# Sample paper for class 11 Mathematics

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Sample paper for Class 11 Maths

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## Sample paper for class 11 Mathematics

Here is Sample paper for class 11 Mathematics. To get the answers and more sample papers, visit myCBSEguide App or website stated above.

Time allowed: 3 hours, Maximum Marks: 100

General Instructions:
a) All questions are compulsory.
b) The question paper consists of 26 questions divided into three sections A, B and C. Section A comprises of 6 questions of one mark each, Section B comprises of 13 questions of four marks each and Section C comprises of 7 questions of six marks each.
c) All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
d) Use of calculators is not permitted.

Section A

### 1. Find the domain of the function .

Sol: Domain of is in the open interval

Sol:

### 3. What is the maximum value of if.

Sol: Max value is 2.

Sol: Ellipse

### 5. Check whether the three points (2, 0), (5, 3), (2, 6) are collinear.

Sol: Condition for collinearity is not satisfied here since
=

Sol:

Section B

Sol:

Sol:

Sol:

### 10. Solve the inequality .

Sol: Either both factors are negative or both factors are positive to have this in equality. if both factors are negative and if both factors are positive. Hence the solution is

Sol:

### 12. In a single throw of 2 dies what is the probability of getting a prime number on each die.

Sol: Total number of occurrence =
On each die there are 3 prime numbers
Hence total number of favorable cases
Probability of getting a prime in each die =

Sol:

Sol:

Sol:

### 16. Prove that the equation is impossible if x is real

Sol : Use the inequality

### 17. Find the domain of the function for which .

Sol:

Hence f(x) and {tex}\phi {/tex}(x) are equal when the domain is in the set {tex}\{\frac{1}{3},2\}{/tex}

Sol:

Sol:

Section C

### 20. Differentiate from the first principle w.r.t. x.

Sol:

Note: As

21. Find the sum of terms of the series

Sol: The successive First order of difference is this is an AP.
The second order difference is(Difference of the first difference)
Third order difference (Difference of second order differences) is all
n th term

=
=
Sum =
=
=

22. Find the equation of a circle whose diameter is the line joining the points .

Sol: Let the point A be and B be

Let the point C be a point be (x, y) on the circle

Then AC and BC are perpendicular

Product of Slopes of line AC and BC =-1

23. Calculate the mean deviation about the mean from the following data

 xi 5 7 9 10 12 15 fi 14 6 2 2 2 4

Sol:

 5 14 70 4 56 7 6 42 2 12 9 2 18 0 0 10 2 20 1 2 12 2 24 3 6 15 4 60 6 24

Mean Deviation

24. How many numbers can be formed with the digits so that odd digits are in odd places and even digits are in even places.

Sol: The odd digits can be arranged in their 4 places in ways

Even digits can be arranged in their 3 places in

Hence the total number of arrangements = ways

25. Two engineers go for an interview for two vacancies in the same grade. The probability of engineer 1 (E1) getting selected is and that of engineer 2 (E2) is . Find the probability that only one of them will be selected.

Sol: Probability of one of them getting selected = 1- (Probability of both getting selected + Probability of none getting selected)

=

=

=

=

26. How many numbers are there between 1 and 1000(both included) that are not divisible by 2, 3, and 5?

Sol: Let A denote the set of numbers that are divisible by 2, B set of numbers that are divisible by 3, C set of numbers that are divisible by 5, D set of numbers that are divisible by both 2 and3 , E set of numbers that are divisible by both 2 and 5, F set of numbers that are divisible by 3 and 5, G set of numbers that are divisible by all the three numbers

In this case , Hence

### Numbers that are divisible by 2, 3, 5 are

Numbers that are not divisible by 2, 3, 5 are

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## Sample Paper for class 11

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## Marking Scheme for Class 11 exam

 Subject Board Marks Practical or internal Marks English 100 Marks ZERO Marks Hindi 100 Marks ZERO Marks Mathematics 100 Marks ZERO Marks Chemistry 70 Marks 30 Marks Physics 70 Marks 30 Marks Biology 70 Marks 30 Marks Computer Science 70 Marks 30 Marks Informatics Practices 70 Marks 30 Marks Accountancy 80 Marks 20 Marks Business Studies 80 Marks 30 Marks Economics 80 Marks 20 Marks History 80 Marks 20 Marks Political Science 100 Marks ZERO Marks Geography 70 Marks 30 Marks Sociology 80 Marks 20 Marks Physical Education 70 Marks 30 Marks Home Science 70 Marks 30 Marks