## CBSE Sample Paper for Class 11 Maths (Solved) – Set D

No chapter wise weightage for Class 11 Maths Paper. Care to be taken to cover all the chapters. The above paper is only a sample. Suitable internal variants may be made for generating similar templates keeping the overall weightage to different form of questions and typology of questions same. Set D of Solved CBSE Sample Paper for Class 11 Maths is given below with its solutions.

## Sample Question Paper

**Section-A**

Question numbers 1 to 6 carry 1 mark each.

1. Find the number of subsets of the set A = {a, b, c}.

2. Write the equation of any line which is perpendicular to the line 3x – 4y + 9 = 0.

3. If ^{16}C_{r} = ^{16}C_{r+2,}, then find ^{r}C_{4}

4. Find the centre and radius of the circle x^{2} + y^{2} – 4x + 6y = 12.

5. Write the derivative of log_{a} x(a > 0, a ≠ 1) with respect to x.

6. Find the focus and directrix of the parabola 2x^{2} + y = 0.

**Section-B**

Question numbers 7 to 19 carry 4 marks each.

7. Let A = {1, 2, 3, 4, 5}, B = {2, 3}, C = {5}, verify that A – (B ∩ C) = (A – B) ∪ (A – C).

8. A horse is tied to a pole by a rope. If the horse moves along a circular path keeping the rope tight and describe 176 m when it has traced out 72° at the pole, find the length of the rope.

9. Define modulus function, draw its graph.

OR

For the functions f (x) = ax + b, f(-1) = -5 and f(3) = 3, find a and b.

10. If cos θ + sin θ = √2 cos θ, prove that cos θ – sin θ = √2 sin θ.

If tan α =m/m + 1 and tan β =1/2m + 1, prove that α + β = π/4

11. Prove by the principle of mathematical induction that for all n ∈ N:

1+ 4+7+…+(3n-2)=1/2 n(3n-1).

12. Calculate the variance for the following frequency distribution :

Class |
30.5-36.5 | 36.5-42.5 | 42.5-48.5 | 48.5-54.5 | 54.5 – 60.5 |

Frequency |
4 | 10 | 14 | 27 | 45 |

13. A ball is drawn from the urn containing one red ball and one black ball. If the ball drawn is red, a coin is tossed and if it is black, a die is thrown. What is the probability of getting an even number ?

14. Derive the standard equation of ellipse.

15. A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%.

OR

Solve the given system of in equations graphically :

2x + y > 4, x + y < 3, 2x – 3y < 6.

16. If a + b + c ≠ and b + c/a, c + a/b, a + b/c, are in A.P., then to prove that 1/a, 1/b, 1/c are also in A.P.

17. For the function f (x) = x^{100}/100 + x^{99}/99 + ….. + x^{2}/2 + x + 1, show that f ‘ (1) = 100 f ‘ (0).

18. The girder of a railway bridge is a parabola with its vertex at the highest point, 10 m above the ends. If the span is 100 m, find the height at 20 m from the mid point. [HOTS]

OR

Find the co-ordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latusrectum of the ellipse 16x^{2} + y^{2} = 16.

19. 5 men and 4 women are to be seated in a row so that women occupy even places. How many such arrangements are possible ?

**Section-C**

Question numbers 20 to 26 carry 6 marks each.

20. For what value of p, one root of the equation x^{2} + (2p + 1) x + p^{2} + 2 = 0 is double the other ?

OR

Let z = x + iy and ω = 1 – iz/z – i, show that |ω| = 1, then z is purely real.

21. Prove that : cos^{2} x + cos^{2} (x + π/3) + cos^{2 } (x – π/3) = 3/2 [HOTS]

OR

If in any ΔABC, b+c/12 = c+a/13 = a+b/15 , then prove that cos A/2 = cos B/7 = cos C/11. [Supplementry Material Issued by Board]

22. A survey was conducted on students of a hostel, to know about their drink habits, there are 400 students. Out of these 250 take tea and 200 take milk whereas 50 take neither of these. How many students take both milk and tea ? How will you interprate this result ? [Value Based Question]

23. Find the equation of the circle which passes through the points (2, – 2) and (3, 4) and whose centre lies on x + y = 1.

OR

Find the centroid of a triangle, mid-points of whose sides are (1, 2, – 3), (3, 0, 1) and (- 1, 1, – 4).

24. Find the coefficient of x^{5}y^{7} in (x _ 7y)^{12}.

OR

The 3^{rd}, 4^{th} and 5^{th} a terms in the expansion of (x + a)^{n} are respectively 84, 280 and 560, find the values of x, a and n. [HOTS]

25. A well known thinking about the students of senior secondary school is that they are brilliant, unique in maths. A maths teacher taught them properly and then he decided to take a test to justify them. He prepared a test consists 12 questions divided in two parts say part I and part II, containing 5 and 7 questions respectively. A student is required to attempt 8 questions in all, selecting atleast 3 from each part. In how many ways can a student select the questions ? Suggest any other quality of students, that should be judge by teacher through this test. [Value Based Question]

26. If the sum of n terms of two arithmetic progressions are in the ratio 14 – 5n ; 3n + 5, find the ratio of their 8^{th} terms. [HOTS]

## Sample Question Paper Solutions

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