OB-1103-100

Please check total printed pages before start:- 2 Roll No. :

THIRD TERM UNIT TEST - 2014-15

SUBJECT - MATHEMATICS

CLASS - XI

Time : 11/2 Hrs.

M.M. 40

SECTION A (1 MARK)

Find distance between points (-1,3,-4) & (1,-3,4)

2. Evaluate : <math>\lim_{x\to 0} \frac{\sin ax}{bx}</math>

3/ A coin is tossed & a die is thrown. Write Sample space

Evaluate : <math>\lim_{x \to -1} \frac{x^{10} + x^5 + 1}{x - 1}</math>

SECTION B (4 MARKS EACH)

1. Find the equation of set of points P, the sum of whose distances from A (4,0,0) & B (-4,0,0) is equal to 10.
2. Find 'Co-ordinates of a point on y-axis which are at a distance of <math>5\sqrt{2}</math> from the point P (3,-2,5)

Two dice are thrown & events A,B & C are as follow:

getting an even no. on the first die

В getting an odd no. on the second die C : [P.T.O.]

2

OB-1103-100

Describe the events

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1. A but not C
2. B or C
3. <math>A \cap B' \cap C'</math>
4. Verify that (-1,2,1) (1,-2,5), (4,-7,8) & (2,-3,4) are the vertices of a parallelogram.

9., A letter is chosen at random from the word ASSASSINATION. Find the probability that letter is :

1. a vowel (ii) a consonant

10 Evaluate: <math>\lim_{x\to 0} \frac{\sin ax + bx}{ax + \sin bx} a, b, a+b \neq 0</math>

SECTION C (6 MARKS EACH)

Find the probability that when hand of 7 cards is drawn from a well shuffled deck of 52 cards it contains :

1. all kings
2. 3 kings
3. at least 3 kings

If <math>f(x) = \begin{cases} mx^2 + n & x < 0 \\ nx + m & 0 \le x \le 1 \\ nx^3 + m & x > 1 \end{cases}</math>

For what integers m & n does both <math>\lim_{x\to 0} f(x)</math> & <math>\lim_{x\to 1} f(x)</math> exist?