SSC CGL Previous Paper (Held On: 9 August 2017 Shift 1) (Previous Year Paper)

The logic follows here is:

Metre is the smaller unit of Kilometre to measure distance.

Similarly,

Kilogram is the smaller unit of Tonne to measure weight.

Hence, "Kilogram" is the correct answer.

In AGN : IOV 

A + 8 = I

G + 8 = O

N + 8 = V

Similarly,

B + 8 = J

L + 8 = T

M + 8 = U

Hence the correct answer is JTU.

Adding the digits

(9 + 1 + 4 + 3) : (9 + 9 + 6 + 3) ⇒ 17 : 27

Similarly

(6 + 7 + 3 + 1) : (8 + 9 + 6 + 4) ⇒ 17 : 27

Hence 8964 is the correct answer.

Daman is a place in a union territory whereas the other three places are in states.

The alphabetical position of W is an odd number whereas the alphabetical positions of the other three letters are even numbers.

313 is a prime number, other three are composite numbers.

According to the dictionary, the correct arrangement of words would be:

4. Balance

5. Balanced

6. Balancing

7. Ball

8. Balls

A + 11 = L; L + 11 = W; W + 11 = H; H + 11 = S

G + 11 = R; R + 11 = C; C + 11 = N; N + 11 = Y

Hence the correct answer is SY.

13 + 3 = 16; 16 – 5 = 11; 11 + 7 = 18; 18 – 9 = 9; 9 + 11 = 20; 20 – 13 = 7

2 is increasing with alternate opposite signs.

Lady’s father’s wife à Lady’s mother

Lady’s mother's sister is Punit’s aunt à Lady is Punit’s cousin sister or Sister.

But in the option only given cousin sister so, 4th option is the correct answer.

The rank of lemon tree from left end = (45 – 20) + 1 = 26^th.

The word ‘Annuity’ cannot be formed using the word ‘Uniformity’ because letter ‘A’ is missing in the given word.

Adding the alphabetical positions of the letters,

TIRED à 20 + 9 + 18 + 4 + 5 = 56

BRAIN à 2 + 18 + 1 + 9 + 14 = 44

Similarly,

LAZY à 12 + 1 + 26 + 25 = 64

18 ÷ 6 × 9 = 27

The above signs make the equation correct.

18 ÷ 6 = 3 × 3 = 9

36 ÷ 6 = 6 × 5 = 30

Similarly

19 ÷ 6 = 3.17 × 18 = 57

Thus 57 is correct answer.

1512 ÷ 168 = 9

504 ÷ 56 = 9

Hence 56 is the correct answer.

The given figure has 17 triangles in total.

Conclusions:

I. Some pencils are not pens -  It’s possible but not definite, hence false.

II. Some erasers are not pens - It’s possible but not definite, hence false.

Hence neither conclusion I nor II follows.

The four sides adjacent to face containing ‘4’ are faces containing ‘5’, ‘2’, ‘6’, and ‘3’. Thus the side opposite to ‘4’ is ‘1’.

Piano and Guitar are two types of music instruments. Thus, option figure 2 is correct.

The final pattern will be as shown in below,

Thus image 3) completes the given pattern.

On close observation, we find that fig. 1 is embedded in question figure as shown below:

Hence, Image of option 1) is ​correct answer.

The paper cutting folding image is given below:

Hence, the correct answer is option 4.

1 ) 00, 13, 57, 76 ⇒ SPAM

2) 11, 04, 86, 59 ⇒ SCAM

3. 23, 22, 99, 95 ⇒ SNAM

4. 32, 40, 66, 68 ⇒ SCJM

Hence option 2 is correct.

Option 2 is correct, i.e Leon Walras.

• First-time general equilibrium formulated by French economist Léon Walras.
• General equilibrium theory, or Walrasian general equilibrium, seeks to describe the workings of the macroeconomy as a whole, rather than assets of individual market anomalies.
• General Equilibrium Theory was first propounded by Leon Walrus in 1874.
• It attempts to explain that interaction of demand and supply will result in an overall general equilibrium.

Extra information:

• Born in 1723, Adam Smith is regarded as the Father of Economics due to his immense contribution to the subject.
• Amongst his many books, the most famous is the "Wealth of Nations" (1776) which is regarded as the first work in modern economics.
• Smith influenced many later thinkers such as Karl Marx, Joseph Schumpeter, David Ricardo, and many more.

A demand draft cannot be dishonoured by a bank for lack of funds, this is because it guarantees the amount of money for which it is pledged and that money is taken before the draft is made.

The correct answer is option 2 i.e Chief Justice of India

• Chief Justice of India administers the oath to the President of India.
• In the absence of CJI, the senior-most judge of the Supreme Court can administer the oath to the President of India.
• The President of India is elected not directly by the people but by members of an electoral college which consist of elected members of-
• Both the houses.
• State legislative assemblies
• Legislative assemblies of Union Territories of Delhi and Puducherry.

Option 1 is correct, i.e. Austin.

• The monistic theory of sovereignty was given by John Austin.
• It is called the Monistic Theory of Sovereignty because it envisages a single sovereign in the state.

Extra facts:

Charles Darwin:

• Charles Robert Darwin was an English naturalist, geologist, and biologist best known for his contributions to the science of evolution.

Aristotle:

• Aristotle is also known as the Father of Biology, he was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidice in 384 BC.

Marx:

• Karl Marx was a German philosopher and economist.
• His theories were understood as Marxism.

Option 3 is correct, i.e. III, I, II, IV.

Key Points

• The Poona Pact refers to an agreement between Dr Bhimrao Ambedkar and Mahatma Gandhi signed on September 24, 1932.
• This Pact ended the fast that Mahatma Gandhi had undertaken in the jail to protest against British Prime Minister Ramsay Macdonald’s award of a separate electorate to the Depressed Classes.
• The famous Quit India Movement is also known as the 'August Movement'. It was launched by Mahatma Gandhi on 8 August 1942 at Gowalia Tank Maidan, Bombay.
• Most of the prominent Congress leaders were imprisoned in the initial days of the Quit India Movement.
• The Simla Conference was held in 1945.
• It was a meeting between the Viceroy Lord Wavell and the major political leaders of British India at Shimla, India.
• It was conducted to discuss the provisions of the Wavell Plan
• Cabinet Mission Plan, 1946 was the basis of the formation of the Indian Constituent Assembly.
• The constitution of India was drafted by the Constitution Assembly.

Option 1 is correct, i.e. Satyagraha.

• In 1917, the Satyagraha movement was launched by Mahatma Gandhi from Champaran to protest against the injustice done by Britishers to the indigo farmers.

Extra facts:

• Non-cooperation Movement
• It was conducted from September 1920 to February 1922.
• It was initiated by Gandhi Ji after the Jallianwala Bagh Massacre. People started protesting with Non-Ahimsa and at the same time boycotted British goods.
• After the Chauri-Chaura incident, Gandhi Ji withdrew the movement.
• Quit India movement:
• The famous Quit India Movement is also known as the 'August Movement'.
• It was launched by Mahatma Gandhi on 8 August 1942 at Gowalia Tank Maidan, Bombay.
• Most of the prominent Congress leaders were imprisoned in the initial days of the Quit India Movement.​
• Swadeshi Movement:
• Swadeshi Movement started on 7th August 1905 at the Calcutta Town Hall in Bengal.
• It involved in boycotting the British products and the revival of the domestic products and production processes.

The correct answer is Typhoon.

• Tropical cyclones in the China Sea are called typhoons.
• This region is referred to as the Northwestern Pacific Basin and is the most active tropical cyclone basin on Earth.

Key Points

• A cyclone is known by different names in different parts of the world:

Key Points

Scandinavian countries:

• Scandinavia is a region in Northern Europe, with strong historical, cultural, and linguistic ties.
• The term Scandinavia in local usage covers the three kingdoms of Denmark, Norway, and Sweden.

Hence, only Finland among the options is not a part of Scandinavia.

Additional Information

• Finland comes under Nordic countries.
• Nordic has become a common term to bring together all five northern European countries called, Sweden, Norway, Iceland, Finland, and Denmark.

Cattle store their food after swallowing in Rumen. It is the first chamber in the alimentary canal of ruminant animals. It serves as the primary site for microbial fermentation of ingested feed.

​The correct answer is Red blood cells.

Important Points

• Red blood cells (Erythrocytes):
• RBCs are the biconcave cells without nuclei in humans; also known as erythrocytes.
• RBCs contain the iron-rich protein called hemoglobin.
• RBCs are the most copious blood cell produced in bone marrows.
• Their main function is to transport oxygen from and to various tissues and organs.
• Haemoglobin, aside from being a transport molecule, is a pigment.
• It gives the cells their red color (and their name).

Additional Information

• White blood cells (Leucocytes):
• ​Leucocytes are colorless blood cells.
• They are colorless because it is devoid of hemoglobin.
• They are further classified as granulocytes and agranulocytes.
• WBCs mainly contribute to immunity and defense mechanism.
• Blood plasma is a yellowish liquid component of blood that normally holds the blood cells in whole blood in suspension.
• It is the liquid part of the blood that carries cells and proteins throughout the body.

Option 1 is correct, i.e. Excretion.

Concept:

• Kidneys are the excretory organs in the majority of mammals including humans.
• Kidneys regulate water and electrolyte balance (osmoregulation) along with the excretion of metabolic waste and foreign chemicals.
• Nephrons are the functional unit of kidneys.

Important Points

• Kidneys perform a very crucial function of excretion in the human body.
• The main function of the kidney is to purify the blood that is present in the body and excrete waste in the form of urine.
• A nephron is a functional and structural unit of the kidney (organ), which is involved in the process of excretion.
• It is made up of renal corpuscle or Bowman’s capsule, Glomerulus, Proximal Convoluted tubule, Loop of Henle, and Distal Convoluted Tubule.
• Bowman’s capsule is a double-walled cup-like structure in which the dense network of blood capillaries (Glomerulus) is present.

