# CBSE Class 12 Maths Question Paper 2017 with Solutions

**CBSE Class 12 Maths Question Paper 2017 with Solutions** - The performance of students in the 12th board exams is very significant, so make important strategies for the exam to perform well. Solving CBSE previous year question papers Class 12 Maths 2017 helps to understand the difficulty level. Referring to CBSE previous year question papers with solutions plays a very significant role in their final performance. However, students often solve these CBSE 12 Maths question paper 2017 only a few days before the exam. Students should solve as many possible CBSE previous year class 12 maths papers. It will help you to understand the important concepts and quick revision before the exam. In this article, you will get a detailed CBSE class 12 Maths question paper 2017 with solutions for all three sets.

**Latest Updates for CBSE Class 12th **

**04 Jun 2021:**Class 12 exams cancelled. CBSE 12th result to be announced soon.

Stay up-to date with CBSE Class 12th News

First, students should try to solve all the questions on their own. If they are not able to solve, then, take help from CBSE class 12 Maths question paper 2017 solved pdf. In this article, the questions are explained in a step-by-step manner which will help you to perform well in the Central Board of Secondary Education (CBSE) Class 12 exam.

**Set-wise CBSE Class 12 Maths Question Paper 2017 with Solutions**

Below, we have provided the solutions to unique questions of CBSE previous year question papers Class 12 Maths 2017. Students can also check CBSE 12th previous question papers for all subjects.

### CBSE 12 Class 2017 Paper: 65-1 Maths

Question 2)

Determine the value of ‘k’ for which the following function is continuous at x = 3:

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Question 7)

The volume of a cube is increasing at the rate of 9 . How fast is its surface area increasing when the length of an edge is 10 cm ?

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Question 9)

The x-coordinate of a point on the line joining the points P(2, 2, 1) and Q(5, 1, – 2) is 4. Find its z-coordinate.

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Question 10)

Two tailors, A and B, earn Rs 300 and Rs 400 per day respectively. A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP.

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Question 21)

Show that the points A, B, C with position vectors respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

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Question 23)

There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.

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Question 24)

Of the students in a school, it is known that 30% have 100% attendance and 70% students are irregular. Previous year results report that 70% of all students who have 100% attendance attain A grade and 10% irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has 100% attendance ? Is regularity required only in school ? Justify your answer.

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Question 27)

Consider given by Show that f is

bijective. Find the inverse of f and hence find and X such that

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Question 28)

Let and let be a binary operation on A defined by for Determine, whether is commutative and associative. Then, with respect to on A

(i) Find the identity element in A.

(ii) Find the invertible elements of A.

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Question 29)

Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube.

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Question 30)

Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4).

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Question 32)

Find the particular solution of the differential equation given that y = 0 when x = 1.

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Question 33)

Find the coordinates of the point where the line through the points (3, – 4, – 5) and

(2, – 3,1), crosses the plane determined by the points (1, 2, 3), (4, 2, – 3) and (0, 4, 3).

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Question 34)

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is

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Question 35)

A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed.Let A be the event ‘‘number obtained is even’’ and B be the event‘‘number obtained is red’’. Find if A and B are independent events.

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### CBSE 12 Class 2017 Paper: 65-2 Maths

Question 1)

The length x, of a rectangle is decreasing at the rate of 5 cm/minute and the width y, is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.

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Question 3)

Solve the following linear programming problem graphically :

Maximise

under the following constraints

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Question 4)

Find the value of x such that the points A (3, 2, 1), B (4, x, 5), C (4, 2, – 2) and D (6, 5, – 1) are coplanar.

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Question 6)

AB is the diameter of a circle and C is any point on the circle. Show that the area of triangle ABC is maximum, when it is an isosceles triangle.

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### CBSE 12 Class 2017 Paper: 65-3 Maths

Question 1)

The volume of a sphere is increasing at the rate of 8 cm^{3}/s. Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.

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Question 2)

Solve the following linear programming problem graphically :

Maximize

subject to the constraints

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Question 4)

If then express in the form of where is parallel to and is perpendicular to .

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Question 6)

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

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### CBSE 12 Class Compartment 2017 Paper: 65-1 Maths

Question 1)

If the following function f(x) is continous at x = 0, then write the value of k.

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Question 2)

If A is an invertible matrix of order 2 and det then write the value of det(A^{-1}).

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Question 7)

A particle moves along the curve . Find the points on the curve at which y-coordinate is changing 2 times as fast as x-coordinate.

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Question 12)

An aeroplane can carry a maximum of 250 passengers. A profit of Rs1,500 is made on each executive class ticket and a profit of Rs1,000 is made on each economy class ticket. The airline reserves at least 25 seats for executive class. However, at least 3times as many passengers prefer to travel by economy class than by executive class. Frame the Linear Programming Problem to determine how many tickets of each type must be sold in order to maximize the profit for the airline.

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Question 13)

A school wants to award its students for regularity and hardwork with a total cash award of Rs 6,000. If three times the award money for hardwork added to that given for regularity amounts to Rs 11,000, represent the above situation algebraically and find the award money for each value, using matrix method. Suggest two more values, which the school must include for award.

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Question 17)

Find the intervals in which the function given by

is

(a) Strictly increasing

(b) Strictly decreasing

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Question 22)

If are mutually perpendicular vectors of equal magnitudes, find the angles which the vector makes with the vectors .

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Question 23)

Find the co-ordinates of the foot of perpendicular drawn from a point A (1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).

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Question 24)

Solve the following linear programming problem graphically :

Minimize :

when :

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Question 25)

Bag A contains 3 red and 2 black balls, while bag B contains 2 red and 3 black balls. A ball drawn at random from bag A is transferred to bag B and then one ball is drawn at random from bag B. If this ball was found to be a red ball, find the probability that the ball drawn from bag A was red.

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Question 26)

If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by

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Question 28)

Given a non-empty set X, consider the binary operation given by where is the power set of X.show that is commutative and associative and X is the identity element for this operation and X is the only invertible element in with respect to the operation .

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Question 29)

Let be a function defined as Show that f is a one-one function. Also check whether f is an onto function or not. Hence find f^{-1} in

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Question 30)

Show that the right circular cone of least curved surface and given volume has an altitude equal to times the radius of the base.

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Question 31)

Find the equation of tangent to the curve at any point of the curve. Also show that at any point of the curve the normal is at a constant distance from origin.

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Question 32)

Find the distance between the line and the plane determined by

the points A(2,-2,1).B(4,1,3) and C(-2,-2,5).

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Question 33)

A coin is biased so that the head is 4 times as likely to occur as tail. If the coin is tossed thrice, find the probability distribution of number of tails. Hence find the mean and variance of the distribution.

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Question 34)

Using method of integration find the area of the triangle ABC, co-ordinates of whose vertices are A(1, –2), B(3, 5) and C(5, 2).

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### CBSE 12 Class Compartment 2017 Paper: 65-2 Maths

Question 5)

Find the co-ordinates of the foot of perpendicular drawn from the point (2, 3, –8) to the line

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Question 6)

From a lot of 30 bulbs, which includes 6 defectives, 3 bulbs are drawn one by one at random, with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean and variance of the distribution.

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Question 7)

Find the distance between the line and the plane determined by the points A(1, 1, 0), B(1, 2, 1) and C(–2, 2, –1).

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Question 8)

The radius r of a right circular cylinder is increasing at the rate of 5 cm/min and its height h, is decreasing at the rate of 4 cm/min. When r = 8 cm and h = 6 cm, find the rate of change of the volume of the cylinder.

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### CBSE 12 Class Compartment 2017 Paper: 65-3 Maths

Question 3)

A balloon, which always remains spherical, has a variable diameter . Find the rate of change of its volume with respect to x.

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Question 4)

Solve the following linear programming problem graphically : Find the maximum value of when

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Question 7)

Find the coordinates of the point of intersection P of the line and the plan determined by points A(1, –2, 2), B(4, 2, 3) and C(3, 0, 2).

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Question 8)

A biased die is such that and the other score are equally likely. The die is tossed twice. If X is the ‘number of fours obtained’, find the variance of X.

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## CBSE Class 12 Maths Question Paper 2017 with Solutions

CBSE has conducted the Mathematics exam for students of class 12 on 20th March 2017 from 10:30 AM to 1:30 PM. This year's paper pattern was completely different from last year’s question paper.

About 30-40 % of the questions asked from the CBSE frequently asked important concepts. Section D of the CBSE 12 Maths question paper 2017 was quite easy in comparison to other sections.

Overall question paper was an easy level as compared to last year's paper but a bit lengthy as some questions worth 4-6 marks were the two mark category. An average student can score about 80 percent in exam.

**Also, check**

**CBSE class 12 maths 2017 Question Paper pattern**

CBSE class 12 Maths question paper 2017 with solutions contains 29 questions divided into four sections A, B, C, and D as per the latest CBSE Class 12 Maths Syllabus. All questions are compulsory where no overall choice has been given.

In section A of CBSE class 12 maths question paper 2017, there are four questions of one mark each where you need to answer in one word, one sentence or as per the exact requirement of the question. No internal choice for this section.

Section B of CBSE previous year question papers Class 12 Maths 2017 consists of eight short answer type questions of two marks each where you need to answer as per the exact requirement of the question. There is no internal choice in this section.

CBSE 12 Maths question paper 2017 section C comprises 11 questions of four marks each where you need to provide stepwise solutions for each question. The internal choice has been provided in the three questions of this section.

Section D of CBSE class 12 maths question paper 2017 comprises six long answer type questions of six marks each where you need to write a step-by-step complete solution for each question. The internal choice has been provided in three questions of this section. You have to attempt only one of the alternatives in all such questions.

**CBSE Class 12 Maths Question Paper 2017 with Solutions - Question Types**

Section | Types of Questions | No. of Questions | Marks per Question | Total marks |

A | Very Short Answer Type Questions | 4 | 1 | 4 |

B | Short Answer Type Question - I | 8 | 2 | 16 |

C | Short Answer Type Question - II | 11 | 4 | 44 |

D | Long Answer Type Questions | 6 | 6 | 36 |

Total | 29 | 100 |

## Analysis of CBSE class 12 Maths Question Paper 2017 with Solutions

CBSE had followed the above-mentioned distribution pattern to design class 12 maths question paper 2017. The paper was an average level question paper but a bit lengthy.

Students who have solved all the NCERT problems including solved examples won’t find this paper tough as most of the questions are directly taken from the NCERT textbook.

Also, those who have practised well with CBSE Class 12 Maths Sample Papers can solve this paper on time. The chapter-wise and unit-wise marks distribution is given below.

### CBSE 12 Maths Question Paper 2017: Chapter-wise Weightage

S. No | Unit | No. of Questions | Total Marks |

1 | Relation and Function | 1 | 6 |

2 | Inverse Trigonometric Functions | 1 | 4 |

3 | Matrices | 3 | 9 |

4 | Determinants | 1 | 4 |

5 | Continuity and Differentiability | 3 | 7 |

6 | Applications of Derivatives | 3 | 10 |

7 | Integrals | 4 | 11 |

8 | Applications of Integrals | 1 | 6 |

9 | Differential Equations | 2 | 10 |

10 | Vector Algebra | 2 | 6 |

11 | Three Dimensional Geometry | 3 | 11 |

12 | Linear Programming | 2 | 6 |

13 | Probability | 3 | 10 |

Total | 29 | 100 |

From the above analysis, you can see that the chapter ‘Integrals’ has a maximum number of questions and maximum weightage followed by 3-D geometry in the question paper.

**Unit wise weightage in terms of total marks:-**

1 | Relation and Functions | 10 |

2 | Algebra | 13 |

3 | Calculus | 44 |

4 | Vector and 3-D Geometry | 17 |

5 | Linear Programming | 6 |

6 | Probability | 10 |

Total | 100 |

The unit marks distribution is more important as CBSE follows this weightage system to prepare the CBSE question paper.

**Conclusion:- **CBSE maths question paper 2017 was an average level question paper. Students who have worked hard can score full marks easily. About 90 marks is a good score in this paper as most questions are directly taken from NCERT textbook.

It is advised to solve CBSE previous years papers. It will strengthen your grip on the subject and you will be able to solve different types of questions in the least time with full confidence.

You can take help from these solutions provided in this article which were explained by the experts who know how best to answer the questions in the board exam in order to get maximum marks.

