Revision Test no.2

     Revision Test No.2 Chapter - Circles and Probability Time: 1 hour Marks:30
 

 

1.    In the given figure, O is the centre of the circle and ÐBOD=150°. Find ÐBAD and ÐDCP.(2)

2.    To know the opinion of the students about the subject statistics, a survey on 350 students was conducted. The data recorded is as given below :

Opinion      Number of students

Like                  147

Dislike              203

Find the probability that a student chosen at random

(i)            likes statistics. (ii) dislikes statistics.   (2)

3.    Some families with 2 children were selected randomly and the following data were recorded :

Number of girls in a family         0         1          2

Number of families                  184      714      425

If a family is chosen at random, compute the probability that it has

(i)            exactly 1 girl. (ii) exactly 2 boys.    (2)

4.    ·The marks scored by some students in an examination are given in the form of a

frequency distribution table.

Marks :            600-640     640-680   680-720   720-760   760-800   800-840   840-880

No. of Students    16            45            156           284          172           59           18

If a child is selected at random, find the probability that the child :

(i)            scored at least 800 marks (ii) scored at most 680 marks

(iii) has marks between 600  and 880  (3)

5.    In the figure ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at P. If O is  the centre of the circle and AB = DC, prove that : (i) DPAB @ DPDC  (ii) PA=PD and PC=PB    (iii) AD çç BC  (4)

 

6.    Two dice are thrown simultaneously number of times. Each time the sum of two

numbers appearing on their tops is noted and recorded as given in the following table

Sum of numbers  2      3     4     5     6       7      8      9      10    11     12

Frequency           20   16   28   18    24     22    52   66     48     38     68

If the dice are thrown once more, what is the probability of getting a sum

            (i) which is a multiple of 3 (ii) which is a prime number   (2)

 

7.      In the given figure, O is the centre of the circle. Find the value of x (2)

 

                 

 

8.      The probability of guessing the correct answer to a certain question is  x/3

If the probability of not guessing the correct answer is  5x/3 ,                                     then find the value of x. (2)

9.      The circle passing through the vertices A, B and C of a parallelogram ABCD intersects side CD at a point P as shown in the figure.

 Prove that ∟APD  = ∟ADP. (3)

 

              

10.  In the given figures, BACD is a cyclic quadrilateral in which AC ççBD.

       (i) If ∟BAD=52° and ∟BCA =35°, find ∟ACX.

       (ii) Prove that ∟CBD = ∟ADB. Also deduce that DY = BY.

       (iii)Prove that  ∆XBD is an isosceles triangle.

       (iv) Prove that XA=XC.    (4)

                   

11.  In a bottle there are 7 red buttons, 5 green buttons and 8 purple buttons. What is the probability that randomly drawn button from the bottle is a purple button ? If one extra green button is put in side the bottle, what will be the probability that randomly drawn button is purple ?  (2)

12.  In the given figure, ABCDE is a pentagon. Whose vertices lie on the semicircle with centre O. Find the sum of ∟ACD and ∟DEB ? (2)