Additional Information

Respiration - 

• The breaking of the C-C bonds of complex compounds through oxidation within the cells, leading to the release of a considerable amount of energy is called respiration.

Digestion - 

• The process of conversion of complex food substances to simple absorbable forms is called digestion and is carried out by our digestive system through mechanical and biochemical methods

Transportation -

• It is the movement of substances across the cell membrane either into or out of the cell.

The bending of light when it passes around a corner or a slit is due to diffraction. In classical physics, the diffraction phenomenon is described as the interference of waves.

The correct answer is option 3.

• The mirage is caused by the total internal reflection of light at layers of air of different densities.

• In a desert, the sand is very hot during day time and a result the layer of air in contact with it gets heated up and becomes lighter. The lighter air rises up and the denser air from above comes down.

• As a result, the successive upper layers are denser than those below them. A ray of light coming from a distant object, like the top a tree, gets refracted from a denser to a rarer medium.

• Consequently, the refracted ray bends away from the normal until, at a particular layer, the light is incident at an angle greater than the critical angle.

• At this stage, the incident ray suffers total internal reflection and is reflected upwards.

• When this reflected beam of light enters the eyes of the observer, it appears as if an inverted image of the tree is seen and the sand looks like a pool of water.

So, Mirage is an example of total internal reflection which occurs due to atmospheric refraction.

The correct answer is FORTRAN.

Key Points

• FORTRAN
• ​FORTRAN is the first high-level programming language developed by John Backus in 1957.
• It was basically designed to write programs for high-performance computing.
• FORTRAN is a programming language that is used for numeric computation and scientific computing.
• It stands for FORmula TRANslation.

The correct answer is Hydrogen bond.

Concept:

Chemical bond:

• A chemical bond is a force or linkage which holds two or more atoms together in a stable molecule.
• The driving force for atoms to combine is related to their tendency to attain stable electronic configuration.
• A chemical bond may be formed either by electron transfer or electron sharing.
• Ionic Bonds:
• ​Ionic bond formation occurs via electrostatic attraction between two ions.
• One ion is positively charged and the other is negatively charged like in NaCl.​
• Covalent bonds:
• Covalent bond formation occurs when there is electron sharing occurs between two atoms.
• The electron pair is shared equally between the atoms forming the bond-like in Cl2.
• When there exists a single bond between two atoms, there is only a sigma bond.
• When there exist multiple bonds between atoms, there is only one sigma bond and others are pi bond.

​Explanation:

• Whether a bond is weak or strong depends on the extent of linkage or interaction among the molecules or atoms.
• Besides the chemical bond, there exist interactions between the molecules, which are not actual bonds, which means that there is no sharing or transfer of electrons but only interaction between the molecules is there.
• The types of interactions are:
• Electrostatic: They are interactions between charged molecules.
• Induction: These types of interactions arise when there is induction of dipole in the molecule.
• Dispersion: These are also called London forces or Van der Waals forces and exists mostly in covalent molecules.
• Hydrogen bonds: Hydrogen bonds are the dipole-dipole interactions that occur when a Hydrogen is bonded to a very electronegative atom like oxygen, Nitrogen. It is not a covalent bond.
• So, the Hydrogen bond is just an interaction between the Hydrogen and an electronegative element where there is no electron exchange leading to weak bonding between molecules whereas a single bond, double bond, and triple bond are covalent bonds and not just interactions.
• Chemical bonds are much much stronger than chemical interactions.
• It is difficult to break chemical bonds whereas Hydrogen bonds are easily and rapidly formed and broken under normal biological conditions.
• Hence, the bond strength order is:

triple bond > double bond > single bond > H-Bond.

Hence, the weakest among the bonds is the Hydrogen bond.

Acid and base react together to give salt as a precipitate and water. This type of reaction is called the acid - base reaction.

Bishnoi movement was started against cutting of trees in 1730 when Amrita Devi, a member of the sect inspired 362 other Bishnois die in protest of the cutting down of Khejri trees.

The major aim of Pradhan Mantri Ujjwala Yojana is to provide LPG connections. It was launched on 1st May 2016 from Ballia in Uttar Pradesh.

John Logie Baird was a Scottish engineer who was the also the inventor of mechanical television. He demonstrated the first working television system on 26 January 1926. 

There are 6 players in one team in a volleyball match. 

The correct answer is 1 - c, 2 - a, 3 - b

Key Points

• Lingaraj Temple is dedicated to Lord Shiva.
• It was built in the 11th century AD by King Jajati Keshari of the Somavanshi dynasty.
• It is built of red stone.
• Tijara Temple is dedicated to Chandra Prabhu.
• Tijara Jain temple, this temple is located in the Tijara tehsil in the Alwar district, Rajasthan at a distance of 55 kilometers from the main city of Alwar.
• The area wherein the Alwar Jain temple stands are known as the “Atishaya Kshetra” or the region where the extraordinary happens.
• The Tijara Jain temple is dedicated to Chandra Prabhu, the eighth Tirthankar.
• Venkateswara Temple is dedicated to Lord Vishnu.
• It is situated on Venkata Hill in the Chittoor district of Andhra Pradesh, India.
• It is also known by its famous name, the Tirupati Temple.
• The Architectural Style of the temple is Dravidian.
• It is also one of the richest temples in the world.

