STRATEGIES & TRICKS

FOR
MENTAL MATHS
QUIZ
COMPETITION
2
BY : (SHA) NK VOHRA
M : (9810663810)(9810663816)  9
It is a process of working
out Maths calculations
and carrying out problem-
solving mentally, without
going through entire
physical or formal written
process.
• To sharpen their calculation skills.
• To prepare students for various competitive
examinations such as CUET, CET, SSC, JEE
etc.
• To make learning of Mathematics joyful
& interesting.
 To develop quantitative and analytical skills among the
students..
students
 To stimulate the brain and boost learning Capabilities of
the students.
students.
 To inculcate better observation skills
skills..
 To correlate Mathematics with real life.
life.
 To increase concentration, confidence and self esteem of
the students.
students.
 MENTAL MATHS QUIZ COMPETITION

There will be 2 rounds

From School level to Zonal level
Calculation round : 3 Questions for each team
Visual round : 3 Questions for each team

For District level

Calculation round : 4 Questions for each team
Visual round : 4 Questions for each team
 MENTAL MATHS QUIZ COMPETITION

Calculation Round : 4 Questions for each team.

Visual Round : 4 Questions for each team.

Rapid Fire Round

3 Questions to be answered by each student
in 20 seconds.
 Time allotted

Main Question : 20 seconds

Pass Over Question : 10 seconds

Marks allotted

Main Question : 2 marks

Pass Over Question : 1 mark

Individual student is selected up to
Regional Level MMQC.

Marks will be awarded, only if the answer

given is in the lowest / standard form and
with proper units (wherever required).
• Time will be started after reading the
Question in any one language.

• If the first answer is correct then the

participant giving the right answer will be
awarded 2 Marks and no other participant
will be given chance thereafter.
Exact questions from Mental Maths
Question Banks are not to be asked in
the Mental Maths Quiz Competitions.
Multiple Choice Questions, True/False,
Yes/ No, definition Type and multiple
answer questions are not asked at any
level in MMQC.
 LEVEL – IV

CLASSES: XI & XII

NOTE: STUDENTS HAVE TO
GIVE THE CORRECT ANSWER
TO EACH QUESTION WITHIN
20 SECONDS WITHOUT
USING PEN & PAPER

नोट: छा ों को पेन और पे पर
का उपयोग िकए िबना 20
से कंड के भीतर ेक का
सही उ र दे ना होगा।
 A

CALCULATION
M

ROUND
H
 RELATIONS
If the Number of reflexive relations on A is 'p'
p
where A = {d, o, e}, then find the value of .
8
If the Number of symmetric relations on A is 2q
where A = {m, a, t, h, s}, then find the value of q.
How many equivalence relations are possible on set A where
(i ) A  {1}
(ii ) A  {a, b}
(iii) A  { p, q, r}
 IMPORTANT POINTS
If number of elements in the set A are 'n' then
n2
Number of Relations on A  2
n2  n
Number of REFLEXIVE Relations on A  2
n ( n 1)
Number of SYMMETRIC Relations on A  2 2

For Number of Equivalence Relations on A

Remember Bell Numbers 1, 1, 2, 5, 15, 52...
 RELATIONS

Let R be the smallest Equivalence relation on

A ={3, 4, 6, 9}. Find the cardinality of R.

Let R be the Largest Equivalence relation on

A  {x : x 2  x, x  W }. Find the cardinality of R.

Let R be a relation on A ={1,2,3}.

If m & n be the number of elements in Smallest & Largest
Equivalence Relation on A respectively,then find (m + n).
 FUNCTIONS
Find the value of ( y1  y2  y3 ) such that
f :{1, 2,3}  {5, 6,7} where f = {(3,y1 ), (1,y2 ),(2, y3 )}
is an Injective function.

Find the value of 'p' so that f ( x) is a Surjective function.

where f :[0, )  [ p, ), f ( x)  x 2 +2

Find the value of (a  b) such that f ( x ) is a Surjective function

where f : R  [a, b], f ( x)  sin x  cos x.
INVERSE TRIGONOMETRIC FUNCTIONS
If sin 1 a  sin 1 b   , then find the value of (a  b  ab).

 2023 
1 1 
If sin    sec x  , then find the value of
 2024  2
(2023x  2022).

