SSC CGL Previous Paper (Held On: 7 June 2019 Shift 1) (Previous Year Paper)

Pattern followed is:

325 ÷ 13 = 25 - completely divisible by 13

195 ÷ 13 = 15 - completely divisible by 13

544 ÷ 13 not divisible by 13

416 ÷ 13 = 32 - completely divisible by 13

Hence 544 is odd among them.

Pattern is as follows:

Circle is moved by one place in clockwise direction after every step.

Lines are moved by one place after first step two places after second step and so on.

After 4^th step line will move by four places.

Hence, the correct answer is option 4).

Hence, option 2 is the correct answer.

We get knowledge by Studying

Same way, we get experience by working.

Pattern followed is:

Hence DFOP is the answer.

Let Number of Men employed = X

Number of men remaining to work = X – 6

Total work = Men working × number of days

12 × X = (X – 6) × 20

8X = 120

X = 15

Hence Number of men originally employed were 15.

Hence, the correct answer is option 2).

Pattern followed is:

Series pattern is: bacdbc.

“b a c d b c b a c d b c b a c d b c” is full series.

Hence cbacc is answer.

If we rotate the 1^st cube so that face which have 1 goes to bottom and face 3 comes to front.

If 3 comes to front then upper face is 2 as shown in figure 2^nd cube.

Hence 1 will be opposite to 6 and 2 will be opposite to 4

Hence 2 will come on top if 4 is on the bottom.

Hence total number of triangles is 15.

Pattern followed is:

N + 2 = P, P + 2 = R, R + 2 = T

J + 3 = M, M + 3 = P, P + 3 = S

W - 1 = V, V - 1 = U, U - 2 = S

D + 1 = E, E + 1 = F, F + 1 = G

Only WVUS non positive and nonuniform.

Hence WVUS is the odd among the given options.

Pattern followed is:

(1^st term + 3^rd term) × 2 = (8 + 6) × 2 = 28

(3 + 7) × 2 = 20

(17 + 13) × 2 = 60 ≠ 70

(5 + 9) × 2 = 28 ≠ 26

(12 + 14) × 2 = 52 ≠ 70

Hence (3, 20, 7) is answer.

Conceal, Camouflage and Mask has similar meaning that is to hide.

While Horde means large group of people.

Hence Horde is the odd among them.

All Crocodile are Aquatic animal and reptiles, and some aquatic animals can be Reptiles.

Hence is correct answer.

Consolation is given to people who are grieving

Similarly

Sedative is given to people who are in pain.

Hence, Pain : Sedative is the correct answer.

Logical Sequence is:

Interview - Job - Probation - Confirmation - Promotion

Hence, the correct sequence is 4, 3, 1, 5, 2.

There are two possible family tree diagram

or

Hence, V is the niece of M.

Pattern followed is:

Hence “U I H J S C” is the answer.

Pattern followed is:

S = 8, M = 1, O = 6, K = 4, E = 3.

P = 7, R = 2, A = 9, N = 5, K = 4.

Hence,

ROSE = 2683

I. Some cutters are instruments → True.

II. All knives are cutters → False (It is possible but not definite)

III. Some knives are not instruments → False.

Hence, only conclusion I follows.

Pattern followed is:

5 × (5 + 2) = 35

so, 35: 5

Similarly,

7 × (7 + 2) = 63

so, 63: 7

Hence 63 : 7 is answer.

Hence option 1 is the correct answer. 

Mistake Points

Options 1 and 2 are different because the 4 corners of options 1 and 2 are different.

Pattern followed is:

Hence 63 is answer.

Interchanging - and ÷

$15 + 5 \div 10 \times 6 - 12 = 15 + \frac{{5 \times 6}}{{10}} - 12$

15 + 3 - 12 = 6

Interchanging + and ÷

15 ÷ 5 – 10 × 6 + 12 = 3 - 60 + 12

15 – 60 ≠ 6

Interchanging + and ×

$15 \times 5 - 10 + 6 \div 12 = 75 - 10 + \frac{1}{2}$

$65 + \frac{1}{2} \ne 6$

Interchanging + and -

15 - 5 + 10 × 6 ÷ 12 = 15 - 5 + 5

15 – 5 ≠ 6

Hence by interchanging - and ÷ we get the correct equation.

The pattern followed is:

3rd number - 1st number = 2nd number(Middle no.)

(4, 12, 16)

16 - 4 = 12

Similarly,

(64, 36, 100)

100 - 64 = 36

Hence (64, 36, 100) is the answer.

• Babur was the founder of the Mughal Empire and the first Mughal emperor in India.
• Humayun was the second Mughal Emperor in India.
• Akbar was the third Mughal Emperor.
• Jahangir was the fourth Mughal Emperor.
• Shah Jahan was the fifth Mughal Emperor.

• Asian Development Bank (ADB) in its Outlook Supplement retained India’s growth forecast at 7.3% for the current fiscal (2018-19) and 7.6% for the following financial year (2019-20).
• India's GDP growth moderate was 7.1% in Q2 of the financial year 2018.
• While, it was 8.2% in Q1.

