The document appears to be a blueprint for a mathematics exam for class 12. It lists various topics that could be covered in the exam such as functions, derivatives, integrals, differential equations, 3-dimensional geometry, and matrices. For each topic it indicates the number and type of questions that may be asked, such as very short answer (1 mark), short answer (4 marks), and long answer (6 marks). The total number of questions is 29 with 10 short answer questions worth 1 mark each, 12 questions worth 4 marks each, and 7 questions worth 6 marks each. The document also includes sample questions that cover the listed topics as examples of what may be asked on the exam.
This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
The pattern of question paper in the subject Mathematics has been changed in CBSE,India.I am uploading the paper with marking scheme so that students will be benefitted-Pratima Nayak,KVS
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
The pattern of question paper in the subject Mathematics has been changed in CBSE,India.I am uploading the paper with marking scheme so that students will be benefitted-Pratima Nayak,KVS
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
I feel happy to make a presentation in odia language.
I am unable to make the alphabet for obtuse ,either it is "stu" or "stha" not exact one.Still I feel proud.
Adolescent should know that they are not one who faces the problems,all the adolescents have some common problems.They should develop certain life skills to grow smoothly.
The presentation is meant for Teachers.We as teachers think that due some lack of social skills students face self control problem but it may be due to learning disability
You have so many things in your life to be happy about. Appreciate those things, and suddenly your sadness will feel smaller and your happiness will grow larger
sometimes when you're in a really bad mood and you're not sure why?
A bad mood could be described as restless, dull, boredom, blah, dull, listless, melancholy or being just plain sad with no real explanation.
How to improve mood which is very important for success
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2. Sample Question Paper - II
Mathematics - Class XII
Time : 3 Hours
Max. Marks : 100
General Instructions
1.
All questions are compulsory.
2.
The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of
10 questions of one mark each, section B comprises of 12 questions of four marks each and section C
comprises of 07 questions of six marks each.
3.
All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the
question.
4.
There is no overall choice. However, internal choice has been provided in 04 questions of four marks each
and 02 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
5.
Use of calculators is not permitted. You may ask for logarithmic tables, if required.
SECTION - A
Q.1.
If A is a square matrix of order 3 such that |adj A| = 64, find |A|.
Q.2.
If A, B, C are three non zero square matrices of same order, find the condition on A such that AB = AC ⇒ B = C
Q.3.
Give an example of two non zero 2 × 2 matrices A, B such that AB = 0.
Q.4.
If f (1) = 4; f ′ (1) = 2, find the value of the derivative of log f(ex) w.r.t x at the point x = 0.
Q.5.
Find a, for which f(x) = a(x + sin x) + a is increasing.
Q.6.
Evaluate,
Q.7.
dy
dy
Write the order and degree of the differential equation, y = x + a 1 +
dx
dx
(where [x] is greatest integer function)
(32)
2
3. →
Q.8.
→
→
→
→
→
ˆ ˆ
ˆ j
j ˆ
If a = i + ˆ ; b = ˆ + k ; c = k + i , find a unit vector in the direction of a + b + c
Q.9.
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Find the probability that the number
is divisible by 5.
Q.10.
The probability that an event happens in one trial of an experiment is 0.4. Three independent trials of the
experiment are performed. Find the probability that the event happens at least once.
SECTION - B
Q.11.
Q.12.
5 2
+ 2 tan −1 1
7
8
1
5
−1
−1
Find the value of 2 tan + sec
0 1
If A =
, prove that (aI + bA )n = a n .I + na n −1bA where I is a unit matrix of order 2 and n is a
0 0
positive integer
OR
Using properties of determinants, prove that
a + b + 2c
a
c
b + c + 2a
c
a
b
b
= 2 (a + b + c )3
c + a + 2b
d2 y
Q.13.
If x = a sin pt and y = b cos pt, find the value of
Q.14.
