'Amoebiasis' (amoebic dysentery) is caused by

The area (in square units) of the triangle formed by $x+y+1=0$ and the pair of straight lines $x^2-3xy+2y^2=0$ is

Half-life of a radioactive substance is $20 \ minutes$. The time between $20\%$ and $80\%$ decay will be ........... $minutes$.

Two adjacent sides of a parallelogram $ABCD$ are given by $\overline{AB}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overline{AD}=-\hat{i}+2 \hat{j}+2 \hat{k}$. The side $AD$ is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that $AD$ becomes $AD^{\prime}$. If $AD^{\prime}$ makes a right angle with side $AB$,then the cosine of the angle $\alpha$ is given by

Which of the following cations cannot give the borax bead test?

Which one of the following statements is incorrect?