SSC CHSL Previous Paper 7 (Held On: 19 March 2020 Shift 1) (Previous Year Paper)

The correct answer is 'than hot coffee'.

Key Points

• In the given sentence, the use of the preposition 'than' is incorrect.
• From the given sentence, the word 'Prefer' is usually followed by 'to' and not 'than' because the word itself means 'like something or someone more than another'.
• 'To' here refers to the relationship between orange juice and hot coffee or chilled grapes.
• Also, we use prefer "than" when the comparison is between infinitives to infinitives ( infinitives are to+ first form of the verb).
• We use prefer "to" when the comparison is between noun to noun and gerund to gerund ( gerund is V+ing form of the verb).
• Therefore, the preposition 'to' should be used in place of the preposition 'than'.
  

Hence, the correct answer is option 2.

Correct Sentence: The invited guests preferred orange juice to hot coffee or chilled grapes.

The correct answer is 'As much as'.

Key Points

• In the underlined segment, the adjective 'many' is incorrect.
• The adjective 'many' means a large number. We use "as many as" for countable nouns.
• The adjective 'much' means a great amount or quantity. We use "as much as" for uncountable nouns.
• Therefore, the adjective 'much' should be used in place of the adjective 'many'.
  

Hence, the correct answer is option 1.

The Correct Sentence is: As much as I care for her, I still have to disagree with her on this topic.

The correct answer is 'The members of the team were received by the coach with great excitement'.

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice and 'The coach' is the subject and 'the members of the team' is the object.
• When we convert this sentence into passive voice, the subject 'The coach' of the active voice becomes the object, the object 'the members of the team' becomes the subject.
• The passive format "'were + V3 (received)" should be used.
• This is the active and passive voice rule for the past simple tense.
  

Hence, the correct answer is option 4*.*

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:
  

The correct answer is 'ACDB'.

Key Points 

• The sentence 'A' is independent of any other sentences as it is giving general information about the noun "Anush". Hence, 'A' is the first part.
• The "street dog" mentioned in the sentence 'C' refers back to the 'stray dogs' mentioned in the sentence 'A'. Hence, 'C' follows 'A'.
• The pronoun "him" mentioned in the sentence 'D' refers back to the noun "Anush" mentioned in the sentence 'C'. Hence, 'D' follows 'C'.
• The sentence 'B' is the concluding sentence. Hence, 'B' is the last sentence.
  

Paragraph after rearranging the sentences: Anush was very afraid of stray dogs. One evening, when a street dog barked at him, Anush turned and started running. The dog ran after him barking loudly and fiercely. Anush’s mother saw the dog chasing her son.

Hint

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'relocate'.

Key Points

• Let us explore the given options:-
• The word 'reschedule' means to change the time of a planned event.
• The word 'relocate' means to move to a new place and establish one's home or business there.
• The word 'reinstate' means to restore someone or something to their former position or state.
• The word 'restart' means to start again.
  

Hence, the correct answer is option 2*.*

The correct answer is 'its'.

Key Points

• Let us explore the given options:-
• The word 'their' means belonging to or associated with the people or things previously mentioned or easily identified.
• The word 'its' means belonging to or associated with a thing previously mentioned or easily identified.
• The word 'their's' is a contraction of ''there is'' or ''there has''.
• The word 'it's' is a contraction of ''it is'' or ''it has''. "'It’s'' is the same type of contraction as ''where’s'' or ''there’s''.
  

Hence, the correct answer is option 2*.*

The correct answer is 'hit'.

Key Points

• Let us explore the given options:-
• The word 'produced' means caused a particular result or situation to happen or exist.
• The word 'bagged' means succeeded in securing something.
• The word 'hit' means to reach a particular level, point, or figure.
• The word 'leaped' means moved quickly and suddenly.
  

Hence, the correct answer is option 3*.*

The correct answer is 'severely'.

Key Points

• Let us explore the given options:-
• The word 'dissatisfied' means not content or happy with something.
• The word 'conditionally' means in a way that is subject to one or more conditions or requirements being met.
• The word 'separate' means different; distinct.
• The word 'severely' means to an undesirably great or intense degree.
  

Hence, the correct answer is option 4*.*

The correct answer is 'respiratory'.

Key Points

• Let us explore the given options:-
• The word 'brain' is a person's mind.
• The word ''respiratory' is relating to or affecting respiration or the organs of respiration.
• The word 'abdominal' is relating to the abdomen.
• The word 'renal' is relating to the kidneys.
  

Hence, the correct answer is option 2*.*

The correct answer is 'Planned'.

Key Points  

• The word 'Casual' means happening by chance.
• The antonyms of the word 'Casual' are "planned, intended, intentional".
• From the antonym of the given word, we can say that the word 'Planned' is the opposite in meaning.
• The word 'Planned' means design or make a plan in advance.
  

Hence, the correct answer is option 1. Let's see the meaning of other given options-

Additional Information

• The synonyms of the word 'Casual' are "unintended, unintentional, unplanned".
• Example of 'Casual​​' in a sentence:
• She had a purposeful air, and it became evident that this was not a casual visit.

The correct answer is 'The traveler inquired if there would be a shelter for strangers'

Key Points

• The given sentence is a direct speech.
• The basic rules for changing or converting direct speech into indirect speech:​
• The commas and inverted commas are removed and the 'question mark' is replaced by 'full stop' and 'if' is included.
• The present simple tense format 'Subject + V1 (will) + Object' will be changed into the past simple tense format 'Subject + V2 (would) + Object'.

Hence, the correct answer is option 3.

Additional Information

• The following table will enable us to know how tense changes into Indirect speech:-

The correct answer is 'Something promising is there in any difficult situation'.

Key Points

• Given Idiom: Every cloud has a silver lining means there is something good in everything that’s bad.
• Example: Don't be so grumpy and pessimistic every cloud has a silver lining.
• From the given options, the second option is the most appropriate meaning of the given idiom.
  

