SSC CHSL Previous Paper 14 (Held On: 13 Oct 2020 Shift 2) (Previous Year Paper)

The correct answer is 'placque'.

Key Points

• Out of the given options only option 3 has an incorrect spelling.
• The meaning of the words are listed in the following table along with their usage in a sentence.

Additional Information

• The word 'plaque' can also mean a sticky deposit on teeth in which bacteria proliferate.

The correct answer is 'for more than 16 years'.

Key Points

• The underlined part begins with the preposition 'since'.
• When 'since' is used a preposition of time, it is used to refer to a specific point in time.
• So to use it for a period of time (more than 16 years) is incorrect.
• The correct preposition to be used with a period of time is 'for'.
• So, to improve the sentence we need to replace the underlined part with 'for more than 16 years'.

Additional Information

• 'By' as a preposition of time is used to indicate a deadline or the end of a particular time period. (I have to submit this report by Monday.)
• 'From' as a preposition of time is used to indicate the point in time at which a particular process, event, or activity starts. (The charity show will run from 4 p.m. to 6 p.m.)

The correct answer is 'if India will win'.

Key Points

• ​In the given context, the main clause is in 'simple future tense'

• Thus, 'If clause' will be in present tense; i.e. 'will win' will be replaced with 'wins'

• The given context is a conditional sentence The structure of the conditional sentence is- If + Simple Present, Simple Future

• In such sentences 'If clause' will be in simple present tense and the 'main clause' in simple future tense

• Let's see the example:

• If I will come to Lucknow,  I will meet you.

• If I come to Lucknow,  I will meet you.

Hence the correct sentence is- If India wins this match they will win the series.

The correct answer is 'portfolio'.

Key Points

To find the correct answer we need to know the meaning of the given options. This has been shown in the table below - 

​

• 'Portfolio' and 'Dossier' are often confused.
• A portfolio contains creative work like designs, art, or photographs.
• The dossier contains documents and may include photographs of the subject under discussion.

The correct answer is 'among'.

Key Points

• To find the correct word for the given blank, we need to first understand the meaning of the given words in the options - ​
• along - moving in a constant direction on (a road, path, or any more or less horizontal surface). (Preposition)
• aside - to one side; out of the way. (Adverb)
• away - to or at a distance from a particular place, person, or thing. (Adverb)
• among - being a member or members of (a larger set). (Preposition)
• The line with blank (1)  talks about the various attractions at a heritage site.
• The given blank needs a preposition to show that the attractions are part of a bigger set.
• This makes option 4, i.e. 'among' the best fit word for the given blank based on its meaning and grammatical position.

The correct answer is 'are'.

Key Points

• The given blank needs a verb.
• The nouns following the blanks are plural. (temples, palaces etc)
• To maintain subject-verb agreement we need to use the plural verb 'are' in the given blank.

​

Additional Information

• Although 'were' is also a plural verb, it cannot be used as it represents the past tense.

The correct answer is 'remains'.

Key Points

• To find the correct word for the given blank, we need to first understand the meaning of the given words in the options - ​
• returns - come or go back to a place or person.
• remains - historical or archaeological relics.
• refunds - a repayment of a sum of money.
• revenues - income, especially when of an organization and of a substantial nature.
• The line with blank (3)  talks about the various archaeological relics that are found in Hampi.
• This makes option 2, i.e. 'remains' the best fit word for the given blank based on its meaning.

The correct answer is 'endless'.

Key Points

• To find the correct word for the given blank, we need to first understand the meaning of the given words in the options - ​
• endless - countless; innumerable.
• finite - limited.
• finished - completed.
• written - mark (letters, words, or other symbols) on a surface, typically paper, with a pen, pencil, or similar implement.
• The line with blank (4)  talks about the various archaeological relics that are found in Hampi and the list is never ending.
• This makes option 1, i.e. 'endless' the best fit word for the given blank based on its meaning.

The correct answer is 'located'.

Key Points

• To find the correct word for the given blank, we need to first understand the meaning of the given words in the options - ​
• located - situated in a particular place.
• fitted - made or shaped to fill a space or to cover something closely or exactly.
• placed - put in a particular position.
• settled - resolve or reach an agreement about (an argument or problem).
• The line with blank (5)  talks about the location of the train station where tourists first arrive to visit Hampi.
• This makes option 1, i.e. 'located' the best fit word for the given blank based on its meaning.

The correct answer is 'on the top branch of the tree'.

Key Points

• The underlined part is incorrect as it uses the wrong preposition 'over' to show the location of the kitten.
• 'Over' means beyond and falling or hanging from a point.
• The correct preposition here is 'on' which means that physically in contact with and supported by (a surface).
  

Additional Information

• Both 'in'  and 'across' can also be used as prepositions.
• 'In' means inside something.
• 'Across' means to from one side to the other of (a place, area, etc.).

The correct answer is 'BDCA'.

Key Points

• The passage should begin with a sentence that introduces the subject under consideration.
• This is done by sentence B, which introduces us to a certain well-known dancer. So, sentence B becomes the first sentence.
• From the remaining sentences it is clear that her views regarding the concept of 'respect' is being illustrated in the passage. 
• So, sentence D, which introduces this viewpoint should become the second sentence.
• The past views regarding the concept should follow, making sentence C the third sentence.
• The present view as told in sentence A, becomes the fourth sentence.

The correct answer is 'selfish'.

Key Points

• To find the correct antonym for the given word, we need to understand the meaning of it.
• 'Altruistic' means showing a disinterested and selfless concern for the well-being of others or being unselfish.
• From the above meaning it is clear that the correct antonym for it is 'selfish' which means (of a person, action, or motive) lacking consideration for other people; concerned chiefly with one's own personal profit or pleasure.

Additional Information

• The meaning of the other options are as follows - 
• outstanding - exceptionally good.
• soft-spoken - speaking or said with a gentle, quiet voice.
• serene - calm, peaceful, and untroubled

The correct answer is 'greenery'.

Key Points

• To find the correct synonym for the given word, we need to understand the meaning of it.
• 'Foliage' means plant leaves collectively.
• Example: The hiking trail was surrounded by a thick canopy of foliage, with leaves of various shapes and colors covering the trees.​
• From the above meaning it is clear that the correct synonym for it is 'greenery' which means green foliage, growing plants, or vegetation.

