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Common Errors in Class 12 Mathematics
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COMMON ERRORS DONE BY STUDENTS
Chapter 1
Relations and Functions
Let A = { 1, 2, 3}. Check whether R = { (1, 2), (2, 1), (1, 1), (1, 3)} is symmetric or not.
Common Error : Here, (1, 2) ∈ R , (2,1) ∈ R. So, it is symmetric.
If A = {1, 2, 3}, check whether R = {(1, 1), (1, 2), (2, 1)} is transitive or not.
Common Error : (1,2) ∈ R , (2,1) ∈ R ⇒ that (1,1) ∈ R. So it is transitive.
Show that relation R in the set A ={1, 2, 3, 4, 5 } given by R = {(a, b) : |a - b| is even }, is an equivalence relation.
Common Error : Student forget to write ± while proving transitive
Chapter - 2
INVERSE TRIGONOMETRIC FUNCTIONS
Functions |
Domain (Value of
x) |
Range
(Principal Value Branch) (Value of
y) |
\[y=sin^{-1}x\] |
\[[-1,1]\] |
\[\left
[ -\frac{\pi }{2},\frac{\pi }{2} \right ]\] |
\[y=cos^{-1}x\] |
\[[-1,1]\] |
\[[0,\pi
]\] |
\[y=tan^{-1}x\] |
\[R\] |
\[\left
(-\frac{\pi }{2},\frac{\pi }{2} \right )\] |
\[y=cot^{-1}x\] |
\[R\] |
\[(0,\pi
)\] |
\[y=sec^{-1}x\] |
\[R-(-1,1)\] |
\[[0,\pi
]-\left \{ \frac{\pi }{2} \right \}\] |
\[y=cosec^{-1}x\] |
\[R-(-1,1)\] |
\[\left
[ -\frac{\pi }{2},\frac{\pi }{2} \right ]-\left \{ 0 \right \}\] |
GENERAL DISCUSSION:-
S. No. |
Expression |
Substitution |
1 |
|
|
2 |
|
x = a tan Ó¨ or |
3 |
|
|
4 |
|
|
5 |
|
x = a cosec Ó¨ |
6 |
|
|
7 |
|
|
8 |
|
|
9 |
|
|
Chapter - 4
Determinants
Common error : Finding the adjoint of a matrix. Students find co-factors without taking proper sign
Students don't take the transpose of a matrix made from the co-factors.
Common Error:
-1(0-6)+4(0-1)=42)
It is wrong answer
Common Error : While using the matrix method of finding the area of triangle
Prove
that A2 - 5A + 7I = O, and hence find A-1
Common Error: For finding the value of A-1 , some students apply the formula
In this question using above formula is a wrong working
Remedy: Here first of all we prove that A2 - 5A + 7I = O
Now multiply on both side by A-1 we get
A-1 ( A2 - 5A + 7I) = A-1.O
(A-1A)A -5(A-1A) + 7 A-1I = O
IA - 5I + 7A-1 = O
Now we substitute the value of A and I to get A-1
Common Mistakes while solving the linear equations
Common Error: In this problem some of the students opts the following procedure
Chapter 5
Continuity and Differentiability
Common Error: Solving Implicit functions when y is a explicit function of x
Students should use chain rule here.
Common Error: Finding second derivative when parametric function is given
NCERT Book Page No. 192 Q. No. 17
Again differentiating w.r.t x we get
Putting this value above we get
Common Error: Improper use of log during logarithmic differentiation. Students generally use wrong log properties.
Chapter 6
Application of Derivatives
Common Error: Incorrect identifications of intervals after obtaining the critical points.
Common Error: Incorrect sign of f ' (x) to identify the increasing / decreasing functions.
Common Error: Incorrect factorization of an algebraic function to obtain the critical point.
Common Error: Finding intervals for Trigonometric Functions involving multiples and sub-multiples of angles.
Chapter 7
Integration
Common Error: Solving Definite Integral Problems by using Substitution Method.
While making the substitution students forget to change the limit and committed mistake
Remedy:
Common Error: Dropping the absolute value when integrating 
Common Error: In indefinite integral students forget to write constant.
Common Error: Some time students write more than one constants when they do integration of terms in one problem separately.
Chapter 9
Differential Equations
Common Error: In finding the degree of a differential equation when it is not defined.
Common Error: Difference between General solution and Particular solution .
Chapter 10
Vector Algebra
Common Error : Here students commonly use the following concept
Common Mistake : 
Common Error: Here students may use the concept 
Chapter 11
Three Dimensional Geometry
Common Mistake : Students start using the cartesian form of equation of line without converting them into standard form.
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