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8 months ago

Maths Matrices Class 12th

For real numbers a, b(a > b > 0), let

$A r e a {(x, y) : x^{2} + y^{2} \leq a^{2} a n d \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \geq 1} = 30 π a n d$

$A r e a {(x, y) : x^{2} + y^{2} \geq b^{2} a n d \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1} = 18 π$

Then the value of (a – b)² is equal to

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Payal Gupta

Contributor-Level 10

Given a > b

Area common to x2 + y2 $\leq a^{2} a n d \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1$

is $π a^{2} - π a b = 30 π . . . . . . . . . . . . . . (i)$

Similarly $π a b - π b^{2} = 18 π . . . . . . . . . . . . . . . . . (i i)$

Equation (i) and equation (ii) $\frac{a}{b} = \frac{5}{3}$

Equation (i) + equation (ii) $a^{2} - b^{2} = 48$

a²= 75, b² = 27

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8 months ago

Maths Matrices Class 12th

Let $A = (\begin{matrix} 2 & - 1 \\ 0 & 2 \end{matrix}) .$ If $B = I -^{5} ? C_{1} (a d j A) +^{5} ? C_{2} {(a d j A)}^{2} - . . .^{5} ? C_{5} {(a d j A)}^{5},$ then the sum of all elements of the matrix B is

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Payal Gupta

Contributor-Level 10

B = (I – adjA)⁵

^{fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff}

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8 months ago

Maths Matrices Matrices

Let f : R -> R be defined as f(x) = x – 1 and g : R – {1, -1} ® R be defined as g(x) = $\frac{x^{2}}{x^{2} - 1} .$ Then the function fog is:

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Vishal Baghel

Contributor-Level 10

f : R defined as

$f (x) = x - 1 a n d g (x) : R - {1, - 1} \to R$

$g (x) = \frac{x^{2}}{x^{2} - 1}$

$∴ f o g (x) = \frac{x^{2}}{x^{2} - 1} - 1 = \frac{1}{x^{2} - 1}$

domain of fog (x) R – {-1, 1} and range $(- \infty, - 1] \cup (0, \infty)$ $∴$

fog (x) is neither one-one nor onto

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8 months ago

Maths Matrices Class 12th

Let f(x) = $\frac{x - 1}{x + 1}, x \in R - {0, - 1, 1} .$ If $f^{n + 1} (x) = f (f^{n} (x)) f o r a l l n \in N,$ then f⁶ (6) + f⁷ (7) is equal a to

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Payal Gupta

Contributor-Level 10

$f (x) = \frac{x - 1}{x + 1} \Rightarrow f (f (x)) = \frac{\frac{x - 1}{x + 1} - 1}{\frac{x - 1}{x + 1} + 1} = - \frac{1}{x}$

$f^{3} (x) = - \frac{x + 1}{x - 1} \Rightarrow f^{4} (x) = \frac{\frac{x - 1}{x + 1} + 1}{\frac{x - 1}{x + 1} - 1} = x$

$S o, f^{6} (6) + f^{7} (7) = f^{2} (6) + f^{3} (7)$

= $- \frac{1}{6} - \frac{7 + 1}{7 - 1} = - \frac{9}{6} = - \frac{3}{2}$

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8 months ago

Maths Matrices Maths NCERT Exemplar Solutions Class 12th Chapter Three

Let A = $[a_{i j}]$ be a square matrix of order 3 such that aij = 2ji, for all I, j = 1, 2, 3. Then, the matrix $A^{2} + A^{3} + . . . + A^{10}$ is equal to:

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alok kumar singh

Contributor-Level 10

$A = [\begin{matrix} 1 & 2 & 4 \\ \frac{1}{2} & 1 & 2 \\ \frac{1}{4} & \frac{1}{2} & 1 \end{matrix}]$

$A^{2} =$ $[\begin{matrix} 1 & 2 & 4 \\ \frac{1}{2} & 1 & 2 \\ \frac{1}{4} & \frac{1}{2} & 1 \end{matrix}] [\begin{matrix} 1 & 2 & 4 \\ \frac{1}{2} & 1 & 2 \\ \frac{1}{4} & \frac{1}{2} & 1 \end{matrix}]$

