|
SAMPLE
PAPER
MATHEMATICS
SET - III
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 |
Determine the paid of
linear equation from the three given equations which has infinite number of solutions 2x+3y=5; y+2/3x=5;4x+6y=10 |
| Q.2. |
Draw the graph of the
linear equation 3x-y = 6 and check by plotting the point x=2, y=1 whether it lies on the
line. |
| Q.3. |
For p(x) = (x-1)2
and q(x) =(x+1) (x-1), verify that the product of p(x) and q(x) is equal to the product of
g.c.d. and l.c.m. |
| Q.4. |
If a, b are the roots
of the equation 4x2 - 1 = 0, find the value of a2+b2. |
| Q.5. |
Vinod bought a
refrigerator for Rs. 10.355 which includes 9% sales tax. Find the marked price of
refrigerator. |
| Q.6. |
In the given figure,
find the area of shaded region. |
| Q.7. |
The minute hand of a
clock is 3.5 cm long. What distance does it tip move in 20 minutes ? |
| Q.8. |
Prove that 1/1+cos(900-q) - 1/1-cos(900-q) = -2tan q coses
(900-q) |
| Q.9. |
Prove that tan2q
/(secq-1)2 = 1+cos q / 1-cos q |
| Q.10. |
Two poles of heights
6m and 11 m stand vertically on the ground. If the distance between their feet is
12m. Find the distance between their tops. |
| Q.11. |
DABC is similiar to DPQR,
or (DABC) = 36 sq cm and ar (DPQR) = 49sq. cm. IF BC = 12 cm find QR. |
| Q.12. |
In the given figure,
find the value of P. |
| Q.13. |
In the given figure,
if AB=AC, AC=CD and Ð ADC = 330, find the
value of x. |
| Q.14. |
The size of ten shirts
in cm are given below 90, 95,90,105,100,95,90,95,100,90 find the modal size. If the
size of one shirt is misread as 90 instead of 95, find the correct modal size. |
|
SECTION-B |
| Q.15. |
The distance between
Mumbai and Pune is 192 km. Travelling by Deccan Queen, it takes 48 minutes less than
another train. Calculate the speed of the Deccan Queen if the speed of two trains differ
by 20km.hr. |
| Q.16. |
If x2-3x+2
is a factor of x4-ax2+b, find a and b. |
| Q.17. |
Solve for x : = [
2x-7/2x-1]1/2 + [2x+1 / 2x-7]1/2 =3 1/3 |
Q.18. |
The maximum number of
straight lines y, which can connect x points is given by y=1/2x9z-1). Calculate the
number of points, if maximum number of lines connecting them are 28. |
| Q.19. |
The rate of interest
decreases from 5 1/2 % to 4 % with effect from 1.6.99. Compute the interest at the
end of year on a S.B. account for the entries shown in the table if the interest is
payable yearly. |
|
Year |
Date |
Balance in Rs. |
|
1996 |
Jan. 1 |
600 |
|
|
Feb. 9 |
1200 |
|
|
Mar. 11 |
2500 |
|
|
June 25 |
3500 |
|
|
Sept. 10 |
1500 |
|
|
Nov. 5 |
4000 |
|
|
Dec. 23 |
500 |
| Q.20. |
Ashish has total
annual salary income of Rs. 2,50,000 exclusive of H.R.A. He donates Rs. 20,000 to Prime
Minister Relief Fund which has 100 % tax exemption. His total contribution to P.F.
and L.I.C. premium for the financial year is Rs. 64,000, find the income tax liability of
Ashish for the financial year. |
| (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
amount 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.21. |
Prove : tan q / 1 - cot q + cot q / 1-tan q = sec q
coses q + 1 |
| Q. 22. |
Find the mean of the
following data : |
|
Class - interval |
Frequency |
|
150-200 |
14 |
|
200-250 |
26 |
|
250-300 |
17 |
|
300-350 |
23 |
|
350-400 |
20 |
| Q.23. |
If a line is drawn
parallel to one side of a triangle, then the other two sides are divided in the same
ratio. Prove it. |
| Q.24. |
Compute the cost of
living index number for the year 1999 taking 1996 as base year, for the following data : |
|
Commodity |
Quantity |
Price in Rs. per kg. |
|
|
|
1996 |
1999 |
|
A |
7 |
6 |
7 |
|
B |
15 |
12 |
13 |
|
C |
8 |
8 |
14 |
|
D |
18 |
9 |
8 |
|
E |
12 |
23 |
25 |
| Q.25. |
Find the numbers such
that their mean proportion is 8 and their third proportion is 64. |
| Q.26. |
A spherical ball of
copper was melted and made into smaller balls of half the radius of the original.
How many such balls were made ? Also, find the ratio of total surface area of all
the smaller balls to that of the original one. |
| Q.27. |
From the top of a
building 96 m high, the angle of depression of two vehicles on a road at the same level
and in the same line with the foot of the building and on the same side of it are x0
and y0, where tan x0 = 3/4 and tan y0 = 1/2. |
| Q.28. |
The degree measure of
an arc of a circle is twice the angle subtended by it at any point of alternate
segment of a circle with respect to the arch - Prove. Using the above theorem find
the value of x in the given figure, if O is the centre of the circle. |
| Q. 29. |
Construct a DABC in which BC =6 cm, Ð A = 600 and median AD = 5 cm, Also, construct another DBPQ similar to DBCA such that the side BP = 3/2 BC, Also write the steps of construct. |
