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
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
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