• The leader of the Bhakti movement focusing on Lord Rama was Ramananda.
• He was a 14th century Vaishnava poet who founded the Ramanadi Sampradaya.
• He taught that Lord Rama is the supreme Lord, and that salvation could be attained only through love for and devotion to him, and through the repetition of his sacred name.
• Bhakti movement was a devotional trend that saw its emergence in medieval Hinduism and was revolutionized in Sikhism.
• Some of the popular saints of the Bhakti Movement include Ramananda, Chaitanya, Jaydeva, Vivekananda, and Namdeva, etc.

• The motto of Special Olympics World Games 2019 was "Let me win. But if I cannot win, let me be brave in the attempt."
• The event was held from 14-21 March 2019 in Abu Dhabi, UAE.
• It was for the first time that it was hosted in a North African and Middle East region.

• Bihar Diwas is celebrated on March 22 across the state every year.
• On this day, in 1912, Bihar was carved out of the Bengal Presidency.
• It is a public holiday in Bihar.
• The year 2021 marked the 109th foundation day of the state.

• In March 2019, Superstats, a new metrics to analyse the game of cricket was launched by Indian Institute of Technology (IIT) Madras researchers and ESPNcricinfo experts.
• Superstats uses data science for forecasting, to give context to every event in a game, and to explore the idea of luck assessment.
• The algorithms analyze the real value of a player’s performance in real-time and quantify the impact of luck.

• Zat and Sawar are related to the Mansabdari administrative system.
• Mansabdar was a military unit introduced by Akbar.
• It means position or rank.
• The mansab had dual representation, one was cavalry rank called sawar, while the other was personal rank called zat.

• The Global Business Summit 2019 was held in New Delhi.
• It was inaugurated on 22 February 2019 and was the 5th edition of the summit.
• The summit was first launched on 15 January 2015 as a flagship initiative by Times Group.

• Carbon monoxide reduces the oxygen carrying capacity of the blood.
• It gets deposited in the haemoglobin of the RBC's, thus preventing the oxygen carrying capacity.

• Kapurthala is the least populated city in India according to the 2011 census.
• Banswara is the second least populated, while Nagda is third least populated city of India.
• Datia is the fourth least populated city of India.

https://www.census2011.co.in/city.php

The correct answer is Chittorgarh Fort.

• In Chittorgarh Fort, 'chattris’ (cenotaphs) were built in honor of Jaimal and Kalla, heroes who laid down their lives in the 1568 siege by Emperor Akbar.
• Chittorgarh fort is spread across 240 hectares and is set atop a 180m high hill.

Additional Information

• Surajpol is the main gate of the fort.
• Amer Fort is in Amer, near Jaipur.
• Kumbhalgarh, also known as the Great Wall of India, is a Mewar fort on the western border of the Aravalli Hills in Rajsamand district near Udaipur in the state of Rajasthan in western India.
• Ranthambhore Fort is situated near Sawai Madhopur.

• In March 2019, India extended a financial grant of 35.5 million Nepalese rupees for the construction of an educational campus in Nepal under the Development Partnership Programme.
• The new 3-story building comprises of faculty room, 12 class rooms. principal room, library, a meeting hall, laboratory room and toilets for girls and boys.
• The Siddheshwar Education Public Campus is situated in the Ramechhap district.

• Marble cancer is the corrosion of statues and buildings made up of marbles by the action of nitric acid or sulphuric acid.
• It also happens because of acid rain. This rain corrodes the marble monuments by dissolving the calcium and making salt.
• Yellowing of Taj Mahal is one of the examples of marble cancer.

• Metal oxides are basic in nature since they react with dilute acids to form water and salt.
• Metal oxides dissolve in water to form metal hydroxides (alkaline in nature).
• Non-metal oxides are acidic in nature.

• In case the President of India wants to resign, he would address his resignation to the Vice President.
• This has been mentioned in article 56 of the Indian Constitution.
• The term of the President is of 5 years.
• The Prime Minister and the Vice President address their resignations to the President of India.

• Tsunami is caused by underwater volcanic activity.
• A sudden movement of the ocean because of earthquakes or landslides on the sea floor causes tsunami waves.
• They can also be initiated because of volcanic eruptions beneath the sea, but that is a rare phenomenon.

• Cyanides, carbides and carbonates are amongst the few carbon-containing compounds which are not classified as organic.
• The carbon atom is not considered as an organic compound since it is bonded with 2 oxygen atoms.
• Methane is a chemical compound that has the formula CH₄.
• Nucleic acids are biomolecules or biopolymers which are essential for all life forms.
• Propane is a hydrocarbon gas, also called as LPG.

• The Vivekananda Rock Memorial is located in Vavathurai, Kanyakumari.
• It was built in the honour of Swami Vivekananda in the year 1970.
• It is believed that he attained enlightenment on the rock.
• It is also believed Goddess Kumari had performed austerity on this rock.

• Sonam Kapoor was named People for the Ethical Treatment of Animals (PETA) India's Person of the Year for 2018.
• She is known to be an advocate for animal rights.
• Apart from taking actions for animal welfare, she also keeps animal skin out of her brand Rheson.

• In March 2019, Indian-American television personality and food expert Padma Lakshmi was appointed by the United Nations Development Programme as its new Goodwill Ambassador.
• She will mobilise support for the Sustainable Development Goals with a focus on discrimination, fighting inequality, and empowering the disenfranchised.
• She has been a judge, host and the executive producer, of Bravo Television’s series Top Chef.

• In case of death of the President and the Vice President of India, the Chief Justice of India acts as the President of India.
• In the case of the death of the President, Vice President acts as the President of India.

• Admiral Karambir Singh assumed command of the Indian Navy on 31 May 2019 as the 24th Chief of the Naval Staff.
• General Bipin Rawat is the 27th Chief of Army Staff. He assumed charge on 31 December 2016.
• Admiral Sunil Lanba served as the 23rd Chief of the Naval Staff of the Indian Navy.
• Vice Admiral Bimal Verma is the Commander in Chief of the Andaman and Nicobar Command.
• Air Chief Marshal Birender Singh Dhanoa is the 25th Chief of the Air Staff of the Indian Air Force.

Explanation:

Pollination:

• Pollination takes place in the flowers.
• It is the act of transferring pollen grains from the male part of the flower, anther to the female part of the flower, stigma.
• Insects, birds, bats and the wind take pollen transferring agents between flowering plants.
• Pollination takes place in two forms: self-pollination and cross-pollination.

Pollination of the flowering shrubs by birds is known as Ornithophily.

• Entomophily is a pollination caused by insects.
• Anemophily is a pollination caused by wind.
• Autogamy means self-pollination of a flower.

• The leading light of the Rama cult was saint-poet Tulsidas who also wrote the poem 'Ramacharitamanasa'.
• Tulsidas was a Hindu saint and poet who was devoted to the deity Rama.
• His epic Ramacharitamanasa was written in Awadhi dialect.

• Uttar Pradesh is the most populous state according to the 2011 census.
• It has a population of 19.96 crores.
• The least populated state is Sikkim with a population of 60,7688.
• Maharashtra is the second most populated state, while Bihar is the third most populated state.
• | Uttar Pradesh | 199,812,341 | | --- | --- | | Bihar | 104,099,452 | | Rajasthan | 68,548,437 | | Maharashtra | 112,374,333 |

(x³ – 2√2y³) ÷ (x – √2y)

As we know,

⇒ (x³ + y³) = (x + y) (x² + y² – xy)

⇒ (x – √2y) (x² + 2y² + √2xy) ÷ (x – √2y)

⇒ x² + 2y² + √2xy

Comparing on Ax² + Bxy + Cy²

⇒ A = 1, C = 2 and B = √2

⇒ 2A + 4√2 B – 4C

⇒ 2 × 1 + 4√2 × √2 – 4 × 2

⇒ 2 + 8 – 8

⇒ 2

Given, SD = 6 cm, BP = 4 cm, BC = 7 cm

As we know,

BP = BQ = 4      [∵ Tangent to the circle]

⇒ BC = BQ + QC

⇒ 7 =  4 + QC

⇒ QC = 3

⇒ SD = DR = 6      [∵ Tangent to the circle]

⇒ QC = RC = 3      [∵ Tangent to the circle]

⇒ DC = DR + RC = 6 + 3 = 9 cm

Area of sector = $\frac{{\rm{\theta }}}{{360}} \times {\rm{\pi }}{{\rm{r}}^2} = \frac{{22}}{7} \times 21 \times 21 \times \frac{{150}}{{360}} = 577.5;c{m^2}$

⇒ x = 2 – P,

⇒ x + P = 2

⇒ (x + P)³ = 2³

⇒ x³ + P³ + 3xP (x + P) = 8

⇒ x³ + P³ = 8 – 3px(x + P)

Now,

⇒ x³ + 6xP + P³

⇒ x³ + P³ + 6xP

⇒ 8 – 3px (x + P) + 6xP

Put x = 2 – P

⇒ 8 – 3P(2 – P)(2 – P + P) + 6(2 – P)P

⇒ 8 – 12P + 6P² + 12P – 6P²

⇒ 8

⇒ x + P = 2

⇒ (x + P)3 = 23

⇒ x3 + P3 + 3xP (x + P) = 8

⇒ x3 + P3 = 8 – 3px(x + P)

⇒ x3 + P3 + 6xP = 8 – 3px(x + P) + 6xP

Put x = 2 - p

⇒ x3 + P3 + 6xP = 8 - 3P(2 – P)(2 – P + P) + 6(2 – P)P

⇒ x3 + P3 + 6xP = 8

Let the speed of the boat be x km/hr and the speed of the stream be y km/hr.

∴ Speed of boat in downstream = (x + y) km/hr

∴ Speed of boat in upstream = (x – y) km/hr

According to the question

$\Rightarrow \frac{7.2}{\text{x}+\text{y}}+\frac{3.2}{\text{x}-\text{y}}=2$

$\Rightarrow \frac{1.5}{\text{x}+\text{y}}+\frac{0.6}{\text{x}-\text{y}}=\frac{24}{60}$

Suppose 1/(x + y) = a, and 1/(x – y) = b, then

⇒ 7.2a + 3.2b = 2

⇒ 0.9a + 0.4b = 2/8 = 1/4      ----(1)

⇒ 1.5a + 0.6b = 2/5

⇒ 0.5a + 0.2b = 2/15      ----(2)

Multiply by 2 in equation (2)

⇒ a + 0.4b = 4/15      ----(3)

Subtract equation (1) from (3)

⇒ 0.1a = 1/60

⇒ a = 1/6

⇒ 1/(x + y) = 1/6

∴ Speed of the boat in downstream is 6 km/hr.

Total production of type A cars in 2014 and 2016 and type C cars in 2013 = 56 + 64 + 45 = 165 thousands

Total production of type B cars and type D cars in 2014 = 63 + 57 = 120 thousands

∴ Required ratio = 165 : 120 = 11 : 8

$\frac{1}{{\sec x{\rm{;}}-\tan x{\rm{;;}}}} - \frac{1}{{\cos x}}$

$\Rightarrow \frac{1}{{\frac{1}{{\cos x}} - \frac{{\sin x}}{{\cos x}}}} - \frac{1}{{\cos x}}$

$\Rightarrow \frac{{\cos x}}{{\left( {1{\rm{;}} - {\rm{;}}\sin x} \right)}} - \frac{1}{{\cos x}}$

$\Rightarrow \frac{{{\rm{co}}{{\rm{s}}^2}{\rm{x}} - 1 + \sin x{\rm{;;}}}}{{\cos x{\rm{;}}\left( {1 - \sin x} \right){\rm{;}}}}$

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

$\Rightarrow \frac{{\sin x\left( {{\rm{;}}1 - \sin x} \right)}}{{\cos x\left( {1 - \sin x} \right)}}$

⇒ tanx

Let the ratio of present age of A and B be 8x : 15x.

According to the question

$\Rightarrow \frac{{8{\rm{x;}} - {\rm{;;}}8{\rm{;}}}}{{15{\rm{x;}} - 8{\rm{;}}}} = \frac{6}{{13}}$

⇒ 104x – 104 = 90x – 48

⇒ 14x = 56

⇒ x = 4

Present age of A = 8x = 8 × 4 = 32 years

Present age of B = 15x = 15 × 4 = 60 years

Ratio of their age after 8 years = (32 + 8) : (60 + 8)= 40 : 68= 10 : 17

Given, AB = c, AC = b, BC = a

Suppose BD = x then DC = a – x

As we know,

⇒ AB/AC = BD/DC      (angle bisect theorem)

⇒ c/b = x/(a – x)

⇒ ca – cx = bx

⇒ x(c + b) = ac

⇒ x = ac/(b + c)

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 in 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.

$\Rightarrow \frac{8}{9}{\rm{of}}\left( {5\frac{1}{4} \div 2\frac{1}{3}{\rm{of;}}4} \right) \div \left( {8 \div \frac{2}{3}{\rm{of}}\frac{4}{5}} \right){\rm{of}}\left( {8 \times \frac{2}{3} \div \frac{4}{5}} \right)$

$\Rightarrow \frac{8}{9}{\rm{of}}\left( {\frac{{21}}{4} \div \frac{7}{3} \times 4} \right) \div \left( {8 \div \frac{2}{3} \times \frac{4}{5}} \right){\rm{of;}}\left( {8 \times \frac{2}{3} \times \frac{5}{4}} \right)$

$\Rightarrow \frac{8}{9}{\rm{of}}\left( {\frac{{21}}{4} \div \frac{{28}}{3}} \right) \div \left( {8 \div \frac{8}{{15}}} \right){\rm{of}}\frac{{20}}{3}$

$\Rightarrow \frac{8}{9}{\rm{of}}\left( {\frac{{21}}{4} \times \frac{3}{{28}}} \right) \div \left( {8 \times \frac{{15}}{8}} \right){\rm{of}}\frac{{20}}{3}$

$\Rightarrow \frac{8}{9} \times \frac{9}{{16}} \div \frac{{20}}{3} of 15$

$\Rightarrow \frac{8}{9} \times \frac{9}{{16}} \times \frac{3}{{20}} of(1/ 15)$

⇒ 1/200

Average production of type C cars during 2012 to 2016 = (44 + 45 + 67 + 63 + 76)/5 = 295/5 = 59 thousands

Production of type D cars in 2012 and type E cars in 2014 = 46 + 64 = 110 thousands

⇒ Required percentage = [(110 – 59)/110] × 100 = 46.36%

$\Rightarrow \frac{{{\rm{cose}}{{\rm{c}}^2}{\rm{\theta }} - {\rm{se}}{{\rm{c}}^2}{\rm{\theta }}}}{{{\rm{cose}}{{\rm{c}}^2}{\rm{\theta ;}} + {\rm{;se}}{{\rm{c}}^2}{\rm{\theta }}}}$

Multiply by sin²θ

$\Rightarrow \frac{{1 - {\rm{ta}}{{\rm{n}}^2}{\rm{\theta }}}}{{1 + {\rm{ta}}{{\rm{n}}^2}{\rm{\theta }}}}$

⇒ cotθ = √7

⇒ tan²θ = 1/7

$\Rightarrow \frac{{1 - \frac{1}{{7}}}}{{1 + \frac{1}{{7 }}}} \Rightarrow {{6\over 7}\over {8\over7}} = {3\over4}$

Let the price of the article be 100x.

Dealer bought the article at 20% discount, then

CP of the article for the dealer = 100x × [80/100] = 80x

Marked price of the article = 100x × [125/100] = 125x

SP of the article after 20% discount = 125x × [80/100] = 100x

∴ Required profit percentage = [(100x – 80x)/80x] × 100 = 25%

Total production of type E cars in 2015 and type C cars in 2013 taken together = 65 + 45 = 110

Total production of type A cars and type D cars = 46 + 48 + 56 + 57 + 64 + 46 + 49 + 57 + 55 + 72 = 550

∴ Required percentage = [110/550] × 100 = 20%

Shortcut Trick

When the time interval for the second amount is exactly double the first (3 years and 6 years), use the direct formula for Principal (P):

P = (Amount₁)² ÷ Amount₂

⇒ P = (18,600 × 18,600) ÷ 27,900

⇒ P = 18,600 × (186 ÷ 279) = 18,600 × (2 ÷ 3)

⇒ P = 6,200 × 2 = 12,400

∴ The correct answer is ₹12,400.

Alternate Method

Given:

Amount after 3 years (A₁) = ₹18,600

Amount after 6 years (A₂) = ₹27,900

Formula Used:

Amount (A) = P(1 + r/100)ⁿ

Calculations:

⇒ 18,600 = P(1 + r/100)³ → (Eq. 1)

⇒ 27,900 = P(1 + r/100)⁶ → (Eq. 2)

Divide (Eq. 2) by (Eq. 1):

⇒ 27,900 ÷ 18,600 = [P(1 + r/100)⁶] ÷ [P(1 + r/100)³]

⇒ (1 + r/100)³ = 279 ÷ 186 = 3 ÷ 2

Substitute this value back into (Eq. 1):

⇒ 18,600 = P × (3 ÷ 2)

⇒ P = (18,600 × 2) ÷ 3

⇒ P = 6,200 × 2 = 12,400

∴ The correct answer is ₹12,400.

Additional Information

Constant Multiplier Property

In Compound Interest, the ratio of amounts over equal time intervals remains constant. If A₁, A₂, A₃ are amounts after t, 2t, and 3t years respectively, then A₂/A₁ = A₃/A₂ = (1 + r/100)^t.

CI vs SI Difference

The difference (D) between CI and SI for 2 years is P(r/100)². For 3 years, it is P(r/100)² × (3 + r/100).

Rule of 72

A quick way to estimate the time required for a sum to double at a given interest rate (r) is Time ≈ 72 ÷ r.

As we know, ∠BGA = 90

In right angled triangle BGA

AB = 12 cm (diameter of circle)

⇒ (AB)² = (AG)² + (BG)²

⇒ 12² = 8² + (BG)²

⇒ BG = 4√5

In right angled triangle BCG

Let CG be x cm.

⇒ (BC)² = (CG)² + (BG)²

⇒ (BC)² = x² + (4√5)²      ----(1)

As we know,

⇒ (BC)² = CG × CA      ----(2)

From equation (1) and equation (2)

⇒ x² + (4√5)² = x × (x + 8)

⇒ x² + (4√5)² = x² + 8x

⇒ 8x = 80

⇒ x = 10 cm

From equation (2)

⇒ (BC)² = CG × CA

⇒ (BC)² = 10 × 18 = 180

⇒ BC = √180 = 6√5 cm

Efficiency ratio of A, B and C = 7 : 5 : 8

Total work = 42 × (7 + 5 + 8) = 840

Work done by B and C in 21 days = (5 + 8) × 21 = 273

Remaining work = 840 – 273 = 567

Remaining work A will complete in = 567/7 = 81 days

Total time = 21 + 81 = 102 days

Net profit = [300/12000] × 100 = 2.5%

Using Allegation method

(+15)                            (-10)

                   (+2.5)

12.5                             12.5

1                      :           1

2 unit = 12,000

1 unit = 6,000

Now we can say cost price of 6 tables are Rs. 6,000 and cost price of 12 chairs are Rs. 6,000.

Alternate Method Sushma bought 6 tables and 12 chairs for Rs. 12,000

Let the cost of each chair & table is C & T Respectively.

6T + 12C = 12000             (i)

Now, selling price of each table = 1.15T

Now, selling price of each chair = 0.9C

Since her total gain is Rs. 300, then the total selling cost  = 12000 + 300 = 12300

So,

6 × 1.15T + 12× 0.9C = 12300 

6.9T + 10.8 C = 12300  (ii)

By solving the equation (i) & (ii)

T = 1000Rs, & C = 500Rs

So, total cost for table = 6T = 6×1000 = 6000Rs

Given:

∠A = 92°

Concept used:

The angle between the external bisectors of two angles of a triangle is difference between right angle and half of the third angle.

Calculation:

Using the concept:

⇒ ∠O = 90° – ∠A/2

⇒ ∠O = 90° – 92°/2 = 90° – 46° = 44°

The correct answer is 44°.

Suppose there are three number a, b and c.

According to the question

⇒ a + (b + c)/2 = 164

⇒ 2a + b + c = 164 × 2 = 328      ----(1)

⇒ b + (c + a)/2 = 158

⇒ 2b + c + a = 158 × 2 = 316      ----(2)

⇒ c + (a + b)/2 = 132

⇒ 2c + a + b = 264      ----(3)

Add equation (1), (2) and (3)

⇒ 4(a + b + c) = 908

⇒ a + b + c = 227

∴ Required average = 227/3 = $75\frac{2}{3}$

Identity Used:

(a - b)³ = a³ - b³ - 3ab (a - b)

Calculation:

x⁴ – 6x² – 1 = 0

⇒ x² – 6 – 1/x² = 0

⇒ x² – 1/x² = 6

From the above expression, we can obtain x6 – 1/x6 by using Identity mentioned above as:

⇒ (x⁶ – 1/x⁶) = (x² – 1/x²)³ + 3(x² – 1/x²)

⇒ x⁶ – 1/x⁶ = 6³ + 3 × 6 = 216 + 18 = 234

⇒ x⁶ – 5x² + 5/x² – 1/x⁶ + 5

⇒ x⁶ – 1/x⁶ – 5(x² – 1/x²) + 5

⇒ 234 – 5 × 6 + 5

⇒ 239 – 30

⇒ 209

tan²θ – 3secθ + 3 = 0

Given, (0° ≤ θ ≤ 90°)

Put θ = 60°

⇒ tan²60°– 3sec60° + 3 = 0

⇒ 3 – 2 × 3 + 3 = 0

⇒ 3 – 6 + 3 = 0

⇒ 0 = 0 (Satisfied)

⇒ sinθ + cotθ

⇒ sin60° + cot60°

⇒ (√3/2) + (1/√3)

⇒ (5/2√3) × (√3/√3)

⇒ 5√3/6

Total production of type E cars = 48 + 55 + 64 + 65 + 68 = 300 thousands

Production of type E cars in 2013 = 55

300 thousands represents = 360°

∴ 55 thousand will represent = [360°/300] × 55 = 66°

We know, 20% = 1/5, 30% = 3/10 & 25% = 1/4

Ratio of A to B = 4 : 5      ----(1)

Ratio of C to D = 13 : 10      ----(2)

Ratio of D to A = 3 : 4      ----(3)

⇒ Ratio of A,B and D = 4 : 5 : 3      ----(4)

∴ Ratio of A, B, C and D = 40 : 50 : 39 : 30

⇒ C : B = 39 : 50

⇒ C/B = 39/50

⇒ C = 39/50 × B

⇒ C = 0.78B

Shortcut Trick

For divisibility by 88, the number must be divisible by both 8 and 11.

For divisibility by 8, the last three digits 8y2 must be divisible by 8 → y = 3 (as 832 ÷ 8 = 104).

For divisibility by 11, the difference between sum of odd position digits and even position digits must be 0 or a multiple of 11.

Sum of odd positions (1st, 3rd, 5th, 7th, 9th) = 1 + 3 + x + 5 + y = 9 + x + y = 12 + x (since y = 3).

Sum of even positions (2nd, 4th, 6th, 8th, 10th) = 3 + 0 + 5 + 8 + 2 = 18.

To make (18) − (12 + x) = 0 → 6 − x = 0 → x = 6.

Thus, x + y = 6 + 3 = 9.

∴ The correct answer is 9.

Alternate Method

Given: The 10-digit number is 1330x558y2 and it is divisible by 88.

Formula Used:

A number is divisible by 88 if it is divisible by both 8 and 11 (co-prime factors of 88).

Divisibility rule of 8: Last 3 digits must be divisible by 8.

Divisibility rule of 11: Absolute difference of the sum of digits at odd places and even places must be 0 or divisible by 11.

Calculations:

⇒ Divisibility by 8 check: last three digits = 8y2

⇒ For y = 3, 832 ÷ 8 = 104 (completely divisible)

⇒ Therefore, y = 3

⇒ The 10-digit number becomes 1330x55832

⇒ Divisibility by 11 check:

⇒ Sum of digits at odd places = 1 + 3 + x + 5 + 3 = 12 + x

⇒ Sum of digits at even places = 3 + 0 + 5 + 8 + 2 = 18

⇒ Difference = 18 − (12 + x) = 6 − x

⇒ For the difference to be 0, 6 − x = 0

⇒ x = 6

⇒ Value of (x + y) = 6 + 3 = 9

∴ The correct answer is 9.

Additional Information

Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8, or if the last three digits are all zeros.

Divisibility Rule of 11

A number is divisible by 11 if the absolute difference between the sum of the digits at odd positions and the sum of the digits at even positions is 0 or a multiple of 11.

Composite Divisibility

To check divisibility by a composite number like 88, express it as a product of co-prime numbers (e.g., 8 × 11). The number must be divisible by each of these co-prime factors.

The word to be used in the blank is --to.

--Rose to-- is the past tense of the phrasal verb --rise to-- and in this context, it means that the Marathas were ready to deal successfully with a problem or situation that is especially difficult.

The rest of the options are incorrect as they are meaningless.

Hence the correct answer is option 1.

The word to be used in the blank is --country.

Country-- is a nation with its own government, occupying a particular territory.

The sentence now means that after the decline of the Mughal empire, no further Indian power emerged to unite the country, which is India, under a central authority.

The rest of the options are incorrect as they mean:

Territory: an area of land under the jurisdiction of a ruler or state

State: The word --state-- is sometimes used to denote subdivisions of the country as in India or as areas with a lot of powers like states in the United States or even for countries. An example of the latter is international conventions and agreements which refer to --state parties to the convention...etc.

So India is a country. It can also be referred to as a --state-- in some international conventions and legal documents

 Region: an area, especially part of a country or the world having definable characteristics but not always fixed boundaries.

Hence the correct answer is option 3.

The correct answer is didn't he

Key Points

• Tag questions (or question tags) turn a statement into a question. They are often used for checking the information that we think we know is true.
• Tag questions are made using an auxiliary verb (for example: be or have) and a subject pronoun (for example I, you, she). Negative question tags are usually contracted: It's warm today, isn't it (not 'is it not')
• Usually if the main clause is positive, the question tag is negative, and if the main clause is negative, it's positive.
  

For example

• It's cold (positive), isn't it (negative)?
• It isn't cold (negative), is it (positive)?
• If the main clause has an auxiliary verb in it, you use the same verb in the tag question. If there is no auxiliary verb (in the present simple and past simple) use do/does/ did (just like when you make a normal question). That is why the question tag here is --didn’t he? ('he' according to subject)
• The rest of the options makes the sentence grammatically incorrect.

​Thus, the correct sentence is: He came late, didn't he?

The --She forgot lock-- part of the sentence is grammatically incorrect.

The correct phrase that should be used here is ---She forgot to lock--. The infinitive form of the verb --lock-- should be used.

Basically, an infinitive verb is a verb with the word to in front of it.

• to be
• to have
• to hold
• to sleep
• to dream

When you use an infinitive verb, --to--- is a part of the verb. It is not acting as a preposition in this case. And the verb is always just the verb. It's not conjugated in any way - no -ed, no -ing, no -s on the end.

There are several possible ways to use infinitive verbs. You can use them:

1. as the subject of a sentence - To err is human; to forgive, divine.
2. like an adjective or adverb phrase that expresses purpose or intent - My instructions are to press this button every hour.
3. following an indirect object - He told me to give this to you.
4. following certain other verbs:

• afford - We can't afford to eat out every night.
• agree - Let's agree to disagree.
• aim - I aim to please.

Hence the correct answer is option 1.

The correct answer is completely

Key Points

• Lock, stock, and the barrel is afigure of speech used predominantly in the United Kingdom and North America, meaning all, total, everything.
• The effective portions of a gun (or more specifically a musket) are the lock (used to hold ready the sparking mechanism), the stock (the portion held), and the barrel (the aiming guide and conveyor for the explosive-driven projectile). Collectively they are the whole weapon, and therefore everything.
• Example of use: Much to his wife's surprise, he cleaned out the basement, lock, stock, and barrel.

The correct answer is The customs officers were thoroughly checking one of the passengers.

Key Points

• The structures for both the active and passive forms for past continuous tense are given below:
• Active form- Subject +was/were + V1 + ing + Object
• Passive form- Object + was/were + being + V3 + by + Subject
• Example:
• He was playing a Cricket match. (active voice)
• A Cricket match was being played by him. (passive voice)
• The given sentence is an assertive one and in the passive voice form.
• Follow the active form structure for the past continuous tense given above:
• Exchange the places of the subject and object. (One of the passengers - the custom officers)
• At last line up the remaining part

Following these steps, we finally get- The customs officers were thoroughly checking one of the passengers.

The correct answer is "You are requested to take these students round the biscuit factory.".

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice.
• When we convert this sentence into passive voice, we use the verb 'request' instead of the adverb ';please'.
• The passive format "are + V3" should be used.
• This is the active and passive voice rule for the present simple tense.
• Hence, the correct answer is option 1.

Hence the answer is You are requested to take these students round the biscuit factory.

The correct answer is LETHAL

Key Points​

• Lethal: A substance that is lethal can kill people or animals.
  

Example: chemicals lethal to fish and aquatic mammals

• Fatal: A fatal accident or illness that causes someone's death.
  

Example: A hospital spokesman said she had suffered a fatal heart attack.

• Thus, 'fatal' is the synonym of 'lethal'.

