MPPEB Group 2 Subgroup 4 Official Paper (Held On: 31 Jan 2021 Shift 1) (Previous Year Paper)

The correct answer is 'misfired.'

Key Points   

• Out of all the options, the correct word is "misfired."
• The prefix that goes with 'fire' is "mis-".
• The prefix "mis-" means bad or wrong; badly or wrongly. (अप्रिय या अनुचित; अप्रिय या अनुचित रूप से)
• For example: mislead, misbehaviour.
• The meaning of the verb "misfired" is to fail to have the intended result or effect. (अभीष्‍ट परिणाम या प्रभाव उत्‍पन्‍न न कर पाना)​
• So, the correct answer is Option 3*.*

Correct sentence: The king planned to murder his stepson, but his evil plan misfired.

Given:

Lines 4x - y = 4; 8x - 4y = 8

Calculation:

Let 4x - y = 4 → (1)

equation (1) multiplied with 2 we get 8x - 2y = 8 → (2)

8x - 4y = 8 → (3)

By subtracting equations (2) and (3), we get

⇒ (8x - 2y) - (8x - 4y) = 8 - 8

⇒ 2y = 0

⇒ y = 0.

From equation (2), we get

⇒ 8x - 2y = 8

⇒ 8x = 8

⇒ x = 1.

∴ The lines intersect at x = 1 and y = 0.

The correct answer is Oxalo acetic acid.

Key Points

• In C4 plants, the first stable product of CO2 fixation is Oxalo acetic acid
• Plants use carbon dioxide from the atmosphere to synthesize sugar through the process of photosynthesis.
• Carbon dioxide fixation is the first major step in the Calvin cycle.
• The Calvin cycle is a biosynthetic pathway that occurs in all photosynthetic plants (C3 as well as C4 plants).

Additional Information

• Carbon dioxide fixation, called carboxylation, is the first major step in the Calvin cycle.
• The carbon dioxide assimilation in plants is of two types:
• In some plants, the first product of carbon dioxide fixation is 3-phosphoglyceric acid (PGA) or C3 acid. These plants are called C3 plants.
• In some plants, the first product of carbon dioxide fixation is oxaloacetic acid (OAA) or C4 acid. These plants are called C4 plants.
• Maize or sorghum is an example of a C4 plant.

"नीम एक बहुपयोगी पेड़ है।" - वाक्य में रेखांकित शब्दों के तत्सम रूप क्रमशः हैं -निम्ब - वृक्ष।

Key Points

• तत्सम दो शब्दों से मिलकर बना है – तत + सम जिसका अर्थ होता है ‘ज्यों का त्यों’। तत्सम शब्द ऐसे शब्द होते हैं, जिन्हें संस्कृत भाषा से सीधे बिना किसी परिवर्तन के हिंदी भाषा में शामिल कर लिया गया है।
• उदाहरण -आम्र, अग्नि, अमूल्य, क्षेत्र, अज्ञान, अन्धकार, चंद्र, बांग्ला आदि।

Important Pointsकुछ अन्य उदाहरण -

Additional Informationअन्य विकल्प -

शांत रस का स्थायी भाव है:निर्वेद है।

Key Points

• स्थायी भाव- सहृदय के हृदय में जो भाव स्थायी रूप से विद्यमान रहते हैं उन्हें स्थायी भाव कहते हैं। प्रत्येक रस का एक स्थायी भाव होता है।
• इनकी संख्या 9 है।

Additional Informationअन्य विकल्प -

विशेष -शृंगार रस में ही वात्सल्य और भक्ति रस भी शामिल हैं।

The correct answer is 'The squirrel was gathering nuts.'

Key Points  

• The given sentence is in Past Continuous Tense and in Passive Voice.
• The rule for changing a Past Continuous Tense from Active voice to Passive voice or Passive to Active Voice:
• Interchange the object and subject with each other, i.e. object of the active sentence become the subject of the passive sentence.
• Structure: 
• Subject + was/were + v1 + ing + object (Active Voice)
• Object + was/were + being + V3 + by Subject (Passive Voice)
• Example: 
• Esha was singing a song. (Active Voice)
• A song was being sung by Esha. (Passive Voice)
• The subject of the given sentence is **' Nuts'.**​​
• The object of the given sentence is 'squirrel.'
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'were being gathered' will be changed into 'was gathering'.
• "Squirrel" is a singular noun so we must "was" with it.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.

Correct Answer: The squirrel was gathering nuts.

'यथार्थ (सच) कहनेवाला' के लिए एक शब्द यथार्थवादी है।

Key Points

• परिभाषा - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।
• उदाहरण - 
• जो इंद्रियोँ द्वारा न जाना जा सके – अगोचर
• जिस पुस्तक में आठ अध्याय हो — अष्टाध्यायी
• जिसका भाषा द्वारा वर्णन असंभव हो — अनिर्वचनीय
• अत्यधिक बढ़ा–चढ़ा कर कही गई बात — अतिशयोक्ति

Additional Informationअन्य विकल्प -

The correct answer is Magnesium.

Key Points

• Magnesium is present in the pigment chlorophyll.
• Chlorophyll or leaf green is a porphyrin derivative with magnesium (Mg) as the central atom and is hence a metal complex dye.
• It is present in the chloroplasts in all green parts of plants as a mixture of blue-green chlorophyll a and yellow-green chlorophyll b and constitutes the catalyst for photosynthesis.
• Chlorophylls are porphyrins, whose molecules contain a flat ring of four-linked heterocyclic groups, based upon magnesium.
• Chlorophyll is a green photosynthetic pigment found in plants, algae, and cyanobacteria.
• Chlorophyll absorbs mostly in the blue and to a lesser extent red portions of the electromagnetic spectrum, hence its intense green color.
• This pigment is involved in photosynthesis, the process by which light energy is converted to chemical energy.

Calculation:

The algebraic expression \(3\sqrt{y} - 6y\) is not a polynomial as there is radical power of y. Means there is a term 3y^1/2 whose power is not an integer.

∴ \(3\sqrt{y} - 6y\) is not a polynomial.

Given:

Slope m = -1

point is (-3, 5)

Formula Used:

Equation of the line y - y₁ = m(x - x₁)

Calculation:

Equation of the line y - y1 = m(x - x1)

⇒ y - 5 = -1[x - (-3)]

⇒ y - 5 = -x -3

⇒ x + y - 2 = 0.

∴ The equation of the line is x + y - 2 = 0.

The correct answer is 'shall we?'

Key Points    

• Rules for question tag:
• The sentence and the question tag must be in the same tense.
• For the negative question tag, use the contracted form of 'helping verb' and 'not.'
• If a statement starts with "let's" (Let us) in the imperative sentence then we can use "Shall we?" in the question tag.
• Example: Let' sit in the garden, shall we?
• So, the correct answer is Option 1.

​​Correct sentence: Let’s go for a walk, shall we?

Given:

x : y = 5 : 2

Calculation:

x : y = 5 : 2 ⇒

Let x = 5a and y = 2a

To solve (8x + 9y) : (8x + 2y)

⇒ (8x + 9y) = 8(5a) + 9(2a) = 40a + 18a = 58a

⇒ (8x + 2y) = 8(5a) + 2(2a) = 40a + 4a = 44a

∴ (8x + 9y) : (8x + 2y) = 58a : 44a

∴ (8x + 9y) : (8x + 2y) = 29 : 22.

अनुप्रास के पांच उपभेद होते हैं।

Key Points

• जब किसी काव्य को सुंदर बनाने के लिए किसी वर्ण की बार-बार आवृति हो तो वह अनुप्रास अलंकार कहलाता है।
• उदाहरण -मुदित महापति मंदिर आये। 
• जैसा की आप ऊपर दिए गए उदाहरण में देख सकते हैं की ‘म’ वर्ण की आवृति हो रही है।

Important Points

• कुछ अन्य उदाहरण -
• कूल कदम्ब की डरनी
• कानन कुंडल मोर पखा,
• मधुर मुस्कान मनोहर, मनुज वेश का उजियाला।
• सुरभित सुंदर सुखद सुमन तुम पर खिलते  हैं।
• चारु चन्द्र की चंचल किरणें, खेल रही थी जल-थल में।

Additional Informationअनुप्रास अलंकार के मुख्यतः निम्न पाँच प्रकार माने जाते हैं-

छेकानुप्रास

वृत्यनुप्रास

श्रुत्यनुप्रास

लाटानुप्रास

अन्त्यानुप्रास

The correct answer is 'John has scored better marks in this test, than in the last one.'

Key Points     

• The error lies in the part "more better" of the sentence.
• When two items/people/situations are compared, a comparative degree is used by putting ‘er’ to the adjective word or "more" with the adjective in association with the word ‘than’.
• Example:
• She is more cheerful than her sister.
• *She is smarter than her sister.*​
• The presence of the word 'than' after the blank shows that there must be a comparative degree of the word 'good.'
• Now 'good' is an adjective that has one syllable.
• The comparative degree of 'good' is 'better.'
• The presence of the word "more" is superfluous in this context.
• The given sentence is in the Present Perfect Tense.
• Structure: Subject + has/have + V3 + Object
• Example: She has left that book.
• So, the correct answer is Option 4.

​​Correct sentence: John has scored better marks in this test, than in the last one.

