MP Forest Guard/Jail Prahari: (09 June 2026, All Shift) Memory-Based Paper (Previous Year Paper)

The correct answer is revenue budget and capital budget.

Key Points

• The Government Budget is an annual financial statement that is prepared to account for the revenue and expenditure of a government for the upcoming fiscal year.
• The Revenue Budget consists of the Government's revenue receipts and the expenditure that is met using said revenue.
• The capital Budget is the Government's plan to purchase, build, maintain, repair and replace assets including infrastructure.

Additional Information

• A balanced budget occurs when revenues are equal to or greater than total expenses.
• A budget deficit occurs when expenses exceed revenue, and it can indicate the financial health of a country.
• Revenue receipts can be defined as those receipts which neither create any liability nor cause any reduction in the assets of the government.
• Revenue expenditures are short-term expenses used in the current period or typically within one year.
• Capital receipts are receipts that create liabilities or reduce financial assets.
• Capital expenditure is the money spent by the government on the development of machinery, equipment, building, health facilities, education, etc.

‘आँखे निकाल उड़ जाते, क्षण भर उड़ कर आ जाते।’ पंक्ति को पढ़कर घृणा भाव मन में पैदा होता है। अत: यहाँ वीभत्स रस विद्यमान है। अत: वीभत्स रस सही उत्तर होगा।

Additional Information

विशेष:

रस नौ हैं –

The correct answer is 'ill feeling'.

Key Points

• Let's take a look at the meaning of the given idiom.
• Bad blood: It is an idiomatic phrase that means ill feeling or bitterness; unfriendly or hostile relations; enmity; hostility; animosity.
• Example: There has always been bad blood between these families.
• Thus, the correct answer is option 1.

Shortcut Trick

Use identity pattern:

a + 1/a = 4

⇒ a² + 1/a² = 4² − 2 = 16 − 2 = 14

⇒ a³ + 1/a³ = 4 × 14 − 4 = 56 − 4 = 52

⇒ a⁵ + 1/a⁵ = (a² + 1/a²)(a³ + 1/a³) − (a + 1/a)

⇒ = (14 × 52) − 4 = 728 − 4 = 724

∴ Answer = 724

Alternate Method

Given:

⇒ a + 1/a = 4

Formula:

⇒ aⁿ + 1/aⁿ formed using recurrence:

aⁿ + 1/aⁿ = (a + 1/a)(aⁿ⁻¹ + 1/aⁿ⁻¹) − (aⁿ⁻² + 1/aⁿ⁻²)

Calculations:

⇒ a² + 1/a² = 4 × 4 − 2 = 16 − 2 = 14

⇒ a³ + 1/a³ = 4 × 14 − 4 = 56 − 4 = 52

⇒ a⁴ + 1/a⁴ = 4 × 52 − 14 = 208 − 14 = 194

⇒ a⁵ + 1/a⁵ = 4 × 194 − 52 = 776 − 52 = 724

Final Answer: 724

Additional Information

1. Basic Identity: a² + 1/a² = (a + 1/a)² − 2

2. Cubic Identity: a³ + 1/a³ = (a + 1/a)³ − 3(a + 1/a)

3. Recurrence Relation: T_n = (a + 1/a)T_n−1 − T_n−2

4. Exam Tip: Always build values stepwise instead of expanding high powers directly

Concept:

• R.H. Whittaker (1969) proposed a Five Kingdom Classification. The kingdoms defined by him were named Monera, Protista, Fungi, Plantae and Animalia.
• The main criteria for classification used by him include cell structure, body organisation, mode of nutrition, reproduction and phylogenetic relationships.

Explanation

• Fungi constitute a unique kingdom of heterotrophic organisms. It shows a great diversity in morphology and habitat.
• Fungi are cosmopolitan and occur in air, water, soil, animals, and plants.
• Fungi are categorized into 4 classes: Ascomycetes, basidiomycetes, Phycomycetes & Deuteromycetes
• Most fungi are heterotrophic and absorb soluble organic matter from dead substrates and hence are called saprophytes.
• Those that depend on living plants and animals are called parasites.
• They can also live as symbionts – in association with algae as lichens and with roots of higher plants as mycorrhiza.
• Thereby the correct option is both 2 & 3

Additional Information

The correct answer is Both I and II.

Key Points

• Direct taxes
• It includes taxes that cannot be transferred to another person, for example, income tax is paid directly by an individual to the government.
• Ex: Income Tax, Corporate Tax, Wealth Tax, Estate Tax, Gift Tax, Fringe Benefits Tax, Securities transaction tax.
• Indirect tax
• It is another type of tax that can be shifted to another person.
• Excise Duty, Sales Tax, Customs Duty, Entertainment Tax, Service Tax, Value added tax.

ऐ रमेश ! यहा आओ। संबोधन कारक का उदाहरण है. अत: सही उत्तर विकल्प 2 है l

Key Points 

• अरे श्याम ! तुम जयपुर से कब लौटे ? - संबोधन कारक
• संबोधन कारक- संबोधन कारक “जिस संज्ञापद से किसी को पुकारने, सावधान करने अथवा संबोधित करने का बोध हो, 'संबोधन' कारक कहते हैं।
• चुँकि उपरोक्त वाक्य में रमेश को पुकारने का कार्य हो रहा है। अतः उपरोक्त वाक्य में संबोधन कारक है।

अन्य विकल्प-

Additional Information 

The correct answer is option 3), i.e. situation.

Explanation:

• The correct spelling of the given word is 'situation'.
• The meaning of the word situation is 'a set of circumstances'.

Hence, option 3) is the answer.

Given:

5 men can prepare 10 toys in 6 days working 6 hours a day

Concept:

We will use the man-hour concept here to solve this problem

Formula:

(M₁ × d₁ × h₁)/ W₁ = (M₂ × d₂ × h₂)/ W₂

Where M, d,h, W are numbers of men, number of days, number of hours and work done respectively.

Calculation:

(M1 × d1 × h1)/ W1 = (M2 × d2 × h2)/ W2

⇒ (5 × 6 × 6)/10 = (12 × d₂ × 8)/16

⇒ 18 = 6 × d₂

⇒ d₂ = 3

⇒ Number of days to make 16 toys = 3 days

Concept:

Levers:

• Levers are the most basic machines which are used to do some work with minimal effort.
• A lever amplifies an input force to provide a greater output force, which is said to provide leverage.
• Types: First class lever, second class lever, third class lever.

Class 1 levers:

• It is a very simple machine comprised of a beam placed upon a fulcrum.
• A load is placed onto one end of a beam, while an effort is directed onto the other end to counter the load.

• In a first-class lever, the effort (force) moves over a large distance to move the load a smaller distance, and the fulcrum is between the effort (force) and the load.
• Examples of first-class levers are pliers, scissors, a crowbar, a claw hammer, a see-saw, and a weighing balance.

Explanation:

• A Class 1 lever has the fulcrum placed between the effort and load.
• The movement of the load is in the opposite direction of the movement of the effort.
• This is the most common lever configuration.
• **The effort in a class 1 lever is in one direction, and the load moves in the opposite direction.**​

Additional Information

Second class lever:

• In this class of lever, the load is applied in between the fulcrum and the effort force.
• Examples: Wheelbarrow, Nutcracker, etc.

Third class lever:

• In this class of lever, the fulcrum is at the one end and the effort force is applied in between the fulcrum and load.
• Examples: Human arms, Tongs, tweezers, etc.
• It consists of two levers which works together.

The correct answer is Presidential Awards

Key Points

• The Sangeet Natak Academy Awards were earlier known as the Presidential Awards.
• These awards are given to artists in the field of performing arts such as music, dance, and drama.
• The awards aim to recognize and honor the outstanding contribution of artists to Indian cultural heritage.
• Established in 1952, the Sangeet Natak Academy is India's national academy for music, dance, and drama.

Additional Information

• The Sangeet Natak Academy functions as an autonomous organization under the Ministry of Culture, Government of India.
• It not only honors artists but also engages in various activities to promote and preserve the rich cultural heritage of India.
• The awards are conferred by the President of India, which adds to their prestige and recognition.
• Recipients of the awards receive a plaque, a shawl, and a cash prize.

'पानी पीकर जात पूछना' मुहावरे के अर्थ को सर्वश्रेष्ठ रूप से व्यक्त करता है - काम करने के बाद जाँच पड़ताल

Key Points

• 'पानी पीकर जात पूछना' का अर्थ - काम करने के बाद जाँच पड़ताल,
• वाक्य प्रयोग - पहले लड़की की शादी अनजान घर में कर दी, अब पूछ रहे हो लोग कैसे हैं ? आप तो "पानी पीकर जात पूछने" वाली कहावत चरितार्थ कर रहे हो।
• मुहावरा - ऐसे वाक्यांश, जो सामान्य अर्थ का बोध न कराकर किसी विलक्षण अर्थ को प्रकट करते है, उसे मुहावरा कहते है।
• जैसे : 'खेत रहना' का अर्थ- शहीद होना।, वाक्य प्रयोग - पाकिस्तान से मुठभेड़ में कई भारतीय सैनिक "खेत रह गए"।

Important Points 

Additional Information  

The correct answer is option 1.)

Key Points

• When the interrogative sentence in the passive form starts with a helping verb, the active form also starts in the same manner and in the same tense.
• Identify the subject and the object and interchange their places.
• Remove the preposition ‘by’ which is used to introduce the agent in the passive form.
• In the case of continuous tense, remove ‘being’ and the verb needs to be in the ‘-ing’ form.
• Use the following syntax for the above sentence-

           Passive voice - Question word + subject+ being + V3 + by + object + other + ?

           Active voice - Question word + new subject + ing form of the verb + new object + other + ?

​Following these steps, we finally get- *“*Were the students enjoying the classes of Prof. Das?”

Given:

21 kg of sugar costs Rs. 280/kg

15 kg of sugar costs Rs. 220/kg

Concept used:

Average = Sum of observations/Number of Observations

Calculation:

Total cost = (21 kg × Rs. 280/kg) + (15 kg × Rs. 220/kg)

⇒ 5880 + 3300 = Rs. 9180.

Total weight = 21 kg + 15 kg = 36 kg.

Average cost per kg = Total cost/Total weight

⇒ (\dfrac{9180}{36}) = 255 Rs/kg

∴ Option (1) is the correct answer.

The correct answer is Muscular force.

Key Points

• The forces acting on a plastic bucket are:

1. Gravitational force
2. Muscular force

• Gravitational force is acting downwards, and muscular force is applied by the hands lifting the bucket upwards.
• Although these forces are acting on the bucket no change is found in its state of motion because the two forces are in the opposite direction & hence balancing each other. As a result net force is zero.
• This force is required whenever the movement of the body occurs. For example,

1. When we lie in a bucket of water, the force acting on the object is Muscular Force.
2. when you pick up a book on the table with your hands, you apply muscular force.

• The Muscular force is exerted by the Earth on every object, which is near or on its surface.

Additional Information

• Magnetic force is attraction, or repulsion that arises between electrically charged particles because of their motion**.**
• The frictional force is defined as the force generated by two surfaces that contact and slide against each other.
• The electrostatic force is defined as an attractive and repulsive force between particles are caused due to their electric charges.

The correct answer is Expenditure which is subjected to the vote of the Assembly.

Key Points

• Voted Expenditure is that part of the budget which requires voting in the Parliament or State legislature.
• Whereas Charged Expenditure is that part of the budget which doesn't require voting in the parliament or State legislature.

Additional Information

• As per Article 202 of the Indian Constitution, the following expenditure shall be expenditure charged on the Consolidated Fund of each State-
• the emoluments and allowances of the Governor and other expenditure relating to his office;
• the salaries and allowances of the Speaker and the Deputy Speaker of the Legislative Assembly and, in the case of the State having a Legislative Council, also of the Chairman and the Deputy Chairman of the Legislative Council;
• debt charges for which the State is liable including interest, sinking fund charges and redemption charges, and other expenditures relating to the raising of loans and the service and redemption of debt;
• expenditure in respect of the salaries and allowances of Judges of any High Court;
• any sums required to satisfy any judgment, decree or award of any court or arbitral tribunal;
• any other expenditure declared by this Constitution, or by the Legislature of the State by law, to be so charged

'सोहत ओढ़े पीत पट स्याम सलोने गात'।

'मनहूँ नीलमनि सैल पर, आतप परयौ प्रभात'।।

दी गई पंक्ति में 'उत्प्रेक्षा अलंकार' है।

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

पहचान- पंक्ति में मनु, मानो, मानहु, जनु, जानो, जनहु, निश्चय, ईव, ज्यों आदि आता है।

• **उदाहरण- ले चला साथ मैं तुझे कनक। **ज्यों भिक्षुक लेकर स्वर्ण।।

दिए गए उदाहरण में कनक का अर्थ धतुरा है। कवि कहता है कि वह धतूरे को ऐसे ले चला मानो कोई भिक्षु सोना ले जा रहा हो।

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

• उदाहरण- पायो जी मैंने राम रतन धन पायो।

उदाहरण में राम रतन को ही धन बता दिया गया है। 'राम रतन' – उपमेय पर 'धन' – उपमान का आरोप है एवं दोनों में अभिन्नता है।

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

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

पंक्ति में एक कनक का अर्थ 'सोना' तथा दुसरे कनक का अर्थ 'धतूरा' है।

श्लेष अलंकार- जब किसी पंक्ति में कोई शब्द एक ही बार प्रयुक्त हों लेकिन उसके अर्थ अलग-अलग हों तब श्लेष अलंकार होता है।

• उदाहरण- 'रहिमन पानी राखिये, बिन पानी सब सून'।

                'पानी गये न ऊबरै, मोती मानस चून'।।

पंक्ति में 'पानी' शब्द के अनेक अर्थ है।

• जैसे- चमक, प्रतिष्ठा, और जल।

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।

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

The correct answer is Option 4.

Key Points

• The preposition "at" is used to indicate direction or attention towards something specific, such as a face.
• The preposition "for" is used to indicate the reason or cause of a feeling or action.
• In the sentence "She looked at his face and felt sorry for him," "at" correctly indicates where she looked, and "for" correctly indicates the reason for her sympathy.

Therefore, the correct answer is Option 4.

Correct Sentence: "She looked at his face and felt sorry for him."

Additional Information

• Option 1: "on ; at" is incorrect because "on" is not typically used to indicate where someone looks and "at" does not correctly indicate the reason for sympathy.
• Option 2: "at ; on" is incorrect because "on" does not correctly indicate the reason for sympathy.
• Option 3: "on ; for" is incorrect because "on" is not typically used to indicate where someone looks.

Given:

The individual weights (in kg) of six boys are 55, 56, 57, 60, 59 and 55.

A new boy joins the group, and the mean weight of the group becomes 62 kg.

Formula used:

Mean = Total weight / Number of boys

Calculation:

Total weight of 6 boys = 55 + 56 + 57 + 60 + 59 + 55

⇒ Total weight = 342 kg

Let the weight of the new boy be x kg.

Total weight of 7 boys = 342 + x

Mean weight of 7 boys = 62 kg

⇒ (342 + x) / 7 = 62

⇒ 342 + x = 62 × 7

⇒ 342 + x = 434

⇒ x = 434 - 342

⇒ x = 92

∴ The correct answer is option (3).

The correct answer is option 3 i.e. Cu (Copper).

• Bell metal is a hard alloy used for making bells and different musical instruments.
• It is made of 80% copper and 20% tin (Sn) with some amount of Zinc and Lead.
• Bell metal is known for its resonance and attractive sound.
• Some other important alloys are:
• German Silver - Cu + Zn + Ni
• Gun Metal - Cu + Sn + Zn + Pb
• Solder - Pb + Sn
• Brass - Cu + Zn
• Stainless steel - Fe + Cr + Ni + C

The correct answer is 1943.

Key Points

• The Satara Parallel government in Maharashtra from August 1943 to May 1946 against British rule was a legendary chapter in the glorious freedom struggle of India.
• It was an armed offshoot of the 1942 Quit India movement, like the parallel governments in Bengal, Bhagalpur etc.
• The leader of this government was Kratisimha Nana Patil.
• British rule was overthrown in most parts of Satara.
• The Parallel government (Prati Sarkar) movement was a guerilla type of Western Maharashtra during those three years.

 Thus, we can say that the parallel government (Prati Sarkar) was established in Satara, Maharashtra in the year 1943.

दिग् + मण्डल = दिङ्मण्डल असंगत विकल्प है।  

Key Points

• दिक् + मण्डल =दिङ्मण्डल
• दिङ्मण्डल में व्यंजन संधि है।

Additional Informationव्यंजन संधि - व्यंजन को किसी व्यंजन या स्वर के साथ मिलाने से जो परिवर्तन होता है।

उदाहरण -अहोरूप, उन्मोचन, भूषण,प्रतिष्ठा, उद्धार, वागीश, आज़ादी, उन्मूलन आदि।

The correct answer is 'to sold their land'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'to sell their land' should be used instead of 'to sold their land'.
• The pronoun 'his' should be used because it agrees with the main subject i.e., 'Raman'.
• We know that after 'to' infinitive 'the base form of the verb is used'. So, 'sell' should be used in place of 'sold'.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

Correct Sentence: Raman went with his wife to the village to sell their land.

If a number is divisible by both 5 and 7 then the number is divisible by 35.

∴ The first number to be divisible by 35 is 35 and last is 105.

⇒ Let a = 35, d = 35 and An = 105

⇒ 105 = 35 + (n - 1)35                                    ∵ n is the no. of numbers divisible by 35.

⇒ 105 - 35 = 35n - 35

⇒ n = 105 / 35 = 3

∴ there are 3 numbers divisible by both 5 and 7 between 11 and 131.

Explanation:

Oxides of nitrogen

• When fossil fuel is burnt,In an automobile engine, (at high temperature) dinitrogen and dioxygen combine to yield significant quantities of nitric oxide (NO) and nitrogen dioxide ( NO₂ ).

• NO reacts instantly with oxygen to give NO₂
• The irritant red haze in the traffic and congested places is due to oxides of nitrogen.
• Higher concentrations of NO2 damage the leaves of plants and retard the rate of photosynthesis.
• Nitrogen oxides also cause acute respiratory disorders.

Correct option is oxides of nitrogen

Additional InformationOxides of Sulphur

• They causes respiratory diseases e.g., asthma, bronchitis, emphysema in human beings.
• Sulphur dioxide causes irritation to the eyes, resulting in tears and redness.
• High concentration of SO₂ gas is responsible for stiffness of flower buds which eventually fall off from plants.

The correct answer is generator.

Key Points

• An electric generator is a machine that converts mechanical energy to electricity.
• The mechanical power for an electric generator is usually obtained from a rotating shaft.
• It is based on the principle of electromagnetic induction.
• It is also called a dynamo.
• Generators also produce the electrical power required for automobiles, aircraft, ships, and trains. electric generator.

Additional Information

• Galvanometer
• ​A galvanometer is used to detect electrical current.
• It is used on electrical circuits to measure the intensity and direction of electrical current.
• It is based on the principle of the magnetic effect of current.
• Motor
• ​Electric motor is a device that converts electrical energy to mechanical energy.
• It works on the principle of electromagnetism.
• Ammeter
• ​An ammeter is a device used to measure electrical current.
• It is based on the principle of the magnetic effect of current.
• An ideal ammeter offers zero resistance.

देवासुर में द्वंद्व समास है।

• देवासुर = देव और असुर
• इतरेतर द्वन्द्व समास में सभी पद प्रधान होते है और दो पदों के बीच में और शब्द का लोप पाया जाता है उसे इतरेतर द्वन्द्व समास कहते हैं।
• अन्य उदाहरण -
• सुरा-सर = सुर और असुर
• तिर-सठ = तीन और साठ

Additional Information

• दो या दो से अधिक सार्थक शब्दों के परस्पर मेल को  समास कहते है।

समास के छ: भेद हैं-

The correct answer is 'He was seen climbing over the fence'.

Key Points 

• The given sentence is in the active voice.
• To change the given sentence in the passive voice. We will do the following changes:
• 'climbing over the fence' will not be changed as it is an independent clause.
• 'They saw him' will be changed into 'He was seen'.
• Hence the correct sentence will be "He was seen climbing over the fence'"

The correct answer will be Option 2.

Shortcut Trick

Rate % = [(n − 1) × 100] ÷ Time

Here, the sum becomes 5 times itself, so n = 5.

Time given is 16 years.

Rate % = [(5 − 1) × 100] ÷ 16 = 400 ÷ 16

Rate % = 25%

∴ Answer = 25%

Alternate Method 

Given:

Principal (P) = Let it be P

Amount (A) = 5 × P = 5P

Time (T) = 16 years

Formula used:

Simple Interest (SI) = Amount − Principal

SI = (P × R × T) ÷ 100

 Initial (P) Final (5P) T = 16 Years  Interest (SI) = 4P

Calculations:

SI = 5P − P = 4P

⇒ 4P = (P × R × 16) ÷ 100 ⇒ 4 = (R × 16) ÷ 100 ⇒ 16R = 400 ⇒ R = 400 ÷ 16 ⇒ R = 25% ∴ The correct answer is 25 (Option 2).

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate per annum, and T is Time in years.

Sum Becomes n Times

For a sum to become n times itself, the Interest earned must be (n − 1) × Principal.

Compound Interest Amount

Under compound interest, the Amount A = P(1 + R ÷ 100)^T, where interest is calculated on the updated principal each period.

Relationship between R and T

For a fixed multiple n, Rate and Time are inversely proportional: R × T = (n − 1) × 100.

Intense light is called Tint.

Key Points

• In color theory, a tint is a mixture of a color with white. Which increases lightness.
• For example, pink is a tint of red, and light blue is a tint of blue.
• Tint refers to any hue or mixture of pure colors to which white color is added. Pastel colors are generally tinted colors. The tinted color remains the same color, but it is paler than the original. For example, pink is a tint of red, and light blue is a tint of blue.​​
• 

Additional Information

The correct answer is Ranchi.

Key Points

• The Indian Institute of Legal Metrology (IILM) is located in Ranchi, the capital of Jharkhand, India.
• IILM is a national-level institute that was established in 1974 by the Ministry of Consumer Affairs, Food & Public Distribution, Government of India.
• The institute is responsible for training and educating personnel in the field of legal metrology, which is the science of measurement and accuracy of weighing and measuring instruments.
• IILM also conducts research in the field of legal metrology and develops new standards and procedures for testing and calibrating weighing and measuring instruments.
• IILM plays an important role in protecting the interests of consumers by ensuring that the weighing and measuring instruments used in commercial transactions are accurate and reliable.

विकल्प 3, "वह पढ़ा तो होगा।" सही है।

Key Points

• "वह पढ़ा तो होगा।" इस वाक्य में 'संदिग्ध भूतकाल' है।
• अन्य विकल्पों का विश्लेषण -

Additional Information

• संदिग्ध भूतकाल का अर्थ:- क्रिया का वह रूप जिससे भूतकाल का बोध होता हो किन्तु कार्य के होने में संदेह हो।
• उदाहरण:- ”बच्चा आया होगा - यह संदिग्ध भूतकाल का उदाहरण है।”
• भूतकाल का अर्थ:- बीता हुआ क्रिया के जिस रूप से बीते हुये समय का पता चले उसे भूतकाल कहते हैं भूतकाल के वाक्यों के अंत में था, थे, थी, जैसे शब्द आते हैं, इन्हीं शब्दों से भूतकाल की पहचान होती हैं।
• जैसे- 
• मैं खाना खा रहा था।
• मैं सो रहा था।
• भूतकाल के मुख्यतः सात प्रकार होते हैं।

1. सामान्य भूतकाल
2. आसन्न भूतकाल
3. पूर्ण भूतकाल
4. अपूर्ण भूतकाल
5. संदिग्ध भूतकाल
6. हेतुहेतुमद् भूतकाल
7. समयकालीन भूतकाल

The correct answer is Option 1)

Key Points

• The idiom "Best thing since sliced bread" means something that is extremely good or interesting. (बेहद अच्छा या रोचक)
• Example: The new smartphone model is the best thing since sliced bread; it has so many innovative features.
• "Extremely good, interesting" refers to something that is very impressive or captivating. (बेहद अच्छा, रोचक)
• Example: Her performance in the play was extremely good and interesting, leaving the audience in awe.

Therefore, the correct answer is: Extremely good, interesting.

Additional Information

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

• Breaking news (ताजा खबर): Information about an event that has just happened or is currently happening.
• Example: The journalist rushed to cover the breaking news of the earthquake.
• Something to be cautious about (सावधान रहने योग्य कुछ): Something that requires careful attention or vigilance.
• Example: The slippery road conditions are something to be cautious about while driving.
• Rated well amongst cooks (रसोइयों के बीच अच्छी रेटिंग): Something that is highly regarded or rated by chefs.
• Example: This brand of olive oil is rated well amongst cooks for its quality and flavor.

Shortcut Trick

Difference (constant) = ?

6 yrs hence: F + 6 = 3(S + 6) ⇒ F = 3S + 12

6 yrs ago: F − 6 = 7(S − 6) ⇒ F = 7S − 36

⇒ 3S + 12 = 7S − 36 ⇒ 4S = 48 ⇒ S = 12

⇒ F = 3(12) + 12 = 48

∴ Answer = Father = 48, Son = 12

Alternate Method

Given:

⇒ Let present ages be Father = F, Son = S

Form Equations:

⇒ (F + 6) = 3(S + 6)

⇒ F + 6 = 3S + 18

⇒ F = 3S + 12 ...(1)

⇒ (F − 6) = 7(S − 6)

⇒ F − 6 = 7S − 42

⇒ F = 7S − 36 ...(2)

Solving:

⇒ From (1) and (2):

⇒ 3S + 12 = 7S − 36

⇒ 4S = 48 ⇒ S = 12

⇒ F = 3(12) + 12 = 48

Final Answer: Father = 48 years, Son = 12 years

Additional Information

1. Age Difference: Difference between ages remains constant over time

2. Linear Equations: Age problems convert into simple linear equations

3. Time Shift: Future → add years, Past → subtract years

4. Exam Tip: Always form equations carefully before solving

Concept:

• Fibers are materials that form clothing.
• Fibers are of two types, Natural and Synthetic (or artificial).
• Natural fibers are obtained from organic sources (plants and animals). Examples: jute, cotton, silk, wool
• Synthetic fibers are chemically processed. Examples: rayon, nylon, dacron, polymer, etc,

Explanation:

• Artificial fibers came into use because they were cheap and easy to maintain compared to natural fibers.
• The cloths made up of artificial fibers get easily dried up when washed.
• They get less wrinkled and are resistant to bugs.
• Though they are not so comfortable compared to natural ones. Cotton cloths are more comfortable in summer compared to synthetic alternatives.
• Also, fire catches easily in synthetic cloths. Therefore, it is recommended to wear cotton clothes while burning crackers on Diwali.
• So, Synthetic fibers are not fire-resistant. They are cheaper, easy to maintain bus less comfortable.

The correct option here is 'They are fire-resistant.'

The correct answer is 2023-24.

Key PointsMadhya Pradesh First e-Budget:

• Honourable Finance Minister of MP, Shri Jagdish Devada presented the budget for the year 2023-24 in the Madhya Pradesh Legislative Assembly.
• According to the MP Government, the first e-budget saved money and was also environmentally friendly.
• It saved 1.5 metric tons of paper and will save Rs 30 lakh every year.
• This budget is 13 per cent bigger than the previous budget.
• About 20 per cent of the total budget provision which is 4% of the state's gross domestic product, to promote capital expenditure by the State to make India a $ 5 trillion economy
• "Atma-Nirbhar MP"-Budget 2023-24 has been prepared in mission mode, keeping in view the objective of a self-sufficient Madhya Pradesh.
• The budget for the year 2023-24 can now be seen through the MP Govt. The Diary app will also be available on Finance Department Official Website.
• The budget for the year 2023-24 is presented in the form of an ‘e-budget’ for the first time. Hence, Option 4 is correct.

'बादल' का पर्यायवाची नही है - 'वारिज'

• 'बादल' का पर्यायवाची है - अमेघ, जलद, जलधर, मेघ, नीरद, अंबुद, अंबुधर, पयोधर, अब्र, अभ्र, घटा।
• 'कमल' का पर्यायवाची है - पंकज, नीरज, सरोज, जलज, अंबुज, अब्ज, अरविंद, वारिज, इंदीवर।

Key Points

• जो शब्द समान अर्थ के कारण किसी दूसरे शब्द की जगह ले लेते हैं उन्हें पर्यायवाची शब्द कहते है।

Additional Informationकुछ महत्वपूर्ण पर्यायवाची शब्द:-

• पृथ्वी - धरा, धरती, वसुधा, भूमि, वसुंधरा, भू, इला, धरा, धरत्री, धरणी।
• पर्वत - शैल, नग, भूधर, पहाड़, अंचल, महीधर, गिरि, भूमिधर, तुंग, अद्रि।
• बिजली - चपला, चंचला, दामिनी, सौदामनी, विधुत्, तड़ित, बीजुरी, क्षणप्रभा।
• मेघ - बादल, जलधर, पयोद, पयोधर, घन।
• राजा - नृप, नृपति, भूपति, नरपति, भूप, महीप, महीपति, नरेश।
• सर्प - साँप, अहि, भुजंग, विषधर, व्याल, फणी, उरग, पन्नग, नाग।
• सागर - समुद्र, उदधि, जलधि, वारिधि, पारावार, सिंधु, नीरनिधि, नदीश।
• सिंह - शेर, वनराज, शार्दूल, मृगराज, व्याघ्र, पंचमुख, मृगेंद्र, केशरी, महावीर।

The correct answer is Option 4)

Key Points

• The idiom "bread and butter" means an activity or job that provides the main source of income. (जीविका का साधन)
• Example: Writing is his bread and butter; it pays all his bills.
• Activity to get money for basic needs refers to something that one does primarily to earn money to cover essential living expenses. (मूलभूत आवश्यकताओं के लिए पैसा कमाने की गतिविधि)
• Example: Many people find that their 9-to-5 job is their bread and butter.

Therefore, the correct meaning of the given idiom is: An activity you do to get money for basic needs.

Additional Information

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

• Option 1: An activity you do with determination (दृढ़ संकल्प के साथ की गई गतिविधि)
• Example: She pursued her studies with determination, never giving up.
• Option 2: An activity you do to improve your culinary skills (अपने पाक कौशल को सुधारने के लिए की गई गतिविधि)
• Example: Taking cooking classes is a great way to improve your culinary skills.
• Option 3: An activity you do to get help others (दूसरों की मदद करने के लिए की गई गतिविधि)
• Example: Volunteering at the shelter is an activity she does to help others.

Calculation:

The sum invested at 10% per annum for 2 years,

Then after 2 years effective interest = 10 + 10 + (\frac{10 × 10}{100}) = 21%

So, total interest on 15,000 after 2 years = 15000 × 21/100 = Rs. 3150

∴ The correct answer is Rs. 3150

A force can be larger or smaller than the other force. The strength of a force is expressed by its magnitude. The magnitude of a force is expressed in the SI unit of force called Newton. 1 Newton is the force which can make an object of 1 kilogram mass to move at a speed of 1 meter per second. The direction in which a force acts is also to be specified. If the magnitude or direction of the applied force changes the effect produced by force also changes.

The correct answer is England.

Key Points

• Magna Carta:-
• It​ was a charter of rights agreed to by King John of England in 1215.
• It established the principle that everyone, including the king, was subject to the law and had certain rights that could not be taken away without due process.
• Fundamental Rights:-
• The concept of fundamental rights is based on the idea that there are certain rights that are inherent to all human beings, regardless of their nationality, race, or gender.
• These rights are often enshrined in national constitutions and international treaties.
• While the Magna Carta was an important precursor to the concept of fundamental rights, it did not include all of the rights that we now consider to be fundamental.
• For example, it did not guarantee freedom of speech or religion..

Additional Information

• United States Constitution:-
• It includes a Bill of Rights that guarantees certain fundamental rights, such as freedom of speech, religion, and the press.
• However, the concept of fundamental rights predates the US Constitution, and the Magna Carta was the first document to establish the principle that everyone is subject to the law and has certain rights that cannot be taken away without due process.
• Canada:-
• It has a Charter of Rights and Freedoms that protects fundamental rights such as freedom of expression, religion, and peaceful assembly.
• However, the concept of fundamental rights predates the Canadian Charter, and the Magna Carta was the first document to establish the principle that everyone is subject to the law and has certain rights that cannot be taken away without due process.
• Australia:-
• It has a constitution that protects certain fundamental rights, such as freedom of religion and the right to vote.
• However, the concept of fundamental rights predates the Australian Constitution, and the Magna Carta was the first document to establish the principle that everyone is subject to the law and has certain rights that cannot be taken away without due process.

'अल्प' शब्द का विलोम शब्द ‘अधिक’ इसका सही उत्तर है।

Key Points

• 'अल्प' शब्द का विलोम है –'अधिक'।
• ‘अल्प' - आवश्यक मात्रा से कम को अल्प कहते है।
• 'अधिक' - आवश्यकता से ज्यादा।

अन्य विकल्प:

 Additional Information विशेष:

The erroneous part is option 1) i.e. 'are necessary.'

Key Points  

• The error lies in part 'are necessary.'
• According to the rules of subject-verb agreement, if two subjects are joined by 'as well as', 'with', 'along with', 'together with' etc, the verb will be according to the first subject.
• Here, the first subject 'Dedication' is an uncountable noun so it will take a singular verb 'is.'
• In the given sentence we need to use 'is' in place of 'are' to make the sentence grammatically correct.
• Hence, the correct answer is option 1.

Correct sentence: Dedication as well as hard work is necessary to achieve success in any field.

Shortcut Trick

Use the direct formula for two pipes: Time = (X × Y) ÷ (X + Y)

X = 10 hrs, Y = 15 hrs

Time = (10 × 15) ÷ (10 + 15) = 150 ÷ 25 = 6 hrs

∴ The correct answer is 6 hrs.

Alternate Method

Given:

Time taken by Pipe A = 10 hrs

Time taken by Pipe B = 15 hrs

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time

Calculations:

⇒ Combined Efficiency of A + B = 3 + 2 = 5 units/hr

⇒ Total Time taken together = Total Work ÷ Combined Efficiency

⇒ Time = 30 ÷ 5

⇒ Time = 6 hrs

∴ The correct answer is 6 hrs.

Additional Information

Pipes and Cisterns

If an inlet pipe fills in X hours and an outlet pipe empties in Y hours, the net work done in 1 hour is (1/X − 1/Y).

Efficiency Relation

Efficiency is inversely proportional to the time taken to complete a task. If the ratio of time is a:b, the ratio of efficiency is b:a.

A simple machine is a device that simply transforms the direction or magnitude of a force.

• The force overcome by the effort is called load or weight (W)
• The force applied to lift the load is called effort or power (P)
• A fixed point in the machine around which the machine rotates is called fulcrum (F)

The correct answer is ​1 and 2 Only.

Key Points

Mahajanapadas

• They were sixteen kingdoms or oligarchic republics that existed in ancient India from the sixth to fourth centuries BCE during the second urbanisation period.
• Most Mahajanapadas had a capital city, and many of these were fortified.
• The sixteen Mahajanapadas included: Kasi, Kosala, Anga, Magadha, Vajji, Malla, Chedi, Vatsa, Kuru, Panchala, Machcha, Surasena, Assaka, Avanti, Gandhara and Kamboja.

Vajji

• Its capital Vaishali (Bihar), was under a different form of government, known as Gana or Sangha.
• In a gana or a sangha there were not one, but many rulers.
• Sometimes, even when thousands of men ruled together, each one was known as a raja. These rajas performed rituals together.
• Women, dasas and kammakaras could not participate in assemblies.
• The territory of the Vajji mahajanapada was located on the north of the Ganga River and extended up to the Terai region of Nepal.
• On the west, the Gandak River was the boundary between it and the Malla mahajanapada, and possibly also separated it from the Kosala mahajanapada. Hence, pair 1 is correct.

Magadha

• It became the most important mahajanapada in about two hundred years.
• Many rivers such as the Ganga and Son flowed through Magadha.
• This was important for (a) transport, (b) water supplies (c) making the land fertile. Hence, pair 2 is correct.
• Besides, there were iron ore mines in the region that could be tapped to make strong tools and weapons.
• Magadha had two very powerful rulers, Bimbisara and Ajatasattu, who used all possible means to conquer other janapadas.
• Mahapadma Nanda was another important ruler.

Avanti

• It was an important kingdom of western India and was one of the four great monarchies in India when Buddhism arose, the other three being Kosala, Vatsa and Magadha.
• Avanti was divided into north and south by the river Vetravati. Hence, pair 3 is Incorrect.
• The country of Avanti roughly corresponded to modern Malwa, Nimar and adjoining parts of the Madhya Pradesh.
• Both Mahishmati and Ujjaini were located on the southern high road called Dakshinapatha extending from Rajagriha to Pratishthana (modern Paithan).
• Avanti was an important center of Buddhism and some of the leading theras and theris were born and resided there.
• Avanti later became part of the Magadhan empire when King Nandivardhana of Avanti was defeated by king Shishunaga of Magadha.

Kosala

• Kosala extended across both banks of the Sarayu (modern Ghaghara) River and north into what is now Nepal. Hence, pair 4 is Incorrect.
• According to the Hindu epic the Ramayana, Kosala was ruled by kings descended from the Sun; one of these kings was Rama, whose capital was Ayodhya (Oudh), near modern Faizabad.
• It rose in political importance early in the 6th century BCE to become one of the 16 states dominant in northern India. It annexed the powerful kingdom of Kashi.

सही उत्तर पत्र - पर्ण है। 

Key Points

• पत्र का तद्भव रूप पत्ता है।
• 'पर्ण' का तद्भव रूप है 'पन्ना' अथवा 'पान'।

अन्य विकल्प-

Additional Information

Note- यहाँ दो विकल्प सही हो सकते हैं-

असंगत युग्म - पत्र- पर्ण और छत्र- छत है।

The correct answer is "Although".

Key Points

• Although means "despite the fact".
• Although and or despite are the meanings of the conjunction "although".
• Although it is a connecting word for sentences, clauses, and phrases.
• The complete sentence is:
• Although the teacher explained the topic several times, some students still did not understand.​

Additional Information

• When stating a fact that, in your opinion, is less significant than a contrasting fact, you use the word "although".
• Although enhances the force of the statement made in the main clause by providing some data that is important to it.
• Although is a conjunction that you use to start a subordinate clause with a statement that differs from the information in the main clause.

Given:

Fixed salary = Rs. 7200

Commission rate = 12%

Bonus rate = 1% (on sales above Rs. 15000)

Total monthly income = Rs. 14850

Formula Used:

Total Income = Fixed Salary + (Commission × Total Sales) + (Bonus × Sales Above Rs. 15000)

Calculation:

Let total sales = x.

Commission = 12% of total sales = 12/100 × x = 0.12x

If sales are greater than Rs.15000, sales above Rs.15000 = x - 15000

Bonus = 1% of (x - 15000) = 1/100 × (x - 15000) = 0.01(x - 15000)

Total Income = Fixed Salary + Commission + Bonus

⇒ 14850 = 7200 + 0.12x + 0.01(x - 15000)

⇒ 14850 = 7200 + 0.12x + 0.01x - 150

⇒ 14850 = 7050 + 0.13x

⇒ 14850 - 7050 = 0.13x

⇒ 7800 = 0.13x

⇒ x = 7800 / 0.13

⇒ x = 60000

The total sales of the company are Rs. 60000.

CONCEPT:

• White light: The light that contains all the wavelengths in the visible light range is called white light.
• It is the combination of seven light colors: 1. Violet, 2. Indigo 3. Blue, 4. Green, 5. Yellow, 6. Orange, 7. Red

• Dispersion of light: The splitting of a composite beam of light into its constituent colors is called dispersion of light.
• The dispersion of white light occurs because the colors of white light travel at different speeds through the glass prism.
• The dispersion was discovered by Sir Issac Newton.
• Newton discovered that light is made up of seven different colors.

EXPLANATION:

From the above discussion, we can say that,

• There are 7 different colours in white light. So option 3 is correct.

The correct answer is Option 4, i.e Hydrogen, and Oxygen.

• Among chemical properties, Mendeleev concentrated on the compounds formed by the elements with Hydrogen and Oxygen.
• The reason why Mendeleev concentrated on the compounds formed by the elements with Hydrogen and Oxygen is they are highly reactive and hence formed compounds with almost all the elements.
• Mendeleev concentrated on the oxides and hydrides of various elements to study their chemical properties.
• Dmitri Mendeleev is known as the father of the Periodic Table.
• Periodic laws were put forwarded by Mendeleev.
• Mendeleev formulated a periodic law, which states that "The properties of elements are the periodic function of their atomic masses".

सही उत्तर 'निषेधात्मक वाक्य' है।

• "नीता घर पर नहीं है!" यह निषेधात्मक वाक्य है।
• उपरोक्त वाक्य में निषेध (न होने) का बोध हो रहा है इसलिए यह निषेधात्मक वाक्य है।

Key Points

अर्थ के आधार पर वाक्य के भेद

• अर्थ के आधार पर आठ प्रकार के वाक्य होते हैं –
• विधानवाचक वाक्य - वह वाक्य जिससे किसी प्रकार की जानकारी प्राप्त होती है, वह विधानवाचक वाक्य कहलाता है।
• उदाहरण -भारत एक देश है।
• निषेधवाचक वाक्य : जिन वाक्यों से कार्य न होने का भाव प्रकट होता है, उन्हें निषेधवाचक वाक्य कहते हैं।
• जैसे-मैंने दूध नहीं पिया।
• प्रश्नवाचक वाक्य - वह वाक्य जिसके द्वारा किसी प्रकार प्रश्न किया जाता है, वह प्रश्नवाचक वाक्य कहलाता है।
• उदाहरण -भारत क्या है?
• आज्ञावाचक वाक्य - वह वाक्य जिसके द्वारा किसी प्रकार की आज्ञा दी जाती है या प्रार्थना किया जाता है, वह आज्ञावाचक वाक्य कहलाता हैं।
• उदाहरण -कृपया शांति बनाये रखें।
• विस्मयादिबोधक वाक्य - वह वाक्य जिससे किसी प्रकार की गहरी अनुभूति का प्रदर्शन किया जाता है, वह विस्मयादिबोधक वाक्य कहलाता हैं।
• उदाहरण: अहा! कितना सुन्दर उपवन है।
• इच्छावाचक वाक्य - जिन वाक्यों में किसी इच्छा, आकांक्षा या आशीर्वाद का बोध होता है, उन्हें इच्छावाचक वाक्य कहते हैं।
• उदाहरण- भगवान तुम्हे दीर्घायु करे।
• संकेतवाचक वाक्य- जिन वाक्यों में किसी संकेत का बोध होता है, उन्हें संकेतवाचक वाक्य कहते हैं।
• उदाहरण-राम का मकान उधर है।
• संदेहवाचक वाक्य - जिन वाक्यों में संदेह का बोध होता है, उन्हें संदेहवाचक वाक्य कहते हैं।
• उदाहरण-क्या वह यहाँ आ गया ?

The correct answer is "Trite".

Key Points 

• Cliche means 'a phrase or idea that has been used so many times that it no longer has any real meaning or interest (इतनी बार दोहराई जा चुकी उक्ति आदि जिसका अब कोई अर्थ या जिससे कोई रुचि नहीं रह गई है; घिसी-पिटी उक्ति)'.
• Example: Cliche is a feature of bad journalism.
• Marked option 'Trite' means 'boring and dull because it has been used or expressed many times before; not original (उबाऊ और नीरस प्रयुक्त होने के कारण या कई बार व्यक्त किए जाने के कारण; मौलिक नहीं; घिसा-पिटा)'.
• Example: Her remarks sounded trite and ill-informed.
• It is clear that Cliche and 'Trite' are similar in meaning.

Therefore, the correct answer is option 3. 

Additional Information 

• Unhackneyed means not appearing trite or commonplace through being overused; original (ताजा, अनोखा, निराला).
• New means that something has recently been built, made, discovered, etc. (नया बना, खोजा आदि).
• Novel means new and different (नया और भिन्‍न).

