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.
Evaluate:
\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]
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2.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
View Solution
3.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).
- \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
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4.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
5.
Find:

If \[ (3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0} \] then find the values of \(p\) and \(q\).
- \(p = -\frac{2}{3}, \, q = \frac{5}{3}\)
- \(p = -\frac{8}{3}, \, q = \frac{20}{3}\)
- \(p = \frac{20}{3}, \, q = -\frac{8}{3}\)
- \(p = 0, \, q = 0\)
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6.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- \(-\frac{\pi}{2}\)
- \(-\frac{\pi}{4}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
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