#solutions for class 12 maths

[ashishkumarletslearn]

Training Teachers to Teach Class 12 Maths — MathYug

In the ever-evolving landscape of education, having access to high-quality learning resources can make a world of difference. For Class 12 students, mastering mathematics is crucial, not only for academic success but also for future endeavors in various fields. At MathYug, we understand this importance and have dedicated ourselves to providing top-tier educational materials. Today, we’re excited to introduce our training program designed specifically for teachers who aspire to elevate their teaching skills and make a significant impact on their students’ learning journey.

Sample Videos: A Glimpse into Quality Education

To give you a taste of what MathYug has to offer, we are sharing a selection of sample videos from our Class 12 Maths tutorials. These videos exemplify the high-quality, in-depth teaching style that Ashish Kumar, affectionately known as Agam Sir, is known for.

Relations and Functions

2. One to One and Onto Functions

3. Inverse Trigonometric Functions

4. Continuity and Differentiability

5. Applications of Derivatives

6. Integrals

7. Inverse Trigonometric Functions

8. Basics of Logarithms, Log Table and Antilog Table

Why Choose MathYug for Teacher Training?

MathYug stands out as a premier platform for learning and teaching mathematics, especially for Class 12 students. Our resources are meticulously designed to cater to the diverse needs of both learners and educators, ensuring that each student can grasp complex mathematical concepts with ease. Here’s why MathYug is the best choice for your teaching journey:

Expert Guidance

All our content is created by Ashish Kumar (Agam Sir), a renowned educator with years of experience in teaching mathematics. His unique teaching style simplifies complex topics, making them easily understandable. By training with MathYug, teachers can learn how to effectively convey these methods to their students.

Comprehensive Coverage

Our tutorials cover the entire Class 12 Maths syllabus, aligned with the NCERT guidelines. This ensures that students are well-prepared for their board exams and other competitive exams. Teachers trained with MathYug will be equipped to offer their students a thorough and well-rounded mathematical education.

Interactive Learning

We believe in making learning engaging and interactive. Our video lessons are complemented by practical exercises, assignments, and downloadable PDFs to reinforce learning. Teachers will be trained to use these resources to create a dynamic and interactive classroom environment.

Elevate Your Teaching Experience with MathYug

At MathYug, we are committed to providing the best possible educational resources to help both students and teachers excel in mathematics. Our Class 12 Maths tutorials are designed to build confidence, enhance understanding, and foster a love for learning. By sharing these sample videos, we hope to give teachers a glimpse of the quality education that awaits them on our platform.

Join MathYug Today!

Experience the difference with MathYug and take your teaching skills to new heights. Subscribe to our Class 12 Maths membership and gain access to a comprehensive collection of video lessons, study materials, and expert guidance from Ashish Sir. Let’s embark on this journey of academic excellence together!

Visit MathYug now and start your journey towards mastering Class 12 Maths with ease and confidence.

[inversetrigonometricfunctions]

Class 12 Maths Inverse Trigonometric Functions Course | JEE Mains की तैयारी | MathYug

��गर आप Class 12 Maths में Inverse Trigonometric Functions अच्छे से समझना चाहते हैं और साथ ही JEE Mains की भी तैयारी कर रहे हैं, तो MathYug का यह कोर्स आपके लिए बहुत फायदेमंद है। इस कोर्स में expert teacher Ashish Sir ने हर concept को आसान भाषा में समझाया है।

आप इस course में सीखेंगे:

Inverse Trigonometric Functions की definition

Domain और range

Principal value branches

Graphs और identities

Elementary properties

सिर्फ समझना ही नहीं, बल्कि concept को और पक्का करने के लिए NCERT textbook, exemplar, RD Sharma और Board’s Question Bank से चुने गए questions को assignments के तौर पर दिया गया है। इन assignments की PDF भी download की जा सकती है।

यह कोर्स Class 12 students के साथ-साथ JEE Mains aspirants के लिए भी designed है, ताकि दोनों ही exams की तैयारी एक साथ हो सके।

MathYug आपको expert guidance, professional notes, और structured learning के साथ एक complete learning experience देता है। Join कीजिए और अपने maths concepts को strong बनाइए।

Join the complete course now at: https://mathyug.com/c/ch2-inverse-trigonometric-functions/

[arihantbooks]

Complete NCERT Exemplar Solutions By Arihant Publication

Arihant Publication offers meticulously crafted NCERT Exemplar solutions, designed to simplify complex concepts for students from Classes 6 to 12. Covering Mathematics, Science, and more, these resources ensure conceptual clarity and exam readiness. Ideal for CBSE exam prep, these exemplars include practice questions, solutions, and explanations to strengthen subject understanding.

[sarthaks24]

How to Use Sarthaks for Free Class XII NCERT Solutions

Attention, Class 12 students! We know you're gearing up for the most important year of your academic life, and let’s be honest—things can get overwhelming. But don’t sweat it. Sarthaks eConnect is here to make life easier with free NCERT Class 12 solutions for all your toughest subjects!

From NCERT Class 12 Maths to NCERT Solutions for Class 12 Physics, we've got you covered. Whether it’s cracking those impossible equations or understanding why the universe works the way it does, our solutions break everything down, making even the most confusing concepts seem like a piece of cake.

Why You’ll Love Our NCERT Class 12 Maths Solutions

Maths doesn’t have to be your worst enemy. Whether it’s calculus, vectors, or probability, our NCERT Class 12 Maths solutions turn those intimidating problems into something you can actually understand. We simplify complex formulas and provide step-by-step answers, so you can stop scratching your head and start solving.

Why should you care? Maths is the backbone of most competitive exams. Mastering these concepts now means you’ll be a step ahead when it’s time to face JEE or any other entrance test. Plus, knowing maths like a pro means less stress and more time to enjoy your senior year!

NCERT Solutions for Class 12 Physics: Unlock the Mysteries of the Universe

Physics can be wild—understanding gravity, electricity, and quantum mechanics feels like you’re solving the universe’s biggest puzzles. But with our NCERT Solutions for Class 12 Physics, it’s not just about memorizing formulas—it’s about understanding the why behind them. Whether you’re struggling with electromagnetism or mechanics, we’ve got easy explanations that make things click.

Why is this important? Physics isn’t just for exams; it’s the foundation of everything from engineering to space exploration. Getting a grip on it now will open doors to all kinds of future careers. Plus, it’s pretty cool to know how the world around you works!

Chemistry Class 12 NCERT Solution: Simplifying the Elements of Success

If Chemistry feels like a never-ending list of elements and reactions, you're not alone. But our Chemistry Class 12 NCERT Solution will change how you see it. From organic reactions to chemical kinetics, we break down each chapter so that even the trickiest reactions make sense.

The best part? Chemistry is a game-changer for medical entrance exams like NEET. Get this subject down, and you’ll ace both your boards and your entrance tests. Plus, it’ll finally make sense why those elements react the way they do—no more blank stares in class!

NCERT Class 12 Biology Solutions: Decode Life Itself

Ever wonder how our body works or how life evolved? Biology answers all those big questions. With NCERT Class 12 Biology Solutions, we simplify everything from genetics to ecology. You’ll understand everything, from how your cells work to why ecosystems are so delicate.

Why bother? If you're aiming for NEET or any bio-related career, nailing biology is essential. Our solutions give you a solid understanding of the subject, so you’re ready to tackle anything your exam throws at you.

Why Choose Sarthaks eConnect?

Free and Accessible: Why pay for expensive tuition or study guides when you can get everything you need for free? With Sarthaks, you have access to top-notch NCERT solutions, anytime, anywhere.

Clear, Step-by-Step Explanations: We break everything down into easy, understandable steps. Whether it’s the trickiest calculus problem or the most confusing physics theory, we make sure you get it.

Perfect for Exams: These solutions aren’t just for daily homework—they're built to help you ace your board exams and any entrance tests coming your way. No fluff, just what you need to succeed.

Boost Your Confidence: Knowing you’ve got the best resources at your fingertips means you can stop stressing and start focusing on what really matters—understanding the subject and scoring big in exams.

So, Class 12 students, are you ready to stop cramming and start mastering your subjects? With Sarthaks eConnect and our NCERT Class 12 Maths, NCERT Class 12 Biology Solutions, NCERT Solutions for Class 12 Physics, and Chemistry Class 12 NCERT Solution, you’ll not only survive this year—you’ll thrive. Jump in today and unlock the path to exam success!

[vasanthasworld]

WBCHSE Solutions For Class 12 Maths Algebra

[vijayadworld]

WBCHSE Solutions For Class 12 Maths Bayes Theorem And Its Applications

[memorysclub]

NCERT Solutions of the ex 9.5 class 12 maths exam-oriented question for your upcoming board exam with Memorysclub expert educator. The ex 9.5 class 12 maths ncert solutions are valuable tools for students preparing for exams and seeking clarity on mathematical concepts covered in their syllabus. Click now to get ex 9.5 class 12 maths pdf solutions.

[doubtlessclass]

Mastering Mathematics with Doubtless Class: Unlocking the Power of NCERT Solutions for Class 10

Embarking on the journey of mastering mathematics can be both exciting and challenging for Class 10 students. However, with the right tools and resources, the path becomes smoother, and doubts transform into clarity. In this blog, we explore the efficacy of Doubtless Class in providing NCERT solutions for Mathematics Class 10, ensuring a comprehensive and doubt-free learning experience.

The Significance of NCERT Solutions:

National Council of Educational Research and Training (NCERT) solutions serve as the cornerstone of a student's academic journey. Developed by experts, these solutions are designed to provide a solid foundation and enhance conceptual understanding. They align with the CBSE curriculum, making them an indispensable resource for Class 10 students preparing for their board exams.

Doubtless Class: Navigating the Maze of Mathematical Queries:

Doubtless Class emerges as a beacon for students seeking clarity and understanding in the realm of mathematics. The platform offers a user-friendly interface where students can access NCERT solutions for Class 10 Mathematics effortlessly. But what sets Doubtless Class apart is its unique approach to addressing doubts in real-time.

Features of Doubtless Class:

1. Live Doubt Resolution:

Doubtless Class features live doubt resolution sessions, where experienced educators address students' queries in real-time. This interactive approach ensures that no doubt lingers, allowing students to progress confidently.

2. Comprehensive NCERT Solutions:

The platform provides meticulously crafted NCERT solutions for every chapter in the Class 10 Mathematics curriculum. From algebraic expressions to trigonometry, Doubtless Class covers it all, offering step-by-step solutions that facilitate easy understanding.

3. Personalized Learning Paths:

Recognizing that every student has a unique learning pace, Doubtless Class tailors learning paths to individual needs. Through adaptive assessments and quizzes, the platform identifies areas of improvement, providing targeted assistance where it's needed most.

How Doubtless Class Enhances the Learning Experience:

1. Boosting Confidence:

By offering instant doubt resolution, Doubtless Class instills confidence in students. The fear of unresolved questions is replaced with a sense of assurance, fostering a positive attitude towards mathematics.

2. Understanding Concepts Thoroughly:

The detailed NCERT solutions on Doubtless Class go beyond mere answers. They break down complex concepts into digestible chunks, ensuring that students not only solve problems but also understand the underlying principles.

3. Efficient Time Management:

With Doubtless Class, students can optimize their study time. By addressing doubts promptly, they avoid spending unnecessary hours grappling with concepts, allowing for a more streamlined and efficient study routine.

Conclusion:

In the realm of mathematics, understanding the 'why' behind the 'how' is crucial for success. Doubtless Class, with its focus on live doubt resolution and comprehensive NCERT solutions, empowers Class 10 students to conquer the challenges of mathematics with confidence. As they say, in the world of Doubtless Class, no question is left unanswered, and no concept remains unclear. Embrace the journey of mastering mathematics with Doubtless Class, and pave the way for academic excellence.

[mathyug]

MathYug is thrilled to announce the reactivation of memberships for Class 10 Maths, Class 11 Maths, and Class 12 Maths. Responding to the overwhelming requests from our dedicated learners, we're reintroducing these exclusive memberships to provide an unparalleled academic experience.

Our memberships are designed to empower students with comprehensive resources, expert guidance, and a supportive learning community. Whether you're navigating the challenges of Class 10 board exams, diving into advanced concepts in Class 11, or preparing for the competitive exams in Class 12, MathYug's reactivated memberships cater to diverse educational needs.

Members will gain access to a wealth of study materials, interactive tutorials, and personalized assistance from our experienced educators. The platform's user-friendly interface ensures a seamless learning experience, allowing students to progress at their own pace.

At MathYug, we understand the importance of continuous improvement and staying ahead in the academic journey. By bringing back these memberships, we aim to further enrich the educational experience for students, helping them achieve excellence in mathematics.

Seize the opportunity to reignite your passion for learning and excel in Class 10, 11, and 12 Maths. Join MathYug's reactivated memberships and embark on a journey towards academic success and mathematical mastery.

[rosabell14]

An analysis of Bianca di Angelo's role in the narrative and why bad writing can screw over a character.

For someone with such a limited time in the narrative, Bianca is one of the most divisive characters in the fandom. I've been in the fandom long enough to see how much nuance the fandom lacks when discussing certain characters and Bianca is no difference. But it's more than just viewing the characters' actions in a vacuum. It's ignoring the larger narrative problems. At the end of the day Bianca suffers from one simple problem: she's barely a character outside of her role in Nico's narrative. Like it or not, her entire character exists to die and give Nico issues down the road but Riordan's writing decisions didn't do her any favours either.

I feel like this is a huge issue when it comes to the pjo fandom they often try to come up with Watsonian solutions to problems that are Doylist in nature and Bianca is one example of that.

Case in point: Riordan's shit math when it comes to the Di Angelo siblings and how it messes up with bianca's character.

So when we meet them they're 10 and 12. We learn that their memories of their past is kinda hazy and that they don't remember their parents but that they were in a boarding school, then they moved to the lotus hotel, then they were taken out of the hotel and put into Westover's. And at the end we learn that they're Hades's children born before the oath of the big 3.

Said oath happened after WW2 btw. So 1945 probably since Bianca remembers FDR's presidency.

Now in TLO we get an update on this backstory. Hades is speaking to Maria about moving his children to the underworld or the lotus hotel since Maria doesn't like the former option because the war has put Hades in a bad situation with his brothers and also the prophecy is out, the oath has been taken and they're running out of time to hide the kids. So logic says that it's 1945. And then Zeus immediately kills Maria and Hades tells Alecto to erase the children's memories and put them in the lotus hotel, and honestly? I like this version much better? Because why in the world would Hades Put his children in a boarding school for a few years and THEN hide them in the hotel after they were nearly assassinated? Why not immediately put them in the hotel?

And so we get to our main dilemma. Bianca having to raise Nico. This was already strange to me because it's not as if this is a Jason and Thalia situation where Jason was a toddler and Thalia had to take care of him. Nico is not a baby they have a two year age difference. But of course these kinds of things might matter more if you're young. Even then, in what situation would Bianca be Nico's main caretaker? They were put into a magic hotel that mind you, makes time go faster so for them it was a month or two at best and they would have been given whatever they needed by the staff? Same type of issue with Westover's and the boarding school if you want consider that canon. They would have been taken care of by the facility. They probably wouldn't even have shared classes or dorms? Or am I misunderstanding American boarding schools?

And then, Riordan's bad math strikes again and this time with the characters' ages. Because Nico's age in HoO becomes 14 which would have made him 11/almost 12 in TTC but that's not the big problem, no no no. The problem comes from his official birthday which is 1932.

1932... Which would have made him 13 and Bianca 15 by the time Maria dies. Which is hilarious because with the way the kids are written during her death scene as absolute non players with nary a reaction, you would think they were written to be toddlers who didn't understand anything that was going on.

That royally screws over Bianca as a character (and me as someone who's trying to write a story centered around her). Because her main thing. The one time she's allowed to have complexity is the moment where she talks about how she wants to be more than Nico's caretaker, and she's barely Nico's caretaker at all. The best in universe explanation I can come up for this is that this is how Bianca perceives things because that's all that she literally remembers. Those months in the hotel and Westovers.

Another time the plot kinda messes her up is at the beginning of TTC. One complaint that I often see in regards to her Is how quickly she makes her decision. She does not even hesitate. She does not even wait to see the camp. You know the place that would have taken care of her and Nico which would have meant she wasn't going to be his supposed primary caretaker anymore? She doesn't even wait to see if it was an actual good place for her brother? Spoiler alert: it's not camp half-blood at the time was not a good place for either of them really. Nico did not have a cabin at camp and people were not accepting of him. Hell, people not being accepting of hades and his children was something established since the first book.

But once again, this is a Doylist problem at its core. We need to turn Bianca into a hunter but we also need Artemis to leave so that she can be kidnapped for the main conflict, so she leaves before the hunters even reach camp. Half-blood. So Bianca as a character doesn't even get to make a proper choice between the camp and the hunters. To people who only look at characters on an in universe level, it comes off as very rash and not well thought out.

To be fair, on an in universe level, she's a kid so it's okay if she's stupid, but Riordan wasn't trying to make her come off as that way? He treats Bianca's decision as a legit serious choice and not the rash decision of a desperate child.

And once again, Bianca is here for Nico's sake more than anything. She needs to die. So she takes the statue for Nico. Which is so ironic and tragic if you decide to play it that way. That Bianca wanted to be more than Nico's sister, but her literal death revolves around being his sister. Normally I'd enjoy this level of angsty irony but unfortunately that's how the very narrative treats her as well. Even her post mortem decisions are there to maximize Nico's angst more than that they're there to say anything about Bianca herself. We need Bianca to only appear at the end of Botl so that Nico and Percy can have a conflict but it once again comes at the cost of Bianca herself coming off as callous. What's the in universe reason for this behavior? It's so stupid because in universe, Nico doesn't even take that much convincing? One conversation. One conversation and Nico was convinced to stop his efforts in reviving her. Does she just not know her brother enough? Maybe since they technically know each other for a year max. Does she genuinely think she's that easy to give up on? Is she that conflict avoidant? I actually like this interpretation and plan to use it. There's much to be done with a character who's rash and bold but an absolute emotional coward who'd try to avoid an emotionally charged conversation until they absolutely can't.

Hell even after Botl, it's the same song and dance. Hades makes an absolute vile remark at Nico's expense. TSATS makes it into a joke moment and has you believe that Hades simple said that Bianca would have been a better demigod. No ladies and gentlemen. Hades literally tells Nico that he wished Bianca had survived instead.(The fact that I still think that hades is the best godly parent just shows you how low the bar is more than anything.)

I swear to God I spent so much time racking my brain trying to understand what this could mean for Bianca's character.

This is how I basically look like trying to milk every scene where Bianca is there as a character or is mentioned for every drop of characterization.

At the end of the day, I can't blame most of the fandom for being ambivalent towards her at best. The story by design is about Nico. It's designed for you to sympathize with him and yeah if I'm to look at it from Nico's perspective. He DID get abandoned, regardless of Bianca's intentions. From his Perspective , which is the one most people would take, his sister took the very first chance she could to ditch him for people she barely knew hoping people either of them barely knew would take care of him even though they haven't even seen the place yet, and then ignored him for months while he was desperate for a single conversation with her. Honestly had Nico outright resented his sister for leaving, I think the reaction towards her would have even been worse.

(Another sidenote, my very hot tea Is that I like to believe that had Bianca lived her and Nico's relationship would have become worse as time went on and as the camp's anti hades sentiments really started taking their toll on Nico. But I'm just an angst lover)

Worse is that this story is told from Percy's perspective and these two only have like 3 actual conversations together. One of them is her dying, one is about her making her first main decision and that's at the expense of Nico who's probably the fandom favorite behind Percy and Annabeth and the other is her trying to explain her aforementioned decision to Percy and even then, she talks about it in such broad strokes. "I want to be more than X" tells us about who you one day wish to be not about who you are at the current moment. And even when we have Nico as a POV character, Bianca is only there for "dead family member" trope. There's barely any moment where Nico remembers anything important about her to give her any depth. The cards are just stacked against her. Even the people who are at the "Bianca did nothing wrong camp" are barely interested in her. I swear to god whenever an AU comes up where she's alive, the focus is STILL on Nico. Oh Nico would have been such a happy person had she lived! And Bianca? Uhhhhh she would have fucked off with the hunters I guess?

Can we talk about the hunters while we're here?

If we WERE to talk about in universe scapegoats, I'd honestly choose the hunters. Honestly I could make a separate post about how much I hate how Riordan handled them. But oh dear God the way they're presented just comes off as creepy. The way they initially (up until TOA) only go for young girls because apparently older girls aren't useful once they hit puberty and start developing feelings for people and lose themselves(TTC and Percy Jackson's Greek gods oh dear lord are they terrible in Percy Jackson's Greek gods). How they're basically the heroine dumping ground for when Riordan doesn't know what to do with a female character. How ultimately in universe, Zoe more than anyone is to blame to for Bianca's death by taking an untrained girl to a mission where she KNOWS two people would die at the very least. And she doesn't even watch her properly during the mission. Honestly I could barely feel anything about Zoe's death upon rereads as an adult for this very reason. Or how stupid it is to basically put a child in front of a candy store and expect them to make a responsible decision. Who in their right mind would have young girls as young as nine take a celibacy vow? Oh but you'll be safe with us (never mind that we're not just normal hunters here like the actual myths but actual monster hunters) and you'll totally be able to see your brother when you want (actually we barely visit camp half-blood) oh but you'll be a FAMILY with us! Except you know if you catch feelings or get assaulted(holy hell how Riordan depicts the myth of Callisto makes me want to tear my hair out of my scalp)

[inversetrigonometricfunctions]

00:00:00 Introduction for inverse trigonometry identities

00:03:34 Derivation of all inverse trigonometric identities

00:15:14 NCERT Solutions Exercise 2.2 Question 1

00:20:04 NCERT Solutions Exercise 2.2 Question 2

00:21:34 NCERT Solutions Exercise 2.2 Question 3

00:23:44 NCERT Solutions Exercise 2.2 Question 4

00:27:54 NCERT Solutions Exercise 2.2 Question 6

00:34:54 NCERT Solutions Exercise 2.2 Question 7

00:36:24 NCERT Solutions Exercise 2.2 Question 8

00:38:54 NCERT Solutions Exercise 2.2 Question 5

00:42:54 NCERT Solutions Exercise 2.2 Question 9

00:45:44 NCERT Solutions Exercise 2.2 Question 10

00:48:54 NCERT Solutions Exercise 2.2 Question 11

00:50:24 NCERT Solutions Exercise 2.2 Question 12

00:51:04 NCERT Solutions Exercise 2.2 Question 13

00:52:54 NCERT Solutions Exercise 2.2 Question 14

00:54:44 NCERT Solutions Exercise 2.2 Question 15

00:59:54 NCERT Solutions Exercise 2.2 Question 16

01:01:24 NCERT Solutions Exercise 2.2 Question 17

01:03:04 NCERT Solutions Exercise 2.2 Question 19

01:04:24 NCERT Solutions Exercise 2.2 Question 20

01:05:34 NCERT Solutions Exercise 2.2 Question 21

01:07:04 NCERT Solutions Exercise 2.2 Question 18

Detailed explanation of 'how to drive identities of Inverse Trigonometric Functions' and questions related to NCERT Solutions for Exercise 2.2 of Inverse Trigonometric Functions Class 12 Maths Chapter 2.

💎 Purchase the Class 12 Maths Membership for full access to video lectures, notes, and assignments: https://mathyug.com/class-12-maths

[boogersparkles]

NOTES ♡

Yuuka hirasaka x gn!reader

Summery: You drown yourself with work and you won't listen to any of Yuuka's concerns! So she finds a solution

Genre: Light angst w/ comfort, happy ending, romantic

Warnings: Unhealthy eating habits, working to the point of passing out

Words: 2278~

Notes: Hiii!! I was thinking about maybe writting more fanfics for the rest of the yuus if anyone's intrested. Im still new to writting so constructive critisism is welcomed :)

The past week had really been exhuasting. Lately, Crowley has been shoving paperwork after paperwork in your hands even though you had just fought another overblot. Yuuka was badly injured, so you had to take care of of all the work that Crowley wasn't bothered to do. You had eyebags from the countless all-nighters that you pulled to catch up on the missed assignments for alchemy... math.. wait, didn't you have a history test tomorrow? Shit, you completly forgot.

"What time even is it?"

You look up at the clock hanging above your desk.

12:03

"Yeah i could squize another hour"

You get up to grab another energy drink, the floorboards squicking with every step, nearly slipping on the last step of the stairs you make your way towards the kitchen. Opening the fridge door, you crouch down to grab a can.

"Damn, this is my last one... I'm gonna need to buy more tomorrow"

"Absolutely not."

You jump at the sound of a stern voice. Turning to your left you see Yuuka crossing her arms while leaning on the side of the counter, you also didn't miss the disaproving look on her face that held concern for your well being.

"When was the last time you slept?"

"During Trein's class because I probably passed out"

Her face scrunches up with discomfort, not being able to tell wether you were being serious or joking. Not that there was something to laugh at.

"Did you even eat anything today?"

"A sandwich"

"You're telling me that you went through the whole day without eating anything but that sandwich from the morning?!"

"Eeh.. you eat like a king for breakfast?"

"Oh please, what kind of king eats a small sandwich for breakfast?"

Okay she had a point, but the stress was getting to you and you needed to get back to studing for that history test.

"Listen Yuuka, if you have nothing better to say then I'm going back to my room. Goodnight"

Before she could respond you get up and storm out of the kitchen, dashing towards your room, not giving her a chance to even call out your name. Guilt starting to eat you up as you go back to studying.

You're definetly not gonna sleep well.

Yuuka just stood there, starting into empty space, contemplating wether she used the right words to aproch you. She knew you were stressed but you just closed yourself off in your room, she offered help but you always waved her off, worried about her injuries from the last overblot.

Fine, if you don't want to listen she won't force you, but she will get in that little head of yours one way or another.

