Class IX Holidays Home work Polynomials Assignment

1.        Find the value of x³ + y³ – 12xy + 64 when x + y = –4.
2.       If x = 2y + 6, then find the value of x³ – 8y³ – 36xy – 216.
3.      The polynomials kx³ + 3x² – 8 and 3x³ – 5x + k are divided by x + 2. If the remainder in each case is the same, find the value of k.
4.      Find the values of a and b so that the polynomial x³ + 10x² + ax + b has (x – 1) and          (x + 2) as factors.
5.      Find the values of p and q, if the polynomial x⁴ + px³ + 2x² – 3x + q is divisible by the polynomial x² – 1.
6.       If x – 3 is a factor of x² – kx + 12, then find the value of k. Also, find the other factor for this value of k.
7.      Find the value of k so that 2x – 1 be a factor of 8x⁴ + 4x³ – 16x² + 10x + k.
8.       If ax³ + bx² + x – 6 has (x + 2) as a factor and leaves a remainder 4 when divided by x – 2, find the values of a and b.
9.     If the polynomial P(x) = x⁴ – 2x³ + 3x² – ax + 8 is divided by (x – 2), it leaves a remainder 10. Find the value of a.
10. If both (x – 2) and ( x − 1/2 ) are factors of px² + 5x + r, show that p = r.
11. Find the value of a if (x + a) is a factor of x⁴ – a²x² + 3x – a.
12. Factorise by splitting the middle term : 9(x – 2y)² – 4(x – 2y) – 13.
13. Find the remainder obtained on dividing 2x⁴ – 3x³ – 5x² + x + 1by x - 1/2.
14. The polynomial p(x) = x⁴ – 2x³ + 3x² – ax + 3a – 7 when divided by x + 1, leaves the remainder 19. Find the value of a. Also, find the remainder when p(x) is divided by x + 2 
15. Without actual division prove that (x – 2) is a factor of the polynomial 3x³ – 13x² + 8x + 12. Also, factorise it completely.

CLASS - IX PHYSICS HOLIDAYS HOME WORK

1.        State two differences between scalar and vector quantities.
2.    State two differences between distance and displacement.
3.    State two differences between speed and velocity.
4.     A car moving along a circular path of radius 140 m, completes one round in 20 s. What is the speed of the car (ii) the displacement of the car?
5.    Give an example of a body moving with a uniform speed and uniform acceleration. Justify your answer.
6.    (a) What do you understand by the term : (i) Distance (ii) Displacement? (b) State the SI units of distance and displacement.
7.    A body is moving along a circular path of radius R. What will be the distance covered and the displacement of the body after half revolution?
8.    A person starts from his house and travels a circular distance of 15 km around the walled city before returning back. What is (a) the distance covered by the person, (b) the displacement of the person
9.     Define the terms : (i) speed and (ii) velocity.
10.    Why is speed considered an incomplete physical quantity? Name a quantity akin to speed which describes the motion of a particle more accurately.
11.    Name a physical quantity which corresponds to: (a) rate of change of displacement (b) rate of change of velocity
12.    Arrange the following speeds in the increasing order : (i) A scooter moving with a speed of 300 m per minute. (ii) A car moving with a speed of 27 km per hour.
13.    Draw a diagram to show the motion of a body whose speed remains constant, but the velocity changes continuously.
14.    Draw a velocity versus time graph of a stone thrown vertically upwards and then coming downwards after attaining the maximum height.
15.     A bus travels at a distance of 120 km with a speed of 40 km/h and returns with a speed of 30 km/h. Calculate the average speed for the entire journey
16.     A bus accelerates uniformly from 54 km/h to 72 km/h in 10 s. Calculate : (i) the acceleration                              (ii) the distance covered by the bus in that time
17.     (a) An object travels 16 m in 4 seconds and the next 16 m in 2 seconds. Calculate the average speed of the object.                                                                                                                                                        (b) Give an example of an object moving under uniform circular motion. 
18.        The driver of a train A travelling at a speed of 54 km/h applies brakes and retards the train uniformly. The train stops in 5 s. Another train B is travelling on the parallel track with a speed of 36 km/h. This driver also applies the brakes and the train retards uniformly. The train B stops in 10 s. Plot speed - time graph for both the trains on the same paper. Also calculate the distance travelled by each train after the brakes were applied.
19.      (a) A car accelerates uniformly from 18 kmh–1 to 36 kmh–1 in 5 s. Calculate : (i) acceleration                (ii) distance covered by the car in that time                                                                                                        (b) The length of minute hand of a clock is 14 cm. Calculate the speed with which the tip of the minute hand moves
20.  A car is moving on a straight road with a uniform acceleration. The following table gives the speed of the car at various instants of time.

                                      Time (s)                 0              10           20           30           40           50

                                     Speed (ms–1)          5              10           15           20           25           30

21 Draw the distance-time graph for the following situations :

(a) When a body is stationary.

(b) When a body is moving with a uniform speed.

(c) When a body is moving with variable speed and uniform acceleration.

22 The displacement of a moving object in a given interval of time is zero. Would the distance travelled by the object also be zero? Justify your answer.

23 A car starts from rest and moves along the x-axis with a constant acceleration of 5 m s–2 for 8 seconds. If it then continues to move with a constant velocity, what distance will the car cover in 12 seconds since it started from rest?

 24 A motorcyclist drives from A to B with a uniform speed of 30 km h–1 and returns back with a speed of 20 km h–1. Find its average speed.

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