# CBSE Board Class 12 Math Sample Papers 2007

## CBSE Board Sample Papers 2007 for Class 12 Math

General Instructions

(i) All questions are compulsory.

(ii) The question paper consists of 25 questions divided into three sections —A, B and C. Section A contains 7 questions of 2 marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each.

(iii) There is no overall choice. However, an internal choice has been provided in tow questions of tow marks each, two questions of three marks each and two questions of five marks each.

(iv) In question on construction, drawing should be near and exactly as per the given measurements.

(v) Use of calculators is not permitted. However, you may ask for mathematical tablets.

Question 1: Find the GCD of the following polynomials:    Marks 2

12x4+324;  36x3+90x2-54x

Question 2: Solve for x and y:  Marks 2

2xa+yb=2,  xy-yb=4

Question 3: Solve for x and y: Marks 2

31x+29y=33,   29x+31y=27

Question 4: Find the sum of all three digit whole numbers which are multiples of 7. Marks 2

Question 5: In Figure 1, PQ | | AB and PR | | AC. Prove that QR | | BC.Marks 2

Question 6: In Figure 2, incircle of A ABC touches its sides AB, BC  and CA respectively. If AB = AC, prove that BE = EC.          Marks 2

Question 7: If the mean of the following frequency distribution is 49, find the missing frequency p:  Marks 2

Class Frequency
0-20 2
20-40 6
40-60 P
60-80 5
80-100 2

Question 8: A wrist-watch is available for Rs.1,000 cash or Rs.500 as cash down payment followed by three equal monthly instalments of Rs. 180. Calculate the rate of interest charged under the instalment plan. Marks 2

Question 9: An unbiased die is tossed once. Find the probability of getting

(i) a multiple of 2 or 3.

(ii) a prime number greater than 2.  Marks 2

Question 10: Solve the following system of equations graphically:  Marks 3
2x+y=8;     x+1=2y

Question 11: Simplify the following rational expression in the lowest terms:

ax2-x3a3+x3×a2-ax+x2a2x2+x4÷a2-2ax+x2a4- x4                  Marks 3

Question 12: If the sum to first n terms of an A.P. is given by Sn = n (n + 1), find the 20th term of the A.P.  Marks 3

Question 13: In a cyclic quadrilateral ABCD, diagonal AC bisects ? C. Prove that the tangent to the circle at A is parallel to the diagonal BD.  Marks 3

Question 14: In Figure 3, O is any point in the interior of ? ABC. OD, OE and OF are drawn perpendiculars to the sides BC, CA and AB respectively. Prove that
AF2 + BD2 + CE2 = OA2 + OB2 + OC2 — OD2 — OE2 — OF2          Marks 3

Question 15:Construct a ? ABC in which base BC = 6 cm, ?B = 450 ? C = 600. Draw a cricumcircle of ? ABC.  Marks 3

Question 16:The diameter of a solid copper sphere is 18 cm. It is melted and drawn into a wire of uniform cross-section. If the length of the wire is 108 m, find its diameter.  Marks 3

Question 17: The expenditure (in rupees) of a family for a month is as follows:

Item Rent Food Education Electricity and Water Others
Expenditure 800 3000 1200 400 1800

Represent the above data by a pie-chart.  Marks 3

Question 18: From a pack of 52 cards, red face cards are removed. After that a card is drawn at random from the pack. Find the probability that the card drawn is

(i) a queen.
(ii) a red card.
(iii) a spade card.     Marks 3

Question 19 : Prove that: Marks 3

1+1tan2? 1+1cot2?=1sin2?-sin4?

Question 20: if A, B and C are interior angles of a triangle ABC, show that

cosB+C2=sinA2            Marks 3

Question 21: The coordinates of the mid-points of the sides of a triangle are (4, 3), (6, 0) and (7,?2). Find the coordinates of the centroid of the triangle.                                          Marks 3

Question 22: If the distance of p(x,y) from two points with coordinates (5, 1) and (-1, 5) is equal, prove thet 3x=2y.  Marks 3

Question 23: A lone of Rs. 24,600 is to be paid back in two equal semi-annual instalments. If the interest is charged at 10% per annum, compounded semi-annually, find the instalment.  Marks 3

Question 24: Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Using the above, prove the following:            Marks 5

Question 25: State and prove Pythagoras theorem. Marks 5

Use the above to prove to the following:
ABC is an isosceles right triangle, right angled at C. Prove that  AB2=2AC2

Question 26: The side of a square exceeds the side of another square by 4 cm and the sum of areas of two squares is 400 sq. cm. Find the dimension of the squares.  Marks 5

Question 27:  A fast train takes 3 hours less than a slow train for a journey of 600Km. If the speed of the slow train is 10 Km/hour less than that of the fast train, find the speeds of the two trains.  Marks 5

Question 28:  A hollow copper sphere of external and internal diameter 8 cm and 4cm respectively is melted into a solid cone of base diameter 8cm.Find the height of the cone.  Marks 5

Question 29: If the radii of the circular ends of a bucket 45 cm high, are 28 cm and 7 cm, find the capacity and surface area of the bucket.Use p=227                                          Marks 5

Question 30: An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line with the base of the lighthouse. The angles of depression of the ships approaching it are 30o and 60o. If the height of the lighthouse is 150m, find the distance between the ships.               Marks 5

Question 31: Satish (aged 67 years) has monthly income of Rs.30,000 (excluding HRA).He donates Rs. 80,000 to a charitable orphanage (50% exemption). He contributes Rs.30,000 towards Public Provident Fund and purchases NSCs worth Rs.20,000. He pays Rs. 1,500 as income tax per month for 11 months. Calculate the income tax to be paid by him in the 12th month of the year.  Marks 5

Use the followimg to calculate income tax:

(a)  Saving  100% exemption for permissible savings  upto Rs.1,00,000
(b) Rates of income tax for Senior Citizens (over 65 years)

(i) Upto Rs. 1,85,000   No tax
(ii) From Rs. 1,85,001 to Rs. 2,50,000 20% of the taxable income exceeding Rs. 1,85,000
(iii) From Rs. 2,50,001 and above   Rs.13,000+ 30% of the taxamble exceeding Rs. 2,50,000

(c)  Education Cess 2% of Income tax payable

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