Additional Information

• The meanings of the rest of the words are:
• Harmless: not able or likely to cause harm
• Healthy: in a good physical or mental condition; in good health
• Strong: having the power to move heavy weights or perform other physically demanding tasks

The correct answer is option 1: BADC.

The paragraph is about why Boeing prevented its 737 Max aircraft from flying.

Sentence B is 1st as it introduces a new topic.

Sentence A is 2nd as the --move-- mentioned here refers to the grounding of Boeing's 737 Max aircraft.

Sentence D is 3rd as it mentions another aircraft that crashed like the Ethiopian Airlines aircraft. Both crashed under similar

circumstances.

Sentence C is last.

The word to be used in the blank is --place.

Place-- in this context means --a person’s/thing’s rank or status.

The phrase --take one’s place-- means --take up one's usual or recognized the position. Here the recognized position of the Mughal empire is being talked about.

The rest of the options are incorrect as they mean:

Seat: a thing made or used for sitting on

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

Niche: a comfortable or suitable position in life or employment

Hence the correct answer is option 2.

The word to be used in the blank is --with.

Here it means --after the decline of the Mughal empire.

The rest of the options are incorrect as they mean:

When: at or on which (referring to a time or circumstance)

In: expressing the situation of something that is or appears to be enclosed or surrounded by something else

On: physically in contact with and supported by (a surface)

Although “in” and “on” have several other meanings, all of them would make the sentence given in the question grammatically incorrect.

Hence the correct answer is option 1.

The correct answer is: Option 1 i.e. definate.

Key Points

• The word "definate" is spelled incorrectly.
• Meaning: This word does not exist in English. The intended word is likely "definite".
• Hindi Meaning: N/A (क्योंकि यह शब्द गलत है)
• "Definite" means clearly defined or determined; not vague or general.
• Hindi Meaning: निश्चित
• Example: He gave a definite yes to the proposal.

Therefore, the correct answer is: definite.

Additional Information

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

• Deform (विकृत करना): To change the shape or structure of something.
• Example: The metal rod can deform under extreme pressure.
• Define (परिभाषित करना): To explain the meaning of a word or concept.
• Example: It’s important to define the problem clearly before suggesting solutions.
• Deflate (हवा निकालना): To let the air or gas out of something.
• Example: He managed to deflate the balloon without popping it.

The correct answer is option 1.

Prevalent means --widespread in a particular area or at a particular time.-- The word that is a synonym of this is --Common: occurring, found, or done often; prevalent.

The meanings of the rest of the words are:

Rare: (of an event, situation, or condition) not occurring very often

Unusual: not habitually or commonly occurring or done

Different: novel and unusual

These options are antonyms of prevalent

The correct answer is cauldron

Key Points

• A cauldron is a large metal pot with a lid and handle, used for cooking over an open fire.
• The rest of the options are incorrect as:
• A barrel is a cylindrical container bulging out in the middle, traditionally made of wooden staves with metal hoops around them.
• A skillet is a small metal cooking pot with a long handle, typically having legs.
• A kettle is a container or device in which water is boiled, having a lid, spout, and handle.

The correct word to be used in the blank is deployed. It means to move (troops or equipment) into position for military action.

Eg: They plan to deploy more American soldiers over the next six months. 

The meanings of the rest of the words are:

Deported: expel (a foreigner) from a country, typically on the grounds of illegal status or for having committed a crime

Departed: left, especially in order to start a journey

Deposited: put or set down (something or someone) in a specific place

Hence, these options are incorrect.

Hence the correct answer is option 3.

When someone’s described as --In the pink, that means he is in peak physical condition and in the best possible health.

Example of use: Jon recovered from his surgery in less than 10 days, and is now in the pink of health.

Hence the correct answer is option 3.

The correct answer is option 1: CBAD.

Sentence C is 1st as it is the introductory statement that presents the topic of the paragraph.

Sentence B is 2nd as it gives the reason why it was thought that dogs were good walking companions.

Sentence A is 3rd as it starts with "however", which shows that it is contradicting the previous sentences.

Sentence D is 4th as it gives information to support what is said in sentence A.

The correct answer is fresh

Key Points 

• Stale means (of food) no longer fresh and pleasant to eat; hard, musty, or dry.
• The word that is an antonym of this is Fresh: (of food) recently made or obtained; not tinned, frozen, or otherwise preserved.

Additional Information

• The meanings of the rest of the words are:
• Flat: having a level surface; without raised areas or indentations.
• Dry: free from moisture or liquid; not wet or moist
• Sour: having an acid taste like lemon or vinegar
• Option 2 is an antonym of stale and options 1 and 4 are neither synonyms nor antonyms of it.

The word to be used in the blank is--other.

Other-- is used as an adjective here which means --further; additional. This part of the sentence means that no additional Indian power emerged.

The rest of the options are incorrect as they mean:

Another: used to refer to an additional person or thing of the same type as one already mentioned or known about; one more; a further.

Eg: "Have another drink." It is incorrect to use “another” after “no”.

One: If we put --one-in the blank, it will become--no one-- which means---no person; not a single person.

More: If we put --more-- in the blank, it will become --o more--which means --no further.

Hence the correct answer is option 4.