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[QUOTE=mariammal;186239][B]Document Described :[/B] Maths Question Paper, Jharkhand Question Paper

[B]MATHEMATICS
Full Marks - 100
Pass Marks-  33
Time - 3 Hours[/B]
Candidates are required to write the Section Code and the Question No. with every answer.
All questions are compulsory.

[URL]http://jac.nic.in/model_questions.htm[/URL]
[URL]http://jac.nic.in/pdf/model_questions/Science_Mathematics12_08.pdf[/URL]

[B]General Instructions  [/B]:
The question paper consists of 26 questions divided into three Sections ? A, B and C.
Section-A is compulsory for al students.
In addition to Section?A, every student has to attempt either Section?B or Section-C.
Use of calculator is not permitted. However, you may ask for logarithmic and statistical tables, if required.
For Section-A:
Question Nos. 1 to 8 are of 3 marks each.
Question Nos. 9 to 15 are of 4 marks each.
Question Nos. 16 to 18 are of 6 marks each.
For Section-B/Section-C:
Question Nos. 19 to 22 are of 3 marks each.
Question Nos. 23 to 25 are of 4 marks each.
Question Nos. 26 is of 6 marks.

[B] Section - A :[/B]
2. Using properties of determinant, prove that  :
a b b c c a
b c c a a b
c a a b b c
0.
3. If  (`{X)  P(A)  =  0.6,  P(B)  =  0.3  and  (VWm) P(A   B) = 0.1, find    P A B a f.
4. A and B appear for an interview. Probability of A?s success is  3 4  and that of B?s success is  1
5 . What is the probability that only one of them is selected ?
9. In a Boolean Algebra B, prove that :
11. Differentiate  x w.r.t. x by the first principle.
13. The radius of a spherical bubble is increasing at  the  rate  of  1
4   cm/sec.  Find  the  rate  at
which  its  volume  is  increasing  when  the radius is 2 cm.
16. Solve  the  following  system  of  equationsby matrix method:
17. Sum of two positive numbers is 24. Find the numbers so that their product is maximum.
18. Find the area of the region between the curve y2 = x and the line x + y = 2.

[B]Section  [/B]: B
20. Show that:
21. A  stone  is  dropped  into  a  well  and  it  hits the  water  after  5  seconds.  Find  the  depth of  the  well  and  the  velocity  of  the  impact. [g = 9.8 m/s2]
22. A bal has a range R on a horizontal plane. If H, H  are the greatest heights and t,  t  the times of flights in the two possible paths, then show that R =  4 1
25. Find the centre and radius of the sphere:
2x2+ 2y2+ 2z2+4x ? 6y +8z ? 12 = 0
19. If A and B are independent events such that P(A) = 1
20. Find  the  binomial  distribution  for  which  the mean is 4 and variance 2.
21. Find the banker?s gain on a bil of Rs. 30,000 due 4 months hence at 5% per annum.
22. The true discount on a bil of Rs. 1,680 due 10 months hence is Rs. 80. Find the rate, the banker?s discount and the banker?s gain.
24. The  demand  function  of  a  new  product  is
given by p = 30 ?  x
5 , where x is the number of units produced and p is the price per unit. Find the maximum revenue.
25. Calculate  the  future  amount  of  an  ordinary annuity of Rs. 3,000 per annum for 10 years at  10%  per  annum,  compounded  annually.
[Use 1.110  = 2.594][/QUOTE]

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