## 15 Questions

In the given context, which property does the relation R={(x, y) : 3x - y = 0} satisfy?

Transitive

For the relation R={(x, y) : y = x + 5 and x < 4}, which property is violated?

Symmetric

Which property is violated by the relation R={(x, y) : y is divisible by x} in the set A={1, 2, 3, 4, 5, 6}?

Transitive

Which property is violated by the relation R={(x, y) : x - y is an integer} in the set of all integers?

Reflexive

For the relation R={(x, y) : x is father of y}, which property does it satisfy?

None of the above

If $y = \cos^{-1}(\frac{\sqrt{3}}{2})$, what is the principal value of $y$?

$\frac{\pi}{3}$

What is the principal value of $\sin^{-1}(-2)$?

$-\frac{\pi}{6}$

What is the principal value of $\csc^{-1}(2)$?

$\frac{\pi}{6}$

If $y = \tan^{-1}(-1)$, what is the principal value of $y$?

$-\frac{\pi}{4}$

What is the principal value of $y$ if $y = \cos^{-1}(-1/2)$?

$-\frac{5\pi}{6}$

What is the principal value of $\sin^{-1}(-2)$?

$-\frac{\pi}{6}$

If $y = \cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$, what is the principal value of $y$?

$\frac{\pi}{3}$

What is the principal value of $\csc^{-1}(2)$?

$\frac{\pi}{6}$

If $y = \tan^{-1}(-1)$, what is the principal value of $y$?

$-\frac{\pi}{4}$

What is the principal value of $y$ if $y = \tan^{-1}(1)$?

$\frac{\pi}{4}$

Test your understanding of relations and functions with NCERT solutions for Class 12 Maths Chapter 1. Determine the properties of given relations including reflexive, symmetric, and transitive.

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