Guess Paper 6 – 2009
Class - X
Subject - Mathematics
Time:3hrs Max.Marks:80
General Instructions
- All questions compulsory
- The question paper consist of thirty questions divided in to 4 sections A,B,C and D. Section A comprises of ten questions of 1 marks each ,Section B comprises of five questions of 2 marks each, Section C comprises of ten questions of 3 marks each and section D comprises of five questions of 6 marks each
- All questions in section A are to be answered in one word , one sentence or as per the exact requirement of the question
- there is no overall choice .However internal choice has been provided in one question of 2 marks each ,three question of three marks each and two questions of 6 marks each .You have to attempt only one of the alternatives in all such questions.
- In question on construction ,drawings should be neat and exactly as per the given measurements
- Use of calculators is not permitted .However you may ask for mathematical tables
SECTION A
1. State the Euclid’s Division Lemma.
2. Find the condition that if the linear equations and
have unique solution.
3. For the polynomial, what is the sum of zeros?
4. How many terms of the AP will give the sum zero
5. If the mean of n observations is
then find
6. One letter is selected at random from the word ‘UNNECESSARY’. Find the probability of selecting an E
7. Evaluate
8. The lengths of two cylinders are in the ratio 3:1 and their diameters are in the ratio 1:2 .Calculate the ratio of their volumes
9. In the given figure DE is parallel to BC and determine
10. A point P is 13 cm from the centre of a circle. If the radius of the circle is 5 cm,
then the length of the tangent drawn from P to the circle is:
SECTION B
11. If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b.
12. The diagonals of a quadrilateral ABCD intersect each other at the point O such that . Show that ABCD is a trapezium.
13. Consider ∆ ACB, right-angled at C, in which AB: AC = . Find ÐABC and also determine the values of Cos2B+Sin2B
14. Find the coordinates of the point P on y-axis, equidistant from two points A(-3,4) and B(3,6) on the same plane.
15. Cards numbered 3, 4, 5, 6, ------ 17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears i)An even perfect square number, ii) A number divisible by 3 or 5.
SECTION C
16. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
17. Solve the following system of linear equation graphically
2x-3y=5
3x+4y+1=0
.Calculate the area bounded by these lines and y-axis
18. Divide 3x2 – x3 – 3x + 5 by x – 1 – x2, and verify the division algorithm.
19. Find the sum of all three digit numbers each of which leave the remainder 3 when divided by 5
OR
How many terms of the AP 78,71, 64 …… are needed to give the sum 468? Also find the last term of this AP
20. In the fig AB and CD are two parallel tangents touching the circle at Q. Show that Ð SOT=900
D
T
R
Q
O
C
B
A
P
S
21. Draw a circle of radius 3.5 cm. Take a point outside the circle. Construct the pair of tangents from this point to the circle without using its centre. Measure the length of tangents.
22. Prove the following identity:
cotθ + cosecθ - 1 = 1 + cosθ
cotθ – cosecθ + 1 sin θ
OR
Evaluate without using tables
23. Show that the points (0, 1), (2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.
24. Find the co-ordinates of the points of trisection of the line segment joining the points (3, -3) and (6, 9).
25. A square ABCD is inscribed in a circle of radius 10 units .Find the area of the circle, not included in the square (use )
SECTION D
26. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
OR
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
27. If a line is drawn parallel to one side of a triangle, to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Prove it.
Using the result, prove the following, In the adjoining figure, if PQRS is a trapezium in which
PQ║SR║XY then P Q
=
X Y
S R
28. A round balloon of radius a subtends an angle at the eye of the observer, while the angle of elevation of its centre is
. Prove that the height of the centre of the balloon is ( a sin
cosec(
/2) )
Or
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60o. When he moves 40 m away from the bank, he finds the angle of elevation to be 30o. Find the height of the tree and the width of the river.
29. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be of the volume of the given cone, at what height above the base, the section has been made?
30. Find the median marks of students from the following table:
Marks | Number of Students |
0 and above | 80 |
10and above | 77 |
20and above | 72 |
30and above | 65 |
40and above | 55 |
50and above | 43 |
60and above | 28 |
70and above | 16 |
80and above | 10 |
90and above | 08 |
100and above | 0 |
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