If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^{2}-10x+15= 0$, then find the quadratic equation whose roots are $\bigg(\alpha+\dfrac{\alpha }{\beta }...

If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true?$c^{2}\geq a^{2}$$c^{4}\geq a^{2}(b^{2}...

The side of an equilateral triangle is $10$ cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same. The triangle is di...

A student is asked to form numbers between $3000$ and $9000$ with digits $2,3,5,7$ and $9$. If no digit is to be repeated, in how many ways can the student do so?$24$$12...

When asked for his taxi number, the driver replied, “If you divide the number of my taxi by $2,3,4,5,6$ each time you will find a reminder of one. But, if you divide it...