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EXTRA QUESTIONS (Quadratic Equations) SET-1
PODAR INTERNATIONAL SCHOOL (CBSE)
Topic : Quadratic Equations
1. The number of quadratic equations having real roots and which do not change by
squaring their root is :
(a) 4 (b) 3
(c) 2 (d) 1
2. For what value of k are the roots of the quadratic equation 3x+ 2 kx+ 27 = 0 are
real and equal?
3. An express train takes 1 hour less than a passenger train to travel 132 km between
Agra and Delhi( without taking into consideration the time they stop at intermediate
stations).If the average speed of the express train is 11km/hr more than that of the
passenger train, find the average speed of two trains
4. A takes 3 days longer than B to finish a work. But if they work together, then work
is completed in 2 days. How long would each take to do it separately? Can you say
cooperation helps to get more efficiency?
5. If x = 1 is a common root of ax2+ ax + 3 = 0 and x2+ x + b = 0, then ab = ?
a. 3 b. - 3
c. 4 d. 6
6. If x2+ 2 ( k + 2) x + 9 k = 0 has a repeated root, thenk = ?
(Repeated root means two roots are equal)
a. 1 or 4 b. 1 or - 4
c. - 1 or 4 d. - 1 or - 4
7. If x2- 4x + p = 0 has real roots, then
a. p ≥4 b. p ≤4
c. p ≥5 d. p ≤- 4
8. Which of the following is not a quadratic equation?
a. x2+ 2 x + 1 = 0 b. 2 x - x2= x2- 5
c. x2+ 9 = 3x2- 5x d. ( x2+ 1 )2= x2+ 3x + 9
9. If is a root of the equation x2+ kx - = 0, then the value of k is
a. 2 b. - 2
c. 1/4 d. 1/2
10 For what value of k ≠0, the polynomial kx2- 3 kx + 9 is a perfect square ?
a. k = 1 b. k = 2
c. k = 3 d. k = 4
11. If D is the discriminant of a quadratic polynomial,the false statement of the following is
a. D can hold negative value b. D can hold positive value
c. D can hold a zero value d. D = 0 always
12. The positive root of the quadratic equation x2+ ( x + 1)2 = 313 is
a. 12 b. 13
c. 12 and - 13 d. 12 and 13
13 The roots of the equation x2+ x - ( k + 1 ) ( k + 2) = 0 are
a. k + 1 b. - ( k + 2 )
c. k + 2 d. k + 1 and - ( k + 2)
14 .The equation 3x2 + 4√3x + 4 = 0 has
a. Two distinct real roots b. Two equal real roots
c. No real roots d. More than two real roots
15 Which of the following equations has the sum of itsroots as 3?
a. 2 x2- 3 x + 6 = 0 b. - x2+ 3 x - 3 = 0
c.√2x2- √x + 1 = 0 d. 3 x2 - 3x + 3 = 0
16.Which of the following equations has the product of its roots as
a. 2 x2+ 7 = 0 b. 2x2+ 4x + 7 = 0
c. 2x2- 4x + 7 = 0 d. 2 x2+ 4 x - 7 = 0
17 Which of the following has no real roots
a.x2- 4x + 3√2 = 0 b. x2+ 4 x - 3√2= 0
c. x2- 4x - 3√2 = 0 d. 3x2+ 4 √3 x + 4 = 0
xv If no roots of the equation x2- px + 1 = 0 is real, then
a. p >2 b. p < - 2
c. p = 2 d. - 2 <p < 2
18. Which constant must be added and subtracted to solve the quadratic equation
9x2+ 6 x - 5 = 0?
a. 1 b. 14
c. 18 d. 49
19. Two numbers whose sum is 27 and the product is 182,is
a. 8, 19 b. 11, 16
c. 13, 14 d. 15, 12
20. Two consecutive odd positive integers , sum of whose squares is 290 are
a. 9, 11 b. 11, 13
c. - 11, - 13 d. 12, 13
21. The hypotenuse of a right angled triangle is √52cm. If the smaller and the larger of the
remaining two sides are respectively tripled and doubled, then the new hypotenuse will be
√288cm. The original lengths of these two sides were ,respectively
a. 4cm and 6 cm b. 2 cm and 3 cm
c. 6cm and 8 cm c. 5 cm and 12 cm
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EXTRA QUESTIONS (Application of trigonometry) SET-1
PODAR INTERNATIONAL SCHOOL (CBSE)
Topic : Heights & Distances
1.The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled ,
then the angle of elevation of its top will also be doubled. Is it true?
