Guess Paper – 2008

Class – X

Subject – Mathematics

** Time: 3 hours Marks: 80 **

__SECTION-A (MARKS 10 x 1 =10)__

1.The LCM and HCF of two numbers are 180 and 6 respectively. If one of the number is 30. Write the relation between LCM, HCF and of two numbers and hence find the other number. **Ans: LXH = aXb , 36**

2. If α and β are the zeroes of the quadratic polynomial f(x) = 6x^{2}+x-2, find the value of **(HOTS)** **Ans: (-25)/12**

3. Find the values of k for which the equation x^{2}+Kx+4 has equal roots? **Ans: k =±4**

4. Express sin A in terms of tan A. ( **HOTS)** **Ans: **

5. Find the 12^{th} term from the end of the A.P. 3, 8, 13, 18, ……..,98 **Ans: 43**

6. In a ΔABC, P and Q are point on sides AB and AC respectively, such that PQ║BC. If AP = 2.4cm, AQ=2cm, QC=3cm and BC = 6cm, find AB and PQ.

**Ans: AB =6, PQ=2.4**

7. If triangle ABC and triangle DEF are similar such that AB = 1.2cm and DE = 1.4cm. Find the ratio of the areas of triangle ABC and DEF. **Ans: 36:49**

8. Find the area of the sector with radius 7cm if angle of the sector is one-third of right angle. **Ans: 51.33 cm ^{2}**

9. A die is thrown once, Find the probability of getting (i) a prime number (ii) a number greater than 5.

10. Find the mean of all prime numbers up to 20. ** Ans: 9.625**

__SECTION-B Marks (5x2 =10)__

11. ABC is an equilateral triangle of side 3a. Find its altitude from A.

12. A lot consists of 144 pens of which 20 are defective and the others are good. A girl will buy a pen it it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it? (ii) She will not buy it? **Ans: (i) 31/36 (ii) 5/36**

13. In what ratio is the line segment joining the points (-2,-3) and (3,7) divided by y-axis? **Ans: 2:3**

**(OR)**

Find the point on X-axis which is equidistant from (2,-5) & (-2, 9). A**ns: (-7,0)**

14. If A, B, C are interior angles of a ∆ABC, then show that Sec() = CosecA/2

15. Check whether the following pair of linear equations 3x-5y = 20 and 6x-10y =40 will represent intersecting or coincident or parallel lines.

__SECTION_-C Marks: (10x3=30)__

16. Prove that (√3 +√5) is an irrational number.

17. The cost of 2kg of apples and 1kg of grapes on a day was found to be Rs.160. After a month, the cost of 4kg of apples and 2kg of grapes is Rs.300. Represent the situation algebraically and geometrically and hence find the solution if any.

18. Find the value of x in the following: 34 +32+30+….+x = 286 **(HOTS)** **Ans: x = 10, (-8)**

**(OR)**

__PAGE: 02__

If the first, Second and last term of an A.P are a , b and 2a respectively then find the sum of all terms. (**HOTS)** **Ans:**

19. Find the lengths of the medians drawn from A and B of the ΔABC if its vertices are A(-1,3), B(1,-1) and C(5,1) **Ans: 5 and √10**

20. If D,E and F are the mid points of sides BC , CA and AB respectively of a ΔABC then prove that Area of ΔABC = 4x ΔDEF.

21. The 7^{th} and 13^{th} terms of A.P are 34 and 64 respectively, Find the sum of its first eighteen terms. **Ans : 837**

22. The area of an equilateral triangle ABC is 17320.5cm^{2}. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the region which is outside of circles and inside the triangle. (Use Π = 3.14 and √ 3= 1.73205) **Ans: 1620.5cm ^{2}**

^{}

23. Prove that **(OR)**

If Cos (40 ^{○}+A) – Sin (50^{○}- A) + + 3cos^{2}30 = 3k . Find k.

24. Draw a pair of tangents to a circle of radius 5cm, which are inclined to each other at an angle of 80^{0} and measure their length approximately.

25 In a right triangle ABC right angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2:1 then prove that 9(AQ^{2}+BP^{2}) = 13 AB^{2}. (**HOTS)** **(OR)**

ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of triangle ABE and triangle ACD. (**HOTS)**

__SECTION: D Marks: (5x6 = 30)__

26. Places A and B are 100Km apart on a highway. One car starts from A and another from at the same time. If the cars travel in the same direction at different speeds they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars? **Ans: 60, 40Kms/hour**

27. The median of the following data is 28.5. Find the missing frequencies x and y if the total frequency is 60.

class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

frequency | 5 | x | y | 15 | 7 | 5 |

**Ans: x=8,y=20**

28. A right circular cylinder having diameter 12cm and height 15cm is full of . ice-cream. The ice-cream is to be filled in cones of height 12cm and diameter 6cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream. **Ans: 10 **

**(OR)**

An engineering student was asked to make a model, which was shaped like a cylinder with two cones attached to its two ends using thin aluminums sheet. The diameter of the model is 3cm and its length is 12cm, if each cone has a height of 2cm, find the volume of air contained in the model. **Ans: 66cm ^{3}**

**PAGE: 03**

29. The angles of depression of the top and the bottom of an 8m tall building from the top of a multi storeyed building are 30^{0} and 45^{0}, respectively. Find the height of the multi-storeyed building and the distance between the two building.. **Ans: 4(3+√3) both.**

** (OR)**

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β . Show that the height in miles of aeroplane above the road is given by (**HOTS)**

** **

30. In a right triangle prove that the square of the hypotenuse is equal to the sum of the square of its other two sides. **Using this to solve the following:** In a right triangle ABC in which angle C is right angle, if D is the mid point of BC, Prove that AB^{2}= 4AD^{2}-3AC^{2}.