NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.1

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.1 is given in this article. Chapter 6 Applications of Derivatives Exercise 6.1 includes questions on the introduction of derivatives and the rate of change of quantities. The exercise includes a total of 18 questions including 10 long questions, 6 short questions and 2 MCQs.

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Class 12 Chapter 6 Applications of Derivatives Topics:

Increasing Decreasing Functions	Tangents and Normals	Approximations
Maxima and Minima	Derivatives formula	Interpolation Formula
Lagrange Interpolation Formula	Linear Approximation Formula	Linear Interpolation Formula
Linear Regression Formula	Differential Calculus approximation	Newton Method Formula

CBSE Class 12 Mathematics Study Guides:

Math MCQs	Difference between in Maths	Math Study Notes
NCERT Solutions for Class 12 Maths	Calculus	Math Formula
Algebra	Mensuration	Trigonometry
Permutation and Combination	Arithmetic	Geometry

CBSE CLASS XII Related Questions

1.
If \( y\sqrt{x^2+1} = \log (\sqrt{x^2+1}-x) \), show that \( (x^2+1) \frac{dy{dx} + xy + 1 = 0 \).}
View Solution
2.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).
View Solution
3.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).
View Solution
4.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}
View Solution
5.
Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{-x-3}{-5} = \frac{1-y}{-2} = \frac{3z+12}{9} \) and hence find the length of the perpendicular.
View Solution
6.
Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \).
View Solution

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.1

CBSE CLASS XII Related Questions

1.
If \( y\sqrt{x^2+1} = \log (\sqrt{x^2+1}-x) \), show that \( (x^2+1) \frac{dy{dx} + xy + 1 = 0 \).}

2.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

3.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

4.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

5.
Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{-x-3}{-5} = \frac{1-y}{-2} = \frac{3z+12}{9} \) and hence find the length of the perpendicular.

6.
Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \).

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives Exercise 6.1

CBSE CLASS XII Related Questions

1.If \( y\sqrt{x^2+1} = \log (\sqrt{x^2+1}-x) \), show that \( (x^2+1) \frac{dy{dx} + xy + 1 = 0 \).}

2.Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

3.If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

4.Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

5.Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{-x-3}{-5} = \frac{1-y}{-2} = \frac{3z+12}{9} \) and hence find the length of the perpendicular.

6.Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If \( y\sqrt{x^2+1} = \log (\sqrt{x^2+1}-x) \), show that \( (x^2+1) \frac{dy{dx} + xy + 1 = 0 \).}

2.
Evaluate : \( \int_0^2 \frac{1}{\sqrt{x^2 + 2x + 3}} \, dx \).

3.
If \( \vec{a} \), \( \vec{b} \) and \( \vec{c} \) are unit vectors, then prove that \( |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 \leq 9 \).

4.
Sketch the graph defined by \( \left\{ (x, y) : \frac{x^2{25} + \frac{y^2}{25} = 1 \right\} \). Find the area of the region of minor segment cut off by the line \( x = \frac{5}{2} \), using integration.}

5.
Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{-x-3}{-5} = \frac{1-y}{-2} = \frac{3z+12}{9} \) and hence find the length of the perpendicular.

6.
Find : \( \int \frac{x - \sin x}{1 - \cos x} \, dx \).