Holidays Homework - X

Probability, Coordinate Geometry & Polynomials

1.       One card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the card drawn is                                                                                                                        i) a non face card                                                                                                                           ii)         Neither a red card nor a queen

iii)        A king, a queen, a jack or an ace
iv)        A heart or a queen
v)         A king or a jack
vi)        Neither a king nor a queen
vii)       Either a king or a queen
viii)      A queen and a card of red order
ix)        A queen or a card of black order
x)         A black face card and a king
2.      Balls marked with 7 to 37 are put in a box. One ball is taken out randomly, find the probability that the ball taken out is                                                                                                          i)   A multiple of 2 and 3
ii)         A multiple of 2 or 3
iii)        A prime number
iv)        A multiple of 3 and odd number
v)         A perfect square 
3.      A number is chosen randomly from first 50 natural numbers, find the number chosen is divisible by 4 or 5
4.      A pair of dice is thrown simultaneously, find the probability of getting                                 i)          sum as 7                                                                                                                                  ii)         sum divisible by 3
iii)        Even on one die and prime on another
5.      The probability of selecting a green marble at random from a jar which contains only green, white and red marbles is ¼. The probability of selecting a white marble at random from the same jar is 1/3. If this jar contains 10 yellow marbles, what is the total number of marbles in the jar?
6.      Find the value of k for which the points (2,5), ( k,11/2) and (4,6) collinear
7.      Two opposite angular points of a square are (-1, 2) and (3,-2). Find the coordinates of other two angular points
8.      An equilateral triangle has two vertices at (3, 4) and (-2, 3). Find the coordinates of the third vertex
9.      Find the coordinates of the centre of a circle passing through the points (5,7), (6,6)               and (2,-2)
10.  If (10, 5), (8, 4) and (6, 6) are the mid points of the sides of a triangle, find the coordinates of its vertices. Hence find its area
11.  Find the ratio in which the point P (-6, a) divides the join of A (-3,-1) and B(-8,9). Also find the value of a
12.  The line segment joining the points (12, 0) and (-6, 15) is trisected at the points X (p, 5) and Y (0, q). Find the values of p and q
13.  Determine the ratio in which the line x – y – 2  = 0 divides the line joining (3,-1) and (8,9)
14.  Prove that ( a , b+c ),( b, c+a ) and ( c, a+b ) are collinear
15.    Find the circumcentre of a triangle whose vertices are (-2,-3), (-1, 0) and (7,-6). Also find its circumradius
16.  A (7,0), B (0,-24) are two vertices of a triangle whose third vertex is at origin. Calculate the length of the hypotenuse
17.    If A (-2,5), B(-1,3) and C(x,y) form an isosceles triangle, show that                                            6x – 16y + 19 = 0
18.  Find the condition that the point (x,y) should be equidistant from (2, 3) and (-1,2)
19.  If the distance between (11,3) and (3,y) is 10 units, find y
20.  Find a quadratic polynomial whose zeros are p + 2q and p – 2q
21.  If the sum of the zeros of the polynomial px² – 4x + 2p is same as their product, find the value of p
22.  Form a cubic polynomial whose zeros are 2, - 2 and 3
23.  If the product of two zeros of the polynomial 2x³ +6x² – 4x +9 is 3, find the third zero
24.  Obtain all other zeros of the polynomial x⁴ – 2x³ – 5x² + 8x + 4 if two of its zeros are                    1 ± √2
25.  Find the zeros of the polynomial x³ – 5x² – 16x + 80, if its two zeros are equal in magnitude but opposite in sign.
 
 

Holidays Home Work

Mathematics – Class X

1. The diameters of front and rear wheel of a tractor are 80 cm and 2 m respectively. Find the number of complete revolutions that the rear wheel will make to cover the same distance as covered by front wheel in 800 revolutions
   
2. A square is inscribed in a circle of radius 'r'. Find the ratio of their areas
   
3. Four circles each of radius 6 cm touch each other externally. Find the area enclosed between the circles
   
4. The area of equilateral triangle is 49√3 cm². Taking each angular point as centre a circle is described with radius half the length of the side of the triangle. Find the area of triangle not included in the circles.
   
