21/8/24
(The Answers of the questions 1, 2, 3 are to be written at the beginning of the answer scripts mentioning the question numbers in the serial order. Necessary calculation and drawing must be given on the right and side by the drawing margins on the first few pages on answer script. Table and calculator for any type are not allowed. Approximate value of π may be taken 22/7, if necessary . Graph paper will be supplied, if required. Arithmatic problems may be solved by algebraic method)
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1) Choose the correct answer: 1x6 = 6
i) if the ratio of the principle and yearly amount be in the ratio 25:28, then the yearly rate of interest is
a) 3% b) 12% c) 75/7% d) 8%
ii) Under what condition one root of the quadratic equation ax²+ bx+ c =0 is zero ?
a) a= 0 b) b=0 c) c=0 d) none
iii) The number of common Tangents of two circles when they do not touch or intersect each other Is-
a) 2 b) 1 c) 3 d) 4
iv) if sinx = cosx then the value of 2x will be
a) 30° b) 60° c) 45° d) 90°.
v) If each of radius of the base and height of a cone be doubled , then the volume it will be--
a) three times b) four times c) six times d) eight times
vi) The medians of the number 2, 8, 2, 3, 8, 5, 9, 5, 6 is
a) 8 b) 6.5 c) 5.5 d) 5.
2) Fill in the blanks(any five ): 1x 5= 5
i) At same rate percent per annum, the simple interest and compound interest of same principal are same in _____year.
ii) If in a quadradic equation ax²+ bx+ c= 0(a≠ 0), b²= 4ac, then the roots of the equation will be real and ___.
iii) if the length of the sides of two triangles are in the proportion, then two triangles are _____.
iv) if cos²x - sin²x = 1/x (x > 1), then cos⁴x - sin⁴x= ____.
v) The numbers of plane surface of a solid hemisphere are____.
vi) if the mean of x₁ , x₂ , x₃ ,.....xₙ be bar x, then the mean of kx₁ , kx₂, kx₃,....kxₙ is ____(k≠ 0).
3) Write true or false( any five): 1x5= 5
i) A starts a business with Rs10000 and B gives Rs20000 after 6 months. At the end of the year their profit be equal.
ii) If x= 2+√3, the value of x+ 1/x is 2√3.
iii) If two circles of radius 7cm and 3cm touch each other externally, then the distance between the centres will be 4cm.
iv) If 0°< xx < 90°, then sinx > sin²x.
v) If the total surface area of a hemisphere be 36π sq.cm, then its radius will be 3cm.
vi) If the perpendicular drawn on x-axis from the point of intersection of both ogives, the abscissa of the point of intersection of this perpendicular with the x-axis will be median.
4) Answer the following questions (any ten): 2x10= 20
i) A sum of money is double in 8 years at r% rate of compound interest per annum. At the same rate in how many years it will be 4 times at the sum ?
ii) A invests 3/2 times more than B invests in a business. At the end of the years B receives Rs1500 as profit. How much profit A will get at the end of that year ?
iii) Without solving, find the values of p for which the equation x²+ (p -3)x + p= 0 has a real and equal roots.nn.
iv) if x ∞ yz and y ∞ zx, show that z is a non zero constant.
v) The perimeter of two similar triangles are 20cm and 16cm respectively. if the length of one side of the first triangle is 9cm, then find the length of the corresponding side of second triangle.
vi) In ∆ ABC , angle ABC=90°, AB= 5cm, BC= 12cm. Find the the length of the circumradius of ∆ abcd.
vii) In ∆ ABC , if AB= (2a -1), AC = 2 √(2a) cm BC = (2a+1)cm, then write down the value of angle BAC.
viii) If x= a seck and y= b tan k then find the relation between x and y free from x and y.
ix) If tan(x +15°)=√3, find the value of sinx + cosx.
x) the diameter of one sphere is double the diameter of another sphere . if the numerical value of total surface area of large sphere is equal to the volume of smaller sphere , then find the radius of the smaller sphere.
xi) If the number of surfaces of a cuboid is x, the number of edges is y, the number of vertices is z and the number of diagonals is P, then find the value of x- y + z+ p.
xii) if 11, 12, 14, x - 2, x + 4, x + 9, 32, 38, 47 are arranged in ascending order and their medians is 24, find x.
