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Mathematics (Class XI)
Sample Paper
Class: XIM.M. 100Subject: MathematicsTime: 3 hrs.
 
GENERAL INSTRUCTIONS
  1. Q. No. 1-12 in section A are of 3 marks each.
  2. Q. No. 13-22 in section B are of 4 marks each.
  3. Q. No. 23-26 in section C are of 6 marks each.
  4. Use of calculators is not permitted.

  1. Prove that tan13A = tan9A + tan4A + tan13A.tan9A.tan4A
  2. Using principle of mathematical induction, prove that 4n2 + 15n – 1 is divisble by 9, " n Є N. 
  3. Evaluate the limit:   lim     sin(2 + x) – sin(2 – x)                                     x→0                 x

     

  1. Differentiate sin(x + 1) w.r.t. x using first principle.
  2. Out of 30 students 10 are to be taken for an excursion. 3 of these students decide either all of them will go or none will go. In how many ways students can be selected for the excursion.
  3.  Find the value of k, for which the roots of the  equation             2kx – 5k = (k – 3)x2 are real and distinct.
  4.  If all the letters of the word ‘AGAIN’ are arranged as per dictionary order, find the 50th word.
  5.  Find the co-ordinates of vertices and foci, lengths of major and minor axis, eccentricity for the ellipse 16x2 + 9y2 = 144.
  6.  Differentiate     (xsinx + cosx)(xcosx – sinx) w.r.t. x.
  7. A pair of dice is thrown. Find the probability of getting sum of either 10 or at most 10.

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