 1/16

⇒ [3 ÷ 8] ÷ 1/16

⇒ [3/8] ÷ [1/16]

⇒ 6

Average of 11 numbers = 54

Sum of 11 numbers = 54 × 11 = 594

Average of the first four numbers = 48

Sum of the first four number = 48 × 4 = 192

Average of the next four numbers = 48 × [5/4] = 60

Sum of the next four numbers = 60 × 4 = 240

Let the 11^th number be x.

∴ 9^th number be x + 8 & 10^th number be x + 4

Sum of 9^th, 10^th and 11^th numbers = 594 – 192 – 240 = 162

According to the question

⇒ x + 8 + x + 4 + x = 162

⇒ 3x = 162 – 12

⇒ x = 50

⇒ 9^th number = x + 8 = 50 + 8 = 58

⇒ 10^th number = x + 4 = 50 + 4 = 54

∴ Average of 9^th and 10^th number = (58 + 54)/2 = 56

Short trick:

Put θ = 90°

⇒ [1/(1 + 1)] + [1/(1 + 1)] = 1

Detailed method:

$\Rightarrow \left( {\frac{1}{{1{\rm{}} + {\rm{}}{{\sin }^2}{\rm{\theta }}}}{\rm{;}} + {\rm{;}}\frac{1}{{1{\rm{;}} + {\rm{;;cose}}{{\rm{c}}^2}{\rm{\theta }}}}} \right)$

$\Rightarrow \left( {\frac{1}{{1{\rm{;}} + {\rm{;}}{{\sin }^2}{\rm{\theta }}}}{\rm{}} + {\rm{}}\frac{{{\rm{si}}{{\rm{n}}^2}}}{{1{\rm{;}} + {\rm{;}}{{\sin }^2}{\rm{\theta }}}}} \right)$

⇒ (1 + sin²θ) / (1 + sin²θ)

⇒ 1

Suppose 99 fruits are bought at a rate of 11 for Rs 100, then cost of 99 fruits = 9 × 100 = Rs. 900

99 fruits are also bought at a rate of 9 for Rs 100, then cost of 99 fruits = 11 × 100 = Rs 1100

Total cost of 198 fruits = 900 + 1100 = Rs. 2000

SP of 10 fruits = Rs. 100

SP of 1 fruit = Rs. 10

SP of 198 fruits = Rs. 1980

⇒ Total loss = 2000 – 1980 = Rs. 20

∴ Required loss percentage = [20/2000] × 100 = 1%

Let income of Sudha be 200x

Saving of Sudha = 200x × [15/100] = 30x

Expenditure of Sudha = 200x – 30x = 170x

New Expenditure of Sudha = 170x × [6/5] = 204x

New Savings of Sudha = 30x × [8/5] = 48x

New income of Sudha = 204x + 48x = 252x

New income increased by = 252x – 200x = 52x

∴ Required percentage = [52x/200x] × 100 = 26%

As we know

⇒ ∠P + ∠R = 180° [∵ ∠P : ∠R = 3 : 1]

⇒ 4 ∠R = 180°

⇒ ∠R = 45°

Similarly,

⇒ ∠S + ∠Q = 180° [∵ ∠S : ∠Q = 5 : 1]

⇒ 6∠Q = 180°

⇒ ∠Q = 30°

⇒ ∠R + ∠Q = 45° + 30° = 75°

As we know,

⇒ (a³ – b³) = (a – b) (a² + b² + ab)

3√3 x³ – 2√2 y³ = (x √3 – y √2) (Ax² + By² + Cxy)

⇒ (√3 x)³ – (√2 y)³ = (√3x – √2y) (Ax² + By² + Cxy)

⇒ (√3 x – √2 y) (3x² + 2y² + √6 xy) = (√3x – √2y) (Ax² + By² + Cxy)

⇒ 3x² + 2y² + √6xy = Ax² + By² + Cxy

On comparing

⇒ A = 3, B = 2 and C = √6

⇒ (A × 2) ÷ C

⇒ (3 × 2) ÷ (√6) = 6 ÷ (√6)

⇒ √6

⇒ 10 digit number = 2094x843y2 is divisible by 88, means number divisible by 11 and 8 both

⇒ 3y2 is divisible by 8 if y = 1,5 and 9

If y = 1, then

⇒ 2094x84312 is divisible by 11 if x = 1

If y = 5, then

⇒ 2094x84352 is divisible by 11 if x = 8

⇒ 5x – 7y

If y= 9 then, 

2094x84392 is divisible by 11, x= 4

For the largest possible value of x if x = 8 and y = 5

⇒ (5x – 7y) = 5 × 8 – 7 × 5 = 40 – 35 = 5

Additional Information

Any number whose absolute difference between the sum of digits in the even positions and the sum of digits in the odd positions is 0 or divisible by 11 is itself also divisible by 11.

Let the radius of the outer circle r₁ be 7x.

Radius of middle circle r₂ = 5x

Radius of inner circle = r₃ = 4x

Area between the inner two circles = π [(r₂)² – (r₃)²] = (22/7) × [25x² – 16x²] = (22/7) × 9x²

Area between the outer two circles = π [(r₁)² – (r₂)²] = (22/7) × [49x² – 25x²] = (22/7) × 24x²

⇒ Required ratio = [(22/7) × 9x²] : [(22/7) × 24x²] = 3 : 8

Put θ = 45°

⇒ 1 + 1 + 1 + 1 = k

⇒ k = 4

⇒ √k = 2

Go through the options

⇒ cosecθ secθ

⇒ cosec45° sec45°

⇒ √2 × √2

⇒ 2

Given, AD = 1, BD = 6 and AB = AD + BD = 1 + 6 = 7

As we know,

⇒ (Area of ΔADE) : (Area of ΔABC) = (AD)² : (AB)² = 1² : 7² = 1 : 49

Let the principal be 100x.

Amount will be after 2 years A = 100x × [11/10] × [11/10] = 121x

According to the question

⇒ [121x – 6634] × [11/10] = 13200

⇒ 121x – 6634 = 12000

⇒ 121x = 18634

⇒ 100x = [18634/121] × 100 = Rs. 15,400

Shortcut TrickPut θ = 60°

$\Rightarrow \frac{{{\rm{cos\theta }}}}{{1 - {\rm{sin\theta }}}}{\rm{}} + {\rm{}}\frac{{{\rm{cos\theta }}}}{{1{\rm{;}} + {\rm{;sin\theta }}}}{\rm{}} = {\rm{}}4$

$\Rightarrow \frac{{\frac{1}{2}}}{{1 - \frac{{\sqrt 3 }}{2}}}{\rm{;}} + {\rm{;}}\frac{{\frac{1}{2}}}{{1{\rm{}} + {\rm{}}\frac{{\sqrt 3 }}{2}}}{\rm{}} = {\rm{}}4$

⇒ 4 = 4 (Satisfied)

⇒ tanθ + cosecθ

⇒ tan60° + cosec60°

⇒ √3 + [2/√3] = (5/√3) × (√3/√3)

⇒ 5√3/3

Detailed Solution:

$\Rightarrow \frac{{{\rm{cos\theta }}}}{{1 - {\rm{sin\theta }}}}{\rm{}} + {\rm{}}\frac{{{\rm{cos\theta }}}}{{1{\rm{;}} + {\rm{;sin\theta }}}}{\rm{}} = {\rm{}}4$

$\Rightarrow {\rm{cos\theta }}\left[ {\frac{{1{\rm{;}} + {\rm{;sin\theta ;}} + {\rm{;}}1 - {\rm{sin\theta }}}}{{1 - {\rm{si}}{{\rm{n}}^2}{\rm{\theta }}}}} \right]{\rm{}} = {\rm{}}4$

⇒ cosθ × [2/cos²θ] = 4

⇒ cosθ = 1/2

⇒ cosθ = cos60°

⇒ θ = 60°

⇒ tanθ + cosecθ

⇒ tan60° + cosec60°

⇒ √3 + [2/√3] = (5/√3) × (√3/√3)

⇒ 5√3/3

Shortcut Trick

In similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Given BD || AE, ΔBDC is similar to ΔAEC (ΔBDC ~ ΔAEC).

Ratio of sides BD : AE = 3 : 8.

⇒ Ratio of Area(ΔBDC) : Area(ΔAEC) = (3)² : (8)² = 9 : 64.

∴ The correct answer is 9 : 64.

Alternate Method

Given:

In ΔACE, BD || AE and AE/BD = 8/3.

Formula Used:

If two triangles are similar, the ratio of their areas is the square of the ratio of their corresponding sides.

Calculations:

In ΔBDC and ΔAEC:

⇒ ∠C = ∠C (Common angle)

⇒ ∠CBD = ∠CAE (Corresponding angles as BD || AE)

⇒ ∠CDB = ∠CEA (Corresponding angles as BD || AE)

⇒ ∴ ΔBDC ~ ΔAEC (By AAA similarity criterion)

⇒ Area(ΔBDC) / Area(ΔAEC) = (BD / AE)²

⇒ Given AE/BD = 8/3 → BD/AE = 3/8

⇒ Area(ΔBDC) / Area(ΔAEC) = (3 / 8)²

⇒ Area(ΔBDC) / Area(ΔAEC) = 9 / 64

∴ The correct answer is 9 : 64.

Additional Information

Similar Triangles Properties

If two triangles are similar, the ratio of their altitudes, medians, and perimeters is equal to the ratio of their corresponding sides.

Thales Theorem (BPT)

A line drawn parallel to one side of a triangle divides the other two sides in the same ratio (CB/BA = CD/DE).

Area Ratio Rule

For any two similar figures, the ratio of their areas is always the square of the ratio of any linear dimension (side, radius, etc.).

If a + 1/a = 3,

As we know, if x + 1/x = a, then x² + 1/x² = a² – 2

⇒ a² + 1/a² = 3² – 2 = 9 – 2 = 7

⇒ a⁴ + 1/a⁴ = 7² – 2 = 49 – 2 = 47

Efficiency ratio of A, B and C = 7 : 5 : 6

Total work = (7 + 5 + 6) × 35 = 18 × 35 = 630

Completed work by B and C in 21 days = (5 + 6) × 21 = 231

⇒ Remaining work = 630 – 231 = 399

∴ A will complete the remaining work in = 399/7 = 57 days

The correct answer is option 2.

Canada is three times the size of India (1) but its population is only about 26 million.

'But' is used to connect two contrasting ideas. In the given sentence, it is mentioned that size of Canada is large as compared to India but its population is less.

'Until' means 'up to (the time that)'

For eg; We danced until midnight.

'So' is used to denote ' a great extent'.

For eg; He is so messy.

'Because' is used when we need to provide a reason for something.

For eg; He got late because of the rain.

So, options 1,3 and 4 are incorrect.

The correct answer is option 2.

Comic means causing or meant to cause laughter.

For eg; It was a comic movie.

Amusing means causing laughter and providing entertainment.

Tragic means causing or characterized by extreme distress or sorrow.

For eg; The terrorist attack was a tragic incident.

It is clear that comic and tragic are antonyms.

Awkward means causing difficulty; hard to do or deal with.

Absurd means wildly unreasonable, illogical, or inappropriate.

So, options 1,3 and 4 are incorrect.

The correct answer is option 4.

Drag means pull (someone or something) along forcefully, roughly, or with difficulty.

For eg; We dragged the boat.

Rest means cease work or movement in order to relax, sleep, or recover strength.

Push means exert force on (someone or something) in order to move them away from oneself.

Rush means move with urgent haste.

Pull means exert force on (someone or something) so as to cause movement towards oneself.

For eg; He pulled him down the couch.

It is clear that drag and pull are synonyms.

So, options 1,2 and 3 are incorrect.

The correct answer is option 4.

The river Yamuna has many non-native species like goldfish that is affecting its ecosystem.

The subject i.e. 'species' is in plural form. So, we will use the plural form of the verb i.e 'are' instead of 'is' for subject-verb agreement.

The correct sentence is - The river Yamuna has many non-native species like goldfish that are affecting its ecosystem.

So, options 1,2 and 3 are incorrect.

The correct answer is option 1.

When we convert command from the active to passive voice, we add 'let' at the beginning of the sentence and use the past participle form of the main verb i.e. shown. So, the correct answer is -

Let these visitors be shown the butterfly farm.

So, options 2,3 and 4 are incorrect.

The correct answer is option 4.

A painting competition was held in the colony and Kavya was declared winner in the age group 3-5 years.

Described means give a detailed account in words of.

Supposed means think or assume that something is true or probable but lack proof or certain knowledge.

Publicized means made (something) widely known.

Declared means openly or formally asserted or announced.

'Declared' is the appropriate word as it is used to describe that Kavya was announced the winner in the given age group.

So, options 1,2 and 3 are incorrect.

The correct answer is option 4.

They didn't see you, is it?

Question tags is used to covert a statement into a question. Here, the question tag is 'is it'. But, we always use the same auxiliary verb in the question tag which is used in the main statement. In the given statement, the auxiliary verb is 'did' , so we will use the question tag 'did they'.

The correct sentence is - 

They didn't see you, did they?

So, options 1,2 and 3 are incorrect.

The correct answer is option 3.

Butterflies in the stomach means a feeling of being very nervous or frightened or excited about something.

So, options 1,2 and 4 are incorrect.

The wrongly spelt word is hasitate

Key Points

• The correct spelling of the word in is hesitate which means a pause in indecision before saying or doing something
• Hazard means any source of potential damage, harm or adverse health effects on something or someone.
• Hazy means made dim or cloudy by or as if by fine dust, smoke, or light vapour in the air
• Hasty means rapid in action or movement

All the other words in options 2,3 and 4 are correctly spelt.

The correct answer is option 4.

Gather means come together; assemble or accumulate.

For eg; They gathered in the hall.

Distract means prevent (someone) from concentrating on something.

Dispute means a disagreement or argument.

To display means to put (something) in a prominent place in order that it may readily be seen.

Disperse means distribute or spread over a wide area.

For eg; All the students have dispersed.

It is clear that gather and disperse are antonyms.

So, options 1,2 and 3 are incorrect.

The correct answer is option 3.

The average density of population is less than three persons per square kilometer (3) in Canada. 

'Into' is used when we talk about the movement of a thing.

For eg; She came into the room.

'On' is used when we describe a position on any surface.

For eg; He slept on the floor.

'At' is used to describe a particular position or location as a point.

For eg; She was sitting at her desk.

'In' is used when we are talking about something enclosed within an area.

For eg; She lives in India.

In the given question, 'in' is used to denote the population density present in Canada.

So, options 1,2 and 4 are incorrect.

The correct answer is option 3.

The distribution of the population is highly (4) uneven.

Rough means not exact or precise; approximate.

Differing means not the same as each other; dissimilar.

Uneven means not regular, consistent, or equal

For eg; The minorities were offered uneven resources.

In the given question, 'uneven' will be used to describe the irregularity or unequal distribution of the population in Canada.

Infrequent means not occurring often; rare.

So, options 1,2 and 4 are incorrect.

The correct answer is option 4.

The first statement should be D i.e. ''  The United States of America (USA) is the 4th largest country in the world. '' This is because it gives a suitable start to the paragraph and describes what the following statements are going to talk about i.e. USA.

After D, it should be B i.e. '' It stretches from the Atlantic Ocean in the east to the Pacific Ocean in the west.'' This is because it gives a reason as to why the USA is the 4th largest country in the world.

After B, it should be C i.e. '' The USA consists of 50 states including Alaska and Hawai.'' This is because A gives the reason for C. So, A should be preceded by C.

So, the correct order is DBCA.

The correct answer is option 4.

Key Points

• In the given question, 'were being moved' is used which indicates that the active voice of the sentence will be in past continuous tense because if a sentence is in past continuous tense, we add 'being' and use the past participle form (v3) of the verb.
• So, in order to convert it to active voice, we first interchange the subject and object i.e. 'the injured' and ' the police'.
• Then, we use the past continuous tense i.e 'were moving'.
• So, the correct sentence will be- '' The police were moving the injured to the hospital.''
• Police is a noun which describes a collection of police officers and therefore cannot be singular. So the verb coming after the plural noun police should always be plural.

Thus the only correct answer option 4. 

Options 1,2 and 3 are incorrect.

The correct answer is option 4.

Offspring means a person's or animal's child or children.

Nest means a structure or place made or chosen by a bird for laying eggs and sheltering its young.

Clutch means grasp (something) tightly.

Brood means a family of birds or other young animals produced at one hatching or birth.

So, options 1,2 and 3 are incorrect.

The correct answer is option 2.

The National war memorial is dedicated to our Armed Forces.

Devoted means are very loving or loyal.

Dedicated means exclusively allocated to or intended for a particular purpose.

In the given sentence, 'dedicated' should be used to describe that the National war memorial is intended for a purpose i.e. towards our armed forces. 

Inscribed means write or carve (words or symbols) on something, especially as a formal or permanent record.

Honoured means regarded with great respect.

So, options 1,3 and 4 are incorrect.

The correct answer is option 4.

 The average (2) density of population is less than three persons per square kilometer.

Frequency means the rate at which something occurs over a particular period of time or in a given sample.

Quantity means a considerable number or amount of something.

Consistency means acting or done in the same way over time, especially so as to be fair or accurate.

Density means the number of people or things in a given area or space.

For eg; These are some areas of low population density.

In the question, 'density' will be the appropriate word as there are three persons living per square kilometer in Canada which is a measure of density.

So, options 1,2 and 3 are incorrect.

The correct answer is option 4.

The first statement should be A i.e.'' What was supposed to be a holiday of a lifetime turned into a dangerous experience for 1,300 passengers on a cruise ship off the coast of Norway.'' This is because all the other statements seem to be in continuation with other statements and A gives the subject which is going to be talked about.

After A, it should be C i.e '' The ship broke down in rough seas and high-speed winds caused it to rock heavily from side to side.'' This is because it gives the reason as to why the holiday turned into a dangerous experience.

After C, it should be B i.e. ''The Norwegian Government decided to evacuate the passengers with the help of helicopters.'' This statement describes what was decided by the government after the ship broke down.

So, the correct order is ACBD.

Options 1,2 and 3 is incorrect.

The correct answer is option 1.

We will rest for some time when we will reach the top.

When we use 'when' as a conjunction and refer to something in the future, we always use the present perfect or simple present tense in the when clause, and not 'will/shall'.  In the given sentence, we have used 'when we will' which is incorrect. It should be 'when we reach' the top.

Also, two 'will's in a single conditional sentence are redundant. 

So, options 2,3 and 4 are incorrect.

The correct answer is option 4.

 Nearly 80 per cent of the people (5) live in a narrow belt less than 300 kilometer wide along the southern border. 

Subsist means maintain or support oneself, especially at a minimal level.

Remain means continue to exist, especially after other similar people or things have ceased to do so.

Survive means continue to live or exist, especially in spite of danger or hardship.

Live means make one's home in a particular place or with a particular person.

For eg; I have lived here all my life.

In the given question, 'live' will be used to denote the people who have made their home in a narrow belt less than 300 kilometers wide along the southern border. 

So, options 1,2 and 3 are incorrect.

The correct answer is 'reminascant'.

Key Points Let's look at the following points-