1
IIT-JEE 2001
Subjective
+6
-0
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that

the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$


represents a straight line.
2
IIT-JEE 2001
Subjective
+4
-0
Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta $$ be the roots of the equation $$a{x^2} + bx + c = 0$$. Express the roots of $${a^3}{x^2} + abcx + {c^3} = 0$$ in terms of $$\alpha ,\,\beta \,$$.
3
IIT-JEE 2001
MCQ (Single Correct Answer)
+2
-1

One quarter section is cut from a uniform circular disc of radius $R$. This section has a mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

IIT-JEE 2001 Physics - Rotational Motion Question 3 English
A

$\dfrac{1}{2} MR^2$

B

$\dfrac{1}{4} MR^2$

C

$\dfrac{1}{8} MR^2$

D

$\sqrt{2} MR^2$

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