She goes upstairs, walking up to the door of your room. She knocks gently but there's no response, entering your room she finds you laying on your desk, the exhuastion probably caught up to you. Sighing softly she picks you up carefuly to not wake you up and tucks you into bed, she glances at the scattered books and notes on your desk. All day you were sucked up by those, not letting anything distance you from them, even declining an invitation to an unbirthday party without hesitation, making Ace and Deuce worry as well.

Looking closer, she sees bold words that say "HISTORY TEST ON MONDAY". She picks up a pen with her bandaged hand, writting some cheat notes for you on small pieces of paper and stuffing them into your pencilcase.

That's when it came to her.

If you didn't want to listen to her words, you will just have to read them!

Monday came, to your surprise you wake up in your bed, too used to the hard wood of your desk it feels weird to not have your back ache like an 80 year old grandpa's for once.

While getting dressed you remember your little fight with Yuuka, anxiety creeping up on you, wondering how to apologize her. Guess you'll apologize when you see her, IF you see her actually, because Crowley had more work for you to do despite having a test on the same day.

You barely make it to first period, thankfuly Crewel seemed to be late as well, so you go to your group with Ace, Epel and.... Yuuka who wasn't present.

"Morning guys"

"Woah, looks like one of the Halloween decorations came to life Haha- OW"

Ace gets roughly nudged at his side by Epel in a way to say without words "This is not the time for jokes"

"How very nice of you Ace" You say monotonously.

"But on a serious note are ya doing okay?"

"I'm fine, there's just a shit ton of work I have to do"

Both of them didn't comment on that, knowing full well just how tired you are by looking at your slummed posture.

"By the way, where's Yuuka? I haven't seen her at all today"

"She was here a while ago, but she said that she forgot something and just bolted out of class in a hurry"

That's odd... Yuuka isn't the type of person to just forget things like that.

While waiting for Crewel to arrive busting through the door comes Crowley who's waayyyy too excited to see you.

"My, my, why isn't it our dearest Prefect!"

"I thought Yuuka was the Prefect" Epel wispered to you

"I have a couple jobs for you to do!"

"But you said that you wouldn't need me until third period!"

"I did say that but it's different now. Come along! There is no time to watse!"

Aaaaaand there he goes, out the window.

Again.

You put your hands on your face and start groaning like you lost the lotery for the tenth time in a row.

" Can you guys watch my stuff? Since i won't be able to take it with me"

"Sure no problem.."

You leave your items and make it out of the classroom. But when you left, Yuuka had just gotten in.

"Hey where were you?"

"I was just getting something... wait, are those-?"

"The workacholic's stuff? Yeah, they just left"

"Oh perfect!"

She opens your pencilcase and shoves some more notes in it.

"What are those?"

"Cheat notes"

"Heyy! You never make those for me!"

"Yeah because they actually NEED these" She says as she shoots Ace a glare

They don't push further and just let her do as she pleases.

After leaving Crowley's office you find Deuce holding your things, waiting for you.

"Hey!.. How was work?"

"Awful."

Deuce akwardly shuffles his feet, not knowing how to comfort you.

"Well... Trein said that you can write the test next period with class 1-D and leave early today"

"Wait. Are you for real?!"

"Yeah! Anyway I gotta go so bye! And good luck!

Deuce shoves all your things in your arms and makes a run for it.

Why was he in such a rush? Class starts in 15 minutes, it was almost like he was hiding something. Looking down at your hands, you see a lunch box with a bright yellow sticky note on the top that said..

"Eat well and good luck on your test! :)"

Thank the heavens above because you were STARVING. You walk towards class 1-D it was a bit far from Crowley's office but you had time to eat. Entering the classroom, you find Trein and some other students including Sebek. Grabbing a test sheet you go to the very back and sit next to Sebek.

" I see that you have chosen to finish early human!"

Surprisingly Sebek's voice was slightly above average volume, unlike the usual roaring.

"Yeah.. I'm just gonna fail the test early and go straight to bed..?"

Multiple colored notes fill your pencilcase and... They're enough to give you a passable grade! But.. who wrote these? Whatever, you just want to get this over with

While you wrote away Sebek noticed how you constantly looked away to copy the answers, but he didn't rat you out, in fact he acted like nothing was happening

The bell rings and you hand over your test to Trein. While you were walking down the hall you accidently bump into a student.

"Oh sorry! Wait. This fell from your pocket"

Handing you the letter he leaves you confused. Since when did you carry this? And where did it even come from? Opening it, you find a note and... A discount for the Monstro Lounge?! Completely baffeled you read the note inside....

"Hey! I know how hard you've been working lately and I wanted to make sure you took proper care of yourself. So here's a little gift from me to you! :)

You don't have to go through everything alone. If you ever need help or a shoulder to cry on, I'll always be here for you ♡

- Love, Yuuka"

OF COURSE IT WAS YUUKA ALL ALONG.

And you didn't even see her to apologize today!

It all made sense now. Why Yuuka was missing during alchemy, why Deuce ran away in a hurry, why Sebek didn't snitch on you. Because it was all part of Yuuka's plan.

Making your way to the Monstro Lounge you can't stop thinking about Yuuka, she goes out of her way just to make you happy. You'll buy something for her too, you sort owe her for well, everything. For carrying anything too heavy for you, for defending you when you were in danger, for comforting and holding you close to her heart to sooth you whenever you had a nightmare...

Your chest tightens up just by the thought of everything she has done.

You get the cheesebuger for yourself and for Yuuka the steak from today's special menu.

For always making you feel special.

Finally you made it back to Ramshackle, taking off your shoes, you notice that the couch has more pillows than usual and a big fluffy blanket, on the top of it there was yet again another note.

"Hi sugar! I hope you feel more relaxed from yesterday, found you passed out on your desk last night so I got some extra pillows for you. You can take the next two days easy, I managed to threaten convince Crowley to do his own work.

Take care - Love Yuuka"

Like the other notes the handwritting was a bit sloppy due to still having those bandages on her hand so you couldn't recognize who's writting it could be, you also couldn't think straight with everything going on, giving you no time to even wonder about those notes. It's insane how much Yuuka fills your day despite not seeing her at all, you really started to miss her too but for now you'll just have to wait until she returns.

After leaving her share of food on the kichen island, you put on a movie and pull the blanket over you as you sit cross-legged on the couch with your cheeseburger on your lap. Yuuka will come home in 35 minutes, you might as well enjoy the movie, though you can't help but occasionaly look at the time, waiting like a little puppy.

Finishing your burger, you start to feel a bit drowsy, putting the empty countainer on the coffee table, you lay down cacooning yourself with the fluffy blanket. Yuuka is ten minutes late but you know that she will come home shortly.

Your eyelids start to feel heavy, you can take a short nap for a minute or two.

"Are you still sleeping?"

You catch the sound of soft wispering but you don't say anything. Sensing the couch sink, you also hear shifting

"Grim, don't wake them up"

A familiar voice hits your ears, somehow the sterness it carries is also familiar.

You feel a gentle hand graze your cheek, pushing aside some strands fo hair along with it.

And then...

A soft kiss on you forhead.

Your cheeks start to heat up and a warm feeling spreads through your chest. Slowly opening your eyes, you see Yuuka kneeling with one knee up right next to you and Grim snuggling up against your stomach.

"Sorry, did i wake you up?"

"No, I woke up myself" you lied sleepily.

Let's be honest, you wouldn't be able to sleep peacefuly after that kiss.

"How was your day today?" She asked, resting her chin in her palm.

"It was... less tiring than the past few days"

"Did you eat anything from the Monstro Lounge?"

"I ate a cheeseburger. Did you find the steak I got for you?"

"Mhm, it was delicious"

Sitting up from your position, the blanket fall off of you as you lean in to hug her, resting your arms on her shoulders.

"I'm sorry for snapping at you last night. I didn't mean to... I was just...."

Struggling to find your words, Yuuka finishes your sentense for you.

"Just too tired to properly function? Yeah, i know. I'm glad you finally got some rest"

She says as she caresses your back softly, her touch lingering, holding more care than you can ever imagine

Your eyeshight blurs up a bit, but you're grateful for always having Yuuka by your side

"Come on, don't go tearing up on me now. Why don't we watch that movie you had put on?"

Leting go of her, you push aside some pillows to make space as she goes to dim the lights. Sitting down next to you, you lean your head on her shoulder, letting her hand rest on your waist as Grim jumps in your lap.

You felt relief, happy and complete. As if Yuuka was the rain and sun to your flower, the last piece to your puzzle. She means eveything to you and you're well aware that she recipercates those feelings too.

Bonus:

"Wait, don't you have homework to do?"

"Eeeh.. I'll do it later"

She ended up making cheat notes for herself with your help.

[sarthaks24]

Class 12th NCERT Solutions for PCM

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[vasanthasworld]

WBCHSE Solutions For Class 12 Maths Bayes Theorem And Its Applications

[vijayadworld]

WBCHSE Solutions For Class 12 Maths Algebra