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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

**2. If **

**Sol:**

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

**Sol:** Max value is 2.

**4. Name the locus of points, the sum of whose distance from two given points is a constant.**

**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

=

**6. Write the condition so that the equation represents a circle.**

**Sol:**

**Section B**

**7. Find the inverse of the function **

**Sol:**

**8. Find the vertex, axis , Focus , Directrix and latus rectum of the parabola **

**Sol:**

**9. Express in the form .**

**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

**11. Find the general value of if .**

**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 =

**13. If Find the value .**

**Sol:**

**14. If prove that .**

**Sol:**

**15. If is defined as follows: Find .**

**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}

**18. Find the limit .**

**Sol:**

**19. Solve **

**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

This is only initial part of the whole sample paper. Download Complete set of **sample paper for class 11 Mathematics**

**Sample Paper for class 11 **

It is Sample paper for class 11 Mathematics. However, myCBSEguide provides the best sample papers for all the subjects. There are number of sample papers which you can download from myCBSEguide website. **Sample paper for class 11** **all subjects**

**Physics****Chemistry****Mathematics****Biology****Accountancy****Economics****Business Studies****Computer Science****Informatics Practices****English Core****Hindi Core****Hindi Elective****History****Political Science****Geography****Sociology****Physical Education****Other Subjects**

These are also Sample Paper for class 11 Mathematics available for download through myCBSEguide app. These are the latest Sample Paper for class 11 Mathematics as per the new exam pattern. Download the app today to get the latest and up-to-date study material.

**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 |

**Download CBSE Sample Papers Class 11**

To download complete sample paper for class 11 Mathematics, Business Studies, Political Science, Economics, Physics, Geography, Computer Science, Home Science, Chemistry and Biology; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through **the best app for CBSE students** and myCBSEguide website.

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