Free Web Hosting Provider - Web Hosting - E-commerce - High Speed Internet - Free Web Page
Search the Web

CBSE Model Paper No 1
On New Pattern
Time allowed : 3 hours
Maximum Marks : 100
General Instructions :

(i) Question number 1 to 10 carry 3 marks each.( Section A)
(ii) Question number 11 to 20 carry 4 marks each..( Section B)
(iii) Question number 21 to 25 carry 6 marks each. .( Section C)
(iv) Write the serial number of the question before attempting it.
(v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted

 ( Section A)
1. Find GCD of 18(4x2 - 25) and 12(2x2 + 11x + 15).
2. Find the length of the largest rod that can be placed in the room of 12 m x 8 m x9 m.
3. 
If a = c Prove that (2a + 3b)(2c - 3d) = (2a - 3b) (2c + 3d).
    b   d

Or

If a/b = c/d then show that 5a + 9c / 5b + 9d = 4a - 3c / 4b - 3d?

 
4. Show that : (Cosec A + Cot A - 1) (Cosec A - Cot A + 1) = 2 Cot A
5. Determine the value of k for which the following system of equations have infinite solutions.
4x + 6y = 8
k x + 3y = 3k 2
6.
.  In the adjoining figure, AD = 6 and BC = 5. AD is a tangent to the circle at D. Find AB
 

 
7.
. Solve
x =              
  OR

A plane left 30 minutes later than its scheduled time. In order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr than its usual speed. Find its usual speed. 
8. Evaluate .
9. If the ratio of the radii of two cylinders is 2 : 1 and the ratio of their heights is 1 : 2, compare their volumes.
10. Factorise
x2(y – z) + y2(z – x) + z2(x – y)

 ( Section B)
11. 
Solve graphically. 
3x + 4y = 12
8x + 5y = 40
12. If x = a cosA + b sinA and y = a sinA - b cosA. Prove that x2 + y2 = a2 + b2.
13. 
Reena goes to a shop to buy a radio, costing Rs. 2568. The rate of sales tax is 7%.
She tells the shopkeeper to reduce the price of the radio to such an extent that she has to pay 
Rs. 2568 inclusive of sales tax. Find the reduction in the price of radio.
14. If h, c and v are height, curved surface area and volume of a cone, respectively, 
then prove 3v h3 c2h2 + 9v2 = 0

. Or

If a, b and c are in continued proportion, prove that .
15. The hypotenuse of a right triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle. 
16. Simplify:
. In ABC, AB = AC, seg AC is a tangent to a circle at point D. The circle passes through B; A–D–C such that AD = AC. Show that 9AP = AB.
8. Construct a ABC, in which BC = 5 cm, A = 75o and altitude through
A = 3.7 cm.
Or

Draw equilateral DPRS with RS = 7.5 cm. Construct circumcircle of DPRS. Measure its radius.
19. AB is a line segment and M is its middle point. On one side of AB, semi-circles have been drawn by taking AM, MB and AB as diameters. A circle has been drawn which touches each of the three semi-circles. Prove that the radius of the circle = 1/6 AB.
20. 
How many bricks each of dimension 25 cm * 16 cm * 10 cm will be needed  to build a wall 24 m long,
6 m tall and 4cm thick. What will be the cost of bricks at the rate of  Rs. 3.5 per 1000 bricks,
10% of the wall is filled with mortar.

( Section C)
21 A man is standing on one side of a large open ground. A pole is fixed on the opposite side of the ground. The angle of elevation made by the top of the pole is 60o. On moving 40 m further away from the pole, the angle of elevation decreases to 30o. Find the width of the ground and the height of the pole.
22 A cylindrical jar of radius 6 cm contains oil. Iron spherical balls each of radius 1.5 cm are immersed in the oil. How many spherical balls are necessary to raise the level of the oil by 2 cm?
23 13 + 36 = 0
24

 

 Mr Kumar opened a savings account in Punjab National Bank on 3rd January 1999 with Rs 5000. His transactions during the year 1999 were as under:
January 12, deposited Rs 3718·46 by cheque
February 7, deposited Rs 2000·00 by cash
May 16, withdrew Rs 4102·50 by cheque
June 3, withdrew Rs 1500·00
June 26, withdrew Rs 700·00
August 13, deposited Rs 6726·80 by cheque
September 10, deposited Rs 3000·00 by cash
November 4, withdrew Rs 2500·00
Write the entries in his passbook. He closed his account on 19th December, 1999. If the bank paid interest (computed annually) at 5·5%, find the amount he received on the day of closing his account

OR
Ramkumar has a total income of Rs. 95,000 excluding HRA. He pays a premium of
Rs. 2,000 half-yearly towards life insurance policy. Calculate the income tax he has to pay.
Assume the following rates:

a) Standard deduction: 1/3rd of total income subject to a maximum of Rs. 20,000. (Rs. 25,000 if income is less than Rs. 1 lakh.)
b) Rate of tax
SLAB
i) Up to Rs. 50,000
ii) from Rs. 50,001 to Rs. 60,000
iii) from Rs. 60,001 to Rs. 1,50,000

iv) from Rs. 1,50,001 onwards
INCOME - TAX
Nil
(10% of the amount exceeding 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
25 
ABC is a right angled triangle, right angle at c . If p is the length of the perpendicular side 
from c  to AB and AB = c , BC = a , CA = b, Prove  that :
i) pc = ab ii )  1  =  1 + 1 
                   p2    a2  b2

 

DISCLAIMER NOTICE    This sample  paper is  just for practice .Students , it is not nessessary paper will  come  surely in this format  .It may differ  .
<