1
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

If $p(t)=\frac{t(t-1) \cdots(t-2019)}{2019!}$, then the value of

$$ \int_0^1\left(\frac{1}{t+1}+\frac{1}{t+2}+\cdots+\frac{1}{t+2020}\right) p(-t-1) d t $$

is:

A
$2019^2$
B
2019
C
$2020^2$
D
2020
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
Let $a, b$ be nonzero real numbers. If $p(x)=x^n+c_{n-1} x^{n-1}+\cdots+c_0$, where $c_{n-1}, \ldots, c_0$ are integers and $n \geq 3$, then which of the following statements is correct?
A
If $a+i b$ is a root of $p(x)$, then $n$ must be even.
B
If $a$ is a root of $p(x)$, then $n$ must be odd.
C
If $a+i b$ is a root of $p(x)$, then $(a+i b)^2$ can never be a root of $p(x)$.
D
If $a$ is a root of $p(x)$, then $a$ must be an integer.
3
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
The number of skew-symmetric matrices $A=\left[a_i j\right]_{3 \times 3}$, where $a_i j \in\{-3,-2,-1,0,1,2,3\}$ is:
A
$7^3$
B
$3^7$
C
$21^3$
D
$7^6$
4
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

$$ \text { Define binary operation * on } Q \text { by } a * b=a+b-3 \text {. The inverse of } 2 \text { with respect to * is } $$

A
4
B
2
C
3
D
5
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