Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Maths Quiz Questions with Answers

Question Bank for Quiz competition for 9th and 10th standard

Maths Quiz Questions with Answers. Let us answer here some of the quizzes which are based on the basic concepts and formulas of classes 7th , 8th , 9th and 10th  concepts.

Mathematics Quiz Questions with Answers

LEVEL – 1

Question: 1

Define fundamental theorem  of arithmetic.

Ans : Every composite number can be expressed as the product of primes and this factorization is unique irrespective of order of factors.

Question: 2

What is the largest prime number of two digit.    

Ans : 97

Question: 3

How many times can you subtract 100 from 2000.

Ans : Only Once

Question: 4

Out of following   -1, 0 & 1, which are integers?  

Ans : All of these

Question: 5

A person has 4 sons. If each brother has one sister, then how many children are there?

Ans : 5

Question: 6

What is the condition of the denominator of a rational decimal .   

Ans : 2x 5n

Question: 7

What are irrational decimals.

Ans : Non-terminating and non-recurring decimals are called rational decimals.

Question: 8

Define   co-prime number, give any example?     

Ans : When HCF of two numbers is 1, then numbers are called co-prime numbers. For Example  5, 6

Question: 9

What is the value of  50 + 50/100              

Ans : 50.5

Question: 10

Define Rational Number.

Ans : The numbers which can be put in the form of p/q (q ≠ 0) are called rational numbers.

Question: 11

Define prime numbers.       

Ans : The numbers which have only two factors are called prime numbers. 2 is the smallest prime number and is the only even prime.

Question: 12

What is the smallest odd composite number.   

Ans : 9

Question: 13

Product of two number is 1800 if LCM of two number is 180 then what is its H.C.F. 

Ans : 10

Question: 14

Who many prime numbers are there in the counting from 1 to hundred

Ans : 25

Question: 15

What is the area of trapezium whose sum of parallel sides is 17 cm and height of trapezium is 4 cm.

Ans : 34 cm2

Question: 16

What is the total surface area of cylinder whose radius is 2cm and height is 5 cm. 

Ans : 88 cm2

Question: 17

What is the  diagonal of cube of side 3 cm. \[Ans:3\sqrt{3}\; cm\]

Question: 18

Expand the identity:-    a- b3

Ans : (a - b)(a2  +  b2  +  ab)

Question: 19

What is the area of circle of radius 7 cm 

Ans : 154 cm2

Question: 20

What is  the diagonal of cuboid of dimension 4 cm, 3 cm, 2 cm  \[Ans:\sqrt{29}\]


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LEVEL - 2

Question:  1

Using suitable identity find the value of:-     (6)+ (5)+ ( - 11)

Ans : -990

Question:  2

What is the smallest no. of three digits which is divisible by  11.  

Ans : 110

Question:  3

Expand the identity:-    a+ b3                      

Ans : (a + b)(a2 + b2 – ab)

Question:  4

What is the common formula used for finding the area of square and rhombus.

Ans : \[\frac{1}{2}(d_{1}\times d_{2})\]

Question:  5

What is the sum of all exterior angles of a regular hexagon (or polygon).

Ans : 360o

Question:  6

What is measure of each interior angle of regular hexagon. 

Ans : [120o] \[\frac{(n-2)}{n}\times 180\]

Question:  7

What we call the  point that lies on all the diameters of the circle. 

Ans : Centre of the circle

Question:  8

What is the probability of getting a spade or 10 in a deck of 52 playing cards.

Ans : 16/52

Question:  9

What is the sum of all interior angles of a regular heptagon  (side 7)

Ans : (n - 2) x 180 = 900o (here n = 7)

Question:  10

Find the class mark of the class interval    156 – 188 

Ans : 172

Question:  11

Find the class size of the class interval    156 – 188 

Ans : 32

Question:  12

How many diagonals an octagon can have ? 

Ans : [20] Formula used is given below \[\frac{n(n-1)}{2}-n\:\:or\: \:^{n}C_{r}-n\]

Question:  13

Expand the identity:-    a+ b+ c- 3abc  

Ans : (a + b + c)(a2 + b2 + c2 – ab – bc - ca)

Question:  14

What is the formula of finding mode of the grouped data. 

Ans : \[l+\left (\frac{\frac{n}{2}-c_{f}}{f} \right )\times h\]

Question:  15

What is the probability of finding at least  two tails when three coins are tossed.

Ans : 4/8 or 1/ 2

Question:  16

What angle is the  50 %  of its complementary.

Ans : 30o

Question:  17

What is the probability of getting face card or ace card.

Ans : 16/52

Question:  18

What is the special name of the quadrilateral whose all sides are equal but diagonals are not equal.  

Ans : Rhombus

Question:  19

Define Altitude of the triangles.

Ans : It is the line segment from the vertex of a tringle and is perpendicular to the opposite side.

Question:  20

What is the probability of getting a queen or a black card in a deck of 52 playing cards. 

Ans : 28/52

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LEVEL - 3

Question:  1

What  is the supplement angle of  35o

Ans : 145

Question:  2

In which ratio the centroid divide the median.  

Ans : 2 : 1

Question:  3

Define Pythagoras theorem.

Ans : (Hypotenuse)2 = (Base)2 + (Perpendicular)2

Question:  4

What is the special name of the quadrilateral whose opposite sides are equal but diagonals are not equal. 

Ans : Parallelogram

Question:  5

Convert  2,00,000 m2 in hectare.

Ans : 20 Ha

Question:  6

What is the special name of the quadrilateral whose opposite sides are equal and   diagonals are also equal. 

Ans : Rectangle

Question:  7

How many cm are there in 1KM.   

Ans : 1 Lakh

Question:  8

How many litres are there in 1m3  

Ans : 1000 litre

Question:  9

What are the possible outcomes when three coins are thrown.

Ans : 8
Question: 10
How many congruency conditions are there and what are these.
Ans : SSS, SAS, ASA, AAS, RHS
Question: 11
What is the measure of the angle in the semi circle.
Ans : Right angle
Question: 12
What is the special name of the quadrilateral whose all sides are equal and diagonals are also equal.
Ans : Square

Question:  13

What is the difference between square and rhombus.

Ans : All angles of a square are = 90o but not in rhombus. Diagonals of a rhombus are equal but not in rhombus.

Question: 14
What is the Formula of finding the compound interest.
Ans : \[CI=P\left [ \left (1+\frac{R}{100} \right )^{t} -1\right ]\]
Question: 15
What is the empirical formula relating mean, mode median
Ans : mode = 3median - 2mean
Question: 16
Define reflex angle.
Ans : 180o < Reflex Angle < 360o
Question: 17
Side of an equilateral triangle is 18cm. what is its area.
 Ans : \[81\sqrt{3}\]
Question: 18
Side of square is 35cm. What is its area.
 Ans : 1225
Question: 19
What is 539 x 1001
Ans : 539539
Question: 20
What is the complementary angle of 59o

Ans : 31

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LEVEL - 4

Question:  1

How many faces are the in triangular prism  

Ans : 5

Question:  2

How many faces are there in square pyramid 

Ans : 5

Question:  3

Funny question with logic

Take last digit of your mobile number then follow these steps

Take last digit of mobile number   Find its square     Add 5    Multiply by 50     add 1768     Minus year of your birth    we get a three digit number  and we get the following result.                                   

First digit is your mobile number and last two digit is your age.

Question:  4

What is the volume of hemi- sphere of radius 7cm.     

Ans : \[\frac{380}{3},\left [ \frac{2}{3}\pi r^{3} \right ]\]

Question:  5

What is the difference between  a Rational number and a Fractional Number

Ans :  Rational number is the ratio of two integers with denominator  0

Fraction is the ratio of two natural numbers. In other words Positive rational numbers are called Fractions.

Question:  6

What are rational decimal.

Ans : Terminating or non terminating but repeating decimals are called rational decimals.

Question:  7

How  we find the median from the graph of frequency ogive.

Ans : Value on the x-axis corresponding to the value n/2 on the y-axis

Question:  8

Define median.

Ans : The line segment which join the vertex of the triangle with the mid-point of the opposite side is called median

Question:  9

Define centroid of the triangle.

Ans : Point of concurrence of medians of triangle is called centroid of triangle

Question:  10

What is the angle made by minute hand in 30 minutes.           

Ans : 30 x 6 = 180o

Question:  11

What is the area of quadrant.      

Ans : \[\frac{1}{4}\pi r^{2}\]

Question:  12

What is the perimeter of semi-circle            

Ans : \[\pi r+2r\]

Question:  13

Area of sector of the circle.         

Ans : \[\frac{\theta }{360}\pi r^{2}\]

Question:  14

Area of the segment of the circle.                

Ans : \[\frac{\theta }{360}\pi r^{2}-\frac{1}{2} r^{2}sin\theta\]

Question:  15

Angle made by hour hand in one minute .   

Ans : \[\left ( \frac{1}{2} \right )^{o}\]

Question:  16

Area of regular hexagon             

Ans : \[6\times \frac{\sqrt{3}}{4}(side)^{2}\]

Question:  17

Three points are collinear if  

Ans : Area of triangle  = 0

Question:  18

What is the value of      

Ans:   

Question:  19

When three coins are tossed then what is the P(At least one head)  

Ans : 7/8 

Question:  20

What is the class size of the interval   31.5 – 55.5      

Ans : 24


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LEVEL - 5

Question:  1

What is the formula of finding the mean by step deviation method.

