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 cofactors without taking proper sign
Students don't take the transpose of a matrix made from the cofactors.
Common Error:
It is wrong answer
Common Error : While using the matrix method of finding the area of triangle
Prove that A^{2}  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 A^{2}  5A + 7I = O
Now multiply on both side by A^{1} we get
A^{1} ( A^{2}  5A + 7I) = A^{1}.O
(A^{1}A)A 5(A^{1}A) + 7 A^{1}I = 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 submultiples 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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