WBCS Mains 2020 Official Paper-VI

If $a+b+c=0$, then $\frac{1}{x^b+x^{-c}+1}+\frac{1}{x^c+x^{-a}+1}+\frac{1}{x^a+x^{-b}+1}$ is equal to:

In an examination, $34\%$ of the candidates fail in Bengali and $42\%$ in English. If $20\%$ fail in Bengali and English, the percentage of those passing in both subjects is:

Mohit went to a shop to buy $50\text{kg}$ of rice. He buys two varieties of rice which cost him $\text{Rs. }4.50$ per kg and $\text{Rs. }5$ per kg. He spends a total of $\text{Rs. }240$. What was the quantity of less expensive rice bought by him?

The ratio of syrup and water in $30$ litre of a mixture is $1:5$, then the amount of water required to mix to make the ratio $1:6$ is:

In an examination $75\%$ passed in Maths, $80\%$ passed in Bengali, $65\%$ in both and $45$ students failed in both subjects. Then the number of students appeared are: