The radius of the sphere $x^2+y^2+z^2=12x+4y+3z$ is

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

The equation of trajectory of a projectile is $y=10 x-\left(\frac{5}{9}\right) x^2$. If we assume $g=10 \ m/s^2$,the range of the projectile (in metres) is:

The work done in moving an object from the origin to a point whose position vector is $r = 3 \hat{i} + 2 \hat{j} - 5 \hat{k}$ by a force $F = 2 \hat{i} - \hat{j} - \hat{k}$ is:

$\int \frac{3^x dx}{\sqrt{9^x-1}}$ is equal to

The sensitivity of a galvanometer that measures current is decreased by $\frac{1}{40}$ times by using a shunt resistance of $10 \Omega$. Then,the value of the resistance of the galvanometer is (in $Omega$)