Guess Paper 7 - 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. Given H.C.F ( 306, 657 ) = 9, find L.C.M ( 306, 657 )
2. For which value of ‘P’ does the pair of equations has unique solutions.
4x + Py + 8 = 0
2x + 2y + 2 = 0
3. For the polynomial, what is the sum of zeros?
4. Find the discriminant of the quadratic equation
5. Write down the empirical relationship between the three measures of central
tendency.
6. One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will not be a joker.
7. If tan 2A = cot ( A – 180 ), where 2A is an acute angle, find the value of A.
8. Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.
9. In fig. DE // BC. Find EC.
A
1.5cm 1cm
D E
3cm
B C
10. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
SECTION B
11. Find the zeros of the quadratic polynomial x2 + 7x + 10 and verify the relationship between the zeros and the coefficients.
A
R
B
C
Q
O
P
12. The adjacent figure PQ||AB and PR||AC Prove that QR||BC.
13. If find the value of
14. The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
15. A coin is tossed three times. Find the probability of getting
(a) atleast two heads
(b) atmost one head
(c) exactly one tail
SECTION C
16. Prove that 2+ is irrational.
17. Draw the graph of x-y+1=0 and 3x+2y-12=0 calculate the area bounded by these lines and x-axis.
18. Find all the zeroes of x4 – 5x3 + 3x2 + 15x -18, if two of its zeroes are √ 3 and -√3.
19. Determine the A.P whose 5th term is 15 and the sum of its 3rd and 8th terms
is 34.
20. In given figure PQR is a right angled triangle with PQ = 12 cm and QR = 5 cm. A circle with centre O and radius x is inscribed in. Find the value of x.
21. 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.
22. If cosθ + sinθ = √2 cosθ , show that cosθ – sin θ = √2 sinθ
OR
If find the value of
23. Determine the ratio in which the points P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also find the value of m.
24. Find the value of p for which the points (-1, 3), (2, p) and (5,-1) are collinear.
25. In given figure, ABCD is a square whose each side is 14 cm. APD and BPC are semicircles. Find
the area of the shaded region.
SECTION D
26. The sum of the digits of two digits number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits of the number Find the number.
OR
A motor boat whose speed is 15km/hr in still water, goes 30km downstream and comes back in a total time of 4 hours 30 minutes. Find the stream
27. State and prove Pythagoras Theorem. Using it , if ABC is a triangle in which AB = AC and D is any point in BC, Prove that: AB2--AD2=BD.CD
28. If the angle of elevation of a cloud from a point h meters above a lake is a and the angle of depression of its reflection in the lake is b, prove that the distance of the cloud from the point of observation is
Or
From the top of a church spire 96 m high the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = 1/4 and tan y° = 1/7. Calculate the distance between the vehicles.
29. Water flows out through a circular pipe, whose internal diameter is 2cm, at the rate of 0.7m per second into a cylindrical tank, the radius of whose base is 4cm. By how much the water level will rise.
Or
A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered in to water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?
30. If the median of the distribution given below is 28.5, find the values of x and y.
Class: 0-10 10-20 20-30 30-40 40-50 50-60 total
Frequency : 5 x 20 15 y 5 60
-------------------------------------------------------------------------------------------------------
www.cbsekey.com
Other Educational Portals
English | cbse | Science | Mathematics
CBSE Sample Guess Paper 1
Comments