IAT (IISER) 2020 | IAT (IISER) Year Wise Previous Years Questions

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?

If $a+i b$ is a root of $p(x)$, then $n$ must be even.

If $a$ is a root of $p(x)$, then $n$ must be odd.

If $a+i b$ is a root of $p(x)$, then $(a+i b)^2$ can never be a root of $p(x)$.

If $a$ is a root of $p(x)$, then $a$ must be an integer.

IAT (IISER) 2020

MCQ (Single Correct Answer)

-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:

$7^3$

$3^7$

$21^3$

$7^6$

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

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

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