5) Answer any one: 5
i)The difference between simple interest and compound interest for 2 years of a sum of money becomes Rs80 at 4% intrest per annum. Calculate the sum of money.
ii) A, B, C start a business jointly investing Rs180000 in together . A gives Rs20000 more than that of B and B gives 20000 more than that of C. Distribute the profit of Rs10800 among them.
6) Solve any one: 3
i) 1/(a+ b + x) = 1/a + 1/b + 1/x, (x≠ 0, -(a+ b)).
ii) If 5 times of a positive whole number is less than by 3 than twice of its square, then find the number.
7) Answer any one : 3
i) Simplify : 7/(√2+ √3) - (√3 +1)/(2+ √3) + (√2+ 1)/(3+ 2√2).
ii) The total expenses of a hostel partly constant and partly vary directly as the number of boarders. When the number of boarders are 120 and 100 the total expenses are Rs2000 and Rs1700 respectively. What will be the number of boarders when the total expenses is Rs1880 ?
8) answer any one question : 3
i) if a/(b + c) = b/(c + a) = c/(a+ b), then prove that each ratio is equals to 1/2 or -1.
ii) if (b + c - a)x = (c + a - b)y = (a+ b - c)z = 2, then show that (1/x + 1/y)(1/y + 1/z)(1/z + 1/x)= abc.
8) answer any one question: 5
i) if in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then and prove that angle opposite to the first side will be a right angle.
ii) if two tangents are drawn to a circle from a point outside it, then the line segments joining the point of contracts and the exterior point are equal.
10) answer any one question : 3
i) prove that the quadrilateral formed by the internal bisectors of the four angles of a quadrilateral is cyclic.
ii) O is the circumcentre of ∆ ABC and OD perpendicular BC; prove that angle BOD = Angle BAC.
11) Answer any one question: 5
i) Draw an equalateral triangle of side 6cm and draw the incircle of the triangle. (Only traces of construction are required)
ii) Construct a rectangle with sides 8cm and 6cm and construct a square equal in area to that of the rectangle.(only traces of constructions are required)
12) answer any two questions: 2x3= 6
i) if the measure of 3 angles of a quadrilateral are π/3, 5π/6, and 90°, then determine the fourth angle in sexagesimal and circular measure.
ii) If (sink)/x = (cosx)/y then prove that sinx - cosx = (x - y)/√(x²+ y²).
iii) If tan 9°= a/b , then show that sec²81/(1+ cot² 81)= b²/a².
13) answer any one question: 5
i) The distance between two pillars is 150m. Height of one is thrice the other. From the midpoint of the line segment joining the foot of the pillars ,the angle of elevation of the top of the pillars are complementary to each other. Find the height of the shorter pillar.
ii) If the angle of depression from a lighthouse of two ships situated in the same line with the lighthouse are 60° and 30° and if the nearer ship is 150m away from the light house, then find the distance of the other ship from the lighthouse.
14) Answer any two questions: 4x2=8
i) Determine the volume of a solid right circular cone which can be made from a solid wooden cube of 4.2dcm edge by wasting minimum quantity of wood.
ii) A hemispherical bowl with radius 9cm is completely filled with water. How many cylinderical bottles of diameter 3cm and height 4 cm can be filled up with the water in the bowl.
iii) Area of the base of a closed cylinderical water tank is 616 sq.m and height is 21 m. Find the total surface area of the tank.
15)i) Answer any two questions: 2x4= 8
i) If the median of the following data is. 32, find the values of x and y when the sum of the frequency is 100.
Class interval frequency
00-10 10
10-20 x
20-30 25
30-40 30
40-50 y
50-60 10
ii) Find the mode from the following distribution table:
Class interval frequency
00-05 5
05-10 12
10-15 18
15-20 28
20-25 17
25-30 12
30-35 8
iii) by preparing a cumulative frequency(greater than type) table from the following data, draw an ogive in a graph paper.
Class interval frequency
00-05 4
05-10 10
10-15 15
15-20 8
20-25 3
25-30 5
2/8/24
MULTIPLE CHOICE QUESTIONS (1 MARK)
1) If a principal becomes twice of it n years, then the rate of simple interest per annum is:
a) 5% b) 10% c) 15% c) 22%
2) In a partnership business, the ratio of share of profit of two friends in 1/2 : 1/3, then the ratio of their principals is
a) 2: 3 b) 3:2 c) 1:1 d) 5:3
3) Interest on Rs a at the simple interest 10% per annum for b months is:
a) Rs ab/100 b) Rsab/120 c) Rs ab/1200 d) Rs ab/10
4) If the ratio of principle and the yearly amount be in the ratio 25: 28, then the rate of yearly rate of interest is
a) 3% b) 12% c) 75 /7% d) 8%
5) if the total interest becomes Rs x for any principal having the rate of simple interest of x% per annum for x years then the principle will be
a) Rs x b) Rs100 x c) Rs100/x d) Rs100/x²
6) The total interest of a principal in n years at the rate of simple interest of r% per annum is p/25, the principal will be
a) Rs 2p b) Rs4p c) Rsn/2 d) n/4 e) none
7) if the interest on Rs p at the rate of simple interest of r% per annum in t years is I, then
a) I= prt b) prt I= 100 x I c) prt= 100 x I d) none
8) A principal becomes twice of its amount in 20 years at a certain rate of simple interest. At that same rate of simple interest, that principal becomes thrice of its amount in
a) 30 years b) 35 years c) 40 years d) 45 years
9) A sum of Rs400 amounts to Rs480 in 4 years. What will it amount to if the rate of re
interest is increased by 2% ?
a) Rs484 b) Rs560 c) Rs512 d) none
10) At what rate of percent per annum will Rs2304 amount to Rs2500 in 2 years at compound interest ?
a) 9/2% b) 21/4% c) 25/6% d) 13/3%
11) An amount doubles itself in 5 years with simple interest. What is the amount of interest percent per annum?
a) 10% b) 20% c) 25% d) 30%
12) Three partners shared in a business in the ratio 5:7: 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their Investments ?
a) 5:7 : 8 b) 20:49 : 64 d) 38:28 :21 d) none
13) A person deposited Rs100 in a bank and got the amount Rs121 for 2 years. The rate of compound interest is:
a) 10% b) 20% c) 5% d) 21/2%
14) in case of compound interest , the rate of compound interest per annum is
a) equal b) unequal c) both equal or unequal d) none
15) in case of compound interest
a) the principal remains unchanged each year
b) principal changes in each year
c) principal may be equal or unequal in each year
d) none
16) The capital of three friends in a partnership business are Rs200, Rs 150, Rs 250 respectively. After sometime the ratio of their profit share will be
a) 5:3:4 b) 4:3:5 c) 3:5:4 d) 5:4:3
17) Surendra and Naushad started business with capital Rs 1500 and Rs1000. After a year there was a loss of Rs75, then the loss of Surendra
a) Rs 45 b) Rs30 c) Rs25 d) Rs40
18) Amal and Bimal started a business. Amal invested Rs500 for 9 months and Vimal invested some money for 6 months. They make a profit of Rs69 in a year, Bimal gets profit of Rs46. The capital of Vimal in the business is
a) Rs1500 b) Rs3000 c) Rs4500 d) Rs6000
19) Pallavi invested Rs500 for 9 months and Rajiv invested Rs600 for 5 months in a business. The ratio of their profit shares will be
a) 3:2 b) 5:6 c) 6:5 d) 9:5
5/5/24 (DAY -1)
1) The salary of a man increases every year by 8%. 2 years ago his salary was Rs18750.
a) What was his salary last year ?
b) What is his present salary ? (2)
2) Solve: 21x²- 8x -4= 0. (2)
3) A largest possible circle is drawn in a rectangle with sides 24cm and 20cm. Find
a) area of the circle.
b) area of the remaining part of the rectangle if the circle is cut off from it. (π=3.14). (2)
4) A man borrows Rs25000 at compound interest and repays Rs33275 at the end of 3 years. Find the rate of interest per annum charged. (3)
5) In the figure, I is the incentre of the circle. AI produce to meet the circle in D.
a) angle DCB
b) angle IBC
c) angle BID
d) Given angle BAC= 50° and angle ABC= 64°. (4)
6)
In the figure AB is a common tangent to two circles intersecting at C and D. Write down the measure of (angle ACB + angle ADB).
Justify your answer. (3)
7) The compound interest for the third year on a certain sum is Rs726. If the simple interest on the same sum is Rs1800, find the rate and the sum. (4)
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