If the domain of f ( x )  cos1 (2 x ) is [a, b], then find

the value of (b  a)3 .
 MATRICES
 1 y 1 z  2 
 
If A   a 2 x  5  is a diagonal Matrix then
b c 3 

find the value of ( xyz  abc).

x a b 
 
If A   0 2 y c  is a scalar Matrix then
 0 0 10 
 
find the value of ( xy  ab  bc  ca).
 DETERMINANTS
1 0 0
 
If A   0 2 0  then | 6 A1 | .
 0 0 3
 

1 0 0 
 
If adjA   0 2 0  then find the value of | A | .NOTE:(|A| < 0)
 0 0 50 
 

 0 1 3 
 
If A   1 0 5  then find the value of | 2 AT | .
 3 5 0 
 
CONTINUITY & DIFFERENTIABILITY
If y | x  1|  | x  2 |  | x  3 | is non-differentiable
at 'n' number of points then find the vaue of nn .

2 tan x 
Find the derivative of y  at x  .
1  tan x
2
4

x d2y
If y  e  e ,then find k such that
x
2
 ky.
dx
 APPLICATIONS OF DERIVATIVES

Out of the following functions, how many functions

are increasing for all values of x  R.
f1 ( x)  x3
f 2 ( x)   x3
f3 ( x)  7  x
f 4 ( x)  2024 x  2023
f5 ( x)  sin x
 APPLICATIONS OF DERIVATIVES

A function f ( x) is defined for all values of x  R,

such that f '( x)  2( x 2  5 x  6)
Find the interval where function f ( x) is Decresing.

Let a function f ( x) is defined as f ( x )  x3 on [2, 2]

Find the absolute Maximum value of f ( x ).
 INTEGRATION
Find the value of f (0) such that

 ( sin x  cos x)dx  f ( x)  c

x
e
Find the value of (2a  3b) if


3 x 3 x
(e 2x
 e )dx  ae2x
 be c
2

  sin x  1) dx.
3
Find the value of ( x
2
 APPLICATION OF INTEGRALS

Find the value of I, where

1
I   12  x 2 dx.
1

Find the area bounded by the lines

x  y  2, x  0 & y  0 in first quadrant.
 DIFFERENTIAL EQUATIONS
Find the Product of order & degree of
5 3
 dy  d y 2
the differential equation    y   2 
 dx   dx 
Find the integrating factor of the differential equation
dy
x yx
dx
If y  f ( x) is the solution of the differential equation
dy
 2, where f (0)  0 then what will be the value of f (5).
dx
 VECTORS
 2  
Find | a  b | , where a  i  j and b  j  k .

   
Find | a  b |, where a  i  0 j +0k and b  0i  2 j +0k .
  

 
Find the projection of a on b, where
 
a  2i  5j and b  3j  4k .
 THREE DIMENSIONAL GEOMETRY
Find the direction cosines of the line

r  (i  j )+ (3 j  4k ).

If  l , m, n  represents the direction cosines of the line

x 1 y 3  z
  , then find the value of (2l 2  2m2  2n 2 ).
1 2 2

Find the value of p, if following lines are parallel to each other.

x 1 y 3  z x y z
  and   .
1 2 3 2 4 p
LINEAR PROGRAMING PROBLEM
The corner point of the feasible region
determined by the system of linear constraints
are  0, 0  ,  0, 40  ,  20, 40  ,  60, 20  ,  60, 0  .
The objective function is Z  x  y.
Find the Maximum value of Z.
Corner points of the feasible region determined by the
system of linear constraints are  0, 3 , 1, 1 and  3, 0  .
Let Z  px  qy, where p, q  0.
If the minimum of Z occurs at  3, 0  and 1, 1 then
q
find the value of .
p
 PROBABILITY
If A & B are Independent Events such that P(A) = 0.2
 A
and P(B) = 0.3, then Find the value of P   .
B
If A & B are Mutually Exclusive events such that P(A) = 0.3
 A 
and P(B) = 0.2, then Find the value of P  .
 A B 
If X is a ran d o m V ariab le s u ch th at
 0 .1, w h en x  1 o r 2
 0 .2, w h e n x  3 o r 4

P ( X  x)  
 k , w h en x  5
 0, o th erw ise
F in d th e va lu e o f k o r P ( x  2 ) o r P ( x  ev en ).
M A VISUAL
T
H ROUND
 FUNCTIONS

The Arrow diagram of a function

f : A  B is shown below. Find the total number of injective
functions from set A to B.

Find the total number of Surjective

functions from set A to B.

FIGURE
 FUNCTIONS

The Arrow diagram of a function

f : P  Q is shown below.
Find the total number of functions
which are Injective & Surjective
Both (Bijective functions) from
set P to set Q.

FIGURE
 INVERSE TRIGONOMETRIC FUNCTIONS
The graph of an Inverse Trigonometric
function f ( x) is shown below: 1
Find the value of f ( ).
2

x
Find the Domain of f ( ).
2


If f ( x)  , then find the value of x.
3

FIGURE
 MATRICES & DETERMINANTS

 1 2  0 0 2 
If (A) ab   &
 0 1  0 1 0  Find the Area of the
rectangle.
OR
Find the perimeter of the

a cm
rectangle.

b cm
FIGURE
 MATRICES & DETERMINANTS

 1 2 3
 
If A  (aij )33   4 5 6
7 8 9
 33

Find the Area of the

a13 cm a21 cm Triangle.

a22 cm
FIGURE
 MATRICES & DETERMINANTS

 2 59 
If A   
 0 1 22

Find the Volume of

| AT | cm
the cuboid.
| A2 | cm
| A | cm

FIGURE
 CONTINUITY & DIFFERENTIABILITY
The graph of a function f ( x )
is as follows:
Find the Value of
(i) f '(1.5)
(ii) f (2.5)  f '(2.5).

FIGURE
 CONTINUITY & DIFFERENTIABILITY
The graph of a function f ( x )
defined on [1, 3] is as follows:
Find the number of integral
points where f ( x) is
differentiable.

FIGURE
 APPLICATION OF DERIVATIVES
The graph showing variation of
Temperature with time shown below :

Find the rate of change of

Temperature with time t.

FIGURE
 INTEGRATION
The graph of a trigonometric function
f(x) is shown below :

2
Find the value of  F ( x)dx,
0

d(f(x))
where  F ( x).
dx

FIGURE
 APPLICATION OF INTEGRAL

The graph of a function f(x) is

shown below : 0
Find the value of  f ( x) dx.
2

OR
0
Find the value of  f ( x) dx.
4

FIGURE
 DIFFERENTIAL EQUATION
The graph of a function y  f ( x) is
dy
shown below such that  2x
dx
Find the function y  f ( x).
OR
Find the value of f (1.1).

FIGURE
 VECTORS
On xy -plane,If O is the origin,
WE represent the x -axis &


NS represent the y -axis.

Find the AB.

FIGURE
 VECTORS
  
In the figure given below A, B & R
represents the sides of a triangle such that
 


A  i  2 j & B  i  k
 

Find | R | .

FIGURE
 THREE-DIMENSIONAL GEOMETRY

It is given that, l1||l2

xa y b z c
Equation of line TP is  
2 1 k Find the value of k.
OR
Find the direction ratio's of line l2
OR
Find the direction cosines of line l2 .
x y 1 z  5
l1 :  
1 2 2
FIGURE
 THREE-DIMENSIONAL GEOMETRY

OP  xi  y j  zk in space represented

by figure below,such that |OP| = 2 2 units
Find the value of y.
OR
Find the value of x  z.
OR
Find the value of (x2  y 2  z 2 ).
x y 1 z  5
l1 :  
1 2 2
FIGURE
 LINEAR PROGRAMIMG PROBLEM
It is given that shaded region
A B C D as the f e as ibl e re gion
O b jec t i v e fu n ction, Z  2 x  y Find the value of Zmaximum .
OR
Find the value of Zminimum .
OR
Find the value of ZA  ZC .

FIGURE
 PROBABILITY

U
 A
Find the value of P   .
B
OR
 A
Find the value of P   .
B

FIGURE
 A

CALCULATION
M

ROUND
H
 SETS
For set A = {b, h, a, r, t}, Find the number of
(i) subset
(ii) Non-empty subsets
(iii) proper subsets
(iv) non-empty proper subsets.

Find the cardinality of the set B where

B  {x : x  5 | x | 6  0, x  R}
2
 RELATIONS & FUNCTIONS

If A = {0,1}, B = {2,3,4}, then find the number of

(a ) subsets of A  B
(b) subsets of A  A
(c) Relations from A to B
(d) Non-empty Relations from A to B
(e) Functions from A to B
 RELATIONS & FUNCTIONS
sgn(0.213)  sgn(9898)
What is the value of
[ 71]
where symbols have their usual meaning.

If the domain of f(x) = x   x is set D,

then What is the cardinality of Set D.
 TRIGONOMETRIC FUNCTIONS

2 tan150
What is the value of .
1  tan 15
2 0

What is the value of (4sin 15  3sin15 ) .

3 0 0 2

3
If p  sin( )  cos(2 ), then what is the
2
value of 0.99 p  0.01.
 COMPLEX NUMBERS

If (1  i )4  a  ib, then find the value of (b  a ).

1  2i
If Z  , then find the value of | Z | .
2  i

If Z   2  i 3, then find the value of Z .Z .

 LINEAR INEQUALITIES
Find the number of integral solutions for the
inequality | x  2 | 3.

2
Find the solution set of the inequality  0.
x

If solution set of the inequalities 2 x  10,  x  1

is [ a, b], then find the value of b  a.
 PERMUATIONS & COMBINATIONS

Find the value of t where,

15
P3  t  15C12  .

Find the number of diagonals in a hexagon.

C2  9C3
9
Find the value of ( 10 ).
C7
 BINOMIAL THEOREM
Find the number of term(s) in the expansion of
(i) (2 x  3 y )12
(ii) (2 x  3 y )12 + (2 x  3 y )12
(iii ) (2 x  3 y )12  (2 x  3 y )12
(iv) (2  3)10

Find the number of terms in the expansion of (a  b  c)9 .

If the middle term in the expansion of (1  x) is Ca .x ,

8 8 a

then find the value of a.

 SEQUENCE & SERIES

1 1 1
  .....
Find the value of 4 4 8 16
.

If 4, 2k , m are in A.P. as well as G.P. then find

the value of (m  k ).
 STRAIGHT LINE
If the slope of a line L,which is perpendicular to
the line x  2 y  0.123456, is 'm' then find the
value of (m  4).

If three non-zero numbers m, n, p are in A.P.

then find a point P through which line
mx  ny  p  0 always passes.
M A VISUAL
T
H ROUND
 SETS

Find the value of

n( A  B)  n( B  C)  n(C  A).
OR
If (A  B)' ={x, y, z}, then find the
value of x  y  z.

FIGURE
 RELATIONS & FUNCTIONS

A function f ( x ) is defined on R.
The part of graph of a function
Find the value of f ( 4.999999).
f ( x) is shown below:
OR
Find the set of all possible values of x
satisfying f ( x)  2.
OR
Find the value of f ( 2 ).

FIGURE
 TRIGONOMETRY

Find the coordinates of Q if x   .

Find the Radian measure of angle x

1 1
when Q ( , ).
2 2

FIGURE
 COMPLEX NUMBERS

A complex num ber Z is shown on

Argand Plane.
Find the distance of Z from
the origin.
OR
Find the sum of coordinates
of the mirror image of Z
along Real axis.

FIGURE
 PERMUTATIONS & COMBINATIONS

In the given figure below,

L1  L 2  L 3 and L 4  L 5  L 6

Find the number of parallelogram

in the given figure.

FIGURE
 SEQUENCE & SERIES

Students of a school are standing

as shown in the figure given below:

Find the number of students

standing in Row 10.

FIGURE
 STRAIGHT LINES

Find the value of 3m if

slope of AB is m.
OR
Find the slope of a line L
which is perpendicular to AC.
OR
Find the slope of a line L
which is Parallel to BC.
FIGURE
 CONIC SECTIONS

Two concentric circles are shown as below:

Equation of Bigger circle is x 2  y 2  36.

Find the equation of

2m
C
smaller circle.

FIGURE
 THREE DIMENSIONAL GEOMETRY

A cuboid is drawn in first octant

with O as the origin and P(3, 4, 5).
(a) Find the coordinates of point Px .
(b) Find the distance of point P
from xy-plane.
(c) Find the distance of point P
from z  axis.

FIGURE
THANK YOU