The correct answer is 'was too little space'. 

Key Points

• In the given sentence, the use of 'less' is grammatically incorrect. Here, in the given question, 'little' should be used.
• We know that 'less' is the comparative degree of 'little'. So, we should use less in comparative structures.
• ​Example: I have less homework to do today than I had yesterday.
• Whereas, the given sentence does not have any kind of comparison.
• In the given sentence, 'was' should be used instead of 'are' because the given sentence is in the past tense.
• Therefore, the correct answer is Option 3.

​

Correct Sentence: There was too little space for Naveen to park his car in front of the shop. 

Additional Information

• Use of 'Very' and 'Too'

• ​These are degree adverbs and are used to give information about the extent or degree of something.

• We use 'very' when we want to show 'to a high degree'.

• Whereas, 'too' is used to show 'more than enough' or 'more than wanted or needed'. 

• Example:

• Monica is too beautiful. 

• Monica is very beautiful.

The correct answer is 'BDCA'.

Key Points

• The initial sentence will be part B because the first statement of a para jumble question is usually a general statement, a noun, a universal fact, or the starting of an incident, etc.
• The given sentence is the start of an incident. Therefore, part B will be the first sentence.
• Part B is directly connected with part D. While they were passing through the forest they saw the bones of an animal. Hence, BD makes a pair.
• Part C explains part D. Therefore, part D is further connected with part C.
• Only Option 1 has these pairs.
• Hence, the correct answer is Option 1.

 

Correct Answer: BDCA.

The correct answer is Balaji said, "I had already paid the instalment when the notice came to me." 

Key Points

• The given sentence is in Indirect Speech. As per the question we have to change it into Direct Speech.
• The process of transformation is as follows:
• There will be no change in the reporting verb 'said' because it has no object.
• Comma and inverted commas will be added.
• 'He' will be changed into 'I'.
• There will be no change in the tense. 'Had already paid' will have no change because we know that while making the transformation, the Past Perfect Tense does not change.
• Lastly, ''him'' will be changed into ''me''.

 

Correct Answer: Balaji said, "I had already paid the instalment when the notice came to me."

The correct answer is 'Did you tell to'. 

Key Points

• The erroneous part 'Did you tell to' should be 'Did you tell' instead.
• The structure of the given sentence is grammatically incorrect.
• The structure should be:
• Did + Subject + V₁ + Object? 
• Example: Did he have a car?
• Therefore, the correct answer is Option 3.
  

Correct Sentence: Did you tell your mother that you saw her friend at the theatre?

Additional Information 

• If the point of time words are mentioned in the sentence like Last, Yesterday, the other day, ago, back, before last, since, or any past word, etc. then we should use Past Indefinite Tense. 
• Example: I saw the movie yesterday.

The correct answer is 'puts'. 

Key Points

• The given passage is about 'Staged tourism'.
• Only Option 2 fits the best in the given blank.
• 'Put Pressure' is a phrase. Its meaning is as follows:
• To try to influence or persuade one to do something or act a certain way; to make demands on or expect something from someone.
• ​Example: My parents have been putting pressure on me to get a job.
• Therefore, the correct answer is Option 2.

 

Correct Sentence: ''This often puts pressure on a certain area...''

Additional Information

• Staged Tourism: Staged tourism is essentially a cultural practice, event, or activity that is 'staged' for the purpose of the tourists.
• It could be that this is an outdated practice or that it has been modified for the purpose of tourism.

The correct answer is 'of'. 

Key Points

• The given passage is about 'Staged tourism'.
• We know that 'horde' is followed by the preposition 'of'.
• Horde: a large group of people.
• Example: Hordes of students on bikes made crossing the road difficult.
• Therefore, the correct answer is Option 3.

 

Correct Sentence: ''with hordes of tourists rushing to a spot...''

Additional Information

• Staged Tourism: Staged tourism is essentially a cultural practice, event, or activity that is 'staged' for the purpose of the tourists.
• It could be that this is an outdated practice or that it has been modified for the purpose of tourism.

The correct answer is 'the'. 

Key Points

• The given passage is about 'Staged tourism'.
• In the given blank, 'the' will be used because we are talking about a particular animal.
• Use of article definite article 'The'
• It is used while we are talking about a specific noun that is expected to be known to the reader and if it is not, we use 'A' or 'An'. 
• Example: The man in black is my boss.
• Therefore, 'the' will be used.

 

Correct Sentence: ''In the case of tigers...''

Additional Information

• Staged Tourism: Staged tourism is essentially a cultural practice, event, or activity that is 'staged' for the purpose of the tourists.
• It could be that this is an outdated practice or that it has been modified for the purpose of tourism.

The correct answer is 'that'.

Key Points

• The given passage is about 'Staged tourism'.
• In the given blank, we need the conjunction 'that'.
• We use 'that' as a conjunction to introduce a subordinate clause expressing a statement or hypothesis.
• She said that she was satisfied.
• Therefore, the correct answer is Option 2. 
  

Correct Sentence: ''it is quite possible that the animal...''

Additional Information

• Staged Tourism: Staged tourism is essentially a cultural practice, event, or activity that is 'staged' for the purpose of the tourists.
• It could be that this is an outdated practice or that it has been modified for the purpose of tourism.

The correct answer is 'disturbance'. 

Key Points

• The given passage is about 'Staged tourism'.
• In the given blank, 'disturbance' is correct.
• Disturbance: something that interrupts someone or makes someone feel worried. 
• Example: Residents are tired of the disturbance caused by the nightclub.
• Therefore, the correct answer is Option 1.

 

Correct Sentence: ''the disturbance caused by a bunch of excited tourists...''

Additional Information

• Staged Tourism: Staged tourism is essentially a cultural practice, event, or activity that is 'staged' for the purpose of the tourists.
• It could be that this is an outdated practice or that it has been modified for the purpose of tourism.

The correct answer is 'You had better not to try'. 

