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Maths Class X 1996(CBSE)
You are on Set no 1 Qno. 21 to 30
Q21) "In a triangle, a line drawn parallel to one side, to intersect
the other side in distinct points, divides the two sides in the same
ratio". Prove. (Marks 4) Q22)
The perpendicular AD on the base BC of a  ABC intersects BC at D so that DB = 3CD.
Prove that
2AB2 = 2AC2 + BC2
(Marks 4)
Q23) Find the mean of
the following data : (Marks 4)
| Class
Interval |
Frequency |
| 0 -
10 |
8 |
| 10 -
20 |
10 |
| 20 -
30 |
9 |
| 30 -
40 |
12 |
| 40 -
50 |
11 |
Q24) Algorithm. Omitted, being out of Syllabus. (Marks
4)
Q25) Flow Chart. Omitted, being out of Syllabus. (Marks 4)
Section - C
Q26) Solve for x :
4(x2 + 1/x2) + 8(x -
1/x) - 29 = 0 (Marks 6)
Q27)
A tower in a city is 150 m high and a multistoried hotel at the
city centre is 20 m high. The angle of elevation of the top of the tower
at the top of the hotel is 5o. A building, h metres high, is
situated on the straight road connecting the tower with the city centre at
a distance of 1.2 km from the tower. Find the value of h if the top of the
hotel, the top of the building and the top of the tower are in a straight
line. Also find the distance of the tower from the city centre.
(Use
tan 5o = 0.0875; tan 85o = 11.43) (Marks
6)
Q28) "The degree measure of an arc of a circle is twice the angle
subtended by it at any point of the alternate segment of the circle with
respect to the arc." - Prove. (Marks 6)
Q29)
Construct ABC in
which BC = 6 cm,  A =
60o and the altitude through A is 4.5 cm. Measure the length of
the median through A. Write the steps of construction. (Marks
6)
Q30) The total salary of Manjeet Singh is Rs. 1,25,500 (excluding
HRA) during a year. He pays a premium of Rs. 10,800 annually towards LIC
and contributes Rs. 2,000 per month towards G.P.F. Rs. 250 are deducted
each month from his salary as income tax. Calculate the income tax Manjeet
Singh is to pay in the last month of the financial year. (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
|
Income Tax
No tax
10% of the amount exceeds Rs.
50,000
Rs. 1,000 + 20% of the amount exceeding Rs.
60,000
|
| (c) Rebate in
Tax |
20% of the total
savings subject to a maximum of Rs. 12,000 |
| (d)
Surcharge |
10% of the tax
payable |
OR
A page from the pass
book of Ram Lal's Saving Bank Account in a particular year is given below
:-
| Date |
Particulars |
Amt.
Withdrawn
Rs. P. |
Amt.
Deposited
Rs. P. |
Balance
Rs. P. |
| Jan. 1 |
By Balance |
|
|
1200.00 |
| Jan. 5 |
By Cash |
|
500.00 |
1700.00 |
| Feb. 20 |
By Cash |
|
700.00 |
2400.00 |
| Feb. 25 |
To Cheque |
500.00 |
|
1900.00 |
| May, 8 |
By Cash |
|
1000.00 |
2900.00 |
| July, 12 |
By Cash |
|
1500.00 |
4400.00 |
| July, 20 |
To Cheque |
1000.00 |
|
3400.00 |
| Sept. 1 |
By Cash |
|
1200.00 |
4600.00 |
| Oct. 5 |
To Cheque |
2000.00 |
|
2600.00 |
| Dec. 15 |
By Cash |
|
500.00 |
3100.00 |
Assuming the rate of interest is 5%
p.a. and interest is paid once in a year, at the end of December,
calculate the interest earned by Ram Lal at the end of the year.
Note: Question done according to the latest
syllabus.
Total salary of Manjeet Singh taken as Rs.125,500 in place
of Rs.120,500.
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