CBSE Class 11 Mathematics Previous Year Question Paper 2004-05

II Terminal examination 2004 - 05

Sub: Mathematics

1. Marks:100

Class : XI

General instructions:

Time: 3Hrs.

All questions are divided into three Parts. Attempt Part A and either of Part B

Or Part C.

1. What is a power set? Write the power set of <math>A = \{2, 3, 1\}</math>. 3
2. <math>(2+3i)^2</math> 3 Simplify <math>1+i</math> (or) How many terms of 20, 18, 16,.... are needed to give sum zero?
3. For what value of x the points <math>(2, 3)</math>, <math>(x,6)</math> and <math>(3,2)</math> lie on a straight line? 3
4. In what ratio is the segment joining the points <math>(2,3)</math> and <math>(4,1)</math> divides the 3 segment joining the points <math>(1,2)</math> and <math>(4,3)</math>.
5. Prove that 3
6. Prove that <math>tan8A - tan7A - tanA = tan8A tan7A tanA</math> 3
7. Find the term independent of x in <math>\left(3x^2 - \frac{1}{3x}\right)^9</math>. 3
8. If the binomial expansion of <math>(m - nx)^{-3}</math> is <math>1 + 9x + ...</math> find the values of m 3 and n.
9. Using principle of mathematical induction prove that 4 <math>4^n + 15 n - 1</math> is divisible by 9 for all <math>n \in N</math>.
10. Evaluate <math>x^4 + 4x^3 + 6x^2 + 4x + 9</math> if <math>x = -1 + \sqrt{-2}</math>. 4

(or)

If a, b, c are in A.P. and x, y z are in G.P. show that <math>x^{b-c}</math>. <math>y^{c-a}</math>. <math>z^{a-b}=1</math>.

1. Find the value of k for which the equation <math>2x^2 + 3x + -2 = 0</math> and 4 <math>3x^2 + 4k + 2 = 0</math> may have a common root.

(or)

Solve graphically: <math>X \ge -4</math>, <math>y \le -4</math>, <math>x + 2y \ge 2</math> and <math>x - y \ge 6</math>

1. Find the vertex, axis, focus and latus rectum of the parabola 4 <math display="block">y^2 + 2x - 4y + 7 = 0.</math>

1. Find the equation of the circle through the intersection of the circles <math>x^2 + y^2 - 8x - 2y + 7 = 0</math> and <math>x^2 + y^2 - 4x + 10y + 8 = 0</math> and passing through 4 the point (-1, -2).
2. Find the coordinates of the orthocenter of the triangle whose vertices are the 4 points (2,6), (1, 1) and (3,2).
3. Using truth table prove that <math>\sim (p \cup q) \cup (\sim p \cap q) = (\sim p)</math> 4
4. Solve and find the general solution for <math>2 \sin^2 x + \sqrt{3} \cos x + 1 = 0</math>. 4
5. Prove that <math>2 \tan^{-1} \frac{1}{3} + \tan^{-1} \frac{1}{7} = \frac{\Pi}{4}</math>. 4
6. The coefficient of three consecutive terms in <math>(1 + x)^n</math> are 1: 7: 42 find the 4 value of n and r.
7. Find standard deviation and variance for the given data: 4 X:5 10 15 20 25 F:7 4 6 3
8. The line <math>4x - 3y = -12</math> is a tangent at the point <math>(-3, 0)</math> and the line <math>3x + 4y =</math> 6 16 is the tangent at the point (4,1) to a circle. Find the equation of the circle.
9. a) Prove that <math>{}^{n}C_{r} + {}^{n}C_{r-1} = {}^{n+1}C_{r}</math> 3
10. An equilateral triangle is inscribed in the parabola <math>y^2 = 4ax</math> with one 3 vertex of the parabola. Find the length of the sides of the triangle.
11. a) Find the coefficient of x 6 in the e 2x. 3

Prove that <math>\frac{1}{2} - \frac{1}{2} \cdot \frac{1}{2^2} + \frac{1}{3} \cdot \frac{1}{2^3} - \frac{1}{4} \cdot \frac{1}{2^4} + \dots = \log \frac{3}{2}</math> (or)

1. prove that <math>1 + \frac{3}{1!} + \frac{5}{2!} + \frac{7}{3!} + \cdots + io \infty = 3e</math> 3

(or)

Prove that <math>\frac{1}{3.4} + \frac{1}{5.6} + \frac{1}{7.8} = \log 2 - \frac{1}{2}</math>

PART [B]

1. Determine the points on Z axis which is equidistant from the points 3 (1, 5, 7) and (5, 1, -4).
2. <math>\rightarrow</math> <math>\rightarrow</math> <math>\rightarrow</math> <math>\rightarrow</math> <math>\rightarrow</math> 4 The side if a parallelogram are <math>2i + 4j - 5k</math> and <math>i + 2j + 3k</math>. Find the unit vector parallel to the diagonal.