On the interval $[0, 1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

If the polar of a point on the circle $x^2+y^2=p^2$ with respect to the circle $x^2+y^2=q^2$ touches the circle $x^2+y^2=r^2$,then $p, q, r$ are in

If $A$ is a square matrix such that $A(\operatorname{adj} A) = \begin{bmatrix} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{bmatrix}$,then $\operatorname{det}(\operatorname{adj} A)$ is equal to

Which of the following magnetic properties is exhibited by the compounds of alkaline earth metals?

If $x=a\left\{\cos \theta+\log \tan \left(\frac{\theta}{2}\right)\right\}$ and $y=a \sin \theta$,then $\frac{d y}{d x}$ is equal to

If \(x_1\) be the size of the magnified image and \(x_2\) the size of the diminished image in Lens Displacement Method, then the size of the object is :