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Maths Class X 1998(CBSE)
You are on Set no 1 Qno. 21 to 30
Q21) In a right triangle ABC, right angled at C, at point D is taken
on AB such that CD is perpendicular to AB, Prove that
1/AC2
+ 1/BC2 = 1/CD2 (Marks 4)
Q22) In Fig. 4, AB is the chord of a circle with centre O. AB is
produced to C such that BC = OB. CO is joined and produced to meet the
circle in D. If  ACD = yo and AOD= xo, prove that x =
3y (Marks 4)
Q23)
Algorithm - Omitted being out
Syllabus. (Marks 4)
Q24) Flow Chart - Omitted, being out of Syllabus. (Marks
4)
Q25) The population of two towns A and B are 8,76,000 and 6,90,000
respectively and the respective crude death rates are 14.3 and 16.2
respectively. Find to the nearest whole number, the crude death rate for
the two towns taken together. (Marks
4)
Section - C
Q26) Solve for x :
 (x2 - 16) - (x - 4) = (x2 -
5x + 4) (Marks 6)
Q27)
A man on the deck of a ship is 16 m above water level. He
observes that the angle of elevation of the top of a cliff is
45o and the angle of depression of the base is 30o,
Calculate the distance of the cliff from the ship and the height of the
cliff. (Marks 6)
Q28)
If a line is drawn parallel to one side of a triangle, the two
sides are divided in the same ratio - Prove
Use the result to prove the
following :
In Fig 5, if ABCD is a trapezium in which AB || DC || EF,
then
AE/ED = BF/FC (Marks 6)
Q29)
Construct a  ABC in which AB = 5cm, B = 60o and
altitude CD = 3 cm. Construct AQR similar to ABC such that each
side of
AQR is 1.5 times that of the corresponding side of ABC. (Marks
6)
Q30) The annual income of Shyam Lal (excluding HRA) is Rs. 1,65,000.
He contributes Rs. 4,000 per month in his provident fund and pays an
annual premium or Rs. 16,000, towards his Life Insurance Policy. Calculate
the income tax paid by Syam Lal in the last month of the year if his
earlier deduction for first 11 months for income tax were at rate of Rs.
400 per month. (changed) (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
No tax
10% of the amount exceeds Rs.
50,000
Rs. 1,000 + 20% of the amount exceeding Rs.
60,000
Rs. 19,000 + 30% of the amount exceeding Rs. 1,50,000
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| (c) Rebate in
Tax |
20% of the total
savings subject to a maximum of Rs. 12,000 |
| (d)
Surcharge |
10% of the tax
payable |
Note: Question done according to the latest
syllabus.
Annual salary taken as Rs.1,65,000 in place of
Rs.1,60,000.
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