SEE 2081_RE1031_KAP

1. Out of 100 students of class ten of a school, 60 liked English and 50 like mathematics. But 20 did not like any of these two subjects. The sets of students who liked English and Mathematics are denoted by 'E' and 'M' respectively.
   1. Write the set of the students who did not like any of these two subjects in the cardinality notation.
   2. Present the given information in a Venn diagram assuming x for the number of students who liked both subjects.
   3. Find the number of students who liked exactly one subject.
   4. If 30 students did not like any of these two subjects, what will be the effect in the number of students who liked both subjects? Find it.
2. Aashal deposited Rs.1,00,000 in a bank. The bank provides 8% per annum interest compounded semi annually.
   1. Write the formula to calculate annually compound interest.
   2. How much interest does Aashal receive in 2 years? Find it.
   3. If the bank provides yearly compound interest for same rate and same period of time, how much would be profit or loss for him? Find it.
3. The population of a village is 10,000. Annual population growth rate is 4%. At the end of first year, 100 people migrated from that village to other places.
   1. Find the population of the village after one year.
   2. If nobody were migrated in second year, what would be the population of the village after 2 years? Find it.
   3. If nobody was migrated in first year, what would be the difference in population growth in 2 years? Find it.
4. According to currency exchange rate of Nepal Rastra Bank, 1 American dollar equals to NRs.138.83 in a day. Nepali currency was devaluated by 2% in the comparison of dollar after some days.
   1. What is called currency exchange? Write it.
   2. How many Nepali rupees can be exchanged with American dollar ($) 1500 before devaluation? Find it.
   3. After devaluation, how many American dollar can be exchanged with NRs.7,08,033? Find it.
5. In the square based pyramid given in the figure, AH = 26 cm and AD = 24 cm.

   1. Write the relation of HD and EF.
   2. Find the value of EF.
   3. Find the total surface area of the pyramid.
6. The given figure is of a combined solid object made with the combination of cylinder and hemisphere. The total height of the solid is 17 cm and circumference of the base is 44 cm.

   1. Write the formula to calculate volume of solid object.
   2. What is the volume of hemispherical part? Find it.
   3. Compare between volume of cylinder and hemisphere.
7. A rectangular tank of 5 m × 1 m × 4 m is filled with water at the rate of 50 paisa per litre.
   1. The water containing in full tank is enough for 20 families distributed equally for one month. How much cost of water should one family have to pay in one year? Find it.
   2. If length, breadth and height each of the tank is increased by 1 m, by how many times the capacity of tank is increased? Find it.
8. The number of words learned by a child daily in the double than previous day is shown in the following table.

   Day	1st	2nd	3rd	4th	........	........
   Number of words	3	6	12	24	........	........

   1. In which sequence is the child learning words? Write it.
   2. How many words does the child learn upto 8 days? Find it using formula.
   3. In how many days will the child learn 6141 words? Find it.
9. A two digit number is four times the sum of digits and three times the product of digits.
   1. If one’s place digit is y and ten’s place digit is x, write the two digit number in algebraic form.
   2. Make a quadratic equation in terms of x according to given conditions.
   3. Find the number.
10. Simplify:
    1. 1/(b−1) − 1/(b+1)
    2. Solve: 7^x + 7^−x = 7 1/7
11. In the figure, triangles APQ and BPQ are standing on the same base PQ and between the same parallel lines AB and PQ.

    1. Write the relation between the area of triangle APQ and triangle BPQ.
    2. If the perpendicular distance between AB and PQ is 8 cm and AB = 10 cm, find the area of ΔAPB.
12. In a quadrilateral PQRS, PQ = 5.1 cm, QR = 7 cm, RS = 4.6 cm, SP = 5.4 cm and QS = 6.6 cm are given.
    1. Construct the quadrilateral PQRS according to above measurement and then construct a triangle which is equal to the quadrilateral in area.
    2. Why the areas of triangle and quadrilateral so constructed are equal? Give reason.
13. In the figure, O is the center of the circle and ABDC is a cyclic quadrilateral.

    1. What is the relation between inscribed angles standing on same arc of a circle? Write it.
    2. If inscribed angle ∠BAC = 35°, find the value of ∠BOC.
    3. If arc BDC and arc ACD are equal, prove that AB // CD.
    4. Verify experimentally that ∠BAC and ∠BDC are supplementary.(Two circles having at least 3 cm radii are necessary.)
14. The height of Himali is 1.22 m. She observed the top of the school building standing 36 m far from the base of school building found the angle of 30°.
    1. What is the name of the angle found when Himali observed at the top of school building according to the given context? Write it.
    2. Sketch the figure from the above context.
    3. Find the height of the school building.
    4. How many meters should Himali have to walk nearer or farther from that place to make the angle of the top of the building to be 60°? Give reason.
15. The age of 300 students of a school are given in the table.

    Age in years	0–4	4–8	8–12	12–16	16–20
    No. of students	50	65	75	60	50

    1. What does c.f denote in the first quartile (Q1) = L + (N/4 − c.f)/f × i ? Write it.
    2. Calculate the mean of the given data.
    3. Find the median of the given data.
    4. Find the percentage of number of students who obtained more marks than median class.
16. From a well shuffled pack of 52 cards two cards are drawn randomly one after another without replacement.
    1. Write the multiplicative law of probability.
    2. Show the probability of all possible outcomes of getting and not getting face cards in a tree diagram.
    3. Calculate the probability of getting both face cards.
    4. Compare between the probability of getting both face cards and the probability of not getting both face cards.