Code: DE01 / DC01                                                                        Subject: MATHEMATICS - I

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1       Choose the correct or best alternative in the following:                                         (2x10)

a. Which term of the series 37+32+27+22+.............. is –103?

(A)  24^th (B)  30^th

(C)   15^th (D)  29^th

b. How many terms are there in the expansion of

(A) 4                                                  (B)  6

(C)  16                                                (D)  10                                                                     

             c.   If  and , find the value of cot

(A) (B)

(C) (D)

             d.   Expansion of  is equal to    

(A) (B)

(C) (D)

             e.   For what value of k do the points  &  lie on a straight line.

(A) 3                                                  (B)  4

(C)  0                                                  (D)  1

             f.    Mid point of the line joining (3, 5) and  is given by

(A) (B)  (1, 2)

(C)  (2, 3)                                           (D)  (2, 1)

g.   is equal to

(A) (B)  2

(C)  (D)

             h.   If y = x sin x, then  is equal to

(A) cos x + sin x                                 (B) cos x + x sin x

(C) x cos x + sin x                               (D) x cos x – sin x

             i.    is equal to

(A)  tan x + c                                       (B)

                   (C) (D)

             j.    The solution of the differential equation  is

(A) (x + y) = k (1 – xy)                       (B) y – x = kxy

(C) (D)

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   How many terms are there in a finite AP whose first and fifth terms are respectively –14 & 2 and the sum of terms is 40.                                          (8)

             b.   The sum of three numbers in G.P. is  and their product is –1.  Find the numbers.                   (8)

Q.3     a.   If , prove that

(8)

             b.   In any triangle ABC, prove that                                                                          (8)

Q.4     a.   The acute angle between two lines is  and slope of one of them is .  Find the slope of the other line.                                                                (8)

b.   Find the vertex, axis, focus, latus rectum and directrix of the parabola .                                                                    (8)

Q.5     a.   Find the equation of the circle which passes through the points (1, 1) &    (2, 2) & whose radius is 1.                                                                     (8)

     b.   Find the equation of the straight line perpendicular to 7x + 9y – 3 = 0  and passing through (3, 8)                                                               (8)

  Q.6     a. Differentiate from the first principle the function y = sin 3x.                                   (8)

             b.   Evaluate .                                                                              (8)

Q.7     a.   Find the points of maxima or minima values of the function .              (8)

b.   Evaluate.                                                                  (8)

Q.8     a.   Evaluate (8)

             b.   Find the area enclosed by the ellipse .                                            (8)

Q.9     a.   Solve .                                                                          (8)

b. Solve .                                                                                 (8)