Ans:   

Question:  2

What is the formula of finding mode. 

Ans:  

Question:  3

Less than type and more than type ogive meet each other at (22, 48). What is the median of the data.      

  Ans  [22]

Question:  4

Area of triangle is 625 cm2 and its perimeter is 20cm. Find the radius of the in-circle.                                     

  Ans  [62.5 cm] Formula used is given below

Question:  5

What is the probability of finding 53 Monday in a leap year.              

Ans  [2/7]

Question:  6

What is the probability of finding 53 Friday in a non-leap year.  

Ans [1/7]

Question:  7

What is the probability of finding a doublet in two tosses of a coin.   

 Ans [6/36]

Question:  8

How many tangents a circle can have. 

Ans [Infinitely many]

Question: 9 How may parallel tangents a circle can have.     

  Ans [Two]

Question:  10

What is the maximum number of tangents through a line can pass.            

 Ans [3]

Question:  11

How many circles can be drawn passing through three non – collinear points.    

 Ans [only one]

Question:  12

Angle made by an arc at the centre of the circle is 160o. What is the measure of angle made by the same arc in the remaining part of the circle.                               

Ans [80o]

Question:  13

At what temperature both Celsius scale Fahrenheit scale shows same reading.          

Ans [At - 40o]

Question:  14

 If the graph of two lines intersect each other then what is the number of solutions.

 Ans [Unique solution]

Question:  15

What is the quadratic formula of solving the quadratic equation. \[ \left [x=\frac{-b\pm \sqrt{D}}{2a} \right ]\]

Question:  16

Formula of finding the nth term from the end of the AP sequence.\[ \left [l-(n-1)d \right ]\]

Question:  17

Formula of finding the coordinates of a point by using section formula .\[ \left [\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right ]\] 

Question:  18

Formula of finding the sum last n terms of an AP. \[ \left [S_{n}=\frac{n}{2}\left [ 2l-(n-1)d \right ] \right ]\]

Question:  19

 Formula of finding the centroid of the triangle.  \[ \left [\frac{x_{1}+x_{2} +x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3} \right ]\]

Question:  20

 If selling price of 5 pens is equal to the cost price of 4 pens, then what is the gain or loss %    

LEVEL - 6

Question:  1

The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

Ans 45.03 m2

Question:  2

A car covers a distance of 200 km in 2h 40 minutes. Whereas a jeep covers the same distance in 2 hours. What is the ratio of their speed ?

Question:  3

Twenty women can do a work in 16 days and 16 men can complete the same work in 15 days. What is the ratio between the capacity of a man and a woman?  

Ans  4 : 3

Question:  4

A man walking at the rate of 3km/h crosses a square field diagonally in two minutes. What is the area of the square field ? 

Ans 5000 m2

Question:  5

If a square is inscribed in a circle, find the ratio of area of the circle and the square.  \[Ans \pi :2\]

Question:  6

If the area of a circle is diminished by 10 % then what is the decrease in the area? 

Ans  13 %

Question:  7

Count the number rectangles   

Ans 10 rectangles

Question:  8

Count the number of circles    

Ans 12 Circles

Question:  9

Count the number of squares.    

Ans 14 Squares

Question:  10

Count the number of circles.   

Ans : 7 Circles

Question:  11

How many hectometers  are there in 5 decimetre? 

Ans 0.005

Question:  12

How many centigrams are there in 0.02 decagrams?    

Ans 20 centigrams

Question:  13

How many hectoliters are there in 3 centilitres?   

Ans 0.0003 hectolitres

Question:  14

How many milligrams are there in 15 decagrams  ?

Ans 150000 milligrams

Question:  15

In the following equation find the value of a.\[\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}\]   Ans  -4     

Question:  16

\[If\; \; x^{3}+\frac{1}{x^{3}}=110,\; then\; \\ find\; \; x + \frac{1}{x}\] Ans 5

Question:  17

Find the factors of   x2 – 1 – 2a – a2    

Ans (x + a + 1)(x – a - 1)

Question:  18

What is the length of the rectangular park of area 800 m sq., whose length is twice its breadth? 

Ans 40

Question:  19

What is the next term of the sequence: 3,6,9,36,27,216, 81, ____ 

Ans 1293

Question:  20

What is the next term of the sequence: 1,6,11,18, _____ 

Ans 27

Question:  21

What is the next term of the sequence: 8,9,17,26,43, _____

Ans 69

Question:  22

Write the term in the blank space of : 4,9,19,34,54, ____, 109           

Ans 79

 


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