Given:

Aman has 10L of a solution that is 10% nitric acid by volume.

He wants to dilute the solution to 4% strength by adding water.

Concept used:

Basic concept of addition and subtraction of quantity in the mixture.

Calculation:

Quantity of nitric acid = 10 × (1/10) = 1 liters

Water = 10 – 1

⇒ 9 liters

Let y liter of water be added,

(10 + y ) × (4/100) = 1

On solving, we get y = 15 liters

∴ 15 liters of water should be added.

The correct answer is option i.e Potash alum. 

• Potash alum is a combination of double sulphate of potash and aluminium salts.
• Its chemical formula is KAl(SO4)2 or, AlK(SO4)2·12 H2O
• Potash alum is also known as an astringent.
• Astringents are substances that cause contraction or shrinkage of tissues and that dry up secretion.
• Used as a post-shaving treatment, it can eliminate bleeding from superficial wounds.
• It has also shown in vitro anti-microbial activity.
• The alum used for purifying water is known as potash alum.
• Potash alum is generally used in water purification, fireproof textiles etc. It is also used in leather tanning.

The correct answer is option 2 i.e. Harihara I & Bukka Raya I.

• The Vijayanagar Empire was founded in 1336 by Harihar I and his brother Bukka Raya I in Deccan in the wake of the rebellions against Tughluq rule.
• The Vijayanagara Empire was ruled by 4 dynasties:
• Sangama Dynasty
• Saluva Dynasty
• Tuluva Dynasty
• Aravidu Dynasty
• Bukka Raya defeated almost all the southern kingdoms and extended his empire till present day Rameshwaram.
• The Vijayanagara Empire would rule till 1646 with Sriranga III as its final ruler.
• The ruins of The Vijayanagar Empire which surround modern World Heritage site Hampi can be found in Karnataka, India.

वर्तनी की दृष्टि से शुद्ध शब्द है- 'परीक्षा'

• परीक्षा - योग्यता, क्षमता आदि को परखना
• अन्य सभी विकल्प वर्तनी की दृष्टि से गलत है।

Mistake Points

• परिच्छा - (इ की मात्रा व क्ष वर्ण से सम्बन्धित त्रुटि)
• परीच्छा - (क्ष वर्ण से सम्बन्धित त्रुटि)
• परिक्षा - (इ की मात्रा से सम्बन्धित त्रुटि)

Key Points 

• किसी शब्द में आये हुए अक्षरों को मात्राओं सहित कहने या लिखने की रीति को वर्तनी कहते हैं। वर्तनी का सीधा सम्बन्ध उच्चारण से होता है।
• यदि उच्चारण शुद्ध होगा तो वर्तनी शुद्ध होगी और यदि उच्चारण अशुद्ध होगा तो वर्तनी भी अशुद्ध होगी।

Additional Information कुछ अशुद्ध से शुद्ध शब्द:-

• अशुद्ध - शुद्ध
• क्षत्रीय - क्षत्रिय
• गृहणी - गृहिणी
• ज्योत्सना - ज्योत्स्ना
• त्यौहार - त्योहार
• दायित्त्व - दायित्व
• कार्यवाई - कार्यवाही

The correct answer is, 'by'.

Key Points

• In order to make the sentence meaningful, the blank must be filled with an appropriate preposition.
• The preposition 'by' is used to show something is done by someone or something.
• Here, the moon shines itself.
• Shine is produced by the moon itself.
• Hence, option 2 is the correct answer.

Therefore, the complete sentence is -'The sun shines by its own light'.

Additional Information

• In- to indicate the presence of an object inside something.
• For- to intend given to.
• At- to indicate the vicinity of a particular object.

Given:

The perimeter of a rectangle and a square is 160 cm each.

The difference between their areas is 600 cm2.

Formula used:

1. Area of rectangle = length × breadth
2. Area of square = side²
3. Perimeter of rectangle = 2(length + breadth)
4. Perimeter of square = 4 × side

Calculation:

Let S and R be the area of square and area of rectangle respectively.

According to the question,

⇒ 2(l + b) = 160

⇒ l + b = 80

⇒ 4a = 160

⇒ a = 40

Side length of the square = 40 cm

Area of square = 40² = 1600

Now, 

⇒ Required difference in their respective area = 600

⇒ Required difference in their respective area = S - R = 600

⇒ 1600 - R = 600

⇒ R = 1000 cm²

Therefore, "1000 cm²" is the required answer.

Thermal conductivity of any material is dependent on two things:

i. The motion of free electrons

ii. Lattice vibrations

The thermal conductivity of gases increases with temperature.

Thermal conductivity of liquids decreases with increasing temperature as the liquid expands and the molecules move apart.

In the case of solids, because of lattice distortions, higher temperatures make it difficult for electrons to flow, hence the thermal conductivity of metals decreases.

Note:

• Thermal conductivity depends on the chemical composition of the substance.
• Thermal conductivity of the liquids is more than the gasses and the metals have the highest.
• Thermal conductivity of the gases increases with the increase in temperature.
• Thermal conductivity of the metal decreases with the increase in temperature.
• Metal, crystalline in structure, have greater thermal conductivity than non-metal.
• Thermal conductivity is affected by the phase change.

The correct answer is rural. 

Key Points

• National Bank for Agriculture and Rural Development(NABARD) is a development financial institution in India that focuses on providing credit and other facilities for the promotion and development of agriculture, small-scale industries, cottage industries, handicrafts, and other rural crafts.
• It is governed by the Indian government's Ministry of Finance.
• Financial inclusion is being developed and implemented by NABARD.

Additional Information

• On July12,1982, Act 61, 1981 of Parliament was passed, implementing the B. Sivaramman Committee's recommendations and creating NABARD to carry out the National Bank for Agriculture and Rural Development Act of 1981.
• One of the top agencies, offering 100% stake of Rs. 14080 crore.
• A share capital of Rs. 30,000 crore has been sanctioned.

'वह दण्‍ड के योग्‍य है।' शुध्‍द वाक्‍य है। अन्‍य सभी विकल्‍प असंगत हैं। 

Key Points

• शुध्‍द वाक्‍य- वह दण्‍ड के योग्‍य है।​​

Important Points

Additional Informationवाक्‍य में अशुद्धियाँ- ​

• वाक्‍य सम्‍प्रेषण की सबसे महत्‍वपूर्ण और सार्थक इकाई है अत: वाक्‍यगत अशुद्धियों को शुद्ध रूप में लिखना वाक्‍य को अधिक सरल बनाता है।
• वाक्‍य में पदक्रम, पुनरावृत्ति, वर्तनी, शब्‍द-अर्थ, संज्ञा, सर्वनाम, लिंग, वचन, क्रिया, विशेषण, क्रिया-विशेषण आदि अशुद्धियॉं हो सकती हैं।

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

Key Points

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

Hence, the correct answer is option 3.

Additional Information

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

Shortcut Trick

Ratio of Length to Breadth = 2 : 1

Perimeter ratio = 2 × (2 + 1) = 6 units

6 units = 42 cm ⇒ 1 unit = 7 cm

Length = 2 units = 2 × 7 = 14 cm

∴ The correct answer is 14 cm.

Alternate Method

Given:

Perimeter of rectangle = 42 cm

Length (L) = 2 × Breadth (B)

Formula Used:

Perimeter = 2 × (L + B)

Calculations:

Let the breadth be x cm.

⇒ Length = 2x cm

⇒ 42 = 2 × (2x + x)

⇒ 42 = 2 × 3x

⇒ 42 = 6x

⇒ x = 42 ÷ 6 = 7 cm

⇒ Length = 2 × 7 = 14 cm

∴ The correct answer is 14 cm.

Additional Information

Area of Rectangle

The total space occupied by the shape, calculated as Area = Length × Breadth.

Diagonal of Rectangle

The distance between opposite corners, given by the formula Diagonal = √(L² + B²).

Properties of Rectangle

Opposite sides are equal and parallel, and all interior angles are 90°.

The correct answer is In Jammu and Kashmir

Key Points Hangul:

• Hangul is also called as the Kashmir stag and is found in the Union Territory of Jammu and Kashmir. Hence option 1 is correct
• It is the state animal of Jammu and Kashmir.
• The species is restricted to the Dachigam National Park.
• It is listed under Critically Endangered in the IUCN Red Data Book.
• The species is also included in Schedule I of the Wildlife(Protection) Act, 1972 and the Jammu & Kashmir Wildlife(Protection) Act, 1978.
• Hangul is the sole survivor of the red deer group in the Indian subcontinent.
• In the 1970s, the Government of Jammu & Kashmir, with the collaboration of the IUCN and the World Wildlife Fund(WWF) started a programme for the conservation of Hangul known as Project Hangul.

The correct answer is Maharashtra.

Key Points

• Elephanta Caves is a network of sculpted caves situated on Elephanta Island, or Gharapuri (literally "the city of caves") in Mumbai Harbour, 10 kilometres east of Mumbai city in Maharashtra Indian state.
• The island is located on an arm of the Arabian Sea and consists of two groups of caves-the first is a large group of five Hindu caves, the second is a smaller group of two Buddhist caves.
• The Hindu caves contain sculptures of rock-cut stone, representing the Shaiva Hindu sect, dedicated to Lord Shiva.
• In 1987, it was declared a UNESCO World Heritage Site to conserve the artwork and is currently managed by India's Archeological Survey (ASI).

• लोकोक्ति-  'झोपड़ी में रह, महलों का ख्वाब देखें'
• अर्थ - अपनी सीमा से अधिक पाने की इच्छा करना
• वाक्य प्रयोग – सीमा देखने में तो बिल्कुल सुंदर नहीं है लेकिन उसने मिस इंडिया प्रतियोगिता में अपना नामांकन करवाया है इसे कहते हैं झोपड़ी में रहकर महलों के सपने देखें।

Key Points 

• लोकोक्ति- जब कोई पूरा कथन किसी प्रसंग विशेष में उद्धत किया जाता है तो लोकोक्ति कहलाता है।
• इसी को कहावत कहते है।

उदाहरण-

The correct answer is "ACDB"

Key Points 

• Let's look at the correct sequence of the passage.
• Statement A is the opening sentence of the passage which explains that In life, both empathy and compassion are crucial.
• Statement C is the second sentence of the passage which explains that But out of the two, empathy is unquestionably more crucial.
• Statement D is the third sentence of the passage which explains What changes in our interactions occur when we have empathy for our clients or employees?
• Statement B is the last sentence of the passage which shows that As we foster understanding, loyalty, and greater productivity, our relationships unquestionably get better.

Hence, the correct sequence is A, C, D, B

The correct answer is option 2.

The correct passage is: A. Both, sympathy and empathy are important in life. C. But of the two, empathy is certainly more important. D. When we empathise with our customers or employees what is the change in our relationships? B. Our relationships surely improve as we generate understanding, loyalty and higher productivity.

Shortcut Trick

For three equal distances, Average Speed = (3 × s₁ × s₂ × s₃) ÷ (s₁s₂ + s₂s₃ + s₃s₁)

Average Speed = (3 × 5 × 8 × 6) ÷ (5×8 + 8×6 + 6×5) = 720 ÷ (40 + 48 + 30)

Average Speed = 720 ÷ 118 = 360 ÷ 59 = 6(6/59) km/h

∴ The correct answer is 6(6/59) km/h.

