SSC CGL Previous Paper (Held On: 11 August 2017 Shift 3) (Previous Year Paper)

When we open figure as it is folded then it would appear like as shown in below diagram,

Therefore, 4 is correct option.

Above shown image represent correct mirror image of given question figure.

Therefore, image of option 3) is correct answer.

The given information can be represented as:

The code for ‘of’ is “fod”.

Drawing a Venn diagram based on the information given in the statement,

Conclusions:

I. Some banks are industry → True

II. All banks are industry → False

Hence, only conclusion I follows.

1. 33, 00, 98, 30, 88 → R, A, T, E, U.

2. 14, 43, 55, 11, 68 → R, A, T, E, P.

3. 14, 24, 86, 42, 56 → R, A, T, E, P.

4) 02, 12, 67, 04, 96 → R, A, T, E, S.

Hence, “02, 12, 67, 04, 96” is a set of number which represent word ‘RATES’

Dictionary order of the given words:

1. Clocklipe
2. Clockwise
3. Cloddier
4. Clodpates
5. Clodpolls

 Clearly, the sequence for the given words occur in the dictionary is “15234”.

The triangles formed are:

ABC, AEG, AGD, EGF, GDF, DFC, ABF, AED, AEF, AEC, AFD, AFC, EDF, ABE and DEC.

Hence, there are ‘15’ triangles in this figure.

Baseball, Football and Hockey are outdoor games but Snooker is an indoor game.

So, Snooker is an odd word from the given alternatives.

Therefore, Snooker is the odd one out due to the difference in the nature and playing area of the sport.

Hence, “Snooker” is correct answer.

Opposite numbers of:

1 → 5

6 → 3

2 → 4

So, from given options 2^nd, 3^rd and 4^th figures are not possible.

Hence, 1^st figure is correct answer.

The question figure is hidden/embedded in this figure:

Therefore, image of option (3) is correct answer.

Given series: 5, 13, 40, 104, ?

13 - 5 = 8 = 2³

40 - 13 = 27 = 3³

104 - 40 = 64 = 4³

Similarly,

The next term - 104 = 5³ = 125

= 125 + 104

= 229

Hence, “229” is correct answer.

1. AREA → ERADICATE → Can be formed

2. CARE → ERADICATE → Can be formed

3. DICE → ERADICATE → Can be formed

4. TASTE → ERADICATE → There is no letter ‘S’ so it can’t be formed.

Hence, the word which can’t be formed from ERADICATE is “TASTE”.

The logic follows here is:

In the given options, except KXR all have one vowel.

Hence, "KXR" is the correct answer.

Both Leopard and Lion are part of Animals.

Therefore, above diagram best express relationship between Animal, Leopard and Lion.

The pattern followed here is:

In first term we have to add first two numbers then we divide it by third number which is equal to second term.

(5 + 3)  ÷  4 = 8  ÷  4 = 2

Among the following options, the same pattern will be followed:

1. 102 : 9

(1 + 0)  ÷  2 = 1  ÷  2 = 0.5 ≠ 9

2. 553 : 6

(5 + 5)  ÷  3 = 10  ÷  3 = 3.33 ≠ 6

3. 884 : 2

(8 + 8)  ÷  4 = 16  ÷  4 = 4 ≠ 2

4. 999 : 2

(9 + 9)  ÷  9 = 18  ÷  9 = 2

Clearly, “999 : 2” is correct answer.

AKP : 1121256

A = 1² = 1

K = 11² = 121

P = 16² = 256

So, AKP = 1121256

Similarly,

L = 12² = 144

N = 14² = 196

O = 15² = 225

So, LNO = 144196225

Hence, “144196225” is correct answer.

1. efgegeffhghhehefffgggheh

2. efggheffhghheheffhggghhh

3) efgheeffgghheeefffggghhh = efghe effgghh eeefffggghhh

4. efghgeffeghhefeffhgggheh

So, hegefh is required to complete this series.

Let the present ages of Aman and Ankit be 2x and x respectively.

So,

2x + x = 72

3x = 72

x = 24

The present ages of Aman and Ankit are 48 and 24 years respectively.

After 6 years Aman’s age will be 48 + 6 = 54 years.

Hence, “54” is correct answer.

T is sitting exactly in the middle of the row.

Q is sitting to the immediate right and immediate left of P and T respectively.

S is not sitting at the extreme end.

Clearly, “Q” is sitting third to the left of R.

Given expression:

13 + 12 × 9  ÷  3 – 6 = ?

After using proper signs:

13 ÷ 12 – 9 × 3 + 6 = –239/12

Hence, “–239/12” is correct answer.

145, 581 and 651 are composite numbers but 463 is a prime number.

Clearly “463” is the odd one.

Ampere is a unit of measurement of an electric current. Similarly, Fathom is a unit of measurement of depth of water.

Hence, “Depth of Water” is correct answer.

6 @ 4 @ 7 = 6² + 4² + 7² = 36 + 16 + 49 = 101

2 @ 5 @ 11 = 2² + 5² + 11² = 4 + 25 + 121 = 150

Similarly,

A @ 8 @ 9 = 289

A² + 8² + 9² = 289

A² + 64 + 81 = 289

A² = 144

A = 12

Hence, “12” is correct answer.

In 1^st figure:

(2 + 3) × (5 - 1) = 20

(3 + 6) × (9 - 1) = 72

In 2^nd figure:

(3 + 7) × (10 - 1) = 90

(7 + 4) × (11 - 1) = 110

Similarly in 3^rd figure,

(1 + 7) × (8 - 1) = 56

(7 + 6) × (13 - 1) = 156

Hence “156” is correct answer.

If we use this figure:

Then it will complete the figure.

Option 3 is correct, Fundamental Rights.

• There are six Fundamental Rights in the Indian Constitution and they are as follows:
• Right to equality
• Right to freedom
• Right against exploitation
• Right to freedom of religion
• Cultural and educational right
• Right to constitutional remedies
• Fundamental Rights are justiciable in nature.

Extra facts:

• Article 21A is added in the Indian Constitution in the 86th Constitutional Amendment Act 2002.
• Article 19 to 22 comes under the Right to freedom of the Fundamental Right of the Indian Constitution.

The correct answer is Sania Mirza.

• Sania Mirza has been awarded the 'Rajiv Gandhi Khel Ratna Award' for the year 2015.

Key Points

• Union Ministry of Youth Affairs and Sports has conferred Sania Mirza with the Rajiv Gandhi Khel Ratna award 2015.
• In this regard, Union Sports Minister Sarbanada Sonowal forwarded Sania’s name for the highest honour given for achievement in sports.
• Sania Mirza -
• She is famous as an Indian female tennis player.
• He won during the doubles at Wimbledon in the year 2004.
• In 2009, she became the first female player to win a Grand Slam for India.
• He was awarded the Arjuna Award in 2005.
• Her autobiography is Ace Against Odds.

Elements of the same group in a periodic table have an identical electronic configuration which means they have same outer shell electronsand these outer electrons are called valence electrons. These valence electrons are used for making chemical bonds with other elements.Elements in the same group in the periodic table have similar chemical properties.

Indian Railways has signed an agreement for Dedicated Freight Corridor with Monash University's Institute of Railway Technology to offer assistance on the establishment of a new state-of-the-art railway research and development institute. On March 2017an agreement was signed between the officials from Monash University and the Indian Ministry of Railways Corporation.

CONCEPT:

• Photoelectric effect: The phenomenon in which the light energy forces a metal surface to release electrons is called the photoelectric effect.
• When the light hits, it shows the particle theory of light, and light is defined as a stream of photons or energy packets.
• The other phenomena such as interference, diffraction, and polarization can only be explained when the light is treated as a wave wherein the photoelectric effect, line spectra, and the production and scattering of x rays demonstrate the particle nature of light.

EXPLANATION:

• From the above discussion, the photoelectric effect shows the particle nature of light. So option 3 is correct.

The Kaladan Multi-Modal Transit Transport Project has been undertaken with the neighboring country Myanmar. According to the project, it will connect the eastern Indian seaport of Kolkata with Sittwe seaport in Rakhine State, Myanmar. In Myanmar, it will then link Sittwe seaport to Paletwa, Chin State via the Kaladan river boat route, and then from Paletwa by road to Mizoram state in Northeast India.

Nickel is a common cause of dermatitis which is an itchy rash that appears where your skin touches a usually harmless substance.It is basically a common skin condition caused by inflammation of the skin and is usually characterized by the red and itchy skin.

• The chemical formula of Bleaching powder is written as CaOCl₂. It is a white powder consisting chiefly of calcium hydroxide, calcium chloride, and calcium hypochlorite and used as a bleach, disinfectant, or deodorant.
• The chemical formula of washing soda or sodium carbonate is Na₂CO3.
• The chemical formula of Baking powder and baking soda is NaHCO3.

Saurabh Duggal is the author of the book 'Akhada: The Authorized Biography of Mahavir Singh Phogat' which is an autobiography of the Indian wrestling coach and amateur wrestler Mahavir Singh Phogat. He is the father and coach of Geeta Phogat, who won India's first gold medal in women's wrestling in the 55 kg freestyle category at the 2010 Commonwealth Games.

The pitch of a sound depends on the frequency of the source of the sound. Frequency is measured in Hertz (Hz), with one vibration per second being equal to one hertz (1 Hz). A high frequency generally produces a high pitched note and a low frequency similarly produces a low pitched note.

Key PointsMycoplasma 

    Figure. Structure of Mycoplasma

• They belong to the genus of bacteria.
• They are the smallest bacterial cells yet discovered, can survive without oxygen, and come in various shapes.
• They completely lack a cell wall.
• They are the smallest living cells known and can survive without oxygen.
• Many Mycoplasma is pathogenic in - animals and plants.
• Ex. M. genitalium (Cause infection of genital), M. pneumoniae (cause atypical pnemonia)

Additional Information​ Fungi

• They are - unicellular or multicellular non-photosynthetic organisms.
• Their cell wall is made of chitin.
• These are saprophytic and parasitic in nature.
• Examples. Yeast, Candida

 Bacteria :

• They are unicellular, microscopic, prokaryotic microorganisms that contain no true nucleus.
• They have cell wall and flagella (tail like structure) for locomotion.
• They are found in different shapes - Cocci (round shape), bacilli (rod shape),, cocco-bacillii (round-rod combined shape), Vibrio (comma shape), Spirillum (spiral shape)
• Examples. Lactobacillus, Streptococcus pneumoniae

Green Algae :

• These are the micro-organisms that are grouped in the kingdom Protista. They are plant-like, in that they are able to manufacture energy from sunlight using chlorophyll pigments.
• The plant body may be unicellular, colonial or filamentous.
• The members of Chlorophyceae (Group of Algae) are commonly called Green algae.
• Examples. Chlamydomonas, Chara.

The correct answer is Battle of Plassey.

Key Points

• Troops of the British East India Company, led by Robert Clive, came up against the forces of Siraj-ud-Daulah, the last Nawab of Bengal, and his French allies.
• Clive's victory eventually led to the British becoming the greatest economic and military power in India.
• The Battle of Plassey had political significance for it laid the foundation of the British Empire in India.; it has been rightly regarded as the starting point of British rule in India.
• Result of Battle of Plassey-
• As a result of this victory, Mir Jafar became the Nawab of Bengal. He gave large sums of money plus the zamindari of 24 Parganas to the English.
• English rivals, French were ousted.

• ‘Mitochondria’ is known as the powerhouse of the cell.
• It is found in the cells of both plant and animals.
• There are many enzymes and coenzymes which are responsible for energy metabolism.
• Mitochondria are the major sites of aerobic respiration within cells since they produce 95 per cent of the ATP molecules in animal cells.

The Forty-second Amendment of India, officially known as The Constitution Act, 1976, was enacted during the Emergency by the Indian National Congress. This amendment brought some of the most important changes to the Constitution in its history. Hence it is sometimes called as “mini-Constitution” of India. Some of the changes that it brought are:

• Added Fundamental Duties by the citizens
• Made the president bound by the advice of the cabinet.
• Provided for administrative tribunals and tribunals for other matters
• Froze the seats in the Lok Sabha and state legislative assemblies on the basis of 1971 census till 2001.
• Made the constitutional amendments beyond judicial scrutiny

Pneumatophores, also called air root are mainly specialized root that grows upwards out of the water or mud to reach the air and from there it obtains oxygen for the root systems of trees that live in swampy or tidal habitats. Ex-The"knees" of mangroves and the bald cypress are examples of pneumatophores.

A direct tax is paid directly by an individual or organization to the imposing entity. For example, a taxpayer pays direct taxes to the government for various reasons and it includes real property tax, corporate tax, income tax or taxes on assets. All these taxes are paid directly to the government. If a person makes 100,000 in a year and owes 40,000 in taxes, the 40,000 would be a direct tax.

Charles Babbage is known as the 'Father of Modern Computer'after he invented the Analytical Engine in 1837. The Analytical Engine contained an Arithmetic Logic Unit (ALU), basic flow control, and integrated memory; hailed as the first general-purpose computer concept.

'Pregnancy Aid Scheme' scheme was launched by P. M. Narendra Modi on 31 December 2016 and the main objective of the scheme is to bring down the maternal mortality rate by increasing the number of institutional deliveries across the nation. According to the scheme, the central government will provide Rs. 6000 to the pregnant women after the delivery of the child in any government hospital.

Ian Donald, a Scottish physician pioneered the use of diagnostic ultrasound.Medical ultrasound is a diagnostic imaging technique based on the application of ultrasound. It is generally used to see the internal structures such as tendons, muscles, joints, blood vessels, and internal organs of the human body.

• The Summer Olympics 2020, also known as the Games of the XXXII Olympiad is a forthcoming international multi-sport event that is scheduled to take place from 24 July to 9 August 2020 will be held in Tokyo, Japan.
• The Summer Olympics 2016, also known as the Games of the XXXI Olympiad is an international multi-sport event that took place from 5^th to 25^th August 2016in Rio de Janeiro, Brazil.
• The Summer Olympics 2012, also known as the Games of the XXX Olympiad is an international multi-sport event that took place from 27^th July to 12^th August 2012in London.

Courier service comes under the tertiary sector or service sector that is the third of the three economic sectors of the three-sector theory. The others are the secondary sector (the same as manufacturing), and the primary sector (raw materials).

'Namami Brahmaputra' tagged as ‘India’s largest river festival’ has been organized across 21 districts of the Assam and will showcase trade, tourism and cultural possibilities of along Brahmaputra River. Bhutan Prime Minister Tsering Tobgay also attended the festival which was inaugurated by Pranab Mukherjee.

The full form of ITCZ is The Intertropical Convergence Zone.

• It is the area encircling Earth near the Equator, where there is a convergence of the northeast and southeast trade winds takes place.
• The ITCZ was originally identified from the 1920s to the 1940s as the "Intertropical Front" but after the recognition in the 1940s and 1950s of the significance of wind field convergence in tropical weather production.

The Alps are the highest and most extensive mountain range system that are located in Europe. The mountain stretches approximately 1,200 kilometers across eight Alpine countries, namely: France, Switzerland, Italy, Monaco, Liechtenstein, Austria, Germany, and Slovenia.

