Questions

What should be done mainly for the conservation of one-horned rhinoceros?

Define blood pressure.

A survey was conducted among 20 students of a Secondary School of class X, where 14 students participated in football and 12 students in volleyball games. Every student has participated in at least one game.

1. Assuming the set of students who participated in football as F and volleyball as V, write the cardinality of the set of students who participated in volleyball or football.
2. Present the above information in the Venn diagram.
3. Find the number of students participating in exactly one game by using Venn diagram.
4. If two students who respond only to football are unable to play the game due to health problems, the cardinality of which set is changed? Give reason.

There are 1 red, 1 black and 1 white ball of the same shape and size in a bag. Two balls are drawn randomly one after another without replacement.

1. If A and B are two independent events, write the formula of P(A $\rm \cap$ B).
2. Show the probability of all the possible outcomes in a probability tree diagram. 
3. Find the probability of getting a red ball and a black ball. 
4. Is there any possibility of getting both balls of the same color? Give reason.

The weight of 20 students is presented here in the table.

1. In a continuous series, what does m represent in the formula ($\rm\overline X$)=$\rm \frac {\sum fm}{N}$ to calculate mean? Write it. 
2. Find the median class of the given data.
3. Calculate the average weight from the given data.
4. Is the class of measure of central tendencies of the given data same? Justify it. 

A tree is broken by wind. The top of the broken part without detaching makes an angle of 30$\circ$ with the ground. The distance from the foot of the tree to the point on the ground where the top of the tree touches the ground is $\rm 9\sqrt 3$ m.

1. Define angle of elevation.
2. Sketch the figure from the above context.
3. Find the length of the broken part of the tree.
4. If the length of the remaining part of the tree after broken is also $9\sqrt 3$ meter, what angle will the top of the tree make with the ground? Write reason.

In the figure, two circles are intersected at the points P and Q. Two lines AB and CD pass through the point Q.

1. What is the relation between the inscribed angles made by the same arc? Write it. 
2. If $\rm \angle$ QAP =  25$^{\circ}$ and $\rm \angle$ QCP =  (2x - 15)$^{\circ}$, find the value of x.
3. Prove that: $\rm \angle $CPA = $\rm \angle $BPD.
4. Verify experimentally that the central angle is double of the inscribed angle standing on the same arc by making two circles having at least 3 cm radii. 

In a $\rm \triangle $ABC, $\rm \angle $ABC=60°, BC=4.4 cm and AB = 5.2 cm are given.

1. Construct a $\rm \triangle$ABC according to above measurements, then construct a rectangle MNOC equal in area to the triangle.
2. Why the areas of triangle and rectangle so formed are equal? Write reason. 

Triangle PQT and parallelogram PQRS are standing on the same base PQ and between the same parallel lines PQ and ST.

1. Write the relationship between the area of parallelogram and area of triangle standing on the same base and between the same parallel lines.
2. If the length of base of parallelogram PQRS is 12 cm with height 8 cm, find the area of $\triangle$PQT.

If $\rm x = 2^{\frac {1}{3}} - 2^{\frac {-1}{3}}$, prove that: $\rm 2x^3 + 6x - 3 = 0$