## Previous Year Mathematics Question Paper for ISC Class 12 Board - 2019 - Free PDF Download

## FAQs on ISC Class 12 Mathematics Question Paper - 2019 Board Examinations

1. If f : A ⟶ A and A = R(8/5), show that the function f(x) = [(8x + 3)/(5x - 8)] is one-one onto. Hence, find f^{-1}.

The given function is:

f : A ⟶ A and A = R - {8/5}

f(x) = [(8x + 3)/(5x - 8)]

Let x1, x2 be any two elements of set A, such that

f(x1) = f(x2)

[(8x1 + 3)/(5x1 - 8)] = [(8x2 + 3)/(5x2 - 8)]

= 40x1x2 - 64x1 + 15x2 - 24 = 40x1x2 + 15x1 - 64x2 - 24

15x2 + 64x2 = 15x1 + 64x1

79x1 = 79x2

x2 = x1

Thus, f is one-one, for all x1, x2 ∈ A.

Let y be an arbitrary element of A, then

f(x) = y

[(8x + 3)/(5x - 8)] = y

8x + 3 = 5xy - 8y

8x - 5xy = -8y - 3

x(5y - 8) = 8y + 3

x = [(8y + 3)/(5y - 8)]

Clearly, x = [(8y + 3)/(5y - 8)] is a real number for all y ≠ 8/5.

⇒ Corresponding to each y ∈ A, there exists [(8y + 3)/(5y - 8)] ∈ A, such that f[(8y + 3)/(5y - 8)] = y

Thus, f is onto. Hence, f is one-one and onto.

Now,

x = [(8y + 3)/(5y - 8)]

⇒f-1(y) = [(8y + 3)/(5y - 8)] for all y ∈ R - {8/5}

2. Where can I get previous years Mathematics question papers for the ISC Class 12 board?

You can get these previous years Mathematics question papers for ISC by clicking here or just visit the official website of Vedantu or download its app from the Google Play Store and you can get a variety of study and learning materials for your exam preparations included with the previous question papers for mathematics for ISC board.

3. How can previous year question papers for Maths help me to attain good marks in the ISC board exams?

The subject Mathematics is all about practice and only by practicing it, you can attain good marks in this particular subject. Previous year's question papers contain not only the questions but the solutions as well so that you exactly know how to go about solving a particular question. You can understand where you are getting wrong and can correct yourself accordingly by referring to the answers which are already mentioned in the previous year's question paper.

3. Is it compulsory to solve the previous year questions before board exams?

It is always recommended to solve previous year's questions before the beginning of any exam to save yourself from the anxiety before the exams, and also to build confidence because now you are aware of the patterns or the type of questions that can be asked in your exam. The practice has made you so experienced that you know how to invest your time wisely during your exam.

5. Is the ISC exam tougher than ICSE?

ICSE exams are conducted for the students of the matriculation level and ISC exams are conducted for the ones of the intermediary levels. So, yes, the ICSE exam is tougher than ISC. It requires double effort and understanding of the subjects. Though the subjects asked in the ICSE board are lesser than ISC but here, you can score well mainly because of the academic stream that you go for because you are interested in them.

6. Can I score well in mathematics in my board exams of Class 12?

You can always score excellent marks in mathematics but it all depends on the amount of practice that you put in this particular subject and also, it depends on the understanding that you have acquired so far in your previous classes. So always practice before your Maths exam, resolve any doubts that you have regarding any topic then and there. Last but not the least, try to develop an interest in this interesting subject by investing in it all around.