Let the speed of boat in still water be a km/hr. and speed of water be b km/hr

According to the problem statement

⇒ 4/(a - b) + 4/(a + b) = 1

Let 1/(a - b) = x and 1/(a + b) = y

⇒ 4x + 4y = 1

⇒ x + y = 1/4       ----(i)

Another equation can be written as

⇒ 5/(a + b) + 3/(a - b) = 55/60

⇒ 5y + 3x = 11/12 Using (i) here

⇒ 5(1/4 - x) + 3x = 11/12

⇒ 2x = 5/4 - 11/12

⇒ x = 1/6

⇒ x = 1/6 put this in (i) to get y

⇒ y = 1/4 - 1/6 = 1/12

⇒ a - b = 1/x = 6 and a + b = 1/y = 12 ,

Now adding these two equations

⇒ 2a = 18

⇒ a = 9

∴ The speed of boat in still water is 9 km/hr

Given that the expression x6 - 18x3 + k is perfect square, so it should be satisfied with all the values of x

⇒ Put x = 1, expression becomes k – 17

Now checking the options

If k = -9

⇒ -9 - 17 = -26 which is not a perfect square

If k = -81

⇒ -81 - 17 = -98 which is not a perfect square

If k = + 9

⇒ 9 - 17 = -8 which is not a perfect square

If k = 81

⇒ 81 - 17 = 64 which is a perfect square

∴ k must be 81 to make the expression x6 - 18x3 + k as a perfect square

Let the marked price be Rs. 100

After discount price be = 100 × (1 - 25/100) = Rs 75

Let the price for which he has bought that object be Rs. y, Now from the problems statement

⇒ y (1 - 15/100) = 75

⇒ 0.85 y = 75

⇒ y = 75/0.85 = 1500/17

Now, when article is sold at M.P then

∴ Profit % = (100 - 1500/17)/(1500/17) × 100 = 200/1500 × 100 = 13.33%

Using Componendo and dividendo in the given equation

\(\begin{array}{l} \Rightarrow \frac{{\sqrt {5{\rm{;}} + {\rm{;x}}} ; + ;\sqrt {5 - {\rm{x}}} }}{{\sqrt {5{\rm{;}} + {\rm{;x}}} - \sqrt {5 - {\rm{x}}} }}; = ;\frac{3}{1}\ \Rightarrow \frac{{\left{ {\left( {\sqrt {5{\rm{;}} + {\rm{;x}}} ; + ;\sqrt {5 - {\rm{x}}} } \right); + ;\left( {\sqrt {5{\rm{;}} + {\rm{;x}}} - \sqrt {5 - {\rm{x}}} } \right)} \right}}}{{\left{ {\left( {\left( {\sqrt {5{\rm{;}} + {\rm{;x}}} ; + ;\sqrt {5 - {\rm{x}}} } \right) - \left( {\sqrt {5{\rm{;}} + {\rm{;x}}} - \sqrt {5 - {\rm{x}}} } \right)} \right)} \right}}}; = \frac{{3; + ;1}}{{3 - 1}}\ \Rightarrow \frac{{\sqrt {5{\rm{;}} + {\rm{;x}}} }}{{\sqrt {5 - {\rm{x}}} }} = 2 \end{array}\)

Now squaring both sides

⇒ 5 + x = 20 - 4x

⇒ x = 3

∴ The value of x is 3

Given that loan for bank 2 in 2014 is 122 and for year 

2010 it is 65

Percentage increase can be given as

⇒ (122 - 65) × 100/65

⇒ 87.69%

∴ Percentage increase in loan is 87.69%

Since we know that ∠OAP and ∠OBP will be 90° because AP and BP are tangents to the circle

Now for quadrilateral OAPB

⇒ ∠O + ∠A + ∠P + ∠B = 360

⇒ ∠P = 360 - 90 - 90 – 120

⇒ ∠P = 60°

Now in triangle OAB

∠O + ∠A + ∠B = 180

Since OA = AB = radius of circle so, ∠A = ∠B, Using this

⇒ ∠B = (180 - 120)/2

⇒ ∠B = ∠OBA = 30° Using this

Since we know that

⇒ ∠OBA + ∠ABP = 90

⇒ ∠ABP = 90 - 30 = 60°

Similarly ∠BAP = 60°

Since all 3 angles of triangle ABP are 60° so it is equilateral triangle of side 6 cm

⇒ Area = √3 × (side)²/4

⇒ Area = √3 ×6²/4 = 9√3

∴ the required area is 9√3 cm²

From the table we can observe that

For bank 1 the trend is:

It is continuously increasing

For bank 2 the trend is:

Increasing, decreasing, Increasing, Increasing

For bank 3 the trend is:

Increase, increase, decrease, increase

For bank 4 the trend is:

It is continuously increasing

For bank 5 the trend is:

It is continuously increasing

∴ We can say that for bank 1,4 and 5 there is continuous trend of increasing

Given that tan θ + cot θ = x

Now, squaring both sides

⇒ (tan θ + cot θ) ² = x²

⇒ tan² θ + cot² θ + 2 = x²

⇒ tan² θ + cot² θ = x² - 2

Now, squaring both sides

⇒ (tan² θ + cot² θ) ² = (x² - 2) ²

⇒ tan⁴ θ + cot⁴ θ + 2 = x⁴ + 4 - 4x²

∴ tan⁴ θ + cot⁴ θ = x²(x² - 4) + 2

Given that loan for bank 1 in 2014 is 352 and for year 2010 it is 265

⇒ Percentage increase can be given as

⇒ (352 - 265) × 100/265

⇒ 32.83%

∴ Percentage increase in loan is 32.83%

Given that loan for bank 2 in 2014 is 122 and for year 2010 it is 65

⇒ Percentage increase can be given as

⇒ (122 - 65) × 100/65

⇒ 87.69%

∴ Percentage increase in loan is 87.69%

Given that loan for bank 3 in 2014 is 211 and for year 2010 it is 138

⇒ Percentage increase can be given as

⇒ (211 - 138) × 100/138

⇒ 52.89%

∴ Percentage increase in loan is 52.89%

Given that loan for bank 4 in 2014 is 122 and for year 2010 it is 65

⇒ Percentage increase can be given as

⇒ (122 - 65) × 100/65

⇒ 44.03%

∴ Percentage increase in loan is 44.03%

Given that loan for bank 5 in 2014 is 158 and for year 2010 it is 80

⇒ Percentage increase can be given as

⇒ (158 - 80) × 100/80

⇒ 97.5%

∴ Percentage increase in loan is 97.5%

∴ we can see that the order is Bank 5 > Bank 2 > Bank 3 > Bank 4 > Bank 1

Let the voted poll be y

From the problems statement

⇒ 70 × y/100 - 30 × y/100 = 15400

⇒ y = (15400 × 100)/40

Votes polled for loosing party are (100 - 70)% of y

⇒ votes polled = (30 × 15400 × 100)/(100 × 40) = 11550

Alternate Method

Given:

Percentage of votes won by winning candidate = 70%

Percentage of votes obtained by losing candidate = 30%

Concept used:

Difference between the two = votes by which winning candidate won

Calculation:

40% = 15400

1% = 385

Then, votes got by losing candidate = 30% = 11550

∴ The votes polled for losing party are 11550

Let the price at it he bought that calculator be Rs. Y

⇒ He sold it for = y × (1 + 15/100)

⇒ He sold it for = 1.15y

If he sells it for triple of this price

⇒ He sold it for Rs. 3 × 1.15y = 3.45y

Now the profit percentage can be given as

⇒ (3.45y - y) × 100/y

⇒ 245%

∴ Profit percentage will be 245%

Let the perpendicular bisector from centre of circle to the cord be C

Now in triangle OCP, Using Pythagoras theorem

⇒ OP² = OC² + CP²

⇒ OC² = 6.5² - (4.5 + 3.5/2)²       ----(i)

Now in triangle COR, using Pythagoras theorem

⇒ OR² = radius² = (3.5/2) ² + OC² From (i)

⇒ radius² = 1.75² + 6.5² - (4.5 + 3.5/2) ²

⇒ radius² = 6.25

⇒ radius = 2.5

∴ The radius is 2.5 cm

Work done by A in 1 day is 1/6 × 1/8 = 1/48^th of the total work

Work done by B in 1 day is 1/4 × 1/10 = 1/40^th of the total work

Let the number of hours needed to work for a day are y

From the problem’s statement

⇒ 5y(1/48 + 1/40) = 1

⇒ y = (40 × 48) / (88 × 5)

⇒ y = 48/11

$\Rightarrow y = 4;\frac{4}{{11}}$

∴ The number of hours required are 4 $\frac{4}{{11}}$ hours per day

If a chord of a circle subtends an angle of 30° at the circumference of the circle then the angle subtended by chord at centre is 2 × 30° = 60°

In the triangle formed by cord at the centre One angle is 60° and other two are same because two sides opposite to that angles are same i.e. radius of circle

⇒ All the angles of triangle are 60° and hence it is equilateral triangle

∴ the ratio of radius and chord is 1 : 1

Let the rate be r%

Interest received can be given as

⇒ 130% of 9500

⇒ Interest = 130 × 9500/100       ----(i)

And simple interest can be written as

⇒ Simple Interest = (9500 × 10 × r)/100       ---- from equation (i)

⇒ (9500 × 10 × r)/100 = 130 × 9500/100

⇒ r = 13

∴ The rate is 13% per annum

Given x³ + y³ + z³ can be written as (x + y + z) {(x + y + z)² - 3(xy + yz + zx)} + 3xyz

⇒ x³ + y³ + z³ = (x + y + z) {(x + y + z)² - 3(xy + yz + zx) } + 3xyz

Using the given values

⇒ x³ + y³ + z³ = 12 × {(12)² - 3 × 44} + 3 × 48

⇒ x³ + y³ + z³ = 288

∴ x³ + y³ + z³ = 288

Let the number of boys be y

Given that average initially is 36kg

⇒ (sum of age of all boys initially)/y = 36

⇒ 36y = sum of age of all boys initially       ----(i)

Now when one boy joins and another leaves

⇒ (sum of age of boys initially - 42 + 30)/y = 35.7 Using (i)

⇒ 36y - 12 = 35.7y

⇒ 0.3y = 12

⇒ y = 40

∴ There are 40 boys in the group

Given that (perimeter of circle)/4 = 44 cm

Let the radius be r

⇒ 2πr/4 = 44

⇒ (22/7) × r = 88

⇒ r = 28

∴ The radius be 28 cm

In the mixture ratio of A : B : C is given as

⇒ 24 : 36 : 84

⇒ 2 : 3 : 7

Type A wheat in C can be founded as

⇒ (2 × 84)/(2 + 3 + 7)

⇒ 14

∴ 14 kg of wheat A is there in Box C

Given:

[1/(1 - tan θ)] - [1/(1 + tan θ)] can be written as

⇒ {(1 + tanθ) - (1 - tanθ) }/{(1 + tanθ) (1 - tanθ)}

⇒ 2tanθ/(1 - tan²θ)

Since we know that tan 2θ = 2 tanθ/(1 - tan²θ)

⇒ [1/(1 - tan θ)] - [1/(1 + tan θ)] = 2tanθ/(1 - tan²θ) = tan 2θ

∴ [1/(1 - tan θ)] - [1/(1 + tan θ)] = tan 2θ

Let the numbers be a = (x - 1), b = (x) and c = (x + 1)

From the problem’s statement

(a + b + c) ² - (a² + b² + c²) = 292

⇒ a² + b² + c² + 2ab + 2bc + 2ca - a² - b²- c² = 292

⇒ ab + bc + ca = 146

⇒ (x) (x - 1) + (x) (x + 1) + (x + 1) (x - 1) = 146

⇒ 3x² = 147

⇒ x = 7

∴ The largest number is x + 1 = 8

Loan amount disbursed by Bank 1 in 2011/Loan amount disbursed by Bank 2 in 2014 can be written as

⇒ 295/122

⇒ Its value is around 2.41

Loan amount disbursed by Bank 3 in 2014/Loan amount disbursed by Bank 4 in 2011 can be written as

⇒ 211/123

⇒ Its value is around 1.71

∴ we can say that I > II

We know that the circle circumscribing the right angled triangle is having hypotenuse of the triangle as its diameter

Radius of circle is ½ × hypotenuse

Now using Pythagoras theorem

⇒ hypotenuse² = 12² + 5²

⇒ hypotenuse = √169

⇒ hypotenuse = 13 cm

∴ Radius is 13/2 i.e. 6.5 cm

Shortcut Trick

If tan² θ + cot² θ = 2, it satisfies the condition x + 1/x = 2, which means tan θ = 1.

For tan θ = 1, the value of θ = 45°.

Substitute θ = 45° in the expression 2sec θ cosec θ.

⇒ 2 × sec 45° × cosec 45° = 2 × √2 × √2 = 2 × 2 = 4.

∴ The correct answer is 4.

Alternate Method

Given: tan² θ + cot² θ = 2

Formula Used: sec θ = 1/cos θ and cosec θ = 1/sin θ

⇒ tan² θ + 1/tan² θ = 2

⇒ tan⁴ θ − 2tan² θ + 1 = 0

⇒ (tan² θ − 1)² = 0

⇒ tan² θ = 1 → tan θ = 1

⇒ θ = 45°

⇒ Value = 2 × sec 45° × cosec 45°

⇒ Value = 2 × (√2) × (√2)

⇒ Value = 2 × 2 = 4

∴ The correct answer is 4.

Additional Information

Reciprocal Identities

Standard relations like tan θ × cot θ = 1, sin θ × cosec θ = 1, and cos θ × sec θ = 1 are fundamental in solving trigonometric equations.

Arithmetic Mean - Geometric Mean (AM-GM) Inequality

For positive values, x + 1/x ≥ 2. The equality x + 1/x = 2 holds true only when x = 1.

Double Angle Relation

The expression 2sec θ cosec θ can be simplified as 2 / (sin θ cos θ) = 4 / (2 sin θ cos θ) = 4 / sin 2θ.

$x = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }}$ ----(1)

Adding 2√a on both sides of eq (1), we get

$\Rightarrow ;x + 2\sqrt a = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }} + 2\sqrt a = \frac{{2\sqrt a \left( {\sqrt a + 3\sqrt b } \right)}}{{\sqrt a + \sqrt b }}$

Now, subtracting 2√a on both sides of eq (1) , we have

$\Rightarrow ;x - 2\sqrt a = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }} - 2\sqrt a = \frac{{2\sqrt a \left( {\sqrt b - \sqrt a } \right)}}{{\sqrt a + \sqrt b }}$

Adding 2√b on both sides of eq (1) , we get

$\Rightarrow ;x + 2\sqrt b = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }} + 2\sqrt b = \frac{{2\sqrt b \left( {\sqrt b + 3\sqrt a } \right)}}{{\sqrt a + \sqrt b }}$

Now, subtracting 2√b on both sides of eq (1) , we have

$\Rightarrow ;x - 2\sqrt b = \frac{{4\sqrt {ab} }}{{\sqrt a + \sqrt b }} - 2\sqrt b = \frac{{2\sqrt b \left( {\sqrt a - \sqrt b } \right)}}{{\sqrt a + \sqrt b }}$

Now,

$\begin{array}{l} \frac{{x + 2\sqrt a }}{{x - 2\sqrt a }} + \frac{{x + 2\sqrt b }}{{x - 2\sqrt b }}\ \Rightarrow ;\frac{{2\sqrt a \left( {\sqrt a + 3\sqrt b } \right)}}{{\sqrt a + \sqrt b }} \div \frac{{2\sqrt a \left( {\sqrt b - \sqrt a } \right)}}{{\sqrt a + \sqrt b }} + \frac{{2\sqrt b \left( {\sqrt b + 3\sqrt a } \right)}}{{\sqrt a + \sqrt b }} \div \frac{{2\sqrt b \left( {\sqrt a - \sqrt b } \right)}}{{\sqrt a + \sqrt b }}\ \Rightarrow ;\frac{{\left( {\sqrt a + 3\sqrt b } \right)}}{{\left( {\sqrt b - \sqrt a } \right)}} + \frac{{\left( {\sqrt b + 3\sqrt a } \right)}}{{\left( {\sqrt a - \sqrt b } \right)}}\ \Rightarrow ;\frac{{\left( {\sqrt b + 3\sqrt a } \right) - \left( {\sqrt a + 3\sqrt b } \right)}}{{\left( {\sqrt a - \sqrt b } \right)}}\ \Rightarrow ;\frac{{2\left( {\sqrt a - \sqrt b } \right)}}{{\left( {\sqrt a - \sqrt b } \right)}} \end{array}$

⇒ 2

The correct answer is ‘secret’.

Surreptitious means ‘kept secret or stealthy.’

Hence, a secret is the correct answer as it has a very similar meaning to the given word.

Hesitation means ‘the action of pausing before doing something’

Impious means ‘showing a lack of respect for God or religion’

Artless means ‘without guile or deception.’

The correct is ‘Water’.

The idiom ‘Adam’s ale’ means water, as a reference to the only drink available to Adam – the first man, according to the Bible.

Hence, Option 3 is the correct answer.

The correct answer is ‘picked at’.

The phrasal verb ‘pick at’ means ‘to eat slowly’.

Hence, it fits the context of the sentence as Rohan was upset and ate his food slowly.

The other options,

Picked out means ‘to choose from something’

Picked on means ‘to bully or single someone out’

Picked up means ‘to lift’.

The correct answer is ‘An essay will be written by me.’

Sentence 1 changes the tense to future perfect and makes the sentence incorrect.

Sentence 3 changes the tense to present perfect and makes the sentence incorrect.

Sentence 4 changes the tense to past perfect and makes the sentence incorrect.

Only Sentence 2 correctly preserves the simple future tense and is the correct answer.

The correct answer is ‘To get puzzled’.

The phrase ‘at one’s wit's end’ means at the end of one’s mental resources; perplexed.

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

An example sentence is: ‘The murder case had the detective at his wit's end’.

The correct answer is ‘Neha asked if she had to write a letter.’

Sentence 1 is grammtically incorrect due to tense mismatch.

Sentence 2 changes the meaning of the sentence from a question of writing a letter to a question of was the letter being written.

Sentence 3 uses an incorrect pronoun, ‘of’, making the sentence incorrect.

Only Sentence 4 accurately converts the given Direct speech into reported speech and is the correct answer.

The correct answer is ‘Thinkers’.

Thinkers means ‘people who think deeply and seriously’.

Hence, it is the correct word to fill in the given blank as the sentence says that people who think deeply have attempted to define a happy life, which has a varied meaning.

The correct answer is: Option 1.

Key Points

• The word "Chaufer" is incorrectly spelt.
• Meaning: This word is a misspelling of the correct word "Chauffeur" which means a person employed to drive a private or hired car. (ड्राइवर)
• Example: He hired a chauffeur to drive him around the city.
• The correct word is "Chauffeur".
• Meaning: A person employed to drive a private or hired car. (ड्राइवर)
• Example: The chauffeur was waiting outside to take them to the airport.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Committee (समिति): A group of people appointed for a specific function.
• Example: The committee will meet to discuss the new policy changes.
• Veterinary (पशु-चिकित्सा): Relating to the medical care and treatment of animals.
• Example: She took her dog to the veterinary clinic for a check-up.
• Repentance (पश्चाताप): The action of repenting; sincere regret or remorse.
• Example: His repentance was evident in his heartfelt apology.

The correct answer is ‘distinctly’.

Distinctly means ‘in a way that is readily distinguishable by the senses’.

Hence, it is the correct word to fill in the given blank as the sentence says that every man has a different definition of a happy life, which is easily distinguishable.

The correct answer is ‘Epitaph’.

Epitaph means a phrase or form of words written in memory of a person who has died, especially as an inscription on a tombstone.

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

Epigram means a short satirical poem

Epitome means a person or thing that is the perfect example

Epicure means a person who takes particular pleasure in fine food or drink

The correct answer is: Option 3 i.e. "Sedentery".

Key Points

• The word "Sedentery" is incorrectly spelt. The correct spelling is "Sedentary".
• "Sedentery" (incorrect spelling) does not have a meaning in English.
• "Sedentary" refers to a lifestyle characterized by much sitting and little physical exercise. (बैठा हुआ)
• Example: Many office jobs are sedentary, requiring employees to sit for long hours.

