NCERT Solutions for Class 11 Maths Chapter 5 Exercise 5.1

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Class 11 Maths NCERT Solutions Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.1 is based on following concepts:

Complex Numbers
Algebra of Complex Number
Modulus and the Conjugate of a Complex Number

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CBSE CLASS XII Related Questions

1.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines $ \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) $ and $ \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) $ and parallel to the line $ \frac{x - 1}{-2} = \frac{7 - y}{-3} = z $.
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2.
A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is
- Reflexive only
- Reflexive and Transitive
- Symmetric and Transitive
- Symmetric only
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3.
Which of the following equations is NOT a Linear Differential Equation?
- $(1 + x^2) \, dy + 2xy \, dx = \cot x \, dx$
- $y + \frac{d}{dx}(xy) = x(\sin x + \log x)$
- $x(1 + y^2) \, dx - y(1 + x^2) \, dy = 0$
- $y \, dx - (x + 3y^2) \, dy = 0$
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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:

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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6.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.