SSC Papers for Practice Geometry Maharashtra Board
Q.1)
Solve any Five (5)
1) ∆ABC
∆PQR. If AB:PQ = 3:4. Find
ratio of areas of their triangles.
2) Two circles
touch each other externally. If radii of the circles are 5 and 7, find distance
between their centres.
3) Draw a
segment of length 7cm and bisect it.
4) Find slope of
line having point (2,3) and (5,7)
5) An initial
arm rotates 205o in anticlockwise direction. Find in which quadrant
the angle lies.
6) Find total
surface area of cube of side 5.5cm.
Q.2)
Solve any Four (8)
1) D is a point
on side BC of ∆ABC such that
ADC =
BAC. Show that AC2 = BC× DC.
2) In figure point A is the
centre of the circle. AN = 10 cm. Line
NM is tangent at M. Determine the radius
of the circle if MN = 5cm
3) Prove that Sec2A
+ cosec2A = sec2A × cosec2A
4) Check whether following points are collinear (P(-2,3), Q (7, -4) and R (2,1)
4) Draw a circle
of radius 3.4cm. Take a point K on the circle and draw tangent without using
centre.
6) A sector of
circle with radius 10cm has central angle 72o. find area of sector.
Q.3.
Solve any Three (9)
1) Prove
that three times the square of any side of an equilateral triangle is equal to
four times the square of an altitude.
2) Prove tangents
drawn from the exterior of circle are congruent
3) Draw a circle of radius 2.7 cm and draw chord PQ of length 4.5 cm.
Draw tangents at P and Q without using centre.
4) If tanΘ + sinΘ = m and tanΘ – sinΘ = n. show that m2 –
n2 = 4√mn
5) Find volume and surface area of sphere of radius 4.2cm.
Q.4.
Solve any Two (8)
1) For an equilateral triangle of side
6.3cm draw a circumcircle and incircle.
2) A(5,4) B(-3,-2) and C((1,-8) are the vertices of ABC. Find equation
of median Ad and line parallel to AC and passsing through point B.
3) ∆ABC is inscribed in a
circle with centre O seg AX is a diameter
of the circle With radius r seg AD ⊥ seg BC.
Prove that (1) ∆ABX ~
4r
Q.5.
Solve any Two (10)
1. Water flows at the rate of 10m per
minute through a cylindrical pipe having its diameter 20mm. how much time will
it take to fill a conical vessel of base diameter 40cm and depth 24cm?
2. A tree 12m
high, is broken by the wind in such a way that its top touches the ground and. makes an angle 60o. with the
ground . At what height from the bottom the tree is broken
by the Wind.
3. From
the information given in the figure. Show that PM = PN = √3