Alternate Method

Given: Speeds s₁ = 5 km/h, s₂ = 8 km/h, s₃ = 6 km/h. Distances are equal.

Formula: Average Speed = Total Distance ÷ Total Time

⇒ Let the equal distance be LCM(5, 8, 6) = 120 km each.

⇒ Time t₁ = 120 ÷ 5 = 24 hours

⇒ Time t₂ = 120 ÷ 8 = 15 hours

⇒ Time t₃ = 120 ÷ 6 = 20 hours

⇒ Total Distance = 120 + 120 + 120 = 360 km

⇒ Total Time = 24 + 15 + 20 = 59 hours

⇒ Average Speed = 360 ÷ 59 = 6(6/59) km/h

∴ The correct answer is 6(6/59) km/h.

Additional Information

Average Speed for Two Equal Distances

When a person covers two equal distances at speeds x and y, the average speed is given by (2xy) ÷ (x + y).

Harmonic Mean Property

When distances are equal, average speed is the Harmonic Mean of the individual speeds.

Relative Speed

In the same direction, relative speed is s₁ − s₂; in the opposite direction, it is s₁ + s₂.

The correct answer is Dichloro diphenyl trichloro ethane.

Key Points

• Dichloro diphenyl trichloroethane is a chemical compound commonly used as Insecticide.
• Dichlorodiphenyltrichloroethane is commonly known as DDT.
• It is also called 1,1,1-trichloro-2,2-bis(p-chlorophenyl)ethane.
• It was first developed by Othmar Zeidler in 1874.
• The insecticidal action of DDT was discovered by the Swiss chemist Paul Hermann Müller in 1939.
• Paul Hermann Müller was awarded the Nobel Prize in Physiology in 1948 "for his discovery of the high efficiency of DDT as a contact poison against several arthropods".
• Dichloro diphenyl trichloroethane became infamous for its environmental impacts.
• It was used to limit the spread of the insect-born diseases malaria and typhus among civilians and troops during the second half of World War II.
• The United States banned the use of DDT in 1972, but some countries still use the chemical.
• DDT can be absorbed by eating, breathing, or touching products contaminated with DDT.
• It is one of 12 pesticides recommended by the WHO for indoor residual spray programs.

Additional Information

• Bordeaux mixture is an effective fungicide and bactericide used to control diseases of fruit and nut trees, vine fruits, and ornamental plants.
• 2, 4-Dichloro phenoxy acetic acid is a systemic herbicide.
• Arsenic is a natural component of the earth’s crust that is highly toxic in its inorganic form.

The correct answer is Art

Key Points

• Bhupen Hazarika was an Indian playback singer, lyricist, musician, poet, actor, artist, editor, filmmaker, professor and politician from India.
• He was widely known as “Sudhakantha”  and his songs were written and sung mainly in the Assamese language, are marked by humanity and universal brotherhood and has been translated and sung in many languages, most notably in Bengali and Hindi.
• His songs, based on the themes of communal amity, universal justice and empathy, are especially popular among the people of Assam.
• He was awarded the
• National Film Award for Best Music Direction,
• The Sangeet Natak Akademi Award,
• The Dada Saheb Phalke Award (1992),
• The highest award for cinema in India and
• The Sangeet Natak Akademi Fellowship (2008),
• The highest award of the Sangeet Natak Akademi.
• He was posthumously awarded both the Padma Vibhushan, India’s second-highest civilian award, in 2012, and Bharat Ratna, India’s highest civilian award, in 2019.
• He also held the position of the Chairman of the Sangeet Natak Akademi from December 1998 to December 2003.

सही उत्तर 'कमर' है।

• 'अव' उर्दू उपसर्ग नहीं है।
• अव हिंदी उपसर्ग है।
• अव उपसर्ग से शब्द –अवकृपा, अवगुण, अवनति, अवसान,अवरोह, अवधारणा, अवमुल्यन, अवशेष, अवरोध, अवतरण,अवगणन।

Key Points

अन्य विकल्पों का विश्लेषण: 

• उपसर्ग के भेद चार भाषा में हैं – हिंदी, उर्दू-फ़ारसी, अंग्रेजी तथा संस्कृत।
• ‘बद’, ‘बे’, ‘गैर’, ला, ‘सर’ इत्यादि उर्दू-फ़ारसी के उपसर्ग हैं।
• उर्दू भाषा के उपसर्ग

Additional Information

• प्रत्यय: शब्द के उपरांत जिस शब्द का प्रयोग किया जाता है वह प्रत्यय है।
• जैसे - ता, औना, अन, अत-  श्रो + ता = श्रोता
• उपसर्ग​:शब्दों तथा धातुओं के पूर्व में संयुक्त हो नये सार्थक शब्दों का निर्माण करने वाले शब्दों को उपसर्ग कहते हैं।
• उपसर्गों से निर्मित शब्द -

The correct answer is 'Has someone verified all the bills?'

Key Points

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the passive voice and it is in the present perfect tense.
• When we convert this sentence into an active voice, the subject 'all the bills' of the passive voice becomes the object, the object 'someone' becomes the subject.
• The passive format "have + been + V3 (verified)" should be converted into the active format "has + V3 (verified)".
• This is the active and passive voice rule for the present perfect tense.

Hence, the correct answer is option 1.

Additional Information

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

Hinglish

• Active Voice में, एक वाक्य विषय पर जोर देता है, एक क्रिया करता है।
• Passive Voice में, एक वाक्य वाक्य की क्रिया या वस्तु पर जोर देता है।
• दिया गया वाक्य passive voice में है और यह present perfect tense में है।
• Passive format "have + been + V3 (verified)" को active format "has + V3 (verified)" में परिवर्तित किया जाना चाहिए।
• यह present perfect tense के लिए active and passive voice rule है।
  

अतः सही उत्तर विकल्प 1 है।

Shortcut Trick

Apply the Chain Rule formula: M₁ × D₁ = M₂ × D₂

34 × 12 = 51 × D₂

D₂ = (34 × 12) ÷ 51 = 2 × 4 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given:

Initial Men (M₁) = 34

Initial Days (D₁) = 12

Final Men (M₂) = 51

Formula Used:

Total Work = Men × Days

Calculations:

⇒ Total Work = 34 × 12 = 408 units

⇒ Required Days (D₂) = Total Work ÷ M₂

⇒ D₂ = 408 ÷ 51

⇒ D₂ = 8 days

∴ The correct answer is 8 days.

Additional Information

Man-Day Concept

The amount of work is proportional to the number of men and the time taken. If work (W) is constant, then M₁D₁ = M₂D₂.

General Chain Rule

For different work amounts and hours: (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂.

Inverse Variation

Men and Days are in inverse variation; as the number of workers increases, the time required to finish the work decreases.

The correct answer is Chlorine.

Key Points

• Chlorine kills pathogens such as bacteria and viruses by breaking the chemical bonds in their molecules.
• Disinfectants that are used for this purpose consist of chlorine compounds which can exchange atoms with other compounds, such as enzymes in bacteria and other cells.
• When enzymes come in contact with chlorine, one or more of the hydrogen atoms in the molecule are replaced by chlorine.
• This causes the entire molecule to change shape or fall apart.
• When enzymes do not function properly, a cell or bacterium will die.
• Chlorine effectively kills a large variety of microbial waterborne pathogens, including those that can cause typhoid fever, dysentery, cholera and Legionnaires' disease.

Additional Information

• Bromine is a chemical element with the symbol Br and atomic number 35. Bromine is used in many areas such as agricultural chemicals, dyestuffs, insecticides, pharmaceuticals and chemical intermediates.
• Iodine is an essential mineral commonly found in seafood.
• A colourless, odourless gas Nitrogen is important to the chemical industry.
• It is used to make fertilisers, nitric acid, nylon, dyes and explosives.
• To make these products, nitrogen must first be reacted with hydrogen to produce ammonia.

The correct answer is 1950

Key Points

• 1950 is the year when China invaded Tibet.
• The invasion marked the beginning of China's control over Tibet, leading to the incorporation of Tibet into the People's Republic of China.
• The invasion and subsequent control have been subjects of international debate and controversy.
• This event significantly impacted the political and cultural landscape of Tibet.

Additional Information

• The invasion of Tibet by China began in October 1950.
• China's People's Liberation Army (PLA) entered Tibet, claiming to liberate it from imperialist forces and to integrate it into the Chinese nation.
• In May 1951, the Seventeen Point Agreement was signed, which affirmed Chinese sovereignty over Tibet while promising autonomy to the region.
• The Dalai Lama, Tibet's spiritual leader, fled to India in 1959 following a failed uprising against Chinese rule.
• The Tibetan government-in-exile continues to seek greater autonomy for Tibet within China.

सही विक्ल्प हैं - 'ऐल'

• 'खपरैल' शब्द में 'ऐल' प्रत्यय है।

Key Points

• खपरैल शब्द खपड़ में ऐल प्रत्यय लगकर बना है जिसका अर्थ होता है 'खपड़े की छाई हुई छत'।
• इसी प्रकार - गुस्सैल, रखैल, बिगडैल आदि ऐल प्रत्यय से बने शब्द है।

Additional Information

प्रत्यय - प्रत्यय वे शब्द होते है जो शब्द के अंत में जुड़ कर अर्थ परिवर्तित कर देते हैं।

• उदाहरण-
• सु +अक्कड = सुतक्कड़
• कार्य + ओं = कार्यों,
• लोहा +आर = लुहार।

उपसर्ग - उपसर्ग वे शब्द होते है जो शब्द के  प्रारम्भ में जुड़ अर्थ परिवर्तित कर देते है।

• उदाहरण-
• अधि + अक्ष = अध्यक्ष,
• सम् + हार = संहार,
• चिर + स्थायी = चिर।

The correct answer is- '(B).'

Key Points

• The error lies in Part (B) of the sentence.
• Countable nouns, as the term suggests, refer to things that can be counted.
• They have singular and plural forms.
• Example: table, tables; month, months; pen, pens, etc.
• Uncountable nouns cannot be counted.
• They have a singular form and do not have a plural form.
• Example: dirt, rice, information, furniture, charity, hair, time, etc.
• Therefore, the use of 'times' should be replaced by 'time' to make it grammatically correct.
• Hence, the correct answer is '(B).'
• Correct sentence: Have you got time for a cup of coffee?

Additional Information 

• Countable nouns, as the term suggests, refer to things that can be counted.
• They have singular and plural forms.
• Example: table, tables; month, months; pen, pens.
• Uncountable nouns cannot be counted.
• They have a singular form and do not have a plural form.
• Example: dirt, rice, information, furniture, and hair.

Hinglish  

• त्रुटि वाक्य के Part (B) में है।
• Countable nouns, जैसा कि शब्द से पता चलता है, उन चीजों को संदर्भित करती हैं जिन्हें गिना जा सकता है।
• उनके singular और plural रूप हैं।
• Example: table, tables; month, months; pen, pens, time, etc.
• Uncountable nouns की गणना नहीं की जा सकती।
• उनका singular रूप है और plural रूप नहीं है।
• Example: dirt, rice, information, furniture, charity, hair, etc.
• इसलिए वाक्य में  'times' के प्रयोग को 'time' से बदल देना चाहिए ताकि वह व्याकरण की दृष्टि से सही हो।​

Shortcut Trick

Ratio of Profit X : Y : Z = (Capital × Time) ratio

X : Y : Z = (5 × 6 + 2.5 × 6) : (3 × 12) : (7 × 12)

X : Y : Z = 45 : 36 : 84 = 15 : 12 : 28

Total units = 15 + 12 + 28 = 55 units = ₹55,000 → 1 unit = ₹1,000

Profit Difference (X − Y) = 15 − 12 = 3 units

∴ Answer = 3000

Alternate Method 

Given:

Initial investment ratio X : Y : Z = 5 : 3 : 7

X withdraws half capital after 6 months. Total profit = ₹55,000. Time = 1 year.

Formula used:

Profit Share ∝ Capital × Time

 X (5 → 2.5)  Y (Cap: 3)  Z (Cap: 7) Time: 6+6m 12 months 12 months Profit Ratio = 15 : 12 : 28

Calculations:

Let initial capitals be 5k, 3k, and 7k.

⇒ X profit share = (5k × 6) + (2.5k × 6) = 30k + 15k = 45k

⇒ Y profit share = 3k × 12 = 36k

⇒ Z profit share = 7k × 12 = 84k

⇒ Ratio of Profit X : Y : Z = 45 : 36 : 84 = 15 : 12 : 28

⇒ Sum of ratio parts = 15 + 12 + 28 = 55 units

⇒ 55 units = ₹55,000 ⇒ 1 unit = ₹1,000

⇒ Difference between X and Y = (15 − 12) × 1,000 = ₹3,000

∴ The correct answer is option (3).

Additional Information

Profit Sharing Rule

In a partnership, profit is always distributed in the ratio of (Capital × Time Period). Formula: P₁:P₂ = C₁T₁ : C₂T₂.

Active vs Sleeping Partner

An active partner manages the business and may receive a salary or commission before the remaining profit is divided according to investment ratios.

Compound Partnership

When partners invest different capitals for different durations, it is a compound partnership where effective capital = Σ(Capital × Duration).

Explanation:

• Nutrition is the science of foods, the nutrients and other substances therein; their action, interaction and balance in relation to health and diseases.
• Nutrition can also be defined as the process by which an organism ingests, digests, absorbs, transports and utilizes nutrients and disposes of its end products.
• Nutrition can also be defined as "food at work in the body"
• It is related to the social, economic, cultural and psychological implications of food and eating.
• Nutrition is the constituents in food that must be supplied to the body in suitable amounts. These can be classified as:
• Proteins
• Carbohydrates
• Fats
• Vitamins
• Minerals
• Water
• Roughage

Thus, nutrition is a process in which all parts of the body receive and use substances for all biological functions.

Additional Information

Nutritional Care:

• It is the application of the science and art of human nutrition in helping people select and obtain food for the primary purpose of nourishing their bodies in health or in disease throughout their lives.

Good Nutrition:

• The nutrition in which essential nutrients are present in correct amounts and proportions; the utilization of nutrients in the body such that the highest level of physical and mental health is maintained throughout the life cycle.

Malnutrition:

• It results from a lack, excess or imbalance of nutrients in the diet. It includes:
• Under Nutrition is the state of insufficient supply of essential nutrients.
• Over Nutrition refers to an excessive intake of one or more nutrients.
• For example: excess Vitamin A consumption leads to Hypervitaminosis.
• An excess of fluorine leads to fluorosis.

The correct answer is January-December.

Key Points

• Financial Year in Madhya Pradesh
• ​The financial year in Madhya Pardesh is from 1st January to 31st December.
• Earlier, it was from 1st April to 31st March.
• Chief Minister Shivraj Singh Chauhan together with his ministers decided to shift its financial year to May 2017.
• This change in the financial year was done in 2017 and it is implemented in the year 2018.
• It was done on the recommendation of the Shankar Acharya Committee formed in 2016.
• Shankar Acharya is the Economic Advisor in Madhya Pardesh Government.
• Madhya Pradesh with this becomes the first state in India to shift its financial year.

Additional Information

• Financial Year
• The financial year is called the period of one year during which one earns and spends.
• In short, it is also called FY.
• Currently in India, it is from 1 April to 31 March.
• The government itself considers the same period as the Financial Year to calculate its income and expenses.
• The budget is also formed and implemented for the same period.

चिन्ह की दृष्टि से 'नहीं कल में तुम्हारे घर नहीं आ सकूँगा।' वाक्य अशुध्द है क्योंकि इसमें 'नहीं' के बाद विस्मयादिबोधक चिह्न आएगा जैसे – नहीं! कल मैं तुम्हारे घर नहीं आ सकूँगा। अन्य विकल्प विराम - चिह्न की दृष्टि से सही हैं। अतः सही विकल्प 'नहीं कल मैं तुम्हारे घर नहीं आ सकूँगा।' है।

Important Points

समस्त विराम चिह्नों का विवरण निम्नलिखित हैं

The correct answer is 'Company'.

Key Points

• "Solitude" means the state or situation of being alone (एकांत).
• "Company" means the fact or condition of being with another or others, especially in a way that provides friendship and enjoyment (संगति).
• Hence the correct antonym is 'Company'.

Therefore, the correct answer is: Option 1.

Additional Information

• "Individual" refers to a single human being as distinct from a group (व्यक्ति).
• "Ex-serviceman" refers to a person who has served in the armed forces and is no longer serving (पूर्व सैनिक).
• "Victim" means a person harmed, injured, or killed as a result of a crime, accident, or other event or action (पीड़ित).

Shortcut Trick

Expression is of the form (a³ + b³) / (x² + y² − xy) where a = 10x and b = 10y.

Numerator = (10x)³ + (10y)³ = 1000(x³ + y³).

Expression reduces to 1000 × (x³ + y³) / (x² − xy + y²) = 1000(x + y).

Substitute x = 73.2 and y = 26.8: 1000 × (73.2 + 26.8) = 1000 × 100 = 100000.

∴ The correct answer is 100000.

Alternate Method

Given: Numerator = 732³ + 268³ and Denominator = 73.2² + 26.8² − 73.2 × 26.8

Formula Used: a³ + b³ = (a + b)(a² − ab + b²)

⇒ Let x = 73.2 and y = 26.8. Then 732 = 10x and 268 = 10y.

⇒ Expression = [(10x)³ + (10y)³] / [x² + y² − xy]

⇒ Expression = [1000x³ + 1000y³] / [x² − xy + y²]

⇒ Expression = 1000 × (x³ + y³) / (x² − xy + y²)

⇒ Expression = 1000 × [(x + y)(x² − xy + y²)] / (x² − xy + y²)

⇒ Expression = 1000 × (x + y)

⇒ Expression = 1000 × (73.2 + 26.8)

⇒ Expression = 1000 × 100 = 100000.

∴ The correct answer is 100000.

Additional Information

Algebraic Identity: Sum of Cubes

The formula a³ + b³ = (a + b)(a² − ab + b²) is a standard identity used to simplify expressions where a cubic sum is divided by a quadratic term.

Algebraic Identity: Difference of Cubes

Similarly, a³ − b³ = (a − b)(a² + ab + b²) is used for simplifying subtractions of cubes.

Decimal and Power Relationship

If a number is multiplied by 10, its square is multiplied by 100 (10²) and its cube is multiplied by 1000 (10³).

Butane is a hydrocarbon and a highly flammable, colourless, odourless, easily liquefied gas. It is typically used as fuel for cigarette lighters and portable stoves, a propellant in aerosols, a heating fuel, a refrigerant, and in the manufacture of a wide range of products. Butane is also found in Liquefied Petroleum Gas (LPG).

The Correct Answer is 25 May.

In News

• World Thyroid Day: 25 May.

Key Points

• World Thyroid Day is celebrated every year on 25th May.
• It was decided during the Thyroid Federation International meeting in September 2007.
• The first World Thyroid Day was celebrated in 2008.
• The theme for this year is “Thyroid Disease and Artificial Intelligence”.
• The European Thyroid Association also started European Thyroid Day on 25th May 2008.

“काली घटा का घमंड घटा।” पंक्ति में 'यमक ​अलंकार' है।

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- “काली घटा का घमंड घटा।”
• इस पंक्ति में पहली बार ‘घटा’ शब्द का अर्थ है काले बादलों से ओर दूसरी बार में ‘घटा’ कर अर्थ है कम होने से।

Key Pointsश्लेष अलंकार- जब किसी पंक्ति में कोई शब्द एक ही बार प्रयुक्त हों लेकिन उसके अर्थ अलग-अलग हों तब श्लेष अलंकार होता है।

• उदाहरण- जे रहीम गति दीप की, कुल कपूत गति सोय । बारे उजियारो करै, बढ़े अंघेरो होय।।
• प्रस्तुत पंक्ति रहीम जी के दोहे से ली गयी है जिसमें दीये एवं कुपुत्र के चरित्र को एक जैसा दिखाने की कोशिश की है। रहीम जी कहते हैं कि शुरू में दोनों ही उजाला करते हैं लेकिन बढ़ने पर अन्धेरा हो जाता है।

उपमा अलंकार- जब उपमेय की तुलना उपमान से की जाये तब उपमा अलंकार होता है।

• उदाहरण- हाय! फूल सी कोमल बच्ची , हुई राख की ढेरी थी।
• पंक्ति में बच्ची की कोमलता को फूल के समान बताया है।

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

• उदाहरण- सिर फट गया उसका मानो अरुण रंग का घड़ा हो।
• दिए गए उदाहरण में सिर की लाल रंग का घड़ा होने कि कल्पना की जा रही है।
• यहाँ सिर – उपमेय है एवं लाल रंग का घड़ा – उपमान है। उपमेय में उपमान के होने कि कल्पना कि जा रही है।

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।

Mistake Points

• यमक अलंकार में समान शब्द का प्रयोग जितनी बार होता है, उतने ही अर्थों की प्रतीति होती है किन्तु, श्लेष में शब्द का प्रयोग तो एक ही बार होता है लेकिन उससे अनेक अर्थों की प्रतीति होती है।
• “काली घटा का घमंड घटा।” में 'घटा' शब्द दो बार प्रयोग हुआ है और उनके अर्थ भी अलग-अलग है। अतः यह 'यमक अलंकार' ही होगा श्लेष नहीं।

The correct answer is 'Seismology'.

Key Points

• The most appropriate word for the given group of words is 'Seismology'.
• It means 'the scientific study of movements in the earth’s surface(earthquakes)'. [भूकंप-विज्ञान]
• Example: Large scale global seismology has helped to identify areas at risk from earthquakes and tsunami.
  

Correct Answer: Seismology.

Additional Information

• Let's look at the meaning of other words:
• Geography: the study of the world’s surface, physical qualities, climate, population, products, etc. [विश्‍व भूगोल की सतह, भौतिक लक्षण, मौसम, जनसंख्‍या आदि का अध्‍ययन]
• Topography: the physical characteristics of an area of land, especially the position of its rivers, mountains, etc. [किसी क्षेत्र की प्राकृतिक विशेषताएँ (विशेषतः नदियों, पर्वतों आदि की स्थिति); स्‍थलाकृति]
• Geology: is the scientific study of the Earth, its structure, composition, and the processes that shape it over time. the study of rocks, and of the way they are formed. (चट्टानों और उनके निर्माण-प्रकार का अध्‍ययन; भूविज्ञान)

Shortcut Trick

⇒ Ratio = 3 : 5 : 4

⇒ After transfer: A = 3x + 15000, B = 5x − 15000, C = 4x

⇒ Given A = C ⇒ 3x + 15000 = 4x

⇒ x = 15000

⇒ Total profit = (3+5+4)x = 12x = 180000

∴ Answer = 180000

Alternate Method

Given:

⇒ Investment ratio = 3 : 5 : 4

⇒ B gives ₹15000 to A

⇒ After transfer: A's share = C's share

Formula:

⇒ Profit ∝ Investment

Calculation:

⇒ Let shares be 3x, 5x, 4x

⇒ After transfer:

⇒ A = 3x + 15000

⇒ B = 5x − 15000

⇒ C = 4x

⇒ Given A = C:

⇒ 3x + 15000 = 4x

⇒ x = 15000

⇒ Total profit = 3x + 5x + 4x = 12x

⇒ = 12 × 15000 = 180000

∴ Final Answer: 180000

Additional Information

1. Partnership Rule: Profit ∝ Investment

2. Transfer Concept: One partner’s gain = another’s loss

3. Ratio Method: Assume shares as multiples of x

4. Shortcut: Equate after adjustment

The correct answer is Methane with air.

Important Points

• Methane explosions occur when methane gas from mining is built up and cannot escape because of high pressure.
• For example, a coal mine methane (CMM) is a mixture of methane and air present in the active mining sites.
• This mixture of gas is released during the process of coal mining causes the explosion in the mining area.

Additional Information

From the above explanation, we can see that most of the explosions in mines occur due to a mixture of air and methane.

Concept-

• Crops are plants or plant-derived products that are produced and harvested for food or profit.
• Food crops, feed crops, fibre crops, oil crops, ornamental crops, and industrial crops are the six main types of crops.

Key Points Rabi crops-

• Rabi crops, also known as rabi harvest, are Indian agricultural crops that are planted in the winter and harvested in the spring.
• Rabi crops are planted in mid-November, ideally, after the monsoon rains have passed, and harvested in April/May.
• Rainwater that has percolated into the ground or irrigation are used to cultivate the crops. Winter rains wreak havoc on rabi crops.
• Wheat is India's most important rabi crop, followed by barley, mustard, sesame, and peas. Peas are picked early because they are ripe early: from January through March, Indian markets are swamped with green peas, with February being the peak month.
• 

Additional Information Kharif crops-

• Kharif crops also known as monsoon crops or autumn crops are domesticated plants grown and harvested in India, during the monsoon season, which lasts from June to November depending on the region.
• In some parts of the Indian subcontinent, monsoon rains can start as early as May, and crops are harvested between the third and fourth weeks of September and October.
• Rice, maize, and cotton are among India's most important Kharif crops.

सही उत्तर है - ‘अव्ययीभाव’।

• ‘यथाशक्ति’ अव्ययीभाव समास का उदाहरण है।
• इसका समास विग्रह होगा - शक्ति के अनुसार।

Key Points

• ‘यथाशक्ति’ में ' ‘यथा’ अव्यय का प्रयोग हुआ है इस कारण यहाँ ‘अव्ययीभाव समास’ होगा।
• अव्ययीभाव समास में पहला पद प्रधान होता है और समस्त शब्द अव्यय का काम करता है।
• उदाहरण :
• आजन्म: जन्म से लेकर
• यथामति : मति के अनुसार
• प्रतिदिन : दिन-दिन

Additional Information

• समास :- समास उस प्रक्रिया को कहते हैं, जिसमें दो शब्द मिलाकर उनके बीच के संबंधसूचक आदि का लोप करके नया शब्द बनाया जाता है।
  

समास से तात्पर्य 'संक्षिप्तीकरण' से है। समास के माध्यम से कम शब्दों में अधिक अर्थ प्रकट किया जाता है।

• जैसे - राजा का पुत्र – राजपुत्र।
• समास के छःप्रकार हैं -
• अव्ययीभाव समास
• तत्पुरुष समास
• कर्मधारय समास
• द्विगु समास
• द्वन्द समास
• बहुव्रीहि समास

The correct answer is Ravina asked her little brother where he was going to play​.

Key Points​

• Let's look at the steps to change the sentence from direct to indirect speech:
• The tense of direct speech is changed only when the reporting verb is in the past tense.
• When the direct speech is in an interrogative form, we follow the steps given below:
• The reporting verb asked will remain the same.
• The word 'where will follow the removal of comma and inverted commas.
• Change the reported speech from interrogative to assertive.
• Present continuous tense (are you going) in direct speech changes to past continuous in indirect speech (he was going).
• ​The personal pronouns will be changed according to the subject and object of the reporting verb.
• Here 'you' will be converted into 'he' as per the subject.
• ​​At last line up the remaining part.
  

Following these steps, we finally get - Ravina asked her little brother where he was going to play.

Shortcut Trick

Solve the expression by simplifying from the innermost square root moving outwards.

First part: √(6 + 3) = √9 = 3

Second part: √(19 − 3) = √16 = 4

Final part: √(21 + 4) = √25 = 5

∴ The correct answer is 5.

Alternate Method

Given: √(21 + √(19 − √(6 + 3)))

Following the BODMAS rule, we evaluate the operations inside the radical signs sequentially:

⇒ √(21 + √(19 − √9))

⇒ √(21 + √(19 − 3))

⇒ √(21 + √16)

⇒ √(21 + 4)

⇒ √25

⇒ 5

∴ The correct answer is 5.

Additional Information

Perfect Squares

A perfect square is an integer that is the square of another integer. Common examples include 3² = 9, 4² = 16, and 5² = 25.

VBODMAS Rule

In nested mathematical operations, Vinculum (Bar), Brackets, and operations inside Orders (Roots/Powers) are prioritized from the innermost level to the outermost level.

Surds Property

While √(a × b) = √a × √b, it is important to remember that √(a + b) ≠ √a + √b.

The correct answer is D.

Key Points

• Sulphur is not alkaline.
• An alkali is a base that dissolves in water.
• The pH level is a measurement of how acidic or alkaline a substance is on a scale of 0 to 14.
• Sulphur makes very strong acid (Sulfuric acid) on a combination of Sulphur, oxygen, and water.
• Its atomic number is 16 and the atomic symbol is S.

Additional Information

• Potassium, Lithium, and Sodium are alkaline and its solution would give a pH number more than 7.

The correct answer is Ellora Caves.

Key Points

• The depiction of Ravana shaking Mount Kailash is found in Cave 16 of the Ellora Caves.
• Ellora is a UNESCO World Heritage Site located in Maharashtra, India.
• It is famous for its Hindu, Buddhist, and Jain cave temples, which were carved out of the rock over a period of centuries.
• Cave 16 is a Hindu cave temple dedicated to Shiva.
• It is one of the largest and most impressive cave temples at Ellora.
• The sculpture of Ravana shaking Mount Kailash is located on the exterior wall of the cave temple.
• It is a large and impressive sculpture that depicts the demon king Ravana attempting to lift Mount Kailash, the home of Shiva and Parvati.
• The sculpture is a popular tourist attraction and is considered to be one of the finest examples of Hindu art.

Additional Information

Important Points

• The depiction of Ravana shaking Mount Kailash is found in Cave 16 of the Ellora Caves.
• Ellora is a UNESCO World Heritage Site located in Maharashtra, India.
• The Ellora Caves were inscribed on the UNESCO World Heritage List in 1983
• It is famous for its Hindu, Buddhist, and Jain cave temples, which were carved out of the rock over a period of centuries.
• Cave 16 is a Hindu cave temple dedicated to Shiva.
• The sculpture of Ravana shaking Mount Kailash is located on the exterior wall of the cave temple.

सांगोपांग में गुण संधि है।  

Key Points

• सांग + उपांग = सांगोपांग
• गुण संधि - जब संधि करते समय अ, आ के बाद इ, ई  हो तो ए बनता है, जब अ, आ के बाद उ,ऊ आए तो ओ बनता है, जब अ, आ के बाद ऋ आए तो अर बनता है।

Additional Information

The correct answer is 'RQPS.'

Key Points

• While arranging the parts of the sentence given in options, we have to find some grammatical or contextual connections between them, so let’s find out.
• In this sentence, we can see that there are different parts like Subject, indirect object, subject of subordinating clause and verb, indirect object, and direct object.
• The sentence must start with R as it is providing an introduction to the context "belief of peoples in several cultures".
• R must be followed by Q as it is expressing what people believe i.e. shooting stars have some power.
• Q must be followed by P as it talks about what the power of shooting stars is believed to be i.e. to make wishes true.
• S must be the last part as it is providing a conclusion to the sentence.
  

​​Correct sentence: In several cultures, people believe that shooting stars have the power to make wishes come true and become successful in life.

Additional Information         

• Before rearranging parts of the sentence, it is very important to read them carefully.
• It is very important to analyse the use of a determiner and conjunction in such cases.
• This confusion can be eradicated by practising more and more questions of Sentence Jumbles.

Shortcut Trick

Total members = 78 + 22 + 34 = 134

⇒ Ratio = 78:22:34 = 39:11:17

⇒ Weighted avg = (39×136 + 11×383 + 17×457) ÷ 67

⇒ = (5304 + 4213 + 7769) ÷ 67 = 17286 ÷ 67 = 258

∴ Answer = 258

Alternate Method

Given:

A: 78 members, avg = 136

B: 22 members, avg = 383

C: 34 members, avg = 457

Formula:

Overall avg = (Σ (n × avg)) ÷ Σ n

Calculations:

⇒ Total amount A = 78 × 136 = 10608

⇒ Total amount B = 22 × 383 = 8426

⇒ Total amount C = 34 × 457 = 15538

⇒ Total amount = 10608 + 8426 + 15538 = 34572

⇒ Total members = 134

⇒ Average = 34572 ÷ 134 = 258

Final Answer: 258

Additional Information

Weighted Average: (Σ n_ix_i) ÷ Σ n_i

Ratio Trick: Simplify group sizes before calculation

Concept: Larger group dominates overall average

Exam Tip: Use reduced ratio to save time

• The launching of a rocket illustrates Newton’s third law of motion.
• Newton's Third Law of Motion states that 'To every action, there is an equal and opposite reaction'.
• When the rocket is ignited, it releases gases from its thrusters thereby creating a force that will push rocket upwards.
• A fielder pulling his hand back while catching a ball is an application of Newton's second law of motion.
• Newton's Second Law of motion states that the rate of change of momentum of an object is proportional to the applied force in the direction of the force. i.e. F=ma. Where F is the force applied, m is the mass of the body, and a is the acceleration produced.
• When a bus starts suddenly, the passengers receive a backward jerk an application of Newton's first law of motion.
• Newton First law states that Every object remains in uniform motion in a straight line unless compelled to change its state by the action of an external force.
• When we stop pedalling, the bicycle slows down due to the frictional force acting on the bicycle.