X CBSE NCERT Board Questions Chapter Probability

1. Which of the following can be the probability of an event ?

(A) 0.05 (B) 1.005 (C) 18/ 23 (D) 9/7

2. The probability of getting 53 Fridays in a leap year is :

(A) 1/7 (B) 2/7 (C) 4/7 (D) 5/7

3. If an event occurs surely, then its probability is (A) 0 (B) 1 (C) 1/2 (D) 3/4

4.Two dice are thrown at the same time. Find the probability of getting an even number on the first die.

5. A coin is tossed two times. Find the probability of getting at least one tail.

6.If there are 2 children in a family, find the probability that there is at least one boy in the family.

6. Two dice are thrown together. Find the probability that a multiple of 2 occurs on one dice and a multiple 

of 3 occurs on the other.

7.A card is drawn from a well shuffled pack of 52 playing cards. What is the probability that the card drawn 

is : (i) either a red or a king (ii) a black face card

8. A bag contains 6 red, 3 black and 6 white balls. A ball is selected at random from the bag. Find the 

probability that the selected ball is : (a) red or black (b) not black

9. A coin is tossed three times. Find the probability of getting exactly two tails

10. Two dice are thrown together. What is the probability of getting a doublet ?

11. A coin is tossed 3 times. Find the probability of getting : (i) at least 2 heads (ii) not getting the same result in all the tosses (iii) exactly 1 tail

12. A card is drawn at random from a well – shuffled deck of 52 playing cards. Find the probability that the card drawn is : (i) either a spade or an ace (ii) a black king

13.One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting : (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) a queen of diamonds

14. Cards marked with numbers 5, 6, 7, ……., 30 are placed in a box and mixed thoroughly and one card is drawn at random from the box. What is the probability that the number on the card is (i) a prime number ? (ii) a multiple of 3 or 5 ? (iii) neither divisible by 5 nor by 10 ? 

15. One card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting :

 (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) a queen of diamonds

Assignment 9th Class Topic:- Linear equation in two variable CBSE/NCERT (For CPS and SDV Samastipur )

       1.  Draw the graphs of 2x + y =  6 and 2x – y + 2 = 0 . Shade the region bounded by these lines and x-axis. Find the area of the shaded region.

      
         2.        Draw the graphs of the equations x – y = 1 and 2x + y = 8. Shade the area bounded by these two lines y – axis. Also determine this area.

 3.       A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs x and per day charge are Rs y. Write the linear equation representing the above information.

4.       A number is 27 more than number obtained by reversing its digits. If is unit’s and ten’s digit are x and y respectively, write the linear equation representing the above statement.

5.       Plot the points (3, 5) and (-1, 3) on a graph paper and verify that the straight line passing through these points also passes through the point (1, 4).

6.       A three – wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation representing the above information.

7.       The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number are x and y respectively, then write the linear equation representing the above statement.

8.       If the point (2, -2) lies on the graph of the linear equation 5x + ky = 4, find the value of K.

9.       Draw the graph of y = |x| .

10.   Draw the graph of the equation 2x + y = 6. Shaded the region bounded by the graph and the coordinate axes.           Also, find the area of the shaded region.

11.   Ravish tells his daughter Aarushi, “Seven years ago, I was seven  times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. If present ages of Aarushi and ravish are x and y years respectively, represent this situation algebraically as well as graphically

12.   Aarushi was driving a car with uniform speed of 60 km/h. Draw distance – time graph. From the graph, find the distance travelled by Aarushi in (a) 2and 1/2Hours   (b) 1/2 hours

13.   Solve the equation 2x + 1 = x – 3, and represent the solution (s) on (i) the number line  (ii) the Cartesian plane.

14.   Draw the graph of each of the following linear equations in Cartesian plane x + 5 = 0

15.   Draw a graph of the equation (i) y = -3  (ii) 2y + 3 = 9

Answer

1.8 sq. units     

2. 13.5 sq. units    

3. X + 4y = 27     

4. X – y + 3 = 0     

6. Y = 8x + 7     

7. X + y = 11    

8. K=3  

10. 9 sq. units   

12. (i) 150 km   (ii) 30 km     

CBSE Board Test Paper Chapter_Coordinate Geometry

CBSE TEST PAPER UNIT: 4 (coordinate geometry)

The method of describing the location of points in this way was proposed by the French mathematician René Descartes (1596 - 1650). (Pronounced "day CART"). He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. In honor of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane.

A system of geometry where the position of points on the plane is described using an ordered pair of numbers.

In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero.

                                                                 
                                                                         











                                                        Section-A

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2                            (B) 3                (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C) 10                          (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5                            (B) 5√ 2          (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                    (D) 4

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the 

ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length 

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis  respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If he coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q. 

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability