Math

In a survey of 300 people, it was found that 150 people liked iPhone and 200 people liked Android phone. But 25 people did not like any of these two phones.
(a) If I and A denote the sets of people who like iPhone and Android Phone respectively, write the cardinality of n(I∪A).
(b) Present the above information in a Venn-diagram.
(c) Find the number of people who liked iPhone only.
(d) Compare the number of people who like both iPhone and Android phone and who do not like any of these two phones.

A retired teacher deposited Rs. 80,000 in his own account of development bank for two years to get the half yearly compound interest at the rate of 10% per annum.
(a) How many times the interest is calculated according to the semi-annual compound interest in 2 years? Write it.
(b) According to the half yearly compound interest, what would be the compound interest received by the teacher at the end of 2 years? Find it.
(c) According to the same rate of yearly compound interest, in how many years will the compound amount of Rs. 80,000 be Rs. 1,06,480? Find it.

A minibus is purchased for Rs. 40,00,000. After using the bus for three years, Rs. 15,00,000 is earned. The value of the bus depreciates by the rate of 15% per annum and the minibus is sold after three years.
(a) If the purchasing price of the bus is Rs. V₀, the annual rate of compound depreciation is R% and price of the bus after T years is Rs. V_T, then express V_T in terms of V₀, R% and T.
(b) Find the selling price of the bus after three years.
(c) Find the total profit or loss in percent through the total transaction of that minibus.

A man went to the Bank to exchange American dollars to visit abroad. In that day, according to the money exchange rate, the buying rate of American Dollar is Rs. 132 and selling rate is Rs. 133.
(a) How many dollars does the man receive while exchanging American dollar with Rs. 332500? Find it.
(b) How much Nepali rupees does his friend receive while exchanging American dollar 2800 in the same day? Find it.
(c) After 10 days, the selling rate for American dollar 1 becomes Rs. 138.32 then by what percent the Nepali currency was devaluated? Find it.

The height of a square based pyramid is 21 cm and the length of the base is 20 cm.
(a) How many triangular surfaces are there in a square based pyramid? Write it.
(b) Find the slant height of the pyramid.
(c) What is the total cost of painting the total surface area of the pyramid at the rate of Rs. 5 per square cm? Find it.

A metallic solid made up of a cone and a cylinder is given in the figure. The radii of the base of the cone and cylinder are equal. The height of the cylinder is 40 cm, height of the cone is 24 cm and radius of the base of cone is 7 cm.(a) If radius of the base and slant height of the cone are given then write the formula for finding the curved surface area of the cone.
(b) Find the volume of the solid object.
(c) Compare the volume of the cylindrical part and the volume of conical part.

The length, breadth and height of a rectangular room are 14 ft, 13 ft, and 10 ft respectively. There are two square windows with 3 feet edges and two doors of size 6 ft × 3 ft in the room.
(a) How much does it cost to paint four walls and ceiling of the room excluding doors and windows at the rate of Rs. 36 per square feet? Find it.
(b) How much the total cost will increase to paint on same part if the cost of painting per square meter is increased by one third of what it was before due to the increase in the market price? Find it.

There are 4 geometric means between 3 and 243.
(a) First term ‘a’, last term ‘b’ and number of geometric means ‘n’ are given. Write the formula for the calculation of common ratio (r) in the given condition.
(b) What is the third mean of the given series? Find it.
(c) In arithmetic mean and geometric mean between 3 and 243, which one is greater and by how much? Compare it.

The perimeter and area of a rectangular ground are 66 m and 260 sq.m. respectively.
(a) Illustrate the roots of x in the quadratic equation ax²+bx+c=0, a≠0.
(b) Find the length and breadth of the given ground.
(c) How many pieces of land can be made with dimension (13 × 4) square meter from that rectangular field? Calculate it.

 (a) Simplify: x+yx−y−x−yx+y.

(b) Solve: 4^x+14^x=16116.

In the given figure, there are two triangles PQR and PQS on the same base PQ and between same parallel lines PQ and RS.

(a) Write the relation between the areas of given two triangles.
(b) Prove that: Area of ∆PQR = Area of ∆PQS.
(c) In the given figure, AC ∥ DE. Prove that the area of quadrilateral ABCD and area of triangle ABE are equal.

In a cyclic quadrilateral PQRS, ∠P and ∠R are opposite angles.
(a) Write the relation between ∠P and ∠R.
(b) Find the value of x when ∠P = 2x° and ∠R = 4x°.
(c) Prove experimentally that ∠Q + ∠S = 180°. Two circles having at least 3 cm radii are necessary.

(a) Construct a quadrilateral ABCD in which AB = BC = 6 cm, AD = CD = 5.1 cm and ∠DAB = 60°. Also, construct a triangle ADM whose area is equal to the area of the quadrilateral.
(b) Are BD ∥ MC? Give reason.

In the given figure, height of pole with bulb (AB) = 20.5 m and the height of man (CD) = 1.5 m.(a) Define the angle of elevation.
(b) How much is the height of man less than the height of the pole with bulb? Write it.
(c) If the angle of elevation ECA = 45°, then find the distance between the man and pole.
(d) When the man looks at the top of the pole with bulb, how far does he move forward or backward from the current position so that the angle of elevation may be 30°? Find it.

The data given below is the marks obtained by 20 students in an exam of Mathematics.

(a) What does i denote in the formula Q₁=L+(N4−cf)×if for the calculation of first quartile of the continuous series? Write it.
(b) Find the first quartile of the given data.
(c) Find the mode from the above data.
(d) How many percentage of students are there who obtained 20 or more than 20 marks? Find it.

Himani planned to have two children at an interval of 4 years after married.
(a) What is the probability scale of any event ‘E’? Write it.
(b) Find the probability of having both children are daughter.
(c) Show the probabilities of possible outcomes of getting son and daughter in a tree-diagram.
(d) Find the probability of having at least one daughter.