HPBOSE 2015 mathematics series C

Special instructions:-

                    विशेष निर्देश:

1:  You must write question paper series in the circle at top left side of title page of your answer sheet.

2: While answering your questions you must indicate on your answer book the same question number as appears in your question paper.

3: Don't leave blank pages/pages in your answer book.

4: All questions are compulsory.

5: Internal choices are given in some questions.

6: Question no 1-10 are MCQ carrying 1 Mark each. Question no 11-14 are short answer type carrying 2 Mark each. Question no 15-26 are short answer type questions carrying 3.5 marks each and question no 27-31 are long answer type carrying 5 marks each.

7: Use of calculator is not                                       permitted,however you ask for log table.   If required from superintendent of        examination.

8: Try to answer the questions in serial order as far as possible.

9: attach the graph properly.

Q11: find the value of x,y and z such that

[x+y     2 ]    =[6   2]

[5+z    xy]    =[5   8]

OR

Using elementary transformation,find the inverse of  [2    -6]

                    [1    -2]

Q12: find the value of k so that function f is continuous at the indicated point:

         f(x) = kx+1 , if x<=π

                    Cos x, if x>π

Q13: find the rate change of area of a circle with respect to its radius r. When r=3cm

Q14: form a differential equation representing the family of parabola is having vertex at origin and axis along positive direction of y-axis

Q15: find gof and fog if f(x) is equal to  |x| and g(x) = |5x-2|

Q16: prove that 

                           tan-¹ 1/2 + tan-¹ 2/11 =tan-¹3/4

                                           OR

                               tan-¹ x/√a²-x² , |x| <a

Q17:  using properties of determinant prove that:

|1    x     x² |

|x²    1     x |     =   (1-x³)²

|x    x²    1  |

18: find dy/dx, when Y + sinY = cos x

                            OR

Differtiate the function

(Log x) power cos x

Q19: integrate  5x/(x+1)(x²+9)dx

Q20: integrate 5x⁴√x5+1 dx within limits -1 to 1

Q21 integrate cosx/(1-sinx)(2-sinx)dx

Q22 solve the differential equation
                     ydx + (x- y²)dy= 0
                         OR
          (x-y)dy - (x+y)dx = 0

Q23: find a unit vector perpendicular to each of the vectors a+b and a-b, where a= 3i+2j+2k and b= î+2j-2k

Q24: find the angle between the pair of lines x-2/2= y-1/5 = z+3/-3  and  x+2/-1 = y-4/8 = z-5/4

Q25: find the mean number of heads in 3 tosses of a fair coin.

Q26: two balls are drawn at random with replacement from a box containing 10 black and 8 red balls find the probability that (1)both balls are red (2) first ball is black and second is red (3)one of them is black and other is red

                  OR

Let A and B be Independent event with P(A) = 0.3 and P(B) = 0.4. find (1) probability of A intersection B (2) probability a/ b

Q27: solve the system of equations using Matrix method

3 X - 2 Y + 3Z= 8 

2 X + Y - Z = 1

 4 x - 3 Y + 2Z =4

Q28: of all closed cylindrical cans (right circular) which and close a given volume of 100cc. find the dimensions of the can which has the minimum surface area.

                 OR

Find the maximum profit which a company can make if the profit function is given by     P(x) = 41 - 24 x -18 x²

Q29: find the area of the region bounded by the two parabola y = x² and x = y²

                               OR
Find the area of the circle 4 x + 4 Y = 9 which is interior to a parabola y = 4 x

Q30: find the angle between the line x+1/2 = y/3 = z-3/6and the plane 

10 X + 2 Y - 11z=3

Q31: maximize Z equal 5 x + 3 y subject to constraints 3 X + 5 y ≤ 15 , 5 x + 2 y ≤ 10 , x≥0 y ≥0