8th Class Mathematics Rational Numbers Question Bank

done Numbers Total Questions - 133

• question_answer1)
  In numbers from 1 to 100 the digit "0" appears____ times.
  A)
  9                                  done clear
  B)
  10 done clear
  C)
  11                   done clear
  D)
  12 done clear
  View Solution play_arrow

• question_answer2)
  How many times the digit "3" appears in numbers from 1 to 100?
  A)
  18                                done clear
  B)
  19 done clear
  C)
  20                      done clear
  D)
  21 done clear
  View Solution play_arrow

• question_answer3)
  How many numbers are there containing 2 digits?
  A)
  90                   done clear
  B)
  99 done clear
  C)
  100                              done clear
  D)
  89 done clear
  View Solution play_arrow

• question_answer4)
  How many times does the digit "1" appear in numbers from 1 to 100?
  A)
  18                                done clear
  B)
  19 done clear
  C)
  20                                done clear
  D)
  21 done clear
  View Solution play_arrow

• question_answer5)
  How many numbers are there containing 3 -digits?
  A)
  999                              done clear
  B)
  899 done clear
  C)
  900            done clear
  D)
  800 done clear
  View Solution play_arrow

• question_answer6)
  The smallest 4-digit number formed by using the digits 5, 0, 3, 1, 7, only once contains
  A)
  0 in thousand's place done clear
  B)
  5 in ten's place done clear
  C)
  3 in ten's place        done clear
  D)
  7 in unit's place done clear
  View Solution play_arrow

• question_answer7)
  Sum of the greatest 8 digit number and the smallest 9 digit number is
  A)
  19999999                    done clear
  B)
  199999999 done clear
  C)
  999999999                  done clear
  D)
  10000999 done clear
  View Solution play_arrow

• question_answer8)
  The whole number which does not have a predecessor is
  A)
  100                  done clear
  B)
  0 done clear
  C)
  1                                  done clear
  D)
  9 done clear
  View Solution play_arrow

• question_answer9)
  The number with which is multiplied by 100 the product remains the same is
  A)
  100                 done clear
  B)
  0 done clear
  C)
   \[\frac{a}{b}+\frac{c}{d}(c\ne 0)=\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}\]                            done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer10)
  Smallest 6-digit number that can be formed by the digits 9,6,0,5,8,1 is                       
  A)
  0,15,689                      done clear
  B)
  1,05,689 done clear
  C)
  5,01,689                      done clear
  D)
  9,86,510 done clear
  View Solution play_arrow

• question_answer11)
  \[ad,bc\in I,bc\ne 0\] is an example of
  A)
  Closure property                                done clear
  B)
  Commutative property                           done clear
  C)
  Associative property                                done clear
  D)
  distributive property            done clear
  View Solution play_arrow

• question_answer12)
  \[a=\frac{p}{q},b=\frac{r}{s},c=\frac{l}{m}\] is an example of
  A)
  Commutative property done clear
  B)
  Associative property done clear
  C)
  Closure property done clear
  D)
  Distributive property done clear
  View Solution play_arrow

• question_answer13)
  Successor of 301,999 is_______.
  A)
  30,200                         done clear
  B)
  302,000 done clear
  C)
  302,010                       done clear
  D)
  301,100 done clear
  View Solution play_arrow

• question_answer14)
  The least natural number is ____ .
  A)
  0                                  done clear
  B)
  1           done clear
  C)
  9                                  done clear
  D)
  does not exist done clear
  View Solution play_arrow

• question_answer15)
  The property represented by \[p,q,r,s,l,m\in I,q\ne 0,s\ne 0,m\ne 0.\]is
  A)
  Commutative property done clear
  B)
  Associative property done clear
  C)
  Distributive property done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  The product of two odd numbers is
  A)
  An even number      done clear
  B)
  An odd number done clear
  C)
  Cannot be determined done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  What least number must be subtracted from 13,601 to get a number exactly divisible by 87?
  A)
  25                                done clear
  B)
  29 done clear
  C)
  27                                done clear
  D)
  23 done clear
  View Solution play_arrow

• question_answer18)
  The two consecutive prime numbers with difference 2 are called
  A)
  Co-primes                    done clear
  B)
  twin primes done clear
  C)
  Composite                   done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer19)
  An example for twin primes is
  A)
  5, 11                            done clear
  B)
  3, 5 done clear
  C)
  11, 17               done clear
  D)
  3, 7 done clear
  View Solution play_arrow

• question_answer20)
  Successor of every even number is
  A)
  even                done clear
  B)
  prime done clear
  C)
  odd               done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer21)
  The L.C.M of two numbers is x and their H.C.F is y. The product of two numbers is
  A)
   \[a+b=b+a\]                                     done clear
  B)
   \[a\times b=b\times a\] done clear
  C)
   \[(a+b)+c=a+(b+c)\]                      done clear
  D)
   \[(a\times b)\times c=a\times (b\times c)\] done clear
  View Solution play_arrow

• question_answer22)
  The H.C.F of two number is 28 and their L.C.M is 336. If one number is 112 then the other number is
  A)
  64                                done clear
  B)
  84 done clear
  C)
  34                                done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  Which of the following statement is true?
  A)
  1 is the smallest prime number done clear
  B)
  Every prime number is an odd number done clear
  C)
  The sum of two prime numbers is always a prime number done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  Which of the following number is divisible by 11?
  A)
  3,116,365                    done clear
  B)
  901,351 done clear
  C)
  8,790,322                    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer25)
  The sum of the prime numbers between 90 and 100 is
  A)
  188                              done clear
  B)
  281 done clear
  C)
  376                              done clear
  D)
  97 done clear
  View Solution play_arrow

• question_answer26)
  The HCF and LCM of two numbers is 16 and 192 respectively if one of the numbers is 64, the other one is
  A)
  48                 done clear
  B)
  24 done clear
  C)
  72                   done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer27)
  Thesma Uest number which when divided by 4,6,10,15 gives the same remainder 3 is
  A)
  57                                done clear
  B)
  123 done clear
  C)
  63                                done clear
  D)
  39 done clear
  View Solution play_arrow

• question_answer28)
  The set of negative natural numbers and whole numbers is called as
  A)
  Natural numbers          done clear
  B)
  integers done clear
  C)
  Positive numbers         done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer29)
  The number which is neither positive nor negative is
  A)
  1                                  done clear
  B)
  5 done clear
  C)
  0                  done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer30)
  Smallest negative number
  A)
   \[-1\]                           done clear
  B)
   \[-10\] done clear
  C)
  0                                  done clear
  D)
  does not exist done clear
  View Solution play_arrow

• question_answer31)
  Madhavi eats one full bar of chocolate. Then she divides another one into 5 equal parts and eats 3 of those parts. The total number of chocolates that she has eaten is
  A)
   \[a+0=a=0+a\]                                done clear
  B)
   \[a\times 1=a=1\times a\] done clear
  C)
   \[a+(-a)=0=(-a)+a\]                        done clear
  D)
   \[a\times \frac{1}{a}=1=\frac{1}{a}\times a\] done clear
  View Solution play_arrow

• question_answer32)
  If\[\frac{1}{a}\], then \[a\times (b+c)=a\times b+a\times c\]
  A)
  1.1                               done clear
  B)
  1.01 done clear
  C)
  0.11                             done clear
  D)
  11        done clear
  View Solution play_arrow

• question_answer33)
  The smallest possible decimal fraction up to three decimal places is
  A)
  0.101                           done clear
  B)
  0.111 done clear
  C)
  0.001         done clear
  D)
  0.011 done clear
  View Solution play_arrow

• question_answer34)
  The H.C.F of two numbers is 68 and their LCM is 2142. If one of the numbers is 204, the other number is:
  A)
  741                              done clear
  B)
  742 done clear
  C)
  714          done clear
  D)
  357 done clear
  View Solution play_arrow

• question_answer35)
  Division of \[(b+c)\times a=b\times a+c\times a\] by 3 gives
  A)
   \[-\,2.4572\]                done clear
  B)
   \[\bar{1}.7905\] done clear
  C)
   \[\overline{2}.4572\,\]                        done clear
  D)
   \[\overline{2}.5472\] done clear
  View Solution play_arrow

• question_answer36)
  Given \[3=\frac{3}{1}\]the value of \[0=\frac{0}{1}\]correct to 3 decimal places is:
  A)
  15.652                      done clear
  B)
  11.180 done clear
  C)
  18.652                         done clear
  D)
  16.652 done clear
  View Solution play_arrow

• question_answer37)
  The bells begin tolling at the same time and continued to do so at intervals of 21, 28, 30 seconds respectively The bells will toll together again after
  A)
  7 seconds                     done clear
  B)
  420 seconds done clear
  C)
  630 seconds                 done clear
  D)
  1764 seconds done clear
  View Solution play_arrow

• question_answer38)
  The HCF of two numbers is 9 and their LCM is 270. It the sum of the numbers is 99, their difference is equal to
  A)
  18                                done clear
  B)
  15 done clear
  C)
  12                                done clear
  D)
  9 done clear
  View Solution play_arrow

• question_answer39)
  If x, y, z, are positive real number and a, b, c are rational numbers, then the value of \[\frac{1}{1+{{x}^{b-a}}+{{x}^{c-a}}}+\frac{1}{1+{{x}^{a-b}}+{{x}^{c-b}}}+\frac{1}{1+{{x}^{b-c}}+{{x}^{a-c}}}\]is
  A)
   \[-1\]                           done clear
  B)
  1 done clear
  C)
  0                                  done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer40)
  The value of \[a<\frac{a+b}{a}<b\]is equal to
  A)
  0                                  done clear
  B)
  1 done clear
  C)
  2m                               done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer41)
  A number other than one which is either divisible by 1 or itself is called a
  A)
  composite number    done clear
  B)
  prime number done clear
  C)
  coprime number      done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer42)
  \[\frac{p}{q};p,q\in I,\]is a_____.
  A)
  Positive rational number done clear
  B)
  Negative rational number done clear
  C)
  Either positive or negative rational number done clear
  D)
  Does not exist done clear
  View Solution play_arrow

• question_answer43)
  The rational number \[q\ne 0\]
  A)
  has a positive numerator                          done clear
  B)
  has a negative numerator                         done clear
  C)
  has either a positive numerator or a negative numerator done clear
  D)
  has neither a positive numerator nor a negative numerator done clear
  View Solution play_arrow

• question_answer44)
  Addition of rational numbers does not satisfy which of the following property?                                    
  A)
  Commutative               done clear
  B)
  associative done clear
  C)
  Closure                        done clear
  D)
  all of these done clear
  View Solution play_arrow

• question_answer45)
  \[\sqrt{3}\]This property is
  A)
  Closure                        done clear
  B)
  commutative done clear
  C)
  Associative            done clear
  D)
  identity                 done clear
  View Solution play_arrow

• question_answer46)
  \[\sqrt{3}\] can be expressed in the rational form as         
  A)
   \[\sqrt{4}\]                  done clear
  B)
   \[\sqrt{4}=2\] done clear
  C)
   \[\sqrt{2},\sqrt{5},\sqrt{6},2\sqrt{3},5\sqrt{7},\sqrt{2}+\sqrt{3},\]                        done clear
  D)
   \[\sqrt[3]{2},\sqrt[3]{3},\sqrt[3]{4},\] done clear
  View Solution play_arrow

• question_answer47)
  \[2+\sqrt{3}\]
  A)
   \[\pi \]                    done clear
  B)
   \[\frac{22}{7}\]                     done clear
  C)
   \[\pi \]                          done clear
  D)
  0.45 done clear
  View Solution play_arrow

• question_answer48)
  By what number should we multiply \[\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8},\sqrt{11}\] so that the product may be equal to 64?                                 
  A)
   \[0.\overline{3}=3/9\]                        done clear
  B)
   \[1/3\]                  done clear
  C)
   \[0.\overline{387}=387/999\]                        done clear
  D)
  None of these           done clear
  View Solution play_arrow

• question_answer49)
  \[0.74\overline{35}=\frac{7435-74}{9900}=\frac{7361}{9900},\]
  A)
  0                                  done clear
  B)
  1                  done clear
  C)
   \[-1\]                           done clear
  D)
  2                         done clear
  View Solution play_arrow

• question_answer50)
  If \[{{3}^{x}}=500\] then the value of \[{{3}^{x-2}}\] is
  A)
   \[N\subseteq W\]                                 done clear
  B)
   \[|x+y|\le |x|+|y|\] done clear
  C)
   \[|x\times y|=|x|\times |y|\]                        done clear
  D)
   \[|x-y|\le |x|-|y|\] done clear
  View Solution play_arrow

• question_answer51)
  The least number of 4 digits which is a perfect square is
  A)
  1000                            done clear
  B)
  1004 done clear
  C)
  1016                            done clear
  D)
  1024 done clear
  View Solution play_arrow

• question_answer52)
  The least number which must be subtracted from 2509 to make it a perfect square is
  A)
  6                                  done clear
  B)
  9 done clear
  C)
  12                   done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer53)
  The smallest number by which 396 must be multiplied so that the product becomes a perfect square is
  A)
  5                                  done clear
  B)
  11 done clear
  C)
  3                                  done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer54)
  \[\sqrt{2}\]
  A)
  equals 1              done clear
  B)
  Lies between 0 and 1 done clear
  C)
  lies between I and 2   done clear
  D)
  is greater than 2 done clear
  View Solution play_arrow

• question_answer55)
  A four digit perfect square number who?s first two digits and last two digits taken separately are also perfect square numbers is
  A)
  1681                   done clear
  B)
  1636 done clear
  C)
  3664                            done clear
  D)
  6481 done clear
  View Solution play_arrow

• question_answer56)
  The square root of a perfect square containing 'n' digits has_____ digits.
  A)
   \[\sqrt{3}\]                  done clear
  B)
   \[\frac{52}{125}\] done clear
  C)
  1 or 2                           done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  \[\pi \]is
  A)
  Rational                       done clear
  B)
  irrational done clear
  C)
  Imaginary                    done clear
  D)
  an integer done clear
  View Solution play_arrow

• question_answer58)
  Express \[\sqrt{3}=1.732,\] as rational number.
  A)
   \[\frac{\sqrt{2}+\sqrt{3}}{2}\]                                 done clear
  B)
   \[(2+\sqrt{3})\] done clear
  C)
   \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{q} \right),\text{C}-\left( \text{r} \right),\text{D}-\left( \text{p} \right)\]                         done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer59)
  An irrational number is
  A)
  a terminating and non-repeating decimal done clear
  B)
  a non-terminating and non-repeating decimal done clear
  C)
  a terminating and repeating decimal done clear
  D)
  a non-terminating and repeating decimal done clear
  View Solution play_arrow

• question_answer60)
  The value of \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{p} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{q} \right)\] is
  A)
   \[-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\]                                    done clear
  B)
   \[\left( \text{d} \right)~~\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] done clear
  C)
   \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{q} \right),\text{D}-\left( \text{p} \right)\]             done clear
  D)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{p} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{q} \right)\] done clear
  View Solution play_arrow

• question_answer61)
  If \[~\text{A}-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\] then the value of \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] is close to
  A)
  1.2245         done clear
  B)
  0.816 done clear
  C)
  0.613                           done clear
  D)
  2.449 done clear
  View Solution play_arrow

• question_answer62)
  Which of the following statement is true?              
  A)
  Cubes of all even natural numbers are even         done clear
  B)
  Cubes of all odd natural numbers are odd          done clear
  C)
  Cubes of negative integers are negative            done clear
  D)
  All the above                                     done clear
  View Solution play_arrow

• question_answer63)
  The smallest number by which 2560 must be multiplied so that the product is a perfect cube is                    
  A)
  5                                  done clear
  B)
  25             done clear
  C)
  10                    done clear
  D)
  15                     done clear
  View Solution play_arrow

• question_answer64)
  The smallest number by which 8788 must be divided so that the quotient is a perfect cube is                        
  A)
  4                  done clear
  B)
  12 done clear
  C)
  16                   done clear
  D)
  32 done clear
  View Solution play_arrow

• question_answer65)
  The value of \[\sqrt{2}\] is
  A)
  28                                done clear
  B)
  -28 done clear
  C)
  18                                done clear
  D)
  -18 done clear
  View Solution play_arrow

• question_answer66)
  The value of \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{q} \right),\text{D}-\left( \text{p} \right)\]is
  A)
  64 done clear
  B)
  32 done clear
  C)
  Cannot be determined done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer67)
  Simplify \[{{(32)}^{\frac{-2}{5}}}\div {{(125)}^{\frac{-2}{3}}}\]
  A)
   \[\text{A}-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\]                         done clear
  B)
   \[\left( \text{d} \right)~~\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] done clear
  C)
   \[H.C.F\times L.C.M.=a\times b\]                              done clear
  D)
   \[\text{=}\frac{\text{HCF of a and b}}{\text{a }\!\!\times\!\!\text{ b}}\] done clear
  View Solution play_arrow

• question_answer68)
  The value of \[5\sqrt{3}\]is
  A)
  0                                  done clear
  B)
  1 done clear
  C)
   \[a=bq+r.0\le r<b\]                           done clear
  D)
  15 done clear
  View Solution play_arrow

• question_answer69)
  The value of\[q\ne 0\]is
  A)
   \[\frac{5}{16},\frac{15}{24}\]                                  done clear
  B)
   \[\frac{25}{8}\] done clear
  C)
   \[\frac{5}{48}\]                                  done clear
  D)
   \[\frac{5}{8}\] done clear
  View Solution play_arrow

• question_answer70)
  The value of \[\frac{75}{48}\] is
  A)
  1                                  done clear
  B)
  10 done clear
  C)
  100                  done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer71)
  Find the value of \[\frac{75}{8}\]is equal to:            
  A)
  0                                  done clear
  B)
   \[\frac{8}{21},\frac{12}{35},\]             done clear
  C)
  x                                  done clear
  D)
  1/x                        done clear
  View Solution play_arrow

• question_answer72)
  Which one of the following is not true?               
  A)
  There does not exist any rational number whose square is 4    done clear
  B)
  There does not exist any rational number whose square is 5 done clear
  C)
  There does not exist any rational number whose square is 2 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer73)
  If x and y are two positive real numbers, then, x > y implies:
  A)
   \[\frac{32}{7}\]                      done clear
  B)
    \[\frac{4}{105}\] done clear
  C)
   \[\frac{192}{7}\]        done clear
  D)
   \[\frac{4}{7}\] done clear
  View Solution play_arrow

• question_answer74)
  If A and B are real numbers and\[\frac{5}{109}\], then:
  A)
   \[\left[ {{\left( \frac{1}{4} \right)}^{2}}-{{\left( \frac{1}{4} \right)}^{3}} \right]\times {{2}^{6}}\]                    done clear
  B)
   \[\frac{p}{q}={{\left( \frac{2}{3} \right)}^{3}}\div {{\left( \frac{3}{2} \right)}^{-3}}\] done clear
  C)
   \[{{\left( \frac{p}{q} \right)}^{-10}}=\_\_\_\_\_\_\_\_\]          done clear
  D)
   \[x*y=\sqrt{{{x}^{2}}+{{y}^{2}}}\] done clear
  View Solution play_arrow

• question_answer75)
  The value of\[(1*2\sqrt{2})(1*-2\sqrt{2})\]is
  A)
  3/2                  done clear
  B)
  -3/2 done clear
  C)
  2/3                  done clear
  D)
  -1/2 done clear
  View Solution play_arrow

