X Standard - 10th - Maths - Second Midterm Question Paper - Samacheer Kalvi

 

        

                                           II Mid Term Test

Class:   X STD                                                                                            Marks :  50

Sub : MATHEMATICS                                                                           Time : 2 Hrs

I. Choose the correct answer.                                                                            7 × 1 = 7

1. If number of columns and rows are not equal in a matrix then it is said to be a

     (a) diagonal matrix    (b) rectangular matrix     (c) square matrix      (d) identity matrix

2. Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance

    between their feet is 12 m, what is the distance between their tops?

    (a) 13 m            (b) 14 m                (c) 15 m              (d) 12.8 m

3. The electric pole subtends an angle of 30° at a point on the same level as its foot. At

     a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°.

    The height of the pole (in metres) is equal to

     (a)  b                  (b)               (c)                    (d)  

4. The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

     (a) 12 cm              (b) 10 cm               (c) 13 cm                   (d) 5 cm

 5. A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same

      radius. The height of the cone is

     (a) 3x cm             (b) x cm                     (c)4x cm                   (d)2x cm

6. If A is a 2 3   matrix and B is a  3 4 matrix, how many columns does AB have

     (a) 3             (b) 4                      (c) 2                   (d) 5

7.Number of tangents drawn from an external point of a circle is

       (a)  1                         (b)  2                              (c)  0                                (d)   4

II. Answer any 5 questions. (Q. No. 14 is compulsory)                                  5 × 2 =10

8. Construct a 3 × 3  matrix whose elements are given by

9. If A =  , B =  then Find  2A+B.

10. What length of ladder is needed to reach a height of 7 ft along the wall when the

       base of the ladder is 4 ft from the wall? Round off your answerto the next tenthplace.

11.Show that the angle bisectors of a triangle are concurrent.

12. A kite is flying at a height of 75 m above the ground. The string attachedto the

      kite is temporarily tied to a point on the ground. The inclination of the string with

      the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

 

13. From the top of a rock 50  m high, the angle of depression of a car on the ground

       is observed to be 30°. Find the distance of the car from the rock.

14. If the total surface area of a cone of radius 7 cm is 704 , then find its slant height.

III. Answer any 5 questions. (Q. No. 21 is compulsory)                                5 × 5 = 25

15. If  A =   show that

16. State and prove  “Baudhayana theorem”.

17.From the top of a tower 50 m high, the angles of depression of the top and  bottom

     of a tree are observed to be 30° and 45° respectively. Find the height of the tree.(=1.732)

18. A man is standing on the deck of a ship, which is 40 m above water level. He observes

      the angle of elevation of the top of a hill as 60° and the angle of depression of the  base

      of the hill as 30°. Calculate the distance of the hill from the ship and the height

      of the hill.(=1.732)

19. An industrial metallic bucket is in the shape of the frustum of a rightcircular cone

      whose top and bottom diameters are 10 m and 4 m and whose height is 4 m.

      Find the curved and total surface area of the bucket.

20. A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small

      cylindrical metal of radius 5 cm and height 4 cm is immersed completely. Calculate

      the raise of the water in the glass?

21. If  A =   and  B =   show that .

IV. Answer the following question.                                                                  1× 8 = 8     

 22. a) Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its

            centre. Draw the two tangents PA and PB to the circle and measure their lengths.

                                                                        (OR)

        b) Draw a circle of radius 4.5 cm. Take a point on the circle. Draw the tangent at that

           point using the alternate segment theorem.