** Subject
– Mathematics****Class – X**

__General Instructions:__

** SECTION
–A**All questions
are compulso the drawing should

**Use Euclid’s algorithm to find the HCF of 4052 and 12576.****Find the value of k for which the quadratic equation kx(x – 2) + 6 = 0 has two equal roots.****Write the relationship between the three measures of Central tendency.****If 2 and 3 are the zeros of the quadratic polynomial 3x**^{2}– 2kx + 2m, find the values of k and m.**If The first term of an A. P. is 5 and its 100th term is – 292 find the 50th term of this A. P.**- Find the mean of the following data, also find the missing frequency.

C.I |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
Total |

Frequency |
2 |
3 |
7 |
2 |
f |
4 |
8 |
36 |

- A quadrilateral ABCD is drawn to circumscribe a circle. Prove that : AB + CD = AD + BC.
- The In an equilateral triangle of side 24cm, a circle is inscribed, touching its sides. Find the area of the remaining portion of the triangle.
- The perimeter of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm, determine the corresponding sides of the second triangle.
- A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box,

what is the probability that it will be : (i) white ? (ii) blue ? (iii) red ?

__SECTION – B__

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__ __

*
*

- If the 10
^{th}of an AP is 52 and the 17^{th}term is 20 more than its 13^{th}term, find the AP . - The sum of the digits of a two digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- ABD
is a triangle right angle at A and AC
is perpendicular to BD. Prove that AD
= BD X CD.^{2} - If the three consecutive vertices of a parallelogram ABCD are A (1, -2), B (3, 6) and C (5, 10), find its fourth vertex D.

__SECTION –C__

- Show that any positive odd integer is of the form 6q +1, or 6q +3, or 6q+5, where q is some integer.
- Solve by the method of substitution , .
- Obtain
all other zeros of 3x
^{4}+ 6x^{3}– 2x^{2}– 10x – 5, if two of its zeros are √(5/3) and – √(5/3). - Find the area of the quadrilateral whose vertices, are in order ( -4, -2 ), ( -3, -5 ), ( 3, -2 ) and

( 2, 3 ).

- Prove the following identity:

1. 2.

- In a class test, the sum of Bhavya marks in Math and Science is 30. Had she got 2 marks more in Science and 3 marks less in Maths, the product of their marks would have been 210. Find Bhavya marks in the two subjects
- The coordinates of A and B are ( 1, 2 ) and ( 2, 3 ). Find the coordinates of R so that AR : RB = 4 : 3.
- In , right angled at
A, if AD perpendicular to BC prove that AB
^{2}+ CD^{2}= BD^{2}+ AC^{2 } - Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
- A chord of a circle of radius 15 cm subtends an angle of 60 at the centre. Find the areas of the corresponding minor and major segments of the circle.

__SECTION –D__

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- The angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of the reflection of cloud in the lake is 60. Find the height of the cloud.
- A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
- State and prove Thale’s Theorem. Using the above, find the ratio AX : AB, if the line segment XY is parallel to side AC of triangle ABC and divides the triangle in two parts of equal areas.
- a). A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled.

b ) Find the number of coins 1.5 cm in diameter and 0.2 cm thick be melted to form a right circular

cylinder whose height is 8 cm and diameter 6 cm.

- The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

C.I |
0 - 100 |
100 to 200 |
200 to 300 |
300 to 400 |
400 to 500 |
500 to 600 |
600 to 700 |
700 to 800 |
800 to 900 |
900 to 1000 |

Frequency |
2 |
5 |
X |
12 |
17 |
20 |
Y |
9 |
7 |
4 |

Change the distribution to a more than type distribution and draw its ogive.

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TEACHERS**

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