Preeti Shenoy has been recently awarded with ‘Indian of the year’ award by Brands Academy. She is an Indian author and writes fiction. 

The correct answer is Aravind Adiga.

Key Points

• Aravind Adiga is the author of the book titled 'Selection Day.
• He is an Indo - Australian writer and journalist.
• His debut novel, The White Tiger, won the 2008 Man Booker Prize.
• Aravind Adiga is the fourth Indian born-author to win the prize.
• He was one of four writers shortlisted for the 2017 DSC Prize for South Asian Literature.

BRICS stands for Brazil, Russia, India, China and South Africa. It doesn’t have Iceland in it and is an association of five emerging national economies of the world.

Kalapani is a territory disputed between India and Nepal. It is situated on the Kailash Manasarovar route, at an altitude of 3600 meters.

Firstly, we have to find the L.C.M. of all the powers so that we can equate the bases.

L.C.M. of 3, 4, 6, 12 = 12

⇒ (5)^1/3 = (5⁴)^1/12 = (625)^1/12

⇒ (6)^1/4 = (6³)^1/12 = (216)^1/12

⇒ (12)^1/6 = (12²)^1/12 = (144)^1/12

⇒ (276)^1/12

Since, the powers are equal, we can equate the bases

Hence, (5)^1/3 is the largest

Let the total amount of work be a

⇒ Work done by A and B together = 0.6a

⇒ Work done by C alone = a – 0.6a = 0.4a

⇒ Work done by B and C together = 0.7a

⇒ Work done by B alone = 0.7a – 0.4a = 0.3a

⇒ Work done by A alone = a – 0.7a = 0.3a

∴ the most efficient is C

Given: R₁ = 3 cm, R₂ = 4 cm, R₃ = 5cm

Surface area of all the 3 spheres = 4 x π x (3² + 4² + 5²) = 4 x π x 50 = 200π

Now, let the radius of the new sphere be R₄

⇒ 4/3 x π x (R₄)³ = 4/3 x π x ((R₁) ³ + (R₂) ³ + (R₃)³)

⇒ (R₄)³ = 3³ + 4³ + 5³ = 216

⇒ R₄ = 6 cm

Surface area of bigger sphere = 4 x π x (6)² = 144π

∴ Percentage decrease = [(200π - 144π)/200π] x 100 = (56/200) x 100 = 28%

Marked Price = Rs. 4800

Selling price = 3672

⇒ Total discount = MP – SP = Rs. 1128

Price after first discount = 4800 – 4800 x (10/100) = Rs. 4320

Second discount = [(4320 – 3672)/4320] x 100 = 15%

∴ the second discount = 15%

Given:-

A : B : C = 3 : 4 : 5

Interest rates -

For A, B, and C = 20%, 15%, and 10%

Calculation:-

Let the amount invested = 3a, 4a, 5a respectively

Compound interest for A = P(1 + 0.2) – P

⇒ 3a x 1.2 – 3a = 0.6a

Compound interest for B = P(1 + 0.15) – P

⇒ 4a x 1.15 – 4a = 0.6a

Compound interest for C = P(1 + 0.1) – P

⇒ 5a x 1.1 – 5a = 0.5a

∴ required required = 0.6a : 0.6a : 0.5a

⇒ 6 : 6 : 5

Mistake PointsIn the question, it is clearly stated that the scheme offered at the compound interest, 

Hence only Interest shall be considered,

the Amount should not be considered.

Given: Number of members earlier = 120

⇒ Total age of all the members earlier = 120 x 60.7 = 7284      …..(i)

⇒ Total age of all the members presently = 150 x 56.3 = 8445        …..(ii)

⇒ Total age of new members = (ii) – (I)

⇒ 8445 – 7284 = 1161

∴ Average age of newly joined members = 1161/30 = 38.7

Let the selling price of 1 apple be a

⇒ S.P. of 175 pineapples = 175a

⇒ gain = 50a

⇒ Cost price = 175a – 50a = 125a

∴ gain percent = [50a/125a] x 100 = 40 %

Let the marks of B be c

⇒ marks of A = c (1 + 0.2) = 1.2c

Now, required percent = (marks of A –marks of B) /marks of A

∴ required percent = [(1.2c – c)/1.2c] x 100 = 100c/6c = 16.66%

Let the total distance between Delhi and Jaipur be a

Travel time of train A going from Delhi to Jaipur = 4 p.m – 10 a.m = 6 hours

⇒ Speed of train A = a/6 km/hr

Travel time of train B going from Jaipur to Delhi = 5 p.m – 12 p.m = 5 hours

⇒ Speed of train B = a/5 km/hr

⇒ Distance covered by train A in 2 hours = (a/6) x 2 = a/3

Distance left for train A to cover when time is 12 : 00 pm = a – a/3 = 2a/3

Relative velocity for train A w.r.t B = a/6 + a/5 = 11a/30

⇒ Time Taken = Distance/speed= (2a/3)/(11a/30) = 20/11 hours

∴ required time = 12 : 00 pm + 20/11 hours = 1 : 49 pm

Calculating compound interest = P(1 + 0.04) ² – P

Calculating simple interest = P x 0.08 x 1

⇒ P(1 + 0.04) ² – P – (P x 0.08 x 1) = 64

⇒ P(1.04) ² – 1.08P = 64

⇒ (1.0816 – 1.08) P = 64

⇒ P = 64/0.0016

⇒ P = 40000

Shortcut Trick

If (x + a) and (x + b) are factors of a quadratic equation, then the equation is given by x² + (a + b)x + ab = 0.

Comparing (x − 2) and (x + 3) with (x + a) and (x + b), we get a = −2 and b = 3.

The coefficient k₁ = a + b = −2 + 3 = 1.

The constant term k₂ = a × b = −2 × 3 = −6.

∴ The correct answer is k₁ = 1, k₂ = −6.

Alternate Method

Given: The factors of the quadratic equation x² + k₁x + k₂ = 0 are (x − 2) and (x + 3).

Formula Used: If (x − r₁) and (x − r₂) are factors, then the polynomial P(x) = (x − r₁)(x − r₂).

⇒ P(x) = (x − 2)(x + 3)

⇒ P(x) = x(x + 3) − 2(x + 3)

⇒ P(x) = x² + 3x − 2x − 6

⇒ P(x) = x² + x − 6

⇒ Comparing this result with the given equation x² + k₁x + k₂ = 0:

⇒ k₁ = Coefficient of x = 1

⇒ k₂ = Constant term = −6

This confirms that k₁ = 1 and k₂ = −6 is the correct solution.

∴ The correct answer is k₁ = 1, k₂ = −6.

Additional Information

Factor Theorem

If (x − a) is a factor of a polynomial f(x), then f(a) = 0. This can be used to set up simultaneous equations to find unknown coefficients.

Vieta's Formulas

For a quadratic equation ax² + bx + c = 0 with roots α and β, the sum of roots is −b/a and the product of roots is c/a.

Quadratic Construction

A quadratic equation can be formed as x² − (Sum of roots)x + (Product of roots) = 0 when the roots are known.

Since all the options are different.

⇒ Lets take x = 7, y = 0

∴ required value = (7 – 15)³ – (0 – 8)³ = (-8)³ – (-8)³ = 0

Given: x – y = –1 + √18      ----(i)

⇒ x + y = 1 + 3√2       ----(ii)

Multiplying (i) and (ii) . We get

⇒ x² – y² = (–1 + √18) (1 + 3√2)

⇒ x² – y² = -1 + 18 = 17

Now, from (i) and (ii)

⇒ x = 3√2 and y = 1

So, 12xy = 12(3√2) = 36√2

∴ Required value = 12xy(x² – y²) = (36√2) (17) = 612√2

Here, p = √5q

⇒ r = √5s

⇒ t = √5u

Now, substituting above values in required value

⇒ [(3(√5q) ² + 4(√5s) ² + 5(√5u) ²) /(3q² + 4s² + 5u²) ]

⇒ 5[(3q² + 4s² + 5u²)/(3q² + 4s² + 5u²) ]

∴ answer is 5

Given:

CD = 3 cm and BC = 9 cm

Calculation

BD = BC - CD = 9 - 3 = 6cm

In ΔABD and ΔACD

Both the triangles have the same height, AD = AD

The area of a triangle = $1\over2$ x base x height

Area of ΔABD : Area of ΔACD

⇒ $1\over2$ × BD × AD : $1\over2$ × CD × AD

⇒ BD : CD

⇒ 6 : 3 = 2 : 1

∴ The ratio of the areas of ΔABD and ΔADC is 2 : 1.

Given:

ΔPQR is a right-angled triangle and RS ⊥ PQ.

∠R = 90°, PR = 3 cm, and RQ = 4 cm

Calculation:

Using Pythagoras theorem,

PR² + RQ² = PQ² 

⇒ 4² + 3² = PQ²

⇒ PQ² = 25 

⇒ PQ = √25 = 5 cm

Now, ΔPQR and ΔRQS are similar triangles

So, $PQ\over PR$ = $RQ\over RS$

⇒ $5\over 3$ = $4\over RS$

⇒ RS = $12\over 5$

∴ The value of RS is $12\over 5$ cm.

Given:

In ΔPQR, A is the point of intersection of all the altitudes.

B is the point of intersection of all the angle bisectors of the triangle.

∠PBR  = 105°

Calculation:

Let PX, QY, and RZ be the angle bisectors

In ΔPBR

⇒ ∠BPY + ∠BRY + 105° = 180°

⇒ ∠BPY + ∠BRY = 180° - 105° = 75°

Now, this sum is half of ∠P and ∠R

⇒ ∠P + ∠R = 75° x 2 = 150°

In ΔPQR

∠Q = 180° - 150° = 30°

Let PM, QN, and RO be the altitudes

In ΔRQO

⇒ ∠QRO + ∠RZO + ∠Q = 180°

⇒ ∠QRO = 180° – 90° – 30°

⇒ ∠QRO = 60°

In ΔAMR

⇒ ∠MAR = 180° – 90° - 60°

⇒ ∠MAR = 30°

Now, ∠PAR + ∠MAR = 180°

⇒ ∠PAR = 180° – 30° = 150°

Alternate Method ∠Q/2 + 90 = ∠PBR

⇒ ∠Q/2 + 90°  = 105° 

⇒ ∠Q = 30°

Now, A is the orthocenter.

∠Q + ∠PAR = 180° 

⇒  30° + ∠PAR = 180° 

∠PAR = 150° 

∴ ∠PAR is 150°.

Given:-

4 lines in a plane

Formula used:-

Max. Number of intersections = n(n – 1)/2,

where n is the number of lines

Calculation:-

Put n = 4

Max. number of intersections = 4(3)/2 = 6

So, an option having a value greater than 6, cannot be possible.

Hence, 7 can't be the number of points of intersection.

Given:

cosec2A + cot2A

Formula used:

sin2A = 2sinA cosA

cos2A = 2cos²A - 1 = 1 - 2sin²A 

Calculation:

cosec2A + cot2A

⇒ $1\over sin2A$ + $cos2A\over sin2A$

⇒ ${1+cos2A}\over sin2A$

cos2A = 2cos2A - 1

⇒ 1 + cos2A = 2cos²A

⇒ ${2cos^2A}\over 2sinAcosA$ = $cosA\over sinA$ = cotA

Given :

A = 30° 

B = 60° 

C = 135° 

Calculation :

To find : sin³(30°) + cos³(60°) + tan³(135°) – 3sin (30°) cos (60°) tan (135°)

⇒ (1/2) ³ + (1/2) ³ + (-1) ³ – 3 x (1/2) x (1/2) x (-1)

⇒ 1/8 + 1/8 -1 + 3/4

⇒ 1/4 – 1 + 3/4

⇒ 0

∴ The correct answer is 0.

Given:

tan2 θ + cot2 θ + sin2 θ + cos2 θ + sec2 θ + cosec2 θ

Formula used:

Using these trigonometric identities:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

cot² θ + 1 = cosec² θ

Calculation:

tan² θ + cot² θ + sin² θ + cos² θ + sec² θ + cosec² θ

⇒ (tan2 θ + cot2 θ) + (sin2 θ + cos2 θ) + (tan2 θ + 1 + cot2 θ + 1)

⇒ (sin2 θ + cos2 θ) + (tan2 θ + cot2 θ) + 2 + (tan2 θ + cot2 θ) 

⇒ 1 + 2 + 2 (tan2 θ + cot2 θ)

⇒ 3 + 2(tan2 θ + cot2 θ)

The least value of tan2 θ + cot2 θ = 2

⇒ 3 + 2(2) = 3 + 4 = 7

∴ The minimum of the given expression is 7.

Mistake Points We can not put values directly in such questions, 

We have to reduced the fraction to the co-related terms and then only we can substitute the values, 

Here in the solution we have substituted the values only when we reduced the given expression into tanθ & cotθ, 

We can not substitute the values for different ratios at once.

Number of hours dedicated to algebra = (9/100) x 500 = 45 hours

Number of hours dedicated to modern maths = (4/100) x 500 = 20 hours

∴ difference in number of hours of teaching algebra and modern Maths = 45 – 20 = 25 hours.

Number of hours dedicated to geometry = 36 hours

Since, 36 hours is 6% of the total hours taught

⇒ 1% of total hours = 36/6 = 6 hours

⇒ Total hours = 6 x 100 = 600 hours

Number of hours dedicated to arithmetic = (46/100) (600) = 276 hours

∴ Number of hours dedicated to ratio = 276/4 = 69 hours

% of time dedicated to Data Interpretation and Modern Maths = 8 + 4 = 12%

⇒ Given : 12% of total hours = 96 hours

⇒ 1% of total hours = 96/12 = 8hours

Hence, total hours = 8 x 100 = 800 hours

⇒ % time dedicated to Number system and Geometry taught = 23 + 6 = 29%

So, total hours dedicated to Number system and Geometry = 800 x (29/100) = 232 hrs

∴ answer is 232 hours

% left after removing arithmetic = 100 – 46 = 54%

⇒ 10% of the left percentage is dedicated to problem solving

⇒ % dedicated to problem solving = (10/100) x 54 = 5.4%

∴ the central angle = (5.4/100) x 360° = 19.44°

The correct answer is 3

Key Points

• The subordinate clause of the sentence: "If you had told me" is in the past perfect tense (subject + had + third form verb).To maintain the uniformity of the sentence the main clause will have the structure as "would have + past participle". Hence, the main clause will take the verb phrase as:- "would have helped".
• The given sentence is a third conditional sentence.
• A third conditional sentence is used to imagine a different past that did not happen.
• Some Examples:-
  

If I had been present, I should have enjoyed it a lot. 

If I had been present, I would have enjoyed it a lot. 

Thus, the correct sentence is: If you had told me earlier I would have helped you.

The correct answer is 2

Key Points

• 'angry with' should be used in place of 'angry'
• If two verbs/ adjectives etc take two different prepositions, we must mention both the prepositions, we cannot simply use one preposition with the last verb/ adjective.
• Examples:
• She is conscious of and engaged in her work.
• I was surprised at as well as pleased with her performance.
• She is younger and taller than her brother. (Single 'same' preposition is used with both the adjectives, it is used only one)
• ​Thus, the correct sentence is: Her mother is angry with and indifferent to me.

Correct Answer: around  

To ‘loiter around’ means to linger about aimlessly in a place. ‘Loiter’ is followed by four prepositions, each having a slightly different meaning to it. ‘Loiter on’ means to move in a slow idle manner. ‘Loiter over’ means to waste time over work. ‘Loiter away’ means to waste time aimlessly.

Correct Answer: he comes  

Solution: This sentence is an example of the first conditional sentence that talks about possible future events and their likely results. First conditional sentences follow the blueprint of a ‘conditional clause’ + the ‘main clause’ where the conditional clause is in simple present tense, while the main clause is in simple future. Thus, the sentence must be: I will scold him when he comes.

The correct answer is: Dulcet.

Key Points

• The word "mellifluous" means something that is sweet or musical; pleasant to hear. (मधुर)
• Example: Her mellifluous voice captivated everyone in the room.
• "Dulcet" refers to something that is generally sweet and soothing, especially in sound. (मधुर)
• Example: The dulcet tones of the piano filled the room with a calming atmosphere.

Therefore, the correct answer is: Dulcet.

Additional Information

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

• Shiver (कंपकंपी): A slight trembling movement or sound, typically one caused by cold or fear.
• Example: He began to shiver uncontrollably in the freezing weather.
• Frank (स्पष्टवादी): Open, honest, and direct in speech or writing, especially when dealing with unpalatable matters.
• Example: She was frank about her concerns regarding the new policy.
• Immoral (अनैतिक): Not conforming to accepted standards of morality.
• Example: Stealing is considered an immoral act.

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

Key Points

• The word "Dodge" means to avoid something or someone by a sudden quick movement. (बचना)
• Example: He managed to dodge the question skillfully.
• "Avoid" means to keep away from or stop oneself from doing something. (बचाना)
• Example: She managed to avoid the busy traffic by taking a different route.
• Hence, we can infer that the word similar in meaning to 'Dodge' is 'Avoid'.

Therefore, the correct answer is: Avoid.

Additional Information

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

• Soften (मुलायम करना): To make or become less hard.
• Example: The butter will soften if left out of the fridge.
• Order (आदेश): An authoritative command or instruction.
• Example: The officer gave the order to advance.
• Chaotic (अराजक): In a state of complete confusion and disorder.
• Example: The city's traffic is always chaotic during rush hour.

The correct answer is 'Option 2' i.e. 'Natural'. 

Key Points

• The word 'Meretricious' means something that is apparently attractive but having, in reality, no value or integrity.(धोखेबाज).
• Natural - This word refers to something that comes from nature, not artificial or involving anything made or caused by people.(प्राकृतिक)
• It is the opposite of 'Meretricious' as 'Natural' implies authenticity and lack of pretense.

Therefore, the correct answer is: 'Natural'.

Additional Information

• Now, let's examine the given alternatives:
• Brazen - It means bold and without shame. It can be associated with a lack of regret or embarrassment.(निर्लज्ज)
• Exemplary - It means representing the best of its kind; excellent. It could also mean serving as a desirable model or outstanding.(आदर्श)
• Gaudy - This word describes something that is extravagantly bright or showy, typically to the point of being tasteless.(आडम्बरपूर्ण)

Correct Answer: Definite  

Solution: ‘Nebulous’ means ‘indistinct’ or ‘unclear’. Its antonym must be ‘definite’ which means ‘clear’.

• Definite: Clearly stated, decided, or fixed; not vague or uncertain. Something that is certain or conclusive, without any doubt.
• Inchoate: Just beginning or not fully formed; not fully developed or organized. Something that is in an early or incomplete stage.
• Dismal: Gloomy, depressing, or bleak; characterized by a lack of hope or optimism. Something that is dark, depressing, or miserable.
• Sullen: Silent, morose, or showing irritation or anger by refusing to speak or being sociable. Something that is sulky, gloomy, or resentful in attitude or appearance.

Correct Answer: Neat and clean  

Solution: ‘Spick and span’ means ‘neat and tidy’.

Example: He is always cleaning because he likes his place to be spick and span.

Correct Answer: To exaggerate

Solution: ‘To draw the longbow’ is to exaggerate something or to overstate something. Example: Every time he speaks of his achievements, it seems as if he is drawing the longbow.

The correct answer is option 4.

Key Points

• Since the sentence is correct, no improvement is required.
• The meaning of the given idiom "a feather in someone's cap" is an achievement or honor that someone can be proud of.
• Example: The promotion was a feather in his cap.
• Hence, option 4 is correct.

Here the correct answer is No improvement.

Key Points:-

• To ‘take something up’ means to become interested or engaged in a work or a pursuit.
• For Example - She took up tennis at the age of 11.
• The phrase fits perfectly in the sentence and thus requires no improvement.

Therefore, the correct sentence is The government plans to take up the construction project soon.

The correct answer is callous.

Key Points

• Let us look at the meanings of all the words:
• ‘Callous’ is someone cruel and unsympathetic.
• ‘Credulous’ is someone who easily believes in things.
• ‘Gullible’ is someone who is easily persuaded.
• ‘Bohemian’ refers to a socially unconventional person (normally involved in arts).
• From the above meanings, it is clear that the correct one word for the given group of words is "Callous".
• Hence, the correct answer is option 1.

Correct Answer: Glutton  

‘Imposter’ is a person who pretends to be someone else. ‘Glutton’ is an excessively greedy eater. ‘Hypochondriac’ is a person who is abnormally conscious about their health. ‘Intestate’ is a person who died without having a will made.

Correct Answer: Blissfull  

The correct spelling should have only one 'l'. 'Blissful’ is the correct spelling.

The correct answer is: Option 2 i.e. "Translusent".

Key Points

• The word "Translusent" is incorrectly spelt. The correct spelling is "Translucent". (पारदर्शक)
• Example: The windows were made of translucent glass, allowing light to come through but not detailed images.
• "Translucent" means allowing light, but not detailed shapes or images, to pass through; semi-transparent. (अर्धपारदर्शक)
• Example: The bathroom had a translucent shower door for privacy.

Therefore, the correct answer is: Translusent.

Additional Information

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

• Afforestation (वनरोपण): The process of planting large numbers of trees on land that has few or no trees.
• Example: Afforestation efforts have helped improve the environment.
• Foreigner (विदेशी): A person born in or coming from a country other than one's own.
• Example: As a foreigner, he often found it difficult to understand local customs.
• Achievement (उपलब्धि): A thing done successfully with effort, skill, or courage.
• Example: Winning the championship was a significant achievement for the team.

Correct Answer: QRSP  

The opening line must give us an insight into the paragraph. Sentence Q does exactly that and does not refer to any previously mentioned term or phrase. Thus, it must be the first sentence and that is Sentence Q.

R carries forward the idea of Q and refers to the nation’s growth which has already been mentioned in Q. Therefore, R must be the second sentence.

Sentence S names the different sectors in reference to the phrase ‘different sectors of national growth’ used in sentence R. So, S logically forms the third sentence.

The concluding sentence is P as it sums up the gist of the entire paragraph in a sentence.

Correct Answer: QSPR  

Solution: Sentence Q talks about how arrogant managers can evaluate themselves better than what they already are. This is what the entire paragraph rests upon and therefore must be the introductory sentence. Sentence S just carries forward the idea of Q by saying that these employees are not good at viewing the threats and opportunities. This must be the second sentence. P talks about the environmental situation faced by the organization due to the bureaucratic culture. P is the third sentence and is followed by R which comments on how the lack of leadership makes the organization crippled in such situations. It sums up the gist of the paragraph and is therefore the concluding sentence.

Correct Answer: We are taught English by her.  

In the sentence ‘she teaches us English’, ‘she’ is the subject who is performing an action while ‘us’ is the object on which the action is being performed. Thus, in the passive form, the sentence must be 'We are taught English by her'.

The correct answer is- Nisha asked Swati if she would help her in her project just then.

Key Points​

• Let's look at the steps to change the sentence from direct to indirect speech:
• The tense of direct speech is changed only when the reporting verb is in the past tense.
• When the direct speech is in an interrogative form, we follow the steps given below:
• The reporting verb said to is converted into asked.
• Connectors 'whether' or 'if' are used in place of comma and inverted commas.
• Change the reported speech from interrogative to assertive.
• The personal pronouns will be changed according to the subject and object of the reporting verb.
• ​Here the 2nd person 'you' will change into the 3rd person 'she' as per the object.
• Similarly 'my' is converted into 'her'.
• The auxiliary verb (will) in direct speech changes to (would).
• Words showing time and place are changed accordingly. (now- then)
• ​At last line up the remaining part.
  
• Following these steps, we finally get- Nisha asked Swati if she would help her in her project just then.

Correct Answer: ensure  

‘Built’ cannot be the answer as it is in simple past. ‘Dignity’ is the quality to be worthy of honour. It cannot be kept or supported. However, it can be ensured.

Correct Answer: greatest  

‘Greatest good’ refers to the best alternative that offers the greatest utility to us.

Correct Answer: number

‘The greatest good for the greatest number’ is a principle which says that right and wrong must be judged by which actions brings the greatest utility to the largest number of subjects.

Correct Answer: oppose  

The answer must be a verb (an action word). This eliminates option 2. Option 1 and 3 are inconsistent with logic. Wrong plans must be opposed, not supported or relied on.

Correct Answer: genuine

In order to win the trust and support of its people, the government needs to cater to the most basic and genuine needs of its people.