2. If the angle of depression of an object from a 75m high tower is 30°.Find the distance of the
object from the base of the tower.
3. A balloon is connected to a meteorological ground station by a cable of length 215 m
inclined at 60° to the horizontal. Determine the height of the balloon from the ground.
Assume that there is no slack in the cable.
4. A tree of 12 m height is broken by the wind in sucha way that its top touches the ground
and makes an angle 60° with the ground. At what height from the bottom, the tree is broken
by the wind?
5. The angle of elevation of the top of a hill from the foot of a tower is 60° and the angle of
elevation of top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what
is the height of the hill?
6. Two men on opposite sides of the cliff 80 m high observe the angles of elevation of the top
of the cliff to be 30° and 60° respectively. Find the distance between the two men.
7. A ladder is placed against a wall such that it reaches the top of the wall. The foot of the
ladder is 1.5 m away from the wall and the ladder is inclinedat an angle of 60° with the ground. Find
the height of the wall.
8. Find the angle of elevation of the Sun (Sun's altitude) when the length of the shadow of a
vertical pole is equal to its height.
9. From a point 20 m away from the foot of a tower, the angle of elevation of the top of the
tower is 30°. Find the height of the tower.
10. The horizontal distance between two towers is 140 m. The angle of elevation of the top of
the first tower when seen from the top of the second tower is 30°.If the height of the second
tower is 60 m, find the height of the first tower.
11. Find the angular elevation of the Sun when the shadow of a 10 m long pole is 10 √3m.
12. The angles of elevation of the top of a hill, at the city centres of two towns on either side of
the hill are observed to be 30° and 60°.If the distance uphill from the first city centre is 9
km, find the distance uphill from the other city centre in kilometres up to two places of
decimals.
13. An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°.
After 10 seconds its elevation is observed to be 30°. Find the speed of the aeroplane in km/
hr.
14. An aeroplane at an altitude of 200 m observes the angles of depression of opposite points
on the two banks of a river to be 45° and 60°. findin metres, the width of the river.
15. The angle of elevation of the top of the tower fromtwo points at a distance of 25m and
36m from the base of the tower and in the same straight line with it are complementary. Prove
that the height of the tower is 30m.
16. Monica is a 1.5 m tall girl. She is standing at a distance of 28.5 m from a multi-storeyed
building. The angle of elevation of the top of thebuilding from her eyes is 45°.Find the
height of the multi - storey building.
17. Two pillars of equal heights are on either side of a road, which is 100 m wide. At a point on
the road between the pillars, the angles of elevation of the top of the pillars are 60° and 30°
respectively. Find the position of the point between the pillars and the height of each pillar.
18. The angle of elevation of an aeroplane from a pointon the ground is 45°.After a flight of 15
seconds, the elevation changes to 30°.If the aeroplane is flying at a constant height of 3000
metres, find the speed of the aeroplane.
19. An aeroplane, when 3000 m high , passes vertically above another aeroplane at an instant
when the angles of elevation of the two aeroplanes from the same point on the ground are
60° and 45° respectively. Find the vertical distance between the two planes.
20. From the top and foot of a tower 40m high, the angles of elevation of the top of a lighthouse
are found to be 30° and 60° respectively. Find the height of the light house. Also find the
distance of the top of the light house from the foot of the tower.
21. A 1.6 m tall girl stands at a distance of 3.2 m from a lamp - post and casts a shadow of 4.8 m
on the ground. Find the height of the lamp - post by using
a. Trigonometric ratios b. property of similar triangles
22. A man on a cliff observes a boat at an angle of depression of 30° which is approaching the
shore to the point immediately beneath the observerwith a uniform speed. Six minutes later,
the angle of depression of the boat is found to be 60°.Find the time taken by the boat to
reach the shore.
23. A man standing on the deck of a ship, which is 10 mabove the water level, observes the
angle of elevation of the top of a hill as 60° and the angle of depression of the base of the
hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
24. A man standing on the deck of a ship, which is 10 mabove the water level, observes the
angle of elevation of the top of the hill as 60° and the angle of depression of the base of the
hill as 30°, calculate the distance of the hill from the ship and the height of the hill.
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