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SEE 2079 Bagmati Province — Maths Past Paper

Full marks: 100 · Time: 3 hours · With step-by-step model answers in Nepali & English.

  1. Q1.
    • (a) If the initial population of a certain place is M and the population after T years is Mₜ = M(1 + G/100)ᵀ, what does G represent?
    • (b) The lengths of the sides of a triangle are x cm, y cm and z cm. What is the semi-perimeter of the triangle?
  2. Q2.
    • (a) What is the order of the surd ⁵√(y⁴)?
    • (b) In the formula for finding the first quartile (Q₁) = L + [(N/4 − c.f.)/f] × i in grouped data, what does i represent for?
  3. Q3.
    • (a) In the figure, P is any point on the side BC of parallelogram ABCD. What is the relation between the area of parallelogram ABCD and ΔPAD?
    • (b) Write the relation between the angle at the centre and the angle at the circumference subtended by the same arc.
  4. Q4.
    • (a) What rate of VAT should make the price of an article costing Rs.5,000 to Rs.5,650? Find it.
    • (b) The population of a city is 1,30,000 at present. If it increases at the rate of 2.5% per year, what will be its total population after 2 years?
  5. Q5.
    • (a) Find the area of an equilateral triangle having perimeter 60 cm.
    • (b) If the radius of a football is 7 cm, find its surface area.
    • (c) If the curved surface area of a cone is 550 sq.cm and the height of slant surface is 25 cm, find the height of the cone.
  6. Q6.
    • (a) Find the L.C.M. of: p⁴ − p, p² + p + 1
    • (b) Solve: 7^(x²) = 2401
  7. Q7.
    • (a) Evaluate: (125/27)^(−1/3) ÷ (25/9)^(−1/2)
    • (b) Simplify: (a−1)/(a²−3a+2) + (a−2)/(a²−5a+6)
    • (c) Simplify: 1/(p−q) - (p+q)/(p²-q²)
  8. Q8.
    • (a) In the figure, PQRS is a rectangle and PQMN is a parallelogram. If PQ = 8 cm, QR = 5 cm, MQ = 10 cm and MO ⊥ NP, find the length of MO.
    • (b) In the figure, O is the centre of the circle. If SO ⊥ PQ and ∠PQR = 55°, find the value of ∠OSR.
    • (c) In the figure, O is the centre of the circle, TAN is a tangent and A is the point of contact. If ∠TNB = 60°, find the value of ∠AOC.
  9. Q9.
    • (a) In the figure, if AB = 12 cm, ∠ABC = 60° and area of ΔABC = 36√3 sq.cm, what is the length of BC?
    • (b) Find the median class from the given continuous data.
  10. Q10.
    • (a) A card is drawn randomly from a well-shuffled pack of 52 playing cards. What is the probability that the card drawn is king or ten?
    • (b) A basket contains 5 green and 3 black grapes of same shape and size. Two grapes are drawn one after another with replacement. Represent the possible outcomes in a probability tree diagram.
  11. Q11.

    In a survey of 150 people of a community, it was found that the ratio of the people who liked Mathematics and Science is 2:3. Out of them, 45 people liked both Mathematics and Science but 30 people didn't like both Mathematics and Science. Using a Venn diagram, find the number of people who liked Mathematics only.

  12. Q12.

    A shopkeeper allows the same rate of discount for all articles available in his shop. If he sells a heater for Rs.8,000 marked as Rs.10,000, for what amount does he sell a mixer of marked price Rs.3,000 levying 13% VAT on the discounted price? Find it.

  13. Q13.

    A person plans to make a combined solid of a cone and a hemisphere for decoration material from gold. If the diameter of the hemisphere and base of the cone is 10 cm and the slant height of the cone is 13 cm, find the total volume of gold required to make the combined solid.

  14. Q14.

    Find the H.C.F. of: x² + 2xy + y², x² − y², x³ + y³

  15. Q15.

    Solve: (x − 1)/(√x + 1) = 1 + (√x − 1)/2

  16. Q16.

    Prove that the areas of triangles PAB and MAB standing on the same base AB and in between AB ∥ XY are equal.

  17. Q17.

    Construct a square PQRS whose one side is 5 cm. Also construct a parallelogram QRNM whose one angle is 60° and its area is equal to the area of square PQRS.

  18. Q18.

    Verify experimentally that the sum of opposite angles of a cyclic quadrilateral is 180°. (Two circles of different sizes having radii at least 3 cm are necessary.)

  19. Q19.

    The distance between a tower and a man is 20 meter and the height of the tower is 36.1 meter. If he finds the angle of elevation to the top of the tower 60°, find the height of the man.

  20. Q20.

    If the mean of the given data below is 39, calculate the value of p.

  21. Q21.

    Ram borrowed Rs.45,000 for 2 years at 10% p.a. compounded annually. He paid only one third of the principal at the end of 2 years. He paid the remaining principal and interest at the same rate at the end of the next 2 years. How much amount did he pay at last to clear the debt? Find it.

  22. Q22.

    In the given square based pyramidal house, how much does it cost for metal plating the roof at the rate of Rs.12,000 per square meter? Find it.

  23. Q23.

    In 2050 B.S., the sum of the ages of Madan Bahadur and Hari Bahadur was 40 years. If in 2065 B.S. the ratio of their ages was 3:4, find their ages in 2080 B.S.

  24. Q24.

    In ΔABC, the perpendiculars AM and BN drawn from vertices A and B on their opposite sides meet (when produced) the circumcircle of the triangle at point D and E respectively. Prove that: (i) ABMN is a cyclic quadrilateral. (ii) arc CD = arc CE.

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