Given:

Diameter of upper circular part of a frustum = 14m

Diameter of lower circular part of a frustum = 26m

Height of frustum = 8m

Slant height of the conical cap = 12m

Formula used:

Curved surface area of a cone = πrl

where r → radius of the base of a cone

Curved surface area of frustum of a cone = π(R + r)l

l² = h² + (R - r)²

where R  → Upper radius and r  → lower radius of frustum of a cone

h → height of the frustum 

​l → slant height of frustum of a cone

Calculation:

Let slant height of the frustum be l₁ and the conical cap be l₂

l₁ = √8² + (13 - 7)² = √8² + 6² = √100 = 10m

Now, Area of canvas = π(R + r)l₁ + πrl₂

⇒ π(7 + 13) × 10 + π × 7 × 12

⇒ 200π + 84π

⇒ 284π m²

∴ The area of canvas required to make the tent = 284π m2

The correct answer is Lightning.

Key Points

• Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
• The universal law of gravitation explained the following phenomena:
• The force that binds us to the earth.
• Revolution of the Moon around the Earth.
• The orbit of the planets around the Sun.
• Tides caused by the Moon and the Sun.

Additional Information

• Lightning is a massive spark of electricity in the atmosphere or between the atmosphere and the ground.
• Lightning is a naturally occurring electrostatic discharge during which two electrically charged fields, both in the atmosphere or one on the ground, temporarily neutralize themselves, causing an instantaneous release of energy on average one gigajoule.

The correct answer is 'was determined, ventured'

Key Points     

• Verb tense consistency refers to keeping the same tense throughout a clause.
• We don’t want to have one time period being described in two different tenses.
• Now, let us examine the given options:
• Is determined, had been venturing:
• Is determined: Present Tense and Passive voice
• Had been venturing: Past Perfect Continuous Tense
• As both the options are in different tenses, so this answer is incorrect.
• Had determined, is ventured:
• Had determined: Past Perfect Tense
• Is ventured: Present Tense and Passive voice
• As both the options are in different tenses, so this answer is incorrect.
• Was determined, ventured:
• Was determined: Simple Past Tense and Passive voice
• Ventured: Simple Past T​ense and Active voice
• As both the options are in same tenses, so this answer is correct.
• Determines, venturing:
• ​Determined: Simple Present Tense
• Venturing: Incorrect structure
• So, this option is incorrect.
• So, the correct answer is Option 3.

​​Correct sentence: Manik, a poor merchant, was determined to make money and so he bravely ventured into a dense forest to collect wood.

The correct answer is 30.

Key Points

 

• Atomicity is the number of atoms present in a given molecule or compound.
• The number of atoms in NO₂ is 3 so atomicity will be 3.
• It consists of one nitrogen atom and two oxygen atoms.
• Its name is nitrogen dioxide.
• The total number of atoms present in 10 molecules of NO₂ is 30.

अर्थालंकार का उदाहरण नहीं है- 'यमक'।

'उत्प्रेक्षा', 'संदेह', 'रूपक' 'अर्थालंकार' के भेद है।

• 'यमक अलंकार' शब्दालंकार का भेद है।
• शब्दालंकार- 5 भेद ( अनुप्रास, यमक, श्लेष, वीप्सा, वक्रोक्ति)।

Key Points

उत्प्रेक्षा अलंकार- 'जहाँ उपमेय में उपमान की संभावना की जाती है, वहाँ 'उत्प्रेक्षा' अलंकार होता है'।

• उदाहरण- 'यह मुख है या चन्द्र है'।

संदेह अलंकार- जब उपमेय व उपमान में संदेह हों कि, उपमेय है या उपमान तब संदेह अलंकार होता है।

• उदाहरण- 'यह काया है या शेष उसी की छाया'।

रूपक अलंकार- जब उपमेय का उपमान मे अभेद हों, तब रूपक अलंकार होता है।

• उदाहरण- चरण-कमल बंदौ हरी राई।

Additional Information

अर्थालंकार- जिसमें अर्थ के माध्यम से चमत्कार उत्पन्न हों, ऐसे अलंकार अर्थालंकार कहलाते है।

अर्थालंकार के भेद- 

1. उपमा अलंकार
2. उत्प्रेक्षा अलंकार
3. रूपक अलंकार
4. भ्रान्तिमान अलंकार
5. अतिश्योक्ति अलंकार

Mistake Points

• संदेह अलंकार और उत्प्रेक्षा अलंकार में भेद होता है।
• संदेह में Doubt होता है और उत्प्रेक्षा में Guess.

The correct answer is 'The, the, the.' 

Key Points

• The only articles in English are ‘the’ and ‘a/an’.
• We use the article "a or an" to indicate any non-specified member of a group or category.
• If a word begins with a vowel sound, then the correct article is 'an'; otherwise, if it begins with a consonantal sound, the correct article is 'a'.
• The definite article 'the' is used before a noun to indicate that the identity of the noun is known to the reader.
• When we’re talking about a particular organization or country, there is only one Chairman or Police Commissioner, we could be referring to, so we would use the definite article "the" for the first and third blanks.
• Here, we are talking about the particular position "right" where the Chairman is sitting, so we must use "the" in the second blank.
• Hence, the correct answer is Option 1.

​

​Correct sentence: The Chairman is sitting to the right of the Police Commissioner.

The correct answer is Medulla oblongata.

Key Points

• The part of the brain from which the spinal cord originates is the Medulla oblongata.
• The spinal cord is a long, tubular structure that extends from the medulla oblongata to the lumber part of the vertebral column.
• It is a part of the central nervous system.
• It controls the reflex actions and transmits sensory impulses from the skin and muscles to the brain.
• The spinal cord is the nerve center and associated neurons are present in it.
• The medulla is part of the hindbrain.
• The spinal cord emerges from the medulla oblongata and the medulla connects it to the brain.
• The medulla contains centers that control respiration, cardiovascular reflexes, and gastric secretion.
• Thus its functions are related to the autonomic (involuntary) functions of breathing, sneezing, swallowing, digestion, regulating heart rate and blood pressure, etc.

Additional Information 

Cerebrum :

• The cerebrum is one of the parts of the forebrain and the site of intelligence, memory, behavior, and reasoning.
• The cerebrum regulates vision, hearing, and speech, and involves in voluntary activities.

​​Pons :

• Pons is the part of hindbrain.
• It consists of fiber tracts that interconnected different regions of the brain.

Cerebellum :

• The cerebellum is also the part of hindbrain.
• It maintains balance and posture of the body and also coordinates voluntary movements.

Given:

Height of observer is 2 m

angle of elevation = 45°

The observer away from tower = 18 m

Calculation:

According to the drawing,

Tan 45° = \(\frac{x}{18}\)

1 = \(\frac{x}{18}\)

x = 18 m

∴ The total height of the tower is 18 m + 2 m = 20 m.

The correct answer is 'many.'

Key Points   

• Let's understand the meaning and usage of given determiners:
• ​​Little: We use "little" with uncountable nouns. 
• Example: I’m not very happy about it but I suppose I have little choice.
• Any: We use "any" before nouns to refer to indefinite or unknown quantities or an unlimited entity.
• Example: Mr. Jacobson refused to answer any questions.
• Many: We use "many" to refer to a large number of something countable.
• We most commonly use it in questions and in negative sentences.
• Example: I don't have many relatives.
• Few: We use the word "few" when we want to talk about the quantity of something. Usually, we use it when we want to talk about a small quantity.
• Example: Few members of the family leave their hometown each year.
• Here, we are referring to "shoppers" which were not big in numbers.
• Hence, the correct answer is 'Option 3.'

Correct sentence: This being COVID time, there aren’t many shoppers in the mall.

The correct answer is XY.

Key Points

• Atoms of X crystalize in a simple cubic lattice and atoms of Y occupy alternate face centers in the lattice formed by X.
• In the given compound; there must be 8 corners in a cube,
• So, as the Y atoms are at corners, so each of the Y atoms will contribute 1/8 part towards a particular unit cell.
• The no. of Y atoms per unit cell = 8*1/8 = 1
• Further, the X atoms are at the alternate faces so they will be available only at one of the opposite faces, so the contribution of each of the X-atoms will be 1/2 towards the face center.
• The no. of X-atoms = 1*1/2 = 1​
• Hence, the formula of the compound will be "XY".

Shortcut Trick

Speed in cm/min = (132 × 1,00,000) ÷ 60 = 2,20,000 cm/min

Circumference (distance per revolution) = 2 × (22/7) × 14 = 88 cm

Revolutions per min = 2,20,000 ÷ 88 = 2500

∴ The correct answer is 2500.

Alternate Method

Given:

Radius (r) = 14 cm

Speed = 132 km/hr

Formula Used:

Total Distance = Number of Revolutions × Circumference of the wheel

Circumference = 2 × π × r

Calculations:

⇒ Circumference = 2 × (22/7) × 14

⇒ Circumference = 2 × 22 × 2 = 88 cm

⇒ Speed in km/min = 132 ÷ 60 = 2.2 km/min

⇒ Distance covered in 1 minute = 2.2 × 1,00,000 cm = 2,20,000 cm

⇒ Number of revolutions = 2,20,000 ÷ 88

⇒ Number of revolutions = 2500

∴ The correct answer is 2500.

