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Maths Class X 1999(CBSE)
You are on Set no 1 Qno. 21 to 30
Q21) The arc of a circle subtending a right angle at any point of
the circle in its alternate segment is a semicircle - prove.
(Marks 4) Q22) Through the mid-point M of the side CD of a parallelogram ABCD,
the line BM is drawn intersecting AC in L and AD produced in E. Prove that
EL = 2BL. (Marks 4)
Q23) Flow Chart. Deleted from the syllabus. (Marks 4)
Q24) Algorithm. Deleted
from the syllabus (Marks 4)
Q25) Find the cost of living index number for the year 1998 assuming
1996 as the base year from the following data: (Marks
4)
| Commodity |
Quantity
(in units) |
Price per unit
(in rupees) |
| 1996 |
1998 |
| A |
15 |
13 |
14 |
| B |
10 |
12 |
18 |
| C |
25 |
9 |
10 |
| D |
12 |
25 |
30 |
| E |
8 |
70 |
75 |
Section - C
Q26) Solve for x :
2(x2 + 1/x2) - 3(x -
1/x) - 4 = 0 (Marks 6)
Q27)
A pole 5 m high is fixed on the top of a tower. The angle of
elevation of the top of the pole observed from a point A on the ground is
60o and the angle of depression of the point A from the top of
the tower is 45o. Find the height of the tower. (Marks
6)
Q28) Construct a triangle ABC with BC = 6 cm,  A = 60o and the
median AD through A is 5 cm. Construct a triangle AB'C' ~  ABC with BC' = 8 cm.
Write steps of construction. (Marks 6)
Q29)
If a line is drawn parallel to one side of a triangle, the
other two sides are divided in the same ratio. Prove
Using the result,
prove the following:
In the figure PQRS is a trapezium, PQ || SR || XY,
then PX/XS = QY/YR (Marks 6)
Q30) Salma has the
total annual income of Rs. 98,000 during a year (HRA not included). She
contributes Rs. 800 per month towards P.F. and pays an annual premium of
Rs. 1200 towards L.I.C. Calculate the income tax payable in the last month
if she had been paying Rs. 120 per month towards income tax for for first
11 months. (Marks 6)
Assume the following for calculating
income tax :
| (a) Standard
Deduction |
1/3 of the total income
subject to a maximum of Rs. 20,000
(Rs. 25,000 if income is less
than Rs. 1 lac) |
| (b) Rates of
Income tax
Slab
(i) Upto Rs. 50,000
(ii)
From Rs. 50,001 to 60,000
(iii) From Rs. 60,001 to Rs.
1,50,000
(iv) From Rs. 1,50,001 onwards
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Income Tax
Nil
10% of the amount exceeds Rs.
50,000
Rs. 1000 + 20% of the amount exceeding Rs.
60,000
Rs. 19,000 + 30% of the amount exceeding Rs.
1,50,000 |
| (c) Rebate in
Tax |
20% of the total
savings subject to a maximum of Rs. 12,000 |
| (d)
Surcharge |
10% of the tax
payable |
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