NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.3

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.3 is provided in this article. Chapter 6 Exercise 6.3 includes questions that deal with concepts of tangents and normals. The exercise includes a total of 27 questions.

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Check out solutions of Class 12 Maths NCERT solutions chapter 6 Exercise 6.3:

Check out other exercise solutions of Class 12 Maths Chapter 6 Applications of Derivatives:

Class 12 Chapter 6 Applications of Derivatives Topics:

Linear Approximation Formula	Approximations	Differential Calculus approximation
Linear Interpolation Formula	Derivatives formula	Interpolation Formula
Lagrange Interpolation Formula	Maxima and Minima	Increasing and Decreasing Functions

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Difference between in Maths	Math Study Notes
Math Formula	Math MCQs	Calculus
Algebra	Mensuration	Trigonometry

CBSE CLASS XII Related Questions

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
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2.
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as

(i) Find \(f'(x)\) for \(0<x>3\).
(ii) Find \(f'(4)\).
(iii)(a) Test for continuity of \(f(x)\) at \(x=3\).
OR
(iii)(b) Test for differentiability of \(f(x)\) at \(x=3\).
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3.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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4.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.
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5.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.
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6.
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.
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