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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Class - X Physics Holidays H.W

1.         Draw a schematic diagram of a circuit consisting of a cell of 1.5 V, 10 Ω resistor and 15 Ω resistors and a plug key, all connected in series.
2.           A wire of resistivity ‘r’ is pulled to double its length. What will be its new resistivity?
3.      What is meant by saying that the potential difference between two points is 1V?
4.      What is electrical resistivity? In a series electrical circuit comprising a resistor made up of a metallic wire, the ammeter reads 5 A. The reading of the ammeter decreases to half when the length of the wire is doubled. Why?
5.      Calculate the resistance of a conductor, if the current flowing through it is 0.2 A when the applied potential difference is 0.8 volt.
6.      If 12 J of work is done in moving 2 coulomb of electric charge through a conductor, what is the potential difference at the ends of the conductor?
7.      The resistance of a wire of length 80 cm and of uniform area of cross-section 0.025 cm², is found to be 1.50 ohm. Calculate specific resistance of wire in SI units?
8.      What should be the length of nichrome wire of resistance 4.5Ω, if the length of similar wire is 60 cm and resistance 2.5 Ω?
9.       A charge of 5000 C flows through an electric circuit in 2.5 hours. Calculate the magnitude of current flowing through the circuit.
10.      A battery can supply a charge of 2.5 × 10³C. If the current drawn from the battery is 12.5 A, calculate the time in which battery will get discharged.
11.     What is the resistance of (hot) electric arc lamp when it uses a current of 25 A, while working at 440 V? 
12.          A current of 0.2 A flows through a conductor of resistance 4.5 Ω. Calculate the p.d. at the endsof the conductor.
13.      A wire is 1.0 m long, 0.2 mm diameter has resistance of 20 Ω. Calculate the resistivity of material.
14.       Give reason why (a) tungsten is used for making filament of electric lamps.  (b) The elements of heating electrical appliances are made up of an alloy rather than pure metal.
15.       Copper wire has resistance R. If the length of the wire is doubled, find the new resistance in terms of original resistance? 
16.      A battery of 9 V is connected in series with resistors of 0.2 Ω, 0.3 Ω, 0.4 Ω, 0.5 Ω  and 12 Ω resistors. How much current would flow through the 12 Ω  resistor?
17.     An electric iron draws a current of 0.5 A, when the voltage is 200 V. Calculate the amount of  electric charge flowing through it, in one hour
18.      Name an instrument used for measuring electric potential difference by drawing diagram showing how this instrument is connected in an electric circuit. Why does not this instrument practically consume any electric energy from the electric circuit
19.     (a) Why are conductors of electric heating devices, such as toasters and electric iron made of an alloy, rather than pure metals (b) Why is an ammeter likely to burn, if connected in parallel?
20. A piece of wire is redrawn by pulling it, until its length is trebled. Compare the new resistance of wire with the original resistance.

Linear Equations In Two Variables - Holidays H.W

1.  Solve: 47x + 31y = 63, 31x + 47y = 15.
2. The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.
3. The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expenditures are in the ratio of 7 : 5. If each saves Rs. 3000 per month, find the monthly income of each.
4. A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food 26days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of the food per day.
5. Nine times a two-digit number is the same as twice the number obtained by interchanging the digits of the number. If one digit of the number exceeds the other number by 7, find the number.
6. If 4 times the area of a smaller square is subtracted from the area of a larger square, the result is 144 m². The sum of the areas of the two squares is 464 m². Determine the sides of the two squares.
7. Half the perimeter of a rectangular garden, whose length is 4 m more than its breadth is 36 m. Find the dimensions of the garden.
8. A man travels 370 km partly by train and partly by car. If he covers 250 km by train and rest by car, it takes him 4 hours. But if he travels 130 km by train and rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.
9.   The age of a father is equal to sum of the ages of his 6 children. After 15 years, twice the age of the father will be the sum of ages of his children. Find the age of the father.
10.  The auto fare for the first kilometre is fixed and is different from the rate per km for the remaining distance. A man pays Rs. 57 for the distance of 16 km and Rs. 92 for a distance of 26 km. Find the auto fare for the first kilometre and for each successive kilometre.
11. A two digit number is obtained by either multiplying the sum of the digits by 8 or adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number. How many such numbers are there?
12. A man wished to give Rs 12 to each person and found that he fell short of Rs 6 when he wanted to give to all persons. He therefore, distributed Rs 9 to each person and found that Rs 9 were left over. How much money did he have and how many persons were there?
13. A person sells two articles together for Rs. 46, making a profit of 10% on one and 20% on the other. If he had sold each article at 15% profit, the result would have been the same. At what price does he sell each article?
14.   The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
15. A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from station A to B cots Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B cost Rs 3810. Find the full first class fare from station A to B and also the reservation charges for a ticket.
16. It takes 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long would it take for each pipe to fill the pool separately?
17. In a rectangle, if the length is increased and breadth reduced each by 2 meters, the area is reduced by 28 sq. m. If the length is reduced by 1 m and the breadth is increased by 2 m, the area increases by 33 sq. m. Find the length and the breadth of the rectangle.
18.  There are two classrooms A and B containing students. If 5 students are shifted from room A to room B, the resulting number of students in the two rooms become equal. If 5 students are shifted from room B to room A, the resulting number of students in room A becomes double the number of students left in room B. Find the original number of students in the two rooms.
19. Students of a class are made to stand in rows. If four students are extra in each row, there would be two rows less. If 4 students are less in each row, there would be 4 more rows. Find the number of students in the class.
20.  A person invested some amount @ 12% simple interest and some other amount @ 10% simple interest. He received an yearly interest of Rs. 13000. But if he had interchanged the invested amounts, he would have received Rs. 400 more as interest. How much amount did he invest at different rates?