Area And Simultaneous Equations

Omtex – classes “THE HOME OF TEXT”

NAME OF THE STUDENT ROLL NO SUBJECT

TOTAL MARKS 100 TIME 3 HRS. Algebra

I. Answer the following any 3

(15 marks)

1. In the figure, PR and QS are two diameters of the circle. If PR = 28cm and PS = 14√3 cm, find_ a. areas of triangle OPS b. The area of the segments g & h .

(5 MARKS) p g S 1200

h

Q

R

2. In the following figure, three semicircles of diameters AB = 8 cm, BC = 4 cm, and CD = 2 cm are drawn. Find the following: (5 MARKS) 1. area of the shaded portion 2. The length of the boundary of the shaded region. 4 CM C A 8CM B 2 CM D A

3. In the figure, a circum circle of an equilateral triangle of side 6 cm is drawn. Find the area of the shaded region.

O B

C 600

4. In the figure, segment PQ is a diameter of semicircle PNQ The center of arc PMQ is O. OP = OQ = 10 cm and ∟POQ = 600. Find the area of the shaded portion.

P

Q

M

N

II. Answer the following ( any 10 )

(30 marks)

1. The measure of arc BCD of a circle having radius 7√2 cm and centre O is 450 . Find the area of segment BCD. 2. The centre of a circle is O and radius is 5 cm. If m (arc PRQ) = 900 , find the area of segment PRQ. 3. In the figure, O is the centre and segment PQ is a chord O of a circle. If OP = 12 cm and chord PQ is at a distance of 12 6 cm from the centre, find the area of the segment PRQ. 6 P Q M

R

4. The centre of a circle is O and the radius of the circle is 7 cm. The ratio of the area of circle to the area of sector O – PRQ is 6:1. Find the area of the segment PRQ. 5. In the figure, PQRS is a rectangle. SP = 100 cm and PQ = 70 cm. A semicircle is drawn with segment PQ as a diameter. Find the following. 1. Area of rectangle PQRS S P 2. Area of semicircle 70 cm 3. Area of shaded region R

100 cm

Q

6. The measure of the arc of a sector is 600 and the radius is 7 cm. Find the 1 OMTEX – CLASSES “The home of text”

OMTEX – CLASSES “The home of text”

Omtex – classes “THE HOME OF TEXT”

NAME OF THE STUDENT ROLL NO SUBJECT

TOTAL MARKS 100 TIME 3 HRS. Algebra

difference of areas of major sector and minor sector. 7. The area of a rhombus whose diagonals are Ac and BD is 49 sq cm. If BD = 7cm, find the area of semicircle on seg AC as a diameter. 8. In the figure, ∆ABC is an equilateral triangle of side 7 cm. Segment BC is a diameter of semicircle. Find the area of the shaded region. (√3 = 1.732) A

B

C A

B

9. In the figure, ABCD is a rectangle in which DC = 4.2 cm, and AD = 7cm. Seg Dc is a diameter of the semicircle. Find the area of the shaded portion.

D C 10. The measure of arc BCD of a circle having radius 7√2 cm and centre O is 450. Find the area of segment BCD. 11. A regular hexagon of side 6 cm is inscribed in a circle. Find the area of the region in the circle which is outside the hexagon. [ π = 3.14, √3 = 1.732] Attempt the given question (5 marks) C

ABC is an right angles triangle with ∟A as a right angle. AB = 8, AC = 6. Three semicircles are drawn on three sides of the triangle. Find the area of the triangle. Find the area of the shaded portion .

6 cm 8cm B A

2 OMTEX – CLASSES “The home of text”

OMTEX – CLASSES “The home of text”

Omtex – classes “THE HOME OF TEXT”

NAME OF THE STUDENT ROLL NO SUBJECT

TOTAL MARKS 100 TIME 3 HRS. Algebra

1. Solve the following simultaneous equations by graphical method. (Any 3 ) 9 marks. i. X + Y = 7; X – Y = 1. ii. 3X – 11 = Y; X – 3Y = 9. iii. X + 3 = 2Y; 2X + Y = 14. iv. X + 2+ Y = 6 ; 2X – Y = 1. 5 2. Solve the following simultaneous equations. (ALL) 12 marks. i. 3x – 2y = - 12; x + 6 = y. ii. 33x + 12y = 123; 33y + 12x = 102 iii. x + y = 5; x + y = 49 15 12

12 15 10

3. m – 2 + n + 2 = 5; m – 2 + n + 2 = 49 15 12 12 15 10

( 5 marks)

4. I have certain amount with me. If I give Rs. 3 to each ( 5 marks) student in a class, Rs. 30 are left with me and if I decide to give Rs, 4 to each student, then I need Rs. 10 more. Find the amount and the number of students in the class. 5. Cost of a table is three times the cost of a chair. One table ( 3 marks) and one chair together cost Rs. 800. Find the cost of a table. 6. In a cyclic quadrilateral ABCD, measure of angle A is ( 3 marks) double the Measure of angle C. Find the measures of angles A and C. 7. In a Parallelogram ABCD, the measure of Angle A is ( 3 marks) thrice the measure of Angle B. Find measure of Angle A & B. 8. Ramesh distributed certain number of pencils among ( 5 marks) his friends. If the number of friends were 4 more, then each would have got 1 pencil less. But if the number of friends were 4 less, then each would have received 2 pencils more. Find the number of friends and total number of pencils distributed. 9. Some part of journey of 765 km was made by ( 5 marks) car with a speed 60 km/hr; and remaining journey was made by train with a speed 96 km/hr. If total time required was 9 hrs. find the time taken by the train and distance covered by train

3 OMTEX – CLASSES “The home of text”

OMTEX – CLASSES “The home of text”