## Maths CBSE Model Paper

12/18/2011 CBSE

CBSE Model Paper

Time
allowed : 3 hours
Maximum Marks : 100
General
Instructions
:

(i) Question
number 1 to 10 carry 3marks each.     (Section  A
)
(ii) Question number 10 to 20carry 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. Determine K so that the
equation x2 + 4x – K = 0 has two equal roots.
2. A rectangular piece of paper
is 44 cm long and 20 cm wide. A cylinder is formed    by
rolling the paper along its length. Find the volume of the cylinder.
3.

Calculate the mean and mode
of 21, 16, 15, 14, 15, 18, 17, 22, 28, 15, 26,
15

.OR

State the mean by `direct
method' -
X
4  8  12 16
20
Y   6 10 12
8   4

4 From the diagram given below
calculate
(i)
AB
(ii) AP
(iii)
DAPC : DABC
5 If the areas of three
adjacent faces of cuboid are p, q and r and volume is v,
prove
that
V2 = p q r
6 Prove that

Sin(90-q) Cos (90-q) =
(1-sin2
q}

tan
q
7 If x3 + y3 / x3 - y3 = 91 / 37 . Show that x : y = 4
:3
8
`Aarti buys a saree costing Rs. 2500/- at Rs. 2700/- after paying sales tax.Calculate the ratio of sales tax paid by her.OR`
`Find side of square whose diagonal is 12 cm.`
9 3x + 2y = 6 ;(k + 1 )x + 4y = (2k +
2)
For what value of k, will the above system of equation have
infinite solution.
10 The mean of 5 numbers is 15.
If one number is excluded, the mean becomes 12.5, find the excluded
number.

Section
B

11. In figure ABCD is a cyclic
quadrilateral. AE is drawn parallel to CD and BA is produced. If ABC = 92o, FAE
= 20o, find BCD.

12. In a
trapezium PQRS, PQ || SR and SR = 2 PQ. XY drawn parallel to PQ cuts PS in
X and QR in Y such that . Diagonal QS intersects XY in Z. Prove that .
13.

Find the GCD of the polynomials 4(X-3)2 (X-1)
(x+1)3 ; 6(X-1)2 (X+1)2
(X+7)

OR

If
Cos
245 + Sin 30 = 2 Cos2A , Find Sec2A.

15. In the given figure DE || BC and AD :
DB = 5 : 4
Find ( DFE)/( CFB)
ABCD in which BD = 4cm,A = 900, CD = 2.5cm and AB = 3cm
17.
`Calculate cost of living index from the following data :-     `

 `Commodity ` Quantity Price in 1999 Price of 2000 P 5 4.20 6.00 R 4 5.00 8.50 A 3 8.00 10.50 G 7 9.00 11.50 S 8 12.50 16.00
18. An
aeroplane takes 1 hour less for a journey of 1200 km. If its speed is
increased by 100 km/hr, from its usual speed, find its usual
speed.
19. The
dimensions of a rectangular tank are 2 m, 7 m and 2 m. It is being filled
with water using a pipe of diameter 3.5 cm through which water flows at
the rate of 2 m/s. Calculate the time required to fill the
tank.
20. 80% and 60% pure acid solutions are mixed to obtain
10 litres of 75% pure
acid
solution . Find
the amount of each type of acid to be mixed to form the
mixture.

SectionC

21a

.

b

Draw graphically the following equations:
2y
=

x
+ 4
x + 2y = 4
A
circle with centre O. AB and CD are two parallel chords on the same side
of the centre. If the radius of the circle is 65 cm and the length of the
chords are 112 cm and 126 cm respectively, find area of rectangle
ABCD.
22a

.
22b

Construct
ABC such that AXB = 116o, AB = 7.8 cm, CF = 5 cm, CF AB.
X is the point of intersection of the altitudes
AD and BE. Measure seg. AC

23  Page from a saving bank passbook for the year 2000
is given below. Calculate the interest at the end of the year at the rate
of 5% p.a.

 Date Particulars Amount withdrawn Rs. P. Amount deposited Rs. P. BalanceRs. P. 2000 Jan 1 By balance – 1,120.00 1,120.00 11 By cash – 800.00 1,920.00 Feb 2 To cheque 300.00 – 1,620.00 Mar 10 By cash – 1,400.00 3,020.00 June 28 To cheque 500.00 – 2,520.00 Sept 5 By cash – 480.00 3,000.00 Dec 13 By cash – 1,200.00 4,200.00
24 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:
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

Solve for x
:
4(x2 + 1/x2) + 8(x - 1/x) - 29 = 0

or

A tower in a city is 150 m high and a
multistoried hotel at the city centre is 20 m high. The angle of elevation
of the top of the tower at the top of the hotel is 5o. A
building, h metres high, is situated on the straight road connecting the
tower with the city centre at a distance of 1.2 km from the tower. Find
the value of h if the top of the hotel, the top of the building and the
top of the tower are in a straight line. Also find the distance of the
tower from the city centre.
(Use tan 5o = 0.0875; tan
85o = 11.43