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Posted Date: 03 Aug 2009 Posted By: Naveen Kumar Khandelwal Member Level: Silver
|
2008 School Level Courses Maths CBSE Sample Paper Mathematics 2008 University Question paper
Time 3hours MM 100
General Instructions
1. All questions are compulsory.
2. The question paper consists of 25 questions divided into three sections A, B & C. Section
A contains questions of 2 marks each. Section B is of 12 questions of 3 marks each &
Section C is of 6 questions of 5 marks each.
3. There is no overall choice. However, an internal choice has been provided in two
questions of 3 mark each, two questions of 4 mark each & two questions of 6 mark
each.
4. Write the serial number of the question before attempting it.
5. In question on construction, the drawing should be neat & exactly as per the given
measurements.
6. Use of calculators is not permitted. However you may ask for mathematical tables.
Section A
1. Solve graphically.
x ? y = 10, 3x ? 4y = 0
2. Find the three terms in A.P. such that their sum is 3 and product is ?8.
3. A mobile is available for Rs.78, 000 cash or for 33 3
1 % cash down
payment and 11 equal monthly installments of Rs.4900 each. Calculate
the rate of interest charged.
4. A man borrowed a sum of money and returned it in 3 equal quarterly
instalments of Rs.43, 940 each. Find the sum borrowed, if the rate of
interest charged was 16% per annum compounded quarterly. Find also
the total interest charged.
5. A number is selected from 2 to 21 (both inclusive). Find the probability that
the selected number is (1) a prime number, (2) an odd number,
(3) a composite number
6. Prove (1 + cot? - cosec?) (1 + tan? + sec?) = 2
Or
cot A cosecA 1
sinA
cotA cosecA 1
? ?
?
? ?
7. The pie-chart represents the amount spent on
different sports by a school administration in a
calendar year. If the money spent on football
is Rs.18000, answer the following questions:
(a) What is the total amount spent on sports?
(b) What the amount spent on Tennis?
(c) How much more amount is spent on cricket
than Hockey?
8. In a right ?ABC, right angled at C, CD? AB where D is
7
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a point on AB. Prove that
2 2 CD2
1
BC
1
AC
1
? ?
9. A solid is in form of a cylinder with hemi spherical ends.
The total height of cylinder is 19 cm and diameter of cylinder
is 7cm. Find volume and surface area of the cylinder.
10. Water in a canal, 30 dm wide and 12 dm deep is flowing with a velocity of
10 km/h How much area will it irrigate in 2hours if 4 cm of standing
water is required.
Or
The internal and external radii of a hollow sphere are 3 cm and 5cm
respectively. The sphere is melted to form a solid cylinder of height
3
2
2 cm.
Find the diameter and curved surface area of cylinder.
Section B
11. Students of a class are made to stand in rows. If four students are extra in a
A row, there would be two rows less.If four students are less in a row, there
would be 4 more rows. Find number of students in the row.
Or
The sum of two digit number and the number obtained by reversing the order
of digits is 99.If the digits differ by 3, find the number.
12. If x ? 2 is a factor of x3 + ax2 + bx +18 and a ? b = 7. Find a and b
13. What rational expression should be added to ? ? 1
2
2
2
?
? ?
x x
x x to get
1
1
2 ?
?
x
x
14. A shopkeeper buys a number of books for Rs 80. If he had bought 4 more
books for the same amount each would have cost Re1 less. How many books
did he buy?
Or
A plane left 30min. later than the scheduled time and in order to reach its
destination 1500 k.m. away in time it has to increase its speed by 250 km /h
from its usual speed .Find its usual speed.
15. Two pipes running together fill a cistern in
11
8
2 minutes. If one pipe takes
1 minute more than the other to fill the cistern, find the time in which each
pipe would fill the cistern
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16. In the given figure TM is bisector of
?ATB Prove that PT = PM
17. Construct a triangle ABC in which AB=6cm,
?B=95?, AC=8cm. Now construct a triangle
similar to triangle ABC such that each of its
side is three fourth of the corresponding
side of triangle ABC.
18. A sphere has a radius of 420cm. 120 hemispheres of radius 2·1cm are cut
from its surface. Find percentage change in surface area.
19. Prove that quadrilateral formed by joining following points is a parallelogram
(2, 1), (8, 9), (-3, 11) and (-9, 3).
20. Find the co-ordinate of the point which divides the line-segment joining the
points (-7, 4) and (-6, -5) internally in the ratio 7:2.
Section C
21. If two circles touch each other (internally or externally), the point of contact
lies on the line through the centers-prove it.
Use it to prove the following:
?If two circles C (O, r) and C (O?, r) touch externally at a point A and PAQ is a
line segment intersecting the circles at P and Q respectively,
prove that ?OPA = ?O?QA?.
22. If two sides and a median bisecting the third side of a ? are respectively
proportional to the two sides and the corresponding median of another
triangle, then prove that the triangles are similar.
Or
In figure ÄABC, ? B = 90°, AD is its bisector.
If DE ? AC, prove that DE (AB + AC) = AB ? AC
23. An aeroplane left 30 minutes later than its scheduled time and in order to
reach its destination 1500Km away in time, it increased its speed by
250 km/h from its usual speed. Find its usual speed.
Or
From the top of a tower, the angles of depression of two objects on same side
of tower are found to be ? and ? ( ? > ? ). If the distance between the objects
is ?p? metres, show that the height ?h? of the tower is given by h =
? ? ?
? ?
tan tan
ptan tan
.
Also determine the height of tower if p = 50 metre, ? = 60° and ? = 30°.
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24. Find, the mean for the above data
25. A aged 68 years has annual income (excluding HRA) of Rs.4, 80,000. She
contributes Rs.1500 per month in her provident fund and pays Rs.8,500 as
premium for an insurance policy twice a year. She buys NSC worth Rs.5,000.
She buys infrastructure bonds worth Rs.50, 000. Find tax payable at end of
year if her employer deducted Rs.2000 as income tax per month for first 11
months at source.
TAX RATES FOR SENIOR CITIZEN ASSESSEE
Taxable Income Rate of Tax Surcharge Educational cess
Up to Rs.1,85,000 Nil Nil Nil
Rs.1,85,001 to
Rs. 2,50,000
20% of total Income exceeding
Rs.1,85,000
Nil 2 % of income tax
Rs.2,50,001 to
Rs.10,00,000
Rs.13,000 + 30% of total
income exceedingRs.2,50,000
Nil 2% of income tax
Above Rs.10,00,000 Rs.2,38,000 + 30% of total
income exceedingRs.10,00,000
10% of
income
tax
2% of income tax
and surcharge
Maximum Savings allowed : Rs.1,00,000
For answers log on to our site www.cbsemath.com open contact us page and fill up the form
there.
or
you may download from cbsemath.com after few days
Marks 0-9 10-19 20-29 30-39 40-49 50-59 60-69
Frequency (f) 323 135 217 156 534 400 234
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