Hence, the correct answer is option 2.

Mistake Points

• We may think from the phrase "Every cloud has a silver lining" that it is all about a silver lining on a cloud, but the correct answer is option 2. So be careful while dealing with such questions.
  

Additional Information

• It appears that the origin of this phrase is in 1634 from John Milton’s poem “Comus.” The phrase has been in use in its exact form since the mid-1800s.

The correct answer is 'funniest'.

Key Points

• Let us explore the given options:
• The adjective 'primary' means of chief importance; principal.
• The adjective 'major' means important, serious, or significant.
• The adjective 'funniest' means causing laughter or amusement; humorous.
• The adjective 'real' means actually existing as a thing or occurring in fact; not imagined or supposed.
  

Complete Sentence: The funniest part of this issue is that the investigation officer himself turned out to be the culprit.

Hence, the correct answer is option 3.

The correct answer is 'DCAB'.

Key Points 

• The sentence 'D' is independent of any other sentences as it is giving general information about the nouns "Navin and Jathin". Hence, 'D' is the first part.
• The pronoun "They" mentioned in the sentence 'C' refers back to the nouns 'Navin and Jathin' mentioned in the sentence 'D'. Hence, 'C' follows 'D'.
• The phrase "group of young men" mentioned in the sentence 'A' is linked with the noun "village" mentioned in the sentence 'C'. Hence, 'A' follows 'C'.
• The sentence 'B' is the concluding sentence. Hence, 'B' is the last sentence.
  

Paragraph after rearranging the sentences: Navin and Jathin were brothers and brave fighters. They lived in a jungle hideout on the banks of a river in the village. Navin and Jathin gathered a group of young men and trained them in the fighting. They wanted to build their own village where people could live without fear.

Hint

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is 'Entirely false and fabricated'.

Key Points

• Given Idiom: Made out of whole cloth means completely fabricated and not based on reality at all.
• Example: This report is positively denied in official circles, who affirm that nothing of the kind occurred, but that the story is made out of whole cloth.
• From the given options, the third option is the most appropriate meaning of the given idiom.
  

Hence, the correct answer is option 3.

Mistake Points

• We may think from the phrase "Made out of whole cloth" that it is all about something made out of the cloth, but the correct answer is option 3. So be careful while dealing with such questions.
  

Additional Information

• In the 15th century, this expression referred to something fabricated from cloth that ran the full length of the loom. However, by the 1800s it was common practice for tailors to deceive their customers and, instead of using whole cloth, actually make garments from pieced goods. Their advertising slogan, "cut out of whole cloth," thus came to mean "made up, false."

The correct answer is 'Hymn'.

Key Points

• Let us explore the given options:-
• 'Epic' is a long poem.
• 'Hymn' is a religious song or poem of praise to God or a god.
• 'Elegy' is a poem of serious reflection, typically a lament for the dead.
• 'Ode' is a classical poem of a kind originally meant to be sung.
  

Hence, the correct answer is option 2*.*

The correct answer is 'Homogeneous'.

Key Points

• Let us explore the given options:-
• 'Homosexual' means sexually attracted to people of one's own sex.
• 'Homogeneous' means of the same kind; alike.
• 'Homonymous' means having the same name.
• 'Homophony' is the quality or state of being having the same sound.
  

Hence, the correct answer is option 2*.*

The correct answer is 'Querulous'.

Key Points

• The word 'Quarrelsome' means 'the feeling or displaying an eagerness to fight'
• The synonyms of the word 'Quarrelsome' are "querulous, rude, petulant".
• From the synonym of the given word, we can say that the word 'Querulous' has the same in meaning.
• The word 'Querulous' means complaining in a rather petulant or whining manner.
  

Hence, the correct answer is option 2. Let's see the meaning of other given options:-

Additional Information

• The antonyms of the word 'Quarrelsome' are "calm, quiet, relaxed".
• Example of 'Quarrelsome' in a sentence:
• The boy is quarrelsome and ready to fight at the drop of a hat.

The correct answer is 'Unlikely'.

Key Points  

• The word 'Plausible' means worthy of being accepted as true or reasonable.
• The antonyms of the word 'Plausible' are "unlikely, unbelievable, unplausible".
• From the antonym of the given word, we can say that the word 'Unlikely' is the opposite in meaning.
• The word 'Unlikely' means not likely to be true or to occur.
  

Hence, the correct answer is option 4. Let's see the meaning of other given options-

Additional Information

• The synonyms of the word 'Plausible' are "dependable, reliable, trustworthy".

• Example of 'Plausible​​' in a sentence:

• She could find no plausible explanation for its disappearance.

• 'Plausible' शब्द का अर्थ है सत्य या उचित के रूप में स्वीकार किए जाने योग्य।

• शब्द 'Plausible' का विलोम "unlikely, unbelievable, unplausible" कर रहे हैं।

• दिए गए शब्द की विलोम से, हम कह सकते हैं कि शब्द 'Unlikely' अर्थ में विपरीत है।

• 'Unlikely' शब्द का अर्थ है   सच होने या होने की संभावना नहीं है।

इसलिए, सही उत्तर विकल्प 4 है । आइए देखते हैं अन्य दिए गए विकल्पों का अर्थ-

The correct answer is 'Balancing'.

Key Points

• The word 'Adjustment' means the act or process of changing something to fit a new use or situation.
• The synonyms of the word 'Adjustment' are "balancing, attunement, adjusting".
• From the synonym of the given word, we can say that the word 'Balancing' is the same in meaning.
• The word 'Balancing' means to make equal in amount, degree, or status.
  

Hence, the correct answer is option 4. Let's see the meaning of other given options:-

Additional Information

• The antonyms of the word 'Adjustment' are "unbalancing, disproportioning, supporting".
• Example of 'Adjustment' in a sentence:
• The company made an adjustment in my salary.

The correct answer is 'As long as'.

Key Points

• In the underlined segment, the phrase 'So much as' is incorrect.
• The phrase 'So much as' means even.
• The phrase 'As long as' means provided that.
• The phrase 'In as much as' means since, because or to the extent that.
• The phrase 'As much to' means the same to.
  

Hence, the correct answer is option 2.

Correct Sentence: As long as you are their class teacher, you are responsible for their performance in the examination.

The correct answer is 'Simultaneoues'.

Key Points    

• Let us explore the options:-
• 'Simulation' means the imitation of a situation or process.
• 'Simultaneoues': There is no such word in English or we can say that there is some spelling mistake in this word.
• The correct spelling is 'Simultaneous' which means occurring, operating, or done at the same time.
• 'Stylistics' is the study of the distinctive styles found in particular literary genres and in the works of individual writers.
• 'Synthetic' means (of a substance) made by chemical synthesis, especially to imitate a natural product.
  

Hence, the correct answer is option 2.

The correct answer is 'tumor'.

Key Points

• Let us explore the given options:
• The noun 'tremor' means a sudden feeling of fear or excitement.
• The noun 'treasure' means a number of precious metals, gems, or other valuable objects.
• The noun 'tumor' means the swelling of a part of the body, generally without inflammation.
• The noun 'tuber' means a much thickened underground part of a stem or rhizome.
  

Complete Sentence: There was a huge tumor in the stomach.

Hence, the correct answer is option 3.

The correct answer is 'Everyone are'.

Key Points

• In the given sentence, the use of the plural form of the verb 'are' is incorrect.
• We know that a singular 'subject' will always take a singular 'verb'.
• The singular subject 'Everyone' will take the singular verb 'ís'.
• Therefore, the singular verb 'is' should be used in place of the plural verb 'are'.
  

Hence, the correct answer is option 3.

Correct Sentence: Everyone is very well equipped with his own weapons.

Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if a subject is plural, its verb must also be plural.
• दिए गए वाक्य में, verb के plural रूप 'are' का उपयोग सही नहीं है।
• हम जानते हैं कि एक singular 'subject' हमेशा एक singular verb लेगा ।
• Singular subject 'everyone' singular verb 'ís' लेगा ।
• इसलिए,  singular verb 'is' का उपयोग plural verb के स्थान पर किया जाना चाहिए।

इसलिए, सही उत्तर विकल्प 3 है ।

सही वाक्य: Everyone is very well equipped with his own weapons.

The correct answer is 'Navigetion'.

Key Points    

• Let us explore the options:-
• 'Combination' is a joining or merging of different parts or qualities in which the component elements are individually distinct.
• 'Molestation' is a sexual assault or abuse of a person.
• 'Condonation' means the implied pardon of an offense by treating the offender as if it had not been committed.
• 'Navigetion': There is no such word in English or we can say that there is some spelling mistake in this word.
• The correct spelling is 'Navigation' which means the process or activity of accurately ascertaining one's position and planning and following a route.
  

Hence, the correct answer is option 4.

The logic is:

Boxing : Ring → A boxing ring, often referred to simply as a ring or euphemistically the squared circle, is the space in which a boxing match occurs.

Similarly,

Race : ? → A race track (racetrack, racing track or racing circuit) is a facility built for racing of vehicles, athletes, or animals.

Hence, ‘Track’ is the correct answer.

The logic is:

25 × 5 – 5 = 120

23 × 7 – 7 = 154

Similarly,

? × 13 – 13 = 156

⇒ ? × 13 = 156 + 13

⇒ ? × 13 = 169

⇒ ? = 13

Hence, ‘13’ is the correct answer.

The logic is:

2197 : 12167 → 13³ : (13 + 10)³

Similarly,

343 : ? → 7³ : (7 + 10)³

⇒ ? = 17³

⇒ ? = 4913

Hence, ‘4913’ is the correct answer.

According to given conditions,

T is the brother of M.

Hence, ‘Brother’ is the correct answer.

Let the number be a.

According to question:

a + 1/a = 17/4

⇒ (a² + 1)/a = 17/4

⇒ 4(a² + 1) = 17a

⇒ 4a² + 4 = 17a

⇒ 4a² – 17a + 4 = 0

⇒ 4a² – (16 + 1)a + 4 = 0

⇒ 4a² – 16a – a + 4 = 0

⇒ 4a (a – 4) – 1(a – 4) = 0

⇒ (4a – 1) = 0 or (a – 4) = 0

⇒ a = 1/4 or a = 4

Hence, ‘4 and 1/4’ is the correct answer.

The logic is:

1. 224 → 15² - 1

2. 196 → 14²

3. 360 → 19² - 1

4. 528 → 23² - 1

Hence, ‘196’ is the odd one out.

When the mirror is placed on line MN in the question figure, then the correct mirror image of the question figure is shown below:

Hence, ‘option 1’ is the correct answer.

The number of cubes in the given figure is 6 × 6 × 6

= 216

Hence, ‘216’ is the correct answer.

The paper when unfolded will appear as shown below:

Hence, ‘option 2’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Note: Sum of the place value of the letters is equal to the number between the letters.

C10G

H20L

L17E

L?Q

So ‘?’ will be replaced by 29 in L?Q.

Hence, ‘29’ is the correct answer.

Number of persons who like only teaching and playing but NOT cooking = 21 + 6 + 14

= 41

Hence, ‘41’ is the correct answer.

1. oomn

mnop / mnoo / mnop / mnop

No particular pattern is formed/repeated when the series is divided into four equal parts.

2. oppn

mnop / mnop / pnop / mnop

No particular pattern is formed/repeated when the series is divided into four equal parts.

3. opmn

mnop / mnop / mnop / mnop

‘mnop’ is repeating itself when the series is divided into four equal parts.

4. mpmo

mnmp / mnop / mnop / moop

No particular pattern is formed/repeated when the series is divided into four equal parts.

Hence, ‘opmn’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Instead of ‘LKM’, it should be ‘LMK’.

Hence, ‘LKM’ does NOT belong to the following series.

The pattern followed here is:

According to the alphabetical positions of the letters,

Letters are coded by their place values.

Similarly,

Hence, ‘OBCF’ is the correct answer.

The logic is:

3³ + 3 = 30

5³ + 5 = 130

7³ + 7 = 350

9³ + 9 = 738

Hence, ‘738’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘OOLXSJ’ is the correct answer.

The number of triangles in the given figure is shown below:

Total triangle in the given figure = 32

1. Counting triangle only in one square.

Number of partition in square = 8

Total number of triangle in square= 8 × 2 = 16

2. There is another symmetrical square inside the first square. 

So,

Total number of triangle = 16 × 2 = 32.

Hence 32 is the correct answer.

The answer figure ‘2’ when placed in the blank space of the question figure will complete the pattern, which is shown below:

Hence, ‘option 4’ is the correct answer.

The least possible Venn diagram is:

1. All animals are birds. → False (It is definite)
2. All animals are men. → False (It can be possible but it is not definite)

Hence, neither conclusion 1 nor 2 follows.

The pattern followed here is:

According to the alphabetical positions of the letters,

In place of ‘T’, it should be ‘S’.

Hence, ‘T’ is the odd one out.

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

Hence, ‘option 2’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘G’ is the correct answer.

Given expression: 15 @ 2 ÷ 900 & 10 # 50

By replacing the symbols by their meaning, we get:

15 × 2 + 900 ÷ 10 – 50

= 30 + 90 – 50

= 120 – 50

= 70

Hence, ‘70’ is the correct answer.

The logic is:

1^st column: (11 + 5 + 3)² = 361

2^nd column: (17 + 3 + 7)² = 729

Similarly,

3^rd column: (8 + 15 + ?)² = 1225

⇒ (8 + 15 + ?) = $\sqrt {1225}$

⇒ (8 + 15 + ?) = $\sqrt {35 \times 35}$

⇒ 23 + ? = 35

⇒ ? = 35 – 23

⇒ ? = 12

Hence, ‘12’ is the correct answer.

The logic is:

Hence, ‘331’ is the correct answer.

Given:

In ΔABC

∠ABC = 90º 

AC = 10 cm 

BC = 8 cm 

Formula Used:

Pythagoras therom 

AC2 = AB2 + BC2

Calculation:

Using pythagoras therom

10² = AB² + 8²

100 - 64 = AB²

AB² = 36

AB = 6 cm  

 ∴ The length of AB is 6 cm

Given:

18% of 15% of 25/9 of 3800 

Calculation:

18% of 15% of 25/9 of 3800 = (18/100) × (15/100) × (25/9) × 3800

18% of 15% of 25/9 of 3800 = 15 × 19 ⇒  285 

∴ The value of 18% of 15% of 25/9 of 3800 is 285

Given:

x : y = 3 : 2

x + y = 90

Calculation:

Let us take the value of x and y be 3a and 2a

x + y = 3a + 2a 

⇒ 3a + 2a = 90

⇒ 5a = 90 

⇒ a = 18

⇒ x = 3a = 54 

⇒ y = 2a = 36

⇒ x - y = 54 - 36 = 18

 ∴ The value (x - y) is 18

Given:

The average age of 65 men = 32 years

Number of new men added = 5

The average ages of 70 men = 34 years

Formula Used:

Average  = Sum of the observation/Total number of observation

Calculation:

Sum of the age of men =  Average × Total number of men 

Sum of the  age of 65 men = 32 × 65 = 2080

Sum of the age of 70 men = 70 × 34 = 2380

Sum of the age of 5 men = Sum of the age of 70 men - Sum of the  age of 65 men

Sum of the age of 5 men = 2380 - 2080 = 300 

Average of 5 men added newly = 300/5 = 60 

 ∴ The average of the ages of those 5 men joined later is 60

Given:

 In Δ ABC

DE is parallel to BC 

AE = 4 cm

AD = 3 cm

AC = 10 cm 

Concept Used:

AAA' similarity rule

If three angles of two triangles are equal then corresponding sides of similar triangles are proportional

Calculation:

If DE is parallel to BC 

∠A = ∠A (Common)

∠ADE = ∠ABC (corresponding angles of parallel sides are equal)

∠AED = ∠ACB (corresponding angles of parallel sides are equal)

By AAA similarity Δ ABC and Δ ADE are similar

then corresponding sides of two triangle  are in ratio

AD/AB = AE/AC = DE/BC 

(AD/AB) = (AE/AC)

⇒ 3/AB = 4/10

⇒ AB = 15/2 = 7.5 cm

As, AB = AD + BD

⇒ 7.5 = 3 + BD

⇒ 7.5 - 3 = BD

⇒ BD = 4.5 cm

∴ The value of BD is 4.5 cm

Given:

Dividend₁ = kx3 + 4x2 + 3x - 4

Dividend₂ = x3 - 4x + k

Divisor = (x - 3)

Formula Used:

Dividend = (divisor × quotient) + Reminder

Calculation:

x - 3 = 0 

Then, x = 3

By substituting the value of x, we'll get

kx3 + 4x2 + 3x - 4 = k(3)³ + 4(3)² + 3(3) - 4 = 27k + 36 + 9 - 4 = 27k + 41      ----(i)

x3 - 4x + k = 3³ - 4(3) + k = 27 - 12 + k = 15 + k      ----(ii)

Both the dividends leave equal reminders  then equating (i) and (ii)

