In a survey three questions $({\mathrm{Q}}_1, {\mathrm{Q}}_2 \mathrm{and} {\mathrm{Q}}_3)$ were asked from $600$ people. $20\%$ of them answered only question ${\mathrm{Q}}_1$ and double of them answered question ${\mathrm{Q}}_3$. $\frac{1}{4}$ of the total people surveyed answered only Question ${\mathrm{Q}}_2$. $\frac{1}{24}$ of the total people surveyed answered all three questions and this number is $20$ less than the number of people who answered question ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_3$ but not ${\mathrm{Q}}_2$. The number of people who answered question ${\mathrm{Q}}_2$ and ${\mathrm{Q}}_3$ but not question ${\mathrm{Q}}_1$ is $25\%$ of the number of people who answered question ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ but didn’t answer question ${\mathrm{Q}}_3$. The number of people who didn’t answer any of the three questions is $10.$

What is the difference between the number of people who answered at least one question and the number of people who answered at most one question?

Direction: In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the difference between the number of boys studying Mathematics and the number of girls studying Physics?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the ratio of the total number of boys to the total number of girls?

Direction: In a University there are $1200$ students studying four different subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

In which subjects is the difference between the number of boys and girls equal?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $4\left(C{P}^2-A{Q}^2\right)$ equal to?

Direction: In a University there are $1200$ students studying four difference subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

What is the total number of boys studying Statistics and Physics?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What percentage of students passed in exactly one subject?

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

If the number of students is $360$, then how many passed in at least two subjects?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $A{B}^2+4B{Q}^2$ equal to?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

What is the percentage of candidates who failed in at least two subjects?

In a University there are $1200$ students studying four difference subjects, Mathematics, Statistics, Physics, and Chemistry. $20\%$ of the total number of students are studying Mathematics, one-fourth of the total number of students are studying Physics, $320$ students are studying Statistics and remaining students are studying Chemistry. Three-fifth of the total number of students studying Chemistry is girls. $150$ boys are studying Mathematics.$60\%$ of students studying Physics are boys.$250$girls are studying Statistics.

The number of girls studying Statistics is what percent (approximate) of the total number of students studying Chemistry?

Consider the following for the question that follows:

$500$ candidates appeared in an examination comprising tests in English, Hindi and Mathematics. $30$ candidates failed in English only; $75$ failed in Hindi only; $50$ failed in Mathematics only; $15$ failed in both English and Hindi; $17$ failed in both Hindi and Mathematics; $17$ failed in both Mathematics and English; $5$ failed in all three tests.

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What is the ratio of number of students who passed in both Physics and Chemistry to number of students who passed in both Biology and Physics but not Chemistry?

$ABC$ is a triangle with $AB=1.6 \mathrm{cm}, BC=6.3 \mathrm{cm} \text{and} CA=6.5 \mathrm{cm}$. Let $P \text{and} Q$ be the mid-points of $AB and BC$ Respectively.

What is $A{Q}^2+C{P}^2$ equal to?

Direction: Consider the following for the next 04 (four) items that follow:

In an examination of Class XII, $55\%$ of students passed in Biology, $62\%$ passed in Physics, $60\%$ passed in Chemistry, $25\%$ passed in Physics and Biology, $30\%$ passed in Physics and Chemistry, $28\%$ passed in Biology and Chemistry. Only $2\%$ failed in all the subjects.

What percentage of students passed in all three subjects?