Q1.The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then, in metre, the height of the building is
(a) (h cotx)/(cotx+coty )
(b) (h coty)/(cotx+coty )
(c) (h cotx)/(cotx-coty )
Q2.ABC is a triangle in which DE || BC and AD: DB = 5 : 4, Then DE : BC is
(a) 4 : 9
(b) 5 : 9
(c) 4 : 5
(d) 9 : 5
Q3.One of the angles of a right-angled triangle is 15°, and the hypotenuse is 1 m. The area of the triangle (in sq. cm.) is
(a) 1200
(b) 1215
(c) 1220
(d)1250
Q4.G is the centroid of ∆ABC. If AG = BC, then angle BGC is -
(a) 90°
(b) 30°
(c) 60°
(d) 120°
Q5.Two sides of a triangle are of length 4 cm and 10 cm. If the length of the third side is ‘a’ cm, then
(a) a>5
(b) 6<a<12
(c) a<6
(d) 6<a<14
Q6.Taking any three of the line segments out of segments of length 2 cm, 3cm, 5 cm and 6 cm, the number of triangles that can be formed is:
(a) 3
(b) 2
(c) 1
(d) 4
Q7.Internal bisectors of angles ∠B and ∠C of a triangle ABC meet at O. If ∠BAC=80°, then the value of angle BOC is
(a) 120°
(b) 140°
(c) 110°
(d) 130°
Q8.By decreasing 15° of each angle of a triangle, the ratios of their angles are 2 : 3 : 5, the radian measure of greatest angle is
(a) 11π/24
(b) π/12
(c) π/24
(d) 5π/24
(a) (3√3)/2
(b) 9/4
(c) 3/4
(d) 3/2
Q10.If 29tanθ=31, then the value of (1+2 sinθ cosθ)/(1-2 sinθ cosθ ) is equal to
(a) 490
(b) 810
(c) 900
(d) 540
1-
2-
3-
4-
5-
(d);
The sum of any two sides of a triangle is greater than third side and their difference is less than third side.
∴ a+4>10
⇒a>10-4
⇒a>6
Again, a-4<10
⇒a<14
∴6<a<14
6-
b);
The sum of two sides of a triangle is greater than the third side.
(3, 5, 6) and (2, 5, 6)
7-
8-
(a);
2x+3x+5x=180°-45°=135°
⇒10x=135°
⇒x=135/10=27/2
∴ Largest angle
=5x+15°=(5×27/2)^°+15°
(135+30)/2=(165°)/2
∴180°=π radian
∴(165°)/2=π/180×165/2=11π/24 radian
9-
10-