• question_answer76)
  The value of \[{{3}^{3x-5}}=\frac{1}{{{9}^{x}}}\]is:
  A)
   \[{{(64)}^{\frac{-2}{3}}}\times {{\left( \frac{1}{4} \right)}^{-3}}\]                  done clear
  B)
   \[x=7+4\sqrt{3},\] done clear
  C)
   \[\sqrt{x}+\frac{1}{\sqrt{x}}\]                                 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer77)
  If A is the HCF of 546, 294 and 3066; and B is the L.C.M of 42, 14 and 21, what is the relationship between A and B?
  A)
   \[=(99-10)+1=89+1=90\]            done clear
  B)
   \[=(999-100)+1\] done clear
  C)
   \[=899+1=900\]                   done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer78)
  A two digit number is divisible by 3 and 4. Also the difference between the unit's digit and the ten's digit is equal to 4. The number is:
  A)
  96                                done clear
  B)
  48 done clear
  C)
  36                                done clear
  D)
  72 done clear
  View Solution play_arrow

• question_answer79)
  The only prime number which is even is
  A)
  2                      done clear
  B)
  4 done clear
  C)
  6                                  done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer80)
  Choose the rational number which does not lie between rational numbers \[100\times 1=100\]and \[a(b+c)=(a\times b)+(a\times c)\]:
  A)
   \[301999+1=30200\]                                    done clear
  B)
   \[=\frac{{{2}^{1/2}}\times {{3}^{1/3}}\times {{4}^{1/4}}}{{{10}^{-1/5}}\times {{5}^{3/5}}}\div \frac{{{2}^{-4/3}}\times {{5}^{-7/5}}}{{{2}^{-6/5}}\times {{2}^{-1/3}}\times {{3}^{-1/3}}}\] done clear
  C)
   \[=\frac{{{2}^{6/5}}\times {{3}^{1/3}}}{{{5}^{2/5}}}\div \frac{{{2}^{1/5}}\times {{3}^{1/3}}}{{{5}^{7/5}}}\]                  done clear
  D)
   \[={{2}^{\frac{6}{5}-\frac{1}{5}}}\times {{5}^{\frac{7}{5}-\frac{2}{5}}}=2\times 5=10.\] done clear
  View Solution play_arrow

• question_answer81)
  The simplest rationalizing factor of \[\frac{{{6}^{n+3}}-{{32.6}^{n+1}}}{{{6}^{n+2}}-{{2.6}^{n+1}}}=\frac{{{6}^{n+1}}.(36-32)}{{{6}^{n+1}}(6-2)}=1.\] is
  A)
   \[p,q,r,s,l,m\in I,q\ne 0,s\ne 0,m\ne 0.\]                                   done clear
  B)
   \[a+b=b+a\] done clear
  C)
   \[a\times b=b\times a\]                                   done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer82)
  The value of \[(a+b)+c=a+(b+c)\] on simplification is
  A)
  13                                done clear
  B)
  12 done clear
  C)
  11                       done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer83)
  The exponential form of\[(a\times b)\times c=a\times (b\times c)\] is
  A)
   \[a+0=a=0+a\]                                done clear
  B)
   \[a\times 1=a=1\times a\] done clear
  C)
   \[a+(-a)=0=(-a)+a\]                   done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer84)
  The value of \[a\times \frac{1}{a}=1=\frac{1}{a}\times a\] is equal to
  A)
  1                                  done clear
  B)
   \[\frac{1}{a}\] done clear
  C)
   \[a\times (b+c)=a\times b+a\times c\]                      done clear
  D)
   \[(b+c)\times a=b\times a+c\times a\] done clear
  View Solution play_arrow

• question_answer85)
  The value of \[\frac{{{2}^{1/2}}\times {{3}^{1/4}}\times {{4}^{1/4}}}{{{10}^{-1/5}}\times {{5}^{3/5}}}\div \frac{{{4}^{-2/3}}\times {{5}^{-7/5}}}{{{4}^{-3/5}}\times {{6}^{-1/3}}}\]is equal to
  A)
  10                done clear
  B)
  1 done clear
  C)
  6                                  done clear
  D)
  18 done clear
  View Solution play_arrow

