SSC Papers for Practice Geometry Maharashtra Board
Q.1)
Solve any Five (5)
1) In ∆ABC ∠C = 60o, ∠B= 90o, AC = 10cm. Find AB and BC.
2) Draw an angle of measure 120o and
bisect it.
3) Find area of
sector of a circle of radius 6cm and arc length 15cm.
4) Find slope of
inclination of line if Θ= 30o.
5) The terminal
arm is on negative y axis what are the possible angles?
6) Two circles
having radius 5cm and 4cm touch each other internally. Find distance between
their centres.
Q.2)
Solve any Four (8)
1) In Fig. 2.17, Q is the centre
of circle and PM and PN are tangent
segments to the circle. If ∠MPN = 40°,
find ∠MQN.
2) In the
figure ray PT is the bisector of ∠QPR. Find value of x and the perimeter of ∆PQR.
3) Find
value of cosΘ and sinΘ if the ray passes through point(4,5)
4) Check whether following points are collinear P(2,4), Q (4,6) and R (6,8)
5) Draw a circle
of radius 3.4cm. Take a point K on the circle and draw tangent without using
centre.
6) Find measure of arc of circle if the radius is 3.5cm and area of sector is 3.85 sqcm.
Q.3.
Solve any Three (9)
1) As shown in Fig. 2.55, two chords AB and CD of the same circle are parallel to each
other. P is the centre of the
circle, Show that ∠CPA = ∠DPB.
2) Prove Areas
of similar triangle.
3) Construct the incircle of ∆STU in which
ST = 7 cm, ∠T = 120°,
TU = 5 cm.
4) The volume of
cylinder is 6160cm3 and height is 10cm. Find its curved surface
area.
5) Prove
that 1 + Sin A = 1 + Sin A + Cos A
Cos A 1 + Cos A - Sin A
Q.4.
Solve any Two (8)
1) In the adjoining figure, O is the centre and seg AB is a diameter. At the point C on the circle, the tangent CD is drawn. Line BD is a tangent to the circle at
the point B. Show that seg OD|| chord
AC.
2) Show that P(-2,4), Q(4,8), R(10,5) and S(4,1) are the vertices of a
parallelogram.
3) In∆PQR ∠Q= 90o,
seg QM is median. PQ2 + PR2 = 169. Draw a circumcircle of
∆PQR
Q.5.
Solve any Two (10)
1. A man on a cliff observes a boat at an angle of depression 30o,
which is sailing towards the point of
the ‘shore immediately beneath him . Three minutes later the angle of depression of the boat is found to be 60o.
Assuming that the boat sails at a uniform
speed , determine how much more time it will take to reach the shore .
2. Marbles of diameter 1.4cm are dropped into a beaker containing some
water and are fully submerged. The diameter of beaker is 7cm. find how many
marbles are dropped if the water rises by 5.6cm.
3. Two poles of height a meters and b meters are p metres
apart. Prove that the height h of the point of intersection N of the lines
joining the top of each pole to the foot of the opposite pole is ab
a+b