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

Additional Information

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

• Accurate (सटीक): Free from errors, exact.
• Example: His calculations were accurate and reliable.
• Business (व्यवसाय): The practice of making one's living by engaging in commerce.
• Example: She started her own business at a young age.
• Jewellery (आभूषण): Decorative items worn for personal adornment, such as rings, necklaces, and bracelets.
• Example: She wore elegant jewellery to the party.

The correct answer is ‘simple’.

Simple means ‘easily understood or done’.

Hence, it is the correct word to fill in the blank as the sentence says that hedonists have a easily understood and plain idea about happiness.

The correct answer is ‘done for’.

Key Points

• The phrasal verb ‘done with’ means brought to an end: decisively abandoned or dismissed.
  

Example: I'd rather turn myself over to my enemies and be done with it than bring the slightest harm to you.

• The correct phrasal verb to be used in the sentence is ‘done for’, meaning in serious difficulty
  

Example: He was looking a lot more at ease than he'd done for some time.

• Done in means very tired
  

Example: Poor Tom was done in when he got home.

• 'Done for' is most appropriate to use here.
  

The correct sentence is: **‘**I had not completed my project so I thought I was done for when the manager asked me to hand it in.’

The correct answer is ‘gratification’.

Gratification means ‘pleasure gained from the satisfaction of a desire’.

Hence, it is the correct word for the given blank as the sentence says that hedonists believe that happiness lies in the pleasure gained from satisfaction of physical appetites.

The correct answer is ‘Withdraw’.

Key Points

• Bequest- is money or property which you legally leave to someone when you die (वसीयत वह पैसा या संपत्ति है जिसे आप कानूनी रूप से किसी के मरने पर छोड़ देते हैं)
• For e.g.- The library has received a generous bequest from a local businessman.
• Withdraw- Remove or take away (something) from a particular place or position. (किसी विशेष स्थान या स्थिति से (कुछ) हटाना या हटाना)
• For e.g.-  They withdrew 100 dollars from a bank account after checking out of their hotel.
• Thus, according to the above mentioned meaning of both words 'Withdraw' is the antonym of 'Bequest'
  

Additional Information

• Accord- ‘give or grant someone power or status’
• Damage- ‘physical harm that imparts the value or usefulness of something’
• Complex- ‘consisting of many different and connected parts’

The correct answer is: Option 1.

Key Points

• The word "Inanition" means a state of exhaustion caused by lack of nourishment or vitality; it can also mean lack of mental or spiritual vigor. (भूखमरी या थकावट)
• Example: After days of wandering without food, the travelers were in a state of complete inanition.
• "Lethargy" refers to a lack of energy and enthusiasm; it denotes sluggishness or inactivity. (सुस्ती)
• Example: His lethargy was evident as he lay on the couch all day, doing nothing productive.
• Hence, we can infer that the word similar in meaning to 'Inanition' is 'Lethargy'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Offensive (अपमानजनक): Causing someone to feel deeply hurt, upset, or angry.
• Example: His offensive remarks caused a lot of distress among the team members.
• Vacillating (दुविधा में पड़ा): Wavering between different opinions or actions; being indecisive.
• Example: She kept vacillating between choosing a career in medicine or law.
• Grasping (लालची): Greedy; excessively eager to acquire or possess.
• Example: His grasping nature made him unpopular among his colleagues.

The correct answer is ‘Abdicate’.

 Key Points

• Abdicate means to renounce one’s throne.
• ​For example: He has abdicated his responsibilities and he should resign.
• Hence, it has the closest meaning to the given phrase and is the correct one-word substitute.
• Therefore, the correct answer is "Option 3".

Additional Information

• Archer means 'a person who shoots with bow and arrows'
• For example: He is the great sportsman, the incomparable archer.
• Bigot means 'a person who is intolerant towards those holding different opinions'
• For example: The person who stands proclaiming to know the truth is often called a bigot.
  
• Delegate means 'a person sent to represent others.'
• For example:  He plans to delegate more authority to his deputies.

The correct answer is ‘through’.

Fall through means to fail or come to nothing. When used in a sentence, it means that the subject it is talking about has failed.

Hence, Option 2 fits in the context of the sentence and is the correct answer.

The correct answer is ‘Composure’.

Imbroglio means ‘an extremely confused or complicated situation or predicament.’

On the other hand, composure means ‘the state of feeling calm and in control.’

Hence, the two words have opposite meanings.

Misery means ‘a state of great physical or mental distress or discomfort’

Censure means ‘express severe disapproval of something’

Dilemma means ‘a difficult situation or problem.’

The error is in part 2 of the sentence

The comparative degree, ‘greater’ does employ the use of the definite article as it is a comparison between two things. Only the superlative degree uses ‘the’ to signify the superiority.

Hence, the correct sentence is:

‘The student asked me if I knew that Kalidas was greater than any other poet’.

The correct answer is QRPS.

Q is the first sentence as it forms the beginning, seen from ‘one night’.

It is followed by R, showing that Lakshmi tightly held the knife.

It is followed by P, showing what happened when the robber was near her bed.

It is followed by S, showing what happened when the robber was shocked.

Thus, the correct combination is QRPS, as seen in Option 3.