Mathematics Test – 01

All questions are compulsory.

[ Q. No. 1 ] 40% of the students of a school play football, 30% play volleyball and 20% play both football and volleyball. If 90 students play neither football nor volleyball, then
a) Show the above information in Venn-diagram. [ 1 ]
b) Find the total number of students in the school. [ 2 ]
c) Find the ratio of students who play football only to that who play volleyball only. [ 2 ]

[ Q. No. 2 ] In a survey conducted among students studying in a class 10 of Shree Sharada Secondary School, which of Pokhara, Lumbini and llam would be suitable for an educational trip, 40 students said that they would go to Pokhara, 30 students would go to Lumbini and 45 students would go to llam while 15 students of that class said that all three places are suitable and 5 students did not express any opinion.
a) If P, L and I represents the number of students for whom pokhara, Lumbini and llam respectively are suitable, write the group of students for whom all places are suitable by cardinality notation. [ 1 ]
b) Represent the above information in Venn-diagram. [ 1 ]
c) How many students are studying in class 10 of Sharada Secondary School ? Calculate. [ 1.5 ]
d) If 5 students who did not express their opinion in the survey said that Lumbini is a suitable place, what would be the ratio of students who said that Pokhara was the only suitable place and Lumbini was the only suitable place ? [ 1.5 ]

[ Q. No. 3 ]
a) Find the compound interest on Rs. 2,000 for 3 years at 15% per annum compounded annually. [ 1 ]
b) In how many years will Rs. 15,625 amounts to Rs. 17,576 at 4% p.a., compound interest? [ 2 ]
c) The S.I. and C.I. on a sum of money for 2 years is Rs. 200 and 210 respectively. If the rate of interest is the same. Find the sum and rate. [ 2 ]

[ Q. No. 4 ] Bipin wants to deposit Rs 1.00,000 in a bank for 2 years. The bank offers 10% per annum compound interest with three alternates (annual compound interest, half-yearly compound interest and quarterly compound interest)
a) Which option among the three alternatives helps Bipin get more interest? Write it. [ 1 ]
b) How much amount does he receive after 2 years from compound interest compounded semiannually? [ 2 ]
c) At the end of 1 year, if Bipin withdraws the total amount received according to the semi-annual compound interest and deposits it for the rest of the period to get quarterly compound interest, how much amount will he get at the end? [2]

[ Q. No. 5 ]
a) List any two characteristics of Arithmetic Series. [ 1 ]
b) Find two numbers whose arithmetic mean is 5 and geometric mean is 4. [ 2 ]
c) The sum of three terms in an arithmetic series is 24. If 1, 6 and 18 are added to them respectively, the results
are in geometrical series, find the terms. [2]

[ Q. No. 6 ]
a) Show that (a – b)², (a² + b²) and (a + b)² are in AP. [ 2 ]
b) A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes. [ 3 ]

[ Q. No. 7 ]

[ Q. No. 8 ] A pyramid of height 12 m has its base area 49 m².
a) Find its slant height. [ 1 ]
b) Find the total surface area and volume of the pyramid [ 2 ]
c) What would be the base area if the lateral surface area is twice its base area and its total surface area is 600 m² ? [2]

[ Q. No. 9 ] The height of the square based pyramid is 12 cm and the length of base is 10 cm.
a) How many triangular faces are there in square base pyramid? [ 1 ]
b) Find the slant height of the pyramid.[1]
c) Find the volume of the pyramid. [ 1 ]
d) Find the cost of coloring in the triangular parts of the pyramid when the cost of per square cm is 50 paisa.[2]

[ Q. No. 10 ] A parallelogram ABCD and a triangle BCE are standing on same base BC and between same parallel lines AD//BC.
a) If the area of the parallelogram is 400 m², what would be the area of the triangle ? [ 2 ]
b) Show theoretically that the area of the parallelogram ABCD is twice of the area of the triangle BCE. [ 3 ]

[ Q. No. 11 ]

[ Q. No. 12 ]

* Best Of Luck *