CBSE Board Class 12 Math Sample Papers 2009

CLASS 12
SAMPLE PAPER

General Instructions

1)  All questions are compulsory.
2) The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 01 mark each, Section B comprises of five questions of 02 marks each, Section C comprises ten questions of 03 marks each and Section D comprises of five questions of 06 marks each.
3)  All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
4)  There is no overall choice. However, internal choice has been provided in one question of 02 marks each, three questions of 03 marks each and two questions of 06 marks each. You have to attempt only one of the alternatives in all such questions.
5)  In question on construction, drawing should be near and exactly as per the given measurements.
6) Use of calculators is not permitted.



Question 1: Find the [HCF X LCM] for the numbers 100 and 190.        

Question 2: If 1 is a zero of the polynomial p(x) = ax2 – 3(a – 1)x – 1, then find the value of a.    

Question 3: In ?LMN, ?L = 50? and ?N = 60?. If ? LMN ~ ?PQR, then find ?Q.        

Question 4: If sec2? (1 + sin ?)(1 – sin ?) = k, then find the value of k                   

Question 5: If the diameter of a semicircular protractor is 14  cm, then find its perimeter.    
             
Question 6: Find the number of solutions of the following pair of linear equations:

                   x + 2y – 8 = 0
                   2x + 4y = 16                                           
                       
Question 7: Find the discriminant of the quadratic equation 33x2+10x+3  =0        

Question 8: If  45 a, 2 are three consecutive terms of an A.P., then fine the value of a.   

Question 9: Two coins are tossed simultaneously. Find the probability of getting exactly one head.                

Question 10: Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6, if two of its zeroes are -2 and. 2    

Question 11: Which term of the A.P. 3, 15, 27, 39, … will be 120 more than its 21st term?        

Question 12: In the figure below, ?ABD is a right triangle, right-angled at A and AC ?? BD. Prove that   AB2 = BC . BD.                                   

Question 13: If cot? =158 then evaluate 2+2 sin?(1- sin?)1- cos ?(2-2 cos ?)     

Question 14: If the points A(4, 3) and B(x, 5) are on the Circle with the centre O(2, 3), find the value of x. 

Question 15: Solve the following equation for x.
  9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0

Question 16: If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then find the values of p and k.

Question 17: Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Using the above theorem, prove that:If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC 

(i) SF4
(ii) XeF4

Question 18: An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30? and 60? respectively. Find the distance between the two planes at that instant.

Question 19: A juice seller serves his customers using a glass as shown in figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical portion raised which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use ?? = 3.14)
 
Question 20 : During the medical checkup of 35 students of a class, their weights were recorded as follows:
                                    Weight (in kg)              Number of students
                                                38 – 40                                    3
                                                40 – 42                                    2
                                                42 – 44                                    4
                                                44 – 46                                    5
                                                46 – 48                                    14
                                                48 – 50                                    4
                                                50 – 52                                    3
Draw a less than type and a more than type o give from the given data. Hence obtain the median weight from the graph.