1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
What is the largest area of a rectangle, whose sides are parallel to the coordinate axes, that can be inscribed under the graph of the curve $y=1-x^2$ and above the $x$-axis?
A
$\frac{2}{3 \sqrt{3}}$
B
$\frac{4}{3 \sqrt{3}}$
C
$\frac{1}{3}$
D
$\frac{4}{3}$
2
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1
Let $\alpha$ be a real number. What is the total number of distinct point(s) of intersection between the parabola $y=x^2+4 x \sin \alpha+6$ and the pair of lines $y^2=1$ ?
A
Zero
B
One
C
Two
D
Four
3
IAT (IISER) 2023
MCQ (Single Correct Answer)
+4
-1
Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true
A
$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$.
B
$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$
C
$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and decreasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.
D
$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and increasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.
4
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1

Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,

$$ \left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4 $$

and

$$ \frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5} $$

Then $f(5)=$

A
25
B
35
C
55
D
105
IAT (IISER) Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12