Question Paper - Geometry 2013 - 2014-S.S.C-Board Exam Maharashtra State Board (MSBSHSE)



      Forgot password?

View all notifications
Books Shortlist
Your shortlist is empty
Year2013 - 2014 (March)

Marks: 40
Q: 1 | Solve any five sub-questions:[5]
Q: 1.1[1]

In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK).

view solution
Q: 1.2[1]

If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.

view solution
Q: 1.3[1]

If the angle θ = -60° , find the value of sinθ .

view solution
Q: 1.4[1]

Find the slope of the line passing through the points A(2,3) and B(4,7).

view solution
Q: 1.5[1]

The radius of a circle is 7 cm. find the circumference of the circle.

view solution
Q: 1.6[1]

If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.

view solution
Q: 2 | Solve any four sub-questions:[8]
Q: 2.1[2]

In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .

view solution
Q: 2.2[2]

In the following figure, Q is the center of the circle. PM and PN are tangents to the circle. If ∠MPN = 40° , find ∠MQN.


view solution
Q: 2.3[2]

Write the equation 2x - 3y - 4 = 0 in the slope intercept form. Hence, write the slope and y-intercept of the line.

view solution
Q: 2.4[2]

If cosθ=1/√2, where θ is an acute angle, then find the value of sinθ.

view solution
Q: 2.5[2]

If (4,-3) is a point on the line AB and slope of the line is (-2), write the equation of the line AB.

view solution
Q: 2.6[2]

Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.

view solution
Q: 3 | Solve any three sub-questions:[9]
Q: 3.1[3]

In a triangle ABC, line l || Side BC and line l intersects side AB and AC in points P and Q, respectively. Prove that: `"AP"/"BP"="AQ"/"QC"`

view solution
Q: 3.2[3]

In figure, ΔABC is an isosceles triangle with perimeter 44 cm. The base BC is of length 12 cm. Side AB and side AC are congruent. A circle touches the three sides as shown in the figure below. Find the length of the tangent segment from A to the circle.

view solution
Q: 3.3[3]

Draw tangents to the circle with center ‘C’ and radius 3.6 cm, from a point B at a distance of 7.2 cm from the center of the circle.

view solution
Q: 3.4[3]

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ

view solution
Q: 3.5[3]

Write the equation of each of the following lines:

  1. The x-axis and the y-axis.
  2. The line passing through the origin and the point (-3, 5).
  3. The line passing through the point (-3, 4) and parallel to X-axis.
view solution
Q: 4 | Solve any two sub-questions:[8]
Q: 4.1[4]

From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)

view solution
Q: 4.2[4]

Prove that the “the opposite angles of the cyclic quadrilateral are supplementary”.

view solution
Q: 4.3[4]

The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.

view solution
Q: 5 | Solve any two sub-questions:[10]
Q: 5.1[5]

In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:

1. cp = ab

2. `1/p^2=1/a^2+1/b^2`

view solution
Q: 5.2[5]

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

view solution
Q: 5.3[5]

There are three stair-steps as shown in the figure below. Each stair step has width 25 cm, height 12 cm and length 50 cm. How many bricks have been used in it, if each brick is 12.5 cm x 6.25 cm x 4 cm?

view solution