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CBSE Model Paper No 2
Time allowed : 3 hours
Maximum Marks : 100
General Instructions :

(i) Question number 1 to 10 carry 3marks each.(SectionA)
(ii) Question number 11 to 20 carry 4 marks each.(SectionB)
(iii) Question number 21 to 25 carry 6 marks each.(SectionC)
(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. Given, 5 cos A - 12 sin A = 0, evaluate without using tables
    sin A + cos A   
   2 cos A - sin A
2. Show that :
(Cosec A + Cot A - 1) (Cosec A - Cot A + 1) = 2 Cot A
3. For what value of k will the following system of linear equations have an infinite number of solutions: 2x + 3y = 2; (k + 2)x + (2k + 1)y = 2(k - 1) ? 
4. The length, breadth and height of a rectangular room are 3 m, 5 m and 6 m respectively. Find the cost involved in painting the inner walls of the room at the rate of Rs. 15 per square metre.
5. In the adjoining figure,  QR is a tangent to the circle with centre P.
PR = 12 cm and PQ = 6 cm. Find the area of segment PQT region.

6. Evaluate the following without using logarithmic tables: cosec2 68o– tan222o.
7 The mean weight of 21 students of a class is 52 kg. If the mean weight of first 11 students of the class is 50 kg and that of last 11 students is 54 kg, find the weight of the 11th student. (Marks 2)
8. Find two consecutive numbers, whose square have sum 85

                                                                          OR

A solid metal sphere is cut into two equal hemispheres of radii 7 cm. Find the surface area of each hemisphere
 
9. If A = (x + 1)/(x - 1), find A - 1/A in the simplified form.
10. Find whether the number 6, 10, 14 and 22 are in proportional or not. If not what number be added to each number so that they become proportional ?
                                                                           OR

Form the quadratic equation in x whose roots are 2 + 5 and 2 - 5.
                                                                               SectionB
11

 

 The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.

                                                                            OR

Find the value of k such that sum of the roots of the quadratic equation

3x2 + (2k + 1)x - (k + 5) = 0 is equal to the product of its roots.
12 A furniture shop marks a dining room set at Rs. 35000.00.
The present taxation structure is as follows :
    • Sales Tax @ 12%
    • A surcharge of 10% of the sales tax amount
    • A turnover tax @ 1% of the net bill value of Rs. 35000.00

Find the total value a customer would have to pay for the dining set.
13 Find x from the following equations :
                      
    a +x +a -x   = c                                                       
   a + x -a - x      d
 
14 In the adjoining figure, ABC is a right angled triangle with AB = 6 cm, and BC = 8 cm. A circle with center O has been inscribed inside the triangle. Calculate the value of x, the radius of the inscribed circle ima-circles11.gif (1003 bytes)
15
 

 

 

 

 

OR

 A gas tank is made by joining a cone to a hemisphere of radius 3 m as shown in the figure. If the volume of the hemisphere is one and a half times that of the cone, calculate the height of the cone and the surface area of the tank. Also, find the volume of gas that the tank can hold. cylinder09.GIF (2864 bytes)
If a, b and c are in continued proportion, prove that .
16 If L.C.M. and G.C.D. of the two polynomials are 27 x3 (x + a) (x3 - a3) and x2(x - a) respectively and if one of the polynomial is 3x2 (x2 - a2). Find the other.
17 In the following figure, D and E are mid-points of the sides BC and CA respectively of a ABC, right angled at C. Prove that

4(ADČ +BEČ) = 5ABČ
[5
18 From the table given below, derive the equation of the line and draw its graph. From the graph, find the values of p and q.                                                                                    
x 1 p 4 -1
y 1 7 10 q
19 In fig. AB is a diameter of circle with centre O, OA = 7 cm. Find the area of the shaded region (use = 22/7).
20 Find the cost of living index number for the year 1995 assuming 1990 as the base year. (Marks 4)

Commodity Quantity(kg) Rate per kg (in Rs.) 1990

A                   10                7                            10
B                   15              12                             20
C                    8               25                             25
D                   25              12                             20
E                     5               50                             60
                                                                                    SectionC
21 Mr Raunak Singh is an administrative officer in LIC. His annual income (excluding HRA) in financial year 2000-2001 is Rs 191734. He contributes Rs 875 per month to provident fund, and pays Rs 260 per month as LIC premium. He buys National Savings Certificates worth Rs 40000 and contributes Rs 12000 in mutual fund. He donates Rs 2500 in Prime Minister relief fund (eligible for 100% deduction U/S 80G) and Rs 500 to a charitable trust (eligible for 50% deduction U/S 80G). If Rs 1000 per month has been deducted by the employer as income tax at source in the first 11 months, find his taxable income and the balance of the income tax he shall has to pay in the last month

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
22 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
23 Prove that sum of either pair of opposite angles of a cyclic quadrilateral is 180o. Using the above solve the following:

In fig POQ is a diameter and PQRS is a cyclic quadrilateral. If PSR = 150o, find RPQ.
24 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.

                                                                                        OR
                                                                                           

  Find the missing value of x for the following distribution whose mean is 12.58.
 
xi: 5 8 10 12 x 20 25
fi: 2 5 8 22 7 4 2
25 fig. AB and CD are two parallel tangents to a circle with centre O. ST is tangent segment between two parallel tangents touching the circle at Q. Show that SOT = 90o.

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