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# Class 11 CBSE Last Year’s Maths Question Paper

Here 11 th Class CBSE Maths Last Years Questions Paper is presented that will help all class 11 maths students of the CBSE board. The study of this question paper will let you know about the type of questions asked in the exams. Questions in this question paper represent all the chapters of the class maths NCERT book, therefore students can check their updated knowledge of NCERT maths by solving this question paper.

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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 CBSE Maths Question Paper

### Half Yearly Examination,2015-16

#### Subject: Mathematics

Duration : 3 hr                                                                                                              MM: 100

General Instructions:

1. All questions are compulsory.

2. The question paper consists of  26 questions divided into three sections A, B, and C.Section A comprises of 6 questions of 1 mark each. Section B comprises of 13 questions of 4 marks each and Section C comprises of o7 questions of 6 marks each.

3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

4. There is no overall choice, However, internal choice has been provided in 04 questions of 4 marks each and 02 questions of 6 marks each. You have to attempt only one of the alternatives in all such questions.

5. Use of calculators is not permitted. You may ask for a logarithmic table

#### Section: A

Questions numbers 1 to 6 carries one mark each.

$\mathbf{Q1.}\; {\color{DarkGreen} \mathbf{If\; z= \frac{1}{1 -cos\Theta-isin\Theta }\; then \; Re\left ( z \right )=?}}$

Q2. Write the domain of the f(x) = √(x-1) + √(3-x).

Q3. The third term of GP is 4. Write the product of its first 5 terms .

Q4. Write the length of the latus rectum of the Parabola 4(y-1)²= -7(x-3).

Q5. Write the value of x ,if cosec(Π/2 +Φ) + xcosΦcot(Π/2+Φ) = sin(Π/2 +Φ).

${\color{DarkGreen} \mathbf{Q6.\; Write\; the\; argument\; of\; \frac{1+i\sqrt{3}}{1-i\sqrt{3}}.}}$

#### Section B

Question numbers 7 to 19 carry 4 marks each.

${\color{DarkGreen} \mathbf{Q7.\; If\; a \; real\: function\; defined\: by\; f(x)= \frac{x-1}{x+1}\; then\; prove\; that\; f(2x)=\frac{3f(x)+1}{f(x)+1}}}$

Q8. If x = a +b, y = aω + bω² and z = bω + aω ², where ω  is an imaginary cube root of unity, prove that x² + y² + z² = 6ab.

OR

${\color{DarkGreen} \mathbf{Reduce\left (\frac{1}{1-4i} -\frac{2}{1+i} \right )\left ( \frac{3-4i}{5+i} \right )to\; the\; standard\; form}}$

Q9. Solve the following system of inequalities graphically :

x +2y ≤8,  x + y ≥ 1,  x-y ≤ 0,  x ≥0,  y≥ 0

Q10. Find the sum of the following series up to n terms .6 + .66+ .666+ ……..

${\color{DarkGreen} \mathbf{Q11.\; If a\left ( \frac{1}{b}+\frac{1}{c} \right ), b\left ( \frac{1}{c}+\frac{1}{a} \right ),c\left ( \frac{1}{a}+\frac{1}{b} \right )\; are \; in\; A.P. \; Prove\; that\; a, b, c \; are\; \: in\; A.P}}$

${\color{DarkGreen} \mathbf{Q12.\; By\; using\; PMI , prove\; that 1.3 + 2.3^{2}+3.3^{3}+ .........n.3^{n}= \frac{\left ( 2n-1 \right )3^{n+1}+3}{4}\; n\euro N}}$

Q13. Let L be the set of all lines in a plain and ‘R’ be the relation on  ‘L’ defined as R ={(l.m): l is perpendicular to m}, prove that

i. (x,x) ∉ R, x ∈ L

ii. (x,y) ∈ R ⇒ (y,x) ∈ R, x,y ∈ L

iii.(x,y) ∈ R, (y,z)  ∈ R ⇒ (x,z) ∉ R, x,y,z ∈ L

Q14. Solve the equation 3sec²θ + 2√3tanθ – 6=0

OR

$\dpi{100} {\color{DarkGreen} \mathbf{Prove\; that\; in \; a \; \Delta ABC,\; \left ( \frac{b^{2}-c^{2}}{a^{2}} \right )sin2A+\left ( \frac{c^{2}-a^{2}}{b^{2}} \right )sin2B+\left ( \frac{a^{2}-b^{2}}{c^{2}} \right )sin2C}}\mathbf{=0}$

$\dpi{100} {\color{DarkGreen} \mathbf{Q15.Prove\; that\; cos^{4}\frac{\Pi }{8}+cos^{4}\frac{3\Pi }{8}+cos^{4}\frac{5\Pi }{8}+cos^{4}\frac{7\Pi }{8}=\frac{3}{2}}}$

OR

Prove that in any ΔABC, (b– c)cotA/2 + (c– a)cotB/2 + (a–b)cotC/2  = 0

Q16. (Using properties of sets ) for A and B are any two sets ,prove that A’ – B’ = B – A

Q17. The foci of a hyperbola coincides with the foci of the ellipse

$\dpi{100} {\color{DarkGreen} \mathbf{\frac{x^{2}}{25} +\frac{y^{2}}{9}= 1}}$

Find the equation of hyperbola if its eccentricity is 2.

$\dpi{100} {\color{DarkGreen} \mathbf{Q18.\; Prove\; that:\; 4^{n}+ 15n-1 \; is\; divisible\; by\; 9,n\epsilon N\left ( By\; using\; PMI \right )}}$

OR

Prove that by using PMI, that the sum of cubes of three consecutive natural numbers is divisible by 9.

Q19. If the length of the perpendicular from the point (1,1) to the line ax + by + c =0 be 1

$\dpi{100} {\color{DarkGreen} \mathbf{Show\; that\; \frac{1}{c}+ \frac{1}{a}-\frac{1}{b}=\frac{c}{2ab}}}$

#### Section: C

Question numbers 20 to 26 carry 6 marks each

Q20. Find the sum to n terms of the series 5 + 11 +19 +29 + 41 +…………….

OR

If A.M and G.M between two numbers are in the ratio, m : n, then prove that the numbers in ratio

$\dpi{100} {\color{DarkGreen} \mathbf{m+ \sqrt{m^{2}-n^{2}} : m- \sqrt{m^{2}-n^{2}}}}$

Q21.How many liters of water will have to be added to 1125 liters of 45 % solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

Q22. Solve: x² – (7 – i)x + (18 – i) = 0

OR

${\color{DarkGreen} \mathbf{Evaluate :x^{4 }+4x^{3} +6x^{2}+4x +9,when\; x = -1 + i\sqrt{2}}}$

${\color{DarkGreen} \mathbf{Q23.(i) If\; z _{1} \; and z_{2}\; are\; different\; complex \; numbers\; with\left | z_{1} \right |=1, find\left | \frac{z_{1}-z_{2}}{1-z_{1}\bar{z_{2}}} \right |= ?}}$

${\color{DarkGreen} \mathbf{(ii)Solve :\frac{\left | x +3 \right |+3}{x +2}> 1}}$

Class 11 maths question paper 2019-20-CBSE Board

Q24. (i) Find the sum to n terms of the series : 3 ×8 + 6 ×11 + 9 ×14 +………….

(ii) If the p, q, r are in G.P and the equations px² + 2qx + r =0 and dx² +2ex + f =0 have a common roots.

${\color{DarkGreen} \mathbf{\; Then \; show \; that \frac{d}{p},\frac{e}{q},\frac{f}{r} \; are\; in A.P}}$

Q25. (i) Find the equation which passes through the center of the circle x² +y² + 8x + 10y–7 =0 and is concentric with the circle 2x² +2y² –8x –12y –9 =0.

(ii) Find the distance of the point (1,2) from the straight line whose slope is 5 and passing through the point of intersection of  x +2y = 5 and x –3y =7.

Q26. (i) If m tan(θ– 30°) = n tan(θ +120), show that

${\color{DarkGreen} \mathbf{cos2\Theta =\frac{m+n}{2\left ( m-n \right )}}}$

(ii) Solve : tan²θ + sec2θ = 1

## 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

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 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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