There are two families A and B. There are 4 men, 2 women and 1 child in family A
Chapter 3 Matrices Class 12 Maths
There are two families A and B. There are 4 men, 2 women and 1 child in family A and 2 men, 3 women and 2 children in family B. They recommended daily allowance for calories i.e. Men: 2000, Women: 1500, Children: 1200 and for proteins is Men: 50 gms., Women: 45 , Children: 30 gms. Represent the above information by matrices, using matrix multiplication calculate the total requirements of calories and proteins for each of the families.

Exercise 6.3 Question 18 prove that the function given by
Updated
October 8, 2022, 4:10 pm
Exercise 6.3 Question 18: Prove that the function given by {\displaystyle f(x) = x^3 - 3{x^2} + 3x - 100 } is increasing in R.

Show that the function given by f (x) = sin x is
Updated
October 8, 2022, 4:02 pm
NCERT Exercise 6.2 Question 3: Show that the function given by {\displaystyle f(x) = \sin x } (a) increasing in {\displaystyle \left ( 0, \frac{\pi}{2} \right ) } (b) decreasing in {\displaystyle \left ( \frac{\pi}{2}, \pi \right ) } (c) neither increasing nor decreasing in {\displaystyle (0, \pi) }

Find the integral of sinx over 1 plus sinx
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October 8, 2022, 3:44 pm
Question: Show that {\displaystyle \int{\frac{\sin x}{1 + \sin x}} = \sec x - \tan x + x + \text{C} }

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground
Updated
September 20, 2022, 4:00 pm
NCERT Exercise 6.1 Question 10 A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

If x sin t and y sin pt prove that
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September 18, 2022, 10:09 am
If {\displaystyle x = \sin t} and {\displaystyle y = \sin pt } , prove that {\displaystyle (1 - x^2)\frac{d^{2}y}{dx^2} - x\frac{dy}{dx} + p^2y = 0 } .

If then show that dy over dx times dx over dy equals 1
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September 18, 2022, 9:59 am
If {\displaystyle a x^2 + 2hxy + b y^2 + 2gx + 2fy + c = 0 } , then show that {\displaystyle \frac{dy}{dx} . \frac{dx}{dy} = 1 } .

NCERT Example – 47 Continuity and Differentiability Chapter 5
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September 18, 2022, 9:42 am
NCERT Example – 47 Continuity and Differentiability Chapter 5: Find {\displaystyle \frac{dy}{dx} } in the following parametric function {\displaystyle x = a^{\left ( t+\frac{1}{t} \right )}, y = {\left ( t+\frac{1}{t} \right )}^a} .

y = (log x)^x + (sin^(-1)x)^(sin x)
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September 18, 2022, 9:06 am
Differentiate the following function w. r. t. x, Question 12: {\displaystyle y = (\log x)^x + (\sin^{-1}x)^{\sin x} }

Find the derivative of the following function w.r.t x
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September 17, 2022, 10:25 am
Question: Find the derivative of the following function w.r.t x, {\displaystyle y = \cos^{-1}\left( \frac{a + b\cos x}{b + a \cos x} \right) }

Find the value of k, if the following function is continuous
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September 17, 2022, 10:13 am
Question 8. Find the value of k, if the following function is continuous {\displaystyle f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} }

If (x - a)^2 + (y - b)^2 = c^2 is a constant independent of a and b.
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September 16, 2022, 2:07 pm
Question 15. If { \displaystyle (x - a)^2 + (y - b)^2 = c^2 } , for some c > 0, prove that {\displaystyle \frac{\left[ 1 + \left( \frac{dy}{dx}\right )^2 \right ]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} } is a constant independent of a and b.

Continuity and Differentiability Class 12 Maths NCERT Exercise – 5.7 Question – 14
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September 20, 2022, 4:09 pm
Question 14. If { \displaystyle y = Ae^{mx} + Be^{nx}} , show that { \displaystyle \frac{d^2{y}}{dx^2} - (m + n)\frac{dy}{dx} + mny = 0 } .

Ch05. Continuity and Differentiability Class 12 Maths NCERT Exercise – 5.6 Question – 7
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September 20, 2022, 4:13 pm
Question 7 : { \displaystyle x = \frac{\sin^3{t}}{\sqrt{\cos 2t}}, y = \frac{\cos^3{t}}{\sqrt{\cos 2t}} }

NCERT Example 26 Chapter 5 Class 12 Maths Find the derivative of f given by
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September 16, 2022, 2:07 pm
Example 26 Find the derivative of f given by { \displaystyle f(x) = \sin^{–1} x } assuming it exists.

Find the value of a, if the following function is continuous
Updated
September 16, 2022, 2:08 pm
Find the value of a, if the following function is continuous
Question 17: {\displaystyle f(x) = \begin{cases} a \sin \frac{\pi }{2} (x+1), & \text{ if } x \le 0 \\ \frac{\tan x-\sin x}{x^{3} }, & \text{ if } x > 0 \end{cases}}

Given a square matrix of order 3×3 such that | A | = 12 find the value of ∣A adj(A)∣
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November 1, 2022, 5:13 am
Question: Given a square matrix of order 3×3 such that | A | = 12 find the value of ∣A adj(A)∣

Express the following matrices as the sum of symmetric and a skew symmetric matrix
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October 2, 2022, 10:23 pm
Question 4. Express the following matrices as the sum of symmetric and a skew symmetric matrix: {\displaystyle {\begin{bmatrix} 2&{ - 2}&{ - 4}\\ { - 1}&3&4\\ 1&{ - 2}&{ - 3} \end{bmatrix}} }

Show that the matrix B′AB is symmetric or skew symmetric according
Updated
November 1, 2022, 5:14 am
NCERT Miscellaneous Exercise Question 5 : Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Show that AB is a zero matrix, provided θ − ϕ is an odd multiple of π over 2
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September 16, 2022, 2:48 pm
Question 7. If {\displaystyle A = { \begin{bmatrix} {\cos^2\theta} & {\cos \theta \sin \theta} \\ {\cos \theta \sin \theta } & {\sin^2 \theta} \end{bmatrix} } } , {\displaystyle B = {\begin{bmatrix} {\cos^2 \phi} & { \cos \phi \sin \phi } \\ {\cos \phi \sin \phi } & {\sin^2 \phi } \end{bmatrix}} } then show that AB is a zero matrix, provided {\displaystyle (\theta - \phi )} is an odd multiple of {\displaystyle \frac{\pi }{2}} .

Simplify sin inverse 5 over 13 cos x plus 12 over 13 sin x RD Sharma Question
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November 1, 2022, 5:14 am
Simplify: {\displaystyle \sin ^{-1} \left ( \frac{5}{13} \cos x+\frac{12}{13} \sin x \right ) }

NCERT Exercise 2.2 Question 9 Inverse Trigonometric Functions
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November 1, 2022, 5:14 am
NCERT Exercise 2.2 Question 9 Inverse Trigonometric Functions { \displaystyle {\tan }^{-1} \left ( \frac{x}{\sqrt{a^2-x^2}} \right ), | x | < a}

Check if a function is one-one and onto
Updated
November 1, 2022, 5:14 am
Question. Let A = R – {3} and B = R – {1}. Consider the function {\displaystyle f: A \rightarrow B } defined by {\displaystyle f(x) = \frac{x-2}{x-3} } . Is f one-one and onto? Justify your answer.

Equivalence Relations and Equivalence Classes
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November 1, 2022, 5:14 am
A relation R on set A is said to be reflexive if (a, a) ∈ R, ∀ a ∈ A or aRa,∀a ∈ A symmetric if(a, b) ∈ R ⇒ (b, a) ∈ R, ∀ a, b ∈ A or aRb ⇒ bRa,∀ a, b ∈ A transitive if (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R, ∀ a, b, c ∈ A or aRb and bRc ⇒ aRc , ∀ a, b, c ∈ A If a relation is reflexive, symmetric and transitive then the relation is said to be equivalence relation.