## 11 th class 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**

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**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 tha**t

**(ii) Solve : tan²θ + sec2θ = 1**

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