Addition of Matrices Assignment Class X ICSE Board
free mathematics assignments tailored specifically for the ICSE Class X board exams. Today, we’re diving into the fascinating world of matrices, focusing on the concept of matrix addition.
Quadratic Equations For JEE
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ISC Board Exam 2024 Solution Mathematics Class 12
$ begin{center} textbf{Section A } end{center} textbf{Question 1} begin{enumerate}[label=roman*] item Let L be a set of all straight lines in a plane. The relation R on L defined as “perpendicular to ” is : begin{enumerate} item Symmetric and Transitive item Transitive item Symmetric item Equivalence end{enumerate} item The order and degrees of differential equation $1 + ( frac{dy}{dx})^2 = frac{d^2y}{dx^2}$ begin{enumerate} item 2 and 3/2 item 2 and 3 item 3 and 4 item 2 and 1 end{enumerate} item Let A be a non empty set Statement 1 : Identity relation on A is Reflexive \ Statement 2 : Every reflexive relation on A is an identity relation begin{enumerate} item Both statements are true item bot statements are false item Statement 1 is true and Statement 2 is false item Statement 1 is false and statement 2 is true end{enumerate} item The graph of the function F is shown below : of the following on what all points the function f is not differentiable. begin{enumerate} item at x = 0 and x = 2 item at x = 1 and x = 3 item at x = -1 and x = 1 item at x = -1.5 and x = 1.5 end{enumerate} item The value of $cosec (sin^{-1}(frac{-1}{2}))- sec(cos^{-1}(frac{-1}{2}))$ is equal to begin{enumerate} item -4 item 0 item -1 item 4 end{enumerate} item The value of $int^{sqrt{3}}_1 frac{dx}{1+x^2}$ is begin{enumerate} item $frac{pi}{2}$ item $frac{2pi}{3}$item $frac{pi}{6}$item $frac{pi}{12}$ end{enumerate} item textbf{Assertion:} Let the matrices A = $begin{pmatrix} -3 & 2 \ -5 & 4 \ end{pmatrix}$ and $B = begin{pmatrix} 4 & -2 \ 5 & -3 \ end{pmatrix}$ be such that $A^{100} B = B A ^{100}$ textbf{Reason}: AB = BA implies $A^nB = BA^m$ for all positive integers n. begin{enumerate} item Both assertion and reason are true and Reason is the correct explanation of assertion item Both Assertion and Reason are true but Reason is not the correct explanation of assertion. item Assertion is true and Reason is false item Assertion is false and Reason is true. end{enumerate} item If $int (cotx – cosec^2x)e^x dx = e^x f(x) + c $ then f(x) will be begin{enumerate} item cotx + cosec x item $cot^2x$ item cotx item cosec x end{enumerate} item In which one of the following intervals is the function $f(x ) = x^3-12x$ increasing ? begin{enumerate} item $(-2,2)$ item $(-infty, -2) cup (2,infty)$ item $(-2, infty)$ item $(-infty, 2)$ end{enumerate} item If A and B are symmetric matrices of the same order, then AB – BA is : begin{enumerate} item skew symmetric item symmetric matrix item diagonal matrix item identity matrix end{enumerate} item Find the derivative of $y = logx + frac{1}{x}$ item Teena is practising for an upcoming Rifle Shooting tournament. The probability of her shooting the target in the 1st , 2nd , 3rd and 4th shots are 0.4, 0.3 , 0.2 amd 0.1 respectively. Find the probability of at least one shot of Teen hitting the target. item Which of the following graphs is a function of x ? item Evaluate $int^4_0 |x+3|dx$ item Given that $frac{1}{y}+ frac{1}{x} = frac{1}{12}$ and y decreases at a rate of $1cm/s^{-1}$ find the rate of change of x when x = 5 cm and y = 1 cm. textbf{Question 2 } begin{enumerate}[label=roman*] item Let $f:R-(frac{-1}{3}) rightarrow R – {0}$ be defined as $f(x) = frac{5}{3x+1}$ is invertible . Find $f^{-1}(x)$ begin{center} textbf{OR} end{center} item If $f:R rightarrow R $ be defined as $f(x) = frac{2x-7}{4}$ . Show that f(x) is one and onto. end{enumerate} textbf{Question 3 } begin{enumerate}[label=roman*] item Find the value of the determinant given below, without expanding it at any stage $begin{vmatrix} beta gamma & 1 & alpha (beta + gamma) \ gamma alpha & 1 & beta (gamma + alpha) \ alpha beta & 1 & gamma (alpha + beta) \ end{vmatrix}$ end{enumerate} textbf{Question 4 } begin{enumerate}[label=roman*] item Determine the value of k for which the following function is continuous at x = 3 f(x) = $begin{cases} frac{(x+3)^2 -36}{x-3}; x neq 3 \ k; ~~~~~~~~x = 3 \ end{cases}$ item Find a point on the curve $y =(x-2)^2$ at which the tangent is parallel to the line joining the chord through the points (2,0) and (4,4) end{enumerate} textbf{Question 5 } begin{enumerate}[label=roman*] item Evaluate : int^{2pi}_0 frac{1}{1+e^{sinx}}dx end{enumerate} textbf{Question 6 } begin{enumerate}[label=roman*] item Evaluate : $ P(A cup B)$ if $2P(A) = P(B) =frac{5}{13}$ and $P(A|B) = frac{2}{5}$ end{enumerate} textbf{Question 7 } begin{enumerate}[label=roman*] item If $y= 3cos(logx) + 4sin(logx)$ then show that x^2 frac{d^2y}{dx^2}+x frac{dy}{dx}+y=0 end{enumerate} textbf{Question 8 } begin{enumerate}[label=roman*] item Solve for x : sin^{-1}(frac{x}{2})+ cos^{-1}(x) = frac{pi}{6} begin{center} textbf{Large OR} end{center} item If $sin^{-1}x + sin^{-1}y+ sin^{-1}z =pi$ Show that x^2-y^2-x^2+ 2yz sqrt{1-x^2}=0 end{enumerate} textbf{Question 9 } begin{enumerate}[label=roman*] item Evaluate ;$int x^2cosx dx$ begin{center} textbf{Large OR} end{center} item Evaluate $int frac{x+7}{x^2+4x+7}dx$ end{enumerate} textbf{Question 10 } begin{enumerate}[label=roman*] item A jewellery seller has precious gems in white and red colour which he has put in three boxes. The distribution of these gemes is shown in the table given below : begin{table}[ht] centering begin{tabular}{|c|c|c|} hline Box & multicolumn{2}{c|}{Numbers of Gems} \ cline{2-3} & White & Red \ hline I & 1 & 2 \ II & 2 & 3 \ III & 3 & 1 \ hline end{tabular} label{tab:gem_numbers} end{table} He wants to gift two gems
ISC Mathematics syllabus for Class 12
Unit Description Marks Relations and Functions This unit lays the groundwork for understanding the fundamental aspects of relations and functions. It covers essential topics like domain, range, inverse functions, composite functions, and the basics of matrices and determinants. 10 Algebra Algebra forms the core of mathematical problem-solving. This unit explores complex numbers, quadratic equations, matrices, permutations and combinations, the binomial theorem, and mathematical induction. 10 Calculus As a cornerstone of the ISC Mathematics syllabus, Calculus is divided into Differential and Integral Calculus. It encompasses limits, continuity, derivatives, integration, and their applications. 32 Probability This unit introduces students to the fundamental concepts of probability, including the rules of addition and multiplication, conditional probability, Bayes’ theorem, and random variables, with applications to real-life situations. 13 Vectors and Three-Dimensional Geometry Focusing on the spatial aspects of mathematics, this section covers vectors, scalar and vector products, and three-dimensional geometry. 11 Linear Programming Linear Programming introduces optimization techniques, covering the graphical method, simplex method, and duality theorem, with practical applications in solving real-world problems. 4 Application of Calculus and Additional Topics This includes the practical applications of calculus in various fields, an introduction to differential equations, and a brief overview of coordinate geometry and conic sections. 10 The ISC Mathematics syllabus for Class 12 in the year 2024 is meticulously structured into two main parts, encompassing a wide array of topics aimed at providing a comprehensive learning experience. This curriculum is designed to challenge students and deepen their understanding of mathematical concepts, preparing them for further education and various professional fields. Here’s a detailed exploration of the syllabus, including the distribution of marks across different sections and units. Overview of the Syllabus Structure and Mark Distribution The ISC Mathematics syllabus is strategically divided to cover foundational and advanced topics across three sections, with a total of 80 marks. – Section A (65 Marks) focuses on core mathematical principles and includes units on Relations and Functions, Algebra, Calculus, and