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

The correct answer is 'Now that.'

Key Points 

• Let us see the meanings of given conjunctions:
• As much: We use "as much" in expressions such as 'I thought as much' and 'I guessed as much' after we have just been told something and we want to say that we already believed or expected it to be true.
• Example: You're waiting for a woman–I thought as much.
• Now that: We use "now that" to give an explanation of a new situation.
• Example: Now that I live only a few blocks from work, I walk to work and enjoy it.
• Even though: "Even though" is used to express a fact, something that is real or true.
• 'Even though' precedes a statement of fact.
• It means 'despite/in spite of' the fact.
• Example: Even though John is rich, he lives in a small house.
• ​So that: We use "so that" and in order that to talk about purpose.
• We often use them with modal verbs (can, would, will, etc.).
• Example: I’ll go by car so that I can take more luggage.
• ​The sentence is stating that that the person is now free to take a vacation because his examinations are over.
• Therefore, the correct answer is Option 2.​

Correct sentence: Now that you have finished your exams, you can go on vacation.

The correct answer is 'on.'

Key Points  

• Let us look at the usage of the given options:
• At: We use "at" when we refer to an address.
• Example: Education starts at home.
• ​In: We use "in" when something is located inside of a defined space. ​
• Example: I’m in the building now.
• For: We use "for" to talk about a purpose or a reason for something.
• Example: I bought that for you.
• On: "On" is used to show that something is in a position above something else and touching it, or that something is moving into such a position.
• Example: Look at all the books on your desk!
• ​​The sentence says that the newspapers are lying above the coffee table.
• So, the correct answer is Option 4.

Correct sentence: The newspaper is on the coffee table.

वर्तमान काल की पहचान के लिए वाक्य के अंत में ________ आदि आते हैं। ता, ती, ते, है, हैं आते हैं। 

Key Points

• क्रिया के उस रूप को वर्तमान काल कहते हैं, जिसमें क्रिया के व्यापार का वर्तमान समय में होना पाया जाए।
• पहचान – ता है, ती है, ते हैं, रहा है, रही है, रहे हैं आदि।
• उदाहरण -
• पूजा कार्य करती है।
• सचिन विराट के साथ क्रिकेट खेल रहा है।
• राम आता है।
• सीता पढ़ रही है।
• वे शोर करते है।

Important Pointsवर्तमान काल के पांच भेद होते हैं-

Additional Informationअन्य विकल्प -

Given:

î‚ ĵ and k̂ are unit vectors along X, Y and Z axes respectively

Concept used: 

î × ĵ = k̂ 

Calculation: 

The cross product of two vectors results in a vector that is perpendicular to both of the original vectors.

If î and ĵ are unit vectors along the X and Y axes, respectively, then the cross product of î and ĵ, (î × ĵ), will be equal to the unit vector k̂ along the Z axis.

⇒ î × ĵ = k̂ 

∴ (î × ĵ) = k̂

'कुचैला' शब्द में 'कु' उपसर्ग प्रयुक्त हुआ है।

Key Points

• कुचैला में उपसर्ग है – ‘कु’
• कु + चैला = कुचैला
• कुचैला में उपसर्ग ‘कु’ का अर्थ है – बुरा
• कुचैला का वाक्य प्रयोग –उसने मैले कुचैले कपड़े उतार कर फेंक दिए।

Important Pointsअन्य उदाहरण-

Additional Informationअन्य विकल्प निरर्थक है। 

The correct answer is Methane.

Key Points

• The major component of bio-gas and Compressed Natural Gas (CNG) is Methane.

Additional Information

• Bio-CNG contains about 92-98 % of methane and only 2-8 % carbon dioxide. 
• The high methane content and calorific value combined with the low quantity of moisture, hydrogen sulphide and impurities makes Bio-CNG an ideal fuel for automobiles and power generation.
• Compressed natural gas is a fuel that can be used in place of gasoline, diesel fuel and liquefied petroleum gas (LPG).
• CNG is made by compressing natural gas, which is mainly composed of methane (CH4).

Given :

Point P is (3, 5) and Point R is (3, 9) .

Formula used :

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

Calculation:

According to question, If a perpendicular passes through P(3, 5) and B(6, 0) and the intersection point is Q.

Then, the coordinates of Q is (6, 5)

Now, Distance QR = \(\sqrt{(6-3)^2+(5-9)^2}\) = \(\sqrt{9+16}\) = 5

∴ The answer is 5 .

शिल्पकार शब्द में कर्म तत्पुरुष समास है।

Key Points

• कर्म तत्पुरुष समास -जिस तत्पुरुष समास में कर्म कारक के कारक चिन्ह (को) का लोप हुआ हो उसे कर्म तत्पुरुष समास कहते हैं।
• शिल्पकार - शिल्प को बनाने वाला

Important Pointsकुछ अन्य उदाहरण -

Additional Informationअन्य विकल्प -

ऐसे शब्द जो विशेषण शब्दों की विशेषता बताते हैं, वे प्रविशेषण कहलाते है। 

Key Points

• विशेषण की विशेषता बताने वाले शब्द को प्रविशेषण कहते हैं।
• जैसे:- बहुत मोटा आदमी, बिल्कुल दुबली औरत आदि में बहुत एवं बिल्कुल प्रविशेषण शब्द हैं क्योंकि ये शब्द मोटा एवं दुबली शब्दों की विशेषता बता रहे हैं।

Important Points

• कुछ अन्य उदाहरण -
• चाय बेहद गर्म है।
• भोजन बड़ा स्वादिष्ट है।
• राम बहुत अच्छा लड़का है।
• विजय बहुत चालाक आदमी है।
• शंकर अत्यधिक शर्मिला छात्र है।
• हिमालय पर अत्यंत ऊँचे ताड़ वृक्ष पाए जाते हैं।
• चाय बहुत मीठी है।

Additional Informationअन्य विकल्प-

The correct answer is saponification.

Key Points

• Soaps used for cleaning purposes are sodium or potassium salts of long chain fatty acids, e.g stearic, oleic and palmitic acids.
• Soaps containing sodium salts are formed by heating fat with an aqueous sodium hydroxide solution. This reaction is known as saponification.

Additional Information

• Vulcanization is a chemical process in which rubber is heated at 140–160 °C with sulfur, accelerators, and activators.
• This process involves the formation of cross-links between long rubber molecules to achieve improved elasticity, flexibility, tensile strength, viscosity, hardness, and weather resistance.
• Galvanization is the process of applying a protective zinc coating to iron or steel to prevent it from rusting.
• In file system maintenance, defragmentation is a process that reduces the degree of fragmentation.
• It does this by physically organizing the contents of the mass storage device used to store files into the least number of contiguous areas.

The correct answer is Exonuclease.

Key Points

• Exonuclease enzymes remove nucleotides from the ends of strands: nucleic acids and nucleic acids will attack either way.
• Exonuclease and endonuclease nucleases are different nucleases.
• Exonucleases remove nucleotides one at a time from the end of a nucleic acid while endonucleases can break internal phosphodiesterase bonds within a nucleic acid.
• Exonucleases split DNA sequences into palindromic sequences.

Additional Information

• DNA gyrase is an essential bacterial enzyme that catalyzes ATP-dependent negative super-coiling of double-stranded closed-circular DNA.
• Gyrase belongs to a class of enzymes known as topoisomerases that are involved in the control of topological transitions of DNA.
• In molecular biology, endonucleases are enzymes that break phosphodiester bonds within a polynucleotide chain.
• Helicases are enzymes that bind and can also refold nucleic acids or nucleic acid-protein complexes.

The correct answer is Parent divides to form offspring.

Key Points

• There is no natural death in unicellular organisms like bacteria because the paternal body is distributed among the offspring.

Additional Information

• An amoeba often known as amoeboid is a microscopic single cell organism found in pond water. 
• Amoeba has a cell membrane, a rounded, dense nucleus, and many small bubble-like vacuoles in its cytoplasm.
• Amoeba constantly changes its shape and position.
• It pushes out one, or more finger-like projections, called pseudopodia or false feet for movement and capture of food.
• Amoeba feeds on some microscopic organisms.
• When it senses food, it pushes out pseudopodia around the food particle and engulfs it.

CONCEPT :

• Electric Potential (V): This is the amount of work needed to move a unit of electric charge from a reference point to a specific point in an electric field without producing an acceleration.

\(V= \frac{1}{4\pi\epsilon_o}\frac{q}{r}\)

Where q = charge, ϵo = permittivity of free space., r = the distance from the charge

The value of \(\frac{1}{4\pi\epsilon_o} = 9 × 10^9\)

CALCULATION:

Given:

 q = 2 × 10-7 C

r = 9 cm = 9 × 10^-2 m = 0.09 m

The electric potential is calculated by, 

\(V= \frac{1}{4\pi\epsilon_o}\frac{q}{r}\)

\(V= 9 \times 10^9 \times (\frac{2 \times 10^{-7}}{0.09})\)

V = 2 × 104 v

The correct answer is material of the wire.

Key Points

• The value of Young’s Modulus depends upon the nature of the material of the body and the manner in which the body is deformed.
• Its value depends upon the temperature of the body.
• Its value is independent of the dimensions (length, radius, volume, etc.) of the body.
• As we know young's modulus of elasticity is a material's property. Therefore, Young's modulus does not depend upon the length of the radius of the wire. It is constant for the material.

Additional Information

• Young's modulus is a modulus of elasticity, applicable to the stretching of wire, etc., equal to the ratio of the applied load per unit area of the cross-section to the increase in length per unit length.
• It is denoted as E or Y.
• The unit of Young’s modulus is N m^-2.

Given:

Radius of the circle = 14 cm , and θ = 90°

Formula used:

Area of a sector = \(\dfrac{θ}{360}\) πr²

Calculation:

Area of minor sector = \(\dfrac{90}{360}\)πr2 

⇒ \(\dfrac{1}{4}\times \dfrac{22}{7}\times 14\times 14\) = 154 cm²

∴ The answer is 154 cm².

The correct answer is '​should.'

 

Key Points  

• Let us see the usage of the given modal verbs:​
• "Must" is used to express obligation, give orders, and give advice. 
• Example: All pupils must bring a packed lunch tomorrow.
• 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" 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.
• ​​The sentence talks about an opinion i.e. the person ought to have met her sooner if he needed assistance.
• Therefore, the correct answer is Option 3.

Correct sentence: If you wanted help, you should have met her earlier.

सादृश्य वाचक शब्द उपमा अलंकार में प्रयुक्त होते हैं।

Key Points

• उपमा अलंकर - जब किन्ही दो वस्तुओं के गुण, आकृति, स्वभाव आदि में समानता दिखाई जाए या दो भिन्न वस्तुओं कि तुलना कि जाए, तब वहां उपमा अलंकर होता है।
• वाचक शब्द - सा, सी, सम, सरिस, जैसा, ज्यो।
• उदाहरण - 
• पीपर पात सरिस मन डोला - पीपल के पत्तों के समान मन के डोलने का वर्णन।
• उतर रही है संध्या सुंदरी परी सी - संध्या को परी के रूप में चित्रित किया है।

Important Pointsकुछ अन्य उदाहरण -

• मखमल के झूले पड़े हाथी सा टीला - टीले की तुलना हाथी से की गई है।
• तब बहता समय शिला सा जम जायेगा - समय को पत्थर सा जमने के लिए कहा गया है।
• सहसबाहु सम रिपु मोरा - शत्रु को सहत्रबाहु के सामान माना है।
• चाँद की सी उजली जाली - चांद के समान ऊजली बताया गया है।
• वह दीपशिखा सी शांत भाव में लीन दीप से उठने वाली - ज्वाला के समान शांत बताया है।
• कमल सा कोमल गात सुहाना - गाल के कोमलता की तुलना कमल पुष्प से की है।

Additional Informationअन्य विकल्प - 

Given :

To find possible solutions of pair of linear equations

2x + 3y = 7

6x + 9y = 3

Concept used:

If \(\dfrac{a_1}{a_2}\) = \(\dfrac{b_1}{b_2}\) ≠ \(\dfrac{c_1}{c_2}\), then there will be no solution.

Calculation:

2x + 3y = 7 →(1)

6x + 9y = 3 →(2)

Subtracting (1) from (2), we get

4x + 6y = 4 →(3)

Adding (1) and (2), we get

8x + 12y = 10

⇒ 4x + 6y = 5 →(4)

From Eqn (3) and (4), 

\(\dfrac{4}{4}\) = \(\dfrac{6}{6}\) ≠ \(\dfrac{4}{5}\)

∴ The system of equations has no solution.

Calculation:

Checking option (1),

\(\sqrt7, \sqrt{28}, \sqrt{63}, ...\) = \(\sqrt{7},2\sqrt{7},3\sqrt{7}, ...\)

This follows A.P as the difference is constant.

Checking option (2),

8, 11, 14, ....

This also follows A.P as the difference is constant.

Checking option (3),

45, 43, 41, ...

This also follows A.P as the difference is constant.

Checking option (4),

\(\sqrt3, \sqrt{6}, \sqrt{9}, ...\)

This doesn't follow A.P as the difference is not constant.

∴ The answer is \(\sqrt3, \sqrt{6}, \sqrt{9}, ...\) .

'राम के मन में सीता के प्रति रति का भाव जगता है।' वाक्य में आश्रय 'राम'।

तथा 'सीता' 'विषय'है।

Key Pointsविभाव- जो व्यक्ति वस्तु या परिस्थितियाँ स्थायी भावों को उद्दीपन या जागृत करती हैं, उन्हें विभाव कहते हैं।

विभाव के दो भेद हैं-

• आलंबन विभाव
• उद्दीपन विभाव

आलंबन विभाव के दो पक्ष होते है- आश्रयालंबन व विषयालंबन।

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

• उदाहरण- यदि राम के मन में सीता के प्रति रति का भाव जगता है तो राम आश्रय होंगे और सीता विषय।

Additional Information

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

रस के ग्यारह भेद होते है।

रस के चार अंग है-

1. विभाव
2. अनुभाव
3. व्यभिचारी भाव
4. स्थायी भाव

The correct answer is '​keeping our fingers crossed​.'

 

Key Points  

• Let us see the usage of the given idioms:​
• Taking the lion's share: taking the largest part or most of something. (किसी चीज का सबसे बड़ा हिस्सा या अधिकांश भाग लेना)
• Example: She didn't do much, but she took the lion's share of the attention from the teachers.
• Painting the town red: go out and enjoy oneself flamboyantly. (खूब मौज़ उड़ाना)
• Example: You want to have a good time and paint the town red this weekend.
• Counting the chickens: If you say that someone is counting their chickens, you mean that they are assuming that they will be successful or get something, when this is not certain. (यदि आप कहते हैं कि कोई अपनी मुर्गियां गिन रहा है, तो आपका मतलब है कि वे मान रहे हैं कि वे सफल होंगे या कुछ प्राप्त करेंगे, जबकि यह निश्चित नहीं है)
• Example: I don't want to count my chickens before they are hatched.
• Keeping our fingers crossed: to hope strongly that something will happen. (दृढ़ता से आशा करना कि कुछ होगा)
• Example: We're keeping our fingers crossed that he'll be healthy again very soon.
• ​​The sentence talks about the release of the final results, so the most appropriate idiom will be "keeping our fingers crossed."
• Therefore, the correct answer is Option 4.

Correct sentence: We were keeping our fingers crossed​ till the final results were out.

The correct answer is Isoprene.

Key Points

• The monomer (“one-part”) of natural rubber is isoprene.
• The chemical name for natural rubber is polyisoprene.
• Its IUPAC name of isoprene is 2-methyl but-1,3-diene.

Additional Information

Important Points

• An addition polymerization joins thousands of isoprene units together to form poly(isoprene) or natural rubber.
• Vulcanization is a manufacturing process discovered by Charles Goodyear in 1839 to convert raw rubber into a tough useful product.
• In this process, about 1 – 3% by weight of sulphur is added to raw rubber and the mixture is heated carefully.

Here, the erroneous part is 'tell you.'

Key Points 

• The given sentence is a conditional sentence (Third conditional as it is describing a regret.).
• A conditional sentence is based on the word ‘if’.
• There are always two parts to a conditional sentence – one part beginning with ‘if’ to describe a possible situation, and the second part which describes the consequence.
• We use the third conditional to talk about impossible situations, as in the second conditional, in the past.
• We often use the third conditional to describe regrets.
• Structure: First part (If + past perfect), Second part (would have/could have + past participle)
• Example: If we had left earlier, we would have arrived on time.
• ​So we have to replace "tell you" with "have told you" to make the sentence grammatically c​orrect.
• ​Therefore, the correct answer is Option 2.

​

Correct sentence: If you had spoken to my mother, she would have told you where I was.

The correct answer is ​Water is solvent and physical state of solution is liquid.

Key Points

• The term 'solvent' can be defined as a substance that has the ability to dissolve a given solute to form a solution with it.
• Common examples of solvents include water, ethanol, methanol and acetone.
• The ability of a solvent to dissolve another molecule is dependent on molecular structure and physical properties of both the solvent and the solute.
• Solvents can be categorized as organic or inorganic, and in terms of chemical polarity.
• Polar solvents include water, alcohols, and other –OH containing chemicals, such as acetic acid, that have the ability to donate a H+ and form hydrogen bonds.
• A solute is a substance that can be dissolved by a solvent to create a solution. A solute can come in many forms. It can be gas, liquid, or solid. The solvent, or substance that dissolves the solute, breaks the solute apart and distributes the solute molecules equally. This creates a homogenous mixture, or solution that is equal throughout.

The correct answer is Its kinetic energy gets converted into potential energy.

Key Points

• As the particle goes upward, its velocity decreases and height increases.
• Therefore kinetic energy diminishes as it goes up and gets converted into potential energy.

Additional Information

• When a body is thrown vertically upwards, at the highest point the velocity is zero because the acceleration due to gravitational force is acting downward continuously and that is the reason for velocity being zero at the highest point, hence velocity is zero because of the acceleration.
• At the starting of throwing off the body's initial velocity is zero and its Potential energy is minimum.
• After throwing the body vertically upward its kinetic energy goes on decreasing while potential energy increases.
• At the highest point, kinetic energy becomes zero and potential energy is maximum and again the same cycle repeats.

दीर्घ संधि के नियमानुसार, यदि 'अ' या 'आ' के बाद 'अ' 'आ' आए तो दोनों के स्थान पर 'आ' ध्वनि हों जाती है।

• जैसे- शिव + आलय= शिवालय (अ + आ= आ)।

Key Pointsदीर्घ संधि-  यह स्वर संधि का एक भेद है। जब ह्रस्व या दीर्घ के बाद जैसे, 'अ, आ' + 'अ, आ' हो तो 'आ' बनता है, जब 'इ, ई' + ' इ, ई' हो तो 'ई' बनता हैऔर जब 'उ, ऊ' + 'उ, ऊ' हो तो 'ऊ' बनता है। दीर्घ स्वर संधि कहलाती है।

• उदाहरण- मही + इंद्र = महींद्र (ई + इ = ई)।
• महा + आशय= महाशय (आ + आ= आ)।
• गिरि + इन्द्र= गिरीन्द्र (इ + इ= ई)।
• गिरि + ईश= गिरीश (इ + ई= ई)।

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

• जैसे- महा+आत्मा= महात्मा।
• वीर+अंगना= वीरांगना।

स्वर संधि के पाँच भेद होते है -

1. दीर्घ संधि
2. गुण संधि
3. वृद्धि संधि
4. यण संधि
5. अयादी संधि

Mistake Points

 

• अ, आ के साथ इ, ई का मेल होने पर 'ए' और  उ, ऊ का मेल होने पर 'ओ' तथा 'ऋ' का मेल होने पर 'अर्' हो जाए तब गुण संधि होती है।
• जैसे- देव + इन्द्र= देवेन्द्र (अ + इ= ए )।

1. तथा अ, आ का मेल ए, ऐ के साथ होने से 'ऐ' तथा ओ, औ के साथ होने से 'औ' में बदल जाने पर वृद्धि संधि होती है।

• जैसे- महा + ऐश्र्वर्य=महैश्वर्य (आ + ए=ऐ)।
• परम + ओजस्वी =परमौजस्वी (अ + ओ =औ)।

Given :

To find H.C.F of 4060 and 18705.

Calculation:

Prime factorisation of 4060 = 2² × 5 × 7 × 29

Prime factorisation of 18705 = 3 × 5 × 29 × 43

Hence, the HCF of 4060 and 18705 is 29 × 5 = 145.

HCF (4060, 18705) = 145

∴ The answer is 145.

'महात्मा' का विलोम शब्द- 'दुरात्मा'।

• महात्मा अर्थ- 'महान आत्मा'।
• दुरात्मा अर्थ- 'दुष्ट आत्मा'।

Key Points

Additional Information

Mistake Points

• महात्मा का विलोम 'दुरात्मा' होगा। न कि 'संत'।
• क्योंकि संत , साधु , महात्मा के पर्यायवाची शब्द है।

The correct answer is '​could.'

 

Key Points  

• Let us see the usage of the given modal verbs:​
• “Ought” can indicate correctness or duty, often when criticizing the actions of another.
• Example: She ought to slow down so she doesn't get a ticket.
• 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.
• "Should" can be used to show obligation, give recommendations, or even an opinion.
• Example: You should stop eating fast food.​
• Could: used to indicate possibility.
• Example: When I was younger, I could run for miles.
• Here, the sentence talks about people not getting to meet the person though there was a possibility as the meeting was planned.
• Therefore, the correct answer is Option 4.

Correct sentence: They could not meet me as planned.

The correct answer is 'will they?'

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 the sentence is positive, the question tag must be negative, and vice-versa.
• Always use pronouns in the question tag.
• Example*: didn't, haven't, doesn't*
• ​​The given sentence is negative, so we must use a positive question tag.
• Example: did, have, does, has, will, shall​**
• ​In the given sentence, the helping verb is "will" and pronoun is "they."
• So, the correct answer is Option 3.

​​Correct sentence: They won’t shout at me, will they?

The correct answer is 6.25 x 10¹⁸. 

Key Points

• One coulomb (C) of charge represents an excess or deficit of 6.25 x 1018 electrons.
• The quantity of charge (Q) on an object is equal to the number of elementary charges on the object (N) multiplied by the elementary charge (e).
• Change on 1^e− = 1.602 × 10⁻¹⁹ C
• If total charge = 1 C
• Total no. of e⁻ =1/1.602×10⁻¹⁹
• 1 C  = 6.24×10¹⁸ e⁻

The correct answer is Gross error.

Key Points

Gross error

• ​It is caused by careless handling of experimental set up.
• These types of error mainly comprise of human mistakes in reading instruments and recording and calculating.
• Computational mistakes, incorrect adjustment, and improper application of instruments can lead to gross errors.
• It can be avoided by taking thorough care and verifying the calculations and observations.

Additional Information

Systematic errors  ​

• They occur as a result of a flaw in the experiment design or apparatus.
• Since there is a flaw in the design set up, it cannot be reduced by conducting repeat trials.
• They can cause the measured values to be consistently higher or lower than the actual value.
• They can also be divided into following-
• Environmental Errors
• Observational Errors
• Instrumental Errors

Random errors

• ​They occur irregularly and hence are random.
• They can arise due to random and unpredictable fluctuations in experimental conditions such as unpredictable fluctuations in temperature, voltage supply, mechanical vibrations of experimental set-ups, etc.
• These errors can be reduced by calculating the mean and median of the number of repeated measurements.
• It cannot be eliminated, but it can be controlled by using larger sample sizes and efficient statistical analysis..

विभावना अलंकार का उदाहरण- 'बिनु पद चलइ सुनइ बिनु काना'।

• विभावना अलंकार का उदाहरण 'बिनु पद चलइ सुनइ बिनु काना' है क्योंकि यहाँ पर बिना कारण के भी कार्य का होना पाया जा रहा है।
• अन्य पंक्ति विभावना अलंकार के नियम अनुसार उचित नहीं है।

Key Pointsविरोधाभास अलंकार- जहाँ पर संयोग में विरोध दिखाया जाए अर्थात जहां विरोध न होने पर भी विरोध दिखाया जाता है, वहां पर विरोधाभास अलंकार होता है।

• **उदाहरण- '**मीठी लगे अँखियान लुनाई'।

यथासंख्य/क्रम अलंकार- जहाँ जिस क्रम में कुछ वस्तुओं का वर्णन किया, उसी क्रम में उनसे सम्बंधित विशेषताओं का वर्णन किया जाता है, यथासंख्य अलंकार कहते है।

• **उदाहरण- '**मनि मानिक मुकुता छबि जैसी'।

यमक अलंकार- जब किसी पंक्ति में एक से अधिक बार कोई शब्द आये,और उनके अर्थ भी अलग-अलग हों, तब यमक अलंकार होता है।

• उदाहरण- 'कनक-कनक ते सौगुनी, मादकता अधिकाय'।

विभावना अलंकार- जहाँ पर बिना कारण के भी कार्य का होना पाया जाता है, वहाँ विभावना अलंकार होता है।

• उदाहरण- 'बिनु पद चलइ सुनइ बिनु काना'।

Additional Information

अलंकार- 'काव्य की शोभा बढ़ाने वाले शब्दों को अलंकार कहते है'।

अलंकार सम्प्रदाय के प्रतिष्ठापक 'भामह' को माना जाता है।

अलंकार के भेद- 3 भेद होते।

1. शब्दालंकार- 5 भेद ( अनुप्रास, यमक, श्लेष, वीप्सा, वक्रोक्ति)।
2. ​अर्थालंकार- उपमा, रूपक, उत्प्रेक्षा, अन्योक्ति, अतिश्योक्ति आदि।
3. उभयालंकार- शब्द व अर्थ दोनों के माध्यम से चमत्कार उत्पन्न करने वाले शब्दों को उभयालंकार कहते।

'दुधारू' शब्द में 'दु' उपसर्ग है।

'दु' उपसर्ग के अन्य शब्द जैसे- दुबला, दुलारा आदि।

Key Points

Additional Informationहिन्दी में उपसर्गों की संख्या- 13।

Mistake Points

• 'दुधारू' शब्द में 'दु' उपसर्ग है अन्य उपसर्ग जैसे, 'दू', 'दूध', 'दुध' उपसर्ग की दृष्टि से अनुचित उपसर्ग है।

The correct answer is 18 g.

Key Points

Explanation:

• 0.1 mole of C₆H₁₂O₆ = Molecular mass of C6H12O6 in grams
• 0.1 (Mass of 6C + Mass of 12H + Mass of 6O)
• 0.1 (12 × 6 + 1 × 12 + 16 × 6)
• 0.1 (72 + 12 + 96)
• 18 grams

Given:

P = Rs. 7350

Time = 4 years 5 months

Rate = 8.5%

Formula used:

SI = (P × R × T)/100

Calculation:

Rate per month = 8.5/12

Time in months = 48 + 5 = 53 months

SI = (P × R × T)/100

⇒ \(\dfrac{7350\times85\times53}{120\times100}\)

⇒ Rs. 2759.31 ≈ Rs. 2759

∴ The simple interest is Rs. 2759.

'अंधे के हाथ बटेर लगना' मुहावरे का सही अर्थ- 'अयोग्य व्यक्ति को मूल्यवान वस्तु मिल जाना'।

वाक्य प्रयोग- रोहिणी सिर्फ आठवीं पास है फिर भी उसकी सरकारी नौकरी लग गई। इसी को 'अंधे के हाथ बटेर लगना' कहते है।

Key Points

Additional Information

Mistake Points

• 'अंधे के हाथ बटेर लगना' मुहावरे के लिए सही अर्थ- 'अयोग्य व्यक्ति को मूल्यवान वस्तु मिल जाना'।
• अन्य अर्थ मुहावरे की दृष्टि से उचित नहीं है।

वाक्यांश के लिए एक शब्द- 'स्वार्थी'। 

वाक्य- संतोष अपना हित चाहने वाला है। 

अतः कह सकते है कि, संतोष 'स्वार्थी' है।

Key Points

Additional Information

The correct answer is 'in, before.'

Key Points  

• Let us look at the usage of the given options:
• In: We use "in" when something is located inside of a defined space. ​
• Example: I’m in the building now.
• Of: We use "of" when we want to show that people or things relate to other things or people.​
• Example: Tiffany stared at the floor of her room.
• At: We use "at" when we refer to an address.
• Example: Education starts at home.
• Before: "Before" means earlier than the time or event mentioned.
• Example: I met her just before she left.
• When: We use "when" to refer to a future situation or condition that we are certain of.
• Example: When I see Gary, I’ll tell him that you said hello.
• After: "After" means ‘later than’ and ‘next in time or place’.
• "After" can be used before a noun phrase (as a preposition).
• Example: The bank is just after the park, on the left.
• ​​The first blank talks about something located inside of a defined space, so we must use "in" in the first blank.
• The second blank is referring to something earlier than the play begins, so we must use "before" in the first blank.
• So, the correct answer is Option 1.

Correct sentence: Guests have to be seated in their chairs before the play begins.

Additional Information

• Is it sitting on or sitting in a chair?
• If the chair has arms, it's always 'in'. But if it can seat more than one person, like a bench or sofa, then it's 'on'. If the chair has no back, you also sit 'on' it.

The correct answer is 'themselves, they.' 

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.
• "Children" is a plural subject, so we need the reflexive pronoun "themselves" in the first blank.
• After "when" we need a subject pronoun "they" as it is performing the action.
• Therefore, the correct answer is Option 2.

​​Correct sentence: The children can take care of themselves when they are grown up enough.

The correct answer is 'Repel.'

Key Points 

• Let us see the meaning of Enthrall:
• Enthrall: to hold somebody’s interest and attention completely. (पूरा-पूरा ध्यान खींच लेना, मंत्रमुग्‍ध कर देना, मोहित करना)
• Example: He was enthralled by her story.​
• Let us see the meanings of the given options:
• Delight: to give somebody great pleasure. ((किसी को) अत्‍यधिक आनंदित कर देना)
• Repel: to send or push somebody/something back or away. (किसी व्‍यकि्त या वस्‍तु को पीछे या दूर भेज या धकेल देना)
• Fascinate: to attract or interest somebody very much. (आकृष्‍ट करना या रुचि जगाना; मोहित करना)
• Enrapture: give intense pleasure or joy to. (तीव्र सुख या आनंद देना)
• From the meanings of the given words, we can say that "Enthrall" is opposite in meaning to "Repel."
• Hence, the correct answer is Option 2.

Here, the correct answer is "illegible."

Key Points    

• Among the given options, the correctly spelt word is 'illegible'.
• It means difficult or impossible to read. (जिसे पढ़ना कठिन या असंभव हो; अपाठ्‌य, दुर्वाच्य)
• Example*: Your handwriting is quite illegible.*
• Therefore, we find that the correct answer is Option 1.

​

Correct sentence: Write neatly. Your handwriting is illegible.

 

Additional Information       

• The synonyms of "illegible" are unreadable, scrawl, scribble: 
• Unreadable: not clear enough to read; illegible.
• Scrawled: an example of hurried, careless writing.
• Scribbled:  to write or draw something quickly or without thought, or to make meaningless marks.

Given:

x2 - 2x - 8

Calculation:

x2 - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) =0

⇒ (x + 2)(x - 4) = 0

⇒ x = -2, 4

∴ The correct answer is -2 and 4.

'वन' का विलोम शब्द- 'मरु'।

• वन अर्थ- 'जंगल'।
• मरु अर्थ- 'रेगिस्तान'।

Key Points

Additional Information

'राजसभा' शब्द में 'सम्बन्ध तत्पुरुष' समास है।

संबंध कारक की विभक्ति 'की' का लोप।

• राजसभा: राजा की सभा

Key Points

तत्पुरुष समास के भेद- 6 भेद।

• कर्म तत्पुरुष- कर्म कारक विभक्ति 'को' का लोप।
• उदाहरण- 'स्वर्गप्राप्त' = स्वर्ग को प्राप्त।
• करण तत्पुरुष- करण कारक विभक्ति 'से', 'के द्वारा' का लोप।
• उदाहरण- 'भयाकुल' = भय से आकुल।
• सम्प्रदान तत्पुरुष - सम्प्रदान कारक की विभक्ति 'के लिए' का लोप।
• उदाहरण- 'देशभक्ति' = देश के लिए भक्ति।
• अपादान तत्पुरुष- अपादान कारक की विभक्ति 'से' (अलग होने का भाव) का लोप।
• उदाहरण- 'पापमुक्त' = पाप से मुक्त।
• संबंध तत्पुरुष- संबंध कारक की विभक्ति 'का', 'की', 'के' का लोप।
• उदाहरण- 'देशरक्षा'= देश की रक्षा।
• अधिकरण तत्पुरुष- अधिकरण कारक की विभक्ति 'मे', 'पर' का लोप।
• उदाहरण- 'लोकप्रिय' = लोक में प्रिय।

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

'घटिका' शब्द का तद्भव रूप- 'घड़ी'। 

'घटिका' 'घड़ी' का तत्सम रूप है

Key Points

Additional Information

Mistake Points

• 'घटिका' शब्द का तद्भव रूप- 'घड़ी' होगा। न कि, 'घट' और 'घड़ा'।
• 'घट' तत्सम शब्द है जिसका तद्भव 'घड़ा' होगा।
• तथा 'कम' शब्द जिसका अर्थ है- 'अल्प'। जो न तो तत्सम है नहीं इसका तद्भव होगा।

Given:

y3 + y2 + 4y - 3 is divided by y - 2. 

Calculation:

Put y - 2 = 0 

⇒ y = 2

Let f(y) = y3 + y2 + 4y - 3

⇒ f(2) = 2³ + 2² + 4 × 2 - 3

⇒ f(2) = 8 + 4 + 8 - 3

⇒ f(2) = 20 - 3 = 17

∴ The remainder is 17.

Alternate Method

The reminder when y3 + y2 + 4y - 3 is divided by y - 2 is 17.

वर्तमान काल से तात्पर्य है- 'जो समय चल रहा है'।

• उदाहरण- राहुल खाना खाता है।

Key Pointsभूतकाल- जो समय बीत चुका है।

• उदाहरण- मैंने पुस्तक पढ़ ली थी।

वाक्य बीते हुए समय में क्रिया के होने का बोध हों रहा हैं।

​भविष्यत काल- जो समय आने वाला है।

• उदाहरण- किसान खेत में बीज बोयेगा।

उपर्युक्त वाक्य की क्रिया से पता चलता है कि ये कार्य आने वाले समय में पूरा होंगा।

सम्भाव्य वर्तमानकाल- जो समय आ सकता है।

• उदाहरण- वह आगरा जा सकता है।

निकट समय में कार्य के पूरा होने की संभावना है।

Additional Information

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

काल के भेद- 3 भेद होते है।​

• वर्तमान काल- वह पढ़ रहा है।
• भूतकाल- वह पढ़ रहा था।
• भविष्य काल- वह पढ़ रहा होगा।

Given:

side = 14 cm

Formula used:

The volume of the sphere = \(\dfrac{4}{3}\) πr³

Calculation:

Radius, r = \(\dfrac{14}{2}\) = 7 cm

The volume of the sphere = \(\dfrac{4}{3}\)πr3

Volume = \(\dfrac{4}{3}\) x \(\dfrac{22}{7}\) x 7³ 

⇒ 88 x \(\dfrac{49}{3}\)

⇒ 1437.33 cm³ 

∴ The volume of the sphere is 1437.33 cm³.

Here, the correct answer is "every."

Key Points 

    

• Let us see the meanings of the given options:
• Every: We use "every + singular noun" to refer individually to all the members of a complete group of something.
• Example: There's a photograph on the wall of every child in the school.
• That: We use "that" most commonly to point to a thing or person. We use it with singular nouns.
• The thing or person is often distant from the speaker and sometimes closer to the listener, or not visible to either the speaker or listener.
• Example: Can you pass me that green bowl over there?
• Last: We use "last" in front of a word such as week or month to say when something happened.
• Example: Wolfgang and I had lunch with her last month.
• 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?
• ​​The given sentence has the structure of "every + noun" to refer to the tenth day of all the months.
• Therefore, we find that the correct answer is Option 1.

​

Correct sentence: My credit card bill is received on the tenth day of every month.

The correct answer is functional.

Key Points

• The phenomenon that two or more different chemical compounds have the same molecular formula is called isomerism, from the Greek isos meaning “equal”, and meros meaning “part”, a concept and term introduced by the Swedish scientist Jacob Berzelius in 1830.
• Isomerism is a consequence of the fact that the atoms of a molecular formula can be arranged in different ways to give compounds, called isomers, that differ in physical and chemical properties.
• There are two types of isomerism: structural isomerism and stereoisomerism, which can be divided into further subtypes.
• Tautomerism is a phenomenon where a single chemical compound tends to exist in two or more interconvertible structures that are different in terms of the relative position of one atomic nucleus which is generally the hydrogen.
• Metamers are the isomers with the same molecular formula but different alkyl groups around the same functional group.

The correct answer is Iron (solid).

Key Points

• Intermolecular Forces:
• Intermolecular forces are the forces of attraction or repulsion that act between neighboring particles (atoms, molecules or ions).
• These forces are weak compared to intramolecular forces, such as covalent or ionic bonds between atoms in a molecule.
• The intermolecular/interatomic force of attraction is maximum in solids. Due to this, the molecules of solids become tightly packed with each other.
• The order of strength of the intermolecular force of attraction is in the following order:
• solid > liquid > gas
• Therefore, the intermolecular force of attraction is maximum in Iron (solid).

'अग्नि' का पर्यायवाची शब्द- 'वैश्वानर'।

'अग्नि' के अन्य पर्यायवाची शब्द- रोहिताश्व, वायुसखा, विभावसु।

Key Points

Additional Information

Mistake Points

• द्युति, ज्योति का पर्यायवाची शब्द है न कि अग्नि का।
• अन्य पर्यायवाची शब्द हैं - ज्योति= द्युति, प्रभा, भा, रुचि,।
• अमिय = सुधा, सोम, पीयूष, अमिय।

Given:

The length of a tangent from an external point A to a circle with center O is 

Solution:

It is always less than the distance from the external point A to the center of the circle, OA.

This is because the tangent is a straight line that touches the circumference of the circle at only one point, T.

On the other hand, the radius of the circle, OA, passes through the center of the circle and touches the circumference of the circle at two points, T and another point T'.

The length of the radius is greater than the length of the tangent, since it covers the distance from T to T' on the circumference of the circle.

Shortcut Trick

Identify the corresponding vertices by looking at the common letters in the given ratios.

In AB/DF = BC/ED, the common vertex in the numerator is B and in the denominator is D, so B ↔ D.

In BC/ED = AC/EF, the common vertex in the numerator is C and in the denominator is E, so C ↔ E.

The remaining vertex in the first triangle is A and in the second is F, so A ↔ F.

Matching the order A-B-C with their counterparts F-D-E, we get the similarity relation.

∴ The correct answer is ΔABC ~ ΔFDE.

Alternate Method

Given: In ΔABC and ΔDEF, AB/DF = BC/ED = AC/EF.

Formula Used: SSS (Side-Side-Side) Similarity Criterion states that if the corresponding sides of two triangles are in the same ratio, then their corresponding angles are equal and the triangles are similar.

Calculation:-

If, in ΔABC and ΔDEF,

The ratios of the corresponding sides are equal,

⇒ AB/DF = BC/ED = AC/EF

Then, the two triangles are similar.

This means that they have the same shape and their corresponding angles are equal.

Therefore, the correct relation is:

∴ ΔABC ~ ΔFDE

i.e., triangles ABC and FDE are similar.

Additional Information

SSS Similarity Criterion

If in two triangles, sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.

SAS Similarity Criterion

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, then the two triangles are similar.

AA Similarity Criterion

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

Properties of Similar Triangles

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides: Area(Δ1)/Area(Δ2) = (Side1/Side2)².

Given:

The probability of getting a number greater than 1 in a single throw of a dice is

Calculation:

This can be calculated by finding the total number of favorable outcomes (rolling a number greater than 1) divided by the total number of possible outcomes (rolling any number from 1 to 6).

The favorable outcomes are 2, 3, 4, 5, and 6, for a total of 5.

The total number of possible outcomes is 6, so the probability is 5/6.

The correct answer is 'and.'

Key Points 

• Let us see the meanings of given conjunctions:
• Or: "Or" is used to connect different possibilities.
• Example: You can pay now or when you come back to pick up the paint.
• And: "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.
• But: "But" is a coordinating conjunction used to connect ideas that contrast.
• Example: I like him but I can't meet him.
• ​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.
• ​The sentence talks about two qualities of a single person.
• Therefore, the correct answer is Option 2.​

Correct sentence: She is a rare combination of beauty and brains.

Calculation:

f(5) = 5.

This means that when the input to the function f(x) is 5,

the output is 5.

In mathematical notation, we write f(5) = 5.

कुण्डलिया 'विषममात्रिक' प्रकार का एक छन्द है।

• उदाहरण- घर का जोगी जोगना, आन गाँव का सिद्ध।

Key Points'कुण्डलिया छंद'- यह छंद दोहे और रोले के योग से बनता है। प्रथम दो चरणों में दोहा का और बाद के चार चरणों में ‘रोला’ का होता है।

• अतः प्रथम दो चरण – 13 + 11 मात्राएं = 24 मात्राएँ।
• बाद के चार चरण – 11 + 13 = 24 मात्राएँ।
• उदाहरण- रहिये लट पट काटि दिन, बरु घामें माँ सोय।छाँह न वाकी बैठिये, जो तरु पतरो होय ॥

                जो तरु पतरो होय, एक दिन धोखा दै है। जा दिन चले बयारि, टूटि तब जर ते जैहे ॥

                कह ‘गिरधर’ कविराय, छाँह मोटे की गहिये। पातो सब झरिजाय, तऊ छाया में रहिये॥

Additional Informationमात्रिक छंद- मात्रा की गणना के आधार पर की गयी पद की रचना को मात्रिक छंद कहते हैं। मात्रिक छंद के सभी चरणों में मात्राओं की संख्या सामान रहती है।

मात्रिक छंद- 3 प्रकार के होते हैं-

1. सम मात्रिक छंद
2. अर्धसम मात्रिक छंद
3. विषम मात्रिक छंद

'सममात्रिक छंद- छन्द के प्रत्येक चरण में मात्राओं की संख्या समान होती है। इसमें चौपाई, रोला, हरिगीतिका आदि छंद आते है।

• उदाहरण- यही सयानो काम, राम को सुमिरन कीजै।

                         पर-स्वारथ के काज, शीश आगे धर दीजै॥ (रोला)

'अर्द्धसम मात्रिक छंद'- छंद के पहले और तीसरे चरण तथा दूसरे और चौथे चरण में मात्राओं की संख्या समान होती है। जैसे- दोहा, सोरठा, बरवै तथा उल्लाला आदि।

• उदाहरण- गुरु गोविंद दोउ खड़े, काके लागूं पाँय ।

                          बलिहारी गुरु आपने, गोविंद दियो मिलाय॥ (दोहा)

'विषम मात्रिक छंद'- छंद के चरणों में अधिक समानता न हों, वहाँ विषम मात्रिक छंद होता है। जैसे-कुण्डलिया (दोहा + रोला) , छप्पय (रोला + उल्लाला)।

• उदाहरण- नीलांबर परिधान,  हरित पट  पर सुंदर है। सूर्य चंद्र युग  मुकुट , मेखला  रत्नाकर  है।

                          नदिया  प्रेम  प्रवाह,  फूल तारा मंडल  है। बंदीजन खगवृन्द,  शेष फन रत्नाकर है।

                          करते अभिषेक पयोद है, बलिहारी इस वेष की। हे मातृभूमि ! तू सत्य ही, सगुण मूर्ति सर्वेश की। (छप्पय)

Mistake Points

• मात्रा के आधार पर छंद सिर्फ 3 प्रकार के होते है जिनका वर्णन ऊपर किया गया है। 'अर्द्ध विषममात्रिक छंद', 'छंद' का कोई प्रकार नहीं होता।

The correct answer is "filled with.'

Key Points  

• A prepositional phrase is simply a group of words that consists of a preposition and the object of the preposition.
• It can also include words that modify the object.
• Normally, the modifier will be a noun or the infinitive or gerund form of the linking verb.
• 'Fill with' is a phrasal verb meaning to cause a person, place, thing or period of time to have a lot of something.
• Examples:
• His childhood was filled with happiness.
• The kitchen is filled with the smell of fresh coffee.
• ​Therefore, the correct answer is Option 3.

​

Correct sentence: Hot air balloons are filled with air heated by a gas burner.

Given:

The edge length of simple cubic unit cell of a metal is 141.4 pm and radius of metal atom is x pm.

Solution:

Radius = \(\dfrac{Side}{2}\)

⇒ \(\dfrac{141.4}{2}\)141.4/2

⇒ 70.7 pm

⇒ x = 70.7 pm

∴ The value of x is 70.7 pm.

The correct answer is μ0 times the total current through the surface.

Explanation: 

According to Ampere's circuital equation, if the electric field inside the loop is constant, ∮ B.dl  of the resultant magnetic fields along a closed, plane curve is equal to μ0 times the total current crossing the area limited by the closed curve.

\(\oint \vec{B}. \vec{dl} = μ _{0}I\)      ----- (1)

Where dl is a small element, μ0 is the permeability of free space and I is the electric current.

  

for r > a we get: B.2πr = μ0I  ⇒ B = μ0I /2πr     ----- (2)

for r < a we get: B.2πr = μ0Ir2/ a2  ⇒ B = \(\frac{\mu _{0}Ir}{2\pi a^{2}} \)    ----- (3)

व्यंजन संधि के संदर्भ में सही कथन है- "व्यंजन संधि में व्यंजन और स्वर के योग से विकार उत्पन्न होता है"। 

• उदाहरण-  वाक्+ईश= वागीश।

Key Pointsव्यंजन संधि के उदाहरण- 

• (क् + ई = गी) वाक् + ईश = वागीश ।
• (च् + अ = ज्) अच् + अंत = अजंत ।
• (ट् + आ = डा) षट् + आनन = षडानन ।
• (प + ज + ब्ज) अप् + ज = अब्ज ।
• (क् + म = ड़्) वाक् + मय = वाड़्मय ।
• (च् + न = ञ्) अच् + नाश = अञ्नाश ।
• (ट् + म = ण्) षट् + मास = षण्मास ।
• (त् + न = न्) उत् + नयन = उन्नयन ।

Additional Information'संधि'- 'दो वर्णों के मेल से जो विकार उत्पन्न होता है, उसे संधि कहते है।

• उदाहरण- पीत+अम्बर= पीताम्बर।
• सत् + भावना = सद्भावना।

संधि- 3 प्रकार की होती है।

स्वर संधि- 'दो स्वरों के मिलने से जो परिवर्तन होता है, स्वर संधि कहते है'।

• जैसे- हिम+आलय=हिमालय।

व्यंजन संधि- 'व्यंजन के बाद स्वर या व्यंजन आने पर जो परिवर्तन होता है,व्यंजन संधि कहते है'।

• जैसे- निर्+आशा=निराशा।

विसर्ग संधि- 'विसर्ग के बाद स्वर या व्यंजन के आने से जो परिवर्तन होता है,विसर्ग संधि कहते है'।

• जैसे- निः+धन=निर्धन।

Mistake Points

• व्यंजन संधि के संदर्भ में सही कथन है- "व्यंजन संधि में व्यंजन और स्वर के योग से विकार उत्पन्न होता है"। अन्य कथन व्यंजन संधि के नियम के अनुसार सही नहीं है।
• दो निकटवर्ती शब्दों के योग से नहीं बल्कि दो निकटवर्ती वर्णों के योग से  नवीन शब्द की उत्पत्ति होती है। उसे हम संधि कहते है न कि व्यंजन संधि।

The correct answer is Fe.

Key Points

• Anode, the terminal or electrode from which electrons leave a system.
• Cathode, negative terminal or electrode through which electrons enter a direct current load.
• In the above question Fe is giving away two electrons to become  Fe²⁺.
• The equation given in the question tells us that Fe is spontaneously oxidized to Fe²⁺(at the anode).
• The solid Fe anode gradually disappears as it is converted to the soluble Fe²⁺ ions.
• The Ag⁺ ions are spontaneously reduced to solid silver (at the cathode).
• In any galvanic cell with reactive electrodes, the mass of the cathode increases and the mass of the anode decreases while the cell is operating.

Given: 

Army Contingent of 616 members and Army Band of 32 members

Concept used: 

HCF = Highest Common Factor 

HCF of two numbers is the largest number that divides both the numbers.

Calculation:

To find the maximum number of columns in which both groups can walk, we need to find the HCF (Highest Common Factor) of 616 and 32.

⇒ Factors(32) = 2 x 2 x 2 x 2 x 2

⇒ Factors(616) = 2 x 2 x 2 x 7 x 11

⇒ HCF (616, 32) = 8

⇒ The maximum number of columns in which both groups can walk is 8.

∴ The maximum number of columns in which the Army Contingent of 616 members and the Army Band of 32 members can walk is 8.

The correct answer is 'told , would be teaching , assist.'

 

Key Points 

• Let us start with the third blank.
• We can see the presence of "might" before the third blank.
• Structure: Subject + might + V1
• Example: He might know you.
• So we need to have V1 form of the verb in the third blank.
• Therefore, options 1 and 2 can be ruled out.
• According to the sentence, the action of teaching will be performed in the future.
• Therefore, option 4 can be eliminated.
• ​Thus, the correct answer is Option 3.

Correct sentence: When an old college friend told me he would be teaching a course in proverbs, I immediately began to think about how I might assist him.

The correct answer is Pepsin.

Key Points

• Pepsin:
• Pepsin is the digestive enzyme that breaks down proteins.
• The Gastric Glands secrete the enzyme Pepsin.
• Gastric glands are found in the stomach.
• They secrete enzymes like Pepsin, and Rennin which act upon the Proteins.
• Glands in the mucous membrane that line the stomach make and store an inactive protein known as pepsinogen.
• Pepsin partially degrades proteins into smaller units called peptides.

Additional Information

• Lipase:
• It is an enzyme that is found in pancreatic juice and is responsible for the breakdown of emulsified fat.
• It is secreted by the Pancreas.
• Lipases hydrolyze triglycerides (fats) into their component fatty acid and glycerol molecules.
• Emulsification is the process of breaking down large fat globules into smaller globules and making them water-soluble.​​​
• Zymase is an enzyme complex that catalyzes the fermentation of sugar into ethanol and carbon dioxide.
• It occurs naturally in yeast.
• Zymase activity varies between yeast strains.
• Zymase is also the brand name of the drug pancrelipase.
• Maltase is a type of alpha-glucosidase enzyme located in the brush border of the small intestine.
• This enzyme catalyzes the hydrolysis of the disaccharide maltose into two simple sugars, glucose.
• Maltase is found in plants, bacteria, yeast, humans, and other vertebrates.

Given: 

a_n = 40 

a = 3

Concept used: 

Arithmetic Progression

a_n = a + (n - 1)d, 

where a = first term, 

d = common difference, 

n = number of terms

Calculation:

⇒ a_n = 7 + (n - 1)3

⇒ 40 = 7 + (n - 1)3

Solving for n,

⇒ 40 - 7 = 3n - 3

⇒ 33 + 3 = 3n

⇒ n = 36/3

⇒ n = 12

∴ The term that has a value of 40 is the 12^th term in the sequence.

Shortcut Trick

Ratio of Height to Base = 20 : 20√3 = 1 : √3.

In a standard 30°−60°−90° triangle, the ratio of the side opposite to 30° and the adjacent side is 1 : √3.

Since the ratio is 1/√3, the angle of elevation is 30°.

∴ The correct answer is 30°.

Alternate Method

Given:

Height of the aeroplane (AB) = 20 m

Distance from the point directly below the plane (BC) = 20√3 m

Angle of elevation = θ

Formula Used:

tan θ = Perpendicular / Base

Calculations:

⇒ In right-angled triangle ABC, tan θ = AB / BC ⇒ tan θ = 20 / 20√3 ⇒ tan θ = 1 / √3 ⇒ Since tan 30° = 1 / √3 ⇒ θ = 30°

∴ The correct answer is 30°.

Additional Information

Angle of Elevation

The angle formed between the horizontal line and the line of sight when looking at an object above the horizontal level.

Trigonometric Ratios for Standard Angles

Common values for tan θ: tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.

Height and Distance Relationship

If Height = Base × √3, the angle is 60°. If Base = Height × √3, the angle is 30°.

The correct answer is 'some.'

Key Points  

• Let's understand the meaning and usage of given determiners:
• Much: We often use "much" with uncountable nouns and it is used in negative sentences.
• Example: I don't have much money.
• 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?
• 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.
• ​Any: We use "any" before nouns to refer to indefinite or unknown quantities or an unlimited entity. It is used in negative sentences.
• Example: Mr. Jacobson refused to answer any questions.​
• Here, we are referring to indefinite amount of good news and the given sentence is positive.
• Hence, the correct answer is 'Option 2.'

Correct sentence: My brother has some good news for you.

'तीर मारना' का अर्थ है-  'बड़ा कार्य करना'।

वाक्य प्रयोग- बड़ा होकर कौन-सा तुमने 'तीर मार' दिया।

Key Points

Additional Information

Mistake Points

• 'तीर मारना' का अर्थ है-  'बड़ा कार्य करना' होगा। न कि, 'युद्ध कला मे निपुण होना' या 'शिकार करना'।
• शिकार करना के लिए अर्थ 'किसी को अपनी गिरफ्त में लेना' होगा तथा 'युद्ध कला मे निपुण होना' किसी मुहावरे का स्पष्ट अर्थ नहीं है।

The correct answer is 'Jill required a lot of encouragement and practice to perform well in her test.'

Key Points  

• In the given sentence, the error lies in the part "encourage and practical."
• "A lot of" can both be used with plural countable nouns and with singular uncountable nouns for affirmatives, negatives, and questions.
• The phrase "a lot of" is always followed by a noun.
• Here, we need the noun form of the word "encourage" and "practical."
• The noun form of the word "encourage" is "encouragement" and "practical" is "practice."
• Hence, the correct answer is 'Option 2.'

Correct sentence: Jill required a lot of encouragement and practice to perform well in her test.

जो कान को कटु लगे, के लिए एक शब्द- 'कर्णकटु'।  

• जैसे- राघव बहुत 'कर्णकटु' बातें करता है।

Key Pointsएक शब्द- कई शब्दों को एक शब्द में बोलना बिना उसका अर्थ बदले हुए।  

• जैसे- 'कंटकाकीर्ण' अर्थात् काँटों से भरा हुआ (मार्ग)।
• वाक्य- सत्य का रास्ता सदैव 'कंटकाकीर्ण' होता है।
• 'कटुभाषी' अर्थात् 'कड़वी बात बोलने वाला'।
• वाक्य- सत्य बोलने वाले अक्सर 'कटुभाषी' होते है।
• 'कृतध्न' अर्थात् 'उपकार को न माननेवाला'।
• वाक्य- किसी के लिए कितना भी करलो लेकिन, आजकल के लोग 'कृतघ्न' है।

Additional Information

Calculation:

Let's call the original salaries of Aman, Bimal, and Charan as x, 2x, and 3x respectively.

After the increments, the new salaries will be:

Aman :  x + 0.25x = 1.25x

Bimal :  2x + 0.1(2x) = 2.2x

Charan : 3x + 0.2(3x) = 3.6x

So the new ratio of their salaries is:

1.25x : 2.2x : 3.6x = 25 : 44 : 72

Therefore, the new ratio of their salaries is 25 : 44 : 72.

The correct answer is "The surgery is being performed by the doctor."

Key Points 

• The given sentence is in the Present Continuous Tense and in Active Voice.
• The rule for changing a Present 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 + is/am/are + v1 + ing+ object (Active Voice)
• Object + is/am/are + being + V3 + by Subject (Passive Voice)
• Example: 
• Esha is singing a song. (Active Voice)
• A song is being sung by Esha. (Passive Voice)
• The subject of the given sentence is 'The doctor'.​​
• The object of the given sentence is 'the brain surgery'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'is performing' will be changed into 'is being performed'.
• "The surgery" is a singular noun so we must "is" with it.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.

​​

Correct sentence: The brain surgery is being performed by the doctor.

Given:

2x - 3y = 6; x + 2y = 1 

Solution:

2x - 3y = 6 →(1)

x + 2y = 1 →(2)

On multiplying Eqn (2) by 2 & then subtracting Eqn (2) from it,

4y + 3y = 2 - 6

⇒ 7y = - 4

⇒ y = - \(\dfrac{4}{7}\)

⇒ x = 1 - 2y

⇒ x = 1 + \(\dfrac{8}{7}\)

⇒ x = \(\dfrac{15}{7}\)

∴ x = \(\dfrac{15}{7}\) and y = -\(\dfrac{4}{7}\)

The correct answer is- 'Immigration.'

Key Points

• Let us see the meanings of the given words:
• Emigration: the act of leaving one's own country to settle permanently in another; moving abroad. (उत्‍प्रवासन)
• Asylum: protection that a government gives to people who have left their own country, usually because they were in danger for political reasons. (किसी राज्‍य या देश द्वारा अन्‍य देश के नागरिक को दी गई शरण (विशेषतः राजनैतिक कारणों से))
• Immigration: the process of coming to live permanently in a country that is not your own; the number of people who do this. (दूसरे देश मे आकर वहाँ स्‍थायी रूप से बसने की प्रक्रिया, आप्रवासन; आप्रवासियों की संख्‍या)
• Banishment: the punishment of being sent away from a country or other place. (किसी देश या अन्य स्थान से दूर भेजे जाने की सजा)
• Therefore, the act of passing or coming into a new habitat or country is called "Immigration."
• So, option 3 is the correct answer.

The correct answer is R.H. Whittaker.

Key Points

• Five Kingdom Classification was proposed by R.H. Whittaker.
• Five kingdoms defined in this classification were named Monera, Protista, Fungi, Plantae, and Animalia.
• The main basis for classification was cell structure, body organization, mode of nutrition, reproduction and phylogenetic relationships.

Additional Information

• The five-kingdom system was proposed by R.H. Whittaker (1969).
• The main criteria for classification used by him- 
• (1) Cell structure (2) Body organization (3) Mode of nutrition (4) Reproduction (5) Phylogenetic relationships.
• The kingdom defined by him was named-
• Monera- All the prokarytotes
• Protista- All the Unicellular eukaryotes
• Fungi- True fungi
• Plantae- All the multicellular plants
• Animalia- All the multicellular animals

Given:

Two numbers are in the ratio 5 ∶ 8.

The remainders are in the ratio 1 ∶ 2.

Calculation:

Let the numbers be 5x and 8x.

According to the question,

If 6 be subtracted from each of them then the remainders are in the ratio 1 ∶ 2.

⇒ \(\frac{5x-6}{8x-6}\) = \(\frac{1}{2}\)

⇒ 2(5x - 6) = 8x - 6

⇒ 10x - 12 = 8x - 6

⇒ 2x = 6

⇒ x = 3.

∴ 5x = 15 and 8x = 24

∴ The numbers are 15 and 24.

The correct answer is 'are you?'

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 the sentence is positive, the question tag must be negative, and vice-versa.
• Always use pronouns in the question tag.
• Example*: didn't, haven't, doesn't*
• ​​The given sentence is negative, so we must use a positive question tag.
• Example: did, have, does, has, will, shall​**
• ​The helping verb in the given sentence is "are."
• So, the correct answer is Option 3.

​​Correct sentence: Mother said, “You are not hungry yet, are you?”

Given:

Equation x2 + x + 2 = 0.

Concept Used:

The roots of quadratic equation ax2 + bx + c = 0 is 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\).

Calculation:

The given equation is in the form of ax2 + bx + c = 0 

where a = 1, b = 1 and c = 2.

⇒ \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

⇒ \(x = {-1 \pm \sqrt{(1)^2-4(1)(2)} \over 2(1)}\)

⇒ \(x = {-1 \pm \sqrt{-7} \over 2}\)

∴ \(x = {-1 \pm \sqrt{7}i \over 2}\).

The correct answer is 'The, a, 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. 
• Example: 
• We are looking for an apartment.
• I own a cat and two dogs.
• I love to visit the building.
• In the given sentence, we are referring to the "little boy" who purchased bread, so the first blank must have "the."
• The word "bread" is an uncountable noun.
• We never say "one bread" or "fifty breads."
• So, the correct answer for the second blank is the indefinite article "a."
• The third blank must be filled with "the" as it is referring to the particular bakery.
• Hence, the correct answer is Option 2.

​

​Correct sentence:The little boy purchased a loaf of bread from the bakery for breakfast.

The correct answer is 'One of my friends lives in Manchester.'

Key Points   

• The thumb rule is that we use 'one of' when the noun in question is countable, or quantifiable into individual units.
• Rules with the phrase "one of":
• The "one of" is a singular term and generally used to talk about a noun or a pronoun.
• The noun or a pronoun used after the phrase “one of” is always in the plural form ( as we are talking of one person/place/thing out of many)
• The helping verb will always be in the singular form, as the helping verb agrees with “one of” and not with the plural noun in the sentence.
• Example: One of the students was selected to visit NASA.​
• 'Lives' is a singular verb and 'friends' is a plural noun.
• Hence, the correct answer is Option 1.

​

​Correct sentence: One of my friends lives in Manchester.