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SAMPLE
PAPER
MATHEMATICS
SET - II
General Instructions :
(1)
All questions are compulsory.
(2)
This question paper consists of 30 questions
divided into three sections - Section A (Q.
1-15). Section B(Q. 16 to 25) and Section
C (Q. 26 to 30).
(3)
Question numbers 1 to 15 carry 2 marks each,
ques. numbers 16 to 25 carry 4 marks each, ques.
number 26 to 30 carry 6 marks each.
(4)
Write down the serial number of the question
before attempting it.
(5)
Use of logarithmic and Trigonometric tables is
permitted. However, use of calculator is
not permitted.
(6)
In Ques. 24 the drawing should be neat and
accurate as per measurement given.
|
| Q.1. |
Solve the
following system of equations using cross
multiplication method : 2x +
5Y = 1 and 2x + 3y =
3 |
| Q.2. |
Reduce the
rational expression to its lowest terns.
36x5 - 36x /
(4x2 + 4)
(3x-3) |
| Q.3. |
The g.c.d. of
two polynomials is (x-1) and their l.c.m. is
x6-1. If
one of the polynomials is x3 - 1, find the other.
|
| Q.4. |
Form a quadratic
equation, of which one root is 2
-Ö5 and the sum of the
roots is 4. |
| Q.5. |
A Page
from the saving bank pass book is given below.
|
|
Date
|
Particular
|
Amount
withdrawn Rs. P. |
Amount
deposited Rs. P. |
Balance Rs.
P. |
|
1999 |
|
|
|
|
|
April
11 |
By cash ( new
a/c) |
-- |
2,000 |
2,000 |
|
April
28 |
By cash
|
-- |
5,000 |
7,000 |
|
April 30
|
To cheque
|
1,500 |
-- |
5,500 |
|
May
9 |
To cheque
|
500 |
-- |
5,000 |
|
May
10 |
By
cash |
-- |
800 |
5,800 |
|
May
12 |
To cheque
|
1,200 |
-- |
4,600 |
|
July
10 |
By
Cash |
-- |
400 |
5,000 |
|
July
12 |
To self
|
1,000 |
-- |
4,000 |
|
July 30
|
To cheque
|
500
|
-- |
3,500 |
|
Determine the
amount, which will earn interest for month of
April, 99 and June,99. |
| Q.6. |
John purchased
a packet of biscuits with list price Rs. 55 on
which the rate of sales tax is 8%. He also
purchased a tube of shaving cream with list
price Rs. 36 on which the rate of sales tax is
10 %. Calculate the total amount he paid
for the purchase of a packet of biscuits and a
shaving cream. |
| Q.7. |
A sphere of
radius r is divided into four identical
parts. Find the total surface area of one
part. |
| Q.8. |
If
Ö
3 tanq = 1, find the
value of sin2q - cos2q given 00 £q
£ 900. |
| Q.9. |
Prove :
Ö1 + sinq/Ö1-sin q = sec
q + tan
q, (q
¹ 900) |
| Q.10. |
In the
adjoining figure, DPQR
~
DPRS If PR = 8
cm and PS = 4cm. Calculate the length of
PQ. |
| Q.11. |
The sides of a
triangle are 7 m, 24cm and 26 cm long.
Determine whether the triangle is a right
triangle. |
| Q.12. |
In the adjoining
figure, AB is parallel to Cd. Prove that
BD @
CA.
|
| Q.13. |
For the data
1,5,7,x + 1,9, x -2, 3 if the mean is 4, find
the value of x. Using this value of x, also find
the mode of the data.
|
| Q.14. |
Define the
terms (i) Crude death rate (ii) Infant mortality
rate. |
| Q.15. |
Three cubes of
metal whose edges are 3 cm, 4 cm and 5 cm are
melted and formed into a single cube. Find
its edge. |
|
SECTION - B
|
| Q.16. |
Draw the graphs
of the following equations on same graph paper.
3x -
2y =6 and 3x + y = 15
Find
the coordinates of the vertices of the
triangle formed by these two straight lines and
the x - axis. |
| Q.17. |
170 copies of
Mathematics book and 40 copies of English book
cost Rs. 2220. Also, 40 copies of
Mathematics book and 50 copies of English books
cost Rs. 1900. Find the cost of one
mathematics and one English book separately.
|
| Q.18. |
If x/b+c-a =
y/c+a-b = z/a+b-c then prove that (b-c) x+(c-a)
y+(a-b) z = 0 |
| Q.19. |
If a and
b are the roots of the equation x2-3x+2 = 0 then show
that a3
+
b3 = 9.
|
| Q.20. |
A room is 8m
long, 4.5m wide and 2.8m high. It has one
door 1.4m wide and 2 m high with a semicircular
ventilator as shown in the diagram and two
rectangular windows 2m by 1.5m each. Find
the cost of white washing of the inner four
walls of the room @ of Rs. 10 per sq. m. (Table
p= 22/7). |
| Q.21. |
A hollow
cylindrical pipe is made of copper. If the
volume of the metal used in the pipe is
748 cu. cm., its external radius is 9 cm and
length is 14 cm; find the thickness of the pipe.
|
| Q.22
|
If
cosq + sin q =Ö2
cosq, then prove that cosq - sin
q =Ösinq |
| Q.23. |
In the given
figure ABCD is a trapezium in which AB ||
DC. If AC trisects BD, then prove that CD
= AB/2. |
| Q.24. |
Draw a circle
of radius 5cm. Take a point P on it. Construct a
tangent at the point P without using the centre
of the circle. Also write the steps of
construction. |
| Q.25. |
Calculate cost
of living Index Number for the year 1998, taking
1996 as the base year for the following data :
|
|
Item |
Quantity |
Price Per kg.
1996 (in Rs.) |
Price per kg
1998 (in Rs.) |
|
A |
40 |
3.00 |
2.00 |
|
B |
20 |
10.00 |
15.00 |
|
C |
20 |
8.00 |
16.00 |
|
D |
30 |
5.00 |
8.00 |
|
E |
10 |
20.00 |
25.00 |
|
SECTION-C |
| Q.26. |
Reduce the
following equation to a quadratic equation and
then solve for x : x(x-1)(x+2) (x+3) = 24
|
| Q.27. |
From the
window, 1.2m above the ground of a house on one
side of a street, the angle of elevation and the
angle of depression of the top and bottom of a
pole on the opposite side of the street are 230
and 370. Find the height of the pole,
nearest to two place of decimal.
|
| Q.28. |
(i) If PAB is a
secant to a circle intersecting the circle at A
and B and PT is the tangent at T, then Prove
that PA. PB = PT2.
(ii)
Using the above theorem, prove that the
following. In the given figure, two
circles intersect each other at P and
Q. If AB and AC are tangents to the
two circles from a point A on the line joining P
and Q, then show that AB = AC.
|
| Q.29. |
Sharda's
monthly salary is Rs. 22,000 (H.R.A. not
included). Her monthly contribution to
G.P.F. is Rs. 4000. She pays Rs.
12000 annually as L.I.C. premium and invests Rs.
2000 in N.S.C. She donates Rs. 10,000 towards
Prime Minister Relief Fund ( 100 % tax
exemption) and Rs. 8000 to a Charitable Trust
(50 % exemption), Rs. 2600 are deducted each
month from his salary as income tax for
11months. Calculate the income tax payable
including surcharge by her in the last month of
the year. The rates of income tax are as
follows : - |
| (a) |
Standard
Deduction |
1/3 of the
annual income subject to a maximum of Rs.
20,000. |
| (b) |
Slab |
Rate of Income
Tax |
| (i) |
Upto Rs. 50,000
|
Nil |
| (ii) |
From Rs. 50,001
to Rs. 60,000 |
10 % of the
amount exceeding Rs.
50,000. |
| (iii) |
From Rs. 60,001
to Rs. 1,50,000 |
Rs. 1,000 + 20%
of exceeding Rs.
60,000. |
| (iv) |
From Rs.
1,50,001 onwards |
Rs. 19,000 + 30
% of the amount exceeding Rs. 1,50,000.
|
| (c) |
Rebate in Tax
|
20 % of the
total annual savings subject to a maximum of Rs.
12,000. |
| (d) |
Surcharge |
10 % of the net
tax payable. |
| Q.30. |
In the given
figure, x/3 = y/4 = z/5, then calculate the
value of x,y and z.
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