General Maths Geometry March 2016 Board Paper

General Maths Geometry March 2016 Board Paper

Q. 1. Solve any five of the following sub - questions: [5]

(i) △ ABC ~ △ PQR. If AB/PQ = 1/2, then find the value of BC/QR.

(ii) If the diameter of circle is 10 cm, then find the radius of the circle.

(iii) What is the midpoint of class 16 - 20?

(iv) In the adjoining figure, find the value of cos Θ.

(v) How many tangents can be drawn to a circle from a point on the circle?

(vi) If a coin is tossed, what is its sample space?



Q. 2. Solve any four of the following sub - questions: [8]

(i) The lengths of sides of a triangle are 6 cm, 8 cm and 10 cm. Is this triangle right - angled? Give reason.

(ii) Radii of two internally touching circles are 10 units and 4 units.Find the distance between centres of the circles.

(iii) In the adjoining figure, 口PQRS is a trapezium. Seg PQ || Seg MN || seg SR. If PM = 6, MS = 8, NR = 4, then find QN.

(iv) Radius of a sphere is 7 cm. Find its curved surface area.

(v) A card is drawn from a well - shuffled pack of 52 cards. What is the probability that a card will be an ace?

(vi) Radius and slant height of a cone are 21 cm and 30 cm respectively. Find its curved surface area. (ㄫ = 22/7 )



Q. 3. Solve any three of the following sub - questions: [9]

(i) △ ABC ~ △ PQR and A( △ABC) = 144 cm2, A(△PQR) = 64 cm2. If BC = 12 cm, then find the value of QR.

(ii) Find the value of : tan245 + cot245.

(iii) Construct a regular hexagon with side 4 cm.

(iv) Volume of a cylindrical toy is 1570 cm2. Radius of its base is 10 cm. Find the height of the toy. (ㄫ = 3.14)

(v) Draw a histogram for the following data:

Marks
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
No. of Students
30
50
40
20
15


Q. 4. Solve any two of the following sub questions: [8]

(i) In △ABC seg AD is median. If AB = 11, AC = 17, BC = 12, then find the value of AD.

(ii) In the given figure, 口 ABCD is a cyclic quadrilateral. Chord AB Chord BC, Chord AD Chord CD, If ㄥADC = 3x0 and ㄥABC = 2x0, then find the measures of ㄥB and ㄥD.

(iii) Draw a circle with centre O and radius 4 cm. Take point A such that d(O,A) = 9 cm. Draw tangents from point A.

Q. 5. Solve any two of the following sub - questions. [10]

(i) In the given figure a player is sitting on a top of a tower 20 m high. It is observed that an angle of depression of a ball lying on the ground is 900. Find the distance between the foot of the tower and the ball.


(ii) The volume of a cone is the same as that of volume of a cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.

(iii) The following data indicate the number of students using different modes of transport.

Mode of Transport
Bicycle
Bus
Walk
Train
Car
Total
Number of students
140
100
70
40
10
360

Represent the above data using a pie diagram.

General Maths Geometry July 2016 Board Paper

General Maths Geometry July 2016 Board Paper

Q. 1. Solve any five of the following sub - questions: [5]

(i) In figure, △ PQR and △QRT are right angled triangle. If PQ = 4 and RT = 2, then find A(△PQR) / A(△QRT).
(ii) In the given figure A is the centre of the circle. Write the name of inscribed angle.

(iii) Draw seg AB of length 5 cm and bisect it.

(iv) Write the upper class limit of class 40 - 60.

(v) Using the information given in figure, find XY.

(vi) In figure, point C is the centre of circle. Write the name of the diameter.

Q. 2. Solve any four of the following sub - questions: [8]

(i) The circles with radii 7 cm and 3 cm touch internally, then find the distance between centres.

(ii) In figure, △PQR is a right angled triangle, ㄥQ = 900, ㄥR = 400, Write the ratios of sin 400 and cos 400.

(iii) Draw ㄥXYZ of measure 1200 and bisect it.

(iv) Ray BP is the bisector of ㄥABC. Find the value of x from the information given in the figure.

(v) Two coins are tossed. Write a sample space (S) and n(S). If A be the event of getting exactly one head, then write event A and find n(A).

(vi) Draw a tangent at any point P on the circle of radius 2 cm with centre O.


Q. 3. Solve any three of the following sub - questions: [9]

(i) Find the height of right - angled triangle whose base is 4 and hypotenuse is 3.

(ii) The radius of a sphere is 14cm. Find its surface area. (ㄫ = 22/7 )

(iii) Find the value of cos2 300 - sin2 600.

(iv) In the figure, m(arc APC) = 500. Find ㄥABC.

(v) Construct the incircle of an equilateral △ ABC having side 5 cm.

Q. 4. Solve any two of the following sub questions: [8]

(i) An observer is at a distance of 80 metres from a tower, makes an angle of elevation of 600 with the top of the tower. What is the height of the tower?

(ii) The marks obtained by a student in an examination in various subjects are given below.

Subjects
Marathi
English
Science
Mathematics
Social Science
Total
Marks
65
55
80
90
70
360
Represent the above data using a pie diagram.

(iii) Total volume of 21 steel balls in a bearing is 88 cm2. Find the diameter of each ball.

Q. 5. Solve any two of the following sub - questions. [10]

(i) In △ABC, AP is a median. If AP = 7, AB2 + AC2 = 260, then find BC.

(ii) The dimensions of a rectangular parallelepiped are in the ratio 4: 3: 2. If the surface area of vertical faces is 448 sq. cm. Find its length, breadth and height.

(iii) Represent the following data with a frequency polygon.

Class interval
18 - 20
21 - 23
24 - 26
27 - 29
30 - 32
Frequency
5
4
8
6
2

General Maths Algebra July 2015 Board Paper

Q.1. Attempt any five of the following sub - questions. [5]

(i) Write any two arithmetic progressions with common difference 3.

(ii) Write the following quadratic equation in the standard form.
ax2 + bx + c = 0.
x2 = 3x - 5.

(iii) Write the following equation in the general form of a linear equation in two variables. 7x = 3y + 23.

(iv) If y varies directly as x and y = 40 when x = 15, find the constant of variation.

(v) If the printed price is Rs. 50 and discount is Rs. 10, then find the selling price.

(vi) If the cost price is Rs. 100 and selling price is Rs. 120, then find the profit.


Q. 2. Attempt any four of the following sub - questions. [8]

(i) If tn = 2n + 3, then find the first two terms of a given sequence.

(ii) Solve the following quadratic equation by factorization method. n2 + n - 42 = 0.

(iii) If tn = 3n + 5, then find the A.P.

(iv) Write the following quadratic equation in the form of ax2 + bx + c = 0 and write the values of a, b and c. 3(m2 - m + 2) = 0.

(v) An agent sold an article for Rs. 4,000 at 6% commission. Find the commission of the agent.

(vi) If the rate of C.S.T. is 2%, then find C.S.T. for the printed price Rs. 800.


Q. 3. Attempt any three of the following sub - questions:

(i) Find the sum of all even natural numbers which are less than 75.

(ii) If x = 2 and y = 5 are the roots of the equation 7x + by = 54, then find the value of b.

(iii) Complete the following table in which x y.

x
4
5
2
.............
3
y
12
15
..........
21
...........

(iv) A salesman is offered 4% discount. Still he gets 20% profit. If the printed price of an article is Rs. 850, then find the cost price of the article.

(v) The printed price of an article is Rs. 500. If the rate of C.S.T. is 2%, then find the actual selling price if discount is not given.


Q. 4. Attempt any two of the following sub - questions: [8]

(i) Find S23 of an A.P.: 4, 8, 12, 16, .....

(ii) Solve the following simultaneous equations.
12x + 13y = 62 and 13x + 12y = 63.

(iii) A salesman is paid 7% commission on the total sales and an additional incentive at 4/5 on excess sales over Rs. 50,000. Find his total earnings on a total sales of Rs. 75,000.


Q. 5. Attempt any two of the following sub - questions: [5]

(i) The sum of two squares of two consecutive natural numbers is 85. Find the numbers.

(ii) y 1/√x and y = 10 when x = 6.25. Find y when x = 100.

(iii) The taxable income of Smt. Rekha (Age 45 years) is Rs. 6,50,000 for the financial year 2012 - 13. Complete the income tax she will have to pay for F.Y. 2012 - 13.