Key Points

• The erroneous part 'You had better not to try' should have 'You had better not try'.
• We use had better to refer to the present or the future, to talk about actions we think people should do or which are desirable in a specific situation.
• The verb form is always had, not have.
• It is followed by the 'infinitive' without 'to'.
• Therefore, the correct answer is Option 1.

 

Correct Sentence: You had better not try and feed the animals in the zoo, it is forbidden. 

Additional Information

• The other usage of 'had better'. 
• We normally shorten it to ’d better in informal situations.
• Had better is a strong expression. We use it if we think there will be negative results if someone does not do what is desired or suggested
• Example: She’d better get here soon or she’ll miss the opening ceremony.

The correct answer is 'Lata told her team leader'. 

Key Points

• In the given question 'Lata told to her team leader' should be 'Lata told her team leader'.
• The given sentence is in the Indirect Speech.
• We know that while making the transformation, 'told' is used without 'to'.
• We also know that 'told' is used instead of 'said' when Reporting Verb has any object. In the given sentence 'Her team leader' is the object.
• Therefore, the correct answer is Option 4.

 

Correct Sentence: Lata told her team leader that she would be leaving office early as she had some urgent personal work.

The correct answer is 'became energetic again'. 

Key Points

• In the given sentence, 'a new lease of life' is an idiom.
• It's meaning is as follows: 
• an occasion when you become more energetic and active than before.
• Example: His grandchildren have given him a new lease of life.
• Therefore, the correct answer is Option 3.

The correct answer is 'Surender'.

Key Points

• In the given question, Option 2 is incorrectly spelt.
• The correct spelling of it is 'Surrender'.
• Surrender: to stop fighting and admit defeat.
• Example: They would rather die than surrender (to the invaders).
• Therefore, the correct spelling is 'Surrender'.
  

Correct Answer: 'Surender'.

Additional Information 

• The meaning of the other words given in the option are as follows: 
• Success: the achieving of the results wanted or hoped for.
• Example: The success of almost any project depends largely on its manager.
• Succulent: Succulent food is pleasantly juicy. 
• Example: It is a big piece of succulent steak.
• Succumb: to lose the determination to oppose something; to accept defeat.
• Example: I'm afraid I succumbed to temptation and had a piece of cheesecake.

The correct answer is 'Dormitory'. 

Key Points

• The one-word substitution for the given group of words is 'Dormitory'.
• Dormitory: a large room containing many beds, for example in a boarding school.
• Example: We were determined to build not just dormitories but communities.
• Therefore, the correct answer is option 2.​​

Additional Information

• The meaning of the other options given in the question as follows: 
• Lodge: a small house in the country, used especially by people on holiday or taking part in sports, or one on land belonging to a large house.
• Residence: officially staying or living somewhere.
• Hostel: a place where people, especially young people, can stay cheaply for short periods when they are travelling, with shared rooms and sometimes some private rooms.

The correct answer is 'Psephologist'. 

Key Points

• The correct one-word substitution for the given group of words is 'Psephologist'.
• Psephologist: someone who studies elections and voting statistics.
• Example: I think that the role of psephologists can be very important.
• ​Therefore, the correct answer is option 1.

Additional Information

• The meaning of the other words given in the options as follows: 
• Reviewer: Someone who writes articles expressing their opinion of a book, play, film, etc.
• Sociologist: Someone who studies or is an expert in sociology.
• Researcher: Someone who studies a subject, especially in order to discover new information or reach a new understanding

The correct answer is 'Lenient'.

Key Points

• The exact antonym of the given word 'Harsh' is 'Lenient'.
• Harsh: unpleasant, unkind, cruel, or more severe than is necessary.
• Example: We thought the punishment was rather harsh for such a minor offence.
• Lenient: not as severe or strong in punishment or judgment as would be expected.
• Example: They believe that judges are too lenient with terrorist suspects.
• By reading the above definitions, we can infer that the correct answer is Option 1.

<br>

Additional Information 

• The meaning of the other words given in the options as follows:
• Robust: (of a person or animal) strong and healthy, or (of an object or system) strong and unlikely to break or fail.
• Example: He looks robust and healthy enough.
• Fragile: easily damaged, broken, or harmed.
• Example: The assassination could do serious damage to the fragile peace agreement that was signed last month.
• Energetic: having or involving a lot of energy.
• Example: I tried aerobics but it was too energetic for me.

The correct answer is 'experienced'. 

Key Points

• In the given sentence, 'old hand' in an idiom. It's meaning is as follows:
• Old Hand: Someone who is very experienced and skilled in a particular area of activity.
• Example: We should be able to trust Silva to negotiate a good deal for us - he's an old hand at the game.
• By reading the above definition, we find that the correct answer is Option 4.

The correct answer is 'Changeable'.

Key Points

• In the given question 'Changeable' is correctly spelt.
• Changeable: often changing.
• Example: The weather in Britain is notoriously changeable.

 

Correct Answer: Changeable.

Additional Information

• The correct spelling and meanings of the other words given in the option as follows: 
• Impending: used to refer to an event, usually something unpleasant or unwanted, that is going to happen soon.
• Unsustainable: something that is unsustainable cannot continue at the same rate.
• Insignificant: small or not noticeable, and therefore not considered important.

The correct answer is DCAB.

Key Points

• In the given question Part D will be the first statement because the first statement of a sentence jumbled question is usually a general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Here, Part D is an incident. And Part C is explicitly connected with Part D because Part D talks about 'Ghat' and Part C further connects it.
• Part C is connected with Part A.
• And the last Part is Part B.
• Therefore, Only Option 2 can be the answer.

 

Correct Answer: DCAB.

The correct answer is 'Official Order'. 

Key Points

• The exact synonym of the given word 'Mandate' is 'Official Order'.
• Mandate: the authority given to an elected group of people, such as a government, to perform an action or govern a country. 
• Example: At the forthcoming elections, the government will be seeking a fresh mandate from the people.
• By reading the above definition, we can infer that the correct answer is 'Official Order'.

The correct answer is 'Humility'.

