OB-1103-175

Printed of pages: 3

Roll No.

Second Unit Test, 2014-2015 Maths

Class-XI

Time: 11/2 hrs.]

[M. M.: 40

Note:-All questions are compulsory.

Section (A)

(1 marks each)

Prove for n=1

<math>1 + \frac{3}{1}</math> 1八 4八 9) <math>\left(1+\frac{5}{4}\right)\left(1+\frac{7}{9}\right)</math>

<math>\left(1 + \frac{(2n+1)}{n^2}\right) = (n+1)^2</math>

Express in a+ib form

<math>i^{35} + \frac{1}{.35}</math>

,3 Solve <math>5x-3 < 3x+1</math>, when x is an integer.

Find total no. of ways of answering 6 multiple choices questions having 4 choices.

(P.T.O.)

OB-1103-175-XI-Math

(2)

Section (B)

(4 marks each)

5 Prove that <math>5^n - 5</math> is divisible by 4 for all <math>n \in N</math>. Hence prove that <math>2.7^n + 3.5^n - 5</math> is divisible by 24 for all <math>n \in \mathbb{N}</math>. Chapter Ex. 6 6 Prove by mathematical Induction : <math>(n \in N)</math>

<math display="block">\frac{1}{1.2.3} + \frac{1}{2.3.4} + \frac{1}{3.4.5} + \dots + \frac{1}{n(n+1)(n+2)}</math>

<math display="block">= \frac{n(n+3)}{4(n+1)(n+2)}</math>

Solve the following system of inequalities graphically:

<math>3y-2x \le 4</math>, <math>x+3y > 3</math>, <math>x+y \ge 5</math>, <math>y < 4</math>

8 Example-15" Page-111

Find real values of <math>\Theta</math> such that <math>3 + 2i\sin\theta</math> <math>1 - 2i\sin\theta</math>

is a real number.

A solution of 8% boric acid is to be delluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of 8% solution,

how many litres of 2% solution will have to be added?

Find n if

<math>2^{n+1}P_{n-1}:^{2^{n-1}}P_n=3:5</math>