• question_answer86)
  The value of \[0=\frac{0}{1}\] is equal to
  A)
  36                                done clear
  B)
  1/6 done clear
  C)
  2                                  done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer87)
  The number which is neither prime nor composite is
  A)
  0                                  done clear
  B)
  1 done clear
  C)
  2                                  done clear
  D)
  5 done clear
  View Solution play_arrow

• question_answer88)
  The H.C.F of \[\frac{2}{5},\frac{6}{25}\] and \[\frac{8}{35}\] is
  A)
   \[\frac{p}{q};p,q\in I,\]                                   done clear
  B)
   \[q\ne 0\] done clear
  C)
   \[\sqrt{3}\]                  done clear
  D)
   \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer89)
  Which of the following is not a composite number?
  A)
  4                                  done clear
  B)
  6 done clear
  C)
  7                      done clear
  D)
  8 done clear
  View Solution play_arrow

• question_answer90)
  \[3.\overline{25}\] is equal to
  A)
   \[\sqrt{4}=2\]             done clear
  B)
   \[\sqrt{2},\sqrt{5},\sqrt{6},2\sqrt{3},5\sqrt{7},\sqrt{2}+\sqrt{3},\] done clear
  C)
   \[\sqrt[3]{2},\sqrt[3]{3},\sqrt[3]{4},\]                        done clear
  D)
   \[2+\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer91)
  The smallest number which when divided by 20, 25, 35 and 40 and leaves a remainder of 14, 19, 29 and 34, respectively is
  A)
  1394             done clear
  B)
  1404 done clear
  C)
  1664                            done clear
  D)
  1406 done clear
  View Solution play_arrow

• question_answer92)
  The LCM of two numbers is x and their HCF is y. The product of two numbers is
  A)
   \[\pi \]                          done clear
  B)
   \[\frac{22}{7}\] done clear
  C)
   \[\pi \]              done clear
  D)
  xy done clear
  View Solution play_arrow

• question_answer93)
  The least number which when decreased by 7 is exactly divisible by 12, 16, 18, 21 and 28 is
  A)
  1012                            done clear
  B)
  1008 done clear
  C)
  1015                done clear
  D)
  1022 done clear
  View Solution play_arrow

• question_answer94)
  Four bells ring at intervals of 6, 7, 8 and 9 seconds respectively. All the bells ring together after_______ seconds.
  A)
  504                     done clear
  B)
  516 done clear
  C)
  508                              done clear
  D)
  512         done clear
  View Solution play_arrow

• question_answer95)
  The greatest number that will divide 137, 182 and 422 leaving a remainder of 2 in each case is
  A)
  15                done clear
  B)
  12 done clear
  C)
  21                                done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer96)
  The greatest number which when divides 258 and 323 leaving remainders 2 and 3, respectively is
  A)
  32                                done clear
  B)
  64 done clear
  C)
  16                                done clear
  D)
  128 done clear
  View Solution play_arrow

• question_answer97)
  There are 264 girls and 408 boys in a school. These children are to be divided into groups of equal numbers of boys and girls. The maximum number of boys or girls in each group will be
  A)
  11                                done clear
  B)
  17 done clear
  C)
  24             done clear
  D)
  26 done clear
  View Solution play_arrow

• question_answer98)
  When a number is divided by 125, the remainder is 82. When the same number is divided by 25, the remainder will be
  A)
  8                     done clear
  B)
  9 done clear
  C)
  6                                  done clear
  D)
  7 done clear
  View Solution play_arrow

• question_answer99)
  The last digit of the number\[{{(373)}^{333}}\]is
  A)
  1                                  done clear
  B)
  2 done clear
  C)
  3                done clear
  D)
  9 done clear
  View Solution play_arrow

