List of practice Questions

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
A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. If, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks -
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.
For any arbitrary motion in space, which of the following relations are true : 
  1. \(v_{average}\)= \(\bigg(\frac{1}{2}\bigg)\) (\(v\) (\(t_1\) ) + \(v\) (\(t_2\) )) 
  2. \(v_{average}\) = \(\frac{[r(t_2)-r(t_1)]}{(t_2-t_1)}\)
  3. \(v(t)\) = \(v(0)\) + \(at\) 
  4. \(r(t)\) = \(r(0)\) + \(v(0)t+\bigg(\frac{1}{2}\bigg)at^2\)
  5. \(a_{average}\) =\(\frac{[v(t_2)-v(t_2)}{(t_2-t_1)}\) 
    (The ‘average’ stands for average of the quantity over the time interval \(t_1\) to \(t_2\) )
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.
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 \(m\,s^{-1}\), what is the recoil speed of the gun ?
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.
A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?
Two billiard balls each of mass 0.05 \(\text {kg}\) moving in opposite directions with speed 6 \(\text m \,\text s^{-1}\)collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?
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.
A man of mass 70 \(\text {kg}\) stands on a weighing scale in a lift which is moving 
  1. upwards with a uniform speed of 10 \(\text m \,\text s^{-1}\) , 
  2. downwards with a uniform acceleration of 5 \(\text m \,\text s^{-2}\) , 
  3. upwards with a uniform acceleration of 5 \(\text m \,\text s^{-2}\) . What would be the readings on the scale in each case? 
  4. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity ?
A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.
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.