CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.1 Question 1
1. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
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CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.1 Question 1
1. In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Question 5
5. Is it possible to design a rectangular park of perimeter
metres and area
. If so, find its length and breadth.
Solution:
Let length of park =
metres
We are given area of rectangular park =
Therefore, breadth of park =
metres {Area of rectangle = length
}
Perimeter of rectangular park =
metres
We are given perimeter of rectangle =
metres
Therefore, we can write
Comparing equation,
with general quadratic equation
, we get
and
.
Discriminant is equal to 0. Therefore, two roots of equation are real and equal which means that it is possible to design a rectangular park of perimeter 80 metres and area
.
Using quadratic formula
to solve equation, we get
Here, both the roots are equal to
.
Therefore, length of rectangular park =
metres
Breadth of rectangular park =
metres
Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q4 Download this solution
4. Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q3 Download this solution
3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800
. If so, find its length and breadth.
Nature of Roots of Quadratic Equation:
CBSE Ncert Solutions Chapter 4 Quadratic Equations Exercise 4.4 Q2 Download this solution
2. Find the value of k for each of the following quadratic equations, so that they have two equal roots.
(i)
(ii)