$= 3 [\begin{matrix} 1 & 2 & 4 \\ \frac{1}{2} & 1 & 2 \\ \frac{1}{4} & \frac{1}{2} & 1 \end{matrix}]$

A² = 3A

A³ = 3A²

A³ = 3²A

A⁴ = 3³A

Aⁿ = 3^n-1A

now, A² + A³ +….+A¹⁰

= 3A + 3² A +…. + 3⁹A

= 3A (1 + 3 +….+ 3⁸

$= 3 A \cdot \frac{(3^{9} - 1)}{3 - 1}$

$= \frac{3^{10} - 3}{2} A$

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8 months ago

Maths Matrices Maths NCERT Exemplar Solutions Class 12th Chapter Three

If the system of linear equations

2x + y – z = 7

x – 3y + 2z = 1

x + 4y + $δ z = k,$ where $δ, k \in R$

has infinitely many solutions, then $δ + k$ is equal to:

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alok kumar singh

Contributor-Level 10

$= | \begin{matrix} 2 & 1 & - 1 \\ 1 & - 3 & 2 \\ 1 & 4 & δ \end{matrix} | = 0 \Rightarrow δ = - 3$

and $Δ_{1} = | \begin{matrix} 7 & 1 & - 1 \\ 1 & - 3 & 2 \\ k & 4 & - 3 \end{matrix} | = 0 \Rightarrow k = 6$

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8 months ago

Maths Matrices Maths NCERT Exemplar Solutions Class 12th Chapter Three

The probability that a randomly chosen 2 * 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to:

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alok kumar singh

Contributor-Level 10

Set of first 10 prime numbers

= {2,3,5,7,11,13,17,19,23,29,31}

So sample space = 104.

Favourable cases

So required probability

$= \frac{10 + 4 *^{10} ? C_{2}}{1 0^{4}} = \frac{10 + \frac{4 * 10.9}{2}}{1 0^{4}} = \frac{19}{1000}$

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a year ago

Maths Matrices Maths Spl

Where can I find Class 12 Maths Matrices NCERT Solutions?

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Piyush Vimal

Beginner-Level 5

NCERT Textbooks helps student to get clear understanding of the fundamental concepts and usage of concepts in various problems. Students must solve NCERT Textbooks before advancing their prep. Candidates also some time get stuck while solving the NCERT questions. Candidates can take help of NCERT Solutions of class 12th Maths, we have prepared complete solution of Class 12thMathematics of all chapters with help of experts. Below given are links to get solution of class 12 Matrices chapter;

Class 12 Matrices NCERT Solution

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Maths Matrices CBSE 12th

What are the important topics in Matrices in Class 12th Maths?

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Anushree Tiwari

Beginner-Level 5

Class 12th Matrices is very significant chapter in CBSE Boards. There are several important topics in Matrices, students can check few of the m below;

Types of Matrices: Row Matrix, Column Matrix, Square Matrix, Diagonal Matrix, Scalar Matrix, Identity Matrix, Zero Matrix, Upper and Lower Triangular Matrices
Matrix Operations: Addition, Subtraction, Scalar Multiplication, and Matrix Multiplication (Properties and Rules)
Transpose of a Matrix: Properties of Transpose, Symmetric and Skew-Symmetric Matrices
Determinants of Matrices: Determinant of a 2*2 and 3*3 Matrix, Properties of Determinants, and Adjoint & Inverse of a Matrix
Cofacto

...more

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a year ago

Maths Matrices JEE

What is the weightage of Matrices in JEE Mains Exam?

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Pallavi Arora

Beginner-Level 5

Matrices is generally combined with determinants, Matrices and Determinants carry significant weightage in the competitive exams. Matrices carries a weightage of around 6-8% of the total marks in JEE Mains. Students can expect 1-2 questions in JEE Mains from this chapter. Students must have a clear conceptual understanding of the syllabus to perform better. Students can take help of NCERT soluition of Matrcies chapter to build strong foundation of this chapter.

There are several important Topics in Matrices for JEE Mains such as Types of Matrices, Operations on Matrices, Adjoint and Inverse of a Matrix, solving system of Linear Eq

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