**Also Check CBSE Class 12 Previous year question papers: **

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## Questions related to CBSE Class 12th

### i have an academic doubt. here why does a battery lose its power when used for a long time. is it due to decrease in emf or decrease in terminal potential? pls explain in detail...

Batteries are electrochemical device that convert chemical energy into electrical energy. Batteries are of two types - primary and secondary batteries. Primary batteries loose their charge with time while the secondary batteries can be recharged for repeated use. Battery cells loose power when the chemical that powers the reaction is finished up. This leads to an increase in internal resistance of the battery and a time comes when there are no reactants are left for chemical reaction and only products of chemical reaction are left in electrolyte in the battery.

### By passing electric current , NaclO3 is converted into NaclO4 . How many moles of NaclO4 will be formed when 3 faradays of charge is passed through NaclO3 ?

The balanced chemical equation for above question is-

NaClO3 + H2O -> NaClO4 + H2

The oxidation state of Cl atom in NaClO3 is +5 and the oxidation state of Cl atom in NaClO4 is +7. So, the net change in oxidation state = 7-5 = +2.

This show that 2 faradays of charge is required to get 1 mole of NaClO4.

So if 1 faradays of charge is passed through NaclO3 then (1/2) mole of NaClO4 obtained.

Then 3 faradays of charge is passed through NaclO3 then (1/2)x3 mole of NaClO4 obtained that is 1.5 mole NaClO4 is obtained.

### sir, eagerly waiting for decision on CBSE 12TH board exam dates. Bhairavi Hardik

Hello,

The tussle of if and but is still going on regarding the cbse class 12th exam and final decision will be made in 3-4 days. The most recent and last update is Class 12 board exams are scrapped and there is a proposal to assess students on the results of Classes 9, 10 and 11. Though most states have backed CBSE’s option for a truncated exam, a few states disagreed and some demanded vaccination of candidates and staff before holding the exams. But keep preparing as of now until any final decision.

I hope this helps.

### Hello sir/maam, in this current situation there has been some news that class 12th cbse exam will be cancelled and the marks will be calculated on the basis of internal markings in that case I fear that my percentage will drop and I wouldnt get my dream college. What should I do?

Hello Aspirant,

See as of now we cannot predict anything about class 12th board examination because these exams have been already postponed till further notice and till now there is no any further decision regarding the new dates or any cancellation so we have to wait till June because in the month of June some decision is expected on CBSE class 12th board examinations.

Don't worry for marking because if the exams will be cancelled then some altrnative would be given as given for class 10th that if any candidate is unsatisfied with his/her result then he/she can appear for an examination which will be conducted when the situations become normal so like this any alternative can be introduced for class 12th as well but till now there is no any notice regarding any cancellation or further postponement of class 12th board examinations.

You can get the latest updates about CBSE examinations from the official website given below :-

http://cbseacademic.nic.in/index.html

I hope this information helps you.

Good Luck!!

### my score is 111 marks on 18 th march morning shift. I belongs to OBC category what will be my percentile according to my shift and expected rank?? Also pls suggest some colleges on this score I am from maharashtra.

Hello Aspirant,

If we go through the analysis of marks Vs Percentile Vs rank for JEE-Main 2020 then according to the marks mentioned by you in the question your percentile is expected to be in the range of 94.07 - 96.21 and your rank is expected to be in the range of 51150 - 57500, you can check out marks Vs ranks Vs Percentile from the link given below :-

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile

Or

You can also use JEE-Main Rank Predictor to predict your rank :-

https://engineering.careers360.com/jee-main-rank-predictor

So on such rank and category you have chances to get the enlisted NITs :-

NIT Raipur

NIT Goa

NIT Puducherry

NIT Meghalaya

NIT Hamirpur

You can check out previous year's cut-offs from the official website of JOSAA as given below :-

__
https://josaa.nic.in/Result/Result/currentorcr.aspx
__

To have a list of all those colleges which you can get based upon your marks, category, and state you can use JEE-Main College Predictor:-

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

If you are preparing for JEE-Main 2021 or 2022 then I would recommend you to check the resources made by our experts to help aspirants like you in the best and smart preparation of JEE-Main 2021 or 2022 :-

https://learn.careers360.com/jee-main-coaching/?utm_source=%20QnA

I hope this information helps you.

Good Luck!!