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Posted By: Atul Member Level: Diamond Posted Date: 04 Apr 2008
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2007 Himachal Pradesh State Mathematics Question paper
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Mathematics
Paper II - Class X
Time Allowed :2 ½
Maximum Marks : 100
N. B. :
The question paper consists of six Sections - A. B, C. D, E and F.
Read the instructions under each Section before you start answering.
Diagrams should be drawn, wherever necessary.
Rough work and calculations should be shown legibly at the bottom of the pages in the answer-book.
--------------------------------------------------------------------------------
SECTION – A
Note :
Answer all the ten questions.
Each question carries one mark. (10 × 1 = 10)
1.
In the diagram. OD = 5 cm, OB = 13 cm, then AB =
12 cm
24 cm
6 cm.
2.
The corresponding sides of two similar triangles are in the ratio 2 : 3, then the ratio of their areas is equal to
1 : 9
8 : 27
4 : 9.
3.
Slope of x-axis is
1
- 1
0.
4.
The equation of the line passing through the point ( - 2, 5 ) and parallel to y-axis is
y = 5
x = - 2
- 2x + 5y = 0.
5.
sin x . sec ( 90° - x ) - cot x . cot ( 90° - x) is equal to
1
0.
6.
cosec2 37° - cot2 37° is equal to
0
1
- 1.
7.
Order of matrix A is
4 × 2
2 × 4
4 × 4.
8.
If the S.D. of a given data is 5, then the variance of the data is
10
25.
9.
The probability of getting an odd number in throwing a dice once is
0.
10.
The Basic statement which is used to assign a value to a variable is
REM
LET
INPUT.
SECTION – B
Note :
Answer any ten of the following questions.
Each question carries three marks. (10 × 3 = 30)
11.
In the diagram ? A = ? B and AD = BE show that DE ? AB.
12.
In the diagram AD is bisector of ? BAC. Find x.
13.
In ? ABC. ? A is a right angle and If AD = 24 units, DC = 18 units, find BD.
14.
A ladder 24 m long leans on the top of a building making an angle of elevation of 30° with the horizontal line. Find the height of the building.
15.
Find the value of
16.
Find the value of
17.
If ( x, - 5 ). ( - 5, 1 ) and ( - 1, 2 ) are colllnear, find x.
18.
Find the slope and y-intercept of the line 7x - 3y + 4 = 0.
19.
Find the equation of the line passing through the points ( - 3, 1 ) and ( 2, - 4 ).
20.
Find the S.D. of 100, 200. 300, 400.
21.
A dice is thrown twice. Find the probability of getting the sum 5 or 9.
22.
If and find P( A n B ).
23.
Find x, if
24.
If find find A2.
25.
Write the output for the following program
SECTION – C
Note :
Answer all the questions, choosing either (a) or (b) in each question
Each question carries five marks. (4 × 5 = 20)
26.
State and prove Basic Proportionality theorem.
(Or)
State and prove AAA-similarity theorem.
27.
Prove that three parallel lines cut any two transversals proportionally.
(Or)
In a parallelogram ABCD, A is Joined to any point P on BC and if it meets DC produced at Q, prove that PQ : AP = CQ : AB.
28.
Find the equation of the straight line passing through (-1,3) and parallel to the line Joining ( 5, - 2) and ( - 3. 1 ).
(Or)
Find the ratio in which the line joining the points ( 2, - 1 ) and ( 4, - 6 ) is divided by the x-axis.
29.
Find the area of the quadrilateral whose vertices are ( 1, 2 ), ( - 3, 4 ). ( - 5, 6 ) and ( 4, - 1 ).
(Or)
Find the equation of the line passing through ( - 3, 6 ) and making intercepts on the axes equal in magnitude but opposite in sign.
SECTION – D
Note :
Answer all questions, choosing either (a) or (b) in each question.
Each question carries five marks. (4 × 5 = 20)
30.
Prove that
(OR)
From the top of a cliff the angles of depression of the top and bottom of a tower of height 400 m are seen to be 45° and 60°. Find the height of the cliff.
31.
Calculate the S.D. for the following data :
24, 32, 27, 40, 34, 29.
(Or)
Two dice are rolled and the products of the numbers found. What is the probability that the product so found is a prime number or an odd number ?
32.
Find X and Y if and
(Or)
If and show that PQ ? QP.
33.
Write a BASIC program to find area of circle where its radius is given.
(Or)
Draw a flowchart to find area of a rectangle whose length and breadth are given.
SECTION – E
Note :
Answer the question, choosing one of the alternatives (a) or (b).
The question carries ten marks. (1 × 10 = 10)
34.
Construct a pair of tangents to a given circle of diameter 7 cm from a point 5 cm away from the centre. Measure the length and verify it.
(Or)
Construct a rectangle of length 5 cm and breadth 4 cm and enlarge it such that the areas should be in the ratio 1 : 3.
SECTION – F
Note :
Answer the question, choosing one of the alternatives (a) or (b).
The question carries ten marks. (1 × 10 = 10)
35.
Draw the ‘less than Ogive’ and find median for the following data :
Class : 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30
Frequency : 4 2 8 12 10 6
(OR)
Draw the ‘greater than Ogive’ and find the median for the following data
Class : 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100
Frequency: 5 7 10 3 16
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