Additional Information

• The meaning of the other options are as follows - 
• firmness - the quality of having a solid, almost unyielding surface or structure.
• Example: The manager displayed firmness in her decision-making, standing by her choices even in the face of opposition.
• foolishness - lack of good sense or judgement
• Example: Jumping into the lake without knowing how to swim is an act of foolishness that could lead to danger.
• urgency - importance requiring swift action.
• Example: The doctor emphasized the urgency of seeking medical attention for the persistent symptoms to prevent further complications.

The correct answer is 'CDAB'.

Key Points

• The passage should begin with a sentence that introduces the subject under consideration.
• This is done by sentence C, which introduces us to a person who buys a teapot. So, sentence C becomes the first sentence.
• From the remaining sentences it is clear that the person's interactions with the teapot are listed.  
• So, sentence D, which talks about how he cleaned the teapot should become the second sentence.
• Sentence A that talks about how he kept it down to dry becomes the third sentence. This sentence also talks about how he went away after that to count his money.
• His view about the teapot after he came back as told in sentence A, becomes the fourth sentence.

The correct answer is 'glitches'.

Key Points

• We need to first understand the meaning of the given words to find which word would suit the given blank.
• symbols - marks or characters used as a conventional representation of an object, function, or process, e.g. the letter or letters standing for a chemical element or a character in musical notation
• glitches - a sudden, usually temporary malfunction or fault of equipment.
• illuminations - lighting or light.
• streamers - a long, narrow strip of material used as a decoration or symbol.
• The sentence talks about how a certain equipment is going to be phased out.
• 'Phased out' is a term that means to gradually stop using something.
• The cause behind this is mentioned as technical problems.
• So, 'glitches' is the best fit word for the given blank.

The correct answer is 'fleet'.

Key Points

• To find the correct answer we need to know the meaning of the given options. This has been shown in the table below - 

The correct answer is 'control'.

Key Points

• To find the correct synonym for the given word, we need to understand the meaning of it.
• 'Constraint' means a limitation or restriction.
• From the above meaning it is clear that the correct synonym for it is 'control' which means the restriction of an activity, tendency, or phenomenon.

Additional Information

• The meaning of the other options are as follows - 
• concern - relate to; be about.
• Usage: His concern with/for the well-being of his family is obvious.
• hazard - a danger or risk.
• Usage: Polluted water sources are a hazard to wildlife.
• burden - a load, typically a heavy one.
• Usage: His illness has placed a huge financial burden on the family.

The correct answer is 'pattern'.

Key Points

• We need to first understand the meaning of the given words to find which word would suit the given blank.
• design - a plan or drawing produced to show the look and function or workings of a building, garment, or other object before it is made.
• pattern - a repeated decorative design.
• mound - a rounded mass projecting above a surface.
• structures - the arrangement of and relations between the parts or elements of something complex.
• The sentence talks about mosaic which means a picture or pattern produced by arranging together small pieces of stone, tile, glass, etc.
• 'Phased out' is a term that means to gradually stop using something.
• So, 'pattern' is the best fit word for the given blank.

The correct answer is 'conceal'.

Key Points

• To find the correct antonym for the given word, we need to understand the meaning of it.
• 'Disclose' means make (secret or new information) known.
• From the above meaning it is clear that the correct antonym for it is 'conceal' which means prevent (something) from being known or to keep secret.

Additional Information

• The meaning of the other options are as follows - 
• disguise - give (someone or oneself) a different appearance in order to conceal one's identity.
• complete - having all the necessary or appropriate parts.
• disrupt - interrupt (an event, activity, or process) by causing a disturbance or problem.

The correct answer is '​Brinda said to her doctor, “I am leaving for Boston tomorrow.”'

Key Points

• The given sentence is in indirect form.
• To change it to direct form, we need to do the following - 
• Change in pronoun - In direct speech the pronoun changes to first person. So, 'she' will become 'I'.
• Change in statement sentence - In direct speech, the 'told' is converted either to 'said' or remains the same. So, it either remains 'told' or becomes 'said'.
• Change in tense - The past continuous tense (was leaving) in the indirect speech changes to present continuous tense (am leaving) in direct speech.
• Only option 3 covers all three changes making it the correct answer.

The correct answer is 'learn how to use'.

Key Points

• The sentence talks about how Rohan took a long time to understand the machine in the new factory.
• The meaning of the underlined idiom is - Learn the proper way of doing, using or handling something; acquire the knack of something.
• So, option 3 is the correct answer.

The correct answer is 'Intention'.

Key Points

• Out of the given options, only option 3 has the correct spelling.
• 'Intention' means a thing intended; an aim or plan.
• Example - She had no intention of staying here.

Additional Information

• Let's look at the correct spelling and meaning of the other options:-
• Fashion - a popular or the latest style of clothing, hair, decoration, or behaviour.
• Injection - an instance of injecting or being injected.
• Transition - the process or a period of changing from one state or condition to another.

The correct answer is 'I was not forgotten by her even though I have been away for a year.'

Key Points

• The given sentence is an assertive sentence.
• We need to follow these instructions while changing the voice of an assertive sentence.
• Find the subject and object of the sentence and exchange their places; make changes in their cases as well if subject and object are pronouns.
• In the given sentence the subject is 'she,' while the object is ‘I’.
• Use preposition 'by' before agent 'she'.

Following these steps, we finally get - "I  was not forgotten by her even though I have been away for a year."

The correct answer is 'healthy and strong'.

Key Points

• The meaning of the given idiom is as follows - in very good health.
• So, option 4 is the correct answer.

Additional Information

• The violin/ fiddle was picked out as the exemplar because of the alliteration of fit and fiddle, and because the violin is a beautifully shaped instrument producing a very particular sound. But then fit came to mean 'in good physical shape' and so fit as a fiddle came to mean 'in good condition physically'.

The correct answer is 'I don’t recognize none of'.

Key Points

Let's look at the following points-

• 'Any' is used for negative and Interrogative sentences respectively
• For e.g.- The Government has annexed specimen orders which do not provide any clear reasons for their issuance.
• Since the given sentence is a negative sentence, none will be replaced with any
• The correct word to be used here is 'any'

Additional Information 

• None denotes 'not one' or 'not any'.
• None of is not used when there is already a negative word (not, n’t) in the clause
• For e.g.-They didn't invite none of us.

                        They didn't invite any of us.

​

1. +, ×, ÷, -, =

Given expression: 11 * 15 * 78 * 6 * 18 * 160

After replacing the * by the signs, we get:

11 + 15 × 78 ÷ 6 - 18 = 160

⇒ 11 + 15 × 13 – 18 = 160

⇒ 11 + 195 – 18 = 160

⇒ 205 – 18 = 160

⇒ 187 ≠ 160

2. ×, +, -, ÷, =

Given expression: 11 * 15 * 78 * 6 * 18 * 160

After replacing the * by the signs, we get:

11 × 15 + 78 - 6 ÷ 18 = 160

⇒ 165 + 78 – 0.33 = 160

⇒ 243 – 0.33 = 160

⇒ 242.67 ≠ 160

3. ×, +, ÷, -, =

Given expression: 11 * 15 * 78 * 6 * 18 * 160

After replacing the * by the signs, we get:

11 × 15 + 78 ÷ 6 - 18 = 160

⇒ 165 + 13 – 18 = 160

⇒ 178 – 18 = 160

⇒ 160 = 160

4. +, ×, -, ÷, =

Given expression: 11 * 15 * 78 * 6 * 18 * 160

After replacing the * by the signs, we get:

11 + 15 × 78 - 6 ÷ 18 = 160

⇒ 11 + 1170 – 0.33 = 160

⇒ 1181 – 0.33 = 160

⇒ 1180.67 ≠ 160

Hence, ‘×, +, ÷, -, =’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1. NTZ → N + 6 = T; T + 6 = Z

2. LRX → L + 6 = R; R + 6 = X

3. FLR → F + 6 = L; L + 6 = R

4. BGQ → B + 5 = G; G + 10 = Q

Hence, ‘BGQ’ is the odd one out.

The logic is:

8 : 81 → 8 : (8 + 1)²

11 : 144 → 11 : (11 + 1)²

Similarly,

12 : ? → 12 : (12 + 1)²

⇒ ? = 169

Hence, ‘169’ is the correct answer.

The least possible venn diagram is:

I. Some robots are boys. → True (As all boys are robots so some robots will be definitely boys)

II. No robot is a girl. → False (As all girls are robots so some robots are girls, hence false)

III. Some robots are girls → True (As all girls are robots so some robots will be definitely girls)

Hence, only conclusions I and III follow.

The paper when unfolded will appear as shown below:

Hence, ‘option 1’ is the correct answer.

The logic is:

The logic followed here is:

First number × ( First number+ 1) = second number

1. 11 : 142 → 11 × (11 + 1) = 132 ≠ 142

2. 22 : 506 → 22 × (22 + 1) = 506

3. 17 : 306 → 17 × (17 + 1) = 306

4. 14 : 210 → 14 × (14 + 1) = 210

Hence, ‘11 : 142’ is the odd one out.

The logic is:

(13, 17, 442) → (13 × 2) × 17 = 442

Similarly,

1. (11, 19, 628) → (11 × 2) × 19 = 418 ≠ 628

2. (15, 14, 415) → (15 × 2) × 14 = 420 ≠ 415

3. (18, 15, 540) → (18 × 2) × 15 = 540

4. (17, 21, 367) → (17 × 2) × 21 = 714 ≠ 367

Hence, ‘(18, 15, 540)’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘SZUSBN’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘ZRU’ is the correct answer.

The correct order of the given words as they would appear in an English dictionary is:

2. Domestic
3. Dominate
4. Donate
5. Dorsal
6. Dovetail

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

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘W’ is the correct answer.

The logic is:

The capital of Nagaland is Kohima.

Similarly,

The capital of Assam is Dispur.

Hence, ‘Dispur’ is the correct answer.

The logic is:

Wheat : Cereal → Wheat is a cereal.

Similarly,

Cinnamon : Spices → Cinnamon is a spice.

Hence, ‘Cinnamon : Spices’ is the correct answer.

The number of Indian senior lawyers are who are NOT fathers is shown below:

Hence, ‘36’ is the correct answer.

The logic is:

(789, 501, 645) → (789 + 501) ÷ 2 = 1290 ÷ 2 = 645

Similarly,

1. (455, 573, 514) → (455 + 573) ÷ 2 = 1028 ÷ 2 = 514

2. (645, 705, 573) → (645 + 705) ÷ 2 = 1350 ÷ 2 ≠ 573

3. (224, 640, 330) → (224 + 640) ÷ 2 = 864 ÷ 2 ≠ 330

4. (701, 538, 600) → (701 + 538) ÷ 2 = 1239 ÷ 2 ≠ 600

Hence, ‘(455, 573, 514)’ is the correct answer.

All options except ‘spade’ are name of utensils, which is used in the kitchen but ‘spade’ is a tool used for digging and cutting earth.

Hence, ‘spade’ is the odd one out.

The logic is:

Hence, ‘140’ is the correct answer.

The faces opposite to each other is shown below:

Option 1) 1 and 5 → Are not opposite faces

Option 2) 2 and 3 → Are opposite faces

Option 3) 1 and 6 → Are not opposite faces

Option 4) 6 and 3 → Are not opposite faces

Hence, ‘2 and 3’ is the correct answer.

29 January 2003 is a Wednesday

Number of odd days between 29^th January 2003 to 26^th February 2005 = (2 + 0 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3) + 2 + (3 + 26) = 59

59 ÷ 7, we get 3 as remainder.

3 days after Wednesday is Saturday.

29 January 2003 ⇒ Wednesday.

(Number of odd days from 29 January 2003 to 29 January 2004 is 1)

29 January 2004 ⇒ Thursday

(Since February 2004 have 29 days, Number of odd days from 29 January 2004 to 29 January 2005 is 2)

29 January 2005 ⇒ Saturday 

Number of odd days from 29 January 2005 to 26 February 2005 is 28. i.e. 0 odd days.

26 February 2005 ⇒ Saturday

Hence, ‘Saturday’ is the correct answer.

