PYQ Collection:
Unique questions extracted from Series 30/1 to 30/6.
Duplicate/repeated questions have been consolidated while retaining
the relevant Series and Question Numbers.
Section A — Multiple Choice Questions (1 Mark)
A kite is flying at a height of 150 m from the ground.
It is attached to a string inclined at an angle of \(30^\circ\)
to the horizontal. The length of the string is:
(A) \(100\sqrt{3}\) m
(B) 300 m
(C) \(150\sqrt{2}\) m
(D) \(150\sqrt{3}\) m
Assertion (A):
A ladder leaning against a wall stands at a horizontal distance
of 6 m from the wall. If the height of the wall up to which the
ladder reaches is 8 m, then the length of the ladder is 10 m.
Reason (R):
The ladder makes an angle of \(60^\circ\) with the ground.
Assertion is true by Pythagoras theorem, but the Reason is not correct.
A 30 m long rope is tightly stretched and tied from the top of a
pole to the ground. If the rope makes an angle of \(60^\circ\)
with the ground, the height of the pole is:
(A) \(10\sqrt{3}\) m
(B) \(30\sqrt{3}\) m
(C) 15 m
(D) \(15\sqrt{3}\) m
A peacock sitting on the top of a tree of height 10 m observes a
snake moving on the ground. If the snake is \(10\sqrt{3}\) m away
from the base of the tree, then the angle of depression of the
snake from the eye of the peacock is:
(A) \(30^\circ\)
(B) \(45^\circ\)
(C) \(60^\circ\)
(D) \(90^\circ\)
Section B — Very Short Answer Questions (2 Marks)
A 1.5 m tall boy is walking away from the base of a lamp post
which is 12 m high, at the speed of 2.5 m/sec.
Find the length of his shadow after 3 seconds.
Section D — Long Answer Questions (5 Marks)
Two ships are sailing in the sea on either side of a lighthouse.
The angles of depression to the two ships as observed from the
top of the lighthouse are \(60^\circ\) and \(45^\circ\),
respectively.
If the distance between the ships is
\[
100\left(\frac{1+\sqrt{3}}{\sqrt{3}}\right)\text{ m},
\]
find the height of the lighthouse.
The angles of depression of the top and bottom of an 8 m tall
building from the top of a multi-storeyed building are
\(30^\circ\) and \(45^\circ\), respectively.
Find the height of the multi-storeyed building and the distance
between the two buildings.
The angle of elevation of a helicopter flying at a constant height
of 2000 m from a point A on the ground is \(45^\circ\).
After 15 seconds of flight, the angle of elevation changes to
\(30^\circ\).
Find the speed of the helicopter.
Take \(\sqrt{3}=1.732\).
A 1.5 m tall girl is standing at some distance from a 30 m tall
tower. The angle of elevation from her eyes to the top of the
tower increases from \(30^\circ\) to \(60^\circ\) as she walks
towards the tower.
Find the distance she walked towards the tower.
Section E — Case Study Based Questions (4 Marks)
Lighthouse Observation
Amruta is standing at a distance from the foot of a lighthouse
and observes the top at \(60^\circ\). She then ascends 40 m to an
observation deck and finds the angle of elevation to be \(45^\circ\).
(i) If \(CD=h\) metres, find distance \(BD\)
in terms of \(h\). (1)
(ii) Find distance \(BC\) in terms of \(h\).
(1)
(iii) (a) Find the height of the lighthouse
\(CE\). Use \(\sqrt{3}=1.73\). (2)
OR
(iii) (b) If \(AC=100\) m, find distance
\(AE\). (2)
Ship Approaching Rock
A lighthouse is situated on a rock. The height of the lighthouse
is 50 m. The angle of depression of a ship changes from
\(30^\circ\) to \(45^\circ\) as it moves from point P to Q.
(i) Find the distance of the ship from the base
of the lighthouse when it is at Q, where the angle of depression
is \(45^\circ\). (1)
(ii) Find the measure of
\(\angle PBA\) and \(\angle QBA\). (1)
(iii) (a) Find the distance \(PQ\) covered by
the ship. (2)
OR
(iii) (b) If the ship takes 10 minutes to go
from Q to A, calculate its speed in km/h. (2)
Drone for Emergency
A drone is hovering at a height of 100 m above point Q.
The angle of depression to the accident site P is \(30^\circ\).
(i) Represent the information through a
labelled sketch. (1)
(ii) Find the distance between the ambulance
at P and the accident site at the given moment. (1)
(iii) (a) Find the time taken if the angle
changes from \(30^\circ\) to \(45^\circ\). (2)
OR
(iii) (b) If the drone moves to a point T and
the angle of depression is \(60^\circ\), find the time.
(2)
Statue of Unity
A student uses an inclinometer to find the height of the
Statue of Unity.
Situation I:
The angle of elevation from Point A, which is
\(80\sqrt{3}\) m from the base, is \(60^\circ\).
Answer the questions based on the given situation and
observations to determine the height of the Statue of Unity
and related distances/angles.
End of Chapter 9 PYQs
Total Unique Questions: 13
MCQs: 4 |
2 Marks: 1 |
5 Marks: 4 |
Case Study: 4