## sample paper for class XI

sample paper for class xi and question paper for class 11

**MATHEMATICS**

**Sample Paper for xi – 2013
Class – XI
Subject –**

**Mathematics**

**Maximum Marks-100 Time:3 Hours sample paper for class XI **

Below is sample paper for class xi and these questions for class 11 can be asked in Board Paper of class xi

*General instructions:*

(i) All the questions are compulsory.

(ii) Question Nos. 1 to 10 contain 1 mark each, Question Nos. 11 to 22 contain 4 marks each and Question Nos. 23 to 29 contain 7 marks each. sample paper for class XI

**SECTION-A (1 X 10 =10)**

1. A={x: x is an integer , –}, write in A roster form.

2. If A={-1,1}, Find A x A x A.

3. If f(x) = — , write its domain and range.

4 Express in the form of a + ib .

5 Find the 20^{th } term of ,………………

6 Find the equation of straight line passing through (1,5) and origin.

7 Solve : 4x + 2

8 Find the length of the radius of the circle x^{2} + y^{2} – 4x –8y – 45 = 0

9 How many triangles can be obtained by joining 12 points, five of which are collinear?

10 Find the probability of getting a prime number when a die is thrown once.

**SECTION-B (4 X12 =48)**

11 If X={1,2,3,4……………….15}and A={2,4}, B={3,4,10,12,15}.

Find (A)^{׳} — ( A^{׳}B^{׳ } )

^{ }^{ OR }

In a survey, it was found that 21 people liked apple,26 people liked banana and 29 liked mango. If 14 people liked apple and banana, 12 people liked apple and mango, 14 people liked mango and banana and 8 liked all the three.(i) Find how many liked mango only. .(ii) Find how many liked banama only.

^{ }

12. Prove that cos^{2} A + cos^{2} B – 2 cos A cos B cos (A+B) = sin^{2} (A+B).

OR

Prove that cot x cot 2x– cot 2x cot 3x – cot 3x cot x = 1

13. IF 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 general solution cos 3x +cos x—cos2x = 0

14 If ( x + iy)^{3}= u + iv , then show that (u/x)+(v/y) = 4 (x^{2} – y^{2})

15 Find the equation to the set of points which are equidistance from the points (1,2,3) and (3,-2.1)

16 How many words , with or without meaning, can be formed from the letter of the word MONDAY, assuming no letter is repeated , if (i) 4 letters are used at a time?(ii) All letters are used at a time?

17. The coefficient of 5^{th}, 6^{th} ,7^{th} terms in the expansion of (1+x)^{n} are in A.P find n.

18 Find the value of ‘k’ , line passing through the point (-2,3) and ( k,1) perpendicular

to the 4x-3y + 7 = 0.

19. Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

OR

Find the derivative of : (cos x)/(1+sin x)

20 (a)Change the following statement into contra positive and converse

“ I go to a beach when ever it is a sunny day.”

(b) Identify the quantifier and write the negation of the statement.

For every real number x ,x is less than x + 1..

21 Solve Prove: (cos x + cos y)^{2} + ( sin x – sin y)^{2} = 4 cos ^{2}

22 If the p^{th}, q^{th} and r^{th} terms of a G.P. are a, b and c respectively. Prove that a^{q-p} b ^{r-p} c^{p-q }=1

OR

The sum of two numbers is 6 times their geometrical means, show that the numbers are in the ratio (3 + 2√2) : (3 – 2√2) .

**SECTION-C ( 6 X 7= 42 )**

23. Calculate Mean, Variance and Standard Deviation for the following distribution

classes | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

frequency 3 7 12 15 8 3 2

24. Graphically solve the following system of linear inequations

3x + 2y

x + 4y 80

x

y ≥ 0

25. Find the image of the point (3,8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

OR

Find the equation of the ellipse whose centre is (0,0), major axis on the y-axis and passes through the point (3,2) and ( 1,6 ).

26. Prove the following by using Principle of Mathematical Induction

41^{n} – 14^{n} is divisible by 27 for every natural number n.

27. If cos x = -(1/3) , x in 3^{rd} quadrant, find the value of sin(x/2) cos (x/2) tan(x/2).

28. A box contains 10 red marbles, 20 blue marbles and 30 green marbles. % marbles are drawn from the box, what is the probability that (i) all will be blue ? (ii) at least one will be green?

29. Prove that the coefficient of x^{n} in (1 + x)^{2n} is twice the coefficient of x^{n} in (1 + x) ^{2n–1}

** **

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