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Maths Class X 1999(CBSE)
You are on Set no III Qno. 1 to 30
Time allowed : 3 hours
Maximum Marks :
100
General Instructions :
(i) Question number 1 to 15 carry
2 marks each.
(ii) Question number 16 to 25 carry 4 marks
each.
(iii) Question number 26 to 30 carry 6 marks each.
(iv) Write
the serial number of the question before attempting it.
(v) Use of
logarithmic and trignometric tables is permitted. Use of calculator is not
permitted.
Q9) Evaluate without using trignometric table:
cos
75o/sin 15o + sin 12o/cos 78o
- cos 18o cosec 72o (Marks 2)
Q11)
If cot A = b/a where a, b are real numbers, find the value of
sin2 A. (Marks 2)
Q15)
The height of a cylinder is 15 cm. The curved surface area is 660
sq.cm. Find its radius ( = 22/7). (Marks 2)
Q16)
Solve the following system of equation graphically:
2(x - 1)
= y, x + 3y = 15. Also, find the co-ordinates of the points where the line
meet the axis of y. (Marks 4)
Q19)
Prove that the angle in the same segment of a circle are
equal. (Marks 4)
Q30) Salma has the total annual income of Rs. 99,000 during a year
(HRA not included). She contributes Rs. 600 per month towards P.F. and
pays an annual premium of Rs. 1000 towards L.I.C. Calculate the income tax
payable in the last month if she had been paying Rs. 180 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
|
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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