Key Points

• The exact antonym of the given word 'Arrogance' is 'Humility'.
• Arrogance: the quality of being unpleasantly proud and behaving as if you are more important than, or know more than, other people.
• Example: He has self-confidence that is sometimes seen as arrogance.
• Humility: the quality of not being proud because you are aware of your bad qualities. 
• Example: He doesn't have the humility to admit when he's wrong.
• By reading the above definitions, we can infer that the correct answer is Option 2.
  

Additional Information

• The meaning of the other words given in the options as follows: 
• Honesty: the quality of being honest.
• Example: I appreciate your honesty.
• Familiarity: good knowledge of something, or the fact that you know it so well. 
• Example: I love the familiarity of my old chair.
• Ignorance: lack of knowledge, understanding, or information about something. 
• Example: Public ignorance about the disease is still a cause for concern.

The correct answer is 'under'.

Key Points

• In the given blank, the use of 'under' is correct.
• Usage of 'Under': 
• At a position directly lower than or covered. 
• Example: Dog is under the table.

Additional Information

• The usage of other prepositions are as follows: 
• Over:
• Vertical position.
• Example: Fan is moving over the table.
• Covering: Someone or something covering. 
• Example: She put her hands over her ears.
• Into: 
• Used to show that something is inside. 
• Example: The cat is into the hutch.

The correct answer is You are requested to make a cup of coffee for me

Key Points

• The given sentence is in Active Voice. This is an example of an Imperative Sentence.
• The notion of the sentence is 'Request'.
• The structure should be:
• ​​Sub + are requested + to + V1. ​​​
  

​

Correct Answer: You are requested to make a cup of coffee for me

Additional Information

• Imperative Sentence: Someone gives a command, does a request, expresses a desire or wish, in sentences then such sentences are called imperatives sentences.

The correct answer is 'comparison'. 

Key Points

• In the given blank, 'comparison' should be used.
• 'In comparison to' is a phrase.
• 'In comparison to' - the act of comparing two or more people or things.
• Example: In comparison to the French, the British eat far less fish.
• Therefore, the correct answer is Option 2.
  

Correct Sentence: Students who are capable of understanding and managing their ‘emotional intelligence’ do better at school in comparison to their peers who lack the ability.

The correct answer is 'Round'. 

Key Points

• The exact synonym of the given word 'Rotund' is 'Round'.
• Rotund: (especially of a person) round or rounded in shape.
• Example: A rotund, smiling, red-faced gentleman appeared.
• Round: in a circular direction or position; around. 
• Example: He tried to go round the keeper​.
• By reading the above definitions, we find that the correct answer is Option 3.
  

Additional Information 

• The meaning of other words given in the options as follows: 
• Range: the amount, number, or type of something between an upper and a lower limit.
• Example: The product is aimed at young people in the 18–25 age range.
• Rocky: made of rock and therefore usually rough and difficult to travel along.
• Example: She scrambled along the rocky path.
• Rolled: to (cause something to) move somewhere by turning over and over or from side to side.
• Example: The dog rolled over onto its back.

The meaning of the given words in the option are as follow:

1) Create → to cause something new to happen or exist.

2) Disband → to stop existing as a group; to separate.

3. Assemble → something together in a group.

4) Construct → to build or make something

Meaning of option 1, 3 and 4 is positive or to make some thing but option 2 meaning is negative or to extract something.

Hence, 'Disband' is odd among all.

The least possible Venn diagram for the given statement is:

Explanation:

I. Some horses are fishes → True (Some fishes are horses)

II. Some kites are fishes →False (it is possible but not definite)

III. Some kites are horses → True (Some horse are kites)

Hence, only conclusion I and III follow.

The question figure is embedded in,

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

The pattern followed here is :

Logic: The numerical value of each letter get decreased by 1 to get the code.

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Similarly

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So, the code for 'FIRST' is '58171819'.

Hence, '581718179' is the correct answer.

The pattern followed here is:

1. 30 : 961

30 + 1 = 31²  → 961

2. 25 : 676

 25 + 1 = 262  → 676

3) 24 : 529

24 - 1 = 232  → 529

4. 21 : 484

21 + 1 = 22² → 484

Hence,'24:529' is odd among all.

The pattern followed here is :

3 : 25

3 + 2 = 5² → 25

Similarly, 

1 : ?

1 + 2 = 3²→ 9

? = 9

Hence, '9' is the correct answer.

The pattern followed here is :

Function of school is to education.

Similarly,

Function of hospital is treatment.

Hence, 'Treatment' is the correct answer.

1) A is husband of M who is sister - in - law of N.

2) N is daughter of R and U. 

3) M is daughter-in-law of U.

Here, gender of 'R' and 'U' is not definite. But we can conclude that A is son of U.

Hence, 'Son' is the correct answer.

According to the position of letters in English alphabet series.

Insert alphabet table:

The pattern followed here is :

1. LNQU

L + 2 → N ; N + 3 → Q ; Q + 4 → U

2. VXAE

V + 2 → X ; X + 3 → A ; A + 4 → E

3) UQNL  

U - 4 → Q ; Q - 3 → N ; N - 2 → L

4. YADH

Y + 2 → A ; A + 3 → D ; D + 4 → H  

Hence, 'UQNL' is odd among all.

The pattern followed here is :

Logic:

Consonant = -2, Vowel = Next vowel

Similarly,

Hence, 'JOUL' is the correct answer.

The mirror image would be as follows :

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

The pattern followed here is:

Given,

(6, 18, 162)

6 × 3 → 18

18 × 3² → 162

Similarly, in option 3 :

(4, 8, 32)

4 × 2 → 8

8 × 2² → 32

Hence, (4, 8, 32) is the correct answer.

The question figure is embedded in,

Hence, the figure in option 3 th correct answer.

The paper when unfolded looks like,

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

Let the age of Arun is X.

12 year ago age of Arun is X - 12.

According to the question age of Arun will be twice of his age that was 12 year ago.

X + 1 = 2 × (X - 12)

X + 1 = 2X - 24

2X - X = 24 + 1

X = 25

Hence, Arun is 25 year old.

The logic is:

46, 92, 69 → 92 – 46 = 46; 92 – 69 = 23

First difference is double of second difference.

Similarly,

1. 56, 78, 60 → 78 – 56 = 22; 78 – 60 = 18

First difference is not equal to double of second difference.

2. 48, 82, 63 → 82 – 48 = 34; 82 – 63 = 19

First difference is not equal to double of second difference.

3. 50, 88, 59 → 88 – 50 = 38; 88 – 59 = 29

First difference is not equal to double of second difference.

4. 34, 72, 53 → 72 – 34 = 38; 72 – 53 = 19

First difference is equal to double of second difference.

Hence, ‘34, 72, 53’ is the correct answer

The total number of the triangle in the given figure is :

 

So the number of tringle in the given figure is 5

Hence, '5' is the correct answer.

The pattern followed here is :

Hence, '7' is the correct answer.

The positions of letters according to the English alphabet series.

Here, the logic is :

The Middle alphabet is a vowel in all options except option 4.

BIZ → Here "I" is the vowel

MOW → Here "O" is the vowel

CUZ → Here "U" is the vowel

Except, 

ABY → Here "A" is the vowel but Not in the middle place.

Hence, 'ABY' is odd among all.

Position of letters in English alphabet series according to English alphabet series.

Insert the alphabet table:

The pattern followed here is :

Numerical position of letter get added and multiply by total number of letter to get the code.

PATNA :

P (16) + A (1) + T (20) + N (14) + A (1)

16 + 1 + 20 + 14 +  1 = 52

52 × 5 = 260

GOA :

G (7) + O (15) + A (1)

7 + 15 + 1 = 23

23 × 3 = 69

Similarly,

RANCHI :

R (18) + A (1) + N (14) + C (3) + H (8) + I (9)

18 + 1 + 14 + 3 + 8 + 9 = 53

53 × 6 = 318

Hence, '318' is the correct answer.

1) abdddad/ acbcbdc/ accbdad (Does not follow any pattern)

2) abdddad/ acbccbc/ acbddad (Does not follow any pattern)

3) acbddac/ acbddac/ acbddac (Follow the pattern)

4) abdddad/ dcbcbdc/ acacdac (Does not follow any pattern)

Hence, 'cbcaddabdc' is the correct answer.

The pattern followed here is :

Similarly,

Hence, 'FTBII' is the correct answer.

Given,

Rhombus represents geography.

Circle represent mathematics.

The rectangle represents history.

From the given figure we observe that 4, and 7 lie in the region where student like geography and mathematics but not like history.

So the total number of student who like geography and mathematics but not history is:

4 + 7 = 11

Hence, '11' is the correct answer.

Given,

In the first dice '&' and '$' phase are adjacent to '('  phase so these phases are not opposite to '(' phase.

In the second dice '*' and '#' phase are also adjacent to '(' phase so these phases are not opposite to '(' phase.

Now from the third dice only '+' phase has left which is opposite to '(' phase.

Hence, '+' is the correct answer.

Checking the given alternatives:

1. 18 and 9

Given equation : 

3 × 9 + 5 - 18 ÷ 7 = 24

After interchanging according to potion 1.

3 × 18 + 5 - 9 ÷ 7 = 24

3 × 18 + 5 - 2.571= 24

54 + 5 - 2.571 = 24

56.429 ≠ 24

2. 5 and 7

Given equation : 

3 × 9 + 5 - 18 ÷ 7 = 24

After interchanging according to potion 2.

3 × 9 + 7 - 18 ÷ 5 = 24

3 × 9 + 5 - 3.6 = 24

27 + 5 - 3.6 = 24

 28.4 ≠ 24

3. 9 and 7

Given equation : 

3 × 9 + 5 - 18 ÷ 7 = 24

After interchanging according to potion 2.

3 × 7 + 5 - 18 ÷ 9 = 24

3 × 7 + 5 - 2 = 24

21 + 5 - 2= 24

 24 = 24

4)  3 and 5

Given equation : 

3 × 9 + 5 - 18 ÷ 7 = 24

After interchanging according to potion 2.

5 × 9 + 3 - 18 ÷ 7 = 24

5 × 9 + 3 - 2.571 = 24

45 + 3 - 2.571 = 24

 45.429 ≠ 24

Hence, '9 and 7' is the correct answer.

Given:

a + b = 27

a³ + b³ = 5427

Formula:

a³ + b³ = (a + b) [(a + b)² - 3ab]

Calculation:

a3 + b3 = (a + b) [(a + b)2 - 3ab

⇒ 5427 = 27 [27² - 3ab]

⇒ 5427/27 = (729 - 3ab)

⇒ 201 = 729 - 3ab

⇒ 3ab = 729 - 201

⇒ 3ab = 528 

⇒ ab = 528/3

⇒ ab = 176

Given:

Sales of city-1 in 2019 = 4.1

Sales of city-2 in 2019 = 4.3

Sales of city-3 in 2019 = 4.9

Sales of city-4 in 2019 = 4.9

Formula:

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

Calculation:

Sum of sales of all four cities in 2019 = 4.1 + 4.3 + 4.9 + 4.9 = 18.2 thousands 

∴ Required average = 18,200/4 = 4550

Shortcut Trick

Test the options to find the Marked Price (x) that satisfies the given conditions.

For x = 80: Discount % = (80 − 40)% = 40%.

Discount Value = 40% of 80 = (40/100) × 80 = Rs. 32.

Selling Price (SP) = Marked Price − Discount = 80 − 32 = Rs. 48.

Check SP condition: SP = x − 32 = 80 − 32 = Rs. 48. (Condition satisfied)

∴ The correct answer is Rs. 80.

Alternate Method

Given:

Marked Price (MP) = Rs. x

Discount Percentage = (x − 40)%

Selling Price (SP) = Rs. (x − 32)

Formula Used:

SP = MP × (100 − Discount %)/100

Calculations:

⇒ (x − 32) = x × [100 − (x − 40)] / 100

⇒ 100 × (x − 32) = x × (100 − x + 40)

⇒ 100x − 3200 = x × (140 − x)

⇒ 100x − 3200 = 140x − x²

⇒ x² − 40x − 3200 = 0

⇒ x² − 80x + 40x − 3200 = 0

⇒ x(x − 80) + 40(x − 80) = 0

⇒ (x − 80)(x + 40) = 0

⇒ x = 80 or x = −40

⇒ Since price cannot be negative, x = 80.

∴ The correct answer is Rs. 80.

Additional Information

Relationship between SP and MP

The Selling Price is obtained by subtracting the Discount amount from the Marked Price: SP = MP − Discount.

Discount Percentage Formula

The Discount Percentage is calculated on the Marked Price: Discount % = (Discount / MP) × 100.

Quadratic Formula for Roots

For an equation ax² + bx + c = 0, the roots are given by x = [−b ± √(b² − 4ac)] / 2a.

Given:

PQ and RS are two diameters that are perpendicular to each other.

Formula:

(Hypotenuse)² = (Base)² + (Perpendicular)²

Calculation:

Let O is the center of the circle and r is the radius of the circle. 

∴ PQ = RS = 2r

In right angle ΔROP

⇒ (PR)² = (OR)² + (OP)²

⇒ (PR)² = r² + r²

⇒ (PR)² = 2r²

⇒ PR = √2 r

⇒ PR = √2 r × (√2/√2)

⇒ PR = 2r/√2

∴ PR = PQ/√2

Given:

Total sales in 2016 = 4.3 + 3.6 + 5.2 + 4.5 = 17.6

Total sales in 2017 = 3.5 + 3.9 + 4.3 + 4.6 = 16.3

Total sales in 2018 = 3.9 + 4.2 + 4.9 + 5.1 = 18.1

Total sales in 2019 = 4.1 + 4.3 + 4.9 + 4.9 = 18.2

Formula:

x as a percentage of y = (x/y) × 100

Calculation:

Percentage of sales of city-1 in 2019 = (4.1/18.2) × 100 = 22.52%

Percentage of sales of city-3 in 2016 = (5.2/17.6) × 100 = 29.54%

Percentage of sales of city-2 in 2018 = (4.2/18.1) × 100 = 23.20%

Percentage of sales of city-4 in 2017 = (4.6/16.3) × 100 = 28.22%

Now we can say city-3 has the highest sales in 2016.

Given:

Two numbers are respectively 25% and 65% more than the third number.

Formula:

x% more a number = Actual number × (100 + x)/100

Calculation:

Let third number be 100, then

First number = 100 × (125/100) = 125

Second number = 100 × (165/100) = 165

∴ Ratio of the two numbers = 125 : 165 = 25 : 33

Given:

sin θ  - cos θ = 7/17

Formula:

(sin θ + cos θ)² + (sin θ - cos θ)² = 2

Calculation:

(sin θ + cos θ)2 + (sin θ - cos θ)2 = 2

⇒ (sin θ + cos θ)2 + (7/17)2 = 2

⇒ (sin θ + cos θ)2 + (49/289) = 2

⇒ (sin θ + cos θ)2 = 2 - (49/289)

⇒ (sin θ + cos θ)2 = 529/289

⇒ (sin θ + cos θ) = √529/289

∴ sin θ + cos θ = 23/17

Alternate Method

Concept used:

Asin θ + Bcos θ = C then the value of  

⇒ Bsin θ - Acos θ = √(A² + B² - C²)

Calculation:

⇒ sin θ - cos θ = 7/17 [ here A = 1 & B = 1 ]

So, sin θ + cos θ = √{1² + 1² - (7/17)²}

⇒ sin θ + cos θ = √2 - 49/289

⇒ sin θ + cos θ = √529/289 = 23/17

Given:

cos x = -1/2

Formula:

cos 120° = -1/2

π = 180°

Calculation:

cos x = -1/2

⇒ cos x = cos 120°

⇒ x = 120°

120° × (π/180°)

⇒ 2π/3

Given:

Ratio of angles of a triangle = 1 : 2 : 1

Formula:

Sum of all three angles of a triangle = 180°

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

Ratio of angles of a triangle = x : 2x : x

According to the question

x + 2x + x = 180°

⇒ 4x = 180°

⇒ x = 180°/4

⇒ x = 45°

⇒ 2x = 45° × 2

⇒ 2x = 90°

Now we can say triangle is a right angled triangle.

Triangle has two equal angles so, triangle has two equal side.

See figure, ΔABC is a right angled triangle

Let AB = BC = a cm, then

(AC)² = (AB)² + (BC)²

⇒ (AC)² = a² + a²

⇒ (AC)² = 2a²

⇒ AC = √2 a

∴ Ratio of AB : AC : BC = a : √2 a : a = 1 : √2 : 1

Given:

Sachin scored = 120 runs

Number of boundaries = 6

Number of sixes = 4

Formula:

x as a percentage y = (x/y) × 100

Calculation:

Number of runs score made by running between the wickets = 120 - 4 × 6 - 6 × 4 = 120 - 48 = 72

∴ Required percentage = (72/120) × 100 = 60%

Given:

Total sales in 2016 = 4.3 + 3.6 + 5.2 + 4.5 = 17.6

Total sales in 2017 = 3.5 + 3.9 + 4.3 + 4.6 = 16.3

Total sales in 2018 = 3.9 + 4.2 + 4.9 + 5.1 = 18.1

Total sales in 2019 = 4.1 + 4.3 + 4.9 + 4.9 = 18.2

Calculation:

Now we can say, In 2019 the sales are highest.

Shortcut Trick

A loss of 12% means the Selling Price (SP) is 88% of the Cost Price (CP).

SP = CP × 0.88

SP = 3200 × 0.88

SP = 32 × 88 = ₹2,816.

∴ The correct answer is ₹2,816.

Alternate Method

Given: Cost Price (CP) = ₹3,200 and Loss Percentage = 12%.

Formula: Selling Price (SP) = CP − Loss

⇒ Loss Amount = 12% of 3200

⇒ Loss Amount = (12/100) × 3200

⇒ Loss Amount = 12 × 32 = ₹384.

⇒ SP = CP − Loss Amount

⇒ SP = 3200 − 384 = ₹2,816.

⇒ Comparing with the given options, the result corresponds to Option (2).

∴ The correct answer is ₹2,816.

Additional Information

Selling Price for Profit

When there is a profit, SP = CP × (100 + Profit %)/100.

Finding Cost Price

To find CP when SP and loss are known: CP = (SP × 100) / (100 − Loss %).

Profit/Loss Percentage

Profit or Loss percentage is always calculated on the Cost Price unless specified otherwise.

Given

x + 1/x = 8      ----(1)

Calculation

5x/(x² + 1 - 6x)

⇒ 5/(x + 1/x - 6)    [Dividing upper and lower parts by x]

⇒ 5/(8 - 6)        [Using (1)]

⇒ 5/2

⇒ 2.5

∴ The required value is 2.5

Given:

Side of equilateral triangle = 12 cm

Formula:

Area of the equilateral triangle = (√3/4) × a²

Calculation:

Area of the equilateral triangle = (√3/4) × 122

⇒ (√3/4) × 144

⇒ 36 √3

Given:

The diameter of the circle = 20 cm

The length of one chord = 16 cm

Distance between the two chords = 12 cm

Formula:

(Hypotenuse)² = (Base)² + (Perpendicular)²

Calculation:

AB and PQ are two chords and O is the centre of the circle.

M is the mid-point of AB and N is the mid-point of PQ.

OB = OQ = 10 cm (radius of the circle)

AB = 16 cm and MN = 12 cm

Let OM = x, then

ON = (12 - x) cm

MB = 16/2 = 8 cm

In ΔMOB

(OB)² = (OM)² + (MB)²

⇒ 10² = 8² + (OM)²

⇒ OM² = 100 - 64

⇒ OM = √36

⇒ OM = 6

ON = 12 - 6 = 6 cm

In ΔONQ

(OQ)² = (ON)² + (NQ)²

⇒ 10² = 6² + (NQ)²

⇒ (NQ)² = 100 - 36

⇒ NQ = √64

⇒ NQ = 8

PQ = 2NQ

⇒ PQ = 2 × 8

⇒ PQ = 16 cm

∴ Length of other chord is 16 cm

Given:

Principal = Rs. 74,000

Rate = $18 \frac{2}{3}$% = 56/3

Time = 8 months

Formula:

SI = Prt/100

Calculation:

SI = (74000 × 56 × 8)/(3 × 12 × 100)

⇒ SI = Rs. 9208.88

∴ The simple interest is Rs. 9208.88.

Given:

Average of 5 consecutive odd number = 75

Formula:

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

Calculation:

Sum of 5 consecutive odd numbers = 75 × 5 = 375

Average of 6 numbers = 76

Sum of all 6 numbers = 76 × 6 = 456

Let the 6th number be x

According to the question

x + 375 = 456

⇒ x = 456 - 375

⇒ x = 81

∴ The 6th number is 81.

Given:

Total sales of city-1 = 4.3 + 3.5 + 3.9 + 4.1 = 15.8 thousands

Total sales of city-2 = 3.6 + 3.9 + 4.2 + 4.3 = 16 thousands

Total sales of city-3 = 5.2 + 4.3 + 4.9 + 4.9 = 19.3 thousands

Total sales of city-4 = 4.5 + 4.6 + 5.1 + 4.9 = 19.1 thousands

Calculation:

City-3 has the highest sales among four cities.

Given:

The athlete crosses a distance of 900 m in = 10 min

Formula:

Speed = Distance/Time

1 m/sec = 5/18 km/hr

Calculation:

10 min = 600 seconds

∴ Speed of athlete = (900/600) × (18/5) = 5.4 km/hr

Given:

sin x + cosec x = 2

Formula:

sin 90 = 1

cosec 90 = 1

Calculation:

sin x + cosec x = 2

Put x = 90°, then

⇒ sin 90° + cosec 90° = 2

⇒ 1 + 1 = 2

⇒ 2 = 2

L.H.S and R.H.S

Now,

⇒ sin17x + cosec18x

⇒ sin17 90° + cosec18 90°

⇒ 1 + 1

⇒ 2

Given:

x = 255, y = 256 and z = 257

Formula:

x3 + y3 + z3 - 3xyz = 1/2 (x + y + z) [(x - y)² + (y - z)² + (z - x)²]

Calculation:

According to the question

⇒ x3 + y3 + z3 - 3xyz = 1/2 × (255 + 256 + 257) × [(255 - 256)2 + (256 - 257)2 + (257 - 255)2]

⇒ x3 + y3 + z3 - 3xyz = (1/2) × 768 × [(-1)² + (-1)² + (2)²]

⇒ x3 + y3 + z3 - 3xyz = (1/2) × 768 × [1 + 1 + 4]

⇒ x3 + y3 + z3 - 3xyz = (1/2) × 768 × 6

∴ x3 + y3 + z3 - 3xyz = 768 × 3 = 2304

Formula:

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

Calculation:

81 = 9 × 9

If a number divisible by 81, then the number also divisible by 9 × 9.

From option 1

99954

⇒ 9 + 9 + 9 + 5 + 4

⇒ 36

∴ 36 is divisible by 9, then we can say 99954 also divisible by 81.

Shortcut Trick

Ratio of Perimeter to Length = 8 : 1 ⇒ 2(L + B) : L = 8 : 1.

On simplifying, 2L + 2B = 8L ⇒ 2B = 6L ⇒ Breadth (B) = 3 × Length (L).

Area = L × B = L × 3L = 3L² = 1323 cm².

L² = 1323 ÷ 3 = 441 ⇒ L = √441 = 21 cm.

∴ The correct answer is 21 cm.

Alternate Method

Given:

Ratio of Perimeter (P) to Length (L) = 8 : 1

Area of the rectangle = 1323 cm²

 

Formula:

Perimeter of the rectangle = 2 (length + breadth)

Area of the rectangle = Length × Breadth

Calculation:

Ratio of perimeter and length of a rectangle = 8x : x

Let length = x, then

2 × (x + breadth) = 8x

⇒ x + breadth = 4x

⇒ breadth = 4x - x

⇒ breadth = 3x

Area of the rectangle = 1323

⇒ x × 3x = 1323

⇒ x2 = 1323/3

⇒ x2 = 441

⇒ x = √441

⇒ x = 21

∴ Length of rectangle is 21 cm.

Additional Information

Properties of a Rectangle

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. The diagonals are equal and bisect each other.

Diagonal Formula

The length of the diagonal (d) of a rectangle can be found using the Pythagorean theorem: d = √(L² + B²).

Perimeter and Area Relation

For a fixed perimeter, a square (where L = B) has the maximum area among all rectangles.

Shortcut Trick

Efficiency ratio of Ramu to Somu = 4 : 1

Total Work = Somu's Efficiency × Somu's Time = 1 × 20 = 20 units

Combined Efficiency = 4 + 1 = 5 units

Time taken together = 20 ÷ 5 = 4 days

∴ The correct answer is 4 days.

Alternate Method

Given: Ramu is 4 times faster than Somu. Somu takes 20 days.

Formula Used: Total Work = Efficiency × Time

⇒ Somu's efficiency = 1 unit/day

⇒ Ramu's efficiency = 4 × 1 = 4 units/day

⇒ Total Work = 1 × 20 = 20 units

⇒ Combined efficiency of Ramu and Somu = 4 + 1 = 5 units/day

⇒ Time taken by both = Total Work ÷ Combined Efficiency

⇒ Time taken = 20 ÷ 5 = 4 days

∴ The correct answer is 4 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If the ratio of efficiencies of A and B is x : y, then the ratio of time taken is y : x.

Combined Work Formula

If A can do a work in x days and B can do it in y days, then they together can do it in (x × y) ÷ (x + y) days.

Work and Wages

Wages are generally distributed in the ratio of the efficiency or the actual work done by the workers.

Given:

∛15625 - √x = 4

Concept:

∛15625 = 25

Calculation

∛15625 - √x = 4

⇒ 25 - √x = 4

⇒ √x = 25 - 4

⇒ √x = 21

Squaring on both sides

∴ x = 441

The correct answer is Deepa Malik.

Key Points

• Rajiv Gandhi Khel Ratna Award is the highest sporting award given by the Ministry of Youth Affairs and Sports for the spectacular and most exceptional performance in the field of sports by a sportsperson over a period of four years.
• The Prize money for the Rajiv Gandhi Khel Ratna Award has been increased to 25 lakh rupees from the previous amount of 7.5 lakh rupees.
• Deepa Malik is an Indian athlete. She is the first Indian woman to win a medal in Paralympic Games and won a Silver medal at the 2016 Summer Paralympics in the shot put.
• Deepa is also the President's role model and NITI Aayog award for women transforming India.
• Paralympic Games which first took place in Rome, Italy, in 1960 featuring 400 athletes from 23 countries. Since then they have taken place every four years.

The correct answer is Iran.

Key Points

• Iran's parliament passed a bill on Tuesday designating all US forces as "terrorists" after the killing of its top Iranian military commander Gen Qassem Soleimani.
• Qasem Soleimani, the head of the Revolutionary Guards' foreign operations arm, was killed in a US drone strike outside Baghdad airport.
• The assassination of Qassem Soleimani may spark a full-blown war between the US and Iran as self-preservation or preserving the lives of the top leaders is the primary objective of any regime.
• The spiralling of the US-Iran tensions also puts India in a difficult spot. India has perhaps the largest number of the world’s Shia population and the possibility of some of them being radicalised by this event cannot be ruled out.

The correct answer is Virat Kohli.

Key Points

• In the game of cricket, a Man of the Match or Player of the Match and Player of the Series award is given to the outstanding player in a particular match or series.
• The term was first used more often in cricket before being adopted by other sports. This can be a player from either team, normally the winning team.
• In cricket, the man of the match award became a normal feature in Test matches in the mid 1980s.
• In Test matches, Jacques Kallis holds the record for the maximum number of awards won, with 23 in 166 matches played, which is followed by Muttiah Muralitharan with 19 awards.
• In ODI Sachin Tendulkar holds the record for the maximum number of man of the match titles, with 62 awards in 463 matches played.
• The ‘Man of the Series’ award in the three-match ODI series played between India and Australia in January 2020 is Virat Kohli.

The correct answer is MIDI devices.

Additional Information

• Musical Instrument Digital Interface (MIDI) is a standard protocol for interconnecting computers with musical instruments, stage lighting, and other time-oriented media.
• MIDI is irrelevant to audio. But because MIDI is commonly used with music, this article is placed in the audio section.
• Android 10 makes it easier to port professional audio apps using MIDI to the Android platform.

The correct answer is Zoroastrianism.

Key Points

• The most essential texts of Zoroastrianism are those of the Avesta.
• The Avesta also contains the basic teachings of Zoraster known as the Gatha.
• A fire temple in Zoroastrianism is the place of worship for Zoroastrians, usually called Dar-e-Mehr (Persian) or Agiyari (Gujarati). In the Zoroastrian religion, fire, together with clean water, are agents of ritual purity.
• The foundation of the ancient religion of Zoroastrianism was laid by the teachings and wisdom of the spiritual leader and reformist Zoroaster

The correct answer is West Bengal.

Key Points

• Ganga-Sagar Mela is one of such festival of India celebrated on the occasion of Mankar Sankranti, during 13th – 15th January every year in West Bengal, which draws thousands of pilgrims from all over the world.
• The hosting state of West Bengal organises this fair with great pride and devout.
• Ganga Sagar Mela is organised every year during Makar Sankranti.
• The pilgrims take a holy dip in the water of the River Ganga in the morning while worshipping Lord Surya.

The correct answer is B. Sai Praneeth.

Key Points

• The BWF World Championships is a badminton tournament approved by Badminton World Federation (BWF).
• The tournament began in 1977 and was held once every three years until 1983.
• The tournament became band played once every two years until 2005. Starting 2006, the tournament was switched to an annual event on the BWF calendar with the goal to give more chances for the players to be crowned as official "World Champions".
• B. Sai Praneeth scripted history by becoming the second Indian male shuttler after Prakash Padukone to win the title of ‘BWF Badminton World Championships’ in August 2019.

The correct answer is Secondary.

Key Points

• Secondary activities add value to natural resources by transforming raw materials into valuable products.
• Secondary activities, therefore, are concerned with manufacturing, processing and construction (infrastructure) industries.
• People engaged in secondary activities are called blue-collar workers.
• Construction sector, manufacturing and utilities, e.g. electricity.

 

The correct answer is 42°C.

Key Points

• A clinical thermometer is a thermometer used to measure human body temperature.
• Most made in the 20th century are mercury-in-glass thermometers.
• They are accurate and sensitive, having a narrow place where the mercury level rises very fast.
• The temperature of the human body normally does not go below 35^oC or above 42^oC. That is the reason why this thermometer has the range 35^oC to 42^oC.

The correct answer is Rani Rampal.

Key Points

• Koneru Humpy, Prithu Gupta are the Indian Chess Grandmasters.
• Rani Rampal is considered one of the best women hockey players in the world.
• The captain of the Indian hockey women’s team was also a part of the squad that represented India in Rio 2016, the first time the eves had qualified for the Games in 36 years.
• Rampal played in all five of India's group games at the Olympics and her growing influence saw her named captain of the national team soon after their return from Rio 2016.

The correct answer is Abdul Ghaffar Khan.

Key Points

• Abdul Ghaffar Khan (1890-1988), the foremost 20^th-century leader of the Pashtunswas a follower of Mahatma Gandhi and was called the “Frontier Gandhi”.
• Ghaffar Khan met Gandhi and entered politics in 1919 during the agitation over the Rowlatt Acts, which allowed the restriction of political dissidents without trial.
• Ghaffar Khan founded the Red Shirt movement (Khudai Khitmatgar) among the Pashtuns.
• In 1987 he was awarded the Bharat Ratna Prize, the highest Indian honour that can be given to civilians. He was the first non-Indian to receive this honour.

The correct answer is Villi.

Key Points

About Villi:

• The small little projections on the inner surface of the small intestine which help in absorbing the digested food are called villi.
• These serve to increase the surface area of intestinal walls.
• These are found in the inner walls of the small intestine.
• Their purpose is to increase the surface area of the small intestinal wall for the absorption of the digested food.

The Villi are found inside the small intestine to absorption of nutrients from the digested food.

• They are finger-like projection inside the small intestine to increase their surface area to absorb essential nutrients from the food.
• They have thin walls and mostly covered with a thin channel of blood capillaries so, the nutrients can be absorbed by blood and easily transport

Additional Information

About Small Intestine:

• The small intestine is divided into three sections, a ‘C’ shaped duodenum, a long coiled middle portion jejunum and a highly coiled ileum.
• The small intestine is highly coiled and is about 5 meters long. It receives secretions from the liver and the pancreas. Moreover, its wall also secretes juices.
• The inner walls of the small intestine possess thousands of finger-like outgrowths. These are called villi (singular villus). The villi enhance the surface area for absorption of the digested food.

The correct answer is Black.

Key Points

• The railway lines and telephone lines shown in the topographic map are in black color.
• Black Color in the topographic map: All riverbanks, broken grounds, dry streams, surveyed trees, heights and their numbering, railway tracks, telephone and telegraph lines.

Additional Information

• Other Colors used in Topographic map:
• Yellow: All cultivated lands.
• Green: All forested areas.
• Brown: Sand features.
• Blue: Water bodies.
• Red: Grid lines and their numberings.

The correct answer is Health, education and standard of living.

Key Points

• The Human Development Index (HDI) is the geometric mean of normalized indices for each of the three dimensions:
• The health dimension is estimated by life expectancy at birth.
• The education dimension is estimated by mean of years of schooling for adults aged 25 years and more and expected years of schooling for children of school entering age.
• The standard of living dimension is measured by gross national income per capita.
• The HDI uses the logarithm of income, to reflect the diminishing importance of income with increasing GNI.

Additional Information

About UNDP:

• The United Nations Development Programme (UNDP) gives expert advice, training and grants support to developing countries, with an increasing emphasis on assistance to the least developed countries.
• It supports technical and investment cooperation among nations.
• UNDP was founded in 1965 by the General Assembly of the United Nations.
• UNDP operates in 177 countries, serving in nations on their own solutions to global and national development challenges.

The correct answer is Jawaharlal Nehru.

Key Points

• The urban middle class organized themselves into Praja-Parishads or Praja Mandals with nationalistic views emerging in the princely states. The earliest of them was in Baroda in 1917, followed by Kathiawar, Mysore, Hyderabad, etc.
• The All-India States People's Conference was organized in 1927 with an aim to influence state governments to initiate significant reforms in administration and demanding democratic rights.
• The princely states formed two-fifths of British India.
• Jawaharlal Nehru became the All India States People’s Conference President in 1939 and remained so until 1946.

The correct answer is 84^th.

Key Points

• Henley & Partners, the residence and citizenship planning firm has published the Henley Passport Index, according to the number of destinations the corresponding passport holders can access without a prior visa.
• The ranking is based on data from the International Air Transport Association (IATA), a trade association of some 290 airlines, including all major carriers.
• The index incorporates 199 different passports and 227 various travel destinations.
• The Henley Passport Index was begun in 2006 with the aim of providing a global picture of freedom of travelling.
• The Indian passport is ranked 84^th in the world.

Important Points

• Japan has the world’s most powerful passport whereas Afghanistan (107^th rank) has the weakest.