27k + 41 = 15 + k

⇒ 26k = -26

⇒ k = -1

∴ The value of k is -1

Given:

$\frac{{\sin x + \cos x}}{{\sin x - \cos x}} = \frac{6}{5}$

Concept Used:

Componendo & dividendo

a/b = c/d

then (a + b)/(a - b) =(c + d)/(c - d)

Calculation:

$\frac{{\sin x + \cos x}}{{\sin x - \cos x}} = \frac{6}{5}$

By using componendo & dividendo

(sinx + cosx + sinx - cos x)/(sinx + cosx - sinx + cosx)  = (6 + 5)/(6 - 5)

(2sinx/2cosx) = (sinx/cosx) = 11/1

tan²x = (sin²x/cos²x) = 11²/1² = 121

tan²x + 1 = 121 +1 =122

tan²x - 1 = 121 - 1 = 120 

$\frac{{{{\tan }^2}x + 1}}{{{{\tan }^2}x - 1}}$ = 122/120 = 61/60

∴ The value of $\frac{{{{\tan }^2}x + 1}}{{{{\tan }^2}x - 1}}$ is 61/60

Given:

Sinx = 3/5 

Formula Used:

sinθ = perpendicular/hypotenuse 

cosθ = Base/hypotenuse

cotθ = cosθ/sinθ  

Calculation:

cotx × secx = (cosx/sinx) × 1/cosx = 1/sinx 

⇒ cotx × secx = 1/(3/5) = 5/3

∴ The value of  ​$\cot x.\sec x$ is 5/3

Given

MP of book is Rs.900.

Two successive discount is 10% each

Formula used

MP(1 - D/100) = SP

D = Discount5

SP = Selling Price

MP = Marked Price

Calculation

MP of a book is Rs.900.

⇒ Net discount = 10 + 10 - (10 × 10)/100

⇒ 19%

⇒ MP(1 - D/100) = SP

⇒ MP(1 - 19//100) = SP

⇒ MP × 81/100 = SP

⇒ SP = MP × 81 / 100

⇒ SP = 900 × 81 / 100

∴ Selling Price of book is Rs.729

Alternate Method

MP      SP

10         9

10         9

100      81

100 unit = 900

81 unit = 900 × 81 / 100

∴ SP is Rs.729

Given

Calculation:

Sales : Production = 196 : 245

⇒ Sales : Production = 4 : 5

∴ Ratio of Sales : Production is 4 : 5

Given:

If a = 2b

Calculation:

If a = 2b

⇒ (a + b) / (a - b) = (2b + b) / (2b - b)

⇒ 3b / b

∴ The value of $\frac{{a + b}}{{a - b}}$ is 3.

Given:

$8 - [8 - (5 + 8) - { 8 - (8 - 5 + 8)} + 10]$

Concept used:

Calculation:

8 - [8 - 13 - {8 - 11} + 10]

⇒ 8 - [8 - 13 +3 + 10]

⇒ 8 - 8

∴ This value is 0

Given

Ravi sells a chair to Mohan at a profit 10%.

Mohan sells it to Govind at profit 20%.

Govind pays Rs.1,320 for it.

Formula used

Profit ={( SP - CP) / CP} × 100

SP = Selling Price

CP = Cost Price

Calculation

Let Cost Price be Rs.x

⇒ After sells chair to Mohan at 10% CP becomes x × 110 / 100

⇒ This CP becomes SP for Govind. Govind got profit of 20% = x × (110 / 100) × 120 / 100

⇒ x (11 × 12) / 100 = 1320

⇒ x = (1320 × 100) /132

∴ CP of chair is Rs.1000

Alternate Method

Net profit = 10 + 20 + (10 × 20) / 100 = 32%

CP × (1 + 32 / 100) = 13200

CP = Rs.1000

Given:

A sum of money becomes five times itself

Rate =16% p.a

Formula used:

SI = (P × R × T) / 100

SI = Simple Interest

P = Principal

T = Time

R = Rate

Calculation:

Let initially Principal be x

⇒ It becomes 5x in t time perod

⇒ Simple interest = 5x - x 

⇒ 4x

⇒ 4x = (x × 16 × t) / 100

⇒ 4 × 100 = 16t

⇒ t = 25 years

∴ It takes 25 years to become 5 times

Given:

Calculation:

Production difference between F1 and F2 = 660 - 520

⇒ 140

⇒ Percentage = 140 / 660 × 100 = $21\frac{7}{{33}}\%$

∴ $21\frac{7}{{33}}\%$

Given

$[{({a^2} - {b^2})^3} + {({b^2} - {c^2})^3} + {({c^2} - {a^2})^3}] \div [{(a - b)^3} + {(b - c)^3} + {(c - a)^3}]$

Formula used

We know than if (a + b + c) = 0

Then, a³ + b³ + c³ = 3abc

Calculation

(a² - b²) + (b² - c²) + (c² - a²) = 0, then

⇒ (a2 - b2)³ + (b2 - c2)³ + (c2 - a2)³ = 3(a2 - b2)(b2 - c2)(c2 - a2) 

⇒ Similarly

⇒ (a - b) + (b - c) + (c - a) = 0

⇒ Then, (a - b)³ + (b - c)³ + (c - a)³ = 3(a - b)(b - c)(c - a)

⇒ {(a2 - b2)3 + (b2 - c2)3 + (c2 - a2)³} /  {(a - b)3 + (b - c)3 + (c - a)3}

⇒ {3(a2 - b2)(b2 - c2)(c2 - a2)} / 3{(a - b)(b - c)(c - a)}

⇒ {(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)} / {(a - b)(b - c)(c - a)}

∴ (a + b)(b + c)(c + a)

Let put the any values of a , b and c 

L et a be 0, b be 1 and c be 2

{(0 - 1)³ + (1 - 4)³ + (4 -  0)³} / ( 0 - 1)³ + (1 - 2)³ + (2 - 0)³

(-1 -27 + 64) / (-1 + -1 + 8)

36 / 6 = 6

Now satisfy option

1 = (0 + 1((1 + 2)(2 + 0) = 6

∴ Option 1 is correct

Given:

Ravi, Mohan, and Govind can complete a task in 12 days, 10 days and 15 days, respectively.

Calculation:

Ravi can complete a task in 12 days

⇒ Ravi can do one day work = 1/12  

Mohan can complete a task in 10 days

⇒ Mohan can do one day work = 1/10  

Govind can complete a task in 15 days

⇒ Govind can do one day work = 1/15

Ravi, Mohan and Govind work together in one day 

⇒ 1/12 + 1/10 + 1/15

⇒ (5 + 6 + 4)/60

⇒ 1/4

Ravi, Mohan and Govind can finish the wrok in

⇒ 4 days

∴ Ravi, Mohan and Govind together complete the same task in 4 days.

Ravi, Mohan, and Govind can complete a task in x days, y days and z days.

Formula used:

The three person work together, they can finish the work in xyz/(xy + yz + zx)

The number of days taken by Ravi, Mohan and Govind together complete the same task

⇒ 12 × 10 × 15/(12 × 10 + 10 × 15 + 15 × 12)

⇒ 1800/450

⇒ 4 days

∴ Ravi, Mohan and Govind together complete the same task in 4 days.

Ravi + Mohan + Govind work together = total work unit/per day unit

⇒ 180/(15 + 18 + 12)

⇒ 180/45

⇒ 4 days

∴ Ravi, Mohan and Govind together complete the same task in 4 days.

Given:

The radius of circular cone = R

Height of cone = H

Calculation:

The volume of circular cone = (1/3) × Base area × Height 

⇒ The volume of circular cone = (1/3) × πR² × H

⇒ The volume of circular cone = (1/3)πR²H

∴  The volume of cone is (1/3)πR2H.

Given:

A motorboat goes 24 km in 2 hour along the stream and 10 km in 1 hour against the stream. 

Formula used:

Speed of motor boat = 1/2(downstream speed + upstream speed)

Calculation:

Speed of motor boat along with stream(downstream speed) = distance/time

⇒ 24/2

⇒ 12 km/hr

Speed of motor boat against with stream(upstream speed) = distance/time

⇒ 10/1

⇒ 10 km/hr

According to the question,

Speed of motor boat = 1/2(downstream speed + upstream speed)

⇒ (12 + 10)/2

⇒ 11 km/hr

∴ The speed of the motorboat in kilometres per hour, is 11.

Given:

A circle with center O, OX, and OY are two tangents to be the circle drawn from an external point Z.

Construction:

Join OX, OY, and OZ.

Calculation:

It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.

OX perpendicular to ZX

OY perpendicular to ZY

In ΔOXZ and ΔOYZ

⇒ OZ = OZ (common side)

⇒ OX = OY (radius)

⇒ ∠OXZ = ∠OYZ = 90^o (It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact.)

Then, ΔOXZ is congrants to ΔOYZ

⇒ ZX = ZY (Corresponding part of a triangle are equal.)

∴ The length of tangents drawn from an external point to the circle are equal.

Given:

Concept used:

Percentage = (sale/production) × 100

Calculation:

According to the question,

F1 farmer percentage of sales with respect to the production

⇒ (410/520)× 100

⇒ 78.8%

F2 farmer percentage of sales with respect to the production

⇒ (500/660)× 100

⇒ 75.75%

F3 farmer percentage of sales with respect to the production

⇒ (430/550)× 100

⇒ 78.18%

F4 farmer percentage of sales with respect to the production

⇒ (620/720)× 100

⇒ 86.11%

∴ F4 farmers recorded the highest percentage of sales with respect to the production.

Concept used:

Divisibility of 11 – Difference between the sum of digits at odd and even places will be zero or multiple of 11.

Divisibility of 7 – Subtract the twice of unit digit from remaining number and check if Resultant number is divisible by 7

Calculation:

Divisibility of 11 – Difference between the sum of digits at odd and even places will be zero or multiple of 11.

Divisibility of 7 – Subtract the twice of unit digit from remaining number and check if Resultant number is divisible by 7

We firstly check the numbers divisible by 11, if it satisfies then we proceed to check the divisibility of 7

16425 : (5 + 4 + 1) – (2 + 6)

⇒ 10 – 8 = 2

Not equal to zero or multiple of 11, hence not divisible by 11.

12235 : (5 + 2 +1) – (3 + 2)

⇒ 9 – 5 = 4

4 is not equal to zero or multiple of 11, hence not divisible by 11

16257 : (6 + 5) - (7 + 2 + 1)

⇒ 11 – 10 = 1

1 is not equal to zero or multiple of 11, hence not divisible by 11

16324 : (4 + 3 + 1) – (2 + 6)

⇒ 8 – 8 = 0

Difference is equal to zero, hence divisible by 11

For this only we check divisibility of 7

1632 – (2 × 4)

⇒ 1632 – 8 = 1624

162 – (2 × 4)

⇒ 162 – 8 = 154

15 – (2 × 4)

⇒ 15 – 8 = 7

This number is also divisible by 7

∴ 16324 is divisible by both 7 and 11.

Given:

Concept used:

Average of a crop in quintals = sum of all sold crop/number of farmer

Calculation:

Sum of all farmer sold of a crop in quintals = F1 + F2 + F3 + F4

⇒ 410 + 500 + 430 + 620

⇒ 1960 quintals

Average of a crop in quintals, sold by all farmers 

⇒ 1960/4

⇒ 490 quintals

∴ The average of a crop in quintals, sold by all farmers is 490.

Given:

A pair of tangents AB and AC are drawn from a point which is at a distance of 10 cm from the centre O of a circle of radius 6 cm.