Additional Information

Circumference of a Circle

The distance covered by a wheel in one complete revolution is equal to its circumference, given by the formula 2 × π × r.

Speed and RPM Relation

Revolutions per minute (RPM) is calculated as (Distance traveled in one minute) ÷ (Circumference of the wheel).

Unit Conversions

To convert speed from km/hr to cm/min, multiply the value by 100,000 (to get cm) and divide by 60 (to get min).

'प्रति-दिन' द्वंद्व समास का उदाहरण नहीं है। 

अव्ययीभाव समास का उदाहरण है।

Key Pointsअव्ययीभाव समास- 'पहला पद प्रधान तथा अव्यय होता है'।

पहचान- पहला पद अनु, भर, प्रति, यथा, यावत आदि।

• उदाहरण- प्रतिदिन।
• यथासंभव।
• यथाविधि

द्वंद्व समास- दोनों पद प्रधान होते है।

पहचान- योजक चिन्ह (-) का प्रयोग। तथा, मध्य में 'और', 'अथवा', 'या' लगते है।

• उदाहरण- अन्न-जल= अन्न और जल।
• नदी-नाले= नदी और नाले।

Additional Informationसमास-  दो या दो से अधिक शब्दों से मिलकर बने नये सार्थक शब्द को समास कहते है।

समास भेद- 6 भेद होते हैं।

1. अव्ययीभाव समास
2. तत्पुरुष समास
3. द्विगु समास
4. द्वन्द्व समास
5. कर्मधारय समास
6. बहुव्रीहि समास

Mistake Points

1. 'प्रति-दिन' अव्ययीभाव समास का उदाहरण है तथा,
2. अन्य शब्द द्वंद्व समास के उदाहरण है।

• जैसे-रात-दिन।
• राष्ट्र-राज्य।
• भला-बुरा।

'जगण' का सही सूत्र- '।ऽ।'

• उदाहरण- 'मरीन, गरीब, गुलाब'।

Key Pointsगण-  केवल वर्णिक छंद में प्रयोग होते है।

गणों की संख्या 8 है- यगण (।ऽऽ), मगण (ऽऽऽ), तगण (ऽऽ।), रगण (ऽ।ऽ), जगण (।ऽ।), भगण (ऽ।।), नगण (।।।) और सगण (।।ऽ)।

तगण के लिए सूत्र-  ऽऽ।

• उदाहरण- चालाक, आधार आदि।

रगण के लिए सूत्र-  ऽ।ऽ

• उदाहरण- पालना, मारना आदि।

यगण के लिए सूत्र- ।ऽऽ

• उदाहरण- बहाना, नहाना आदि।

Additional Informationछंद परिभाषा-जिस शब्द-योजना में वर्णों या मात्राओं और यति-गति का विशेष नियम हो, उसे छन्द कहते हैं**।छन्दशास्त्र को ‘पिंगल-शास्त्र’ भी कहते हैं क्योंकि, इसके आदि प्रणेता श्री पिंगलाचार्य थे।** 

छंद के 7 अंग होते है- 

1. चरण/पद/पाद
2. वर्ण और मात्रा
3. संख्या और क्रम
4. गण
5. यति /विराम
6. गति
7. तुक

छंद के प्रकार- 3**।**

1. मात्रिक छंद
2. वर्णिक छंद
3. मुक्त छंद

'राकापति' शब्द का पर्यायवाची है- 'चंद्र'।

• चन्द्र के अन्य पर्यायवाची शब्द-  सोम, सुधांशु, द्विजराज विधु।

Key Points

Additional Information

Mistake Points

• 'राकापति' चन्द्र का पर्यायवाची शब्द है 'इंद्र' का नहीं।
• 'इंद्र' के पर्यायवाची शब्द- सुरपति, देवराज, महेंद्र है।

क्रिया के जिस रूप से यह पता चले कि कार्य वर्तमान में हो रहा है उसे 'तात्कालिक वर्तमान काल' कहते है।

• उदाहरण- वह गा रहा है।

Key Points

पूर्ण वर्तमानकाल- इससे वर्तमानकाल में कार्य की पूर्ण सिद्धि का बोध होता है।

• जैसे- वह आया है।

संदिग्ध वर्तमानकाल- जिस क्रिया के वर्तमान समय में पूर्ण होने में संदेह हो, उसे संदिग्ध वर्तमानकाल कहते हैं।

• जैसे- 'माँ खाना बना रही होगी।

वाक्य में 'रही होगी' से खाना बनाने के कार्य को निश्चित रूप से नहीं कहा गया, उसमें संदेह की स्थिति बनी हुई है, अतः यहाँ संदिग्ध वर्तमान है।

सम्भाव्य वर्तमानकाल- इससे वर्तमानकाल में काम के पूरा होने की सम्भावना रहती है। उसे सम्भाव्य वर्तमानकाल कहते हैं।

संभाव्य का अर्थ होता है संभावित या जिसके होने की संभावना हो।

• जैसे- वह आया है।

Additional Information

वर्तमान काल-  क्रिया के जिस रूप से यह पता चले कि कार्य वर्तमान में हों रहा है, उसे वर्तमान काल कहते है।

जैसे- पिता जी समाचार सुन रहे हैं।

वर्तमान काल के भेद- पाँच भेद होते है-

1. सामान्य वर्तमानकाल
2. अपूर्ण वर्तमानकाल
3. पूर्ण वर्तमानकाल
4. संदिग्ध वर्तमानकाल
5. संभाव्य वर्तमानकाल

The correct answer is Methanol.

Key Points

• Methanol is known as wood spirit.
• Methyl alcohol or Methanol (CH3OH) is also called wood alcohol, or wood spirit, i.e. alcohol (an organic compound) consisting of a methyl group (CH3 ) linked with a hydroxyl group (OH).
• Destructive distillation of wood was the method used formerly to produce it.
• The direct combination of carbon monoxide gas and hydrogen in the presence of a catalyst is the modern method of preparing methanol.
• Syngas, a mixture of hydrogen and carbon monoxide derived from biomass, is increasingly used for methanol production in modern times.

Additional Information

• Benzyl alcohol :
• Benzyl alcohol (C6H5CH2OH) appears as a clear colorless liquid with a pleasant odor.
• It is slightly denser than water.
• It has a Flashpoint of 194 °F. and a Boiling point of 401 °F.
• Its contact may irritate skin, eyes, and mucous membranes.
• It may be slightly toxic by ingestion.
• Ethanol :
• Ethanol (CH3CH2OH) is a primary alcohol that is ethane in which one of the hydrogens is substituted by a hydroxy group.
• It has a role as an antiseptic drug, a polar solvent, a neurotoxin, a central nervous system depressant, a teratogenic agent, etc.
• It is a primary alcohol, an alkyl alcohol, a volatile organic compound, and a member of ethanols.
• अल्गल
• Glycerine :
• Glycerol (CH2OH-CHOH-CH2OH) is a triol with a structure of propane substituted at positions 1, 2, and 3 by hydroxy groups.
• It has a role as an osmolyte, a solvent, a detergent, a human metabolite, an algal metabolite, a Saccharomyces cerevisiae metabolite, an Escherichia coli metabolite, a mouse metabolite, and a geroprotector.
• It is an alditol and a triol.

The correct answer is 35.2 g.

Key PointsAtomic mass of sulphur =32

Mass of 1.1 mol of sulphur = 32*1.1= 35.2 g

'बहुव्रीहि समास'- जब दो पद मिलाकर नया शब्द बनाया जाता है और उससे मिलाए गए दोनों पदों से अलग ही तीसरा अर्थ निकलता है, तो वहाँ 'बहुव्रीहि समास' माना जाता है।

• उदाहरण- चतुरानन= 'चार है आनन जिसके' अर्थात् 'ब्रह्मा जी'।

Key Pointsद्विगु समास- 'उत्तर पद प्रधान होता'।

पहचान- पहला पद 'संख्यावाचक' तथा इसमें 'समूह या समाहार' का पता चलता है।

• उदाहरण- अष्टधातु= 'आठ धातुओं का समाहार'।

​कर्मधारय समास- 'उत्तर पद प्रधान होता'।

पहचान- 'दोनों पदों' के मध्य मे 'है जो' , 'के समान' आता हैं।

• उदाहरण- चरणकमल= 'कमल के समान चरण'।

द्वंद्व समास- दोनों पद प्रधान होते है।

पहचान- योजक चिन्ह (-) का प्रयोग। तथा, मध्य में 'और', 'अथवा', 'या' लगते है।

• उदाहरण- धन-दौलत= धन दौलत।

Additional Information

समास-  दो या दो से अधिक शब्दों से मिलकर बने नये सार्थक शब्द को समास कहते है।

समास भेद- 6 भेद होते हैं।

1. अव्ययीभाव समास
2. तत्पुरुष समास
3. द्विगु समास
4. द्वन्द्व समास
5. कर्मधारय समास
6. बहुव्रीहि समास

Mistake Points

• 'बहुव्रीहि समास' में 'अन्य पद' प्रधान होता है तथा कर्मधारय एवं द्विगु में 'उत्तर पद' और द्वंद्व में 'दोंनों पद' प्रधान होते है।

Here, the erroneous sentence is 'There's a saying: A thief believes everyone are thieves?'

Key Points

• Option 1 is a correct sentence:
• The modal verb "must" is always followed by the V1 form of the verb.
• Example: You must call her.
• ​Option 2 is a correct sentence:
• The given interrogative sentence is in the Simple Past Tense.
• Structure: Why + did + subject + V1 + object?
• Example: Why did she ignore me?
• Option 3 is a correct sentence:
• The subject is in proper agreement with the verb.
• Option 4 is incorrect:
• The error lies in the part "everyone are thieves" of the sentence.
• We use "everyone" with singular verbs.
• Example: Everyone is present.
• ​We have to replace "everyone are thieves" with "everyone is a thief."​
• Also, we have to replace the question mark ( ? ) at the end with a full stop ( . ) as the given sentence is a declarative sentence.
• Hence, the correct answer is 'Option 4.'

Correct sentence: There's a saying: A thief believes everyone is a thief.

The correct answer is: Option 1 i.e. 'by hook or by crook'.

Key Points

• The word "by hook or by crook" means to accomplish something by any means necessary, whether fair or foul; using any possible method to achieve a goal. (किसी भी तरह से)
• Example: He was determined to win the race by hook or by crook.
• "by hook or by crook" refers to doing whatever it takes to get something done. (किसी भी तरह से)
• Example: The man tried to dispose of his old car by hook or by crook.

Therefore, the correct answer is: by hook or by crook.

Additional Information

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

• in for a few pennies (कुछ पैसों के लिए): This phrase generally is not idiomatic, and it doesn't fit the context of the sentence.
• Example: N/A, as this is not a common idiom.
• to lay his cards on the table (खुलकर सामने रखना): This idiom means to be open and honest about one's intentions or plans.
• Example: He laid his cards on the table and told them the truth about his plans.
• by throwing cold water (बदम बनाना): This idiom means to discourage or dampen someone's enthusiasm.
• Example: She threw cold water on his proposal by pointing out all its flaws.

Given:

sum and product of the zeros are \(\sqrt{2}\) and \(\frac{1}{3}\) 

Concept used:

Quadratic equation = x² - (a + b)x + ab

Where, a & b are zeroes of the quadratic equation. 

Calculation:

a + b = \(\sqrt2\)

ab = \(\frac{1}{3}\)

Quadratic equation = x2 - (a + b)x + ab

Let's put the values given to form quadratic equation,

⇒ x² - (\(\sqrt2\))x + \(\frac{1}{3}\) = 0

⇒ 3x² - 3\(\sqrt2\)x + 1 = 0

∴ The correct answer is 3x2 - \(3\sqrt{2}\) x + 1

Shortcut Trick

Let the income of C be 100 units.

Since B is 20% less than C, income of B = 100 − 20 = 80 units.

Since A is 10% more than B, income of A = 80 × 1.1 = 88 units.

Required ratio A : B : C = 88 : 80 : 100 = 22 : 20 : 25.

∴ The correct answer is 22 : 20 : 25.

Alternate Method

Given:

Income of A is 10% more than that of B.

Income of B is 20% less than that of C.

Calculations:

⇒ Let the income of C be 100x.

⇒ Income of B = 100x − (20% of 100x) = 80x

⇒ Income of A = 80x + (10% of 80x)

⇒ Income of A = 80x + 8x = 88x

⇒ The ratio of their incomes A : B : C = 88x : 80x : 100x

⇒ Dividing by the common factor 4x, we get:

⇒ A : B : C = 22 : 20 : 25

∴ The correct answer is 22 : 20 : 25.

Additional Information

Combining Ratios

If A : B = m : n and B : C = p : q, the combined ratio A : B : C can be found by making the common term B equal, resulting in (m × p) : (n × p) : (n × q).

Percentage to Ratio Conversion

Percentage changes can be written as fraction multipliers. For example, a 10% increase means multiplying by 11/10, and a 20% decrease means multiplying by 4/5. Using fractions makes ratio calculation much faster.

Given:

1 out of 10 electrical switches inspected are likely to be defective.

Calculation:

Probability of defective bulb = \(\dfrac{1}{10}\)

Probability of non-defective bulb = \(\dfrac{9}{10}\)

Mean, λ = np

90 electrical switches inspected are respectively.

So, n = 90

Mean = 90 × \(\dfrac{9}{10}\) = 81

Standard deviation = \(\sqrt{\lambda}\)

⇒ \(\sqrt{81}\) = 9

∴ The mean and standard deviation are 81 and 9.

'खोदा पहाड़ निकली चुहिया' लोकोक्ति का अर्थ- 'अधिक परिश्रम के बाद साधारण लाभ'।

वाक्य प्रयोग- श्रद्धा ने पूरे महीने जमकर पढाई की लेकिन जब परीक्षा का वक्त आया तो पेपर बहुत आसान आया। इस पर श्रद्धा मन जी मन कहने लगी, लो 'खोदा था पहाड़ निकली चुहिया'।

Key Points

Additional Information

Mistake Points

• 'खोदा पहाड़ निकली चुहिया' लोकोक्ति का उचित अर्थ- 'अधिक परिश्रम के बाद साधारण लाभ'।
• अन्य अर्थ जैसे 'पहाड़ खोदकर चुहिया निकालना' लोकोक्ति का अनुचित अर्थ होगा।

The correct answer is Gibb's free energy change < 0.

Key Points

• Gibbs free energy is a measure of the amount of energy available to do work in an isothermal and isobaric (constant temperature and pressure) thermodynamic system.
• This is where the term "free" comes from; it refers to the amount of energy in a system that is easily available for usage.
• The Gibbs energy is thus the enthalpy (essentially the total energy of the system) minus the entropy times the temperature (a measure of the amount of energy that is unavailable).
• For spontaneity of reduction of metal oxides into metals Gibb's free energy change < 0

Given :

To find the probability of getting number greater than 4 in single throw .

Formula used :

Probability = \(\dfrac{Number\ of\ Favorable\ Outcomes}{Total\ Outcomes}\)

Calculation :

Possible outcomes = 5, 6  

Total no. of outcomes = 6

Probability = \(\dfrac{2}{6}\) = \(\dfrac{1}{3}\)

∴ The answer is \(\dfrac{1}{3}\) .

Concept:

• DNA replication is a semi-conservative process in which two parental strands separate and each acts as a template for synthesizing a complementary strand over it.
• After completion of replication, each DNA had one parental strand and one newly synthesized strand of DNA.

Explanation:

• Replication of DNA occurs in the S phase of mitosis for this reason it is also called as synthesis phase.
• During the S phase, the amount of DNA present in each cell doubles i.e. if previously the cell had a 2C amount of DNA, now it has 4C.
• However, the chromosome number remains the same, if the cell had 2n or a diploid number of chromosomes at G1, even after the S phase number of chromosomes will remain the same i.e. 2n

Important Points 

• Replication of Nuclear DNA occurs at the S phase, while replication of the cytoplasmic DNA may occur at any stage of the cell cycle.  ​

Additional Information

• Interphase  is divided into 3 phases:
• G1 phase/Post mitotic/Pre-DNA synthetic phase/1^st gap phase - Synthesis of different types of RNA and proteins.
• S-phase/Synthetic phase
• G2-phase/Pre mitotic/Post synthetic phase/2^nd gap phase - Formation of tubulin protein required for the spindle fiber formation.
• Interphase is followed by the M phase which is the division phase

'शयन करने की इच्छा' के लिए एक शब्द- 'सुषुप्सा'।

वाक्य प्रयोग- मोहन पूरी रात पार्टी में जागता रहा और अब वह 'सुषुप्सा' लेकर पूरे दिन घूमता रहा।

Key Points

Additional Information

Mistake Points

• 'शयन करने की इच्छा' के लिए एक शब्द होगा 'सुषुप्सा'। न कि, 'सारस्वत'।
• क्योंकि, 'सरस्वती जी का भक्त' के लिए एक शब्द 'सारस्वत' होगा।

'घिनौना' शब्द में 'औना' प्रत्यय प्रयुक्त हुआ है।

घिन+औना= घिनौना।

Key Points

Additional Informationहिन्दी में प्रत्यय के दो प्रकार के होते हैं-

1. कृत प्रत्यय
2. तद्धित प्रत्यय
3. कृदन्त प्रत्यय- कृदन्त या कृत प्रत्यय वे प्रत्यय जो धातुओं अर्थात् क्रिया पद के मूल रूप के साथ लगकर नये शब्द का निर्माण करते हैं कृदन्त या कृत प्रत्यय कहलाते हैं। हिन्दी क्रियाओं में अन्तिम वर्ण ‘ना’ का लोपकर शेष शब्द के साथ प्रत्यय का योग किया जाता है। 

उदाहरण- अक्कड़ = भुलक्कड़, घुमक्कड़, पियक्कड़, आदि।

2. तद्धित प्रत्यय- तद्धित प्रत्यय वे प्रत्यय जो क्रिया पदों के अतिरिक्त संज्ञा, सर्वनाम, विशेषण आदि शब्दों के साथ लगकर नये शब्द का निर्माण करते हैं उन्हें तद्धित प्रत्यय कहते हैं।

• उदाहरण- छात्र + आ = छात्रा।
• देव + ई = देवी।
• मीठा+आस = मिठास आदि।​​

Mistake Points'घिनौना' शब्द में 'औना' प्रत्यय प्रयुक्त हुआ है। न कि, 'अना' , 'न' , 'ना'।

• उदाहरण- अना प्रत्यय- 'वंदना' 'वंद+अना'।
• ना प्रत्यय- 'बेलना' 'बेल+ना'।
• न प्रत्यय- 'गलन' 'गल+न'।

Given :

An A.P. series 4, 11, 18, ........

