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

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 E 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. How many elements has P(A), if A = Φ ?

2. Find the value of tan (13π/12)

3. Solve 5 – 2x/3 ≤ x/6  – 5.

4. Find coefficient of x5 in (x + 3)8

5. Line through the points (- 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

6. Write the converse, if two integers a and b are such that a > b, then a – b is always a positive integer. [HOTS]

Section-B

Question numbers 7 to 19 carry 4 marks each.

7. If A and B are any two sets, then prove that
(A ∪ B)’ =A’ ∩ B’.

8. Find the domain and range of the real function f (x) =√16 – x2

9. Show that : cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1.

OR

Evaluate the value of tan (π/8).

10. A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be atleast 5 cm longer than second. [HOTS]

11. Convert the given complex number z = i – 1/cos π/3 + i sin π/3 in polar form.

OR

If (i + i/1 – i)m =1, then find the least integral value of m.

12. Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements :
(i) do all vowels occur together.
(ii) do the word begins with I and end in P?

OR

How many numbers greater than 10,00,000 can be formed by using the digits, 0, 1, 2, 2, 4, 4, 2.

13. Prove that (1 + x)n ≥ 1 + nx, for all natural numbers n, where x > — 1.

14. If A and G be A.M. and G.M. respectively between the two positive numbers, prove that the numbers are A ± √(A +G)(A—G). [HOTS]

15. From a class of 25 students, 10 are to be chosen for an excursion party. There are three students who decided that either all of them will join or
none of them will join. In how many ways can the excursion party be chosen ?

16. Find the distance of the line 4x — y = 0 from the point P (4, 1). Measured along the line making an angle 135° with positive x-axis. [HOTS]

17. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (— 4, 3b, — 10) and R (8, 14, 2c), then find values of a, b and c.

18. Evaluate :

OR

Evaluate :

19. If z1 = 2 — i, z2 = 1 + i, find |z1 + z2 + 1 / z1 – z2 + i|.

Section-C

Question numbers 20 to 26 carry 6 marks each.

20. In a survey, it was found that, people encourage their wards for science/commerce streams, and it looks commonly at school/college lables, there are 40 students in chemistry class and 60 students in physics class. Find the number of students which are either in physics class or chemistry class in the following cases :
(i) The two classes meet at same hour.
(ii) The two classes meet at different hour and 20 students are enrolled in both subjects.
(iii)How will you analyse the motive of parents ? [Value Based Question]

21. Find the domain of the function f(x)= √4 – x + √1 /X2 —1 [HOTS]

OR

Let A = {1, 2, 3, 4, 5, 61. Define a relation R = {(x, y) : y = x + 1); x, y ∈ A.

(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, co-domain and range of R.

22. There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points ? If no three are in same straight line. Find how many triangles can be formed ?

23. The sum of the coefficients of the first three terms in the expression of (x — 3/x2)m, x ≠ 0, m being natural number, is 559. Find the term of the expansion containing x3.

OR

If a and b are distinct integers, prove that (a — b) is a factor of an — bn, whenever n is a positive integer.

24. A beam is supported at its ends by support which are 12 m apart. Since the load is concentrated at its centre. There is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection 1 cm ? [HOTS]

OR

Find the co-ordinates of the foci, the vertices, the length of major axis and eccentricity of the ellipse 9x2 + 4y2 = 36.

25. One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be :
(i) a diamond,
(ii) a black card,
(iii) not an ace,
(iv) not a diamond,
(v) not a black card,
(vi) a face card.

26. An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, gives the following results :