List of top Mathematics Questions

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground.
Find the \(31^{st}\) term of an AP whose \(11^{th}\) term is 38 and the \(16^{th}\) term is 73.
Check whether –150 is a term of the AP : 11, 8, 5, 2 .......
As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

If sin A = \(\frac{3}{4}\), calculate cos A and tan A.

D is a point on the side BC of a triangle ABC such that \(\angle\)ADC = \(\angle\)BAC. Show that  CA2=CB.CD
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.
In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ∼ ∆ECF
an isosceles triangle ABC with AB = AC
CD and GH are respectively the bisectors of ΔACB and ΔEGF, such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, show that:
(i) \(\frac{CD}{GH}=\frac{AC}{FG}\)
(ii) ΔDCB~ΔHGE
(iii) ΔDCA~ΔHGF
In the following figure, ABC and AMP are two right triangles, right-angled at B and M, respectively. Prove that: 
ABC and AMP are two right triangles
(i) ΔABC ~ ΔAMP 
(ii) \(\frac{CA}{PA}=\frac{BC}{MP}\)

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.

In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P.Show that: 
altitudes AD and CE of ΔABC intersect each other at the point P
(i) ΔAEP ~ ΔCDP 
(ii) ΔABD ~ ΔCBE 
(iii) ΔAEP ~ Δ ADB 
(iv) ΔPDC ~ ΔBEC
In the given figure find tan P - cot R
In the given figure find tan P - cot R
Find the number of terms in each of the following A.P.
  1. \(7, 13, 19, ……, 205\)
  2. \(18,15 \frac 12 ,13,……,−47\)
Which term of the AP : 3, 8, 13, 18, ........ is 78?
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
In the following APs, find the missing terms in the boxes :
Missing terms in the boxes
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.
Choose the correct choice in the following and justify : \(11^{th}\) term of the AP: \(– 3, -\frac 12, 2,.....\) is

Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.

Find the mean deviation about the median for the data.13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.