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Maths Class X 1997(CBSE)
You are on Set no 1 Qno. 21 to 30
Q21) P is a point in the interior of rectangle ABCD. If P is joined
to each of the vertices of the rectangle and the lengths of PA, PB and PC
are 3 cm, 4 cm and 5 cm respectively, find the length of PD. (Marks
4) Q22) In  ABC, if AD is the median, show that AB2 +
AC2 = 2[AD2 + BD2] (Marks 4)
Q23) Flow Chart. Omitted, being out of Syllabus. (Marks 4)
Q24) The data on number of patients attending a hospital in a month
are given below. Find the average number of patients attending the
hospital in a day. (Marks 4)
| Number of
Patients |
Number of
days
attending hospital |
| 0 -
10 |
2 |
| 10 -
20 |
6 |
| 20 -
30 |
9 |
| 30 -
40 |
7 |
| 40 -
50 |
4 |
| 50 -
60 |
2 |
Q25) Algorithm. Omitted, being out of Syllabus. (Marks
4)
Section - C
Q26) Solve for x :
(x2 - 5x)2 -
7(x2 - 5x) + 6 = 0: x R (Marks 6)
Q27)
The angle of elevation of a Jet plane from a point A on the
ground is 60o. After a flight of 15 seconds, the angle of
elevation changes to 30o. If the Jet plane is flying at a
constant height 0f 1500 3 m, find the speed of the Jet plane. (Marks
6)
Q28) Construct a ABC with AB = 4.4 cm,  ACB = 65o and
the median through C is of length 3.2 cm. Also, find the length of the
altitude drawn from the vertex C on AB. (Marks 6)
Q29)
If PAB is a secant to a circle, intersecting the circle at A
and B, and PT is a tangent to the circle at T, then PA x PB =
PT2 - Prove.
Use the above result to prove the
following:
" In Fig 3, ABC is an isosceles triangle in which AB = AC. A
circle through B touches the side AC at D and intersect the side AB at P.
If D is the mid point of side AC, then AB = 4AP." (Marks
6)
Q30) The annual income of Ramesh (excluding HRA) is Rs. 1,65,000. He
contributes Rs. 2000 per month in his Provident Fund and pays annual
premium of Rs. 8,000 towards his Life Insurance Policy. Calculate the
income tax paid by Ramesh in the last month of the year if his earlier
deductions for 11 months for income tax were at the rate of Rs. 800 per
month. (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 |
| (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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