The correct mirror image of the given figure is shown below:

Concept Used:

 $Triangles = n× {{n + 1} \over2}×H$

Where, 

n= number of small triangles

H = number of ‘end to end’ horizontal lines

→ In, ∆ABC:

n= number of small triangles = 2

H = number of ‘end to end’ horizontal lines = 4 (BC, DE, FG, and HI)

$Triangles = 2× {{2 + 1} \over2}×4 = 12$

Hence, Total triangles in ∆ABC = 12

→ Now, the remaining Triangles: 1 (∆AJK)

→ Now Adding all the ∆s:

Total ∆s = 12 + 1 = 13

Hence, ‘13’ is the correct answer.

The option figure that is embedded in the given figure X when rotation is not allowed is shown below:

Hence, ‘option 3’ is the correct answer.

When 1^st image in the series is rotated 180

 clockwise direction, we get the 3^rd image in the series.

Similarly,

When 2^nd image in the series is rotated 180

 clockwise direction, we get the 4^th image in the series.

Hence, ‘option 2’ is the correct answer.

K + U - T × R ÷ M → K is mother of U, U is sister of T, T is son of R, R is father of M.

According to given conditions,

K is mother of M.

Hence, ‘Mother’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

When the position value of letters are added together with the number of letters in the word, we get the code for the word.

Similarly,

Hence, ‘71’ is the correct answer.

Given:

∠ACB = 135

Radius of the circle = 2√2 cm

Formula:

The sum of the opposite angle of the cycle quadrilateral is 180.

The angle at the center of a circle is twice the angle at the circumference

Calculation:

∠ACB + ∠ADB = 180

⇒ 135 + ∠ADB = 180 

⇒ ∠ADB = 180 - 135

⇒ ∠ADB = 45

O is the center of the circle.

∠BOA = 2 ∠BDA

⇒ ∠BOA = 2 × 45

⇒ ∠BOA = 90

OA = OB = 2√2 (radius of the circle)

In right angled triangle BOA

AB² = OB² + OA²

⇒ AB² = (2√2)² + (2√2)²

⇒ AB² = 8 + 8

⇒ AB = √16

∴ AB = 4

Given:

Chord AB subtends double the angle that is subtended by chord CD. 

∠AEB = 2 ∠AOB,

∠AOB = 2 ∠COD

Formula:

Angle made on tangent is perpendicular to radius.

Calculation:

∠OBE = ∠OAE = 90°

In AOBE

∠AOB + ∠AEB + ∠OBE + ∠OAE = 360°

⇒ ∠AOB + ∠AEB + 90° + 90° = 360°

⇒ ∠AOB + 2 ∠AOB = 360° - 180°

⇒ 3 ∠AOB = 180°

⇒ ∠AOB = 180°/3

⇒ ∠AOB = 60°

⇒ 2 ∠COD = 60°

⇒ ∠COD = 60°/2

∴ ∠COD = 30°

Given:

sec A = √11/3

Formula:

sec A = 1/cos A

cosec A  = 1/sin A

tan A = sin A/cos A

cot A = cos A/sin A

Calculation:

$\frac{cosec^2 A + tan^2 A}{sin^2 A + cot^2 A}$

⇒ $\frac{\frac{1}{sin^2A} \ + \ \frac{sin^A}{cos^2A}}{sin^2A \ + \ \frac{cos^2A}{sin^2A}}$

⇒ [(cos² A + sin⁴ A)/(sin² A cos² A)]/[(sin⁴ A + cos² A)/(sin² A)]

⇒ 1/cos² A

⇒ sec² A

⇒ (√11/3)²

⇒ 11/9

Given:

$A = \frac{(0.1)^3 + (0.2)^3+(0.3)^3+3(0.005+0.016+0.027)+0.036}{(0.1)^2+(0.2)^2+(0.3)^2+0.04+0.06+0.12}$

Calculation:

⇒ $A = \frac{(0.1)^3 + (0.2)^3+(0.3)^3+3(0.005+0.016+0.027)+0.036}{(0.1)^2+(0.2)^2+(0.3)^2+0.04+0.06+0.12}$

Multiply by 1000 in numerator and denominator

⇒ A = [1 + 8 + 27 + 3 (5 + 16 + 27) + 36]/[10 + 40 + 90 + 40 + 60 + 120]

⇒ A = (36 + 3 × 48 + 36)/360

⇒ A = (36 + 144 + 36)/360

⇒ A = 216/360

Now

60A = (216/360) × 60

∴ 60A = 36

Given:

The ratio of a man's age to his father's age = 4 : 5

The ratio of his age to his son's age = 6 : 1

Four years ago age ratio of man to his father = 11 : 14

Four years ago age ratio of man to his son = 11 : 1

Calculation:

The ratio of a man's age to his father's age = 4 : 5

Four years ago age ratio of man to his father = 11 : 14

According to the question

(4x - 4)/(5x - 4) = 11/14

⇒ 14 (4x - 4) = 11 (5x - 4)

⇒ 56x - 56 = 55x - 44

⇒ 56x - 55x = 56 - 44

⇒ x = 12

Present age of man = 4 × 12 = 48 years

Present age of father = 5 × 12 = 60 years

The ratio of age of man to his son's age = 6y : y

6y = 48

⇒ y = 8 

Present age of son = 8 years

12 years after, age of father will be = 60 + 12 = 72 years

12 years after, age of his son = 8 + 12 = 20 years

∴ 12 years after age ratio of man' father to that of his son = 72 : 20 = 18 : 5

Given:

Sides of triangle are 25, 39 and 34 units.

Area of square is more than that of triangle = 21 units

Formula:

Area of triangle = √[s (s – a) (s – b) (s – c)]

s = (a + b + c)/2

Perimeter of the triangle = a + b + c

Calculation:

a = 25, b = 39 and c = 34 

S = (25 + 39 + 34)/2

⇒ S = 98/2 = 49 unit

Area of triangle ⇒

⇒ √[49 (49 – 25) (49 – 39) (49 – 34)

⇒ √[49 × 24 × 10 × 15]

⇒ √(7 × 7 × 2 × 2 × 2 × 3 × 2 × 5 × 3 × 5)

⇒ 7 × 2 × 2 × 3 × 5

⇒ 420

Area of square = 420 + 21 = 441

∴ Side of square = √441 = 21 unit

Given:

The number 59a44b is divisible by 36.

