The topics like differential equations, quadratic equations, calculus are excessively used in the derivations and numericals of both Chemistry and Physics as well. In order to make the best use of these books, you need to solve all the problems at the end of every chapter. Thus, the merchant should stock 200 desktop models and 50 portable models to get the maximum profit of Rs 1150000. What, if it has 13 elements? Q18 :If and I is the identity matrix of order 2, show that Answer : Q19 :A trust fund has Rs 30,000 that must be invested in two different types of bonds. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. It covers all the important theorems and formulas with detailed explanations to promote a better conceptual understanding in students. Students must know the mathematics exam thoroughly to score well in the subject.
Determine the minimum cost of the mixture? Q9 :Find and , when Answer : The given matrix is Q10 : Express the following matrices as the sum of a symmetric and a skew symmetric matrix: i ii iii iv Answer : i Thus, is a symmetric matrix. Some of the other different types of solutions primarily deals with the majority of the different problems in Linear programming. All Inverse Trigonometric Functions Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Solving question papers on a regular basis provides an idea about the exam pattern and develop their speed and accuracy. Understanding maths will help students to squeeze conceptual meaning out of every problem quite effectively. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
Therefore, matrix 7X is also of the same order. Thus, is a skew-symmetric matrix. Thus, this determines the different chapters and topics in the syllabus. Hence, the possible orders of a matrix having 13 elements are 1 x 13 and 13 x 1. Question 9: A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Therefore, Xhas to be a 2 ×2 matrix. It also provides a good revision of previous exercises of Determinants.
Thus, to find all the possible orders of a matrix having 18 elements, we have to find all the ordered pairs of natural numbers whose product is 18. From the above given links a student can simply download and learn more about class 12 maths chapter 12. Here, Now, can be written as: Q18 : Find the values of Answer : Let. Two foods F1and F2 are available. Students are suggested to follow these resources on a regular basis to prepare effectively for their exam.
Then, the sum of money invested in the second bond will be Rs 30000 — x. The contains the various solutions for the subjects. Q14 :Find the value of is equal to A π B C D Answer Exercise 2. The are to know the type and pattern of the questions asked which are designed as per latest for the current academic session. In fact, Greeks were the first to recognize the fact that square root of a negative number does not exist in the real number system.
Other than given exercises, you should also practice all the solved examples given in the book to clear your concepts on Integrals. This topic also teaches students about the various constraints both mathematically as well as geometrically. A tennis racket takes 1. Each machine is available for at the most 4 hours on any day. This number is equal to the number of rows in matrix A. Answer : It is given that Aand B are symmetric matrices. Then, The correct answer is D.
Q20 :Find the values of is equal to Answer : Let. Answer : Comparing the corresponding elements of these two matrices, we get: Q13 :If , show that. In order to get inverse of these functions, we must restrict their domain and co-domain in such a way that they become one — one and onto and these restricted values are known as principle values. The resulting feasible region has points in common with the feasible region. The classical approach is given by Blaise Pascal and the axiomatic approach is given by a Russian mathematician A Kolmogorov in 1937. Finding area between two curves.
We have also provided solved examples at the end of every chapter to make concepts clear to our readers. Hence, if A is a symmetric or skew-symmetric matrix, then is a symmetric or skew-symmetric matrix accordingly. The students can use these solutions as guidelines to understand the concepts, the fundamental of these chapters and their applications for better board exam preparation. In the explanation of each chapter of class 12 maths, historical facts about chapters, main points of the chapter, assignments, chapter test, , etc. We will do the next level of statistics in chapter than whatever we have studied in classes 8, 9 and 10.
Thus, is a skew-symmetric matrix. Q21 :Assume X, Y, Z, W and P are matrices of order , and respectively. It also lays a foundation for Physics and Chemistry. Q13 : Find the inverse of each of the matrices, if it exists. Solution: Let, the diet contain x units of food F 1 and y units of food F 2. One is inductive reasoning which is studied in chapter 4 — mathematical induction and the other is deductive reasoning which we intend to study in this chapter.