Formula used :

S_n = \(\dfrac{n}{2}[2a+(n-1)d]\)

Where, a = first term, d = difference between consecutive numbers

n = n^th term

Calculation :

Here, S_n = 795 ,a = 4, d = 18 - 11 = 7

So, 795 = \(\dfrac{n}{2}[2\times 4+(n-1)7]\)

⇒ 1590 = 8n + 7n(n - 1)

⇒ 1590 = 7n² + n

On solving the quadratic equation, we get

n = \(15, -\dfrac{106}{7}\)

∴ The answer is n = 15 .

The correct answer is SA Node.

Key Points

SA Node is known as the 'Natural pacemaker of the heart'.

• The entire heart is made of cardiac muscles.
• SA node generates cardiac impulses whereas the AV node relays and intensifies cardiac impulses.
• The sino-atrial node (SA) is called the natural pacemaker of the heart.
• There are three types of muscles present in the human body.
• Voluntary
• involuntary
• Cardiac
• A specialized cardiac musculature called the nodal tissue is also distributed in the heart.
• A patch of this tissue is present in the right upper corner of the right atrium called the sino-atrial node (SAN).
• Another mass of this tissue is seen in the lower-left corner of the right atrium close to the atrioventricular septum called the atrioventricular node (AVN).
• The pacemaker is a device that is placed in the chest or abdomen to help control abnormal heart rhythms.
• The radioactive element used in heart pacemakers is Plutonium.
• Plutonium-based pacemakers are larger and heavier but have a longer life expectancy.

Shortcut Trick

For concentric circles, the length of the chord of the larger circle that is tangent to the smaller circle is calculated directly using the radii.

Length of chord = 2 × √(R² − r²)

Length = 2 × √(5² − 3²)

Length = 2 × √(25 − 9) = 2 × √16 = 2 × 4 = 8 cm

∴ The correct answer is 8 cm.

Alternate Method

Given:

Radius of larger circle (OA) = 5 cm

Radius of smaller circle (OM) = 3 cm

AB is the chord of the larger circle touching the smaller circle at M.

Calculations:

⇒ The radius drawn from the center to the point of tangency is perpendicular to the tangent.

⇒ ∴ OM ⊥ AB and ∠OMA = 90°

⇒ In right-angled triangle OMA, applying Pythagoras theorem:

⇒ OA² = OM² + AM²

⇒ 5² = 3² + AM²

⇒ 25 = 9 + AM²

⇒ AM² = 16

⇒ AM = 4 cm

⇒ A perpendicular drawn from the center to a chord bisects it, meaning AM = MB.

⇒ Total length of chord AB = 2 × AM

⇒ AB = 2 × 4 = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Properties of Chords

The perpendicular drawn from the center of a circle to any chord bisects the chord into two equal halves. Conversely, a line connecting the center to the midpoint of a chord is always perpendicular to it.

Tangent Theorem

A tangent to a circle touches it at exactly one point, and the radius connecting the center to this exact point of contact is strictly perpendicular to the tangent line.

Concentric Circles

Two or more circles sharing the exact same center point but having different radii are known as concentric circles. The area between two such concentric circles is known as an annulus.

The correct answer is 'Whatever.'

Key Points   

• Let's understand the meaning and usage of given determiners:
• Some: We use "some" before nouns to refer to indefinite quantities.
• Although the quantity is not important or not defined, using "some" implies a limited quantity.
• Example: Can you get me some milk?
• "Whatever" means it is not important what is; it makes no difference what (is).
• Example: We'll go whatever the weather.
• "Whenever" means every or any time.
• Example: I blush whenever I think about it.
• "All" can be used with uncountable nouns and plural countable nouns by itself.
• Example: All the people in the room were silent.
• Here, the sentence is stating that the person is fine with any decision that the other person makes.
• Hence, the correct answer is 'Option 2.'

Correct sentence: Whatever decision you take is fine by me.

The correct answer is 'however.'

Key Points   

• Let us explore the given options:
• ​However: The most common use of "however" is as an adverb that connects two sentences/clauses in order to show a contrasting idea.
• However comes at the beginning of the second sentence (the one that describes the contrast or opposite viewpoint), following the period from the first sentence.
• In this position, however is followed by a comma.
• Example: We were told we would be discussing the new schedule during the meeting. However, our boss never brought it up once.
• "Furthermore" is used to introduce a piece of information or opinion that adds to or supports the previous one.
• Example: Furthermore, they claim that any such interference is completely ineffective.
• Even: We use "even" to refer to something surprising, unexpected, unusual or extreme.
• Example: He didn't even have enough money.
• Although: It means ‘in spite of something.’ 
• It is a subordinating conjunction.
• This means that the clause which they introduce is a subordinate clause, which needs a main clause to make it complete.
• When the although clause comes after the main clause, it can also mean ‘but it is also true that …’
• Example: We didn’t make any profit although nobody knows why.​​
• Here the sentence says that she is not very nice, yet she is a very good student. (contrasting ideas)
• Therefore, the correct answer is Option 1.

​Correct Sentence: She is very good at studies; however she is not very polite.

The correct answer is 'for.'

Key Points 

• Let us see the meanings of the given options:
• And is a coordinating conjunction. We use "and" to connect two words, phrases, clauses, or prefixes together.
• And is used to join two words of the same rank or same qualities.
• Example: He is bold and handsome.
• Yet: We use "yet" as an adverb to refer to a time that starts in the past and continues up to the present. It usually comes in the end position.
• Example: Kevin hasn’t registered for class yet.
• For: We sometimes use "for" as a conjunction meaning 'because'.
• Example: Chasing the white stag through the forests, never catching it, of course, for it is a creature of legend.
• But: "But" is a coordinating conjunction used to connect ideas that contrast.
• Example: I like him but I can't meet him.
• ​The sentence expresses that a person forgives because of being a human.
• Therefore, the correct answer is Option 3.​

Correct sentence: I’ll forgive you, for we are all human.

Given :

 ΔLMN ∼ ΔDEF, and \(\frac{LN}{DF} = \frac{3}{4}\)

Formula used :

Thales theorem,

For  ΔLMN ∼ ΔDEF, and \(\frac{LN}{DF} = \frac{LM}{DE}=\frac{MN}{EF}\)

\(\frac{ar(ΔLMN)}{ar(ΔDEF)}\) = \(\big(\frac{LN}{DF}\big)^2 \)

Calculation :

According to question,

\(\frac{ar(ΔLMN)}{ar(ΔDEF)}\) = \(\big(\frac{3}{4}\big)^2\)  = \(\frac{9}{16}\)

∴ The answer is \(\frac{9}{16}\) .

The correct answer is '​will.'

 

Key Points  

• Let us see the usage of the given modal verbs:​
• Will: We use "will" to express beliefs about the present or future, to talk about what people want to do or are willing to do, to make promises, offers, and requests.
• Example: He will give her a call if I can find her number.
• Should: "Should" can be used to show obligation, give recommendations, or even an opinion.
• Example: You should stop eating fast food.​
• ​Can: We use "can" to talk about the ability to do something at a specific time in the present or future.
• Example: I can see you.
• Must: "Must" is used to express obligation, give orders, and give advice. 
• Example: All pupils must bring a packed lunch tomorrow.
• ​ ​The sentence is stating about the punishment to the trespassers.
• Therefore, the correct answer is Option 1.

Correct sentence: This is a restricted area. Trespassers will be punished.

मुहावरे 'लाक्षणिक अथवा विशिष्ट' अर्थ को प्रकट करते हैं।

• उदाहरण- 'आँखों में धूल झोंकना' अर्थात् 'धोखा देना'।
• वाक्य-प्रयोग- तुमने पुलिस चौकी के सामने से चोरी करके पुलिस वालो की 'आँखों में धूल झोंक' दी।

Key Points

Additional Information

Mistake Points

• मुहावरे 'लाक्षणिक अथवा विशिष्ट' अर्थ को प्रकट करते हैं। तथा आम बोलचाल का अर्थ 'लोकोक्ति' प्रकट करती है
• उदाहरण- उड़ती चिड़िया पहचानना अर्थात् दूर से ताड़ या भाँप लेना।
• एवं 'रूढ़ अर्थ' का आशय 'ऐसे अर्थ जिनके टुकड़े न हों सके'। जैसे- जल।

The correct answer is '​should.'

 

Key Points  

• Let us see the usage of the given modal verbs:​
• "Should" can be used to show obligation, give recommendations, or even an opinion.
• Example: You should stop eating fast food.​
• Will: We use "will" to express beliefs about the present or future, to talk about what people want to do or are willing to do, to make promises, offers, and requests.
• Example: He will give her a call if I can find her number.
• Ought to: We use "ought to" when talking about things which are desired or ideal.
• Example: They ought to have more parks in the city centre.
• Would: We use "would" as the past of "will" and it is used to make hypotheses. In this condition, we imagine a situation.
• Example: I would give you a lift, but my wife has the car today.
• ​ ​The sentence is stating about an opinion of trying a fried ice-cream.
• Therefore, the correct answer is Option 1.

Correct sentence: When you go that restaurant, you should try their fried ice-cream. It tastes awesome.

The correct answer is 'endangered.'

Key Points  

• Let us see the meaning of Jeopardized:
• Jeopardized: to do something that may damage something or put it at risk. (किसी कार्य द्वारा किसी वस्‍तु को ख़तरे में डालना या हानि पहुँचाना)
• Example: She jeopardized his career.
• Let us see the meanings of the given options:
• Safeguarded: protect from harm or damage with an appropriate measure. (संभावित ख़तरों से सुरक्षा देने वाली वस्‍तु)
• Celebrated: to do something to show that you are happy about something that has happened or because it is a special day. (किसी विशेष अवसर पर उत्‍सव मनाना, समारोह करना)
• Endangered: to cause danger to somebody/something. ((व्‍यक्ति या वस्‍तु को) ख़तरे में डालना)
• Rejuvenated: to make somebody/something feel or look younger. (किसी को युवा बना देना)
• From the meanings of the given words, we can say that the correct word similar in meaning to the bold word in the given sentence is 'endangered.'
• Hence, the correct answer is Option 3.

The correct answer is "to, of.'

Key Points  

• The word "committed" means prepared to give a lot of your time and attention to something because you believe it is right or important. ((किसी उचित या महत्वपूर्ण लगने वाले कार्य में) संलग्‍न, प्रतिबद्घ)
• It is always followed by the preposition "to."
• Example: The company is committed to providing quality products.
• The word "cause" means a thing or person that makes something happen. (कारण, हेतु, निमित)
• The word "cause" is followed by the preposition "of."
• The meaning of the phrase “cause of” signifies “a source of something” like “cause of accidents”, “cause of deforestation”, etc.
• ​Therefore, the correct answer is Option 1.

​

Correct sentence: We are all committed to the cause of the country.

'नूतन' का विपरीतार्थक शब्द- 'पुरातन' है।

• 'नूतन' अर्थ- 'नया'।
• 'पुरातन' अर्थ- 'पुराना'।

Key Points

Additional Information

The correct answer is "It looks a bit like Mumbai, isn’t it?"

Key Points   

• The first sentence is stating that it looks a bit like Mumbai and the second sentence is asking for confirmation.
• Question tags are used to confirm that something is true or not and to encourage a reply from the person we are speaking to.
• Tags are formed with the auxiliary or modal verb, from the given statement with the appropriate subject (Pronoun).
• A negative statement is followed by a positive question tag.
• Negative auxiliaries and verbs in tags are usually in the contracted form ‘n’t.
• Structure: Auxiliary /modal + n’t + Pronoun?
• Example: She is a doctor, Isn’t she?
• ​Positive statement is followed by a negative question tag.
• Structure: Auxiliary /modal  + Pronoun?
• Example: She is not a doctor, Is she?
• ​The given sentence is a positive sentence, so we have to add a negative question tag after it.
• ​Therefore, the correct answer is Option 1.

​

Correct sentence: It looks a bit like Mumbai, isn’t it?

The correct answer is 6 bar. 

CONCEPT:

Isobaric process:

• When a thermodynamic process undergoes a physical change in such a way that its pressure remains constant, then the change is known as the isobaric process.

⇒ P = constant

EXPLANATION:

• We know that in an isobaric process, the pressure of the system remains constant.
• So the initial and the final pressure will be equal.

⇒ P1 = P2

• So the final pressure will be  6 bar.

The correct answer is Oxygen.

Key Points

• methanogens are microorganisms.
• Methanogens grow anaerobically on cellulosic material to produce CO2 and H2 with a large amount of methane.
• Methanogens are mostly found in the anaerobic sludge during sewage treatment.
• These bacteria are also found in the rumen (a part of the stomach) of cattle, where they provide nutrition to cattle.
• A lot of cellulosic material present in the food of cattle is also present in the rumen of cattle.
• In the rumen of cattle, these bacteria help in the breakdown of cellulose and play an important role in the nutrition of cattle.
• Methanogens are used in the production of biogas.
• Biogas is a mixture of CH4, SO2, CO2, etc. (inflammable gases) produced by microbial activity that can be used as fuel.

जिसके कारण या जिसके प्रति मन में भाव जगे वह 'विषयालंबन' कहलाता है।

• उदाहरण:- कृष्ण के मन में राधा के प्रति रति भाव जाग्रत होता है, तो राधा विषय होंगी।

Key Pointsआलंबन विभाव के पक्ष :-

1. आश्रयालंबन
2. विषयालंबन

आश्रयालंबन:- जिसके मन में भाव जगते हैं उसे आश्रयालंबन कहते हैं।

• उदाहरण:- कृष्ण के मन में राधा के प्रति रति भाव जाग्रत होता है, तो 'राधा' विषय होंगी। और 'कृष्ण' आश्रय होंगे।

अनुभाव:- वाणी और अंगों के अभिनय द्वारा जिनसे अर्थ प्रकट होता है उन्हें अनुभाव कहते हैं। 

• उदाहरण-  नाक को टेढ़ा करना, मुह बनाना, थूकना, आंखे मीचना आदि।

उद्दीपन विभाव- अर्थ- और बढ़ाना ,और तेज़ करना। जैसे 'आग में घी' डाल कर उसे और तेज़ या उद्दीप्त कर दिया जाता है उसी तरह स्थाई भाव को और तेज़ करने वाले कारण उद्दीपन विभाव कहे जाते है।

• उदाहरण- लक्ष्मण का परशुराम को ललकारना व्यंग्य करना मुस्कुराना उनके क्रोध को और बढ़ा देता है।

Additional Information'रस' ;- रस का शाब्दिक अर्थ है 'आनंद'। काव्य को पढ़ने या सुनने से जिस आनंद की अनुभूति होती है,

उसे 'रस' कहा जाता है।

रस के चार अंग है-

1. विभाव;- जो व्यक्ति वस्तु या परिस्थितियाँ स्थायी भावों को उद्दीपन या जागृत करती हैं, उन्हें विभाव कहते हैं।

विभाव के दो भेद हैं-

a- आलंबन विभाव

b- उद्दीपन विभाव।
2. अनुभाव 3. व्यभिचारी भाव/ संचारी भाव;- उदाहरण- हर्ष, विषाद, त्रास, लज्जा, ग्लानि चिंता, शंका, असूया ,मोह, गर्व,उत्सुकता आदि। 4. स्थायी भाव;- उदाहरण- रति, ह्रास, शोक, क्रोध, उत्साह, भय, जुगुप्सा/घृणा, विस्मय/आश्चर्य, निर्वेद, वात्सल्य रति, भगवद विषयक रति।

संदिग्ध वर्तमान का सही उदाहरण- 'गाड़ी आती होगी'।

Hintसंदिग्ध वर्तमान काल में अन्त में 'होगा', 'होगी' आदि शब्द लगे होते।

• उदाहरण- गाड़ी आती होगी।

Key Pointsसंदिग्ध वर्तमान काल-  जिस क्रिया के वर्तमान समय में पूर्ण होने में संदेह हो।

• उदाहरण- वह पढ़ रही होगी।
• सीमा खाना खा रही होगी।
• रामा गीत गा रही होगी।

सामान्य वर्तमान काल- अन्त में 'ता', 'ति', 'ते' लगा होता।

• उदाहरण- बच्चा रोता है।
• वह आता है।
• श्याम पढ़ता है।

अपूर्ण भूतकाल- जिस क्रिया से यह ज्ञात हो कि भूतकाल में कार्य सम्पन्न नहीं हुआ था - अभी चल रहा था।

• उदाहरण- सरला गीत गा रही थी।
• अमन सो रहा था।
• डीजे भाग रहा था।

पूर्ण वर्त्तमान काल- वर्तमानकाल में कार्य की पूर्ण सिद्धि का बोध होता है।

• उदाहरण- मैंने किताब पढ़ी है।
• तुमने गाना गाया है।
• मोहन आया है।

Additional Information

काल- क्रिया के जिस रूप से कार्य, व्यापार के समय तथा उसकी पूर्णता तथा अपूर्णता का बोध होता है, उसे काल कहते है।

काल के भेद- 3 भेद होते है।​

• वर्तमान काल- उदाहरण- वह सो रहा है।
• रमा खाना बना रही है।​
• भूतकाल- उदाहरण- वह सो रहा था।
• रमा खाना बना रही थी।​
• भविष्य काल- उदाहरण- वह सो रहा होगा।
• रमा खाना बना रही होगी।​

The correct answer is 'themselves, them.' 

Key Points 

• A pronoun (I, me, he, she, herself, you, it, that, they, each, few, many, who, whoever, whose, someone, everybody, etc.) is a word that takes the place of a noun.
• Subject pronouns are those pronouns that perform the action in a sentence.
• They are I, you, he, she, we, they, and who.​
• A reflexive pronoun is used to denote that an action is done and received by the same subject.
• "Themselves" is a reflexive pronoun, being a reflexive form of "they" and it is used after a plural noun.
• "Students" is a plural subject, so we need the reflexive pronoun "themselves" in the first blank.
• Object pronouns are those pronouns that receive the action in a sentence.
• They are me, you, him, her, us, them, and whom.
• Any noun receiving an action in the sentence, like these pronouns, is an object and is categorized as objective case.
• So, the second blank must be filled with "them."
• Therefore, the correct answer is Option 3.

