SEE 2081 Karnali Province — Maths Past Paper
- Q1.
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.
- (a) Write the set of the students who did not like any of these two subjects in the cardinality notation.
- (b) Present the given information in a Venn diagram assuming x for the number of students who liked both subjects.
- (c) Find the number of students who liked exactly one subject.
- (d) 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.
- Q2.
Aashlal deposited Rs.1,00,000 in a bank. The bank provides 8% per annum interest compounded semi annually.
- (a) Write the formula to calculate annually compound interest.
- (b) How much interest does Aashlal receive in 2 years? Find it.
- (c) If the bank provides yearly compound interest for the same rate and same period of time, how much would be profit or loss for him? Find it.
- Q3.
The population of a village is 10,000. Annual population growth rate is 4%. At the end of the first year, 100 people migrated from that village to other places.
- (a) Find the population of the village after one year.
- (b) If nobody were migrated in the second year, what would be the population of the village after 2 years? Find it.
- (c) If nobody was migrated in the first year, what would be the difference in population growth in 2 years? Find it.
- Q4.
According to the currency exchange rate of Nepal Rastra Bank, 1 American dollar equals NRs.138.83 in a day. The Nepali currency was devaluated by 2% in comparison to the dollar after some days.
- (a) What is called currency exchange? Write it.
- (b) How many Nepali rupees can be exchanged with American dollar ($) 1500 before devaluation? Find it.
- (c) After devaluation, how many American dollar can be exchanged with NRs. 7,08,033? Find it.
- Q5.
In the square based pyramid given in the figure, AH = 26 cm and AD = 24 cm.
- (a) Write the relation of HD and EF.
- (b) Find the value of EF.
- (c) Find the total surface area of the pyramid.
- Q6.
The given figure is of a combined solid object made with the combination of a cylinder and a hemisphere. The total height of the solid is 17 cm and the circumference of the base is 44 cm.
- (a) Write the formula to calculate the volume of the solid object.
- (b) What is the volume of the hemispherical part? Find it.
- (c) Compare between the volume of the cylinder and the hemisphere.
- Q7.
A rectangular tank of 5 m × 1 m × 4 m is filled with water at the rate of 50 paisa per litre.
- (a) The water contained in the 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.
- (b) If the length, breadth and height each of the tank is increased by 1 m, by how many times is the capacity of the tank increased? Find it.
- Q8.
The number of words learned by a child daily, double than the previous day, is shown in the following table.
- (a) In which sequence is the child learning words? Write it.
- (b) How many words does the child learn up to 8 days? Find it using formula.
- (c) In how many days will the child learn 6141 words? Find it.
- Q9.
A two digit number is four times the sum of its digits and three times the product of its digits.
- (a) If one's place digit be y and ten's place digit is x, write the two digit number in algebraic form.
- (b) Make a quadratic equation in terms of x according to the given conditions.
- (c) Find the number.
- Q10.
- (a) Simplify: 1/(b−1) − 1/(b+1)
- (b) Solve: 7^x + 7^(−x) = 7⅐
- Q11.
In the figure, triangles APQ and BPQ are standing on the same base PQ and between the same parallel lines AB and PQ.
- (a) Write the relation between the area of triangle APQ and triangle BPQ.
- (b) If the perpendicular distance between AB and PQ is 8 cm and AB = 10 cm, find the area of ΔAPB.
- Q12.
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.
- (a) Construct the quadrilateral PQRS according to the above measurement and then construct a triangle which is equal to the quadrilateral in area.
- (b) Why are the areas of the triangle and quadrilateral so constructed equal? Give reason.
- Q13.
In the figure, O is the centre of the circle and ABDC is a cyclic quadrilateral.
- (a) What is the relation between inscribed angles standing on the same arc of a circle? Write it.
- (b) If inscribed angle BAC = 35°, find the value of ∠BOC.
- (c) If arc BDC and arc ACD are equal then prove that: AB∥CD.
- (d) Verify experimentally that ∠BAC and ∠BDC are supplementary. (Two circles having at least 3 cm radii are necessary.)
- Q14.
The height of Himali is 1.22 m. She observed the top of the school building standing 36 m far from the base of the school building and found the angle of 30°.
- (a) What is the name of the angle found when Himali observed the top of the school building according to the given context? Write it.
- (b) Sketch the figure from the above context.
- (c) Find the height of the school building.
- (d) How many meters should Himali walk nearer or farther from that place to make the angle of the top of the building 60°? Give reason.
- Q15.
The age of 300 students of a school are given in the table.
- (a) What does c.f denote in the first quartile (Q₁) = L + [(N/4 − c.f)/f] × i? Write it.
- (b) Calculate the mean of the given data.
- (c) Find the median of the given data.
- (d) Find the percentage of the number of students who obtained more than the median class.
- Q16.
From a well shuffled pack of 52 cards two cards are drawn randomly one after another without replacement.
- (a) Write the multiplicative law of probability.
- (b) Show the probability of all possible outcomes of getting and not getting face cards in a tree diagram.
- (c) Calculate the probability of getting both face cards.
- (d) Compare the probability of getting both face cards and the probability of not getting both face cards (both non-face).
Open each question on Ujyalo to see the full model answer, marking scheme and step-by-step working — free with an account.