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

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 B 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. If A = 11, 2, 3, 41, B = {1, 3, 5, 7}, find the relation “is less than” from A to B.

2. Solve 5x – 3 < 3x + 1 when (i) x is an integer (ii) x is a real number.

3. Find the equation of the line through the point (- 4, 3) with slope (1,2)

4. Find the equation of the circle whose centre is (- 2, 3) and radius 4.

5. Evaluate : lim_{x->0} sin (2 + x) – sin (2 – x)/x

6. 6. Write the negation of the following statement : “sum of 2 and 3 is 6.”

**Section-B**

Question numbers 7 to 19 carry 4 – marks each.

7. Prove that : cos 2A cos A/2 – cos 3A cos 9A/2= sin 5A sin 5A/2

8. In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee ?

OR

Find the domain and range of the following function :

f(x)=x – 4/|x – 4| [HOTS]

9. If a and f3 are the solutions, of the equation a tan θ + b sec θ = c, then show that tan (α + β) = 2ac/a^{2} – c^{2}

10. If (a + i)^{2}/2a – 1= p + iq , show that p^{2} + q^{2} =(u^{2} + 1)^{2}/4a^{2} + 1

OR

Represent the complex number 1+ √3i in polar form.

11. If tan (α + β) = n tan (α – β), show that (n + 1) sin 2β = (n – 1) sin 2α. [HOTS]

12. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls, if each selection consists of 3 balls of each colour.

OR

On an evening a man planned a party of their friends on his 25th marriage anniversary. When all of his friends have arrived, he introduced all to each other and everybody shakes hand with everybody else. Find the total person in a room, if total shake hands are 66. What moral value do they have shown ? [Value Based Question]

13. Find n, such that ^{n}P_{5} = 42.^{n}P_{3}

OR

If 3 books of Mathematics and 4 books of Economics are kept together. What are the chances that all the three books Of Mathematics are kept together ?

14. Two unbiased dice are thrown. Find the probability that neither a doublet nor a total of 10 will appear.

15. A committee of two members is selected from two men and two women, What is the probability that the committee will have one man.

16. Calculate mean and variance for the following distribution :

Classes |
30 – 40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

Frequencies |
3 | 7 | 12 | 15 | 8 | 3 | 2 |

17. Find the lengths of transverse and conjugate axes, eccentricity, coordinates of foci and vertices for the hyperbola 16x^{2} – 9y^{2} = 144.

18. Find the derivative of 2x + 3/x – 2 with respect to x from first principle.

19. A teacher teaches their students with such a spirit that they must know, what he knows ?After teaching with same spirit, he decided to check the ability of the students through a test. He has given a question, if a, b are roots of x^{2} – 3x +p = 0, c and d are roots of x^{2} – 12x + q = 0, where a, b, c, d are in G.P. Evaluate the ratio of q + p to q – p. Apart from ability of students, suggest one other quality to judge ? [Value Based Question]

**Section-C**

Question numbers 20 to 26 carry 6 marks each.

20. Using binomial theorem, prove that 6^{n} — 5n – 1 is always, divisible by 25.

21. Find n, if the ratio of the fifth term from the beginning to the fifth term from end in the

OR

If three consecutive coefficients in the expansion of (1 + x)^{n} are in the ratio 6 : 33 : 110, find n and r.

22. Using principle of mathematical induction, prove that (10^{2n-1} + 1) is divisible by 11), ∀ n ∈ N.

23. Of the members of three atheletic teams in a certain school, 21 axe in the basketball team, 26 in hockey team and 20 in football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all ?

24. Show that area of the triangle formed by the lines y = m_{1}x + c_{1}, y = m_{2}x + c_{2} and x = 0 is

(c_{1} – c_{2})^{2}/2|m_{1} -m_{2}|

OR

Prove that the product of the lengths of the perpendiculars drawn from the points (±√a^{2} – b^{2} ,0) to the line x/a cos θ + Y/b sin θ =1 is b^{2}.

25. Find Four numbers in G.P. in which third term is greater than the first by 9 and the second term it.3 greater than the fourth by 18.

26. Solve the given system of inequalities graphical1y:

x – 2y ≤ 3, 3x + 4y ≥12, x ≥ 1, y ≥ 1.

## Sample Question Paper Solutions

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