CSIR-UGC NET Question Paper for Mathematical Sciences

CSIR-UGC NET Math. Sciences QP, June 2012.pdf

Website List

1. gate.kinindia.com (For Gate Exam)

GATE Mathematics Previous Year Questions PDF Free Download

GATE 2014 Mathematics Question Papers Sample, Model & Previous Year Questions PDF Free Download

GATE 2014 Question Paper for Mathematics: The GATE exams will be conducted by the IIT every year. Many candidates will be writing this exam for purpose of seeking a PG course. Through GATE exam it is possible to apply for govt jobs also. Those candidates who are writing for Mathematics exam can download the GATE exam mathematics question paper and solve it for gaining enough knowledge. Candidates scoring the high marks in the GATE exam will be given high preference. The GATE exam mathematics question paper is also available in pdf format also.

GATE Previous Year Question Papers for Mathematics

GATE question papers for maths is now available for download in the pdf format. Candidates who expect for scoring high marks need to work hard by solving GATE previous year question paper for mathematics. We have attached the links of various question paper of GATE 2014 Mathematics so that candidates can download it and get benefited.

• Download GATE 2013 Mathematics Question Paper

• Download GATE 2012 Mathematics Question paper

• Download GATE 2011 Question paper for Maths

• Download GATE 2010 Maths Question paper

• GATE 2009 Maths Previous Year Question paper Download

• GATE 2008 Maths Previous Year paper

• GATE Maths Question paper 2007 Download

SOLVING QUADRATIC EQUATIONS

Note:

• A quadratic equation is a polynomial equation of degree 2.
• The ''U'' shaped graph of a quadratic is called a parabola.
• A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
• There are several methods you can use to solve a quadratic equation.:
  1. Factoring
  2. Completing the Square
  3. Quadratic Formula
  4. Graphing
• All methods start with setting the equation equal to zero.

---

Solve for x in the following equation.
Example 2:
The equation is already equal to zero.




Method 1: Factoring
The left side of the equation is not easily factored, so we will not use this method.






Method 2: Completing the square

Subtract 3 from both sides of the equation.






Add to both sides of the equation:






Factor the left side and simplify the right side.






Take the square root of both sides of the equation.






Add to both sides of the equation.

and









Method 3: Quadratic Formula
The quadratic formula is
In the equation , a is the coefficient of the term, b is the coefficient of the x term, and c is the constant. Simply insert 1 for a, -5 for b, and 3 for c in the quadratic formula and simplify
.

and










Method 4: Graphing
Graph y= the left side of the equation or and graph y= the right side of the equation or y=0. The graph of y=0 is nothing more than the x-axis. So what you will be looking for is where the graph of crosses the x-axis. Another way of saying this is that the x-intercepts are the solutions to this equation. The x-intercepts are 4.30277563773 and
The exact answers are and The approximate answers are 4.30277563773 and



Check these answers in the original equation.

Check the solution x=4.30277563773 by substituting 4.30277563773 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:
• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 4.30277563773 for x, then x=4.30277563773 is a solution.




Check the solution x=0.697224362268 by substituting 0.697224362268 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:
• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 0.697224362268 for x, then x=0.697224362268 is a solution.



The solutions to the equation are and rounded to 4.30277563773 and 0.697224362268








Comment: You can use the solutions to factor the original equation.

For example, since , then , and
Since , then , and
Since the product and , then we can say that This means that and
are factors of