Download Geometry First Prelim ( 4 Question Papers )

A1
Date : 15 / 12 /2013
BACHHAV CLASSES PVT LTD
Sub. : Geometry
Std.: 10 th
Time : 2 Hrs.
B
Q.1. Solve any five of the following.
Marks : 40
5
Q
1) In figure, if m ( arc APC ) = 600
Find m ∠ ABC
C
A
P
2) State the slope and y - intercept of the line y = 3x -5.
3) If tan θ = 5, where θ is an acute angle find value of secθ using identity.
4) The terminal arm is in II quadrant, what are the possible angles ?
5) If
l = 5 cm, b = 4 cm, and h = 3 cm then find volume of the cuboid.
6) If radius and perpendicular height of a right circular cone is 6 cm and 8 cm respectively then find slant
height of a cone.
Q.2. Solve any four of the following.
8
M
1) In figure, seg NQ is angle bisector of ∠MNP.
Q
If MN = 15 cm, NP = 20 cm and MQ = 12 cm
0
then find the value of seg PQ.
N
0
P
2) The areas of two similar triangles are 81cm2 and 49 cm2 respectively. Find the ratio of their corresponding
heights. What is the ratio of their corresponding medians ?
3) In figure, point A is the centre of the circle AN = 10 cm
A
Line NM is tangent at M. Determine the radius of the circle if MN = 5 cm.
4) Eliminate θ, if x = a sec θ and
y = b tan θ.
M
N
5) Find the trigonometric ratios tan θ and cosθ if terminal arm passes through the point ( 5, 12 ).
6) Construct the circumcircle of ∆KLM in which LM = 7 cm, ∠K = 600, ∠M = 550.
Q.3. Solve any three of the following.
9
1) A vertical pole of a length 6 m casts a shadow of 4 m long on the ground. At the same time a tower
casts a shadow 28 m. long. Find the height of the tower.
2) Two circles which are not congruent touch externally. The sum of their areas is 130 π cm2 and the distance
between their centres is 14 cm. Find radii of circles.
3) Draw a tangents to a circle with centre M and radius 2.8 cm, from a point L at a distance of 5 cm from
the centre.
4) If ( 1, 2 ), ( ½, 3 ) and ( 0, k ) and are collinear point find the value of k.
5) A building has 8 right cylindrical pillars whose cross sectional diameter is 1 m and whose height is 4.2 m.
Find the expenditure to paint these pillars at the rate of Rs. 24 per m2.
Q.4. Solve any two of the following.
8
T
1) In the Fig. two circles intersects each other in points A and B.
Secants through the point A intersect the circles in point T.
R
A
Q
S
P
Show that : BSTR is a cyclic quadrilateral.
B
2) A pilot in an aeroplane observes that Vashi bridge is on one side of the plane and Worli sea - link is just
on the opposite side. The angle of depression of Vashi bridge and Worli sea - link are 600 and 300
respectively. If the aeroplane is at a height of 550 √3 m, at that time, what is the distance between Vashi
bridge and Worli sea- link?
Y
3) In the adjoining figure,two lines are intersecting at point (3, 4).
Find the equations of line PA and line PB.
P(3, 4)
600
A 450
X'
X
B
Y'
A
Q.5. Solve any two of the following.
1) Seg AN and seg CM are the medians of ∆ABC in which ∠ B = 900.
10
M
Prove that : 4 ( AN2 + CM2 ) = 5AC2
B
2) ∆ABC ~ ∆LMN, In ∆ABC, AB = 5.1 cm,
and
N
C
∠B = 550, ∠C = 650
AC
3
= . Construct ∆LMN
LN
5
3) The diameter of the base of metallic cone is 2 cm and height is 10 cm. 900 such cones are molten to
form 1 right circular cylinder whose radius is 10 cm. Find total surface area of the right circular cylinder
so formed.
( Given π = 3.14 )
BEST - LUCK
A2
BACHHAV CLASSES PVT LTD
Sub. : Geometry
Std.: 10 th
Date : 15 / 12 /2013
Time : 2 Hrs.
Marks : 40
Q.1. Solve any five of the following.
5
A
1) From the fig.
14
find the value of side AB.
30 0
B
C
2) Two circles with radii 8 cm and 3 cm respectively touch each other internally. Find distance between their
centres.
3) Draw the perpendicular bisector of seg AB of length 8.3 cm.
4) For an angle in standard position if the initial arm rotates 2200 in clockwise direction, in which quadrant
the terminal arm will lie ?
5) Write the equation 3x - 2y = 5 in slope intercept form.
6) Using Euler's formula find V, if E = 30 and F = 12.
Q.2. Solve any four of the following.
8
D
Q
1) In figure, seg AB and seg AD are chord of a circle.
Line AC is tangent if m ( arc APB ) = 800 and ∠ BAD = 300.
Find a) ∠ BAC
b) m ( arc BQD )
B
P
A
C
2) Draw a tangent at any point M on the circle of radius 2.9 cm and centre O.
3) If cos θ =
12
13
then find the value of sin θ.
4) 3 sinα - 4 cos α = 0, then the find the values of tan α and sec α, where α is an acute angle.
5) The radius of circle is 10 cm. Find the length of the arc, when the corresponding central angle is 2700.
(π = 3.14)
6) The cuboid water tank has length 2 m, breadth 1.6 m and height 1.8 m. Find the capacity of the tank
in litres.
Q.3. Solve any three of the following.
9
1) If ∆ PQR ~ ∆ XYZ and A ( ∆ PQR ) = 400 cm2, A ( ∆XYZ ) = 225 cm2, PQ = 16 cm. Find XY.
2) Prove that : 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.
3) Two circles with centres A and B are touching externally and a circle with centre C touches both the
circles externally. If AB = 3 cm, BC = 3 cm and CA = 4 cm, find the radii of the circles.
4) Construct the incircle of ∆STU in which ST = 7 cm, ∠T = 1200 and TU = 5 cm.
5) Find the equation of the line passing through ( - 3, - 5 ) and parallel to x - 2y - 7 = 0
Q.4. Solve any two of the following.
8
C
1) Two circles intersect each other in points A and B.
A
D
B
N
Secants through A and B intersect the circles in C, D and M, N.
Prove that : CM || DN.
M
2) ∆AMT ~ ∆AHE. In ∆AMT, MA = 6.3 cm, ∠MAT = 1200,
AT = 4.9 cm and
MA 7
=
HA 5
Construct ∆AHE.
3
and which passes through point P, where P divides
2
the line segment joining A( - 2, 6 ) and B( 3, - 4 ) in the ratio 2 : 3
3) Write down the equation of a line whose slope is
Q.5. Solve any two of the following.
10
1) In fig. A toy is a combination of a cylinder, hemisphere and a cone.
each with radius 10cm. Height of the conical part is 10 cm and total
height is 60 cm. Find the total surface area of the toy
( π = 3.14,
√ 2 = 1.41)
2) A tree is broken by the wind the top struck the ground at an angle of 300. and at a distance of 30 m
from the roots. Find the whole height of the tree.
( √ 3 = 1.73 )
3) Bisectors of ∠ B and ∠ C in ∆ABC
A
meet each other at P. Line AP cuts the side BC at Q.
Prove that : AP = AB + AC
BC
PQ
0
0
B
BEST - LUCK
P
×
Q
×
C
A3
Date : 15 / 12 /2013
BACHHAV CLASSES PVT LTD
Std.: 10 th
Sub. : Geometry
Time : 2 Hrs.
Marks : 40
A
Q.1. Solve any five of the following.
4
1) From the fig.
5
D
9
find the value of seg BD.
C
B
2) Draw ∠ ABC = 1150 and bisect it.
3) Angle of inclination of line AB is 450, find slope of line AB.
4) Find where the angle lies if the terminal arm passes through the point ( 5, -7 ).
T
5) In the figure, RP : PK = 3 : 2.
Find the value of : A ( ∆TRP) : A (∆TPK)
P
R
K
6) Find the slope of the line passing through the points A ( -2, 1) and B ( 0, 3 )
Q.2. Solve any four of the following.
8
1) A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder
from the base of the wall.
C
2) In figure, secants AC and AE intersects at points A.
B
They intersects circle in point B and D
A
E
If CB = 5, AB = 7, EA = 20 find ED.
D
3) Construct the incircle of ∆DEF in which DE = EF = 5.8 cm and ∠DEF = 650.
4) The terminal arm is on negative Y - axis, what are the possible angles ?
What can you say about this angle ?
5) Find x , if the slope of line joining ( x, - 2 ) and ( 8, - 11 ) is -3
4
.
6) The dimensions of a cuboid in cm are 16 × 14 × 20. Find its total surface area.
P
Q.3. Solve any three of the following.
9
1) In ∆PQR, seg PM is median.
If PM = 9 and PQ2 + PR2 = 290
then find QR.
Q
M
R
2) Prove that : Opposite angles of cyclic quadrilateral are supplementary.
3) Draw a circle with centre P and radius 3.1 cm. Draw a chord MN of length 3.8 cm. Draw tangents
to the circle through point M and N.
4) Prove that : sec2θ + cosec2θ = sec2θ × cosec2θ.
5) The curved surface area of the frustum of a cone is 180 sq. cm and the circumference of its circular
bases are 18 cm and 6 cm respectively. Find the slant height of the frustum of a cone.
Q.4. Solve any two of the following.
8
1) ∆LMN ∼ ∆XYZ, In ∆LMN, LM = 6 cm, MN = 6.8 cm, LN = 7.6 cm and
construct ∆XYZ.
LM
4
=
XY
3
2) A flagstaff stands on the top of a 5 metre high tower. From a point on the ground, the angle of elevation
of the top of the flagstaff is 600 and from the same point the angle of elevation of the top of the tower
is 450. Find the height of the flagstaff.
3) A( 5, 4 ), B( - 3, - 2 ) and C ( 1, - 8 ) are the vertices of a triangle ABC. Find the equation of median AD
and line parallel to AC passing through point B.
Q.5. Solve any two of the following.
10
A
1) Two circles intersects each other at A and B. Let DC be
a common tangent touching the circle in point C and D.
B
Prove that : ∠ CAD + ∠ CBD = 1800
C
D
2) The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum
is 8 cm.
Find i) curved surface area of the frustum
ii) Total surface area of the frustum
iii) Volume of the frustum
K
3) In the given figure,
A
AD is bisector of the exterior ∠ A of ∆ ABC.
0
0
Seg AD intersects side BC produced in D.
Prove that :
BD AB
=
CD AC
B
BEST - LUCK
C
D
A4
Date : 15 / 12 /2013
BACHHAV CLASSES PVT LTD
Sub. : Geometry
Std.: 10 th
Time : 2 Hrs.
Marks : 40
Q.1. Solve any five of the following.
5
N
1) In the figure, point Q is on side MP such that MQ = 4 and QP = 5.
0 0
Ray NQ is the angle bisector of ∠ MNP of ∆ MNP.
Q
M
Find MN : NP.
P
2) Find the diagonal of the square whose side is 20 cm.
3) Draw seg MN of length 5 cm and bisect it.
4) Find the value of sin ( - 600 )
5) State the equation of X - axis and Y - axis.
6) Find the slope and y-intercept of the line y = 4x + 7
B
l
6
Q.2. Solve any four of the following.
8
P
1) In the given adjoining fig. line l || side BC. Find the value of x
2) If tan A +
3
A
1
1
= 2, then show that : tan2 A +
= 2
tan2 A
tan A
5 Q
x
C
3) Draw a circle of radius 3.5 cm.Take any point K on it.
Draw a tangent to the circle at K without using the centre of the circle.
C
4) In figure tangent PA and secant PBC are shown.
B
If AP = 10 and BP = 5 find BC.
A
P
5) If ( m, 2 ) is a point on the line 4x - 3y = 6, then find the value of m.
6) Curved surface area of a cone with base radius 40 cm is 1640 π. sq. cm. Find the height of a cone.
Q.3. Solve any three of the following.
9
1) Prove that : In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares
of remaining two sides.
2) Secants containing chords RS and PQ of a circle intersect each other in point A in the exterior of a circle,
as shown in fig.
If m (arc PR) =
S
260
Find: i) m ∠ AQR
and m ( arc QS ) =
ii) m ∠ SPQ
480,
iii) m ∠ RAQ
R
A
P
Q
3) Construct the incircle of ∆RGN, such that RN = 5.9 cm, RG = 4.9 cm, ∠R = 950
4) Find the possible value of cos x if cot x + cosec x = 5
5) A horse is tied to a pole fixed at one corner of a 30m × 30m square field of grass by a 10m long rope.
i) Find the area of that part of the field in which the horse can graze.
ii) Find the area of that part of the field in which the horse can not graze.
(π = 3.14)
Q.4. Solve any two of the following.
1) ∆SHR ∼ ∆SVU,
In ∆SHR,
8
SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SH
3
SV = 5
construct ∆SVU.
2) The angle of elevation of a cloud from a point 60 m above a lake is 300 and the angle of depression of
the reflection of cloud in the lake is 600. Find the height of the cloud.
3) Find the equation of the straight line passing through the origin and the point of intersection of the lines
x + 2y = 7 and x − y = 4.
Q.5. Solve any two of the following.
10
1) In a trapezium ABCD, side AB || side DC. Diagonals AC and BD cut each other in point M.
If 2 AB = 5 DC.
Prove that : 25 A( ∆MDC ) = 4 A (∆MAB)
2) Suppose two circles are touching at A. Through A, two lines are drawn intersecting one circle in P, Q
and the other in X, Y.
Prove that : PQ || XY.
3) An ink container of cylindrical shape is filled with ink upto 91%. Ball pen refills of length 12 cm and inner
diameter 2 mm are filled up to 84 %. If the height and radius of the ink container are 14 cm and 6 cm
respectively. Find the number of refills that can be filled with ink..
BEST - LUCK