1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Let $f: Q \rightarrow Q$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbf{Q}$, and $f(1)=$ 10. Which one of the following statements is Correct?
A
$f$ is neither injective nor surjective
B
$f$ is injective but not surjective
C
$f$ is surjective but not injective
D
$f$ is bijective
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

    Let $[x]$ denote the greatest integer less than or equal to $x$. The number of positive integer solutions of the equation

    $$ \left[\frac{x}{19}\right]=\left[\frac{x}{20}\right] $$

    are:

A
190
B
188
C
189
D
187 $$\sum\limits_{n = 0}^{18} {} $$
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions such that

$$ g \circ f(x)= \begin{cases}x^2, & \text { if } x \geq 0 \\ e^x-1, & \text { if } x<0\end{cases} $$

Then which of the following statements is correct?

A
$g$ is onto.
B
$f$ is onto.
C
$g$ is one-one.
D
$f$ is one-one.
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
For what value of $t$ does $f(x)=x^3+t x^2+(2-t) x-3$ have only real roots?
A
$t=0$.
B
$t=4$.
C
$t=2$.
D
$t=-1$
IAT (IISER) Subjects
EXAM MAP