IPMAT Indore Algebra > Identities PYQs

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Q1:

IPMAT Indore 2026

Algebra > Identities

Hard

Positive reals $x, y$ satisfy $x \neq y$ and $\frac{x^2 + y^2}{xy} = k$. If replacing $x$ by $x + y$ and $y$ by $|x - y|$ leaves the value of $k$ unchanged, then $k$ equals

$2\sqrt{2}$

$\sqrt{2}$

Correct Answer

Option 2

Correct Answer

Explanation →

Q2:

IPMAT Indore 2019

Algebra > Identities

Hard

If $a, b, c$ are real numbers and $a^2 + b^2 + c^2 = 1$, then the set of values $ab + bc + ca$ can take is:

[-1,2]

[-$\frac{1}{2}$, 2]

[-1,1]

[-$\frac{1}{2}$, 1]

Correct Answer

Option 4

Correct Answer

Explanation →