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SAMPLE PAPER
MATHEMATICS
SET - I
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 ne neat and accurate as
per measurement given. |
| Q.1. |
Find the value of a and b for
which the following system of equations has infinite number of solutions. x + 3y = 7, (a+b)x + (4a+b)y = 21 |
| Q.2. |
Find the L.C.M. and G.C.D. of the
following polynomials : 4(x+1)2
(x-2) (x-1)3 and 6(x-2)2 (x-1) (x+1)4 |
| Q.3. |
Which of the following are
rational expressions and why ? (i) (2)1/2
(x)2 - 4x - 7/ x-(8)1/2
(ii) (x)2 - 1/2(x)1/2 + 4
(iii) x3 + 8x2 / 2x-3
(iv) x3 - 3x2 + 23 (x)1/2
/ x2 + 1 |
| Q.4. |
Show that x-1 and x+4 are factors
of the polynomial x3+x2 - 10x + 8. |
| Q.5. |
Find the condition that one root
of the equation ax2 + bx + c = 0, a ¹ 0 may be reciprocal of the
other. |
| Q.6. |
Find the value of k for which the
quadratic equation x2 - kx + 4 = 0 has equal roots. |
| Q.7. |
Show that tan 10 tan20 tan30 tan870
tan880 tan890 = 1 |
| Q.8. |
Find the value of cosec2 q - sec2 q / cosec2 q + sec2 q when tan q = 2/(5)1/2 |
| Q.9 |
In the given figure, PQ ^ RQ, PQ ^ PT and ST ^ PR,
prove that ST, RQ = PS, PQ. |
| Q.10. |
In the given figure, R is a point
on AV such that AR=3 RB. Taking AR and RB as one of their sides, equilateral Ds PAR and QRB are drawn, show that
ar (DPAR) = 9 ar (DQRB). |
| Q.11. |
In the given figure, if O is the
centre of the circle, find the value of x. |
| Q.12. |
Radhika buys crockery having
marked price Rs. 4500. She gets a discount of 8%. If sales tax is 8%, find the
amount, she is required to pay for the crockery. |
| Q.13. |
The mean of 11 observations is 65.
If the mean of first 6 observations is 63 and that of last six observations is 66.
Find the sixth observation. |
| Q.14. |
Find the median of the data given
below. 95,82,91,65,35,59,92,76,55. If in the data, the observation 76 is replaced by 62,
find the new median. |
| Q.15. |
For what value of 'p' the mode of
following data is 5. 1,2,5,7,5,2,7,5,9,2,3,p,11
? |
|
SECTION- B |
| Q.16. |
USe a single graph paper and draw
the graph of the following equations : y=x,
y=-x, and 2x+3y = 6.
Shade the triangle formed by these lines. |
| Q.17. |
Scooter charges at a certain place
consist of fixed charges and the remaining depending upon the distance travelled in
kilometers. If a person travels 10 km, he pays Rs. 28 and for travelling 16 km, he
pays Rs. 43. Formulate simultaneous equations and hence find the fixed charges and
the rate per km. |
| Q.18. |
Using the properties of
proportion, solve for x :
(13+x)1/2
+ (13-x)1/2 / (13+x)1/2 - (13-x)1/2 = 5 |
| Q.19. |
A page from a pass book of saving
bank account is given below : |
|
Date |
Particular |
Amount withdrawnRs. P. |
Amount deposited Rs. P. |
Balance Rs. P. |
|
1998 |
|
|
|
|
|
April 2 |
By balance |
|
|
5,000.00 |
|
April 9 |
By Cash |
|
1,000.00 |
6,000.00 |
|
May 12 |
By cash |
|
2,000.00 |
8,000.00 |
|
May 24 |
By Cheque |
800.000 |
|
7,200.00 |
|
July 5 |
By Cash |
|
1,300.00 |
8,500.00 |
|
July 9 |
By Cash |
|
2,500.00 |
11,000.00 |
|
July 29 |
By Cheque |
5,000.00 |
|
6,000.00 |
|
The account is closed on 3rd of
september. Find the amount received if the rate of interest is 5 % per annum. |
| Q.20. |
Dr. Salim gets Rs. 2,40,000 as his
annual salary excluding HRA. He contributes Rs. 4000 p.m. towards Provident fund and
Rs. 16000 as premium towards LIC annually. Calculate the income tax that Dr. Salim
has to pay on his salary during the financial year. |
| Q.21. |
Find the angle of elevation of the
top of a tower of height 100 Ö3 from a point at a distance of 100 m from the foot of the
tower on a horizontal plane. |
| Q.22. |
In the given figure, AOBPA is a
quadrant of a circle of radius 14 cm. A semicircle with AB as diameter is drawn.
Find the area of the shaded region. |
| Q.23. |
ABCD is a parallelogram. The
circle passing through A,B,C and intersects CD when produced to E. Prove that AD = AE. |
| Q.24. |
Divide a line segment of length 6
cm externally in the ratio :
(i) 3 : 2 (ii)
2 : 3 |
| Q.25. |
Calculate the cost of living index
number for the year 1999 taking 1995 as the base year from the following data : |
|
Commodity |
Quantity in units |
Price per unit ( in Rs.) |
|
|
|
in 1995 |
in 1999 |
|
A |
20 |
12.00 |
14.00 |
|
B |
8 |
7.00 |
8.00 |
|
C |
12 |
15.00 |
18.00 |
|
D |
15 |
35.00 |
40.00 |
|
E |
4 |
16.00 |
29.50 |
| Q. 26. |
Solve for x : Ö(3)3+1 + 6 - Ö(3)x + 3 = 1 |
| Q.27. |
A milk tanker cylindrical in shape
having diameter 2 m length 4.2 m supplies milk to two booths in the ratio 3:2. One of the
milk booth has a rectangular base vessel having base area 3.96 sq. m and other has a
cylindrical vessel having diameter 2m. Find the level of milk in each of two
vessels. |
| Q.28. |
In a right angled triangle, the
square of the hypotenuse is equal to the sum of the squares of other two sides-prove it.
Using this result answer the following : A vertical pillar AB is bent at C at height 2.4 metres and its upper end B
touches the ground at a distance of 1.8 m from the end A on the ground. Find the
height of the pillar AB. |
| Q.29. |
The sum of either pair of opposite
angles of a cyclic quadrilateral is 1800. Prove it. Using this
result answer the following : "In the adjoining figure, ABCDE is a pentagon inscribed
in a semicircle. Find the numerical value of Ð ABC + ÐCDE. |
| Q.30. |
A boy is standing on the ground
and flying a kite with 100 m string making an angle of 300 with the ground.
another boy on the roof of a 10 m high building and is flying a kite making an
angle of elevation 430 with the horigontal. both the boys are on the same
sides of the kites. Find in metres, the length of the sring ( correct to 2 places of
decimals ) that the second boy must have so that the two kites meet. (Assume that the
strings are in the same plane). |
