Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back
Introducing NextGurukul app, India's Largest Collaborative Learning Community for Learners and Educators - Now available with a Fresh UI and Exciting New Features!
Install NowCBSE X (All India)
MATHEMATICS PAPER 2004.
Time allowed: 3 hours; Maximum Marks: 100
| General Instructions: | |
| 1) | All questions are compulsory. |
| 2) | The question paper consists of 25 questions divided into three parts. Questions (1-10) 10 questions of 3 marks each. Questions (11-20)10 questions of 4 marks each. Questions (21-25) 5 questions of 6 marks each. |
| 3) | There is no overall choice. However, an internal choice has been provided in each section. |
| 4) | In question on construction, the drawing should be neat and exactly as per the given measurements. |
| 5) | Use of calculator is not permitted. However, you may ask for Mathematical tables. |
| 6) | Please give the explanation for the answer where applicable. |
21.Prove that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides. Using the above, prove the following: In DABC, ÐA = 90° and AD ^ BC, prove that AB2 + CD2 = BD2 + AC2.
22.Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Using the above, do the following:
Prove that the angle formed by a chord in the major segment is acute.
23.If the radii of the circular ends of a bucket, 45 cm high, are 28 cm and 7 cm (as shown in Fig. 4), find the capacity of the bucket.
Fig.4
24.A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 600 and angle of depression of the base of the hill as 450 . Find the distance of the hill from the ship and height of the hill.
25.Mohan Lal has an annual income of Rs.2,50,000 (excluding HRA). He contributes Rs. 4,000 per month in his Provident Fund and pays an annual premium of Rs. 15,000 for his LIC policy. How much should he invest in N.S.Cs so as to get maximum rebate? He pays Rs. 2,500 per month for 11 months towards income tax. How much income tax has he to pay in the last month of the year? Assume the following for calculating income tax:
(a) Standard Deduction |
|
Gross income |
Deduction |
(i) Upto Rs.75,000 |
40% of gross income |
(b) Rates of Income Taxes |
|
Income |
Income tax |
(i) Upto Rs. 50,000 |
No tax |
(c) Rebate in Tax |
(i) 20% of the savings subject to a maximum
of Rs. 14,000 if the gross income is upto Rs. 1,50,000. |
| Section A | Section B | Section C |