​​Correct sentence: The students have solved the problems themselves; nobody helped them.

Key Points

It is given that,

Power Rating of the bulb = 100 W

Duration for which the bulb is used = 12 hours a day

Number of Days = 30 days

Total Energy Consumed by the Electric Bulb = Power × Duration

= 100 W × 12 hrs/day × 30 days

= 36,000 W-hrs

= 36 kWh is the unit of energy consumed.

Shortcut Trick

Common difference d = (Difference in terms) ÷ (Difference in positions).

Given: 17^th term − 13^th term = 8 ⇒ (17 − 13) × d = 8 ⇒ 4d = 8 ⇒ d = 2.

Check options for common difference 2 and 10^th term as 21.

In option (4): 3, 5, 7... here d = 2. 10^th term = 3 + (9 × 2) = 3 + 18 = 21. Match found.

∴ The correct answer is 3, 5, 7, 9 ……….

Alternate Method

Given: T₁₀ = 21 and T₁₇ = T₁₃ + 8

Formula Used: n^th term of AP (T_n) = a + (n − 1)d

⇒ T₁₇ − T₁₃ = 8

⇒ [a + 16d] − [a + 12d] = 8

⇒ 4d = 8 ⇒ d = 2

⇒ T₁₀ = a + 9d = 21

⇒ a + 9(2) = 21 ⇒ a + 18 = 21

⇒ a = 3

⇒ AP series: a, a+d, a+2d... ⇒ 3, 3+2, 3+4... ⇒ 3, 5, 7, 9...

∴ The correct answer is 3, 5, 7, 9 ……….

Additional Information

Sum of First n Terms

The sum S_n of an AP is given by S_n = (n/2)[2a + (n−1)d] or S_n = (n/2)[a + l], where l is the last term.

Arithmetic Mean (AM)

If a, b, c are in AP, then the arithmetic mean b = (a + c) ÷ 2.

Common Difference Property

The difference between any two terms T_p and T_q is (p − q) × d.

The correct answer is 'about.' 

Key Points  

• We usually say that we "worry about" something, rather than "worry for" it.
• At least, if the "something" here is a thing that could cause trouble.
• We can "worry about" money, health, the future of the country, etc.
• When we say we "worry for" something we mean that we are concerned, not that thing will do harm, but that it will suffer harm.
• That is, if we say, "I worry for Fred", that means that we are concerned that something bad will happen to Fred.
• If we say, "I worry about Fred", that could mean that we think that something bad will happen to Fred, or it could mean that we think Fred will do harm to us or others.
• Therefore, the correct answer is Option 2.

​​Correct sentence: Don’t worry about me. I’ll take care of myself.

The correct answer is 'takes, is said.'

Key Points      

• Verb tense consistency refers to keeping the same tense throughout a clause.
• We don’t want to have one time period being described in two different tenses.
• Also, the subject "town" is singular, so it must take a singular verb.
• Now, let us examine the given options:
• Has taken, Said:
• Has taken: Present Perfect Tense
• Said: Simple Past Tense
• As both the options are in different tenses, so this answer is incorrect.
• Take, Is:
• Take: Plural form of the verb that must be used with plural subjects.
• Is: Singular Be verb in Present Tense
• As "take" cannot be used in the first blank, so this answer is incorrect.
• Takes, Is said:
• Takes: Singular form of the verb that must be used with singular subjects.
• Is said: Singular Be verb in Present Tense, Passive voice structure
• As both the options are in same tenses, so this answer is correct.
• Taking, Said:
• Taking: Incomplete structure of Continuous tense
• Said: Simple Past Tense
• So this answer is incorrect.
• So, the correct answer is Option 3.

​​Correct sentence: The town takes its name from the famous temple and is said to be one of the oldest settlements in India.

The correct answer is Gauss's law is not true for all the closed surfaces.

Key Points

Important points on Gauss's law-

• Gauss’s law is true for any closed surface, no matter what its shape or size.
• The term q on the right side of Gauss’s law includes the sum of all charges enclosed by the surface. The charges may be located anywhere inside the surface.
• In the situation when the surface is so chosen that there are some changes inside and some outside, the electric field [whose flux appears on the left side of is due to all the charges, both inside and outside S. The term q on the right side of Gauss’s law, however, represents only the total charge inside S.
• Gauss’s law is often useful for a much easier calculation of the electrostatic field when the system has some symmetry. This is facilitated by the choice of a suitable Gaussian surface.
• Gauss’s law is based on the inverse square dependence on distance contained in Coulomb’s law. Any violation of Gauss’s law will indicate a departure from the inverse square law

Gauss Law:

This law gives the relation between the distribution of electric charge and the resulting electric field.

According to this law, the total charge Q enclosed in a closed surface is proportional to the total flux ϕ enclosed by the surface, i.e.

ϕ ∝ Q

The Gauss law formula is expressed by:

\(\phi =\frac{Q}{\epsilon_0}\)

This is explained with the help of the following figure:

The correct answer is 'Consistently.'

Key Points

   

• Let us see the meaning of PATCHILY:
• PATCHILY: in a way that only exists or happens in some parts or situations. (एक तरह से जो केवल कुछ हिस्सों या स्थितियों में मौजूद या होता है)
• Example: Banking services are patchily distributed in the smaller towns.
• Let us see the meanings of the given options:
• Decoratively: in a way that is decorative (= made to look attractive). (एक तरह से जो सजावटी है (= आकर्षक दिखने के लिए बनाया गया है))
• Consistently: in every case or on every occasion; invariably. (संगत रीति से)
• Irregularly: in a way that is not even or balanced in shape or arrangement. (अनियमित रूप से)
• Noisily: in a manner that makes a lot of noise. (शोर मचाते हुए)
• From the meanings of the given words, we can say that the word opposite in meaning to the given word is 'Consistently.'
• Hence, the correct answer is Option 2.

Here, the erroneous part is 'chose among.'

Key Points  

• The error lies in the part "choose among" of the sentence.
• The most common use for "among" is when something is in or with a group of a few, several, or many things.
• Example: I sat among the other students.
• The most common use of "between" is when something is in the middle of two things or two groups of things.
• It is sometimes used in the phrase in between.
• "Between" can also be used for times and places that indicate two end points.
• Example: He sat in between Allen and Melissa.
• ​Here, we have to choose between pair of red and green trousers.
• Also, 'chose' should be replaced by 'choose' as 'to' is followed by the first form of the verb.
• ​Therefore, the correct answer is Option 2.

​

Correct sentence: I am finding it difficult to choose between my pair of red and green trousers.

'रक्षा' का तद्भव रूप होगा- 'राखी'।

'रक्षा' शब्द तत्सम शब्द है।

Key Pointsतद्भव शब्द-  ऐसे शब्द जो निकले तो संस्कृत से ही है लेकिन, प्रयोग हिन्दी में हों रहे है।

• उदाहरण- अमृत से अमिय, संध्या से साँझ आदि।

अन्य विकल्प- 

Additional Information

The correct answer is Option 2.

Key Points

• When a solid is heated, more energy is given to the particles and they start vibrating faster.
• A solid turns into a liquid on heating because the particles become free to move after the breaking of the intermolecular bonds.
• At a certain temperature, particles vibrate so much that their orderly structure breaks down.
• At this point, the solid melts into a liquid.

Additional Information

• By heating a substance, you can change its state.
• So by heating a solid, you can convert it into liquid state.
• This process of converting solid into liquid by heating is called melting.
• For example, if you heat ice, it turns into water.

Given :

A = xy3z2 and B = x3y²,

for x, y, and z to be prime numbers.

Calculation :

H.C.F. (xy³z² , x³y²) = xy²(yz² , x²)

So,

H.C.F is xy² as it is the highest common factor between the two variables

∴ The answer is xy².

यदि 'त' के बाद कोई स्वर आए तो 'त' के स्थान पर 'द' हो जाता है।

• जैसे- जगत्+ईश = जगदीश (त् + ई = दी)। (व्यंजन संधि)

Key Pointsव्यंजन संधि- एक व्यंजन का अन्य किसी व्यंजन अथवा स्वर से मेल होने पर जो विकार होता है, उसे व्यंजन संधि कहते हैं।

• उदाहरण- सत्+भावना = सद्भावना (त् + भ = द्भ)।
• जगत्+ईश = जगदीश (त् + ई = दी)।
• तत् + रूप = तद्रूप (त् + र = द्र)।
• सत् + धर्म = सद्धर्म (त् + ध = द्ध)।

Additional Informationव्यंजन संधि बनाने के कुछ नियम-

• किसी वर्ग के पहले वर्ण का मेल किसी भी वर्ग के तीसरे, चौथे वर्ण अथवा य्, र्, ल्, व्, ह् अथवा किसी भी स्वर से हो जाए तो क्, च्, ट्, प् का उसी वर्ग के तीसरे वर्ण में परिवर्तन हो जाता है।

1. उदाहरण- दिक्+गज = दिग्गज। (क् + ग = ग्ग)
2. वाक्+ईश = वागीश। (क् + ई = गी)

• किसी वर्ग के पहले वर्ण का मेल न् या म् से हो जाए तो क्, च्, ट्, प् का उसी वर्ग के पाँचवें वर्ण में परिवर्तन हो जाता है।

1. उदाहरण-  वाक्+मय = वाड़्मय। (क् + म् = ड़्)
2. अच्+नाश = अञ्नाश। (च् + न् = ञ्)

• त् का मेल श् से होने पर त् का च् में और श् का छ् में तथा त् का मेल ह् से हो तो त् का द् और ह् का ध् में परिवर्तन हो जाता है।

1. उदाहरण- उत्+श्वास = उच्छ्वास। (त् + श् = च्छ)
2. उत्+शिष्ट = उच्छिष्ट ।(त् + श = च्छ)

• किसी भी स्वर के बाद यदि छ् वर्ण आ जाए तो छ् का च्छ में परिवर्तन हो जाता है।

1. उदाहरण- स्व+छंद = स्वच्छंद। (अ + छ = अच्छ)
2. आ+छादन = आच्छादन ।(आ + छ = आच्छ)

Given :

To find the Distance between the points A(4,-3) and B(-4,3).

Formula used :

Distance between two points (x,y) and (X,Y) = \(\sqrt{(X-x)^2+(Y-y)^2} \)

Calculation :

Distance = \(\sqrt{(X-x)^2+(Y-y)^2}\) = \(\sqrt{(-4-4)^2+(3-(-3))^2}\) = \(\sqrt{64+36}\) = 10

∴ The answer is 10 .

The correct answer is Colourless.

Key Points

• The compound hydrogen chloride has the chemical formula HCl and as such is a hydrogen halide.
• At room temperature, it is a colourless gas, which forms white fumes of hydrochloric acid when exposed to atmospheric water vapor.
• Hydrogen chloride gas and hydrochloric acid are important in technology and industry.
• Hydrochloric acid, an aqueous solution of hydrogen chloride, is also commonly given the formula HCl.

Shortcut Trick

Distance = Circumference × Number of Revolutions

12 km = 12,00,000 cm

12,00,000 = 2 × (22/7) × Radius × 2000

600 = (44/7) × Radius

Radius = (600 × 7) ÷ 44 = 4200 ÷ 44 ≈ 95.45 cm

∴ The correct answer is 95.45 cm.

Alternate Method

Given:

Total Distance = 12 km = 12 × 1000 × 100 cm = 12,00,000 cm

Total Revolutions (n) = 2000

Formula Used:

Distance = n × 2πr

Calculations:

⇒ 12,00,000 = 2000 × 2 × (22/7) × r

⇒ 12,00,000 ÷ 2000 = 44/7 × r

⇒ 600 = 44/7 × r

⇒ r = (600 × 7) ÷ 44

⇒ r = 4200 ÷ 44

⇒ r = 1050 ÷ 11

⇒ r ≈ 95.4545...

∴ The correct answer is 95.45 cm.

Additional Information

Circumference of a Circle

The distance around the edge of a circle, calculated as C = 2πr or C = πd, where r is radius and d is diameter.

Unit Conversion

Always ensure units are consistent: 1 km = 1000 m and 1 m = 100 cm. For wheel problems, cm is the standard unit for radius.

Distance and Revolutions

The linear distance covered by a rolling wheel is directly proportional to the number of rotations and its perimeter.

Given :

C.I earned after 2 years = Rs. 134.4

Rate of interest(R) = 12%

Formula used :

C.I = \(P\bigg(1+\dfrac{R}{100}\bigg)^t\)- P

Calculation :

C.I = 134.4 = \(P\bigg(1+\dfrac{12}{100}\bigg)^2\) - P

⇒ 134.4 = \(P\bigg(\dfrac{28}{25}\bigg)^2\) - P

⇒ \(\dfrac{159}{625}\times P\) = 134.4

⇒ P = 528.30

∴ The answer is 528.30 .

The correct answer is U = mgh.

Key Points

• Potential energy is the stored energy of position possessed by an object.
• Potential Energy (Pe) = m × g × h
• m represents the mass of the object.
• h represents the height of the object.
• g represents the gravitational field strength (9.8 N/kg on Earth).

Additional Information

• Kinetic energy is the energy that an object possesses due to its motion.
• If we want to accelerate an object, we have to apply a force.
• By applying force we need to do work.
• After the work is done, energy has been transferred to the object, and the object will continue to move with a new constant speed.

Given :

To draw a graph of equation x + y = 5 .

Calculation :

For intersection at x-axis, y = 0

So, x = 5 - y = 5 - 0 = 5

∴ The answer is (5,0) .

Here, the erroneous part is 'refers to.'

Key Points   

• A prepositional phrase is a group of words consisting of a preposition, its object, and any words that modify the object.
• Let us see the usage of the given options:
• Comes with: to be provided together with something.
• Developed by: the advice, proposals, recommendations, analyses and/or policy options must have been created either.
• Refers to: to talk or write about someone or something, especially in only a few words.
• Filled with: to make something full or to become full.
• ​The sentence is stating that the phrase "grey goo" describes a nanotechnology-related catastrophe.
• ​Therefore, the correct answer is Option 3.

​

Correct sentence: The term 'grey goo' refers to a disaster scenario caused by nanotechnology.

संधि में दो वर्णों के मेल से 'विकार' उत्पन्न होता है।

• उदाहरण-  षट् + आनन = षडानन।

Key Points

संधि के अन्य उदाहरण-

• दीर्घाकार = दीर्घ + आकार
• मनोविकार = मन: + विकार
• लघुकार = लघु + आकार
• व्यवस्था = वि + अवस्था
• सीमान्त = सीमा + अंत

Additional Information

संधि के भेद- वर्ण के आधार पर संधि के 3 भेद होते है।

स्वर संधि- दो स्वर के मेल से जो विकार उत्पन्न होता है, स्वर संधि कहलाता है।

• उदाहरण- वीर+अंगना= वीरांगना।

व्यंजन संधि- व्यंजन के बाद स्वर या व्यंजन आने से जो विकार उत्पन्न होता है, व्यंजन संधि कहलाता है।

• उदाहरण- वाक्+ईश= वागीश।

विसर्ग संधि- विसर्ग के बाद स्वर या व्यंजन आने से विसर्ग में विकार उत्पन्न होता है, उसे विसर्ग संधि कहते।

• उदाहरण- निः+आहार= निराहार।

जो सुमिरत सिधि होइ गन नायक करिबर बदन।

S I I I I       I I   SI   I I   SII     IIII      I I I

करउ अनुग्रह सोइ    बुद्धि    रासि    सुभ    गुन सदन।।1।।

 I I I    I I I I I   SI   I I I       S I      I I     I  I  III

 

उपरोक्त पंक्तियाँ 'सोरठा' छन्द के अंतर्गत आती हैं।

(तुलसीदास जी)

Key Pointsरोला छंद उदाहरण-

• पवन तनय संकट हरण, मंगल मूरती रूप।
• राम लखन सीता सहित, हृदय बसहिं सुर भूप।।

मालिनी छंद उदाहरण- 

• प्रिय पति वह मेरा, प्राण प्यारा कहाँ है।
• दुख-जलधि निमग्ना, का सहारा कहाँ है।
• अब तक जिसको मैं, देख के जी सकी हूँ।
• वह हृदय हमारा, नेत्र तारा कहाँ है।।

चौपाई छंद उदाहरण- 

• बंदउँ गुरु पद पदुम परागा। सुरुचि सुबास सरस अनुराग ।।
• अमिय मूरिमय चूरन चारू। समन सकल भव रुज परिवारू ।।

Additional Informationछंद परिभाषा- जिस शब्द-योजना में वर्णों या मात्राओं और यति-गति का विशेष नियम हो, उसे छन्द कहते हैं।

छन्दशास्त्र को ‘पिंगल-शास्त्र’ भी कहते हैं क्योंकि, इसके आदि प्रणेता श्री पिंगलाचार्य थे।

छंद के प्रकार- 3।

• मात्रिक छंद
• वर्णिक छंद
• मुक्त छंद

Given: 

\(\frac{1}{2+3\sqrt{2}}\)

Calculation:

\(\frac{1}{2+3\sqrt{2}}\) x \(\frac{2-3\sqrt{2}}{2-3\sqrt{2}}\)

\(\frac{2-3\sqrt{2}}{(2^2)-(3\sqrt{2})^2 }\)

\(\frac{2-3\sqrt{2}}{(4-18)}\) = \(\frac{2-3\sqrt{2}}{(-14)}\)

\(\frac{3\sqrt{2}-2}{14}\)

Hence, option 3 is correct answer

Given :

The slant height of a frustum of cone is 10 cm and the height of the frustum is 8 cm.

Calculation:

We know, the relationship between slant height, height and radius

\(l^2 = h^2 + (R -r)^2\)

Let R and r be the radius of two circular ends.

Slant height is l = 10 cm

Height is h = 8 cm

\(l^2 = h^2 + (R -r)^2\)

\(10^2 = 8^2 + (R -r)^2\)

\(100 = 64 + (R -r)^2\)

\(R- r = {\sqrt{36}}\)

\(R -r = 6\)

Therefore, The difference of radii of its two circular ends is 6 cm.