Formula used:

Area of triangle = 1/2 × base × height

Area of quadrilateral = 2 × Area of triangle

Calculation:

In Δ ABO is congruent to Δ ACO,

Then, Area of quadrilateral ABOC is twice the Area of Δ ABO.

In Δ ABO

OA = 10 cm

OB = 6 cm

Since, tangent is perpendicular to radius at the point of contact.

By pythagoras' theorem,

⇒  AB² = AO² – OB²

⇒ AB = √(AO2 – OB2) 

⇒ √(100 – 36)

⇒ √64

⇒ AB = 8 cm

Area of Δ ABO = (1/2)× AB × OB

⇒ (1/2)× 8 × 6

⇒ 24 cm²

Area of quadrilateral ABOC = 2 × Area of Δ ABO

⇒ 2 × 24 cm²

⇒ 48 cm²

∴ The area in cm2 of quadrilateral ABOC, is 48.

Shortcut Trick

Substitute standard trigonometric values: Numerator = (1/2 × 1/2) + (1/√2 × 1/√2) = 1/4 + 1/2 = 3/4.

Denominator = √3 × √3 = 3.

Result = (3/4) ÷ 3 = 1/4.

∴ The correct answer is 1/4.

Alternate Method

Given:

Expression: (sin 30° cos 60° + cos 45° sin 45°) ÷ (tan 60° cot 30°)

Trigonometric Ratios:

⇒ sin 30° = 1/2

⇒ cos 60° = 1/2

⇒ sin 45° = 1/√2

⇒ cos 45° = 1/√2

⇒ tan 60° = √3

⇒ cot 30° = √3

Calculation:

⇒ Value = [(1/2 × 1/2) + (1/√2 × 1/√2)] ÷ (√3 × √3)

⇒ Value = [1/4 + 1/2] ÷ 3

⇒ Value = [1/4 + 2/4] ÷ 3

⇒ Value = [3/4] ÷ 3

⇒ Value = 3 / (4 × 3) = 1/4

∴ The correct answer is 1/4.

Additional Information

Complementary Angle Ratios

Sin θ = Cos (90° − θ) and Tan θ = Cot (90° − θ). This confirms sin 30° = cos 60° and tan 60° = cot 30°.

Standard Values

Always remember: sin 45° = cos 45° = 1/√2, tan 45° = 1, and tan 30° = 1/√3.

Pythagorean Identity

sin²θ + cos²θ = 1. For example, sin²45° + cos²45° = (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1.

The correct answer is Sweden.

Important Points

• The first Winter Paralympics Games were held in Sweden in 1976.
• In these games, athletes with physical disabilities (mobility disabilities, amputations, blindness and cerebral palsy) participate.
• 53 athletes from 16 nations participated in 1976.
• These are held after every 4 years.
• Organized and managed by International Paralympic Committee.
• These games are directly preceded by Winter Olympic Games.
• Classification of Paralympic Games –
• Alpine Skiing: 2 events – Slalom and Giant Slalom
• Biathlon: Combination of cross-country skiing with target shooting
• Cross-country Skiing: (known as Nordic Skiing) have 15 classifications
• Ice Sledge Hockey: only for males
• Wheelchair Curling: coed team event and need a wheelchair for mobility
• Para-snowboarding: introduced in 2012

Additional Information

• Russia: 11^th edition in 2014 (opened by President Vladimir Putin)
• Italy: 9^th edition in 2006 (opened by President Carlo Azegilo Ciampi), 14^th edition in 2026 (upcoming)
• Korea: 12^th edition in 2018 (opened by President Moon Jae-in)
• Current President of South Korea: Yoon Suk-yeol (2022)

• The 13^th edition will be held in Beijing China in March 2022.
• In the 1976 edition, there were only 2 sports i.e. Alpine Skiing and Cross-country skiing.

1976 Winter Paralympics Games logo held in Sweden

The correct answer is Virtual Reality Mark Up Language.

Key Points

• VRML stands for Virtual Reality Mark Up Language.​
• It is initials, originally known as the Virtual Reality Markup Language before 1995.
• It is a standard 3-dimensional (3D) interactive vector graphics representation file format, designed especially with the World Wide Web in mind.
• VRML is a text file format where, for example, it is possible to specify vertices and edges for a 3D polygon along with the surface color, UV-mapped textures, shininess, transparency, etc.
• URLs can be associated with graphical components so that when the user clicks on a specific graphical component, a web browser can pick up a web page or a new VRML file from the Internet.
• The user may interact with animations, sounds, lighting, and other aspects of the virtual world or they may be triggered by external events such as timers.
• A special Script Node enables the program code (e.g. written in Java or ECMAScript) to be added to a VRML file.
• VRML files are commonly referred to as "worlds" and have the extension .wrl (for example, island. wrl).
• VRML files are in plain text and usually compress well using gzip.
• It is useful for faster transfers over the Internet (some gzip compressed files use the .wrz extension).
• Many 3D modeling programs can save objects and scenes in VRML format.

Apartment Ground Plan in VRML

The correct answer is 1765.

Important Points

• Treaty of Allahabad was signed in 1765 by Shuja-ud-Daulah and Shah Alam II with Robert Clive marking the beginning of British Rule in India.
• Through this treaty, East India Company was granted to collect taxes from the eastern province of Bengal-Bihar-Orrisa in return for which Shah Alam II was given Kora and Allahabad.
• The company promised to support Shuja-ud-Daulah, Nawab of Awadh against attacks which made him dependent on the company for which he had paid Rs. 53 lakhs.
• This treaty followed the Battle of Buxar in which Mughal emperors were lost to the Company.
• This treaty made the company richer and now they didn’t require any money from England.
• Treaty of Allahabad was written by I’tisam-ud-Din who was a diplomat to the Mughal Empire.

