1
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 $$\sum\limits_{n = 0}^{18} {} $$
2
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.
3
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
$t=-1$
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