Formula:

Divisibility law of 9 ⇒ A number is divisible by 9 if sum of its digit is divisible by 9.

Divisibility law of 4 ⇒ A number divisible by 4 if its last two digit is divisible by 4 

Calculation:

The number 59a44b is divisible by 4 if 4b is divisible by 4.

4b is divisible by 4,

if b = 0, 4 or 8

If b = 0, then 59a440 

59a440 divisible by 9 if

5 + 9 + a + 4 + 4 + 0

⇒ 22 + a (if a = 5)

⇒ 22 + 5

⇒ 27 (27 divisible by 9)

Again,

If b = 4, then

⇒ 5 + 9 + a + 4 + 4 + 4

⇒ 26 + a (if a = 1)

⇒ 26 + 1

⇒ 27 (27 divisible by 9)

Again,

If b = 8, then

⇒ 5 + 9 + a + 4 + 4 + 8

⇒ 30 + a (if a = 6)

⇒ 30 + 6

⇒ 36 (36 divisible by 9)

For maximum value 

b = 8 and a = 6

⇒ a + b

⇒ 6 + 8

⇒ 14

Given:

$\frac{(1 +sinθ-cosθ)}{(1 +sinθ +cosθ)} + \frac{(1 + sinθ +cosθ)}{(1 + sinθ-cosθ)}$ = 4

Formula:

sin 30° = 1/2

Calculation:

$\frac{(1 +sinθ-cosθ)}{(1 +sinθ +cosθ)} + \frac{(1 + sinθ +cosθ)}{(1 + sinθ-cosθ)}$ = 4

⇒ $\frac{(1 +sinθ-cosθ)^2 \ + \ (1 + sinθ +cosθ)^2}{(1 + sinθ +cosθ)(1 + sinθ-cosθ)}$ = 4

$\frac{(1 \ + sin^2θ \ + \ cos^2θ \ + \ 2sinθ \ - \ 2sin θ.cosθ \ - \ 2cos θ \ + \ 1 \ + \ sin^2θ \ + \ cos^2θ \ + \ 2sinθ \ + \ 2sinθ.cosθ \ + \ 2cosθ)}{(1 + sinθ)^2 - cos^2θ}$= 4 

⇒ (1 + 1 + 4sinθ + 1 + 1)/(1 + sin²θ + 2 sinθ - cos²θ) = 4

⇒ (4 + 4 sinθ)/[1 + sin2θ + 2sinθ - (1 - sin2θ)] = 4

⇒ [4 (1 + sinθ)]/(1 + sin2θ + 2 sin θ - 1 + sin2θ) = 4

⇒ [4 (1 + sinθ)]/(2 sin²θ + 2sinθ) = 4

⇒ [4 (1 + sinθ)]/[2sinθ (1 + sinθ)] = 4

⇒ 2/sin θ = 4

⇒ sin θ = 2/4

⇒ sin θ = 1/2

⇒ sin θ = sin 30°

∴ θ = 30°

Shortcut TrickBy hit and trial method, we have

Put θ = 30^∘ 

⇒$\frac{(1\ + \ sin30 \ - \ cos30)}{(1 + \ sin30 + \ cos30)} + \frac{(1 \ + \ sin30 \ + \ cos30)}{(1 + sin30 \ - \ cos30)}$ 

⇒ $\frac{(1\ + \ \frac{1}{2} \ - \ \frac{\sqrt3}{2})}{(1 + \ \frac{1}{2} + \ \frac{\sqrt3}{2})} + \frac{(1 \ + \ \frac{1}{2} \ + \ \frac{\sqrt3}{2})}{(1 + \frac{1}{2} \ - \ \frac{\sqrt3}{2})}$

⇒ $\frac{3 \ -\sqrt3}{3 + \sqrt3} \ + \frac{ 3 + \sqrt3}{3 - \sqrt3}$

⇒ 4 satisfied

Given:

Ratio of volume of the cube to that of sphere = a

Ratio of surface area of the sphere to that of cube = b

Formula:

Volume of cube = a³

Volume of sphere = (4/3)π × a³

Total surface area of cube = 6a²

Total surface area of sphere = 4πr²

Given:

Let side of cube be 3 m, then

Radius of sphere r = 3/2  m 

Volume of cube = 3³ = 27 m³ 

Total surface area of cube = 6 × 3² = 54 m²

Volume of sphere = (4/3) × π × (3/2)³ = (4/3) × π × (27/8) = 9π/2 m³

Total surface area of sphere = 4π × (3/2)² = 4π × (9/4) = 9π m²

According to the question

a = 27/(9π/2)

⇒ a = 6/π

b = 9π/54

⇒ b = π/6

ab = (6/π) × (π/6)

⇒ ab = 1

Given:

∠DAB + ∠CBA = 90°, BC = AD, AB = 20 cm, CD = 10 cm

Formula:

Area of trapezium = (1/2) × (sum of parallel sides) × distance between parallel sides

Calculation:

Drag the point D out side such that the picture becomes trapezium.

Now trapezium ABCD

AD = BC 

CD = PQ = 10

AP = QB 

AP + PQ + QB = AB

⇒ AP + 10 + AP = 20

⇒ 2AP = 20 - 10

⇒ AP = 10/2 = 5 cm

∠DAB + ∠CBA = 90° (Given)

Let ∠DAB = ∠CBA = 45°

Now in right angled triangle APD

∠DAP + ∠APD + ∠PDA = 180°

⇒ 45° + 90° + ∠PDA = 180°

⇒ ∠PDA = 180° - 135°

⇒ ∠PDA = 45°

If ∠PDA = ∠DAP = 45, then

AP = PD = 5 cm

∴ Area of trapezium = (1/2) × 30 × 5 = 75 cm²

Given:

Total number of students (boys and girls in thousands) in Grade 1 to Grade 5 = 20 + 15 + 12 + 22 + 8 + 18 + 14 + 9 + 10 + 12 = 140 thousands or 1,40,000

Percentage of students in school D = 25%

Ratio of boys to girls in school D = 3 : 1

Formula:

x% of any number = Actual number × (x/100)

Calculation:

Number of students in school D = 1,40,000 × (25/100) = 35000

Number of boys in school D = 3,50,00 × (3/4) = 26,250

Shortcut Trick

The number of boys in school D is 3x according to the ratio given.

That means, the number must be a multiple of 3 or we can say the number is divisible by 3.

According to the divisibility rule of 3, we can see that only option 2 is the possible solution.

 Check: number = 26250 = 2+ 6+ 2 + 5 + 0 = 15 divisible by 3.

∴ The number of boys in school D is 26250.

Given:

The given numbers are 24, 45, a, 35, 59, 83, 46, b, 29, 74

Average of 10 numbers when each number is added to its serial number = 55

Formula:

Average = Sum of all observations/total number of all observations

Calculation:

New numbers are when each number is added to its serial number

(24 + 1), (45 + 2), (a + 3), (35 + 4), (59 + 5), (83 + 6), (46 + 7), (b + 8), (29 + 9), (74 + 10)

According to the question

(24 + 1) + (45 + 2) + (a + 3) + (35 + 4) + (59 + 5) + (83 + 6) + (46 + 7) + (b + 8) + (29 + 9) + (74 + 10) = 55 × 10

⇒ 450 + a + b = 550

⇒ a + b = 550 - 450

⇒ a + b = 100

∴ Average of a and b = 100/2 = 50

Given:

a + b = 8 and a + a2 b + b + ab2 = 128

Formula:

a3 + b3 = (a + b) [(a + b)2 - 3ab]

Calculation:

a + a2 b + b + ab2 = 128

⇒ a + b + a2 b + ab2 = 128

⇒ 8 + a2 b + ab2 = 128

⇒ a2 b + ab2 = 128 - 8

⇒ a2 b + ab2 = 120

⇒ ab (a + b) = 120

⇒ ab × 8 = 120

⇒ ab = 120/8

⇒ ab = 15

a³ + b³ = (a + b) [(a + b)² - 3ab]

⇒ a³ + b³ = 8 [8² - 3 × 15]

⇒ a³ + b³ = 8 [64 - 45]

⇒ a³ + b³ = 8 × 19

∴ a³ + b³ = 152

Given:

Distance between H and O = D km

Average speed = S km/hr

The average speed that gets a person from H to O in a stipulated time is S units. He takes 20 minutes more time than usual if he travels at 60 km/h, and reaches 44 minutes early if he travels at 75 km/h. 

Formula:

Speed = Distance/time

Average speed = Total distance/Total time

Calculation:

Let right time for the train to cover its journey (in minutes) be t hrs, then

As we know,

Distance = Speed × Time

According to the question

60 × (t + 20/60) =  75 × (t - 44/60)

⇒ 4 (t + 1/3) = 5 (t - 11/15)

⇒ 4t + 4/3 = 5t - 11/3

⇒ 5t – 4t = 11/3 + 4/3

⇒ t = 11/3 + 4/3

⇒ t = 5 hrs

Distance (D) = 60 × (5 + 20/60)

⇒ D = 60 × (5 + 1/3)

⇒ D = 60 × (16/3)

⇒ D = 320  km

Distance between H and O is 320 km.

Average speed (S) = 320/5 = 64 km/hr

∴ Sum of numerical values of D and S = 320 + 64 = 384

Given:

cos A, sin A, cot A are in geometric progression.

Formula:

If a, b, c are in GP, then

b² = ac

sec2 A - tan2 A = 1

Calculation:

sin² A = cos A cot A

⇒ sin² A = cos A × (cos A/sin A)

⇒ sin² A × sin A = cos² A

⇒ sin³ A = cos² A

Divide by cos³ A

⇒ sin³ A/cos³ A = cos² A/cos³ A

⇒ tan³ A = 1/cos A

⇒ tan³ A = sec A

Square on both sides

⇒ tan⁶ A = sec² A

Now,

tan⁶ A - tan² A

⇒ sec² A - tan² A

⇒ 1

Given:

Sales of Wall stickers in 2018 = 5.01

Sales of Wall stickers in 2019 = 10.19

Sales of Bed sheets in 2018 = 20.15

Sales of Bed sheets in 2019 = 48.17

Sales of Curtains in 2018 = 7.88

Sales of Curtains in 2019 = 12.21

Sales of Wall hangings in 2018 = 14.97

Sales of Wall hangings in 2019 = 29.14

Calculation:

Percentage of sales of Wall stickers increased from 2018 to 2019

⇒ [(10.19 - 5.01)/5.01] × 100 = 103.4%

Percentage of sales of Bed sheets increased from 2018 to 2019

⇒ [(48.17 - 20.15)/20.15] × 100 = 139%

Percentage of sales of Curtains increased from 2018 to 2019

⇒ [(12.21 - 7.88)/7.88] × 100 = 55%

Now we can say sales of Curtains have increased by nearly 55% from 2018 to 2019.

Given:

The imports in 2016 = Rs. 250 million

The total exports in the year 2016 and 2017 = Rs. 500 million

Ratio of import to export in 2016 = 1.25

Ratio of import to export in 2017 = 1.4

Formula:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

Ratio of import to export in 2016 = 1.25 = 125/100 = 5/4 

Ratio of import to export in 2016 = 5x : 4x

According to the question

5x = 250

⇒ x = 250/5 = 50

⇒ 4x = 50 × 4 = 200

Export in 2016 were = Rs. 200 million

Let exports in 2017 be k, then

200 + k = 500

⇒ k = 500 - 200

⇒ k = 300 million

Export in 2017 were = Rs. 300 million

Ratio of import to export in 2017 = 1.4 = 14/10 = 7/5

Ratio of import to export in 2017 = 7y : 5y

According to the question 

5y = 300

⇒ y = 300/5

⇒ y = 60

7y = 60 × 7

⇒ 7y = 420 

∴ Import in 2017 were = Rs. 420 million

Given:

Each edge of a cube is increased by 10%.

Formula:

If each edge of cube is increased by x%, then 

the percentage increase in its surface area = x + x + (x × x)/100

Total surface area of cube = 6a²

Calculation:

Let side of cube be 10 m

Total surface area of cube = 6 × 10² = 600 m²

New side of cube = 10 × (110/100) = 11 m

New total surface area of cube = 6 × 11² = 726 m²

Area increased by = 726 - 600 = 126 m²

∴ Area increased by (in %) = (126/600) × 100 = 21%

Shortcut Trick

The percentage increase in its surface area = 10 + 10 + (10 × 10)/100

⇒ 20 + 1 = 21%

Given:

45 - 5 of (6.3 ÷ 9) + 7 × 0.5

Formula:

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

Calculation:

45 - 5 of (6.3 ÷ 9) + 7 × 0.5

⇒ 45 - 5 × 0.7 + 3.5

⇒ 45 - 3.5 + 3.5

⇒ 45

Given:

Total number of items = 40

MP of the items is more than that of cost price is = 20%

The person sells 10 items at a discount = 10%

He sells 20 items at a discount = 15%

Formula:

Discount = MP – SP

Discount % = Discount/MP × 100 

Calculation:

Let cost price of each items be Rs. 1

Cost price of 40 items = 1 × 40 = Rs. 40

MP of 40 items = 40 × (120/100) = Rs. 48

Selling price of 10 items = 10 × (120/100) × (90/100) = Rs. 10.8

Selling price of 20 items = 20 × (120/100) × (85/100) = Rs. 20.4

MP of the remaining 10 items = 10 × 120/100 = Rs. 12

Net profit = (12 + 20.4 + 10.8) - Rs. 40 = 43.2 - 40 = Rs. 3.2

If he gives discount Rs. 3.2 on Rs. 12 he gets neither profit nor loss.

Required discount = 3.2/12 × 100 = 26.67%

Now we can say after giving 26% discount he still gets some profit.

Given:

$x^4 + \frac{1}{x^4} = \frac{257}{16}$

Formula:

(x + 1/x)² = x² + 1/x² + 2

(x3 + 1/x3) = (x + 1/x)3 – 3 (x + 1/x)

Calculation:

(x2 + 1/x2)2 = x4 + 1/x4 + 2

⇒ (x2 + 1/x2)2 = (257/16) + 2

⇒ (x² + 1/x²)² = (257 + 32)/16

⇒ (x2 + 1/x2) = √(289/16)

⇒ (x2 + 1/x2) = 17/4

Again,

(x + 1/x)2 = x² + 1/x² + 2

⇒ (x + 1/x)2 = (17/4) + 2

⇒ (x + 1/x)2 = (17 + 8)/4

⇒ (x + 1/x) = √(25/4)

⇒ (x + 1/x) = 5/2

(x³ + 1/x³) = (x + 1/x)³ – 3 (x + 1/x)

⇒ (x3 + 1/x3) = (5/2)³ – 3 × (5/2)

⇒ (x3 + 1/x3) = (125/8) – (15/2)

⇒ (x3 + 1/x3) = (125 – 60)/8

⇒ (x3 + 1/x3) = 65/8

⇒ (8/13) × (x3 + 1/x3) = (65/8) × (8/13)

⇒ (8/13) × (x3 + 1/x3) = 5

∴ The required value is 5.

Shortcut TrickIf $x^2 + \frac{1}{x^2}$ = a , then $x + \frac{1}{x}$ = √(a + 2)

So,  if $(x^2)^2 + \frac{1}{(x^2)^2}$ = 257/16, then $x^2 + \frac{1}{x^2}$ = $\sqrt{\frac{257}{16} + 2}~$ = 17/4

Again, $x^2 + \frac{1}{x^2}$ = 17/4, then $x + \frac{1}{x}$ = $\sqrt{\frac{17}{4}+ 2}~$ = 5/2

Now, (x3 + 1/x3) = (x + 1/x)3 – 3(x + 1/x)

⇒ (5/2)3 – 3 × (5/2) = 65/8

∴  (8/13) × (x3 + 1/x3) = (65/8) × (8/13) = 5

Alternate MethodRate of interest half yearly = 5/2 = 2.5%

Equivalent rate of interest for one year = 2.5 + 2.5 + (2.5 × 2.5)/100

⇒ 5.0625%

Compound interest = 4000 × 5.0625/100 = Rs. 202.5

Rate of interest quarterly = 40/4 = 10%

Equivalent rate of interest = [(11/10 × 11/10 × 11/10 × 11/10) - 1] = 46.41%

Compound interest = 2000 × 46.41/100 = Rs. 928.2

Total interest = 202.5 + 928.2 = Rs. 1130.70

Traditional method:

Given

Case-1

Principal = Rs. 4000

Rate = 5%

Time = 1 year

Interest compounded half yearly.

Case-2

Principal = Rs. 2000

Rate = 40%

Time = 1 year

Interest compounded quaterly.

Formula:

A = P (1 + r/100)^t

Calculation:

For case-1

r = 5/2% = 2.5%

Time = 2

According to the formula

A = 4000 × (102.5/100) × (102.5/100) 

⇒ A = 4,202.5

CI = 4,202,5 - 4,000 = 202.5 

For case-2

r = 40/4 = 10%

Time = 4

According to the formula

A = 2000 × (110/100) × (110/100) × (110/100) × (110/100) 

⇒ A = 2,928.2

CI = 2,928.2 - 2,000 = Rs. 928.2

Total interest = 202.5 + 928.2 = Rs. 1,130.70

∴ The total interest is Rs. 1,130.70.

Given:

The oil merchant wants to make a minimum profit = Rs. 2100

50 litres of oil purchased = Rs. 236 per litre

Cost of duplicate oil = Rs. 180 per liter

Selling price of 1 liter oil = Rs. 250

Calculation:

Let quantity of duplicate oil added be x litres.

According to the question

50 × 236 + x × 180 + 2100 = (50 + x) × 250

⇒ 11800 + 180x + 2100 = 50 × 250 + 250x

⇒ 13900 - 12500 = 250x - 180x 

⇒ 70x = 1400

⇒ x = 1400/70

⇒ x = 20 

20 liters of duplicated oil mixed in mixture.

Given:

Total number of males in all five places = 35 + 32 + 30 + 45 + 40 = 182

Total number of females in all five places = 28 + 40 + 35 + 42 + 32 = 177

Formula:

x as a percent of y = x/y × 100

Calculation:

Percentage of the total number of females in all five places approximately the total number of males in all five places is = (177/182) × 100 = 97%

Given:

B takes 45% more number of days to finish the same work independently.

They worked together for 58 days and then the remaining work was done by B alone in 29 days.

Formula:

Total work = Efficiency × Time

Calculation:

Let number of days taken by A to complete the work be 100 days

Number of days taken by B to complete the work = 100 × (145/100) = 145

Time ratio of A to that of B = 100 : 145 = 20 : 29

Efficiency ratio of A to that of B = 29 : 20

Let efficiency of A = 29 unit/day

Efficiency of B = 20 unit/day

Work done by A and B in 58 days = (29 + 20) × 58 = 49 × 58 = 2842 unit

Remaining work which is done by B in 29 days = 20 × 29 = 580 unit

Total work = 2842 + 580 = 3422 unit

∴ Time taken by A to complete the whole work = 3422/29 = 118

The correct answer is Hindustan Petroleum Corporation Limited.

Key Points

• Hindustan Petroleum Corporation Limited was conferred with Maharatna status in October 2019.
• Two separate orders to this effect were issued by the Department of Public Enterprises, under the Ministry of Heavy Industry and Public Enterprises.
• The grant of Maharatna status to the PSUs will impart enhanced powers to their Boards to take financial decisions.
• The Boards of Maharatna central public sector enterprises (CPSEs) can make equity investments to undertake financial joint ventures and wholly-owned subsidiaries and undertake mergers and acquisitions in India and abroad, subject to a ceiling of 15 percent of the net worth of the concerned CPSE, limited to Rs 5,000 crore in one project.
• Boards can also structure and implement schemes relating to personnel and human resource management and training.
• They can also enter into technology joint ventures or other strategic alliances, among others.
• The holding companies of a 'Maharatna' PSU are also empowered to transfer assets, float fresh equity and divest shareholding in subsidiaries, subject to the condition that the delegation will only be in respect of the subsidiaries set up by the holding company.
• HPCL was incorporated in 1974 after the takeover and merger of erstwhile Esso Standard and Lube India through the Esso (Acquisition of Undertaking in India) Act passed by Parliament.
• Power Grid Corporation of India Limited is India's largest electric power transmission utility firm. It is a listed company since 2007.

Additional Information List of Maharatna Companies in India 2022

• Bharat Heavy Electricals Limited
• Bharat Petroleum Corporation Limited
• Coal India Limited
• GAIL (India) Limited
• Hindustan Petroleum Corporation Limited
• Indian Oil Corporation Limited
• NTPC Limited
• Oil & Natural Gas Corporation Limited
• Power Grid Corporation of India Limited
• Steel Authority of India Limited

The correct answer is Rajendra Chola I.

• Rajendra Chola I was popularly called ‘Victor of the Ganges’.

Key Points

• Rajendra I (1014 AD-1044 AD):
• He conquered Orissa, Bengal, Burma and Andaman and Nicobar islands.
• The Chola dynasty was at its zenith during his reign.
• Rajendra I also assumed the title of ‘Gangaikonda Cholam’ and built a city called Gangaikonda Cholapuram.
• Rajendra I conquered complete Sri Lanka and made Anuradhapura his capital.
• He defeated the Pala king Mahipala and took the title of Gangaikonda Cholam.
• He also built the Cholamandalam Lake and the city of Gangikonda Cholapuram.
• He won the Java, Sumatra and Malaya areas from the Shailendra king.

Additional Information

• The Chola Empire (850 AD-1279 AD):
• Capital: Tanjore, Gangaikonda Cholapuram.
• The founder of the Chola dynasty was Vijayalaya, who was at first a feudatory of the Pallavas.
• He captured Tanjore in 850 AD.
• The ancient capital of Cholas was Palyarai.
• Vijayalaya revived the Chola Empire in the 9th century AD.
• He took the title of ‘Narkesari’.

The correct answer is 1995.

• The JavaScript Programming language came into existence in 1995.

Key Points

• JavaScript is a programming language used in web development.
• It was developed by Netscape to add dynamic and interactive elements to websites.
• JavaScript is influenced by Java.
• It is a client-side scripting language.
• A JavaScript code can be inserted anywhere within the HTML of a webpage.

Important Points

• JavaScript is a scripting language that is used to develop websites.
• JavaScript helps to add functionality and behaviors to your website, allowing your website’s visitors to interact with content in many imaginative ways.
• In September 1995, a Netscape programmer named Brandan Eich developed a new scripting language in just 10 days.
• It was originally named Mocha, but quickly became known as LiveScript and, later, JavaScript.

The correct answer is 1946.

Key Points

• The Cabinet Mission envisaged the establishment of a Constituent Assembly to frame a Constitution for the country.
• The first Constituent Assembly election held in India in 1946.
• Members of the Constituent Assembly were elected by the Provincial Legislative Assemblies.
• Dr. Rajendra Prasad was the President of the Constituent Assembly.
• Evolution OF Indian Constitution: The first Constitution of India framed and given to themselves by the people of India was adopted by the Constituent Assembly on 26 November 1949.
• It came into full operation with effect from 26 January 1950.
• The Constitution as originally adopted had 22 parts, 395 articles and 8 schedules.
• It took two years, eleven months and eighteen days for the Constituent Assembly to finalize the Constitution.

The correct answer is Rs. 2,000.

• Rs. 2,000 released in November 2016 features Mangalyaan on the reverse side.

Key Points

• To celebrate India's Mars mission, Rs. 2,000 carry an image of the Mangalyaan on the reverse side along with the motif of animals, right under the Mangalyaan.
• The front side of the currency features an image of Mahatma Gandhi.
• The size of the new notes will be 66mm X 166mm and will be available in a magenta base color.
• There will also be a latent image with a denomination numeral that would be visible when the note is held at a 45-degree angle at the eye level.
• The denomination numerals will be written in Devnagari script
• The security thread will feature three words - 'RBI', 'Bharat' and '2000', which will be imprinted on it and can be viewed on tilting the thread changing colour from green to blue.
  

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Additional Information