If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0, a \ne 0,$ will be

$A$ physical quantity $X$ is given by $X = \frac{2 k^3 \ell^2}{m \sqrt{n}}$. The percentage errors in the measurement of $k, \ell, m,$ and $n$ are $1\%, 2\%, 3\%,$ and $4\%$ respectively. The percentage uncertainty in the value of $X$ is: (in $\%$)

If one of the lines in the pair of straight lines given by $4x^2+6xy+ky^2=0$ bisects the angle between the coordinate axes,then $k \in$

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - x - 1 = 0$. If $p_k = (\alpha)^k + (\beta)^k$ for $k \geq 1$,then which one of the following statements is not true?

Urea upon hydrolysis yields:

$A$ tetrahedron has vertices at $O(0, 0, 0)$,$A(1, 2, 1)$,$B(2, 1, 3)$,and $C(-1, 1, 2)$. The angle between the faces $OAB$ and $ABC$ is: