Guess Paper- 2009
Class - X
Mathematics
Time: 3 hrs Marks: 80
General Instructions:
( i ) All questions are compulsory.
( ii ) The question paper consists of 30 questions divided into four sections –A, B, C
and D. Section A contains 10 questions of 1 mark each, Section B is of 5
questions of 2 marks each, Section C is of 10 questions of 3 marks each and
section D is of 5 questions of 6 marks each.
( iii) There is no overall choice. However, an internal choice has been provided in
one question of two marks each, three questions of three marks each and two
questions of six marks each.
( iv ) In question on construction, the drawing should be neat and exactly as per
the given measurements.
( v ) Use of calculator is not permitted.
SECTION A
( Qns 1 – 10 carry 1 mark each )
- Find the positive p so that 4x2-3px +9 has real roots.
- If a = bq + r in division algorithm, give limits of r.
- Find the value (s) of p for which the system of equations have exactly one solutions
. px + 2y -5 = 0
3x + y - 1 = 0
4. Find the first 4th terms of the sequence whose nth term is n2/ 2n.
5. Express cos 750 + cot 750 in terms of angle between 00 and 450.
6. If PT is a tangent to the circle whose center is O ,OP=10 cm and radius of the circle is 6cm, Find the length of
tangent segment PT.
7. D ABC Similar to D DEF and their areas are respectively 64 cm2 and 121 cm2. If EF= 15.4 cm,
find BC.
8. In a leap year, find the probability of getting 53 Sundays.
9. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 600.
10. Convert the following data into more than frequency distribution and form a more than ogive from it.
Class | 0-20 | 20-40 | 40-60 | 60-80 | 21-23 | 80-100 |
No. of workers | 40 | 51 | 64 | 38 | 5 | 7 |
SECTION B
( Qns 11 – 15 carry 2 marks each )
11.Find a quadratic polynomial with the given numbers as the sum and product of its zeros respectively ¼, -1.
12.Prove that (1 + tan2A) (1-Sin A) ( !+ SinA) =1.
Or
If x = a Sin B and y = b Tan B, prove that ( a2 /x2 - b2/y2) = 1.
13. What point (s) on the X-axis are at a distance of 5 units from the point (5, -4)?
14. If AD and PM are medians of triangles respectively, where D ABC similar to D PQR , prove that
AB/ PQ = AD/ PM.
15. What is the probability of getting a total of less than 12 in the throw of two dice?
SECTION C
( Qns 16 – 25 carry 3 marks each )
- Prove that
is irrational.Some students planned a picnic. The budget for food was Rs 500. But 5 of them failed to go and thus the food
for each member increased by Rs 5. How many students attended the picnic.?
18.Using factorization, find the roots of the following quadratic equation:
(a+ b)2 x2 + 8 ( a2 – b2) x + 16(a – b)2=0
- Solve: x/a = y/b =1 and
(a + b)x + ( a - b ) y = a2+ b2 ; a, b ¹ 0.
20.Prove that Tan2x + Cosec2x = 1
Tan2x-1 Sec2x - Cosec2x Sin2x - Cos2x
Or
sin q + tan q = m and tan q - sin q = n, then prove that ( m2 – n2) = 4Ömn.
21Show that the points (0,-2), (3,1), (0,4) and (-3,1) are the vertices of a square. Also, find the area of the square.
Or
If the segment with the end points (3,4) and (14,-3) meets the X axis at P, in what ratio does P divide the segment?
Also, find the coordinate of P.
22.The vertices of a D ABC are A( 4,6), B(1,5) and C(7,2). A line is drawn to intersect side AB and AC at D and E respectively, such that AD/AB = AE/AC = ¼. Calculate the area of D DEA.
Or
The two vertices of a square are (-1,2) and (3,2). Find the coordinate of other two vertices.
23. Construct a D similar to a given triangle ABC with its sides 7/5 th of the corresponding side of D ABC.
It is given that AB= 6cm, angle BC =7 cm, and angle CA = 8cm.Write the steps of contraction also.
24. If two tangents are drawn to a circle from an external point, then
(i) they subtend equal angle at the center.
(ii) they are equally inclined to the segment, joining the center to that point.
25. An ice cream cone consists of a right circular cone of height 14 cm and diameter of circular top is 5 cm, It has
hemisphere on the top with the same diameter as the circular top. Find the volume of ice cram in the cone.
SECTION D
( Qns 26 – 30 carry 6marks each)
26.Find the median for the following data::
Marks obtained Number of students
Less than 10 0
Less than 30 10
Less than 50 25
Less than 70 43
Less than 90 65
Less than 60 87
Less than 10 96
Less than 10 100
27. State and prove Pythagoras Theorem. Using it, prove that the sum of the squares of the sides of a rhombus is equal
to the sum of the squares of its diagonals.
28. From an aero plane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometer stones on the opposite sides of an aero plane are found to be α and β. Show that the height of the aero plane is:
tan α tan β
tan α + tan β
Or
From a window (60 meters high above the ground) of a house in a street, the angles of elevation and depression of the
top and the foot of another house on opposite side of street are 600 and 450 respectively. Show that the height of the
opposite house is 60(1+Ö3) meters.
29. A metallic right circular cone 20cm height and whose vertical angle is 600 is cut into two parts at the middle of its height by a plane parallel to its base .If the frustum so obtained be drawn into a wire of diameter 1/16cm find the length of the wire
Or
The height of a cone is 30cm; a small cone is cut off at the top by a plane parallel to the base .If its volume be 1/27 of the volume of the given cone at what height above the base is the section made.
30. Determine the vertices of a triangle formed by lines representing the equation using
graph paper 4x-5y-20=0
3x+5y-15=0 and
y = 0
Find the area of the triangle formed by these lines .
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