Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).
Question 22
22.
In Δ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm . Determine the values of sin Q and cos Q.
Question 23
23.
The angle of elevation of a tower at a point is 45°after going 40m towards the foot of the tower , the of elevation of the tower becomes 60°. Find the height of the tower.
Question 24
24.
In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC, Prove that 9 AD2 =7 AB2
Question 25
25.
Prove that
Question 26
26.
A straight highway leads to the foot of the tower. A man standing at the top of the tower observes a car at an angle of depression of 30° , which is approaching to the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.Find the time taken by the car to reach the foot of the tower from this point
Question 27
27.
Prove that the parallelogram circumscribing a circle is a rhombus
1. The diagonals of a rhombus are 16cm and 12cm, in length. The side of rhombus in length is:
a) 20 cm
b) 8cm
c) 10 cm
d) 9 cm
2. If triangles ABC and DEF are similar and AB=4cm, DE=6cm, EF=9cm and FD=12cm, the perimeter of triangle is:
(a) 22cm
(b ) 20cm
(c) 21cm
d) 18cm
3. A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
a) 25.6
b) 20.4
c) 23.7
d) 32.5
4. In the figure if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD
a) 53/3 cm
b) 55/3 cm
c) 64/3 cm
d) 35/7 cm
5. In the figure given below DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, the value of x is:
a) 4
b) 8
c) 16
d) 32
6. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is
-2
2
-1
1
7. The distance of the point P (2, 3) from the x-axis is
2
3
1
5
8. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is
-4
-12
12
-6
9. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
4 only
± 4
– 4 only
0
10. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
I quadrant
II quadrant
III quadrant
IV quadrant
11. (sin30° + cos30°) – (sin 60° + cos60°)
-1
0
1
2
12. If cos A = 4/5, then tan A = ?
3/5
3/4
4/3
4/5
13. If sin A + sin2 A = 1, then cos2 A + cos4 A = ?
1
0
2
4
14. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is
60°
45°
30°
90°
15. If the height of a tower and the distance of the point of observation from its foot,both are increased by 10%, then the angle of elevation of its top
increases
decreases
remains unchanged
have no relation
16. sin 2A = 2 sin A is true when A =
30°
45°
0°
60°
17. A circle can have _____parallel tangents at a single time
one
two
three
four
18. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to
65°
60°
50°
40°
19. The length of the tangent from an external point A on a circle with centre O is
always greater than OA
equal to OA
always less than OA
cannot be estimated
20. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is: