6

Exam practices for Triangles

Time: 35 Minutes                             Maximum Marks- 20

1.  Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? (2 marks)

2.  ΔABC~ΔPQR with BC/QR = 1/3, then find ar(ΔPQR)/ar(ΔABC). (2 marks)

3.  Is the triangle with sides 14cm, 12cm and 17cm a right triangle? Why? (1 mark)

4.  The lengths of diagonals of a rhombus are 24 cm and 32 cm. Find the length of its sides. (2 marks)

5.  PQR is an isosceles triangle with QP=QR. If PR²= 2QR², prove that ΔPQR is rightangled. (2 marks)

6.  In a triangle ABC, line DE is drawn parallel to side BC such that AD/DB = AE/EC. Show that BAC is an isosceles triangle. (3 marks)

7.  A 20 m long vertical pole casts a shadow 10 m long on the ground. At the same time a tower casts a shadow 50 m long on the ground. Find the height of the tower. (2 marks)

8.  State and prove basic proportionality theorem. (4 marks)

9.  L and M are two points on the sides DE and DF of the triangle DEF such that DL=4, LE=4/3, DM=6 and DF=8. Is LM parallel to EF? Why? (1 mark)

10.  In a triangle PQR and MST, ∟P=55°, ∟Q = 25°, ∟M = 100° and ∟S = 25°. Is ΔQPR similar to ΔTSM? Why? (1 mark)

14

Exam practices for Statics

Time: 45 Minutes                             Maximum Marks- 25

1.   Find the median of the following distribution: 2

Class Interval	Frequency
0-10	4
10-20	4
20-30	7
30-40	10
40-50	12
50-60	8
60-70	5
Total	50

2.   Find the mean of the following data: 2

Class	0-50	50-100	100-150	150-200	200-250
Frequency	15	20	35	20	10

3.   The mean of a distribution is 50. Determine value of ‘g’ 3

Class	0-20	20-40	40-60	60-80	80-100
Frequency	17	g	32	24	19

4.   Find the median of the following data: 2

Class interval	Frequency
0-10	5
10-20	8
20-30	23
30-40	17
40-50	7
50-60	8

5.   Find value of ‘q’ when mean is 47. 3

Class	0-20	20-40	40-60	60-80	80-100
Frequency	8	15	20	q	5

6.   The following table shows the ages of staff members in a office. 4

Age	18-27	27-36	36-45	45-54	54-63
Number of members	6	11	21	23	14

        Find mean and the mode

7.   Find the mean, mode and median of the following data: 6

Class	Frequency
0-20	12
20-40	13
40-60	6
60-80	7
80-100	8
100-120	14
120-140	13

8.   The median of the following data is 52.5. Find value of x and y if the final frequency is 100. 3

Class	Frequency
0-10	5
10-20	2
20-30	X
30-40	12
40-50	20
50-60	17
60-70	Y
70-80	7
80-90	9
90-100	4

4

Exam practic for Quadratic equation  

Time: 45 Minutes                             Maximum Marks- 25

1.   If T_n = 3 + 4n then find the A.P. and hence find the sum of its first 15 terms.

(2 Marks)

2.   Which term of the A.P.:

       3, 15, 27, 39, .... will be 120 more than its 53rd term?

(2 Marks)

3.   Find the 31st term of an A.P. whose 10th term is 31 and the 15th term is 66.

(3 Marks)

4.   If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Hence find the sum of the first 15 terms of the A.P.

(3 Marks)

5.   The 5th and 15th terms of an A.P. are 13 and RS 17 respectively. Find the sum of first 21 terms of the A.P.

(4 Marks)

6.   In an A.P. the sum of its first ten terms is RS 150 and the sum of its next erm is RS 550. Find the A.P.

(4 Marks)

7.   The sum of n terms of an A.P. is 3n² + 5n. Find the A.P. Hence, find its 16th term.

(3 Marks)

8.   In an A.P., the first term is 8, nth term is 33 and sum of first n terms is 123. Find n and d, the common difference.

(4 Marks)

15

Exam practic for Probability

Time: 35 Minutes                             Maximum Marks- 40

1.   In the adjoining figure, PA and PB are tangents from P to a circle with center. C If ∠APB = 40° then find ∠ACB.

(1 Mark)

1.   Cards bearing numbers 1, 3, 5, ..., 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card hearing:

        (i) a prime number less than 15.                        (ii) a number divisible by 3 and 5.

(4 Mark)

2.   Red kings, queens and jacks are removed from a deck of 52 playing cards and then well-shuffled. A card is drawn from these fining cards. Find the probability of getting (i) King (ii) a red card (iii) a spade.

(6 Mark)

3.   One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting:

        (i) A king of red suit.                        (ii) A queen of black suit.

        (iii) A jack hearts.                                (iv) A red face card.

(4 Mark)

4.   A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of a red ball, find the number of blue balls in the bag.

(3 Mark)

5.   In a throw of a coin, find the probability of getting a head.

(2 Mark)

6.   Two coins are tossed together find the probability of getting:

        (i) at least one tail.                        (ii) one head

(3 Mark)

7.   An unbiased die is thrown once, find the probability of getting:

        (i) a number greater than 4.                        (ii) a multiple of 3.

(3 Mark)

8.   Two dice are thrown at the same time. Find the probability of getting different numbers on both the dice.

(3 Mark)

9.   Two dice are thrown at the same time. Find the probability of getting same number on both the dice.

(3 Mark)

10.   A pair of dice is thrown once. Find the probability of getting an odd number on each the.

(2 Mark)

11.   A lot consists of 48 mobile phones of which 42 are good, 3 have only minor or defects and 3 have Or defects. Varnika will buy a phone if it is good but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is:

        (i) acceptable to. Varnika?                                (ii) acceptable to the trader?

(4 Mark)

12.   Find the probability that a number selected at random from the numbers 1, 2, 3, ..., 35 is a:

        (i) prime number                                (ii) multiple of 7

        (iii) a prime number less than 15.

(3 Mark)