Find the equations of tangent lines to the curve y = 4 x 3 − 3x + 5 which are perpendicular to the line
dx 2
at t = 0.
9y + x + 3 = 0 .
Q.15.
Show that the function f (x ) = x + 2 is continuous at every x ∈ R but fails to be differentiable at x = –2.
Q.16.
Evaluate
Q.17.
∫x
x2 + 4
dx
Evaluate
4
+ x 2 + 16
(33)
4. OR
Evaluate
Q.18.
→ → →
If a , b , c are the position vectors of the vertices A, B, C of a ∆ ABC respectivily. Find an expression for the
area of ∆ ABC and hence deduce the condition for the points A, B, C to be collinear.
OR
ˆ j ˆ ˆ j ˆ
ˆ
Show that the points A, B, C with position vectors 2i − ˆ + k , i − 3ˆ − 5k and 3i − 4ˆ − 4k respectively, are
j ˆ
the vertices of a right triangle. Also find the remaining angles of the triangle.
Q.19.
Evaluate,
Q.20.
Solve the differential equation,
dy
+ y sec 2 x = tan x sec 2 x ; y (0) = 1
dx
OR
2 xy + y 2 − 2 x 2
Q.21.
dy
= 0 ; y (1) = 2
dx
In a bolt factory machines, A, B and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their
output 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product.
(i) What is the probability that the bolt drawn is defective ?
(ii) If the bolt is found to be defective find the probability that it is a product of machine B.
Q.22.
Two dice are thrown simultaneously. Let X denote the number of sixes, find the probability distribution of X.
Also find the mean and variance of X, using the probability distribution table.
SECTION - C
Q.23.
Let X be a non-empty set. P(x) be its power set. Let ‘*’ be an operation defined on elements of P(x) by,
A*B = A ∩ B v
Then,
(i) Prove that * is a binary operation in P(X).
(ii) Is * commutative ?
(iii) Is * associative ?
(iv) Find the identity element in P(X) w.r.t. *
(v) Find all the invertible elements of P(X)
(vi) If o is another binary operation defined on P(X) as A o B = ,
(34)
then verify that o distributes itself over *.
5. OR
Consider f : R+ → [–5, ∞) given by f(x) = 9x2 + 6x – 5. Show that f is invertible. Find the inverse of f.
Q.24.
A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the
window is 12m, find the dimensions of the rectangle that will produce the largest area of the window.
Q.25.
Make a rough sketch of the region given below and find it’s area using integration
Q.26.
Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohydrates. The corresponding values for
rice are 0.05 gm and 0.5 gm respectively. Wheat costs Rs. 4 per kg and rice Rs. 6 per kg. The minimum daily
requirements of proteins and carbohydrates for an average child are 50 gms and 200 gms respectively. In what
quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins
and carbohydrates at minimum cost. Frame an L.P.P. and solve it graphically.
1 − 1 1
Q.27. font A = 2 1 − 3 , find A–1 and hence solve the system of equations
1 1
1
x + 2y + z = 4
−x + y + z = 0
{(x, y); y
x − 3y + z = 2
2
}
≤ 4x, 4x 2 + 4 y 2 ≤ 9
Q.28. Find the equation of the plane containing the lines,
→
(
ˆ
r = i + j + λ i + 2ˆ − k
j ˆ
)
(
→
and
ˆ j
ˆ j ˆ
r = i + ˆ + µ − i + ˆ − 2k
)
Find the distance of this plane from origin and also from the point (1, 1, 1)
OR
Find the equation of the plane passing through the intersection of the planes,
2 x + 3 y − z + 1 = 0 ; x + y − 2z + 3 = 0 and perpendicular the plane 3x − y − 2z − 4 = 0 . Also find
the inclination of this plane with the xy plane.
Q.29. Prove that the image of the point (3, –2, 1) in the plane 3x − y + 4z = 2 lies on the plane, x + y + z + 4 = 0 .
(35)