Mathematics Tes...

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability they are both yellow?

A stone tied to the end of a string \(80 \mathrm{~cm}\) long is whirled in a horizontal circle with a constant speed. If the stone make \(14\) revolutions in \(25 \mathrm{~sec}\), what is the magnitude of the acceleration of the stone?

An external force of \(1 \mathrm{~N}\) is applied on the block of \(1 \mathrm{~kg}\) as shown in the figure. The magnitude of the friction force \(F_{s}\) is (where, \(\mu=0.3, g=10 \mathrm{~m} / \mathrm{s}^{2}\) ):

The relation \(|3-z|+|3+z|=5\) represents:

If \(a+b+c=18, a^{2}+b^{2}+c^{2}=110\) and \(a^{3}+b^{3}+c^{3}=684\), then find the value of \(a b c\).

If \(x=\frac{\sqrt{3}}{2}\), then the value of \(\left(\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}\right)\) is:

A \(5 ~m\) long ladder is resting on a smooth vertical wall with its lower end \(3 ~m\) from the wall. What should be the coefficient of friction between the ladder and the floor for equilibrium?

The critical point and nature for the function \(\mathrm{f}(\mathrm{x}, \mathrm{y})=\mathrm{x}^{2}-2 \mathrm{x}+2 \mathrm{y}^{2}+4 \mathrm{y}-2\) is: