### 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 : 2m x 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:-    a3 - 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)3 + (5)3 + ( - 11)3  Ans : -990 Question:  2 What is the smallest no. of three digits which is divisible by  11.   Ans : 110 Question:  3 Expand the identity:-    a3 + 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:-    a3 + b3 + c3 - 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: 10How many congruency conditions are there and what are these. Ans : SSS, SAS, ASA, AAS, RHS Question: 11What 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 59oAns : 31

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 LEVEL - 4 Question:  1How many faces are the in triangular prism   Ans : 5 Question:  2How many faces are there in square pyramid  Ans : 5 Question:  3Funny 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:  4What is the volume of hemi- sphere of radius 7cm.      Ans : $\frac{380}{3},\left [ \frac{2}{3}\pi r^{3} \right ]$ Question:  5What 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:  6What are rational decimal. Ans : Terminating or non terminating but repeating decimals are called rational decimals. Question:  7How  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:  8Define median. Ans : The line segment which join the vertex of the triangle with the mid-point of the opposite side is called median Question:  9Define centroid of the triangle. Ans : Point of concurrence of medians of triangle is called centroid of triangle Question:  10What is the angle made by minute hand in 30 minutes.            Ans : 30 x 6 = 180o Question:  11What is the area of quadrant.       Ans : $\frac{1}{4}\pi r^{2}$ Question:  12What is the perimeter of semi-circle             Ans : $\pi r+2r$ Question:  13Area of sector of the circle.          Ans : $\frac{\theta }{360}\pi r^{2}$ Question:  14Area of the segment of the circle.                 Ans : $\frac{\theta }{360}\pi r^{2}-\frac{1}{2} r^{2}sin\theta$ Question:  15Angle made by hour hand in one minute .    Ans : $\left ( \frac{1}{2} \right )^{o}$ Question:  16Area of regular hexagon              Ans : $6\times \frac{\sqrt{3}}{4}(side)^{2}$ Question:  17Three points are collinear if   Ans : Area of triangle  = 0 Question:  18What is the value of   $\sqrt{63^{2}+63^{2}}$   Ans:   $63\sqrt{2}$ Question:  19When three coins are tossed then what is the P(At least one head)   Ans : 7/8 Question:  20What is the class size of the interval   31.5 – 55.5       Ans : 24

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 LEVEL - 5 Question:  1What is the formula of finding the mean by step deviation method.Ans:   $Mean(\bar{x})=a+\frac{\sum f_{i}u_{i}}{\sum f_{i}}$ Question:  2What is the formula of finding mode. Ans:  $Mode=l+\left (\frac{f_{1}-f_{2}}{2f_{1}-f_{2}-f_{0}} \right )\times h$ Question:  3Less than type and more than type ogive meet each other at (22, 48). What is the median of the data.         Ans  [22] Question:  4Area 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$\frac{Area \: of\: triangle}{Semi-perimeter}=Radius \; of\; incircle$ Question:  5What is the probability of finding 53 Monday in a leap year.               Ans  [2/7] Question:  6What is the probability of finding 53 Friday in a non-leap year.   Ans [1/7] Question:  7What is the probability of finding a doublet in two tosses of a coin.     Ans [6/36] Question:  8How many tangents a circle can have.  Ans [Infinitely many] Question: 9 How may parallel tangents a circle can have.        Ans [Two] Question:  10What is the maximum number of tangents through a line can pass.              Ans [3] Question:  11How many circles can be drawn passing through three non – collinear points.      Ans [only one] Question:  12Angle 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:  13At 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:  15What is the quadratic formula of solving the quadratic equation. $\left [x=\frac{-b\pm \sqrt{D}}{2a} \right ]$ Question:  16Formula of finding the nth term from the end of the AP sequence.$\left [l-(n-1)d \right ]$ Question:  17Formula 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:  18Formula 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:  1The 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:  2A 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:  3Twenty 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:  4A 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:  5If a square is inscribed in a circle, find the ratio of area of the circle and the square.  $Ans \pi :2$ Question:  6If the area of a circle is diminished by 10 % then what is the decrease in the area?  Ans  13 % Question:  7Count the number rectangles    Ans 10 rectangles Question:  8Count the number of circles     Ans 12 Circles Question:  9Count the number of squares.     Ans 14 Squares Question:  10Count the number of circles.    Ans : 7 Circles Question:  11How many hectometers  are there in 5 decimetre?  Ans 0.005 Question:  12How many centigrams are there in 0.02 decagrams?     Ans 20 centigrams Question:  13How many hectoliters are there in 3 centilitres?    Ans 0.0003 hectolitres Question:  14How many milligrams are there in 15 decagrams  ? Ans 150000 milligrams Question:  15In 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:  17Find the factors of   x2 – 1 – 2a – a2     Ans (x + a + 1)(x – a - 1) Question:  18What is the length of the rectangular park of area 800 m sq., whose length is twice its breadth?  Ans 40 Question:  19What is the next term of the sequence: 3,6,9,36,27,216, 81, ____  Ans 1293 Question:  20What is the next term of the sequence: 1,6,11,18, _____  Ans 27 Question:  21What is the next term of the sequence: 8,9,17,26,43, _____ Ans 69 Question:  22Write the term in the blank space of : 4,9,19,34,54, ____, 109            Ans 79