Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Triangles

Long Answer Type

221. In the given Fig, O is a point in the interior of a triangle ABC, OD ⊥ BC,OE ⊥ AC and OF ⊥ AB. Show that
(i) OA² + OB² + OC² - OD² - OE² - OF² = AF² + BD² + CE^2,(ii) AF² + BD² + CE² = AE² + CD² + BF².

1753 Views

Short Answer Type

222.

A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

139 Views

223. A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

136 Views

Long Answer Type

224. An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after

1 1 half hours ?

132 Views

225.

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

156 Views

Short Answer Type

226. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE² + BD² = AB² + DE².

1006 Views

Long Answer Type

227. The perpendicular from A on side BC of a ∆ABC intersects BC at D such that DB = 3 CD. Prove that 2AB² = 2AC² +BC².

1138 Views

228. In an equilateral ABC, D is a point on side BC such that

BD equals 1 third BC.

Prove that 9AD² = 7AB².

1843 Views

229. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

352 Views

Short Answer Type

230. Tick the correct answer and justify: In ∆ABC, $AB equals 6 square root of 3 space cm comma space AC space equals space 12 space cm space and space BC space equals space 6 space cm.$ The angle B is:
(A) 120° (B) 60°
(C) 90° (D) 45°

$AB squared equals left parenthesis 6 square root of 3 right parenthesis squared space equals space 108 AC squared equals left parenthesis 12 right parenthesis squared space equals space 144 BC squared space equals space left parenthesis 6 right parenthesis squared space equals space 36$

Now,
$AB squared plus BC squared space equals space 108 plus 36 rightwards double arrow space space space space space space space space space space space space space space space space space space space space equals space 144 space equals AC squared$
∴ ∆ABC is a right angle triangle right angled at B.
Hence, the correct answer is (c) = 90°.