CBSE Board Class 12 Math Sample Papers 2008

CLASS 12
SAMPLE PAPER

General Instructions


i. All questions are compulsory.
ii. The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each. Section B comprises of 12 questions of four marks each and Section C. comprises of 7 questions of six marks each.
iii. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
iv. There is no overall choice. However, internal choice has been provided in 4 question of four marks each, and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
v. Use of calculators is not permitted.



Question 1 : Find the co-factor of a12 in the following:                     (MARKS 1)

                  2-3   56     0    4 1     5-7

Question 2: Evaluate: a+ib       c+id-c+id    a-ib                                 (MARKS 1)

Question 3: If f(x) =x+7 and g(x)=x -7, x?R, find (fog) (7)             (MARKS 1)

Question 4: Evaluate: sin p3-sin-1-12                                                  (MARKS 1)

Question 5: Find the value of x and y if:2  1  30  x+y   01   2=5   61    8        (MARKS 1)
                               
Question 6: Evaluate 01dx1+x2          (MARKS 1)

Question 7: For what value of ? are the vectors a 2i+? j+k and b=i-2j+3k perpendicular to each other?       (MARKS 1)

Question 8: Find the angle between the vectors a= i-j+k  and b= i+j-k               (MARKS 1)    

Question 9: Let A=325413067. Express A as sum of two matrices such that one is symmetric and the other is skew symmetric.                      (MARKS 4)

Question 10: If A =122212221, verify that A2-4A-5I=0                        (MARKS 4)

Question 11: For what value of k is the following function continuous at x=2?
                    F(x) = 2x+1;x<2k         ;x=23x-1;x>2                                         (MARKS 4)

Question 12: Find the equation of tangent to the curve x=sin 3t, y=cos 2t, at t=?/4.   (MARKS 4)                                                         

Question 13: Solve the following differential equation:
                     x2-y2 dx+2 xy dy=0
                    Give that y=1 when x=1                                                            (MARKS 4)

Question 14: Solve the following differential equation:

                    dy dy=x2y-xx2y+x, if y=1 when x=1                                       (MARKS 4)

Question 15: Solve the following differential equation:

                     cos2xdy dx+y=tan x                                                                          (MARKS 4)

Question 16: A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of successes.(MARKS 4)

Question 17: Find the point on the line x+23=y+12=z-32  at a distance from the point (1, 2, 3)         (MARKS 1)

Question 18: If a=i+j+k and b=j-k,  find a vector c such that axc=b and a.c=3                    (MARKS 4)

Question 19: If a+b+c=0 and a=3,b=5 and c=7, show that the angle between a and b is 60.          (MARKS 4)

Question 20: solve for x:                                                                (MARKS 4)

                    tan-1x-1x-2+tan-1x+1x+2=p4

Question 21: If y= cot-1 1+sinx + 1-sinx1+sinx-1-sinx, find dydx        (MARKS 4)

Question 22: Evaluate: 01cot-11-x+x2dx                                              (MARKS 4)

Question 23: Using properties of determinants, prove the following:   (MARKS 6)  

                   a+b+2ca   b  c  b+c+2ab  c  a  c+a+2b=2(a+b+c)3


Question 24: Using integration, find the area lying above x-axis and included between the circle  x2+y2=8x and the parabola                                                        y2=4x.                (MARKS 6)
 
Question 25: Using properties of definite integrals, evaluate the following:

                  0px tanx secx+tanxdx                                                (MARKS 6)

Question 26:  Show that the rectangle of maximum area that can be inscribed in a circle is a square. (MARKS 6)

Question 27:  Show that the height of the cylinder of maximum, volume that can be inscribed in a one of height h is 13h.                                    (MARKS 6)

Question 28: A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines area as follows:
Machine Area Occupied Labour force Daily output
(in units)
A
B 1000m2
1200m2 12 men
8 men 60
40

HE has maximum area of 9000m2 available, and 72 skilled labourers show can operate both the machines. How many machines of each type should be buy to maximise the daily output?                                               (MARKS 6)

Question 29: An insurance company insured 200 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.                                                                           (MARKS 6)

Question 30: Find the equation of the plane passing through the point (-1, -1,2) and perpendicular to each of the following planes:                        (MARKS 6)

2x+3y-3z=2 and 5x-4y+z=6

Question 31 : Find the equation of the plane passing through the points (3,4,1) and (0,1,0) and parallel to the line x+32=y-37=z-25                      (MARKS 6)