Let X be a non-empty set and let P be the collection of all subsets of X. Let R be a relation in P, defined by $R = \{(A, B): A \text{ is subset of } B\}$. Then, R is

A. Reflexive relation

B. Symmetric relation

C. Not a transitive relation

D. Transitive relation

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The domain of the function $\cos^{-1}(2x - 3)$ is

Consider a function $f:[-1,1] \to Y$ defined as $f(x)=\dfrac{x}{x+2}$ and $Y=range(f(x))$, then which of following statements are correct?

(A) Function $f(x)$ is one-one

(B) Function $f(x)$ is not one-one

(C) Function $f(x)$ is onto

(D) Function $f(x)$ is invertible

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The function $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = |x|$ ($\mathbb{R}$ is the set of real numbers) is

A relation $R$ on set of real numbers $(\mathbb{R})$ is defined as $R = \{(a,b): a \le b, a,b \in \mathbb{R}\}$. The relation is :

Let $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is :

A manufacturer can sell $x$ items at a price of Rs $3x+5$ each. The cost price of $x$ items is Rs $x^2 + 5x$. If x is the number of items she should sell to get no profit and no loss, then: