Maharashtra 12th HSC Mathematics and Statistics Question Paper with Solution: Download PDF

Maharashtra 12th HSC Mathematics and Statistics Question Paper with Solution: Download PDF

Edited By Vishal kumar | Updated on Jul 20, 2024 02:02 PM IST | #Maharashtra HSC Board

Preparing for the Maharashtra Board Class 12 Mathematics and Statistics exam demands a comprehensive understanding of the subjects and consistent practice. One of the most effective methods for achieving this is to solve previous years' question papers. This approach not only familiarizes students with the class 12 Maharashtra board exam. format and the types of questions that are commonly asked but also helps identify areas of strength and weakness.

In this article, we provide the question papers from the last three years for the Maharashtra Board Class 12 Mathematics and Statistics examinations, complete with detailed solutions. These solutions, crafted by subject experts at Careers360, guide students in managing their time efficiently, improving their accuracy, and building confidence in their problem-solving abilities. This resource serves as an invaluable tool for thorough exam preparation, enabling students to aim for top grades in their Mathematics and Statistics exams.

Maharashtra State Board 12th math Previous Year Question Papers Trends

• 2024 Trends: The 2024 Mathematics and Statistics exam for the Maharashtra State Board included a variety of problems, with a strong focus on Calculus and Probability. The exam also featured real-world problem scenarios and data interpretation questions, reflecting a shift towards application-based learning. This approach by the Maharashtra board aims to equip students with practical skills and enhance their analytical thinking.

• 2023 Trends: The 2023 Mathematics and Statistics paper indicated a nuanced alteration in question styles, predominantly emphasizing Algebra and Geometry. This shift was notably characterized by questions involving complex numbers and geometric proofs, possibly to bridge the gap with competitive exams in engineering and architecture. The focus on these areas underlines the board’s intention to prepare students for higher technical education by enhancing their problem-solving capabilities.

• 2022 Trends: In 2022, the focus of the mathematics paper was significantly on Statistics and Vectors, alongside a steady emphasis on Algebraic functions and Calculus. The examination included a substantial number of problems requiring detailed analytical solutions, emphasizing the application of mathematical theories over mere theoretical understanding.
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Maharashtra Class 12 Maths Difficulty Level Trends

Over recent years, the Maharashtra Board's Class 12 Mathematics exams have demonstrated a notable evolution in complexity and the depth of knowledge required:

• Integration of Concepts: The examination pattern has increasingly favored questions that necessitate the application of several mathematical principles to solve a single question. This approach encourages students to think holistically and fosters a more integrated understanding of mathematics.

• Increasing Difficulty in Problem Solving: There has been a noticeable rise in both the quantity and complexity of problems requiring higher-order mathematical skills. Particularly, questions involving Calculus and Algebra now demand more sophisticated analytical skills and a deeper understanding of underlying theories.

• Focus on Application-Based Questions: Reflecting a global trend towards practical and applicable knowledge, the recent exam papers have included more questions that tie mathematical theories to real-world scenarios. This not only tests students' theoretical knowledge but also their ability to apply this knowledge effectively in practical situations.

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Maharashtra Class 12 Maths Question Paper with Complete Solution

Q1. Write the compound statement 'Nagpur is in Maharashtra and Chennai is in Tamilnadu' symbolically.

Solution:

To write the compound statement "Nagpur is in Maharashtra and Chennai is in Tamilnadu" symbolically, you can denote each individual statement with a propositional variable and use the logical conjunction symbol:

Let:
P represents "Nagpur is in Maharashtra"
Q represents "Chennai is in Tamilnadu" Then, the compound statement can be expressed as:

p ∧ q

This symbolically states that both

p (Nagpur is in Maharashtra) and

Q (Chennai is in Tamilnadu) is true.

Q2. Construct the truth table for the statement pattern:

[(P→q)∧q]→p

Solution :

The logical statement you're asking about is

(p→q)∧q)→p

To construct the truth table, we consider all possible truth values of ? and ?, and then evaluate the statement step-by-step:

p→q: This conditional is true unless p is true and q is false.

(p→q)∧q: This conjunction is true only when both p→q and q are true.

((p→q)∧q)→p: This final conditional is true unless (p→q)∧q is true and p is false.

Let's compute the truth table:

Q3. Find ?, if the sum of the slopes of the lines represented x2+kxy-3y2=0 is twice their product.

Solution:

Given that the sum of the slopes of the lines represented by the equation:

x2+kxy-3y2 is twice their product, we start by considering the general form of the homogeneous equation of a pair of straight lines:

ax2+2hxy+by2=0

For the given equation

x2+kxy−3y2=0

we can identify the coefficients:

a=1,2h=k,b=−3

Therefore,

b=k2

The slopes of the lines represented by the equation are given by the roots of the quadratic equation derived from:

at2+2bt+b=0

Substituting the values of

a, b and b gives:

t2+kt−3=0

Let the slopes of the lines be

m1 and m2

These slopes are the roots of the quadratic equation

t2+kt−3=0

According to Vieta's formulas, the sum and product of the roots of the quadratic equation

at2+bt+c=0

are given by:

m1 + m2=−ba

m1 m2=ca

For our specific equation:

m1 + m2= −k

m1 m2 = −3

We are given that the sum of the slopes is twice their product:

m1 + m2 = 2m1 m2

Substituting the values from Vieta's formulas:

−k=2(−3)

−k=−6

Solving for k:

k=6

Therefore, the value of k is: 6

Q4. Check whether the matrix

[cos⁡θsin⁡θ−sin⁡θcos⁡θ] is invertible or not.

Solution:

To determine if the matrix

A=[cos⁡sin⁡θ−sin⁡θcos⁡θ]

is invertible, we need to check if its determinant is non-zero. The determinant of a 2×2 matrix [abcd] is given by :

det(A)=ad−bc

For the matrix A, we have:

a=cos⁡θ,b=sin⁡θ,c=−sin⁡θ,d=cos⁡?

Therefore, the determinant of A is:

det(A)=(cos⁡θ)(cos⁡θ)−(sin⁡θ)(−sin⁡θ)

det(?)=cos2⁡θ+sin2⁡θ

we know that:

cos2⁡θ+sin2⁡θ=1

So, the determinant is:

det(A)=1

Since the determinant of A is 1, which is non-zero, the matrix A is invertible.

Therefore, the given matrix is indeed invertible.

Q5. Find the vector equation of the line passing through the point having position vector 4^i−?^+2?^ and parallel to the vector −2i^−j^+k^

Solution:

To find the vector equation of a line passing through a given point and parallel to a given vector, we use the standard formula:

r→=r→0+td→

Where:- r→ is the position vector of any point on the line.- r→0 is the position vector of a known point through which the line passes (in this case 4i^−j^+2k^).- d→ is the direction vector parallel to the line (in this case −2i^−j^+k^).
- t is a scalar parameter. Given:

r→0=4i−j^+2k^

d→=−2i^−j^+k^

Substitute these into the line equation:

r→=(4i^−j^+2k^)+?(−2i^−j^+k^)

Expanding and simplifying gives:

r→=(4−2t)i^+(−1−t)j^+(2+t)k^

So, the vector equation of the line is:

r→=(4−2t)i^+(−1−t)j^+(2+t)k^

This equation represents the line passing through the point with the position vector

4i^−j^+2k^ and parallel to the vector −2i^−j^+k^.

Apart from these questions, you can download the complete last three-year question with solutions by clicking on the link below.

Download the Complete PDF - Maharashtra HSC Mathematics and Statistics Previous Year Question Paper with Solutions

Maharashtra Class 12 Math Consistent and Repetitive Chapter Concepts

In Maharashtra Class 12 Mathematics, certain topics consistently appear in the board exams due to their foundational importance to the curriculum. Identifying these consistent and repetitive concepts can significantly enhance study efficiency. Here are some key areas that are frequently tested:

1. Calculus: This is a major focus in the Class 12 syllabus, with significant emphasis on differential and integral calculus. Commonly tested concepts include finding derivatives, applying differentiation rules (chain rule, product rule, and quotient rule), and solving problems involving maxima and minima. Integral calculus often involves definite and indefinite integrals, techniques of integration, and applications such as calculating areas and volumes.
2. Algebra: Topics like matrices and determinants are regularly featured, with questions often focusing on operations on matrices, finding determinants, and solving systems of linear equations using various methods (Cramer’s rule, matrix inversion). Sequences and series, particularly arithmetic and geometric progressions, are also commonly tested, along with complex numbers and their algebraic properties.
3. Vectors and Three-Dimensional Geometry: Questions frequently involve vector algebra, including operations on vectors, scalar (dot) and vector (cross) products, and their geometrical interpretations. Three-dimensional geometry problems might include finding equations of lines and planes, and determining distances and angles between them.
4. Probability and Statistics: This section often includes questions on probability rules, conditional probability, Bayes' theorem, and probability distributions (binomial and normal distributions). Statistics questions may cover measures of central tendency and dispersion (mean, median, mode, variance, and standard deviation).
5. Trigonometry: While not as heavily weighted as other topics, trigonometry remains a crucial component, with questions on trigonometric ratios, identities, equations, and properties of triangles.

By focusing their revision on these areas, students can prepare effectively for the Maharashtra Class 12 Mathematics exams, ensuring comprehensive coverage of the concepts most likely to be tested.

Benefits of Practicing the Maharashtra 12th Board Maths Question Papers

• Familiarity with Exam Pattern: Understand the format and structure of the exam.
• Identification of Important Topics: Recognize frequently asked questions and key areas.
• Time Management: Improve speed and efficiency in solving questions within the allotted time.
• Boosting Confidence: Build confidence by practicing with actual exam-level questions.
• Error Analysis: Identify and learn from mistakes to avoid them in the actual exam.
• Improved Problem-Solving Skills: Enhance analytical and problem-solving abilities.
• Revision: Reinforce and revise important concepts effectively.
• Stress Reduction: Reduce exam anxiety by becoming more accustomed to the exam environment.

Conclusion

In conclusion, for students preparing for the Maharashtra Class 12 Mathematics exams, a strategic focus on consistently tested topics such as Calculus, Algebra, Vectors and Three-Dimensional Geometry, Probability and Statistics, and Trigonometry is essential.

These areas not only form the core of the syllabus but are also pivotal in developing a deep understanding and proficiency in mathematics that is critical for success in the exams. By concentrating revision efforts on these key concepts, students can enhance their problem-solving skills, improve their ability to apply mathematical principles to complex situations, and significantly increase their chances of achieving high scores.

Frequently Asked Question (FAQs)

1. What topics are most important for the Maharashtra Class 12 Mathematics exam?

Key topics include Calculus, Algebra, Vectors and Three-Dimensional Geometry, Probability and Statistics, and Trigonometry.

2. How can I improve my problem-solving skills in mathematics?

Regular practice, solving past exam papers, and understanding the application of concepts are crucial. Additionally, engaging in group study sessions.

3. Are there any recommended books or resources for Maharashtra Class 12 Mathematics?

Books by publishers such as Navneet or Target and guides like R.D. Sharma is highly recommended.

4. How much time should I dedicate to mathematics revision daily?

It varies depending on individual learning pace, but aiming for 2-3 hours of focused study.

5. What is the best way to manage time during the mathematics exam?

Practice time management by solving sample papers within the allotted time.

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Yes, you can repeat Class 12th from the Maharashtra Board, even if you passed in 2022 and took an improvement exam. You need to re-enrol in a school affiliated with the Maharashtra Board , submit the necessary documents, and pay the required fees. The student may also contact the Maharashtra State Board of Secondary and Higher Secondary Education for specific guidelines and procedures for repeating Class 12.

If you want to repeat the MSBSHSE HSC exam in 2024 , you will have to contact the Maharashtra State Board about your missing MSBSHSE improvement result . You can visit their official website or reach out to your previous school for guidance. You can register as a private candidate to apply, however, it is advisable to get the latest information from the MSBSHSE board directly.

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