Class 11 CBSE Last Year's Maths Question Paper 2015-16 - Future Study Point

Class 11 CBSE Last Year’s Maths Question Paper 2015-16

class 11 maths question paper

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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class 11 maths question paper

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 class 11 CBSE Maths Question Paper

Half Yearly Examination,2015-16

Class: Xl

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.

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).


Section B

Question numbers 7 to 19 carry 4 marks each.

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

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+ ……..

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

 

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

Find the equation of hyperbola if its eccentricity is 2.

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

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

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

 

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.

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

(ii) Solve : tan²θ + sec2θ = 1

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

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NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

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Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
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Chapter 7- Integrals
Chapter 8-Application of Integrals

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