SSC CGL Previous Paper (Held On: 19 June 2019 Shift 3) (Previous Year Paper)

Figure 1 has 2 sides; figure 2 has 3 sides; figure 3 has 4 sides.

Therefore, figure 4 must have 5 sides.

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

The correct logical order is:

City → State → Country → Continent → World

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

The pattern followed here is:

100 - 1 = 99

99 - 3 = 96

96 - 5 = 91

91 - 7 = 84

84 - 9 = 75

75 - 11 = 64

64 - 13 = 51

Hence, 51 is the correct answer.

The pattern followed here is:

4³ = 64; 64 + 3 = 67

Similarly,

8³ = 512; 512 + 3 = 515.

Hence, 515 is the correct answer.

The pattern followed here is:

C + 4 → G; D + 4 → H; F + 4 → J

Similarly

K + 4 → O; L + 4 → P; N + 4 → R

Hence, ‘OPR’ is the correct answer.

There are total 6 faces of a cube. If we paint opposite faces with same colour, then we will need a minimum of 3 colours so that no two adjacent faces have the same colour.

Hence, 3 is the correct answer.

3 + 3 = 6

6 + 5 = 11

11 + 7 = 18

18 + 9 = 27

27 + 11 = 38

38 + 13 = 51

51 + 15 = 66

66 + 17 = 83

83 + 19 = 102

Hence, 102 is the correct answer.

The least possible Venn diagram is:

Hence, the figure in option 4 is the correct answer.

The pattern followed here is:

P + 2 = R; I - 1 = H; C + 2 = E; T - 1 = S; U + 2 = W; R - 1 = Q; E + 2 = G

Similarly,

M + 2 = O; O - 1 = N; U + 2 = W; N - 1 = M; T + 2 = V; A - 1 = Z; I + 2 = K; N - 1 = M

Hence, ‘ONWMVZKM’ is the correct answer.

Hence, the minimum number of straight lines required to construct the given figure are 13.

When folded given figure will appear as shown below:

Hence, ‘TИIM’ is the correct answer.

Additional Information

$\sqrt{961}$ = 31; 961 + 31 = 992 .

Similarly,

√841 = 29; 841 + 29 = 870.

Hence, 870 is the correct answer.

A type of diabetes is caused by deficiency of insulin.

Similarly, a type of anaemia is caused by deficiency of iron.

Hence, ‘iron’ is the correct answer.

Beijing is the capital of China.

Similarly, Baghdad is the capital of Iraq.

Hence, ‘Iraq : Baghdad’ is the correct answer.

Similarly,

Hence, ‘TCASRO’ is the correct answer.

The pattern followed here is:

Now, P + R + O + P + E + R + T + Y = 16 + 18 + 15 + 16 + 5 + 18 + 20 + 25 = 133

E + S + T + A + T + E = 5 + 19 + 20 + 1 + 20 + 5 = 70.

Similarly,

D + E + V + E + L + O + P + M + E + N + T = 4 + 5 + 22 + 5 + 12 + 15 + 16 + 13 + 5 + 14 + 20 = 131.

Hence, 131 is the correct answer.

Hence, the figure in option 3 is the correct answer.

The pattern followed here is:

162 + 18 = 180

180 + 18 = 198

198 + 18 = 216

216 + 18 = 234

234 + 18 = 252

252 + 18 = 270

270 + 18 = 288

Hence, 252 is the correct answer.

Note: To make 11 pieces of equal length from 1 full roll, we need to cut 10 times.

Rate of cutting = 50 cuts per minute.

Therefore, no. of cuts in 25 minutes = 50 × 25 = 1250.

⇒ No. of rolls cuts in 25 minutes

= No. of cuts in 25 minutes ÷  No. of cuts required for 1 roll

= 1250 ÷ 10

= 125.

The pattern followed here is:

18 × 5 = 90

30 × 5 = 150

12 × 5 = 60

But

25 × 4 = 100.

Hence, ‘100, 25’ is the odd pair.

Conclusions:

I. No horse is a duck. → False (it is possible but not definite)

II. No dog is a rabbit. → False (it is possible but not definite)

III. Some ducks are rabbits. → True (some rabbits are ducks)

Hence, only conclusion III follows.

The pattern followed here is:

E + 2 → G; G + 2 → I; I + 2 → K

S + 2 → U; U + 2 → W; W + 2 → Y

L + 2 → N; N + 2 → P; P + 1 → Q

P + 2 → R; R + 2 → T; T + 2 → V

Hence, ‘LNPQ’ is the correct answer.

Using the above symbols, we can draw the following family tree:

Vikram has no brother or sister.

Therefore, Vikram’s father’s son is Vikram.

Now, mother of Kumar is the wife of Vikram.

Hence, Kumar is the son of Vikram.

The pattern followed here is:

1) L + Q = 12 + 17 = 29

2. P + K = 16 + 11 = 27

3. H + S = 8 + 19 = 27

4. C + X = 3 + 24 = 27

Hence, ‘LQ’ is the odd one among the given options.

Dr B R Ambedkar was independent India's first law minister.

• He is popularly known as Babasaheb Ambedkar.
• He was independent India's first law and justice minister, the architect of the Constitution of India, and a founding father of the Republic of India.
• He campaigned against social discrimination towards the untouchables (Dalits).
• In 1990, the Bharat Ratna, India's highest civilian award, was posthumously conferred upon B R Ambedkar.

Amylase, the enzyme in the human body that helps break down carbohydrates.

• Saliva releases an enzyme called amylase.
• Amylase is a protein made by your pancreas and by glands in and around your mouth and throat.

Protease:-

• A protease is an enzyme that catalyzes proteolysis, the breakdown of proteins into smaller polypeptides or single amino acids.

Peptidase:-

• Peptidase is an enzyme which breaks down peptides into amino acids.

Lipase:-

• Lipase helps your body digest fats.

Raja Todar Mal was the Finance Minister of the Mughal empire during Akbar's reign.

Key Points

Raja Todar Mal:-

• He was one of the Navaratna's in Akbar's 'darbar'
• Raja Todar Mal introduced standard weights and measures, a land survey and settlement system, revenue districts and officers.
• He introduced a new system of revenue known as zabt and a system of taxation called dahshala.
• The Kashi Vishwanath Temple was rebuilt in 1585 by Todar Mal.
• The navratnas of Akbar were as follows: Raja Birbal, Tansen, Abul Fazal, Faizi, Raja Man Singh, Raja Todar Mal, Mullah Do Piaza, Fakir Aziao-Din, Abdul Rahim Khan-I-Khana.

Football is officially the state sport of Goa.

• The Sports Authority of Goa(SAG), is a body owned fully by the Government of Goa.
• The Sports Authority of Goa is currently headed by Shri V. M. Prabhu Desai.
• The headquarter of SAG at Panaji, Goa.
• Pramod Sawant is the current Chief Minister of Goa.

CONCEPT:

• The battery has two terminals positive and negative its positive terminal is the anode and its negative terminal is the cathode.
• It works on the principle of Electrochemical Reaction.
• Italian physicist Alessandro Volta built and described the first electrochemical battery, the voltaic pile, in the year 1800.
• The lead-acid batteries used in vehicles and lithium-ion batteries used for portable electronics such as laptops and mobile phones.

EXPLANATION:

• A battery converts chemical energy into electrical energy. So option 3 is correct.

India's first lunar probe was called Chandrayaan-1.

• It was launched by the Indian Space Research Organisation(ISRO) in October 2008 and operated until August 2009.
• The mission included a lunar orbiter and an impactor.
• India launched the spacecraft using a PSLV-XL rocket on 22 October 2008 from Satish Dhawan Space Centre, at Sriharikota, Andhra Pradesh.

Surya-1:-

• The Surya missile is an intercontinental ballistic missile speculated to be in development by India.
• It was launched by DRDO.

Bhaskara-1:-

• Bhaskara-I was satellite built by the Indian Space Research Organisation that formed India's first low orbit Earth Observation Satellite.

Coorg is also known as the 'Scotland of India'.

• Coorg district current name is Kodagu.
• Kodagu is an administrative district in Karnataka, India.
• The main river in Kodagu is the Kaveri, which originates at Talakaveri, located on the eastern side of the Western Ghats, and with its tributaries, drains the greater part of Kodagu.
• Kannada is the official language of Kodagu.

The Securities and Exchange Board of India (SEBI) was established as a  statutory body in 1992.

• SEBI is the regulator for the securities market in India.
• SEBI has its headquarters at the business district of Bandra Kurla Complex in Mumbai.
• Ms. Madhabi Puri Buch​ current Chairman of SEBI.
• The first chairman of SEBI was Dr S. A. Dave.
• SEBI regulates the Indian financial market through its 20 departments.

• Oscar Awards, officially known as Academy Awards, was won by the Bhanu Athaiya in the category of best costume design in 1982.
• She has also won two National Awards in 1992 and 2002.

Pramod Sawant, who took charge as the Chief Minister of Goa in March 2019, is a Member of the Legislative Assembly from Sanquelim.

• Pramod Sawant represents the Sanquelim constituency in the Goa Legislative Assembly.
• He is an Ayurveda practitioner by profession.
• He took charge after death of former chief minister Manohar parrikar.

When a defeat was certain, Rajput men engaged in a ritual called 'Shake' (or 'sake') which was the last fight from which there was no return.

• Jauhar is the act of mass self-immolation by women in parts of the Indian subcontinent, to avoid capture, enslavement and rape by any foreign invaders when facing certain defeat during a war.
• During the Jauhar, Rajput women committed suicide with their children and valuables in the massive fire, to avoid capture and abuse in the face of inescapable military defeat and capture.

Farmers in Odisha can avail crop loans of up to Rs. 50000 at 0% interest under the State Government's KALIA Scheme for the Kharif Season of the year 2019.

• The government of Odisha has launched the Krushak Assistance for Livelihood and Income Augmentation (KALIA) scheme, which would benefit about 92% of the farmers in the State.
• The government has earmarked Rs 10,180 Crore for KALIA in 3 years.
• The scheme will provide financial, livelihood, cultivation support along with insurance support to small, marginal and the landless farmers.

Sikandar Lodi made Agra the capital of his empire.

• Sikandar Lodi was the Sultan of Delhi between 1489 and 1517.
• The second and most successful ruler of the Lodi dynasty of the Delhi sultanate.
• He was also a poet of the Persian language and prepared a diwan of 9000 verses.
• Agra was founded by him.
• Humayun was the 2nd ruler of the Mughal Empire.
• Shah Jahan was the 5th ruler of the Mughal Empire.
• Jehangir was the 4th ruler of the Mughal Empire.

"The Blue Umbrella" wrote by Ruskin Bond.

Ruskin Bond:-

• He is an Indian author of British descent.
• The Room on the Roof is the first novel written by Ruskin Bond.
• He was awarded the Sahitya Academy Award in 1992 for Our Trees Still Grow in Dehra, his novel in English.
• He was awarded the Padma Shri in 1999 and the Padma Bhushan in 2014.

Viswanathan Anand was the first sportsperson to receive the Padma Vibhushan award. 

• He is an Indian chess grandmaster and a former World Chess Champion.
• He occupied the number one position for 21 months, the 6th longest on record.
• Anand was also the first recipient of the Rajiv Gandhi Khel Ratna Award in 1991–92, India's highest sporting honour.
• He is also regarded as one of the greatest rapid players of all time.

The correct answer is option 4) i.e. Archana Ramasundaram.

• Former first woman chief of Sashastra Seema Bal (SSB) Archana Ramasundaram was sworn in as a non-judicial member of Lokpal.
• President Ram Nath Kovind administered the oath of office to Justice Pinaki Chandra Ghose as the country's first Lokpal.
• Former Chief Justices of different high courts - Justices Dilip B Bhosale, Pradip Kumar Mohanty, Abhilasha Kumari and Ajay Kumar Tripathi - took oath as judicial members in the Lokpal.
• Ex-Maharashtra chief secretary Dinesh Kumar Jain, former IRS officer Mahender Singh and Gujarat cadre ex-IAS officer Indrajeet Prasad Gautam were sworn-in as the Lokpal's non-judicial members.
• The members of the Lokpal were administered the oath by Lokpal chairperson Justice Pinaki Chandra Ghose.
• The establishment of the Lokpal at the centre and Lokayuktas in the states is for inquiring into complaints of corruption against certain public servants.

• The World Bank released Doing Business Report' on 31 October 2018.
• According to the 2018 report, India is placed at 77th rank among 190 countries assessed by the World Bank.
• In 2017, India was placed at 100th rank. In the 'Grant of Construction Permits' indicator, India’s ranking improved from 181 in 2017 to 52 in 2018.

Limestone is a sedimentary rock composed primarily of calcium carbonate.

• The chemical formula of calcium carbonate is CaCO_3.
• It most commonly forms in clear, warm, shallow marine waters.
• It is usually an organic sedimentary rock that forms from the accumulation of shell, coral, algal, and fecal debris.

Nitrogen Oxide:-

• Nitrogen oxide is most relevant for air pollution.

Sodium Bicarbonate:-

• This also known as baking soda.

Sodium chloride:-

• Generally, this is known as Cooking salt.

Chandela rulers established their religious capital in Khajuraho.

Chandela:-

• The Chandelas of Jejakabhukti was a royal dynasty in Central India.
• Nannuka was the founder of Chandela dynasty of India.
• They ruled much of the Bundelkhand region (then called Jejakabhukti) between the 9th and the 13th centuries.
• The Chandelas are well known for their art and architecture, most notably for the temples at their original capital Khajuraho.

• Nagpur is also known as '; Zero Mile Center' of India.
• It is because of the Nagpur is the geographical centre point of India and all the distances of major cities marked on pillars are measured starting this point.

The correct answer is option 2) i.e. Legs.

• The hearing organ, which is a large membrane called a tympanum, is located on either side of the first segment of the abdomen, near the base of the hind legs.
• The grasshoppers have three main body parts – the head, the thorax and the abdomen.
• They have six jointed legs, two pairs of wings and two antennae.
• Their body is covered with a hard exoskeleton.
• Grasshoppers breathe through a series of holes called ‘spiracles’ which are located along the sides of the body.
• Most grasshoppers are green, brown, or olive-green.
• The biggest Grasshoppers are about 11.5 centimetres long.
• Their legs are long hind legs that are used for hopping and jumping and the short front legs are used to hold prey and to walk.

The correct answer is option 1) i.e. Makar Sankranti.

• Makar Sankranti is celebrated in various parts of India to observe the day which marks the shift of the sun into ever-lengthening days.
• It also marks the beginning of the end of Winter and the harvest of rabi crops.
• While Makar Sankranti is most popular in West India, down south, the festival is known as Pongal and in the north, it is celebrated as Lohri.
• Uttarayan, Maghi, Khichdi are some other names of the same festival.
• It falls on the same date in the local calendar every year on January 14.

The correct answer is Koshi.

Key Points

• Koshi river originates from Nepal.
• It is known as Saptakoshi, as it is joined by seven upper tributaries.
• It is almost 470 km long from the Himalayan point till it merges to the Ganga river in Bihar.

Additional Information

Mahanadi:-

• The Mahanadi is an important river in the state of Odisha.

Narmada:-

• It is also known as "Life Line of Gujarat and Madhya Pradesh" for its huge contribution to the state of Gujarat and Madhya Pradesh in many ways.

Chambal:-

• The Chambal River is a tributary of the Yamuna River in central India.

• Warren Hastings (1772-1785) was Governor-General of India during the Second Anglo- Mysore War.
• The Second Anglo-Mysore was fought between years 1780-1784.
• Treaty of Mangalore ended the Second Anglo Mysore War with both parties agreeing for status quo and exchange of Prisoners.
• The major event; of war was the death of Hyder Ali in 1782 and the crowning of Tipu Sultan.

The full form of ADF is Automated Data Flow.

• This term belongs to banking parlance.
• RBI(Reserve Bank of India) initiate Automated Data Flow.
• It aimed at the purpose of meeting the needs for the accurate and consistent flow of data.

Since tangent AP makes right angle with radius OA

∴ ∠OAP = 90°

In ΔAOP,

∠AOP + ∠APO + ∠PAO = 180°

⇒ ∠AOP + 15° + 90° = 180°

⇒ ∠AOP = 75°

⇒ ∠AOB = 2 × ∠AOP = 150°

Now, in ΔOAB,

∠AOB = 150°

⇒ ∠OAB + ∠OBA = 30° (∵ OA = OB, ∴ ∠OAB = ∠OBA)

∴ ∠OAB = 15°

The maximum numbers greater than zero will be 38 because at least one number should be negative to make the sum of the other numbers equal to zero.

From the given table,

In the year 2000: B1 = 80, B2 = 75, B5 = 75

In the year 2001: B1 = 105, B2 = 65, B5 = 95

∴ Required number = 80 + 105 + 75 + 65 + 75 + 95 = 495

62.5% of 40000 = 25000 and 10% of 25000 = 2500

Discount on the remaining amount = 4% of (40000 - 25000) = 600

⇒ Total discount offered = 2500 + 600 = 3100

∴ Overall percentage discount = 3100/40000 × 100 = 7.75%

Short trick∶

Total sum of percentage = 90 + 100 + 90 + 80 + 80 + 70 + 65 = 575%

⇒ Average = 575/7 %

∴ Required percentage = 575/7 × 150/100 = 123.21

Detailed solution∶

Total sum of marks = (90% of 150) + (100% of 150) + (90% of 150) + (80% of 150) + (80% of 150) + (70% of 150) + (65% of 150)

⇒ 135 + 150 + 135 + 120 + 120 + 105 + 97.5

⇒ 862.5

∴ Required average marks = 862.5/7 = 123.21

Average amount of tax = (83 + 108 + 74 + 88 + 98)/5 = 451/5 = 90.2

Shortcut Trick

If a sum becomes n times in t years at compound interest, it becomes n^x times in x × t years.

Given, sum becomes 3 times (3¹) in 4 years.

We need to find the time for the sum to become 27 times.

Since 27 = 3³, the multiplier x = 3.

Time required = 3 × 4 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given:

A sum of money at compound interest becomes 3 times in 4 years.

Let Principal = P, Rate = R%, Amount = A, Time = n years.

0 yrs P

4 yrs 3P

8 yrs 9P

12 yrs 27P

× 3

× 3

× 3

Total Time = 4 + 4 + 4 = 12 years

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 3P = P(1 + R/100)⁴

⇒ 3 = (1 + R/100)⁴     — (Equation 1)

Let the sum become 27 times in n years.

⇒ 27P = P(1 + R/100)ⁿ

⇒ 27 = (1 + R/100)ⁿ

⇒ 3³ = (1 + R/100)ⁿ

Substitute the value of 3 from Equation 1:

⇒ [(1 + R/100)⁴]³ = (1 + R/100)ⁿ

⇒ (1 + R/100)¹² = (1 + R/100)ⁿ

On comparing the powers of both sides:

⇒ n = 12 years

∴ The correct answer is 12 years.

Additional Information

Compound Interest Multiplier Rule

If a sum becomes x times in T years at a constant compound interest rate, it will become xⁿ times in n × T years.

Contrast with Simple Interest (SI)

In Simple Interest, if a sum becomes 3 times in 4 years, the interest earned is 2P in 4 years. To become 27 times, the required interest is 26P. It would take (26 ÷ 2) × 4 = 52 years in SI.

Important CI Formats

For half-yearly compounding: Rate becomes R/2 and Time becomes 2T. For quarterly compounding: Rate becomes R/4 and Time becomes 4T.

Let the person goes to office at x km/h and returns from office at 4x km/h. The distance from one side be d km.

Average speed = Total Distance/Total Time

⇒ 15 = (d + d) / {(d/x + d/4x)}

⇒ x = 75/8 km/h

x + 1/x = 4

Taking cube both the sides,

[x + 1/x]³ = 4³

⇒ x³ + 1/x³ + 3[x + 1/x] = 4³ {(a + b)³ = a³ + b³ + 3ab (a + b)}

⇒ x³ + 1/x³ + 3 [x + 1/x] = 64

⇒ x³ + 1/x³ + 3[4] = 64

⇒ x³ + 1/x³ = 64 - 12

⇒ x³ + 1/x³ = 52

Percentage of expenditure on paper = 25

Percentage of expenditure on promotion = 10

Expenditure on promotion Is less than that on paper = (25 - 10)/25 × 100 = 60%

a - 1/a = 3

Taking cube both sides,

(a - 1/a)³ = 3³

a³ - 1/a³ - 3(a - 1/a) = 27{(a³ - b³) = a³ - b³ - 3ab(a - b)}

a³ - 1/a³ - 3(3) = 27

a³ - 1/a³ = 27 + 9

a³ - 1/a³ = 36

Squaring both the sides, we get

(a³ - 1/a³)² = (36)²

a⁶ - 2 × a³ × (1/a³) + 1/a⁶ = 36²

∴ a⁶ + 1/a⁶ - 2 × 1 = 1296

∴ a⁶ + 1/a⁶ = 1298

Formula: Volume of sphere = 4/3 × πr³

Volume of sphere = 4/3 × π × 5³

Volume of new spheres = 4/3 × π × 2³

∴ Required number of spheres = (4/3 × π × 5³) / (4/3 × π × 2³)

= 125/8 = 15.625

∴ 15 spheres can be made.

$\left[ \frac{{{\sin }^{2}}25{}^\circ +{{\sin }^{2}}65{}^\circ }{{{\cos }^{2}}24{}^\circ +{{\cos }^{2}}66{}^\circ }+{{\sin }^{2}}61{}^\circ +\cos 61{}^\circ \sin 29{}^\circ \right]$

$\Rightarrow ~\left[ \frac{{{\sin }^{2}}\left( 90{}^\circ -65{}^\circ \right)+{{\sin }^{2}}65{}^\circ }{{{\cos }^{2}}\left( 90{}^\circ -66{}^\circ \right)+{{\cos }^{2}}66{}^\circ }+{{\sin }^{2}}61{}^\circ +\cos 61{}^\circ \sin \left( 90{}^\circ -61{}^\circ \right) \right]$

$\Rightarrow ~\left[ \frac{{{\cos }^{2}}65{}^\circ +{{\sin }^{2}}65{}^\circ }{{{\sin }^{2}}66{}^\circ +{{\cos }^{2}}66{}^\circ }+{{\sin }^{2}}61{}^\circ +\cos 61{}^\circ \cos 61{}^\circ \right]$

⇒ 1 + sin²61 + cos²61

⇒ 1 + 1 = 2

(a³ - b³) = 210 and a - b = 5

⇒ (a³ - b³) = (a - b)(a² + ab + b²)

⇒ 210 = 5 × (a² + ab + b²)

⇒ 210/5 = (a² + ab + b²)

∴ (a² + ab + b²) = 42

In a quadrilateral, the sum of opposite angles is equal to 180°.

Since ABCD is cyclic quadrilateral,

∴ ∠ADC + ∠ABC = 180°

According to the question, AB is diameter.

∴ ΔABC will be a right angle triangle.

⇒ ∠C = 90°

In ΔABC,

∠BAC + ∠ABC + ∠ACB = 180°

⇒ ∠BAC + 30° + 90° = 180°

⇒ ∠BAC = 60°

39/4 + [13/6 ÷ {13/3 - (5/2 + 3/4)}]

⇒ 39/4 + [13/6 ÷ {13/3 - 13/4}]

⇒ 39/4 + [13/6 ÷ 13/12]

⇒ 39/4 + [13/6 × 12/13]

⇒ 39/4 + 2

⇒ 47/4

Suppose (x - 4) = a, (x - 5) = b and (x - 3) = c

Formula∶ If a + b + c = 0, then a³ + b³ + c³ = 3abc

(x - 4)³ + (x - 5)³ + (x - 3)³ = 3(x - 4)(x - 5)(x - 3)

⇒ a³ + b³ + c³ = 3abc

⇒ a + b + c = 0

⇒ x - 4 + x - 5 + x - 3 = 0

⇒ x = 4

Let the required number of women be x.

A woman does double the work a man does in a day

⇒ W = 2M       ----(1)

A boy does half the work a man does in a day

⇒ M = 2B       ----(2)

Now, using the formula M₁D₁/W₁ = M₂D₂/W₂

⇒ (3M + 4W + 6B) × 5 = x × W × 7

⇒ (3M + 8M + 3M) × 5 = x × 2M × 7

⇒ 14M × 5 = 14M × x

⇒ x = 5 W

In the similar triangle,

[Area of ΔABC] / [Area of ΔQPR] = BC²/PR²

⇒ (9/16) = (6²/PR²)

∴ PR² = 16 × 4

∴ PR = 8 cm

Per day income of A = 80 × 8 = 640

Per day income of B = 60 × 6 = 360

Ratio of per day wages of A and B is = 640 ∶ 360 = 16 ∶ 9

∵ x + 1/x = 2

⇒ x² + 1 = 2x

⇒ x² - 2x + 1 = 0

⇒ (x - 1)² = 0

⇒ x = 1

∴ xⁿ + 1/xⁿ = 2

Similarly, cosθ + 1/cosθ = 2

∴ cos¹¹⁷θ + 1/cos¹¹⁷θ = 2

Let the number be x.

50% of x + 75 = x

⇒ 50/100 × x + 75 = x

⇒ 50x + 75 × 100 = 100x

⇒ 7500 = 50x

⇒ x = 150

Given:

The successive discount are 20%, 10% and 15%.

Formula:

Successive discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount

Calculation:

Successive discount = X + Y - (XY)/100

⇒ 20 + 10 - 200/100

⇒ 28%

Now, again

Successive discount = X + Y - (XY)/100

X = 28%, Y = 15%

⇒ 28 + 15 - (28 × 15)/100

⇒ 28 + 15 - 420/100

⇒ 43 - 4.2% = 38.8%

∴ The single equivalent discount is 38.8%.

Let the amount be 100.

Successive discount on 100 = (100 - 80% of 90% of 85% of 100)

⇒ 100 - 61.2 = 38.8%

Let that integer be n = 10

⇒ 6n = 6 × 10 = 60

⇒ 6n/7 = 60/7

∴ Remainder is 4.

Shortcut Trick

Observe the equation 3cos² A + 7sin² A = 3.

Since the result is exactly the coefficient of the cos² A term (3), the sin² A term must be 0.

For 7sin² A = 0, sin A must be 0.

In the range 0° ≤ A ≤ 90°, sin A = 0 only when A = 0°.

∴ The correct answer is 0°.

Alternate Method

Given: 3cos² A + 7sin² A = 3

Formula Used: sin² A + cos² A = 1 ⇒ sin² A = 1 − cos² A

⇒ 3cos² A + 7(1 − cos² A) = 3

⇒ 3cos² A + 7 − 7cos² A = 3

⇒ 7 − 4cos² A = 3

⇒ 4cos² A = 7 − 3

⇒ 4cos² A = 4

⇒ cos² A = 1

⇒ cos A = 1 (Since A is in the first quadrant)

⇒ A = cos⁻¹(1) = 0°

∴ The correct answer is 0°.

Additional Information

Trigonometric Identities

Fundamental identity: sin²θ + cos²θ = 1. Other relations include 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.

Standard Values

At 0°: sin 0° = 0, cos 0° = 1, tan 0° = 0. At 90°: sin 90° = 1, cos 90° = 0, tan 90° is undefined.

Quadrant Rules

In the first quadrant (0° to 90°), all trigonometric ratios (sin, cos, tan, etc.) are positive.

The correct answer is Humane

Key Points

• Brutal means savagely violent. (अति क्रूर और/या हिंसापूर्ण; पाशविक, अमानुषिक)
• For eg; It was a case of a brutal murder.
• Humane means having or showing compassion or benevolence. (सदय या सहानुभूतिपूर्ण (विशेषतः कष्‍ट पाते व्‍यक्ति या पशु के प्रति), मानवीय, मानवोचित)
• For eg; We must ensure the humane treatment of animals.
• It is clear that brutal and humane are antonyms.
• Hence, the correct answer is option 1.
• Let us look at the meaning of the other given options:
• | WORD | MEANING | HINDI MEANING | | --- | --- | --- | | Fierce | having or displaying an intense or ferocious aggressiveness. | क्रुद्घ, आक्रामक और डरावना; बर्बर | | Sane | sound mind; not mad or mentally ill. | (व्‍यक्ति) मानसिक रूप से सामान्‍य दशावाला, स्‍वस्‍थचित्त; सनकी नहीं, समझदार | | Savage | fierce, violent, and uncontrolled. | बर्बर |

Additional Information

• Synonyms of Brutal are- Savage, cruel, vicious, ferocious, harsh, ruthless.
• Example of Brutal in a sentence- 
• A brutal one but fair nonetheless.

The correct answer is option 2

Pliable means easily bent; flexible.

Fragile means (of an object) easily broken or damaged.

For eg; Do not touch the fragile items in the shop.

It is clear that fragile is the correct word.

Ductile means able to be drawn out into a thin wire.

Malleable means able to be hammered or pressed into shape without breaking or cracking.

So, options 1,3 and 4 are incorrect.

The correct answer is option 2.

Austere means severe or strict in manner or attitude.

For eg; He was an austere man with a rigid outlook.

Unwilling means not ready, eager, or prepared to do something.

Strict means demanding that rules concerning behaviour are obeyed and observed.

For eg; My mother is very strict.

It is clear that austere and strict are synonyms.

Generous means showing a readiness to give more of something, especially money, than is strictly necessary or expected.

Careless means not giving sufficient attention or thought to avoid harm or errors.

So, options 1,3 and 4 are incorrect.

The correct answer is Once.

Key Points

• Once should be used in the given space as a conjunction. it means as soon as, we can say as soon as he was strong enough.
• Hence, 'once' should be used in the given blank.
• Unless is used to denote except if (used to introduce the case in which a statement being made is not true or valid).
• But means used to suggest a contrast.
• Only means and no one or nothing more besides; solely.

So, options 1, 2, and 3 are incorrect.

The correct answer is option 1.

The Committee occupied itself with no other important question but this.

But is always used to join contrasting phrases. In the given sentence, it is clear that that the committee had occupied itself with no other important question except this question. So, we join these contrasting phrases with but.

Either is used when you have an option between two things.

So, options 2,3 and 4 are incorrect.

The correct answer is option 3.

Converse means engage in conversation.

For eg; She was hardly able to converse with her mother.

Oppose means disagree with and attempt to prevent, especially by argument.

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

Talk means speak in order to give information or express ideas or feelings; converse or communicate by spoken words.

For eg; The two men were talking.

It is clear that converse and talk are synonyms.

Agree means have the same opinion about something; concur.

So, options 1,2 and 4 are incorrect.

The correct answer is option 1.

To sit on the fence means how a person lacks decisiveness. It describes his hesitation or inability to choose between two sides.

Clearly, the given sentence means how some people remain unsure and undecided without committing themselves to a particular thing.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

Key Points

• The correct spelling is a C-E-R-T-I-F-I-C-A-T-E.
• Certificate means 'an official document that states that the information on it is true' (एक आधिकारिक दस्तावेज जो बताता है कि इस पर जानकारी सत्य है)
• Example: a birth/marriage/death certificate
• So, options 1,3, and 4 are incorrect.

The correct answer is option 4.

The first sentence should be A i.e When you begin to house train your puppy, follow these steps because all other statements mention the steps which must be followed. So, before giving the steps we must give a brief introduction of what these steps are about.

Therefore, options 1 and 3 are incorrect.

Statement A should be followed by D i.e Take your puppy out first thing in the morning and then once every thirty minutes or so because the statement points out what should be done first thing in the morning. After which all other steps must be followed.

So, option 4 is correct i.e ADCB.

Therefore, options 1,2 and 3 are incorrect.

The correct answer is option 1.

he broke the lock of his cage and.

Broke means separate into pieces as a result of a blow, shock, or strain.

For eg; He broke the window.

It is clear that broke will be used as it is mentioned that he was in captivity. So, once he got strong and broke the lock.

Opened means move (a door or window) so as to leave a space allowing access and vision.

Bent means sharply curved or having an angle.

Loosened means make (something tied, fastened, or fixed in place) less tight or firm.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

and escaped into the jungle.

Marched means walk quickly and with determination.

Escaped means break free from confinement or control.

For eg; The burglars escaped from the prison.

It is clear that Bagheera was kept in captivity so when he got strong, he got free from the control and confinement.

Jumped means push oneself off a surface and into the air by using the muscles in one's legs and feet.

Climbed means go or come up  (slope or staircase); ascend.

So, options 1,3 and 4 are incorrect.

The correct answer is are responsible

Key Points

• 'is responsible' should be there in place of 'are responsible'
• If two subjects are joined by 'neither...nor', 'either...or', 'not only.....but also', 'nor', 'or', 'none...but', the verb will agree with the nearest step.
  

Example: Neither Ram nor Shyam has come.

                 Either Ram or his friends have come.

• Thus, the correct sentence is: I am sure that neither Juhi nor Jaya is responsible for breaking the vase.

The correct answer is surface

Key Points

• Meaning of the words given in the options are:
• Ground means an area of land or sea used for a specified purpose.
• Earth means the planet on which we live; the world.
• Soil means the upper layer of earth in which plants grow, a black or dark brown material typically consisting of a mixture of organic remains, clay, and rock particles.
• Surface means the outside part or uppermost layer of something.
• For eg; The earth's surface is fit for plant growth.
• It is clear that the surface is the most appropriate word as the sentence mentions a discovery on the uppermost layer of an asteroid.
• So, options 1,3, and 4 are incorrect.

Thus, the complete sentence is: Scientists have discovered evidence of abundant water-bearing minerals on the surface of an asteroid Bennu.

The correct answer is shifting.

Key Points

• Stationary means not moving or not intended to be moved. (खड़ा हुआ; स्थिर, गतिहीन)
• For eg; His car collided with a stationary vehicle.
• Shifting means move or cause to move from one place to another, especially over a small distance. (एक स्थिति या स्‍थान से दूसरी में (किसी को) रखना या (स्‍वयं) जाना; खिसकाना, खिसकना)
• For eg; He is shifting to another room.
• It is clear from the examples that stationary and shifting are antonyms.​
• Hence, the correct answer is option 3.
• Let us look at the meanings of the other given options:
• | WORD | MEANING | HINDI MEANING | | --- | --- | --- | | Tired | in need of sleep or rest; weary | थका हुआ, थका-माँदा, पस्‍त | | Motionless | not moving; stationary. | गतिहीन, जड़ | | Still | not moving or making a sound. | (अब भी (कहीं से आरंभ होकर अब तक या बात करने तक जारी रहते हुए) |

Additional Information

• The synonyms of the given word Stationary are - Motionless. halted, stopped, at rest.

The correct answer is option 1.

He regularly appears in the stories of Mowgli.

Appears means to come into sight; become visible or noticeable, especially without apparent cause.

For eg; His news often appears in the newspapers.

Rises means to move from a lower position to a higher one; come or go up.

Involves means have or include (something) as a necessary or integral part or result.

Invites means make a polite, formal, or friendly request to (someone) to go somewhere or to do something.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

Each of the guests was given a return gift.

In the given question, the pronoun each does not agree with the verb were. Pronouns like each/anybody/everyone are singular and they require a singular verb even when they are followed by a phrase which contains a plural noun like of the guests. So, instead of were , was will be used. 

So, options 1,3 and 4 are incorrect.

The correct answer is Friction reduce

Key Points

• 'Friction reduces' should be there in place of 'Friction reduce'
• The subject and verb must agree with each other in a sentence. When the subject is singular, the verb used should be singular, and when the subject is plural, the verb used should be plural.
• Also with uncountable nouns, a singular verb is used.
• Examples: 
• This news is very important.
• Your luggage looks heavy.
• 'Friction' is an uncountable noun. So singular verb should be used.
• Thus, the correct sentence is: Friction reduces the efficiency of machines so their value also gets reduced.

The correct answer is option 1.

The first statement should be Swami looked forward to disrupting every class. The first statement must give a slight idea about the context of the paragraph. Statements B and D start with they, which means they are in continuation with another statement.

Statement A mentions the third person form i.e his, but we do not get an idea about the subject of the sentence if  A is made the first statement.

Statement C has the noun which can be the subject being spoken about.

So, options 2,3 and 4 are incorrect.

The correct answer is The glass table should be rubbed with a soft cloth to make it shine.

Key Points

• Imperative sentences are sentences that express advice, request, or command.
• There are some sentences which contain suggestion.
• Let’s see how to convert these sentences into passive by some examples.

Ex:

• Respect parents. (Active Voice)
  

Parents should be respected. (Passive Voice)

• Love the kids. (Active Voice)
  

The kids should be loved. (Passive Voice)

• Follow your dreams. (Active Voice)
  

Your dreams should be followed. (Passive Voice)

• Thus, we use 'should' in imperative sentences in passive sentences containing 'suggestion'.
• While changing from active to passive voice, we change the subject to the object and vice versa. Thus, the object 'the glass table' will become the subject in passive voice.
• At Last lining up the remaining sentence: with a soft cloth to make it shine.
• Thus, the sentence becomes: The glass table should be rubbed with a soft cloth to make it shine.

The correct answer is pay for everything

Key Points

• Foot the bill means to pay the bill for something, typically when the amount is considered large or unreasonable.
• It is clear that option 3 is most appropriate because it is mentioned that Raju was shocked which is obviously because he had to pay for all his friends.
• So, options 1, 2 and 4 are incorrect.

The correct answer is option 4.

He was born in (1) captivity in the menagerie of the Raja of Udaipur.

Park means a large public garden or area of land used for recreation.

The word menagerie is used, which means a collection of wild animals kept in captivity for exhibition,

Jungle means an area of land overgrown with dense forest and tangled vegetation, typically in the tropics.

Cave means a natural underground chamber in a hillside or cliff.

Captivity means the condition of being imprisoned or confined.

So, options 1, 2 and 3 are incorrect.