Probability. – Section B (15 Marks) delves into applied mathematics, covering Vectors, Three-Dimensional Geometry, and the Application of Integral. – Section C (15 Marks) introduces practical applications of calculus, including Linear Regression and Linear Programming. Let’s delve deeper into each section for a better understanding. Relations and Functions (10 Marks) This unit lays the groundwork for understanding the fundamental aspects of relations and functions. It covers essential topics like domain, range, inverse functions, composite functions, and the basics of matrices and determinants, providing a solid foundation for more complex studies. Algebra (10 Marks) Algebra forms the core of mathematical problem-solving. This unit explores complex numbers, quadratic equations, matrices, permutations and combinations, the binomial theorem, and mathematical induction, equipping students with the tools needed for advanced mathematical operations. Calculus (32 Marks) As a cornerstone of the ISC Mathematics syllabus, Calculus is divided into Differential and Integral Calculus. It encompasses limits, continuity, derivatives, integration, and their applications, offering students a comprehensive understanding of change and motion. Probability (13 Marks) This unit introduces students to the fundamental concepts of probability, including the rules of addition and multiplication, conditional probability, Bayes’ theorem, and random variables, with applications to real-life situations. Vectors and Three-Dimensional Geometry (11 Marks) Focusing on the spatial aspects of mathematics, this section covers vectors, scalar and vector products, and three-dimensional geometry, including equations of planes and lines, enhancing students’ spatial reasoning. Linear Programming (4 Marks) Linear Programming introduces optimization techniques, covering the graphical method, simplex method, and duality theorem, with practical applications in solving real-world problems. Application of Calculus and Additional Topics (10 Marks) This includes the practical applications of calculus in various fields, an introduction to differential equations, and a brief overview of coordinate geometry and conic sections, broadening students’ application skills. 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The ISC Class 12 Mathematics syllabus for 2024 is divided into three main sections: Section A covers Relations and Functions, Algebra, Calculus, and Probability. Section B includes Vectors, Three-Dimensional Geometry, and the Application of Integral. Lastly, Section C focuses on the Application of Calculus, Linear Regression, and Linear Programming. FAQ 2: How much weight does Calculus hold in the ISC Mathematics exam? Calculus is a significant part
Three D Test Paper Class 12 Term 2
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Three D Test Paper Class 12 Pdf
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Three D Class 12
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Test Series For Maths Class 12
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Maths Quiz Questions With Answers For Class 12 Pdf
Maths Quiz Questions With Answers For Class 12 Pdf Are you looking to enhance your mathematical skills and test your knowledge? Look no further! In this blog post, we are delighted to present you with a diverse collection of Maths Quiz Questions with Answers for Class 12 in PDF format. These meticulously crafted test papers are the epitome of excellence, ensuring the best learning experience available on the internet, all at an unbeatable price. www.mathstudy.in provides the best quality E-books on Mathematics. Mathematics holds a pivotal role in education, serving as the foundation for various academic and professional disciplines. Class 12 is a critical juncture where students solidify their mathematical abilities and broaden their horizons. It is essential to not only understand key concepts but also practice extensively to achieve proficiency. 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Maths Mock Test Class 12 Term 1
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