STD : Xth DATE : 10-12-2013 SUB : Geometry PRELIM PAPER – I - 2013 -14 Q. 1 Solve any five. √ then find the value of . Where is an acute angle. 1. If Sin =

MARKS : 40 TIME – 2 hrs (5)1.

2. Find the slope of the line whose Inclination is 600. 3. In the adjoining figure PC = 9, PA = 6 Find PB.

4. The side of a square is 8√2 cm. Find the length of its diagonal. 5. What is the equation of a line passing parallel to y axis and through the point (-2, -5)? 6. Find the values of x in the following figures, if line l is parallel to one of the sides of the given triangle.

P Q

Q. 2 Solve any four. 1. 2. 3. 4. 5.

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If A( 4, -3) is a point on the line 5x + 8y = C then find C. Draw an obtuse angle and bisect it. If Sec = √2 , where is an acute angle, then find the value of tan . If the area of minor sector of a circle with radius 11.2 cm is 49.28 cm2. Find the measure of the arc. In the adjoining figure, if m (arc APC) = 600. and m ∠ BAC = 800. Find a) ∠ ABC b) m(arc BQC)

6. In the adjoining figure, point Q is on the side MP such that MQ = 2 and MP = 5.5,Ray NQ is the bisector of ∠ MNP of ∆ MNP. Find MN : NP.

Q. 3 Solve any three.

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1. If 3tan2 - 4√3 tan + 3 = 0, find the acute angles . 2. Construct ∆ DCE, such that, DC = 7.9cm, ∠ C = 1350. ∠ D = 200. And draw it circumcircle. 3. In the isosceles triangle PQR, the vertical ∠ P = 500. The circle passing through Q and R cuts PQ in S and PR in T. ST is joined. Find ∠ PST.

4. In figure, ∆ ABC is a right angled at B. D is any point on AB. Seg DE Seg AC. If AD = 6cm, AB = 12cm, AC = 18cm. Find AE.

5. In the figure, A(O-AXB) is 12.56cm2 and radius is 12cm, find the area of the segment AXB. ( = 3.14, = √3 1.73)

Q. 4 Solve any two. (8) 1. A tree is broken by the wind. The top struck the ground at an angle of 300 and at a distance of 30m from the root. Find the whole height of the tree. (√3 = 1.73). 2. Prove That - The lengths of the two tangent segments to a circle drawn from an external point are equal. 3. A(3, 7); B(5, 11), C(- 2, 8) are the vertices of ∆ ABC. AD is one of the medians of the triangle. Find the equation of the median AD. Q. 5 Solve any two.

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1. ∆ AMT ~ ∆ AHE, In ∆ AMT, MA = 6.3cm, ∠MAT = 1200, AT = 4.9cm, and

= ; Construct

∆ AHE. 2. Prove That - The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 3. An ink container of cylindrical shape is filled with ink upto 91%. Ball pen refills of length 12cm and inner diameter 2mm are filled upto 84%. If the height and radius of the ink container are 14cm and 6cm respectively, find the number of refills that can be filled with this ink.

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STD : Xth SUB : Geometry Q. 1 Solve any five. 1. If Cos

DATE : 10-12-2013 PRELIM PAPER – I - 2013 -14

MARKS : 40 TIME – 2 hrs (5)

=

find Sec . √ 2. Draw perpendicular bisector of Seg AB of length 7 cm. 3. If area of the circle = 105 sq cm. and area of the minor segment = 30.75 sq.cm. find the area of the major segment. 4. If line PQ || line AB and slope of the line PQ is √3 then find slope of line AB.

5. ∆ DEF ~ ∆ ABC if AB = 4 cm, DE = 3cm. Find the value of

∆ ∆

?

6. In ∆ DEF ∠ E = 90. If DE = 4 cm, EF= 3cm. What is the length of side DF? Q. 2 Solve any four.

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1. If the slope of the line joining points (K, -3) and (4, 5) is 2. 3. 4. 5.

then find the value of k.

Construct a tangent to a circle of radius 3.2cm at a point on it. If the radius of the sphere is 3.5cm. find the volume of the sphere. Write the equation of the line passing through the origin and point ( -3, 5). In the given figure line l is parallel to side BC. Find the values of x.

P

Q 6. In the figure, seg AB and seg AD are the chords of the circle. C is a point on tangent of the circle at point A. If m(arc APB) = 800 and ∠ BAD = 300, then find (i) ∠ BAC (ii) m(arc BQD).

Q. 3 Solve any three. 1. In figure, ∠ LMN = 900 and ∠ LKN = 900, seg MK MK.

(9) seg LN. Prove that R is the mid-point of seg

2. In a clock, the minute hand is of length 14 cm. find the area covered by the minute hand in 5 minutes. 3. In figure, A and B are centres of two circles touching each other at M. Line AC and line BD are tangents. If AD = 6cm and BC = 9cm then find the length of seg AC and seg BD.

4. Find the equation of the line passing through (3, 6) and making intercepts equal in magnitude but opposite in sign. 5. Construct the in circle of ∆ SRN, such that RN = 5.9cm, RS = 4.9cm, ∠ R = 950 and draw in circle of it. Q. 4 Solve any two.

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1. Theorem - The opposite angles of a cyclic quadrilateral are supplementary. 2. In the figure ,Seg QR is a tangent to the circle with centre O, Point Q is the point of contact. Radius of the circle is 10 cm. QR = 20 cm. Find the area of the shaded region . 3.14, √3 1.73 "

3. Prove that :-

#$% & '() & *

+

'() & * #$% &

= 2 cosec

Q. 5 Solve any two.

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1. Theorem – If a line parallel to a side of a triangle intersect the other sides in two distinct points, then the line divides those sides in proportion. 2. ∆ ABC ~ ∆ DEF, In ∆ ABC, AB = 5.2cm, BC = 4.6cm, ∠ B = 450 and

+, -.

=

; construct ∆ DEF.

3. A bird was flying in a line parallel to the ground from north to south at a height of 200 metres. Tom, standing in the middle of the field, first he observed the bird in the north at an angle of 30o. After 3 minutes, he again observed it in the south at an angle of 45o. Find the speed of the bird in Kilometers per hour. (√3= 1.73)

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