12
Jan
2021

### Question of the Day

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A group of individuals contains ten people with blood group O, five with group A and five with group B. Give a formula for the probability that a random sample of size six will contain two people with each blood group.

11
Jan
2021

### Question of the Day

An athlete conceals two performance enhancing tablets in a bottle containing eight vitamin tablets that are similar in appearance. If three tablets are selected at random for testing by drugs surveillance officials, what is the probability the cheating will be detected? You may assume that analysis is not error prone, i.e. if a performance enhancing... Read More

10
Jan
2021

### Question of the Day

Locate the global maximum point on the curve $y=xe^{-x^2}$.

9
Jan
2021

### Question of the Day

Find the inflexion point on $y=e^{-x^2}$.

8
Jan
2021

### Question of the Day

Prove that $1 + x < e^x < \frac{1}{1-x}$ for all $x\in(0,1)$.

7
Jan
2021

### Question of the Day

Prove that $e^a (b-a) < e^b – e^a < e^b(b-a)$ for all $a<b$ in $\mathbb{R}$.

6
Jan
2021

### Question of the Day

Consider the non-zero real-valued function $exp$ on the reals such that $exp(a+b)=exp(a)exp(b)$ and $exp'(a)=exp(a)$ for all real values of $a$ and $b$. Prove that this function is strictly increasing.

5
Jan
2021

### Question of the Day

Where does the following converge $\int_{1}^{\infty} e^{-\alpha x} dx$?

4
Jan
2021

### Question of the Day

For what values of $\alpha$ will $\int_1^\infty \! x^{-\alpha} \, \mathrm{d}x$ converge?

3
Jan
2021

### Question of the Day

Show that $f(x) = x^4 – 3x^2 + 1$ has two positive and two negative roots.