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# Class 11 Maths Second Unit Test Question Paper 2014-15 CBSE

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### NCERT solutions of class 11 maths

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

## Class 11 Second Unit Test Question Paper 2014-15 CBSE

### Class 11  Second Unit Test  2014-15

Maths

Time: 1½ hrs                                                      Class X l                                             M.M: 40

Note: All questions are compulsory.

### Section A

Q1.   Prove for n =1

$\dpi{100} {\color{DarkGreen} \mathbf{\left [ 1 + \frac{3}{1} \right ]\left [ 1 +\frac{5}{4} \right ]\left [ 1 +\frac{7}{9} \right ]......+\left [ 1 +\frac{\left ( 2n +1 \right )}{n^{2}} \right ]}}\mathbf{{\color{DarkGreen} = (n +1)^{2}}}$

Q2  Express in a +ib form

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

Q3.  Solve 5x –3 < 3x + 1, when x is an integer.

Q4.  Find the total number of ways answering 6 multiple choices questions having four choices

### Section (B )  [4 marks each]

Q5.  Prove that        ${\color{DarkGreen} \mathbf{5^{n}-5}}$ is divisible by 4 for all n ∈ N. Hence prove that $\dpi{100} {\color{DarkGreen} \mathbf{2.7^{n }+ 3.5^{n} - 5}}$  is divisible by 24 for all n ∈ N.

Q6.  Prove by mathematical induction: (n∈ N)

$\dpi{100} {\color{DarkGreen} \mathbf{\frac{1}{1.2.3}+ \frac{1}{2.3.4}+ \frac{1}{3.4.5}+..........+\frac{1}{n\left ( n+1 \right )\left ( n+2 \right )}= \frac{n\left ( n+3 \right )}{4\left ( n+1 \right )\left ( n+2 \right )}}}$

Q7.  Solve the following system of inequalities graphically :

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

Q8.  Find real value of θ such that

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

is a real number

Q9.  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?

Q10.  Find n if

25Cn+5 = 25C2n -1

### Section (C ) [ 6 marks each]

Q11.  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.

Q12.   (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 of Science and Maths for Class 9,10,11 and 12

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### NCERT Solutions for class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions for class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

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