WBCS Mains 2021 (Held On May 2022) Official Paper-VI

A boy recorded the weights of some of his friends as $32\text{ kg}$, $30\text{ kg}$, $40\text{ kg}$, $65\text{ kg}$, $54\text{ kg}$, $38\text{ kg}$, $36\text{ kg}$, $45\text{ kg}$, $50\text{ kg}$, $52\text{ kg}$, and $40\text{ kg}$. What is the median?

If $\frac{x}{y}=\frac{a+2}{a-2}$, then find the value of $\frac{x^2-y^2}{x^2+y^2}$.

In a two-digit number, the unit's digit exceeds the ten's digit by $2$. If the product of the sum of the digits and the number itself is $144$, what is the number?

In a Venn diagram monitoring $18$ -year-old students attending online courses during lockdown, the square represents students learning Spanish, the triangle represents those learning music, and the circle represents those learning photography.
The region counts are given as follows:



* Only Spanish = $40$
* Only Music = $45$
* Only Photography = $35$
* Spanish & Music only = $22$
* Music & Photography only = $28$
* Spanish & Photography only = $25$
* All three courses = $50$

What approximately is the percentage of students who are learning one course only?

The sum of the first $16$ terms of the Arithmetic Progression (A.P.): $10,6,2,\dots$ is: