SSC CGL Previous Paper (Held On: 4 June 2019 Shift 2) (Previous Year Paper)

M + 3 → P; P - 2 → N; N + 1 → O

T + 3 → W; W - 2 → U; U + 1 → V

D + 3 → G; G - 2 → E; E + 1 → F

H + 6 → N; N - 2 → L; L - 2 → J

As we can see all options follow a common pattern except for HNLJ.

Hence, HNLJ is the odd among the given options.

Preparing the family tree using the following symbols:

Hence, V is son–in–law of P.

Perseverance, Firmness and Tenacity are words related to determination.

Tendency means proneness or habit of doing something in a particular way.

Hence, Tendency is the odd word out.

56 = 7 × 8

12 = 3 × 4

30 = 5 × 6

14 = 2 × 7

Here, 14 is not a product of two consecutive numbers.

Hence, 14 is the odd among the alternatives.

The logic followed here is:

T - 1 = S;

E - 1 = D;

M - 1 = L;

P - 1 = O;

L - 1 = K;

E - 1 = D; further these codes are written in reverse order. Hence, DKOLDS.

Similarly,

W - 1 = V

O - 1 = N;

R - 1 = Q;

S - 1 = R;

H - 1 = G;

I - 1 = H;

P - 1 = O;

Further these codes are written in reverse order. Hence, 'OHGRQNV' is the correct answer.

Here, we can observe that 1, 2, 4, 5 are adjacent to 3. Thus, 3 will be opposite 6.

Hence, if 6 is at bottom 3 will be at top.

Here, in the set given in question the logic followed is:

7 + 6 = 13; 13 + 8 = 21

The same logic is followed in the set (2, 8, 16)

2 + 6 = 8; 8 + 8 = 16

Hence, the set (2, 8, 16) is the correct answer.

The correct logical order here will be:

4. Illness → 6. Doctor → 2. Diagnosis → 3. Prescription → 1. Medicine → 5. Recovery

Hence, (4, 6, 2, 3, 1, 5) is the correct order.

An action leads to a reaction.

Similarly, a stimulus leads to a response.

Hence, response is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

I. No car is a four-wheeler → False as it is possible but not definite.

II. All four-wheelers are cars → False as it is possible but not definite.

III. Some vehicles are cars → True as some cars are vehicles.

Hence, only conclusion III follows.

Hence, the given figure is embedded in the figure in option 3.

In the above series the water image and mirror image both were taken to obtain the alternate image. For eg: If we take the mirror image of the water image of the first figure then we will obtain the third figure.

Therefore,

Hence, option 3 is the correct answer.

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

Logic followed here is:

Hence, 77 is the correct answer.

1. acbddbccbddaabbddb → does not form a pattern.

2. acbddbacbddbacbddb → acbddbacbddbacbddb →forms a pattern.

3. accdbbdcbddbacbddb → does not form a pattern.

4. acbddbbcbddcaabddb → does not form a pattern.

Hence, bdabc will complete the series.

Hence, there are 18 triangles in the given figure.

Sun is a source of heat.

Similarly, fruit is a source of vitamins.

Hence, Vitamins : Fruit is the correct answer.

i) 18 × 6 - 6 ÷ 3 + 3 = 108 - 2 + 3 = 109 ≠ 6

ii) 18 ÷ 6 - 6 + 3 × 3 = 3 - 6 + 9 = 6

iii) 18 - 6 + 6 ÷ 3 × 3 = 18 ≠ 6

iv) 18 + 6 ÷ 6 - 3 × 3 = 10 ≠ 6

Hence, + and ÷ should be interchanged in the following equation to make it correct.

Here, the logic followed is:

4 : 4 ÷ 2 × (4²) = 4 : 32

Similarly,

6 : 6 ÷ 2 × (6²) = 6 : 108

Hence, 6 : 108 is the correct answer.

Current age of Father = F;

Current age of  Son = S

Ten years ago

(F - 10) = 3.5 (S - 10)

F = 3.5S - 35 + 10

3.5S - F = 25 - (i)

Ten years hence

F + 10 = 2.25 (S + 10)

F - 2.25S = 22.5 - 10

F - 2.25S = 12.5 i.e.2F - 4.5S = 25 (ii)

That implies that

3.5 S - F = 2F - 4.5S

8S = 3F

Multiplying (i) by 3

10.5S - 3F = 75         

10.5S - 8S = 75

2.5 S = 75

S = 30;

Hence 3F = 240,

F = 80

Hence, sum of ages of father and son will be 80 + 30 = 110.

The logic followed here is:

n : (2n - 2) : 4n - 2

Therefore,

10 : (20 - 2) : (40 - 2)

Similarly,

12 : (24 - 2) : (48 - 2)

Hence, (12, 22, 46) is the correct answer.

Here, the logic followed is:

B = 2; A = 1; C = 3; K = 11 and further their positional values are written in reverse order.

Similarly,

CAKE= reverse order of (3) (1) (11) (5) = 51113,

MADE = reverse order of (13) (1) (4) (5) = 54113

Hence, 54113 is the correct answer.

The most appropriate Venn diagram that illustrates the relationship between Parents, Rich Persons, and Farmers is:

Hence, the above Venn diagram is the correct answer.

According to the positional values,

BECD : YVXW → (B, Y), (E, V), (C, X) and (D, W) are reverse pairs.

Similarly,

DGEF : WTVU → (D, W), (G, T), (E, V) and (F, U) are reverse pairs.

Hence, WTVU is the correct answer.

Hence, option 2 is the correct mirror image.

• Abu Dhabi was the host for The Special Olympics World Games 2019.
• This event was organised for the first time in the Middle East and North Africa.
• Athletes competed in 24 different individual and team sports in this event.
• Capital of UAE: Abu Dhabi
• Currency: Dirham
• President : Khalifa bin Zayed Al Nahyan
• Prime Minister: Mohammed bin Rashid Al Maktoum

The correct answer is option 3 i.e Article 44,

• Article 44 is included in Part 4 of the Indian Constitution. It provides for Uniform Civil Code.

• Pulakesin I was the founder of the Chalukya dynasty. He established a small kingdom with Badami as its capital.
• The family of Western Chalukyas had its offshoots like the Eastern Chalukyas of Vengi and the Chalukyas of Kalyani.
• Narasimhavarman I was also known as Mamalla, which means ‘great wrestler’.
• Kirtivarman II was the last of the rulers of the Chalukyas. He was defeated by Dantidurga, the founder of the Rashtrakuta dynasty.

• Control and co-ordination in our body are also brought about with the help of certain chemical substances called hormones. Hormones are secreted by endocrine glands.
• The pituitary gland controls the functioning of other endocrine glands.

• SpiceJet became the first Indian budget carrier to join the International Air Transport Association (IATA).
• IATA reprents 282 airlines.
• Head Office of IATA: Montreal, Canada
• Chairman and Chief Executive Officer : Mr Carsten Spohr

• Ms. Fathimath Dhiyana Saeed was first female Secretary-General of SAARC from 2011 to 2012.
• SAARC was established on 8 December 1985.
• Member States of SAARC: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka
• SAARC Secretariat: Kathmandu, Nepal

Additional Information

• H.E. Esala Ruwan Weerakoon of Sri Lanka assumed office of the Secretary-General of the South Asian Association for Regional Cooperation (SAARC) on 01 March 2020.
• Prior to assuming the post of Secretary-General, Weerakoon served as Senior Additional Secretary to the President of Sri Lanka. Previously, he was Foreign Secretary of Sri Lanka. He had also served as Sri Lanka’s High Commissioner to India and Ambassador to Norway.
• https://www.saarc-sec.org/index.php/about-saarc/about-secretariat/secretary-general.

• Fullerene, an allotrope of carbon, is rarely found in nature. It is found in soot and in interstellar space.
• The first example of fullerene is Buckminsterfullerene (C₆₀). This allotrope of carbon is named fullerene after the architect Richard Buckminster** Fuller** because the structure of C₆₀ resembles the structure of the geodesic dome he designed.
• Harold Kroto, Robert Curl and Richard Smalley were given the Nobel prize in chemistry 1996, for the discovery of this carbon allotrope, fullerene C_60.

• Propanal is an example of an aldehyde  functional group.
• R−CHO is a general structural formula for Aldehyde.

Project Tiger: 

• It was launched on 1^st April 1973.
• It was launched from Jim Corbett National Park, which is located in Uttarakhand
• It was launched by the Union Government of India under the Ministry of Environment, Forest and Climate Change.
• Nodal Implementing Agency: National Tiger Conservation Authority.
• There are around 442 tigers present in Uttarakhand (Jim Corbet National Park) According to the latest census released by All India Tiger Estimation 2018 and this result is declared by PM Narendra Modi on International Tiger Day (29 July).

• Vaishali was the capital of Vrijji, which was a republic state.
• Monarchical states: Magadha, Kashi, Kosala, Vatsa, Chedi, Matsya, Shurasen, Avanti and Gandhara.
• Non-monarchical states/ Republic state: Malla, Vrijji, Kamboj, and Kuru

Do you know?

The ancient and modern names of the 16 mahajanapadas :

(1) Kashi (Benaras), (2) Kosal (Lucknow), (3) Malla (Gorakhpur), (4) Vatsa (Allahabad), (5) Chedi (Kanpur),(6) Kuru (Delhi), (7) Panchal (Rohilkhand),

(8) Matsya (Jaipur), (9) Shurasen (Mathura), (10) Ashmak (Aurangabad,Maharashtra), (11) Avanti (Ujjain), (12) Ang (Champa East Bihar), (13) Magadha (South Bihar), (14) Vrijji (North Bihar), (15) Gandhara (Peshawar), (16) Kamboj (Near Gandhara)

Chyap-Brung is Dholak like in shape but much bigger in size traditional musical instrument of the Limboo community.

Additional information about other options:

• Mizoram has passed the Maintenance of Household Registers Bill in March 2019.
• It aims to detect illegal foreigners residing in Mizoram.

• The idea of residual powers in Indian constitution has been taken from the constitution of Canada.

• Ethyl acetate has a strong fruity fragrance.
• This colourless liquid has a characteristic sweet smell and is used in glues, nail polish removers, decaffeinating tea and coffee.

BHEL got Maharatna status in February 2013. Full form of BHEL is Bharat Heavy Electricals Ltd.

There are 10 Maharatna Companies.

• Rangarajan panel was set up by the Government of India which suggested the total decontrol of the sugar industry.
• Sri Krishna Panel is related to reporting on data protection.
• C. Rangarajan is former Chairman of the Economic Advisory Council (EAC) to the Prime Minister and former Governor, Reserve Bank of India.

Lipu Lekh passes in Uttarakhand is used by pilgrims to Kailash-Mansarovar Yatra.

• There were 16 Mahajanpadas existed in the 7^th and early 6^th centuries BC, during the lifetime of Lord Gautam Buddha.
• The ancient and modern names of the 16 mahajanapadas :

(1) Kashi (Benaras), (2) Kosal (Lucknow), (3) Malla (Gorakhpur), (4) Vatsa (Allahabad), (5) Chedi (Kanpur),(6) Kuru (Delhi), (7) Panchal (Rohilkhand),

(8) Matsya (Jaipur), (9) Shurasen (Mathura), (10) Ashmak (Aurangabad,Maharashtra), (11) Avanti (Ujjain), (12) Ang (Champa East Bihar), (13) Magadha (South Bihar), (14) Vrijji (North Bihar), (15) Gandhara (Peshawar), (16) Kamboj (Near Gandhara)

Chandragupta-I got Pataliputra in dowry from the Lichhavis.

• He married Kumaradevi, a princess of the Lichhavis family.
• The Gupta era is considered to be founded by Chandragupta I. It starts with his accession in A.D. 320.
• At the confluence of the Son river with the Ganges, the city of Pataliputra was situated.
• In the ancient period, Pataliputra had remained the capital for the Mauryas, Sungas, Guptas, and other kingdoms.

• Vidarbha won 2017 Ranji Trophy final.
• Final match was played between Delhi and Vidarbha.
• Venue for for final match was Holkar stadium, Indore, Madhya Pradesh.
• Mumbai team has won maximum number of titles.

• ARPANET was the first working prototype of Internet.
• Full form of ARPANET is Advanced Research Projects Agency Network.
• It was 1^st network to implement TCP/IP protocol.

Nilgiri Biosphere Reserve was the first to be established by the Government of India in the year 1986.

Additional information about other Biosphere Reserve**:**

http://www.wiienvis.nic.in/Database/BiosphereReserves_8225.aspx

Chu-Faat: Meaning of Chu is the Snowy Range and that of Faat is Worship. It is is a group folk dance of Sikkim performed in honour of Mount Khangchendzonga.

Additional information about other options:

• Sirimavo Bandaranaike was the world's first female head of government. She was elected in the year 1960.
• She was representative of Sri Lanka Freedom Party.

Additional information about other Female leaders

• In March 2019, social media platforms and the Internet and Mobile Association of India (IAMAI) presented a Voluntary Code of Ethics for the General Election 2019 to the Election Commission of India.
• To ensure free, fair & ethical usage of Social Media Platforms during Lok Sabha Elections ‘Code of Ethics” was developed.
• Chief Election Commissioner of India:  Sunil Arora

Short trick∶

Put x = y = 1 in [8(x + y)3 – 27(x – y)3] ÷ (5y – x) = Ax2 + Bxy + Cy2 

∴ A + B + C = 16

Detailed Solution∶

⇒ [8(x + y)³ – 27(x - y)³] ÷ (5y - x) = Ax² + Bxy + Cy²

⇒ [{2(x + y)}³ – {3(x – y)}³] ÷ (5y – x) = Ax² + Bxy + Cy²

⇒ {2(x + y)} – {3(x – y)} [{2(x + y)}² + 2(x + y)3(x – y) + {3(x – y)}²] ÷ (5y – x) = Ax² + Bxy + Cy²

⇒ (5y – x) [4x² + 4y² + 8xy + 6x² – 6y² + 9x² + 9y² – 18xy] ÷ (5y – x) = Ax² + Bxy + Cy²

⇒ 19x² – 10xy + 7y² = Ax² + Bxy + Cy²

On comparing

⇒ A = 19, B = -10 and C = 7

⇒ (A + B + C) = 19 + 7 – 10 = 16

The ratio of the efficiency of A, B and C = 4 : 5 : 3

Total work = (4 + 5 + 3) × 25 = 300

⇒ 35% of total work = 300 × [35/100] = 105

A and C together will complete 35% of that work = 105/(4 + 3) = 15 days

MP of the article = Rs. 315

SP of the article = Rs. 288

CP of the article = Rs. 288 [100/96] = 300

⇒ Required percentage = [(315 – 300)/300] × 100 = 5%

⇒ 8 digit number 789x531y is divisible by 72 if the number is divisible by 8 and 9 both.

Divisibility of 8∶ A number will be divisible by 8 if the last three digits of the number are divisible by 8.

Divisibility of 9∶ A number will be divisible by 9 if the sum of the digits of the number is divisible by 9.

⇒ 31y is divisible by 8 if y = 2 as 312 is divisible by 8

⇒ 7 + 8 + 9 + x + 5 + 3 + 1 + 2 = 35 + x is divisible by 9 if x = 1

⇒ 5x – 3y = 5 × 1 – 3 × 2 = (-1)

Let Renu's CP = Rs. 100x

The price at which she sold that article (SP) = 100x × [75/100] = Rs. 75x

With Rs. 75 she bought another article and sold it at a gain of 40%.

SP of the new article = 75x × [140/100] = Rs. 105x

Her overall percentage profit = [(105x – 100x)/100] × 100 = 5%

Follow BODMAS rule to solve this question, as per the order given below:

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first and within the bracket.

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next.

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

⇒ 5 ÷ 5 of 5 × 2 + 2 ÷ 2 of 2 × 5 – (5 – 2) ÷ 6 × 2

We solve OF first

⇒ 5 ÷ 25 × 2 + 2 ÷ 4 × 5 – 3 ÷ 6 × 2

⇒ 2/5 + 5/2 – 1

⇒ 19/10

Total production of cars of type C and E in 2013 taken together = 52 + 36 = 88

Total production of cars of type D in 2014 and 2016 and type E in 2017 = 42 + 46 + 55 = 143

⇒ Required ratio = 88 : 143 = 8 : 13

⇒ 16x² + 9y² + 4z² = 24(x – y + z) – 61

⇒ 16x² + 9y² + 4z² – 24x + 24y – 24z + 61 = 0

⇒ (4x)² – 2 × 4x × 3 + 3² + (3y)² + 2 × 3y × 4 + 4² + (2z)² – 2 × 2z × 6 + 6² = 0

⇒ (4x – 3)² + (3y + 4)² + (2z – 6)² = 0

⇒ (4x – 3)² = 0

⇒ 4x – 3 = 0

⇒ x = 3/4

Similarly,

⇒ y = -4/3 and z = 3

⇒ (xy + 2z) = (3/4) × (-4/3) + 2 × 3 = 5

Given, AD ⊥ BC & BE ⊥ AC

⇒ ∠BDA = ∠FEA = 90°

Also, ∠BFD = ∠AFE = θ (opposite angle)

⇒ ∠FBD = ∠DAC = 90° – θ

⇒ ∠DCA = θ

Now, we can say, ΔDFB is similar to ΔDCA.

⇒ AC/AD = BF/BD [BF = AC]

⇒ AD = BD [∴ ∠ABD = ∠BAD]

In ΔABD

⇒ ∠ABD + ∠BAD + ∠BDA = 180°

⇒ 2∠ABD = 180° – 90°

⇒ ∠ABD = 45°

From figure we can say that,  ∠ABD = 45°= ∠ABC

⇒ cos² θ = 3 (cot² θ – cos² θ)

⇒ cos² θ = 3 cos² θ (cosec² θ – 1)

⇒ 1 = 3 cot² θ

⇒ tan² θ = 3

⇒ θ = 60°

$⇒ {\rm{;}}{\left( {\frac{1}{2}\sec {\rm{\theta }} + {\rm{}}\sin {\rm{\theta }}} \right)^{ - 1}}$

$⇒ ;{\left( {\frac{1}{2}\sec 60^\circ {\rm{}} + {\rm{}}\sin 60^\circ } \right)^{ - 1}}$

sec 60 = 2 and sin 60 = √3/2

⇒ [(1/2) × 2 + √3/2]^-1

⇒ [(2 + √3)/2]^-1

⇒ [2/(2 + √3)]

Rationalizing

⇒ [2/(2 + √3)] ×  [(2 – √3) / (2 – √3)]

⇒ 2(2 – √3)

Given:

Compound Interest, C.I. = Rs. 1623

Rate of Interest, R = 10 percent

Time = $2\frac{1}{2}{\rm{;Years}}$

Formula Used:

When interest is compounded annually but the time is in fraction (suppose time = ${\rm{n}}\frac{{\rm{a}}}{{\rm{b}}}$ years), then,

${\rm{A}} = {\rm{P}}{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^{\rm{n}}}\left( {\frac{{100 + \left( {\frac{{\rm{a}}}{{\rm{b}}}} \right) × {\rm{R}}}}{{100}}{\rm{;}}} \right)$

where A =Amount

P = Principal,

R = Rate of Interest,

n = Whole part of Time

a, b = Numerator and Denominator of the fraction part of the time.

Calculation:

Let the Principal be P.

So, the Amount, 

${\rm{A}} = {\rm{P}}{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^{\rm{n}}}\left( {\frac{{100 + \left( {\frac{{\rm{a}}}{{\rm{b}}}} \right) × {\rm{R}}}}{{100}}{\rm{;}}} \right)$

$\Rightarrow {\rm{A}} = {\rm{P}}{\left( {1 + \frac{{10}}{{100}}} \right)^2}\left( {\frac{{100 + \left( {\frac{1}{2}} \right) × 10}}{{100}}{\rm{;}}} \right)$

⇒ A = P × (11/10)2 × (21/20)

⇒ A = P × (121/100) 

Now, Compound Interest = Amount – Principal

⇒ 1623 = P × (121/100) × (21/20) – P

⇒ 1623 = P × {(2541/2000) – 1}

⇒ 1623 = P × (2541 – 2000)/2000

⇒ 1623 = P × 541/2000

⇒ P = 1623 × 2000/541

⇒ P = 6,000

∴ The Principal is Rs. 6,000

Production of cars of type B over five years = 39 + 45 + 54 + 60 + 72 = 270

Production of cars type B in 2016 = 60

⇒ 270 thousands represents = 360°

⇒ 60 thousands will represent = [360°/270] × 60 = 80°

Production of cars of type B in 2013, 2014, 2015 and 2017 = 39 + 45 + 54 + 72 = 210

Production of all type of cars in 2017 = 36 + 72 + 45 + 47 + 55 = 255

⇒ Required percentage = [(255 – 210)/255] × 100 = 17.6% approx

Shortcut Trick

If x is subtracted from a, b, c, d to make them proportional, then x = (ad − bc) ÷ ((a + d) − (b + c)).

Here, a = 23, b = 39, c = 32, d = 56.

x = (23 × 56 − 39 × 32) ÷ ((23 + 56) − (39 + 32)) = (1288 − 1248) ÷ (79 − 71) = 40 ÷ 8 = 5.

First number = x + 4 = 5 + 4 = 9, Second number = 3x + 1 = 3(5) + 1 = 16.

Mean proportional = √(9 × 16) = √144 = 12.

∴ The correct answer is 12.

Alternate Method

Given:

Numbers: 23, 39, 32, and 56.

x is subtracted from each number to make them proportional.

We need to find the mean proportional between (x + 4) and (3x + 1).

23 − x

39 − x

=

32 − x

56 − x

Mean Proportional = √(9 × 16) = 12

Formula Used:

If four numbers a, b, c, d are in proportion, then a ÷ b = c ÷ d.

Mean proportional between p and q = √(p × q)

Calculations:

⇒ (23 − x) ÷ (39 − x) = (32 − x) ÷ (56 − x)

⇒ (23 − x)(56 − x) = (32 − x)(39 − x)

⇒ 1288 − 56x − 23x + x² = 1248 − 39x − 32x + x²

⇒ 1288 − 79x = 1248 − 71x

⇒ 1288 − 1248 = 79x − 71x

⇒ 40 = 8x

⇒ x = 5

Now, substitute x = 5 in the expressions (x + 4) and (3x + 1):

⇒ x + 4 = 5 + 4 = 9

⇒ 3x + 1 = 3(5) + 1 = 16

⇒ Mean proportional = √(9 × 16)

⇒ Mean proportional = √144 = 12

∴ The correct answer is 12.

Additional Information

Mean Proportional

For two positive numbers a and b, the mean proportional is the square root of their product: √(a × b).

Third Proportional

For two given numbers a and b, the third proportional c satisfies the relation a : b = b : c, giving c = b² ÷ a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d satisfies a : b = c : d, which simplifies to d = (b × c) ÷ a.

Componendo and Dividendo

If a ÷ b = c ÷ d, then according to this rule, (a + b) ÷ (a − b) = (c + d) ÷ (c − d).

Given:

A takes 30 minutes more than B to cover a distance of 15 km

 A doubles his speed and takes one hour less than B to cover 15 km

Concept used:

For a given distance, speed ∝ (1/time)

speed = distance/time

Calculation:

The ratio of A's old to new speed = 1 ∶ 2

Then, the ratio of previous time to new time = 2 ∶ 1

Total time difference 2 unit - 1 unit = 30 mins + 1 hr = 3/2 hr

Or, 1 unit = 3/2 hr

Then, previous time taken by A = 2 unit = 2 × 3/2 = 3 hrs

Then, time taken by B (previously) = 3 hr - 30 mins = 2 hr 30mins

Speed of B = 15/(5/2) = 6 kmph

Go through the options, with the help of option C,

The speed of B is 6 km/h.

⇒ Time taken by B to cover 15 km = 15/6 = 2 hrs 30 min

⇒ Time taken by A to cover 15 km = 2 hrs 30 min + 30 min = 3 hrs

⇒ Speed of A = 15/3 = 5 km/h

 if A doubles his speed, he takes one hour less than B = 2 hrs 30 mins - 1 hour = 1 hour 30 mins (required)

∴ Time is taken by A if A double its speed = 15/10 = 1 hrs 30 min

(Equal and satisfied)

⇒ OP = 8 cm, O’P = 10 cm, PQ = 12 cm and PM = 6 cm

⇒ In ΔPOM

By using Pythagoras Theorem

⇒ (OP)² = (OM)² + (PM)²

⇒ 8² = (OM)² + 6²

⇒ OM = √28 cm

⇒ In ΔPO’M

By using Pythagoras Theorem

⇒ (O’P)² = (O’M)² + (PM)²

⇒ 10² = (O’M)² + 6²

⇒ O’M = 8 cm

⇒ O’O = OM + O’M = √28 + 8 = 5.3 + 8 = 13.3 cm

Given∶ x + y + z = 19 and (xy + yz + zx) = 114

Formula∶ x³ + y³ + z³ – 3xyz = (x + y + z) [(x + y + z)² – 3(xy + yz + zx)]

⇒ x³ + y³ + z³ – 3xyz = 19 (19² – 3 × 114) = 19 × 19

⇒ √[x³ + y³ + z³ – 3xyz] = √(19 × 19) = 19

Given∶ ΔABC is similar to ΔDEF.

As we know,

(Altitude of ΔABC)² / (Altitude of ΔDEF)² = (Area of ΔABC) / (Area of ΔDEF)

⇒ 5²/(Altitude of ΔDEF)² = 100/49

⇒ (Altitude of ΔDEF)² = (49 × 25)/100 ⇒ 49/4

⇒ (Altitude of ΔDEF) = √(49/4) ⇒ 7/2 = 3.5

Given:

The average weight of a certain number of students in a class is 68.5 kg.

4 new students having weights 72.2 kg, 70.8 kg, 70.3 kg and 66.7 kg join the class.

The average weight of all the students increases by 300 g

Formula:

Average weight = Total weight/Total number of students

Calculation:

Let the total number of students in the class be x.

⇒ Average weight of all students = 68.5 kg

Total weight of all students = 68.5x kg

Total weight of four students = (72.2 + 70.8 + 70.3 + 66.7) kg = 280 kg

According to the question,

⇒ 68.5x + 280 = 68.8 (x + 4)

⇒ 68.5x + 280 = 68.8x + 275.2

⇒ x = 16

∴ Total number of students initially is 16.

Let the expenditure of Raju be 100x.

Income of Raju = 100x × [120/100] = 120x

Saving of Raju = 120x – 100x = 20x

New income of Raju = 120x × [160/100] = 192x

New expenditure of Raju = 100x × [170/100] = 170x

⇒ Required percentage = [(22x – 20x)/20x] × 100 = 10% (increase)

Dimension of rectangular tank 10m × 8m × 6m

Total surface area of rectangular tank = 2(10 × 8 + 8 × 6 + 6 × 10) = 376 m²

Radius of circle = 1 m

Area of circle = πr² = 3.14 × 1 × 1 = 3.14

∴ Required area = 376 – 3.14 = 372.9 (approx)

We know∶ cos θ = Base/Hypotenuse

⇒ cos θ = 2p/(1 + p²)

Using Pythagoras Theorem

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ (1 + p²)² = (2p)² + Perpendicular²

⇒ Perpendicular² = (1 – p²)²

∴ Perpendicular = (1 – p²)

⇒ tan θ = Perpendicular/Base = (1 – p²)/2p

Given AD ⊥ BC, ∠B = 80° and ∠C = 64°

Join O to B and join O to C where point O is circum-centre of the triangle.

⇒ ∠BOA = 2∠BCA = 2 × 64° = 128°

In ΔBOA

⇒ OB = OA (radius of the circle)

⇒ ∠AB0 = ∠OAB

⇒ ∠ABO + ∠OAB + ∠BOA = 180°

⇒ 2∠OAB = 180° – 128° = 52°

⇒ ∠OAB = 26°

In ΔABD

⇒ ∠ABD + ∠BDA + ∠DAB = 180°

⇒ ∠DAB = 180° – 90° – 80° = 10°

⇒ ∠DAK = ∠BAO – ∠BAD = 26° – 10° = 16°

${\left( {\frac{{\sin {\rm{\theta }} - 2{{\sin }^3}{\rm{\theta }}}}{{2{{\cos }^3}{\rm{\theta }} - \cos {\rm{\theta }}}}} \right)^2}{\rm{}} + {\rm{}}1$

$\Rightarrow {\left( {\frac{{\sin {\rm{\theta }}}}{{\cos {\rm{\theta }}}}} \right)^2}{\left( {\frac{{1 - 2{{\sin }^2}{\rm{\theta }}}}{{2{{\cos }^2}{\rm{\theta }} - 1}}} \right)^2}{\rm{}} + {\rm{}}1$

⇒ [sinθ/cosθ]² [cos2θ/cos2θ]² + 1 [∵ (1 – 2sin²θ) = (2cos²θ – 1) = cos2θ]

⇒ tan²θ + 1

⇒ sec²θ [∵ sec²θ – tan²θ = 1]

Production of cars of type a is 2015 and of type C in 2013 = 48 + 52 = 100

Production of cars of type D in over five years = 50 + 42 + 45 + 46 + 47 = 230

⇒ Required percentage = [100/230] × 100 = 43.5% approx

The correct answer is option 4.

Due to Cyclone Idai vast areas of land have been flooded, roads destroyed and communications disrupting in Zimbabwe and Mosambique.

It can be clearly observed that the sentence is in past participle form from the words 'have been flooded, roads destroyed'.

So, we will use the past participle form of the verb 'disrupt' i.e 'disrupted'.

The correct answer is 'worker'.

Key Points

• The passage discusses the absence of manual workers to clean the streets, explicitly stating that the town has no manual workers. This implies that the position being referenced involves manual labor tasks.
• The passage notes that the last worker "retired six months ago." This terminology commonly refers to regular employees or laborers rather than officials or high-ranking personnel.
• The mention that they haven't hired anyone since the retirement of the last individual suggests that the role is specific and essential for day-to-day operations, which aligns with the role of a manual worker.
• Other mentioned roles, such as the mayor and councilors, are already identified as performing duties usually outside of their primary responsibilities because of the absence of workers, further emphasizing the need for manual workers.
• The mayor's comment about being "blocked by bureaucracy" when it comes to hiring points to administrative challenges in replacing essential staff, reinforcing that the blank pertains to a key operational role likely filled by a worker.

Therefore, the correct answer is 'Option 4'.

Additional Information

• Option 1 (councillor): This role is not typically associated with manual labor; they are elected officials involved in policy-making.
• Option 2 (member): This term is too generic and does not fit the specific reference to manual labor duties.
• Option 3 (mayor): This option is irrelevant as the passage already describes the mayor doing tasks outside his usual scope due to the absence of manual workers.

The correct answer is option 1.

The State Government argued that it could not afford the increase in the teachers' salaries as awarded by the court. 

Afford means have (a resource such as money or time) available or to spare. 

'Afford' is the correct word as the sentence states that the government did not have enough resources to spare so as to increase the teachers' salaries.

So, options 2, 3 and 4 are incorrect.

The correct answer is option 3.

The first statement should be B i.e 'Environmental groups have tagged the Philippines as one of the world's biggest ocean polluters due to its reliance on single-use plastic.' It gives an introduction of what is being talked about in the following statements.

After B, it should be A i.e 'That sort of pollution, which is also widespread in other southeast Asian nations, regularly kills wildlife like whales and turtles that ingest the waste.' In the previous statement, ocean pollution was mentioned so, B gives the consequences of this pollution.

After A, it should be D as it talks about a case in the Philippines and after D, it should be C as it talks about a case in Thailand.

The correct order is BADC.

So, options 1,2 and 4 are incorrect.

The correct answer is option 2 i.e

Gun-totting guards were guarding the main gate of the building.

Firstly, the 'main gate' becomes the object and 'gun-totting guards' become the subject. Since the passive form contains  'was being guarded' , so it means that the active form is in past continuous form. Therefore, we remove 'being' and convert the verb into the past continuous form i.e 'guarding'.

So, options 1,3 and 4 are incorrect.

The correct answer is option 4.

Costs an arm and a leg means something which is very expensive.

So, options 1,2 and 3 are incorrect.

The correct answer is option 3.

Get out of hand means when something goes out of control.

So, options 1,2 and 4 are incorrect.

The correct answer is option 1.

An Italian mayor has been cleaning the streets along with his councilors after their town (1) was left with no manual workers, it's reported.

In the given sentence, simple past tense will be used i.e 'was left' because it is talking about a present situation i.e. mayor cleaning the streets which is a result of something that has already happened i.e. no manual workers left. 

So, options 2,3 and 4 are incorrect.

The correct answer is option 1.

in front of the (3) local church in preparation for market day

The correct word is 'local' as it correctly defines the church present in the town. Also, 'local' is an adjective used to describe the church whereas 'near' and 'next' are adverbs. We need an adjective in the given blank.

So, options 2,3 and 4 are incorrect.

The correct answer is option 4.

Your car should not be parked in front of my house.

In case of a command, while converting to the passive voice we first write the object i.e. car, then 'not be' and lastly the third form of verb i.e 'parked'.

So, options 1,2 and 3 are incorrect.

The correct answer is option 2.

Tender means showing gentleness, kindness, and affection.

For eg; She was such a kind and tender lady.

Gentle means having or showing a mild, kind, or tender temperament or character.

Rough means not gentle; violent

For eg; He had a rough behavior toward everyone.

It is clear that tender and rough are antonyms.

Soft means not strong or violent.

Warm means having or showing enthusiasm, affection, or kindness.

So, options 1,3 and 4 are incorrect.

The correct answer is option 3.

(4) alongside the deputy mayor's father and a town councilor armed with a high-pressure hose.

'Along' means in a line or next to something long or thin. 'Alongside' means 'next to' or 'close to' something. In the given sentence, 'alongside' will be used to describe the mayor sweeping next to the deputy mayor's father and a town councilor.

So, options 1,2 and 4 are incorrect.

The correct answer is option 3.

Tilt means move or cause to move into a sloping position.

For eg; The floor was tilted.

Cross means go or extend across or to the other side of (an area, stretch of water, etc.).

Support means bear all or part of the weight of; hold up.

Slant means slope or lean in a particular direction; diverge or cause to diverge from the vertical or horizontal.

For eg; The sun slanted through the mountains.

It is clear that slant and tilt are synonyms.

Straighten means make or become straight.

So, options 1,2 and 4 are incorrect.

The correct answer is option 3.

The correct spelling of the word in option 3 is competition.

All the other words in options 1,2 and 4 are correctly spelt.

The correct answer is option 2.

I  have been looking for a better job for the last two months, but nothing is in sight.

The phrase 'for the last two months' states that the speaker has started an activity in the past which is being continued in the present. So, we will use the present perfect continuous tense i.e. have been looking.

So, options 1,3 and 4 are incorrect.

The correct answer is option 2.

 In fact, (2) he was sweeping the piazza

In the  sentence, the mayor is being talked about. So, we will use 'he'. 

'It' is not used before persons.

'They' is plural so it cannot be used before 'was'.

So, options 1,3 and 4 are incorrect.

The correct answer is: Option 2 i.e. examplify.

Key Points

• The word "examplify" is incorrectly spelled. The correct spelling is "exemplify", which means to illustrate or clarify by giving an example. (उदाहरण प्रस्तुत करना)
• Example: Her achievements exemplify the importance of hard work and dedication.

Therefore, the correct answer is: examplify.

Additional Information

Here are the other options with their meanings:

• Example (उदाहरण): A representative form or pattern.
• Example: An example of her work is displayed in the gallery.
• Exhale (सांस छोड़ना): To breathe out.
• Example: He took a deep breath and then exhaled slowly.
• Exempt (मुक्त): Free from an obligation or liability imposed on others.
• Example: His income is exempt from taxes.

The correct answer is option 4.

Alien means belonging to a foreign country.

Occupant means a person who resides or is present in a house, vehicle, seat, etc., at a given time.

Resident means a person who lives somewhere permanently or on a long-term basis.

Native means a person born in a specified place or associated with a place by birth, whether subsequently resident there or not.

So, options 1,2 and 3 are incorrect.

The correct answer is option 2.

If you join this job now, it will prove to be good in the long run. 

In the question, the speaker is talking about what will happen in the future i.e. 'long run' if he joins the job now. So, we will use the simple future tense i.e. 'will prove to be' .

So, options 1,3 and 4 are incorrect.

The correct answer is option 1.

Scientists at Cambridge University are investigating how plants can give us sustainable energy. 

Investigating means to carry out research or study into (a subject or problem, typically one in a scientific or academic field).

Inspecting means to look at (someone or something) closely, typically to assess their condition or to discover any shortcomings.

Scrutinizing means to examine or inspect closely and thoroughly.

Looking means to direct one's gaze in a specified direction.

So, options 2,3 and 4 are incorrect.