CBSE Model Paper no 4

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CBSE Model Paper no 4

Time allowed : 3 hours
Maximum Marks : 100

General Instructions :

(i) Question number 1 to 10 carry 3 marks each. (SectionA)
(ii) Question number 11 to 20 carry 4 marks each. (SectionB)
(iii) Question number 21 to 25carry 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

SectionA

Find the value of ‘k’ so that the equation 9x²-Kx-81 = 0 has equal roots.

Find the value of k for which the system of equations

8x + 5y = 9

Kx + 10y = 15

Find the value of x if p+1=0 and x²+px-6=0

ORThe GCD and LCM of two polynomials p(x) and Q(x) are x (x+a) and
12x²( x + a)(x² - a²) espectively.If P(x) = 4x(x + a)², find Q(x).

Radius of larger circle is 18 and smaller is 5. Determine the ratio in which point P divides segAB

Sheetal buys goods worth of Rs 6800.She gets a rebate of 8%on it After getting the rebate if sales tax is charged at 6% ,find the amount she has to pay for the goods.
                                                                   OR
Without using trigonometric tables, evaluate:
cos 70° +cos 59° -8 sin²30°.
     sin 20°     sin 31°

x ³+ 3xy ² =p ³ + 3pq^{2

----------------- -----------------} 3x²y + y ³ 3p²q + q^{3

prove that}

x = p
y q

The mean of the numbers 1, 7, 5, 3, 4, 4 is m. The numbers 3, 2, 4, 2, 3, 3, p have mean m -1 and median q. Find
(i) p (ii) q (iii) the mean of p and q.

The diagonal of a rhombus are 24cm and 10 cm. Find its perimeter.

If the product of two positive consecutive odd integers is 195, find the integers.

A spherical ball of aluminimum is melted and cast into smaller spheres each with radius equal to quarter the radius of the bigger one. How many smaller spheres can be made ?

SectionB

In the adjoining figure, sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at P, the sides AD and BC are produced to meet at Q. If Ð ADC = 85^o, Ð BPC = 40^o, calculate Ð BAD and Ð CQD.

Simplify

13.

If tan q = 7/24, find the value of
3 sin q + 4 cos q where q is acute.

OR

A school bus trasported an excursion party to a picnic spot 150 km away .While on retuning due to heavy rain the bus had to reduce to its speed 5km/hr ,and it took one hour longer to make the return trip .Find the time taken to return

Find x from the following equations

a +x +a -x = c
a + x -a - x d

The area of a field in the form of a trapezium is 1600 sq.m. If the altitude of the field is 50m, find its parallel sides if each is multiple of 16. How many solutions are possible to the problem ?

In the following figure, ABCD is a square of side 24 cm. Given

EAC = 90° and AE = 12

2 cm.Calculate EC.

The radius of the base of a cone and a sphere are both equal to 8 cm. Given that the volumes of these solids are also the same, calculate the slant height of the cone correct to one place of decimals.

17.

A page from Anshuls savings bank passbook is given below:

Date Year 2000	Particulars	Amount(Withdrawals) Rs P	Amount(Deposit) Rs P	Balance Rs P
January 1	B/F	...	...	8026.15
January 5	By cash	...	650.00	8676.15
February 13	To self	2500.00	...	6176.15
June 4	By Cheque	...	385.00	6561.15
July 19	By Cheque	718.50	...	5842.15

He closed the account on 25th July 2000 and received Rs 6042·45. Calculate the rate of interest.

Draw a circle with radius 3 cm and centre O. Take a chord PQ = 4 cm. Draw a tangent to the circle at P. Measure the acute angle between the tangent and chord PQ.

sin A +cos A +sin A -cos A = 2 = 2
sin A -cos A sin A +cos A sin² A -cos² A 1 -2 cos² A

From the top of a cliff 150 m high, the angles of depression of two boats are 60° and 30°. Find the distance between the boats, if the boats are
(i) on the same side of cliff.
(ii) on the opposite sides of the cliff.

SectionC

Following table gives marks scored by students in an examination:

Marks	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40
No. of students	3	7	15	24	16	18	5	2

Calculate the mean mark correct to 2 decimal places.

Mrs. Ram is a teacher in a public school. Her annual salaried income is Rs 1,16,760. She donates Rs 1,001 to the Prime Minister's Relief Fund, which has 100% tax exemption. She contributes Rs 2,562 per month to her P.F. account, pays an annual premium of Rs 7,376 towards her Life Insurance Policy. Calculate the income tax paid by Mrs. Ram if her earlier deductions for the first eleven months of income tax were at the rate of Rs 145 per month

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

In parallelogram ABCD, M is the mid point of side CD. A line BM is drawn
intersecting AC in L and AD produced in E. Prove that EL @ 2 BL

A)Solve the following equations graphically :
2x + 3y - 1 = 3x + 2y = 12.

B)Solve

A vessel is in the form of an invalid cone with height 8 cm and radius 5 cm. It is completely filled with water. Spherical lead shots of radius of 0.5 cm are dropped into the vessel and hence one fourth of the water overflows. Find the
number of lead - to dropped into the vessel

A)Complete the tabel and find CDR.

Age group	Population	Number of Deaths
0 -10	35650	310
10 - 20	37750	250
20 - 35	-	110
35 - 50	30450	-
above 50	20150	390
1,40,000		1200

B) If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is a cyclic quadrilateral ,prove it

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