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:

Let a relation R = {(a, b) : a is a factor of b, a, b $\in$ N}. Then, R is ______.

Assume that R is a relation on the set Z of integers and it is given by $(x, y) \in R \Leftrightarrow |x - y| \leq 1$. Then, R is

Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$, given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$, given by $g(x)=\cos x$, Where R is a set of real numbers, Which of the following statements are correct?

(A) f and g are one-one

(B) f and g are not one-one

(C) f+g is not one-one

(D) f+g is one-one

Choose the correct answer from the options given below:

For the relations $R_1, R_2, R_3, R_4$ defined on the set $A = \{1,2,3\}$,

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Let a function $f:\mathbb{R}\to\mathbb{R}$ defined as $f(x)=x-[x]$, (where $\mathbb{R}$ is set of real numbers & $[.]$ denotes greatest integer function) .Then the function:

Which of the following is true on the basis of above diagram?