Additional Information

• Treaties signed in 1766: Treaty of Batticaloa (Dutch Imperial possession in Sri Lanka)

• Nawab of Bengal was having only judicial powers but the power to collect revenue and taxed was vested in the company.

The correct answer is Pakistan.

Important Points

• World’s largest field hockey stadium having the maximum seating capacity is in Lahore, Pakistan named Gadaffi Hockey Stadium.
• It has a capacity of 45000.
• It is named after Muammar Gadaffi, the former Libyan leader.
• The final match of the 1990 Hockey World Cup was played at this stadium.

​

Additional Information

Hockey stadiums in –

• Netherlands: Hazelaarweg Stadion, Sportpark Klein Zwitserland, Wagener Stadium.
• Australia: Perth Hockey Stadium, Rockhampton Hockey Association (Stadium), Marrara Hockey Stadium.
• India: Sardar Vallabh Bhai Patel Stadium, Major Dhyan Chand Stadium, Jaypee Sports City Hockey Stadium.

• Birsa Munda International Hockey Stadium in Rourkela is the largest stadium in India.

Gadaffi National Stadium or National Hockey Stadium, Lahore

The correct answer is 1.74 x 10⁶ m.

Important Points

• The radius of the moon is 1737.1 km or 1.74 × 10⁶ m.
• Moon is the only natural satellite of Earth.
• Moon is the 5^th largest satellite in the Solar System.
• Moon’s age is believed to be 4.53 billion years.
• Moon is 2,38,855 miles away from the earth.
• The gravitational influence of the Moon produces tides on Earth and lengthens the Earth’s day.
• Other Points about Moon –
• Planetary mass object and differentiated rocky body
• Lacks atmosphere, hydrosphere, and magnetic field
• Sidereal period: 27.3 days and Synodic period: 29.5 days
• The lunar surface is non-reflective
• Components of Lunar surface: Silica, Alumina, Lime, Iron Oxide, Magnesia, Titanium dioxide, Sodium oxide

Additional Information

• 1^st manmade object to reach the moon: Luna 2 spacecraft (crewless) in 1959 by the Soviet Union
• 1^st successful soft landing: Luna 9 in 1966
• 1^st manned mission: Apollo 8 in 1968

• Lunar Eclipse: (Full moon) Earth is between Sun and Moon
• Solar Eclipse: (New moon) Moon is between Earth and Sun

Tinted reddish moon during the lunar eclipse

The correct answer is a market system of resource allocation, commerce, and trade in which free markets coexist with government intervention.

Key Points

• In a socialist society the government decides what goods are to be produced in accordance with society's needs.
• In a mixed economy, the market will supply whatever goods and services it can produce well, and the government will provide essential goods and services that the market fails to do.
• The mixed economic system is described as an economic system which combines the elements of a planned economy with those of a market economy.
• It is a mixture of capitalism and socialism, comprising both private and public corporations.
• A mixed economy structure is adopted by most developed economies.
• The elements of a capitalist economy and the elements of a command economy are synthesized into a mixed economic structure.
• Free economies co-exist with government interference in a mixed economic environment, and private businesses coexist with public enterprises.
• The benefits of a mixed economy include efficient production and capital distribution, as well as social security development.

Flowchart showing Mixed Economy Model

The correct answer is Christina Koch.

Important Points

• The longest-ever single spaceflight by a woman was accomplished by NASA astronaut Christina Koch.
• At about 09:12 GMT, the Russian Soyuz spacecraft carrying Koch parachuted down to the grasslands of Kazakhstan.
• She spent 328 days on the International Space Station (ISS), surpassing the previous record set by fellow American Peggy Whitson.
• Her stay is only 12 days shy of Scott Kelly, who was on the ISS from 2015-2016, setting the all-time US record.
• On 28 December 2019, Ms. Koch exceeded the 289-day mark held by fellow American Ms. Whitson.
• Yet her return to Earth is setting the marker to beat for future space explorers.
• Koch accomplished 5,248 orbits of the Earth during her mission and traveled 223 million km (139 million miles) - the equivalent of 291 round trips from Earth to the Moon.

Additional Information

• Peggy Whitson currently holds the record for a woman's most time spent in space, recorded over the span of three 2002-2017 spaceflights.

A file photo of Christina Koch

The correct answer is 4.

Important Points

• Based on historical seismic activity, the Bureau of Indian Standards has categorized regions in India into four seismic zones: zones II, III, IV and V.
• Of these, the most seismically active area is Zone V and the least active is Zone II.
• There is a history of devastating earthquakes on the Indian subcontinent.
• The key cause for the high frequency and severity of earthquakes is that the Indian plate is driving into Asia at a rate of roughly 47 mm/year.
• India's geological figures indicate that about 54 percent of the land is prone to earthquakes.
• Research by the World Bank and the United Nations predicts that by 2050, about 200 million urban dwellers in India will be vulnerable to storms and earthquakes.
• The most recent edition of India's seismic zoning map given in India's earthquake-resistant design code [IS 1893 (Part 1) 2002] assigns four degrees of seismicity in terms of zone factors for India.
• In other words, unlike its previous edition, which consisted of five or six zones for the region, India's earthquake zoning map divides India into four seismic zones (zones 2, 3, 4, and 5).
• According to the new zoning map, the maximum degree of seismicity is predicted in Zone 5, while the lowest level of seismicity is correlated with Zone 2.
• ​Additional Information:
• In late 2025, the Bureau of Indian Standards (BIS) released a major revision to the national seismic hazard map (under the new Earthquake Design Code, 2025).
• This update officially introduced Zone VI as the highest-risk category.
• However, later In March 2026, the government withdrew the 2025 seismic code
• The notification introducing Zone VI was cancelled
• India reverted back to the old 2016 code (IS 1893:2016)