If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3}$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

Fructose reduces Tollen's reagent due to

$A$ body is thrown vertically upwards and reaches its maximum height in $t$ seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,then the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

The equation of the image of the circle $x^2 + y^2 + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is

$6.023 \times 10^{22}$ molecules are present in $10 \ g$ of a substance $x$. The molarity of a solution containing $5 \ g$ of substance $x$ in $2 \ L$ of solution is $\dots \dots \dots \times 10^{-3} \ M$.