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CHAPTER 10
VECTORS
POINTS TO REMEMBER
A quantity that has magnitude as well as direction is called a vector. It
is denoted by a directed line segment.
Two or more vectors which are parallel to same line ar
Class X
Chapter 1 Real Numbers
Maths
Exercise 1.1
Question 1:
Use Euclids division algorithm to find the HCF of:
Answer:
(i) 135 and 225
Since 225 > 135, we apply the division lemma to 225 and 135 to
obtain
225 = 135 1 + 90
Since remainder 90 0, we apply
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CHAPTER 9
DIFFERENTIAL EQUATIONS
POINTS TO REMEMBER
Differential Equation : Equation containing derivatives of a dependant
variable with respect to an independent variable is called differential
equation.
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CHAPTER 11
THREE DIMENSIONAL GEOMETRY
POINTS TO REMEMBER
Distance between points P(x1, y1, z1) and Q(x2, y2, z2) is
PQ
(i)
x 2
x 1
2
y 2 y 1
2
2
z 2 z 1 .
The coordinates of point R which divides line
Class X
Chapter 4 Quadratic Equations
Maths
Exercise 4.1
Question 1:
Check whether the following are quadratic equations:
Answer:
It is of the form
.
Hence, the given equation is a quadratic equation.
It is of the form
.
Hence, the given equation is a qua
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CHAPTER 8
APPLICATIONS OF INTEGRALS
POINTS TO REMEMBER
AREA OF BOUNDED REGION
Area bounded by the curve y = f(x), the x axis and between the ordinates,
x = a and x = b is given by
b
Area =
f x dx
a
y
y
y
Class X
Chapter 3 Pair of Linear Equations in Two Variables
Maths
Exercise 3.1
Question 1:
Aftab tells his daughter, Seven years ago, I was seven times as old as you were
then. Also, three years from now, I shall be three times as old as you will be. (Isn
Class X
Chapter 2 Polynomials
Maths
Exercise 2.1
Question 1:
The graphs of y = p(x) are given in following figure, for some
polynomials p(x). Find the number of zeroes of p(x), in each case.
(i)
(ii)
(iii)
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CHAPTER 12
LINEAR PROGRAMMING
POINTS TO REMEMBER
Linear programming is the process used to obtain minimum or maximum
value of the linear objective function under known linear constraints.
Objective Functio