CLASS 11 TH SECOND UNIT TEST QUESTION PAPER 2014-15 CBSE

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CLASS 11 TH SECOND UNIT TEST, 2014-15

Maths

Time: 1½ hrs Class X l M.M: 40

Note: All questions are compulsory.

Section(A) (1 marks each)

1 Prove for n =1

${\color{DarkGreen} \mathbf{\left [ 1 + \frac{3}{1} \right ]\left [ 1 +\frac{5}{4} \right ]\left [ 1 +\frac{7}{9} \right ]......+\left [ 1 +\frac{\left ( 2n +1 \right )}{n^{2}} \right ]}}\mathbf{{\color{DarkGreen} = (n +1)^{2}}}$

2 Express in a +ib form

${\color{DarkGreen} \mathbf{i^{35}+ \frac{1}{i^{35}}}}$

3 Solve 5x –3 < 3x + 1, when x is an integer.

4 Find the total number of ways answering 6 multiple choices questions having four choices

Section (B ) (4 marks each)

5 Prove that ${\color{DarkGreen} \mathbf{5^{n}-5}}$ is divisible by 4 for all n ∈ N. Hence prove that ${\color{DarkGreen} \mathbf{2.7^{n }+ 3.5^{n} - 5}}$ is divisible by 24 for all n ∈ N.

6 Prove by mathematical induction: (n∈ N)

${\color{DarkGreen} \mathbf{\frac{1}{1.2.3}+ \frac{1}{2.3.4}+ \frac{1}{3.4.5}+..........+\frac{1}{n\left ( n+1 \right )\left ( n+2 \right )}= \frac{n\left ( n+3 \right )}{4\left ( n+1 \right )\left ( n+2 \right )}}}$

7 Solve the following system of inequalities graphically :

3y – 2x ≤ 4 , x + 3y > 3, x + y ≥ 5, y < 4

8 Find real value of θ such that

${\color{DarkGreen} \mathbf{\frac{3 +2isin\Theta }{1-2isin\Theta }}}$

is a real number

9 A solution of 8 % boric acid is to be diluted by adding a 2 % of boric acid solution to it . The resulting mixture is to be more than 4 % but less than 6 % boric acid. If we have 640 liters of 8% solution, how many liters of 2 % solution will have to be added?

10 Find n if

${\co\mathbf{_{}^{}\textrm{2n+1}{P_{n-1}}^{}+ \; _{}^{}\textrm{2n-1}{ P_{n}}^{}= 3:5}}$

Section (C ) (6 marks each)

11 Out of 6 boys and 4 girls, a committee of 5 is to be formed, in how many ways can this be done if :

(1) At least 2 girls are included.

(2) At most 2 girls are included.

12 (i) Find the number of words which can be made using all letters of the word AGAIN. If these words are written as in the dictionary. What will be the 50 th word?

(ii) How many four-digit numbers can be formed from digits 1,1,2,2,3,3,4,4,5,5 ?

NCERT Solutions for Class 11 Maths Chapter 5 Complex number-ll