5. It is proposed to add two circular ends to a square lawn on the adjacent sides which measures 50 m on each side. The centre of the circular ends being the point of intersection of diagonals of the square. Find the area of the whole lawn
   
6. A circular park is surrounded by a path of width 0.7 m. If the radius of the park is 41.3 m, find the cost of paving the path at the rate of Rs. 200 per m²
   
7. If the perimeter of a sector of a circle of radius 7 cm is 16.2 cm, find the central angle of the sector
   
8. A wire of length 18 cm is bent to form a sector of a circle of radius 4 cm. Find the area of sector so formed
   
9. If three circles of radius 'a' each, are drawn such that each touches the other two, prove that the area between them is 4a²/25
   
10. Three horses are tethered with 7 m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also find the area of the field which remains ungrazed
    
11. A golf ball has diameter of 4.1 cm. Its surface has 150 hemispherical dimples each of radius 2 mm. Calculate the total surface are of the ball which is exposed to the surroundings
    
12. A rectangular sheet of tin 44 cm x 20 cm is rolled along its length to form a cylinder. Find the volume and its surface area. Find the difference in surface area and volume if it is rolled along its breadth
    
13. A solid cylinder has a total surface area of 231 cm². Its lateral surface area is 2/3^rd of the total surface area. Find the volume of the cylinder
    
14. Water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 7 m/s in to a cylindrical tank whose base radius is 40 cm. By how much will the level rise in 1 hour
    
15. The barrel of a fountain pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used upon writing 990 words on an average. How many words would use up a bottle of ink containing one fourth of a litre
    
16. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27^th of the volume of the given cone, at what height above the surface of the base is the section made
    
17. A semicircular sheet of metal of diameter 28 cm is bent to form a conical cup. Find the capacity of the cup
    
18. The total surface area of a cube is numerically equal to the surface area of a sphere. Show that the ratio of their volumes is √π : √6
    
19. Water flows at the rate of 20 m/s from a cylindrical pipe 5 mm in diameter. Find the time it would take to fill a conical vessel whose diameter of the base is 40 cm depth 24 cm
    
20. The height of a circular cylinder is 6 m. Three times the sum of areas of its two circular faces is twice the area of its curved surface. Find the radius of the base
    

    
     

    Assignments for Chapter 2, 7 & 15 will be uploaded soon
    

Holidays Home Work - Class - IX

 PHYSICS

1.  Car A is moving at a speed of 20 m/s and Car B is moving at a speed of 65 km/h. Which car is faster?
2. A train is moving on a straight and levelled track at a speed of 54 km/h and passes an electric pole in 2 seconds. Find the time taken to pass a bridge of length 540 m
3. Chitra goes to school at a speed of 15 km/h and returns at a speed of 10 km/h. Calculate her average speed.
4. On a 90 km track a train travels the first 30 km at a speed of 30 km/h. How fast must the train travel next 60 km so as to average the speed of 60 km/h for the entire trip.
5. A bus is moving with a velocity of 108 km/h. On applying the brakes it comes to rest in 5 seconds. Find its retardation and distance covered by the bus before it comes to rest
6. A car is moving with a uniform speed of 72 km/h. The driver sees a child at a distance of 50m. He applies the brakes to stop the car just before the child. Calculate the acceleration
7. Find the initial velocity of the car which is stopped in 10 seconds by applying brakes. The retardation due to brakes is 2.5 m/s²
8. A person completes one round of square field of side 10 m in 40 s. Calculate the magnitude of displacement at the end of 2 min 20 seconds
9. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be his distance and displacement at the end of 2 min. 20 seconds
10. A train 50 m long passes over a bridge 250 m long at a speed of 12 km/h. How long will it take to completely pass over the bridge
11. A truck is moving at a speed of 108 km/h, after one second its speed drops to 72 km/h. Calculate the retardation of the truck and also the distance covered in one second
12. A train runs at a speed of 36 km/h for 15 min, at 72 km/h for 10 min and at 18 km/h for 5 min. Calculate the average speed of the train
13.  A boy starting from rest, runs with a uniform acceleration for 5 seconds and covers a distance of 37.5 m. Calculate the acceleration of the boy and also his final velocity?  
14. A body covers 1/4^th of a circle with radius 20m. Find the ratio of its distance to displacement.
15. A body is moving with a velocity of 10 ms^-1. If the motion is uniform, what will be the velocity after 10s?
16. Can a body have zero velocity and still be accelerating?
17. Give one example to show that motion and rest are relative.
18. A body travels a distance of 15m from A to B and then moves a distance of 20m at right angles to AB. Calculate the total distance travelled and displacement.
19. A car travels 100 km at a uniform speed of 40kmh^-1 and the next 125 km at a uniform speed of 50 kmh^-1. Find average speed of car.
20. A car travels along a straight line for first half time with a speed of 40kmh^-1 and the second half time with a speed of 60kmh^-1. Find the average speed of the car.

Holidays Home Work ( Class - IX )

MATHEMATICS

1)      Find the zeros of the following polynomials

i)        2x³ + 3x² – 11x – 6

ii)       2x³ + x² – 2x – 1

2)      Use long division to find the remainder, when  4x³ - 12 x² + 14x – 3 is divided by 2x – 1. Also verify the result by remainder theorem

3)      If ( 4x + 2 ) is a factor of  4x³ – kx² + 56x – 24, find the value of k

4)      If the polynomials ax³ – 3x² – 13and 2x³ – 5x² +a, leave the same remainder when divided by x – 2. Find the value of a and also the remainder in each case

5)      Show that (x +2 ), ( x – 5 ) and ( x + 9 ) are the factors of 

x³ + 6x² – 37x – 90

6)      What must be subtracted from  4x⁴ – 2x³ – 6x² + x – 5 so that the result is exactly divisible by 2x² + x – 1

7)      Find the product 

i)        ( x³ – 6x² – x ) ( x² – 6x + 1 )

ii)       ( 1.5x² – 0.3y² ) ( 1.5x² + 0.3y² )

iii)      ( x³ + 1 )( x⁶ – x³ + 1 )

iv)      ( a² – b² + c² )( a⁴ + b⁴ + c⁴ + a²b² + b²c² – c²a²)

v)       ( 2x – y + 3z )( 4x² + y² + 9z² + 2xy  + 3yz – 6zx )

8)      Evaluate

i)         ( 25 )³ – ( 75 )³ + ( 50 )³

ii)        ( 0.2 )³ – ( 0.3 )³ + ( 0.1 )³

iii)      ( 1002 )³

iv)     29³ – 11³

v)      46³ + 34³

9)      If a + b = 100 and a² + b² = 436, find the value of a³ + b³

10)   If a – b = 40 and ab = 600, find the value of a² + b² +ab

11)   If a + b+ c = 9 and a² – b² + c² = 83, then find the value of a³ + b³ + c³ – 3abc

1)      Factorise

i)        a² + 4b² – 4ab – 4c2

ii)       x⁴ + x² + 1

iii)      ( x + y )² – ( x – y )²

iv)     p² – 4pq + 4q² – 6p + 12

v)      √2x² + 3x + √2

vi)     6√3x2 – 47x + 5√3

vii)   x² – 51x + 378

viii)  8( x + y )³ – 27( x – y )³

ix)     32x⁴ – 500x

x)      x³ + 3x²y + 3xy² + y³ – 0.027

xi)     x⁶ - 729

xii)   a³ – b³ + 1 + 3ab

xiii)  2√2x³ + 16√2y³ + z³ – 12xyz

xiv)  ( 2x – 3y )³ + ( 4z – 2x )³ + ( 3y – 4z )³

xv)    ( 5x – 7y )³ + ( 9z – 5x )³ + ( 7y – 9z )³

PS : Revise the formulae before you attempt these questions