CBSE - X
CBSE X (Delhi)
MATHEMATICS PAPER 2007.
Time allowed: 3 hours; Maximum Marks: 80
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of 25 questions divided into three sections- A, B and C. Section A contains 7 questions of 2 marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in two questions of two marks each, two questions of three marks each and two questions of five marks each. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculators is not permitted. However, you may ask for Mathematical tables. |
Question 20
20. If a line is drawn parallel to one side of a triangle, to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. Using the above, prove the following:
In Fig. 3, 
and 
Prove that ABC is an isosceles
triangle.
Fig.3
Question 21
21. Prove that the sum of either pair of opposite angles of a cyclic
quadrilateral is 
Using the above, find x and y in Fig. 4.
Fig.4
Question 22
22. The difference of two numbers is 5 and difference
of their reciprocals is 
Find the numbers.
Question 23
23. A sphere of diameter 12 cm, is dropped in a right
circular cylindrical vessel, partly filled with water. If the sphere is
completely submerged in water, the water level in the cylindrical vessel rises
by 
Find the diameter of the
cylindrical vessel.
Question 24
24. A boy standing on a horizontal plane finds a bird
flying at a distance of 100 m from him at an elevation of 
A girl standing on the roof of 20
metre high building, finds the angle of elevation of the same bird tobe 
Both the boy and the girl are on
opposite sides of the bird. Find the distance of bird from the girl.
Question 25
25. Ms. Shahnaz earns Rs. 35,000 per month (excluding
HRA). She donates Rs. 30,000 to Prime Minister Relief Fund (100% exemption) and
Rs. 40,000 to a Charitable Hospital (50% exemption). She contributes Rs. 5,000
per month to Provident Fund and Rs. 25,000 per annum towards LIC premium. She
purchases NSC worth Rs. 20,000. She pays Rs. 2,300 per month towards income tax
for 11 month. Find the amount of income tax she has to pay in 
month of the year.
Use the following to calculating income tax :
(a) Saving |
100% exemption for permissible savings upto Rs. 1,00,000 |
(b) Rates of income tax for ladies |
|
Slab |
Income tax |
(i) Upto Rs. 1,35,000 |
No tax |
(ii) From Rs. 1,35,001 to Rs. 1,50,000 |
10% of taxable income Exceeding Rs. 1,35,000 |
(iii) From Rs. 1,50,001 to Rs. 2,50,000 |
Rs. 1,500 + 20% of the amount exceeding Rs. 1,50,000 |
(iv) From Rs. 2,50,001 and above |
Rs. 21,500 + 30% of the amount exceeding Rs. 2,50,000 |
(c) Education Cess : |
2% of Income tax payable |
| Section A | Section B | Section C |