The erroneous spelling is 'Possesions'.

Key Points

• Among the given Options the incorrectly spelt word is 'Possesions'
• Its correct spelling is ' Possessions'.
• It means 'the state of having or owning something किसी पर अधिकार या स्‍वामित्‍व'.
• Example: The gang was caught in possession of stolen goods.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Answer: Possesions.

Let's look at the meaning of other words:

• Irritation: the state of feeling annoyed, impatient, or slightly angry (जलन, दर्द)
• Protection: the act of keeping somebody/something safe so that he/she/it is not harmed or damaged (सुरक्षा, हिफ़ाज़त)
• Invitation: the act of inviting somebody or being invited (किसी को) निमंत्रित करने या (किसी के द्वारा) निमंत्रित होने की क्रिया; निमंत्रण

The correct answer is 'a nasal vaccine'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'a nasal vaccine' should be used instead of 'a nose-based vaccine'.
• In the given sentence the adjective of 'nose' that is 'nasal' should be used. To modify the word 'vaccine' we have to use the adjective 'nasal'.
• The word 'nasal' means 'of or for the nose'. (नाक का या नाक के लिए, नासिका-संबंधी)
• Example: Her voice took on a nasal whine of complaint.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Sentence: India has identified a nasal-based vaccine against Covid-19 that could be a 'game-changer'. 

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।
• यहां 'a nose-based vaccine' के स्थान पर 'a nasal vaccine' का प्रयोग किया जाना चाहिए।
• दिए गए वाक्य में 'nasal' अर्थात 'nose' के Adjective का प्रयोग किया जाना चाहिए। 'vaccine' शब्द को modify करने के लिए हमें 'nasal' के adjective का प्रयोग करना होगा।
• 'Nasal' शब्द का अर्थ है 'नाक के लिए'।
• ​Example: Her voice took on a nasal whine of complaint.
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 2 है।

The correct answer is 'Acoustics'.

Key Points

• The most appropriate meaning of the given group of words is 'Acoustics'.
• It means 'the qualities of a room, etc. that make it good or bad for you to hear music, etc. in किसी कमरे आदि की वे विशेषताएँ जिनसे गीत की ध्वनि अच्‍छी या बुरी सुनाई देती है; श्रवणगुण'.
• Example: The theatre has excellent acoustics.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Answer: Acoustics.

Let's look at the meaning of other words:

• Optics: the scientific study of sight and light दृष्टि और प्रकाश का वैज्ञानिक अध्ययन, दृष्टि-व-प्रकाश विज्ञान
• Photonics: the branch of technology concerned with the properties and transmission of photons, for example in fibre optics (फोटोन के गुणों और संचरण से संबंधित प्रौद्योगिकी की शाखा, उदाहरण के लिए फाइबर ऑप्टिक्स में)
• Mechanics: the science of how machines work यंत्रों या मशीनों की कार्यपद्घति का वैज्ञानिक अध्ययन; यांत्रिकी, यंत्रगति-विज्ञान

The correct answer is 'Contemptible'.

Key Points 

• The word 'Despicable' means 'very unpleasant or evil'. (निंदनीय, जघन्‍य)
• The synonyms of the word 'Despicable' are "cheap, contemptible, cruddy, deplorable, dirty, grubby, lame, lousy, mean, nasty, paltry, pitiable, pitiful, ratty, scabby, scummy, scurvy, sneaking, sorry, wretched".
• From the synonym of the given word, we can say that the word 'Contemptible' is the most similar in meaning.
• The word 'Contemptible' means 'not deserving any respect at all'. (तिरस्‍करणीय; तिरस्‍कार के योग्‍य)
  

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

Additional Information 

• The antonyms of the word 'Despicable' are "admirable, commendable, creditable, laudable, meritorious, praiseworthy".
• Example of 'Despicable' in a sentence:
• Yes, what she did early on was despicable in our minds, but put yourself in her position.

The correct answer is 'had grown quite tall'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'had grown quite tall' should be used instead of 'has grown quite taller'.
• The given sentence is in the past perfect tense. Hence, the use of present tense is grammatically incorrect.
• We need to follow the rule of parallelism as the subject 'Lavanya' is common in the whole sentence, so the same tense shall be used to make it grammatically correct.
• We tend to go for Option 4 but it would be incorrect because 'a superlative adjective is an adjective used in comparisons to describe something as being of the highest degree or extreme'.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Sentence: Lavanya was happy to see that the tree they had planted the previous year had grown quite tall.

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।
• यहां 'has grow quite taller' के बजाय 'had grown quite tall' का इस्तेमाल किया जाना चाहिए।
• दिया गया वाक्य Past perfect  Tense में है। इसलिए, Present Tense का उपयोग व्याकरणिक रूप से गलत है।
• हमें समानता के नियम का पालन करने की आवश्यकता है क्योंकि 'लावण्य' विषय पूरे वाक्य में सामान्य है, इसलिए इसे व्याकरणिक रूप से सही बनाने के लिए उसी काल का उपयोग किया जाएगा।
• हम विकल्प 4 के लिए जाते हैं लेकिन यह गलत होगा क्योंकि 'एक Superlative Adjective एक Adjective है जिसका उपयोग किसी चीज को उच्चतम डिग्री या चरम के रूप में वर्णित करने के लिए किया जाता है'।
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 1 है।

The correct answer is 'CDBA'.

Key Points

• The given question is an example of a  Para Jumble.
• We know that the first statement of a para jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence C will be the first sentence because it is talking about Michael Jackson and this is an introductory sentence.
• Sentence D will be the next sentence because it further explains the kind of work he used to do the exertion he used to put in his songs.
• Sentence B will be the next sentence because it is connected with the previous sentence.
• Lastly, Sentence A will be used.
• Thus, the correct sequence is:
• C: Michael Jackson, called the ‘King of Pop Music’, stayed at the top of his career for many years.
• D: He was respected for his work culture; he would spend long nights at the studio to fix a note correctly in a song.
• B: Unfortunately, he began spending lavishly on anything he desired, not what he actually needed.
• A: As a result, he had a debt of 500 million US dollars at the time of his death.
  

Correct Sequence: Michael Jackson, called the ‘King of Pop Music’, stayed at the top of his career for many years. He was respected for his work culture; he would spend long nights at the studio to fix a note correctly in a song. Unfortunately, he began spending lavishly on anything he desired, not what he actually needed. As a result, he had a debt of 500 million US dollars at the time of his death.

The correct answer is 'Having a close friendship'.

Key Points

• The most appropriate meaning of the given idiom 'Thick as thieves' is 'Having a close friendship'.
• Thick as thieves: of two or more people) very close or friendly; sharing secrets [दो या दो से अधिक लोगों में से) बहुत करीबी या मिलनसार; रहस्य साझा करना]'.
• Example: He and Auntie Lou were as thick as thieves.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

Correct Answer: Having a close friendship.

The correct answer is 'Unusual'.

Key Points 

• The word 'Accustomed' means 'if you are accustomed to something, you are used to it and it is not strange for you'. (किसी बात का आदी या अभ्‍यस्‍त)
• The antonym of the word 'Accustomed' is 'unapt, unlikely, unusual, averse, disinclined, opposed, inexperienced, new, unseasoned, disaccustomed, weaned'.
• The word 'Unusual' means 'not expected or normal'. (अप्रत्‍याशित या असामान्‍य)
  

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

Additional Information 

• The synonyms of the word 'Accustomed' are 'acquaint, familiarize, initiate, introduce, orient, orientate'.
• Example of 'Accustomed' in a sentence:
• She arrived early enough to get her accustomed seat in the front row.

The correct answer is 'Akhila was given a bouquet of lilies on her birthday by Sai Kumari.'

Key Points

• The given sentence is in Active Voice. As per the given question we have to change it into Passive Voice.
• The structure of the given sentence as follows:
• Subject + V2+ Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'Sai Kumari'.​​
• The object of the given sentence is 'Akhila'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'gave' will be changed into 'was given'.
• Lastly, the preposition  'by' will be added.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

​

Correct Sentence: Akhila was given a bouquet of lilies on her birthday by Sai Kumari.

Hinglish 

• ​दिया गया वाक्य Active Voice में है। दिए गए प्रश्न के अनुसार हमें इसे Passive Voice में बदलना है।
• दिए गए वाक्य की संरचना इस प्रकार है:
• Subject + V2+ Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• उदाहरण:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• दिए गए वाक्य का विषय 'Sai Kumari' है।​
• दिए गए वाक्य का object 'Akhila' है।
• Object के स्थान पर Subject रखा जाएगा और Subject के स्थान पर Object रखा जाएगा।
• 'gave' को 'was given' में बदल दिया जाएगा।
• अंत में, 'by' preposition जोड़ा जाएगा।
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 4 है।

The correct answer is 'drowned'.

Key Points

• The most appropriate word for the given blank is 'drowned'.
• It means '(used about a sound) to be so loud that you cannot hear somebody/something else आवाज़ का इतना ऊँचा होना कि कुछ और सुनाई न पड़े'.
• Example: His answer was drowned out by the loud music.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Sentence: His voice was drowned by the sound of the helicopter.

Let's look at the meaning of other words:

• Drawn: (of a person) looking strained from illness, exhaustion, anxiety, or pain. (एक व्यक्ति का) बीमारी, थकावट, चिंता, या दर्द से तनावपूर्ण लग रहा है।
• Dawned: to begin to grow light, after the night. (सवेरा होना, दिन निकलना)
• Driven: to control or operate a car, train, bus, etc. (कार, ट्रेन, बस आदि को नियंत्रित करना या चलाना, ड्राइव करना)

The correct answer is The students asked the teacher, “Where can we find the information for our project?”

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:
• 'Asked' will not be changed because the given question is an example of an interrogative sentence with a question word.
• Comma and inverted commas will be added.
• 'could' will be changed into 'can'.
• 'us' will be changed into 'they' and 'their' will be changed into 'our'. (indirect to direct)
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

Correct Sentence: The students asked the teacher, “Where can we find the information for our project?”

Hinglish

• दिया गया वाक्य Indirect Speech में है। प्रश्न के अनुसार हमें इसे Direct Speech में बदलना होगा।
• परिवर्तन की प्रक्रिया इस प्रकार है: 
• 'asked' नहीं बदला जाएगा क्योंकि दिया गया प्रश्न प्रश्नवाचक शब्द के साथ प्रश्नवाचक वाक्य का उदाहरण है।
• अल्पविराम और उल्टे अल्पविराम जोड़े जाएंगे।
• 'can' को 'could' में बदल दिया जाएगा।
• 'us' को 'they' में बदल दिया जाएगा और 'their' को 'our' में बदल दिया जाएगा। (अप्रत्यक्ष से प्रत्यक्ष)
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 3 है।

The correct answer is 'Prohibit'.

Key Points

• The most appropriate synonym of the given word 'Forbid' is 'Prohibit'.
• Forbid:  to not allow something. (किसी बात की मनाही होना; निषिद्घ, वर्जित होना)
• Example: Smoking is forbidden inside the building.
• Prohibit: to say that something is not allowed by law; to forbid. (क़ानून द्वारा किसी बात को मना करना; निषेध करना, प्रतिबंध लगाना)
• Example: The law prohibits children under 18 from buying cigarettes.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Answer: Prohibit.

Additional Information

Let's look at the meaning of other words:

• Encourage: to give hope, support or confidence to somebody (किसी को) प्रोत्‍साहित करना; (किसी की) हिम्‍मत बढ़ाना
• Close: to shut (बंद करना या होना)
• Adieu: a goodbye (अलविदा)

The correct answer is 'by the incident'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'for the incident' should be used instead of 'by the incident'.
• We know that 'ordered for' means 'to use your position of authority to tell somebody to do something or to say that something must happen आदेश, आज्ञा या हुक्‍म देना'.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Sentence: A probe has been ordered for the incident that occurred at the celebration.

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।
• यहां 'by the incident' के स्थान पर 'for the incident' का प्रयोग करना चाहिए।
• हम जानते हैं कि 'ordered for' का अर्थ है 'किसी को कुछ करने के लिए कहने या यह कहने के लिए कि कुछ होना चाहिए' अपने अधिकार की स्थिति का उपयोग करना।
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 1 है।

The correct answer is 'Hautily'.

Key Points

• Among the given Options the incorrectly spelt word is 'Hautily'.
• Its correct spelling is 'Haughtily'.
• It means 'disdainfully proud; scornfully arrogant (तिरस्कारपूर्वक गर्व; तिरस्कारपूर्वक अभिमानी)'.
• Example: She surveyed me haughtily over the top of her glasses.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Answer: Hautily.

Additional Information

• Let's look at the meaning of other words:
• Evidence: the facts, signs, etc. that make you believe that something is true सबूत, साक्ष्‍य, गवाही
• Discussion: the process of talking about something seriously or deeply चर्चा-परिचर्चा, विचार-विमर्श
• Resolute: having or showing great determination दृढ़निश्‍चयी, कृतसंकल्‍प

The correct answer is 'DBCA'.

Key Points 

• The given question is an example of a  Para Jumble.
• We know that the first statement of a para jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence D will be the first sentence because it is an introductory sentence explaining the sports.
• Sentence B will be the next sentence because it further explains the definition of sports.
• Sentence C will be the next sentence because it is connected with the previous sentence.
• Lastly, Sentence A will be used.
• Thus, the correct sequence is:
• D: Sports are part of every culture, past and present, but each culture has its own definition of sports.
• B: The most useful definitions are those that clarify the relationship of sports to play, games and contests.
• C: “Play,” wrote the German theorist Carl Diem, “is purposeless activity, for its own sake, the opposite of work.”
• A: Humans work because they have to; they play because they want to.
  

Correct Sequence: Sports are part of every culture, past and present, but each culture has its own definition of sports. The most useful definitions are those that clarify the relationship of sports to play, games and contests. “Play,” wrote the German theorist Carl Diem, “is purposeless activity, for its own sake, the opposite of work.” Humans work because they have to; they play because they want to.

The correct answer is 'from 3:30 p.m. and 5:30 p.m.'

Key Points

• The given sentence is grammatically incorrect.
• Here, 'from 3:30 p.m. to 5:30 p.m.' should be used instead of 'from 3:30 p.m. and 5:30 p.m.'.
• We know that the preposition 'from' is followed by 'to'.
• We use 'from … to' to talk about ranges of different things
• Example: Sir Edward Youde was the Governor of Hong Kong from 1982 to 1985.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

Correct Sentence: The sports day events will be conducted from 3:30 p.m. to 5:30 p.m. on Saturday

The correct answer is 'Venture'.

Key Points

• The most appropriate word for the given group of words is 'Venture'.
• It means 'a project which is new and possibly dangerous because you cannot be sure that it will succeed नई और कुछ जोखिम भरी परियोजना (क्‍योंकि सफलता निश्‍चित नहीं)'.
• Example: It wasn't somewhere she'd ever venture, even in daylight.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Answer: Venture.

Additional Information

• Let's look at the meaning of other words:
• Entrepreneur: a person who makes money by starting or running businesses, especially when this involves taking financial risks व्‍यावसायिक उद्यम (विशेषतः जिसमें वित्तीय ख़तरा हो) आरंभ करने वाला या उसमें संलग्‍न व्‍यक्ति; उद्यमी, उद्यमकर्ता
• Experiment: a scientific test that is done in order to get proof of something or new knowledge नई जानकारी या प्रमाण के लिए किया गया वैज्ञानिक प्रयोग
• Taboo: something that you must not say or do because it might shock, offend or make people embarrassed निषिद्घ, वर्जित शब्‍द या कर्म (जो लोगों के लिए आघातकारी, अपमानजनक या कष्‍टप्रद हो सकते हों), वर्जना(एँ); निषेध

The correct answer is 'To be embarrassed because of one’s action'.

Key Points

• The most appropriate meaning of the given idiom 'To have eggs on one's face' is 'To be embarrassed because of one's action'.
• To have eggs on one's face: appearing foolish usually because something one said would happen has not happened (आमतौर पर मूर्ख दिखना क्योंकि जो कुछ कहा गया था वह होगा नहीं हुआ है)
• Example: The unexpected election result left a lot of journalists with eggs on their faces.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

Correct Answer: To be embarrassed because of one’s action.

The correct answer is 'Ordered'.

Key Points

• The most appropriate antonym of the given word 'Disheveled' is 'Ordered'.
• Disheveled: (used about a person’s appearance) very untidy. ((व्‍यक्ति की शकल, कपड़े, बाल आदि) अस्‍त-व्‍यस्‍त, मैला-कुचैला)
• Example: His bleached hair was disheveled.
• Ordered: neatly or conveniently arranged; well-organized. (बड़े करीने से या आसानी से व्यवस्थित; सुव्यवस्थित)
• Example: She led a very ordered existence
• Therefore, as per the point mentioned above, we find that the correct answer is Option 1.
  

Correct Answer: Ordered.

Additional Information

• Let's look at the meaning of other words:
• Untidy: not tidy or well arranged ((वस्‍तु, स्‍थान आदि) मैला-कुचैला या अव्‍यवस्थित, अस्‍त-व्‍यस्‍त)
• Unkempt: (used especially about somebody’s hair or general appearance) not well cared for; not tidy ((बाल या आम शकल-सूरत) अस्‍त व्‍यस्‍त, उपेक्षित; मैला-कुचैला)
• Cluttered: cover or fill (something) with an untidy collection of things (चीजों के अस्वच्छ संग्रह के साथ (कुछ) ढँकना या ���रना)

The correct answer is 'like'.

Key Points

• The most appropriate word for the given blank is 'like'.
• It means 'to find somebody/something pleasant; to enjoy something किसी व्‍यक्ति या वस्‍तु का अच्‍छा लगना; किसी वस्‍तु का आनंद लेना'.
• Example: I like playing tennis.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Sentence: Today you may not like what you hear, but that is the truth and you have to accept it.

Additional Information

• Let's look at the meaning of other words:
• Answer: to say or write something back to somebody who has asked you something or written to you उत्तर देना; जवाब देना
• Enjoy: to get pleasure from something (किसी वस्‍तु का) आनंद लेना
• Reply: to say, write or do something as an answer to somebody/something जवाब या उत्तर के रूप में किसी को कुछ कहना, लिखना या कुछ करना

The correct answer is 'bounded'.

Key Points

• The given passage is about the Indian state of 'Meghalaya'.
• If a country or area of land is bounded by something such as a wall, river, etc, it has the wall, etc at its edge.
• Example: The US is bounded in the north by Canada and in the south by Mexico.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

Correct Sentence: It is bounded by the Indian state of Assam...

The correct answer is 'by'.

Key Points

• The given passage is about the Indian state of 'Meghalaya'.
• In the given context the preposition 'by' means 'beside; very near बग़ल में; बहुत पास, समीप'.
• Example: Come and sit by me.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Sentence: "the north and northeast and by Bangladesh in the south and southwest..."

The correct answer is 'the'.

Key Points

• The given passage is about the Indian state of 'Meghalaya'.
• We know that the article  'The' before a noun shows that what is referred to is already known to the speaker, listener, writer, and/or reader (it is the definite article).  
• Example: We had to paint the apartment before we sold it. (The speaker and the listener know what apartment is being referred to.)
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Sentence: The state capital is the hill town of Shillong...

The correct answer is 'detached'.

Key Points

• The given passage is about the Indian state of 'Meghalaya'.
• The word 'detached' means 'separate, unconnected (अलग, असंबद्ध)'.
• Example: I have detached the watch from the chain.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Sentence: "Meghalaya is an upland area formed by a detached block of the Deccan plateau..."

Additional InformationLe'ts look at the meaning of other words:

• removed: far or different from something किसी से दूर या अलग
• standing: the position that somebody/something has, or how people think of him/her/it किसी की स्थिति, हैसियत या प्रतिष्‍ठा
• withdrawn: (used about a person) very quiet and not wanting to talk to other people (व्‍यक्ति) अलग-थलग, ग़ैर-मिलनसार

The correct answer is 'elevation'.

Key Points

• The given passage is about the Indian state of 'Meghalaya'.
• The word 'elevation' means 'the process of moving to a higher place or more important position ऊपर उठने या उच्‍चतर पद पर पहुँचने की प्रक्रिया'.
• Example: The city is at an elevation of 2000 metres.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

Correct Sentence:  "Its summits vary in elevation from 4,000 to 6,000 feet..."

Additional InformationLet's look at the meaning of other words:

• Increase: to become or to make something larger in number or amount संख्‍या या मात्रा में वृद्धि होना या करना, संख्‍या या मात्रा की दृष्टि से बढ़ना या बढ़ाना
• Distance: the amount of space between two places or things (दो स्‍थानों या वस्‍तुओं के बीच) दूरी
• Rise: an increase in an amount, a number or a levelवृद्धि (मात्रा, संख्‍या या स्‍तर में)

According to BODMAS rule

Given equation 65 + 13 − 119 ÷ 32 × 8 = 175

Option 1 → 9 and 8; + and ÷

65 ÷ 13 − 118 + 32 × 9 = 175

By BODMAS rule

5 − 118 + 32 × 9 = 175

5 − 118 + 288 = 175

293 − 118 = 175

293 − 118 = 175

**175 = 175 (LHS = **RHS)

Option 2 → 2 and 9; + and ×

65 × 13 − 112 ÷ 39 + 8 = 175

65 × 13 – 2.87 + 8 = 175

845 – 2.87 + 8 = 175

853 – 2.87 = 175

850.13 = 175 (LHS ≠ RHS)

Option 3 → 8 and 3; × and ÷

65 + 18 − 119 ÷ 82 × 3 = 175

65 + 18 – 1.45 × 3 = 175

78.65 = 175 (LHS ≠ RHS)

Option 4 → 5 and 8; − and ×

68 + 13 − 119 ÷ 32 × 5 = 178

68 + 13 – 3.71 × 5 = 178

81– 18.55 = 178

62.45 = 178 (LHS ≠ RHS)

Hence, the answer is “9 and 8; + and ÷”.

The logic here is,

Word are arranging according to the in alphabets table.

Now follow the steps:

OUTSTAY : AOSTTUY

=> OUTSTAY → alphabets arrangement →  AOSTTUY

Similarly,

ROUGHLY : ?

=> ROUGHLY → alphabets arrangement →  GHLORUY

Hence, "GHLORUY" is correct answer.

Table show alphabet serial number –

The pattern for the code is as follows,

EXTREME is written as VCGIVNV

Similarly,

INITIAL = ?

Hence, ‘INITIAL’ is coded as ‘RMRGRZO’.

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

 

**Option (1) *** → & is opposite to *.

Option (2) & → * is opposite to &.

Option (3) @ → % is opposite to @.

Option (4) # → $ is opposite to #.

So, when the table will be constructed, the letters ‘$ and #’ will be opposite to each other.

Hence, ‘#’ is the correct answer.

The logic followed here is:

Flock : Sheep → A group of sheep is called flock.

Similarly, 

Crowd : Human → A group of human is called Crowd.

Hence, the correct answer is "Human".

Additional Information

Fish → A group of fish called a school.

Swans → A group of swans is called bevy.

According to the sequence in the dictionary:

The correct order of the given words is:

4. Ingenuous
5. Inhabitant
6. Inhaler
7. Inheritance
8. Inimitable

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

The number of triangles in the given figure is:

 

So, there are a total of 18 triangles in the figure.

Hence, ‘18’ is the correct answer.

The Logic here is as follows:

Step 1 → 1^st Number

Step 2 → 1^st Number + (digit sum of 1^st number) = 2^nd number

Step 3 → 2^nd number + (digit sum of 2^nd number) = 3^rd number

In 47 : 58 : 71

Step 1 → 47

Step 2 → 47 + (4 + 7) = 47 + 11 = 58 = 2^nd number

Step 3 → 58 + (5 + 8) = 58 + 13 = 71 = 3^rd number

Similarly,

72 : 81 : 90

Step 1 → 72

Step 2 → 72 + (7 + 2) = 72 + 9 = 81 = 2^nd number

Step 3 → 81 + (8 + 1) = 81 + 9 = 90 = 3^rd number

Hence, the correct answer is "(72 : 81 : 90)".

The logic followed here is:

Option (1) Sri Lanka → Sri Lanka is an island country**.**

Option (2) Bangladesh → Bangladesh is not an island country.

Option (3) Singapore → Singapore is an island country**.**

Option (4) Indonesia → Indonesia is an island country**.**

Note:- An island country is a nation that is made up of one or more islands or land that is surrounded completely by water.

Hence, “Bangladesh” is an odd one.

Given:- k j i _ k _ _ i k j i _ k _ _ i

We put all the option in blank area and check who create particular pattern:

1) k i j k i j → k j i k - k i j i - k j i k - k i i i

2) i j i i j i → k j i i - k j i i - k j i i - k j i i

A particular pattern is repeating itself when the sequence is divided into equal parts.

3) j k j k j k → k j i j - k k j i - k j i k - k j k i

4) i k j i k j → k j i i - k k j i - k j i i - k k i i

• Option (2) gives a pattern of k j i i - k j i i - k j i i - k j i i.

Hence**,** ‘i j i i j i’ is the correct answer.

Given:

 

Here the pattern followed in each row is:

{2^nd number - (1^st number × 2)} ÷ 3 = 3^rd number

Row 1: 13, 50, 8

{2^nd number - (1^st number × 2)} ÷ 3 = 3^rd number

= {50 - (13 × 2)} ÷ 3

= (50 - 26) ÷ 3

= 24 ÷ 3

= 8 = 3^rd number

Row 2: 12, 39, 5

{2^nd number - (1^st number × 2)} ÷ 3 = 3^rd number

= {39 - (12 × 2)} ÷ 3

= (39 - 24) ÷ 3

= 15 ÷ 3

= 5 = 3^rd number

Similarly,

Row 3: 15, 51, ?

{2^nd number - (1^st number × 2)} ÷ 3 = 3^rd number

= {51 - (15 × 2)} ÷ 3

= (51 - 30) ÷ 3

= 21 ÷ 3

= 7 = 3^rd number

Hence, “7” is correct answer.

The logic followed here is:

Mosquito : Swarm → A group of mosquito is called swarm.

Similarly,

Shark : School → A group of shark is called school.

Hence, ‘Shark : School’ is the correct answer. 

Additional Information

• A group of snakes is called den or pit.
• A group of cats is called a clowder.
• A group of Monkey is called a barrel or a troop.
• A group of Lion is called pride.

Preparing the family tree using the following symbols,

Given:

Ruchi's husband's grandfather is Abhinav, whose grandson's father is Viyan. Abhinav and his wife have only one son

We can draw the following Family Tree from the information given above:

Hence, Viyan is the "father" of Ruchi's husband.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. In first, third and fifth figure the small figure present in rows change it place with adjacent figure and first and third figure is same.

2. In second, fourth and sixth figure the small figure present in rows change it place with adjacent figure and second and sixth figure is same.

Hence, ‘option 3’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Step 1: Consonants coded as its opposite alphabet place value.

Step 2: Vowel’s coded as position number of vowel’s position like,

A = 1; E = 2; I = 3; O = 4; U = 5

VICTORY is coded as 29472435

And,

HASTY is coded as 278119

Similarly,

Hence, 'SUBLIME' is coded as "2143152558".

Let,

Number of girls = G

Number of boys = B

At village P

Number of girls in the bus is one-fourth of the number of boys so,

=> G = 1/4B

=> 4G = B

At village Q

20 boys leave the bus at their college stop and ten girls enter the bus.

Number of girls = G + 10

Number of boys = B - 20

Now the number of boys and girls is equal

=> G + 10 = B – 20

∵ 4G = B

So,

=> G + 10 = 4G – 20

=> 4G - 4 = 20 + 10

=> 3G = 30

=> G = 10

∵ 4G = B

So, B = 4 × 10

B = 40

Total number of students enter the bus in the beginning = B + G = 10 + 40 = 50

Hence, Total number of students enter the bus in the beginning is “50”.

Table show alphabet serial number –

The pattern followed is,

<br> <br> <br> <br>

All follow the same pattern, except ‘TXBV’.

Hence, “TXBV” is the odd one.

The image obtained when the paper is unfolded is,

Hence, option 4 is the correct answer.

The pattern followed here is,

Let (1^st number : 2^nd number)

1^st number × (1^st number ÷ 2) + 1 = 2^nd number

Now follow the steps:

18 : 163

18 × (18 ÷ 2) + 1

= 18 × 9 + 1 = 162 + 1 = 163 = 2^nd number

Similarly,

24 : ?

24 × (24 ÷ 2) + 1

= 24 × 12 + 1 = 288 + 1 = 289 = 2^nd number

Hence, "289" is correct answer.

The correct mirror image of the given figure when the mirror is held at the right side is:

Hence, "option (3)" is the correct answer.

Additional Information 

In Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The embedded part of this image is:

Hence, option (2) is the correct answer.

The pattern followed here is:

Hence, '26' is the correct answer.

Statements:

Some dogs are bulls.

All bulls are donkeys.

The least possible diagram for the given statements is as follows

Conclusions:

I. All dogs are donkeys → False (It is possible but not definite)

II. Some donkeys are dogs → True (because some dogs are bulls and all bulls are donkeys so definitely some donkeys are also dogs)

Hence, “Only conclusions II follows”.

Additional Information

The logic followed here is:

All the given options except option (1), are the prime numbers whereas option 1 is not a  prime number.

Option (1) 308 → It is not a prime number.

Option (2) 137 → It is a prime number.

Option (3) 229 → It is a prime number.

Option (4) 463 → It is a prime number.        

Hence, “308” is the correct answer.

The Venn diagrams best represent the relationship between - Statistician, Men, Pathologists figures are shown below:

Some men are statisticians and some men are pathologists.

Hence, ‘option 2’ is the correct answer.

Given: 

tan x = cot (48° + 2x)

0° < x < 90°

Concept used:

tan θ = cot (90° - θ)

Calculation:

tan x = cot (48° + 2x)

⇒ cot (90° - x) = cot (48° + 2x)

⇒ (90° - x) = (48° + 2x)

⇒ 3x = 42°

⇒ x = 14°

∴ The value of x is 14°.

Given: 

 $\frac{\tan 50^\circ + \sec 50^\circ}{\cot 40^\circ + \text{cosec} \ 40^\circ}$ + cos2 65° + sin 65° cos 25° + tan 30°

Concept used:

Cot (90° - θ) = Tan θ 

Cosec (90° - θ) = Sec θ 

Sin (90° - θ) =  Cos θ 

Sin² θ + Cos² θ  = 1

Calculation:

$\frac{\tan 50^\circ + \sec 50^\circ}{\cot 40^\circ + \text{cosec} \ 40^\circ}$ + cos2 65° + sin 65° cos 25° + tan 30°

⇒ {Cot (90 - 50)° + Cosec (90 - 50)°}/(Cot 40° + Cosec 40°) + cos2 65° + sin 65° sin (90 - 25)° + tan 30°

⇒ (Cot 40° + Cosec 40°)/(Cot 40° + Cosec 40°) + (cos2 65° + sin² 65°) + (1/√3)

⇒ 1 + 1 + (1/√3)

⇒ 2 + √3/3

⇒ (6 + √ 3)/3

∴ The value of $\frac{\tan 50^\circ + \sec 50^\circ}{\cot 40^\circ + \text{cosec} \ 40^\circ}$  cos2 65° + sin 65° cos 25° + tan 30° is  (6 + √ 3)/3.

Shortcut Trick

The altitude of 12 cm divides the isosceles triangle into two congruent right-angled triangles.

Recall the common Pythagorean triplet with a perpendicular of 12: (5, 12, 13).

Let equal side (hypotenuse) = 13 cm and half-base = 5 cm.

Verify perimeter: 13 + 13 + (2 × 5) = 36 cm, which exactly matches the given condition.

Therefore, the total length of base BC is 2 × 5 = 10 cm.

∴ The correct answer is 10 cm.

Alternate Method

A B C D

x x 12 cm

y y

BC = 2y

Given:

⇒ ΔABC is isosceles with equal sides AB = AC = x.

⇒ AD ⊥ BC, and for an isosceles triangle, altitude AD bisects the base.

⇒ Let BD = DC = y, making the full base BC = 2y.

⇒ Perimeter of ΔABC = AB + AC + BC = 2x + 2y = 36 cm.

⇒ Divide the perimeter equation by 2: x + y = 18.

Formula Used:

⇒ Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Calculations:

⇒ In right-angled ΔABD, apply the Pythagoras theorem:

⇒ AB² = AD² + BD²

⇒ x² = 12² + y²

⇒ x² − y² = 144

⇒ Expand using algebraic identity: (x + y)(x − y) = 144

⇒ Substitute (x + y) = 18 into the equation:

⇒ 18 × (x − y) = 144

⇒ x − y = 144 ÷ 18 = 8

⇒ To find y, subtract the new equation from the initial sum equation:

⇒ (x + y) − (x − y) = 18 − 8

⇒ 2y = 10 cm

⇒ Since the base BC is represented by 2y, length of BC = 10 cm.

∴ The correct answer is 10 cm.

Additional Information

Properties of Isosceles Triangle

In an isosceles triangle, the altitude drawn to the unequal side always bisects both the base and the vertex angle. This property effectively divides the main triangle into two congruent right-angled triangles.

Area of Isosceles Triangle

The formula to find the area is Area = (b ÷ 4) × √(4a² − b²), where 'a' is the length of equal sides and 'b' is the length of the base. Alternatively, if altitude is given, Area = ½ × base × height.

Pythagorean Triplets

Memorizing common integer triplets (a, b, c) where a² + b² = c² is a crucial time-saving tool in exams. Examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). These scale up proportionally as well.

Calculation:

Money was spent through Card C as compared to Card D in percentage = (100° - 80°)/360° × 100% = (50/9)%

Money was spent through Card C as compared to Card D = (50/9)% × 3,60,000 = 20,000

∴ Rs. 20,000 was more spent through Card C as compared to Card D.

Calculation:

The total revenue of the company in 2014, 2016 and 2018 = (320 + 380 + 280) = 980 crore

The total expenditure in 2015 to 2017 and 2019 = (250 + 330 + 360 + 210) = 1150 crore

% = (980/1150) × 100 = 85.217 ≈ 85.2%

∴ Required answer is 85.2%

Shortcut Trick

Total percentage gap = Loss% + Gain% = 12% + 10.5% = 22.5%

According to the question, 22.5% of Cost Price (CP) = ₹112.50

⇒ 1% of CP = 112.50 ÷ 22.5 = ₹5

Original Selling Price = CP − 12% Loss = 88% of CP

⇒ 88% = 88 × 5 = ₹440

∴ The correct answer is ₹440.00.

Alternate Method

Given:

Initial loss = 12%

New gain = 10.5%

Difference in Selling Price (SP) = ₹112.50

Formula Used:

SP = CP × (100 ± Profit/Loss%) ÷ 100

Calculations:

⇒ Let the Cost Price of the article be ₹x.

⇒ Original Selling Price (SP₁) = x × (100 − 12) ÷ 100 = 0.88x

⇒ New Selling Price (SP₂) = x × (100 + 10.5) ÷ 100 = 1.105x

⇒ Difference = SP₂ − SP₁

⇒ 1.105x − 0.88x = 112.50

⇒ 0.225x = 112.50

⇒ x = 112.50 ÷ 0.225 = ₹500

⇒ Original Selling Price = 0.88 × 500

⇒ Original Selling Price = ₹440

∴ The correct answer is ₹440.00.

Additional Information

Profit and Loss Percentage

Profit% = (Profit ÷ CP) × 100 and Loss% = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price unless stated otherwise.

Successive Percentage Changes

If an object is sold through multiple hands at profits a% and b%, the net profit is given by [a + b + (ab ÷ 100)]%.

Marked Price and Discount

Selling Price = Marked Price (MP) − Discount. Discount is usually calculated as a percentage of the MP.

Given:

Two successive discounts each of x % on the marked price of an article are equal to a single discount of Rs. 350.

Marked price of the article is Rs. 800.

Concept used:

If two successive discount of A% is given, then the resultant or effective single discount is (A + A - A²/100)%

Middle term factor

Calculation:

According to the question,

800 × (2x - x²/100)% = 350

⇒ (2x - x2/100) = 175/4

⇒ x = 25

∴ The value of x is 25.

Shortcut Trick

Rate (R) = (SI × 100) ÷ (P × T) = (3600 × 100) ÷ (8000 × 3) = 15% p.a.

For 8-monthly compounding, cycle rate = 15% × (8 ÷ 12) = 10% per 8 months.

Total time of 2 years = 24 months, which gives 24 ÷ 8 = 3 compounding cycles.

Amount after 3 cycles at 10% growth = 8000 × (11/10)³

Amount = 8000 × 1.331 = 10648.

∴ The correct answer is ₹10,648.

Alternate Method

Given:

Principal (P) = ₹8000

Simple Interest (SI) = ₹3600

Time for SI (T) = 3 years

Formula Used:

Simple Interest = (P × R × T) ÷ 100

Compound Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ SI = (P × R × T) ÷ 100

⇒ 3600 = (8000 × R × 3) ÷ 100

⇒ 3600 = 240 × R

⇒ R = 15% per annum

⇒ The rate for an 8-monthly period = 15% × (8 ÷ 12) = 10%

⇒ Time duration = 2 years = 24 months

⇒ Number of 8-monthly cycles (n) = 24 ÷ 8 = 3

⇒ Total Amount = P(1 + R/100)ⁿ

⇒ Total Amount = 8000 × (1 + 10/100)³

⇒ Total Amount = 8000 × (11/10) × (11/10) × (11/10)

⇒ Total Amount = 8000 × (1331 ÷ 1000)

⇒ Total Amount = 8 × 1331 = 10648

∴ The correct answer is ₹10,648.

Additional Information

Effective Compounding Rate

When interest is compounded k-monthly, the applicable rate per cycle becomes R% × (k ÷ 12) and total cycles become Total Months ÷ k.

Compound vs Simple Interest Difference

For 2 years, CI − SI = P(R/100)². For 3 years, CI − SI = P(R/100)² × (3 + R/100).

Compounding Frequencies

If compounded Half-yearly: Rate is halved, time cycles are doubled. If Quarterly: Rate becomes one-fourth, time cycles become four times.

Given:

(x - 2y) × (5x + y)3

Concept used:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Calculation:

(x - 2y) × (5x + y)3

⇒ (x - 2y) × (125x³ + 75x²y + 15xy² + y³)

⇒ 125x⁴ + 75x3y + 15x²y2 + xy3 - 250x³y - 150x²y² - 30xy³ - 2y⁴

⇒ 125x4 + (75x3y - 250x3y) + 15x2y2 + xy3- 150x2y2 - 30xy3 - 2y4

⇒ 125x4 + (-175x3y) + 15x2y2 + xy3- 150x2y2 - 30xy3 - 2y4

∴ The coefficient of x³y is (-175).

Given: 

 $\frac{5}{4}× 2 \frac{2}{3}÷ \frac{5}{9}$ of $1\frac{1}{5}+\frac{2}{25}× 4 \frac{1}{6}÷ \frac{2}{7}$ of $2 \frac{1}{3}$ 

Concept used:

Calculation:

 $\frac{5}{4}× 2 \frac{2}{3}÷ \frac{5}{9}$ of $1\frac{1}{5}+\frac{2}{25}× 4 \frac{1}{6}÷ \frac{2}{7}$ of $2 \frac{1}{3}$ 

⇒ 5/4 × 8/3 ÷ 5/9 of 6/5 + 2/25 × 25/6 ÷ 2/7 of 7/3

⇒ 5/4 × 8/3 ÷ 2/3 + 2/25 × 25/6 ÷ 2/3

⇒ 5/4 × 4 + 2/25 × 25/4

⇒ 5 + 1/2

⇒ $5\frac{1}{2}$

∴ The required value of  $\frac{5}{4}× 2 \frac{2}{3}÷ \frac{5}{9}$ of $1\frac{1}{5}+\frac{2}{25}× 4 \frac{1}{6}÷ \frac{2}{7}$ of $2 \frac{1}{3}$ is $5\frac{1}{2}$.

Given: 

The bag contains coins of denominations of Rs. 1, Rs. 2, and Rs. 5 in the ratio of 4 ∶ 5 ∶ 8.

Concept used:

Ratio Proportion

Calculation:

Let the common ratio be P.

So, the number of coins of Rs. 1, Rs. 2, and Rs. 5 = 4P, 5P & 8P respectively.

According to the question,

4P + (5P × 2) + (8P × 5) = 432

⇒ P = 8

⇒ 5P = 40

∴ There are 40 coins of Rs. 2.

The total number of workers whose daily wages are Rs. 450 or above but less than Rs. 500 = 45

The total number of workers whose daily wages are Rs. 650 or above = 35

So, the ratio = 45 : 35 = 9 : 7

∴ 9 : 7 is the ratio of the total number of workers whose daily wages are Rs. 450 or above but less than Rs. 500 to the total number of workers whose daily wages are Rs. 650 or above.

Given: 

A can complete a work in 20 days.

B can complete the same work in 25 days.

Both worked together for 10 days and then C alone completed the remaining work in 10 days.

Concept used:

Entire work = Work done each day × Time taken to finish the entire work 

Calculation:

LCM (20, 25) = 100

Let the entire work be given by the LCM of the time taken by A & B.

So, the entire work = 100 units

Now,

A does each day = 100 ÷ 20 = 5 units

B does each day = 100 ÷ 25 = 4 units

So, in 10 days A and B together do = (5 + 4) × 10 = 90 units

Remaining work = (100 - 90) = 10 units

So, C does each day = (10 ÷ 10) = 1 unit

Then, A, B and C together do each day = (5 + 4 + 1) = 10 units

So, the time is taken by them to finish the work together = (100 ÷ 10) = 10 days

∴ In 10 days A, B and C together will complete the same work.

Shortcut Trick A × 20 = B × 25, A/B = 5/4       ....(efficiency ratio)

(A + B) × 10 + C × 10 = A × 20      ....(1)

Put the value of A and B

9 × 10 + C × 10 = 5 × 20, C = (100 - 90)/10, C = 1

Total work = (A + B + C) × d = 5 × 20

(5 + 4 + 1) × d = 100, d = 10

Given:

Chord PQ of a circle C1 of radius 9.25 cm (CP = 9.25 cm) touches another circle C2 that is concentric to C1, and the radius of C2 is 3 cm (CD = 3cm).

Concept used:

If a radius of a circle is perpendicular to a chord in the circle, then the radius bisects the chord.

Pythagorean theorem

Calculation:

ΔCDP is a right-angled triangle.

Now, we know,

CP² = CD² + PD²

⇒ PD = 8.75

So, PQ = 2 × PD = 2 × 8.75 = 17.5 cm

∴ The length of PQ is 17.5 cm.

Given:

The average height of a certain number of students in a group is 155.6 cm.

12 students having an average height of 150.5 cm join the group

7 students having an average height of 159 cm leave the group

The average height of the students in the group will decrease by 34 mm i.e. 3.4 cm

Concept used:

Let xn be the observations and wn be the weights of the observations; the formula of the weighted average is given below.

W = (w1x1+ w2x2 + w3x3+ ... + wnxn) ÷ (w1 + w2 + w3 + .... + wn)

Calculation:

Let the intial number of students be P.

So, total height of P students = (P × 155.6) cm

Now, total height increased by = (12 × 150.5) = 1806 cm

Then, total height decreased by = (7 × 159) = 1113 cm

Now, the total change in height = (1806 - 1113) = 693 cm

The final number of stundets = (P + 12 - 7) = (P + 5)

According to the question,

155.6 × P + 693 = (155.6 - 3.4) × (P + 5)

⇒ P = 20

∴ The number of students initially in the group was 20.

Given:

x + y + z = 13

x2 + y2 + z2 = 91

xz = y2

Concept used:

(a + b + c)² = a² + b² + c² + 2 (ab + bc + ca)

(a - b)² = a² - 2ab + b²

Calculation:

x + y + z = 13

⇒ (x + y + z)² = 13²

⇒ x2 + y2 + z2 + 2(xy + yz + xz) = 169

⇒ (xy + yz + xz) = 39

⇒ xy + yz + y² = 39

⇒ y(x + y + z) = 39

⇒ y = 3

⇒ y² = 9

⇒ xz = 9

⇒ 3xz = 27

So,

x2 + y2 + z2 = 91

⇒ x2 + xz - 3xz + z2 = 91 - 27

⇒ x2 - 2xz + z2 = 64

⇒ (z - x)² = 64

⇒ (z - x) = 8

∴ The difference between z and x is 8.

Shortcut TrickGo by hit and trial method

Put the value of x = 9, y = 3, and z = 1 which satisfies the below equation.

x + y + z = 13

x2 + y2 + z2 = 91

xz = y2

Given:

AB and DC are two chords. They are produced to meet at P.

PC = 2.8 cm, PB = 3.15 cm and AB = 3.85 cm,

Concept used:

Here, PA & PC are two secants and PT is a tangent at point T on the circle. 

So, we know,

PA × PB =  PC × PD = (PT)2

Calculation:

So, PA = AB + PB = 3.15 + 3.85 = 7 cm

Now,

PA × PB = PD × PC

⇒ 7 × 3.15 = PD × 2.8 

⇒ PD = 7.875

⇒ PC + CD = 7.875

⇒ CD = 5.075

∴ The length of CD  is 5.075 cm.

Percentage change in sales,

For Strawberry = (20.5 - 18.9)% = 1.6%

For Others = (20.6 - 15.7)% = 4.9%

For Butterscotch = (16.6 - 10.8)% = 5.8%

Total percentage change in sales = 1.6% +  4.9% + 5.8% = 12.3%

So, the sales increased by = 12.3% × 10000 = Rs. 1,23,000

∴ The combined strawberry, other and Butterscotch sales increase from 2019 to 2020 increased by Rs. 1,23,000.

Shortcut Trick

Relative speed (same direction) = 78 − 6 = 72 km/h = 20 m/s.

Length of train = Relative speed × Time = 20 × 15 = 300 m.

Total distance for tunnel = 78 × (5/18) × 45 = 975 m.

Length of tunnel = 975 − 300 = 675 m.

∴ The correct answer is 675 m.

Alternate Method

Given:

Speed of train = 78 km/h

Speed of person = 6 km/h

Time to cross tunnel = 45 s

Time to cross person = 15 s

Formula Used:

Distance = Speed × Time

Relative Speed (same direction) = S₁ − S₂

To convert km/h to m/s, multiply by 5/18.

⇒ Speed of train = 78 × (5/18) = 65/3 m/s

⇒ Speed of person = 6 × (5/18) = 5/3 m/s

⇒ Relative speed (same direction) = 65/3 − 5/3 = 60/3 = 20 m/s

⇒ Length of train = Relative speed × Time = 20 × 15 = 300 m

⇒ Total distance when crossing tunnel = Speed of train × Time = (65/3) × 45

⇒ Total distance = 65 × 15 = 975 m

⇒ Length of tunnel = Total distance − Length of train

⇒ Length of tunnel = 975 − 300 = 675 m

∴ The correct answer is 675 m.

Additional Information

Relative Speed Concepts

When two objects move in the same direction, relative speed = V₁ − V₂. When moving in opposite directions, relative speed = V₁ + V₂.

Crossing Stationary Objects

To cross a stationary object of length L, a train of length T must cover a total distance of (T + L).

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.

Shortcut Trick

Volume remains constant: 4/3 × π × R³ = π × r² × h

⇒ 4/3 × 9 × 9 × 9 = 0.3 × 0.3 × h

⇒ 4 × 3 × 81 = 0.09 × h

⇒ 972 = 0.09 × h

⇒ h = 10800 cm = 108 m

∴ The correct answer is 108 m.

Alternate Method

Given:

Radius of Sphere (R) = 9 cm

Radius of Wire (r) = 0.3 cm

Formula Used:

Volume of Sphere = 4/3 × π × R³

Volume of Cylinder (Wire) = π × r² × h

Calculations:

⇒ Volume of Sphere = Volume of Wire

⇒ 4/3 × π × (9)³ = π × (0.3)² × h

⇒ 4/3 × 729 = 0.09 × h

⇒ 4 × 243 = 0.09 × h

⇒ 972 = 0.09 × h

⇒ h = 972 ÷ 0.09

⇒ h = 10800 cm

⇒ h = 10800 ÷ 100 m

⇒ h = 108 m

∴ The correct answer is 108 m.

Additional Information

Conservation of Volume

When a solid object is melted and recast into another shape, its total volume remains unchanged.

Cylinder Properties

A wire is always considered a cylinder where the length of the wire is the height (h) of the cylinder.

Unit Conversion

Always ensure units are consistent. 1 meter = 100 centimeters.

Given:

P is the midpoint of side XZ

Q is a point on side XY such that QZ bisects PY

XQ = 24 cm

Concept used:

Midpoint theorem: - The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side

ASA (Angle-Side- Angle) - If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

Calculation:

Let D be the midpoint of QZ

So, according to the Midpoint theorem,

PD/XQ = 1/2

So, PD = 12 cm

PD ∥ XQ,

So, also PD ∥ QY

∠QYO = ∠OPD

∠QOY = ∠DOP

∠QYO = ∠OPD

∠YQO = ∠ODP

PO = YO

So, ΔPOD ≅ ΔQOY

So, QY = PD = 12 cm

∴ The length (in cm) of QY is 12 cm

Given:

The five-digit number 672 xy is divisible by 3, 7, and 11.

Concept used:

For a given set of numbers, the LCM is the smallest number that is a multiple of every one of the numbers.

Calculation:

LCM (3,7,11) = 231

Since 672xy is a five-digit number, we're considering xy as 00, to get the closest quotient.

So, the quotient when 67200 is divided by 231 = (67200 ÷ 231) = 290

Now, the required number must be the next multiple of 231.

So, the required number = (290 + 1) × 231 = 67221

So, x = 2 and y = 1

Now,

(6x + 5y)

⇒  6 × 2 + 5 × 1

⇒ 17

∴ The required value of (6x + 5y) is 17.

Given:

x2 + 4y2 + 3z2 + 19/4 = 2√3(x + y + z)

Concept used:

(a - b)² = a² - 2ab + b²

If A² + B² + C² = 0, then A = B = C = 0

Calculation:

x2 + 4y2 + 3z2 + 19/4 = 2√, 3(x + y + z)

⇒ (x² - 2√3x + 3) + (4y² - 2√3y + (3/4)) + (3z² - 2√3z + 1) = 0

⇒ (x - √3)² + (2y - (√3/2))² + (√3z - 1)² = 0

So,

(x - √3)2 = 0

⇒ x = √3

(2y - (√3/2))2 = 0

⇒ y = √3/4

(√3z - 1)2 = 0

⇒ z = 1/√3

Now,

x - 4y + 3z

⇒ √3 - 4 × (√3/4) + 3 × (1/√3)

⇒ √3 - √3 + √3

⇒ √3

∴ The required value of (x - 4y + 3z) is √3.

Given:

The price of a commodity increase by 28%.

The expenditure on it increases by 12%

Concept used:

Revised = Initial × (1 + percentage increase/100)

Calculation:

Let the previous price of the commodity be Rs. 100P per unit.

So, the revised price of the commodity = (100P × 1.28) = Rs. 128P

But, the expenditure has become = (100P × 1.12) = Rs. 112P

So, at Rs. 112P, the amount of commodity can be acquired = (112/128) unit = 7/8 unit

So, the lesser quantity than earlier at Rs. 112P = (1 - 7/8) = 1/8

Now, the percentage decrease in its consumption = 1/8 × 100% = 12.5%

∴ The percentage decrease in its consumption is 12.5%

Alternate MethodIn these type of questions, we can use the following method:

EXPENDITURE (E) = CONSUMPTION (C) × PRICE (P)

(28% = 7/25, 12% = 3/25)

⇒ E = C × P

⇒ 28/25 = C × 32/25

⇒ C = 28/32 = 7/8

Therefore, the consumption will decrease by = 1/8 × 100 = 12.5%

Shortcut Trick Now, by the percentage graphics change method,

100 → 128 → 112

So, the percentage change = (128 - 112)/128 × 100% = 12.5%

∴ The percentage decrease in its consumption is 12.5%

Shortcut Trick

Since cos θ = √3/2, the standard value for θ is 30°.

Substitute θ = 30° directly into the expression:

Value = (2 − sin² 30°) / (1 − cot² 30°) + (sec² 30° + cosec 30°)

Value = (2 − 1/4) / (1 − 3) + (4/3 + 2) = (7/4)/(−2) + 10/3 = −7/8 + 10/3

Value = (−21 + 80) / 24 = 59/24.

∴ The correct answer is 59/24.

Alternate Method

Given: cos θ = √3/2

Formula Used:

1. sin² θ + cos² θ = 1
2. cot θ = cos θ / sin θ
3. sec θ = 1 / cos θ
4. cosec θ = 1 / sin θ

Step-by-step Calculations:

⇒ If cos θ = √3/2, then sin θ = √(1 − (3/4)) = √(1/4) = 1/2.

⇒ cot θ = (√3/2) / (1/2) = √3.

⇒ sec θ = 1 / (√3/2) = 2/√3.

⇒ cosec θ = 1 / (1/2) = 2.

⇒ Expression Part 1 = (2 − sin² θ) / (1 − cot² θ) = (2 − (1/2)²) / (1 − (√3)²)

⇒ Part 1 = (2 − 1/4) / (1 − 3) = (7/4) / (−2) = −7/8.

⇒ Expression Part 2 = (sec² θ + cosec θ) = (2/√3)² + 2 = 4/3 + 2 = 10/3.

⇒ Total Value = −7/8 + 10/3 = (−21 + 80) / 24 = 59/24.

∴ The correct answer is 59/24.

Additional Information

Standard Trigonometric Values for 30°

For 30°: sin = 1/2, cos = √3/2, tan = 1/√3, cot = √3, sec = 2/√3, cosec = 2.

Pythagorean Identities

sin² θ + cos² θ = 1 | 1 + tan² θ = sec² θ | 1 + cot² θ = cosec² θ.

Reciprocal Relations

cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.

The correct answer is Middle Andaman.

Key Points

• Mount Diavolo, an important mountain peak in the Andaman and Nicobar Islands, is located in Middle Andaman.
• Mount Diavolo is the highest point of Middle Andaman Island.
• It has an elevation of 295 meters.
• Mount Diavolo (Mount Diavolo) is a mountain (class T - Hypsographic) in the Union Territory of Andaman and Nicobar Islands (Andaman and Nicobar Islands), India (Asia) with the region font code of Asia/Pacific.
• It is located at an elevation of 403 meters above sea level.
• Its coordinates are 12°42'0" N and 92°55'0" E in DMS (Degrees Minutes Seconds) or 12.7 and 92.9167 (in decimal degrees). Its UTM position is DV90 and its Joint Operation Graphics reference is ND46-14.
• A Mountain is an elevation standing high above the surrounding area with a small summit area, steep slopes, and local relief of 300m or more.

Additional Information

• The Andaman Islands are an Indian archipelago in the Bay of Bengal.
• These roughly 300 islands are known for their palm-lined, white-sand beaches, mangroves, and tropical rainforests.
• Duncan passage separates Little Andaman from South Andaman.
• The territory’s capital is the city of Port Blair.
• THE BARREN AND NARCONDAM ISLANDS, north of Port Blair, are volcanic islands [these are the only active volcanoes in India.
• Saddle peak (737 m) in North Andaman is the highest peak.
• State Animal of Andaman is the dugong (sea mammal) really endemic to Indo-Pacific seacoast areas, especially to the Andaman Islands.

The correct answer is Nirmal.

Key Points

• In Nirmal district were Telangana’s first rescue and rehabilitation centre for monkeys, launched in December 2020.
• The first rescue and rehabilitation centre for monkeys was launched in Telangana's northern district of Nirmal.
• The forest department has set up a campus in Chincholi village for housing up to 200 monkeys for a period of 10 to 15 days, after which they will be released in forest areas.
• Four special enclosures are readied with a capacity for 50 monkeys each.
• Monkeys captured by Gram Panchayat will be sterilized and housed at the campus and later released in interior forest areas identified by the department.
• “Adult female monkeys will undergo sterilization by laparoscopy and vasectomy will be taken up on adult male monkeys.
• That apart, they will be vaccinated and checked for diseases, if any.
• Nearly 50 per cent of monkeys in the wild are found to have tuberculosis.
• The treatment will be ensured and only disease-free monkeys will be released in the wild.

The correct answer is Melatonin.

Key Points

• Melatonin hormone is secreted by the brain that helps to regulate sleep-wake cycles.
• Melatonin is a hormone primarily released by the pineal gland at night and has long been associated with control of the sleep-wake cycle.
• As a dietary supplement, it is often used for the short-term treatment of insomnia, such as from jet lag or shift work, and is typically taken orally.
• Evidence of its benefit for this use, however, is not strong.
• A 2017 review found that sleep onset occurred six minutes faster with use, but found no change in total time asleep.
• Side effects from melatonin supplements are minimal at low doses for short durations.
• Melatonin side effects are rare but may occur in 1 to 10 patients in 1000.

Additional Information

• Oxytocin is a hormone that acts on organs in the body (including the breast and uterus) and as a chemical messenger in the brain, controlling key aspects of the reproductive system, including childbirth and lactation, and aspects of human behaviour.
• Insulin is a peptide hormone produced by beta cells of the pancreatic islets.
• It is considered to be the main anabolic hormone of the body.
• It regulates the metabolism of carbohydrates, fats, and protein by promoting the absorption of glucose from the blood into the liver, fat, and skeletal muscle cells.
• Aldosterone is the main mineralocorticoid steroid hormone produced by the zona glomerulosa of the adrenal cortex in the adrenal gland.
• It is essential for sodium conservation in the kidney, salivary glands, sweat glands, and colon.

The correct answer is Odisha.

Key Points

• Raja Parba is a unique festival celebrating the onset of the monsoon and the earth’s womanhood.
• It is celebrated in Odisha.
• The second day of the festival signifies the beginning of the solar month of Mithuna, during which the season of rains starts.
• It falls in mid-June, the first day is called Pahili Raja, the second day is Mithuna Sankranti, the third day is Bhudaaha or Basi Raja.
• The final fourth day is called Basumati snana, in which the ladies bathe the grinding stone as a symbol of Bhumi with turmeric paste and adore with flower, sindoor, etc.
• All types of seasonal fruits are offered to mother Bhumi.
• The day before the first day is called Sajabaja or preparatory day during which the house, kitchen including grinding stones are cleaned, spices are ground for three days.
• During these three days, women and girls take a rest from work and wear new Saree, Alata, and ornaments.
• It is similar to Ambubachi Mela.
• It is believed that the mother Goddess Earth or the divine wife of Lord Vishnu undergoes menstruation during the first three days.
• The fourth day is called Vasumati Snana, or the ceremonial bath of Bhudevi.
• The term Raja came from the Sanskrit word 'Rajas' which means menstruation and when a woman menstruates, she is called 'Rajaswala' or a menstruating woman, and in medieval times the festival became more popular as an agricultural holiday marking the worship of Bhudevi, who is the wife of Lord Jagannath.
• A silver idol of Bhudevi is still to be found in the Puri Temple beside Lord Jagannath.

Additional Information 

• Various festivals being celebrated across the Nations:
• Makar Sankranti: The festival of Makar Sankranti is being celebrated today when the Sun enters the Makar zodiac and the days begin to lengthen compared to nights.
• Pongal: In South India and particularly in Tamil Nadu, it’s the festival of Pongal which is being celebrated over 4 days at harvest time.
• Magha Bihu: In Assam and many parts of the North East, the festival of Magha Bihu is celebrated. It sees the first harvest of the season is offered to the gods along with prayers for peace and prosperity.
• Uttarayan: Gujarat celebrates it in the form of the convivial kite festival of Uttarayan.
• Maghi: In Punjab, Makar Sankranti is celebrated as Maghi. Bathing in a river in the early hours of Maghi is important.
• Saaji: In the Shimla District of Himachal Pradesh, Makara Sankranti is known as Magha Saaji. Saaji is the Pahari word for Sankranti, the start of the new month. Hence this day marks the start of the month of Magha.
• Kicheri: The festival is known as Kicheri in Uttar Pradesh and involves ritual bathing.

The correct answer is Jharkhand.

Key Points

• Kisan Fasal Rahat Yojana, which will replace (PMFBY) Pradhan Mantri Fasal Bima Yojna, has been launched by the Jharkhand state government in December 2020.
• Jharkhand CM Hemant Soren has launched Kisan Fasal Rahat Yojana on 29th December 2020 but it will take three months to come into effect.
• It is a compensation scheme aimed at providing security cover to Jharkhand farmers in case of crop damage due to natural calamity.
• It is a compensation scheme aimed at providing security cover to Jharkhand farmers in case of crop damage due to natural calamity.
• It will cover both land-owning and landless farmers.
• The Department of Agriculture, Animal Husbandry and Co-operative will be the implementing agency and it will work in association with a project management unit, which will be a consultancy firm that will take care of technical requirements.
• “Food safety, crop diversification, rapid development in agriculture and paving the way for competition,” are among the aims of the scheme.
• It is not an insurance scheme where premiums are paid.

Additional Information 

• Pradhan Mantri Sampada Yojana :
• The Central Sector Scheme - SAMPADA (Scheme for Agro-Marine Processing and Development of Agro-Processing Clusters) was approved by the cabinet in May 2017 for the period of 2016-20 coterminous with the 14th Finance Commission cycle.
• It is a central sector scheme introduced by the Ministry of Food Processing Industries.
• It is a comprehensive package aiming to create modern infrastructure with efficient supply chain management from farm gate to retail outlet.
• It is a big step towards creating huge employment opportunities in the rural areas, doubling the farmers’ income, increasing the processing level, reducing wastage of agricultural produce, and enhancing the export of processed foods.
• Pradhan Mantri Garib Kalyan Yojana :
• It was launched in the year 2016 by PM Narendra Modi along with the other provisions of the Taxation Laws (Second Amendment) Act, 2016.
• It came into effect on 17th December 2016 under the Ministry of Finance.
• To provide an insurance cover of Rs 50 lakhs per health worker affected by COVID-19.
• The Central Government has given orders to State Governments to use the Building and Construction Workers Welfare Fund to provide relief to Construction Workers.
• To provide free resources of 5 kg wheat or rice and 1 kg of preferred pulses for 80 crore poor people for the next three months under the PM Garib Kalyan Anna Yojana.
• Shramev Jayate Yojana :
• It is also known as Pandit Deendayal Upadhyay Shramev Jayate Karyakram was launched by PM Narendra Modi in October 2014 under the Government of India.
• It was launched to support the ‘Make in India’ campaign for encouraging the manufacturing sector.
• It also aims to expand government support for imparting skill training to the workers.
• Candidates should have a thorough knowledge regarding the objectives and benefits of all the schemes under the Government of India

The correct answer is Colin Mackenzie.

Key Points

• Colin Mackenzie was appointed as the first Surveyor General of India in 1815.
• In 1815, Colin Mackenzie was appointed as the first Surveyor General of India.
• He holds this post from 1815 to 1821.
• The Surveyor General of India is the Head of the Department of Survey of India, a Department under the Ministry of Science and Technology of the Government of India.

Additional Information

• Thomas Hickey was an Irish painter. Born in Dublin, Hickey was the son of Noah, a confectioner in Capel Street, and Anne Hickey.
• A younger brother was John Hickey, the sculptor.
• He was trained at the Royal Dublin Society Schools under Robert West.
• Hickey painted primarily portraits and genre scenes.
• Henry Walpole (1558 – 7 April 1595) was an English Jesuit martyr, executed at York for refusing to take the Oath of Supremacy.
• Colonel Colin Mackenzie CB (1754–8 May 1821) was a Scottish army officer in the British East India Company who later became the first Surveyor General of India.
• He was a collector of antiquities and an orientalist.
• He surveyed southern India, making use of local interpreters and scholars to study religion, oral histories, inscriptions, and other evidence, initially out of personal interest, and later as a surveyor.
• He was ordered to survey the Mysore region shortly after the British victory over Tipu Sultan in 1799 and produced the first maps of the region along with illustrations of the landscape and notes on archaeological landmarks.
• He was awarded a Companion of the Order of the Bath on 4 June 1815.

The correct answer is Pangong Tso.

Key Points

• Pangong Tso is a salt-water lake.
• Pangong Lake, situated at a height of almost 4,350m, is the world’s highest saltwater lake.
• Its water, which seems to be dyed in blue, stands in stark contrast to the arid mountains surrounding it.
• Extending to almost 160km, one-third of the Pangong Lake lies in India and the other two-thirds in China.
• Pangong Lake, one of the most famous lakes in Leh Ladakh, derives its name from the Tibetan word, “Pangong Tso”, which means “high grassland lake”.
• During winter the lake freezes completely, despite being saline water.
• It has a land-locked basin separated from the Indus River basin by a small elevated ridge but is believed to have been part of the latter in prehistoric times.
• The lake is in the process of being identified under the Ramsar Convention as a wetland of international importance.
• This will be the first transboundary wetland in South Asia under the convention.

Additional Information

• Kolleru Lake is one of the largest freshwater lakes in India located in the state of Andhra Pradesh and forms the largest shallow freshwater lake in Asia (with 245 sq km of the lake area and 302 sq km of total Ramsar designated wetland), 15 kilometres away from the Eluru and 65 km from Rajamahendravaram.
• It is located between Krishna and Godavari deltas.
• Kolleru spans two districts – Krishna and West Godavari.
• Nainital, also known as Naini Lake, is a natural freshwater body, situated amidst the township of Nainital in Kumaon.
• It is tectonic in origin and is kidney-shaped or crescent-shaped and has an outfall at the southeastern end.
• Nainital, along with other lakes of Kumaon, is integral to tourism and recreation in Kumaon.
• The lake is also an integral part of Kumaoni folklore.
• Nainital Lake in the Nainital district, often called the Lake District of India, is one of the four important lakes of Kumaon; the other three are Sattal Lake, Bhimtal Lake, and Naukuchiyatal Lake.
• Loktak Lake is the largest natural freshwater lake and ancient super volcanic caldera in India.
• The largest of all the phumdis covers an area of 40 km2 (15 sq mi) and is situated on the southeastern shore of the lake.
• Located on this phumdi, Keibul Lamjao National Park is the only floating national park in the world.

The correct answer is Karnataka.

Key Points

• Dandeli Wildlife Sanctuary is located in Karnataka.
• Dandeli Wildlife Sanctuary is a birdwatcher's paradise, housing nearly 200 species of birds, most famous for the great hornbill (great Indian hornbill or great pied hornbill) and the Malabar pied hornbill.
• It is also the only known tiger reserve in India to report frequent sightings of the elusive black panther.
• It is also known to house the Indian sloth bear, the Indian pangolin, the giant Malabar squirrel, dhole, the Indian jackal, and the muntjac (barking deer).
• Sightings of the Indian elephant and the Indian peafowl are pretty common.
• The king cobra and the mugger crocodile (Indian crocodile) are the prime reptilians in Dandeli Wildlife Sanctuary.
• The forests in Dandeli are a mixture of dense deciduous trees interspersed with bamboo and teak plantations.
• The sanctuary is rich in flora and fauna.

Additional Information 

• Kaziranga National Park is a protected area in the northeast Indian state of Assam.
• Spread across the floodplains of the Brahmaputra River, its forests, wetlands, and grasslands are home to the world's largest population of tigers, elephants, and the Indian one-horned rhinoceros.
• The one-horned rhinoceros, Royal Bengal tiger, Asiatic elephant, bison, and swamp deer are collectively known as the 'Big Five' of Kaziranga.
• In the year 1985, the park was declared a World Heritage Site by UNESCO.
• It has been declared a national park in 1974.
• Guindy National Park :
• Guindy National Park is a beautiful place, located in the Chennai district of the state of Tamil Nadu.
• The park is home to spotted deer, blackbucks, white bucks, river otter, hyena, bonnet monkey, civet cat, jackals, pangolin, hedgehog and common mongoose, etc.
• Guindy National Park was established in the year of 1976.
• Ranthambore National Park :
• Ranthambore National Park is located about 13.5 kilometers from the city of Sawai Madhopur in Rajasthan.
• It is a former royal hunting ground and home to tigers, leopards, and marsh crocodiles.

The correct answer is Science and Technology.

Key Points

• Shanti Swarup Bhatnagar Prize is associated with Science and Technology.
• The Shanti Swarup Bhatnagar Prize for Science and Technology (SSB) is a science award in India given annually by the Council of Scientific and Industrial Research (CSIR) for notable and outstanding research, applied or fundamental, in biology, chemistry, environmental science, engineering, mathematics, medicine, and physics.
• The prize recognizes outstanding Indian work (according to the view of the CSIR awarding committee) in science and technology.
• It is the most coveted award in multidisciplinary science in India.
• The award is named after the founder Director of the Council of Scientific & Industrial Research, Shanti Swarup Bhatnagar.
• It was first awarded in 1958.
• Any citizen of India engaged in research in any field of science and technology up to the age of 45 years is eligible for the prize.
• The prize is awarded on the basis of contributions made through work done in India only during the five years preceding the year of the prize.
• The prize comprises a citation, a plaque, and a cash award of ₹5 lakh.
• In addition, recipients also receive Rs. 15,000 per month up to the age of 65 years.

Additional Information

• Shanti Swarup Bhatnagar Prize is divided into seven disciplines, namely:
• Biological Sciences
• Chemical Sciences
• Earth, Atmosphere, Ocean and Planetary Sciences
• Engineering Sciences
• Mathematical Sciences
• Medical Sciences
• Physical Sciences.