Assignment -1 Questions (20)

The relation R defined in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x} is

Which of the following functions from Z into Z are bijections?

Assertion (A): The possible number of reflexive relations of a set A whose n(A) = 4 is 212. Reason (R): Number of reflexive relation on a set contain n elements is \(2^{n^2-n}\).

Let S be the set of all real numbers and let R be a relation on S, defined by a Rb \(\Leftrightarrow\) (1 + ab) > 0. Then, R is

The principal value of cos-1 \(\left(\frac{\sqrt{3}}{2}\right)\) is

The principal value of \(\sin ^{-1}\left(\sin \left(-\frac{10 \pi}{3}\right)\right)\) is:

The value of sin (2 sin–1 (0.6)) is

Let f : \(N \rightarrow N: f(n)=\left\{\begin{array}{l} \frac{1}{2}(n+1), \text { when } n \text { is odd } \\ \frac{n}{2}, \text { when } n \text { is even. } \end{array}\right.\) then, f is

Assertion (A): Domain of \({y}=\cos ^{-1}(x)\) is \([-1,1]\). Reason (R): The range of the principal value branch of \({y}=\cos ^{-1}(x)\) is \([0, \pi]-\left\{\frac{\pi}{2}\right\}\).

Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = {a, b, c}. Then, R is

The value of x satisfies the inequality [tan-1x]2 - 2 [tan-1x] - 3 \(\leq\) 0, where [\(\cdot\)] represent greatest integer function, then x lies between

Range of sec-1x is

The value of sin-1\(\left(\cos \frac{3 \pi}{5}\right)\) is

Given an arbitrary equivalence relation R in an arbitrary set X, R divides X into

\({\sin ^{ - 1}}\left( {\frac{1}{{\sqrt 5 }}} \right) + {\cot ^{ - 1}}(3) = \)

if \(\theta = co{s^{- 1}}\left( {\frac{1}{x}} \right),\) then tan θ is equal to

f : N \(\rightarrow\) N : f(x) = x2 + x + 1 is

Let A = {2, 3, 4, 5, …, 17, 18}. Let \(\simeq\) be the equivalence relation on A \(\times\) A, cartesian product of A with itself, defined by (a, b) \(\simeq\) (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is

If A and B have 4 and 6 elements respectively then the number of one-one function from A to B is

Which of the following functions from\(A=\{x:-1 \leq x \leq 1\}\) to itself are bijections?