• question_answer100)
  The two missing numbers shown with asterisk in the equation\[5\frac{3}{*}\times *\frac{1}{2}=19\]are
  A)
  6, 3                              done clear
  B)
  7, 3 done clear
  C)
  8, 3                              done clear
  D)
  11, 3 done clear
  View Solution play_arrow

• question_answer101)
  The least perfect square exactly divisible by each of the numbers 6, 9, 15 and 20 is
  A)
  3600                            done clear
  B)
  900 done clear
  C)
  400                              done clear
  D)
  225 done clear
  View Solution play_arrow

• question_answer102)
  Choose the wrong statement:
  A)
  There is no largest natural number done clear
  B)
  There is no largest whole number done clear
  C)
  Every natural number is a whole number done clear
  D)
  All natural numbers together with zero are called integers done clear
  View Solution play_arrow

• question_answer103)
  If \[0.\overline{3}=3/9\], then the value of \[1/3\]is
  A)
  34                   done clear
  B)
  35 done clear
  C)
  36                                done clear
  D)
  37                        done clear
  View Solution play_arrow

• question_answer104)
  If \[0.\overline{387}=387/999\]then the value of \[0.74\overline{35}=\frac{7435-74}{9900}=\frac{7361}{9900},\] is
  A)
  194                              done clear
  B)
  196 done clear
  C)
  198          done clear
  D)
  200 done clear
  View Solution play_arrow

• question_answer105)
  If\[0.1\overline{27}=\frac{127-1}{990}=\frac{7}{55}\]then the value of\[W=N\cup \{0\}\]is          
  A)
  193                              done clear
  B)
  194                  done clear
  C)
  195                              done clear
  D)
  196         done clear
  View Solution play_arrow

• question_answer106)
  Which of the following statement is true?              
  A)
  Every whole number is a natural number           done clear
  B)
  Every natural number is a whole number       done clear
  C)
  '1' is the least whole number                      done clear
  D)
  None of these                done clear
  View Solution play_arrow

• question_answer107)
  The property represented by \[N\subseteq W\] is
  A)
  Associative property done clear
  B)
  Commutative property      done clear
  C)
  Closure property                                     done clear
  D)
  Additive identity           done clear
  View Solution play_arrow

• question_answer108)
  Which of the following statements is correct?          
  A)
  0 is called the additive identity for rational numbers, done clear
  B)
  1 is called the multiplicative identity for rational numbers. done clear
  C)
  The additive inverse of 0 is zero itself.                 done clear
  D)
  All the above           done clear
  View Solution play_arrow

• question_answer109)
  If x and y are two rational numbers, then which of the following statements is wrong?
  A)
   \[|x+y|\,\le \,|x|+|y|\]        done clear
  B)
   \[|x\times y|\,=\,|x|\times |y|\] done clear
  C)
   \[|x-y|\,\le \,|x|-|y|\]   done clear
  D)
  None of these      done clear
  View Solution play_arrow

• question_answer110)
  Which of the following statement is false?             
  A)
  Every fraction is a rational number done clear
  B)
  Every rational number is a fraction         done clear
  C)
  Every integer is a rational number                  done clear
  D)
  All the above done clear
  View Solution play_arrow

• question_answer111)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column-I	Column-II
  A. An irrational number between \[\sqrt{2}\] and \[\sqrt{3}\] is	(p)  \[\frac{52}{125}\]
  B. Value of 0.424 is	(q)  \[2-\sqrt{3}\]
  C. If \[\sqrt{3}=1.732,\] then	(r) \[\frac{\sqrt{2}+\sqrt{3}}{2}\]value of \[(2+\sqrt{3})\]is
  D. Rationalising factor of \[(2+\sqrt{3})\] is	(s) 3732

  A)
   \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{q} \right),\text{C}-\left( \text{r} \right),\text{D}-\left( \text{p} \right)\] done clear
  B)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{p} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{q} \right)\] done clear
  C)
   \[\text{A}-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\] done clear
  D)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] done clear
  View Solution play_arrow

• question_answer112)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column ? I	Column - II
  A. Only even prime is	(p) 9
  B. Number which is neither prime nor composite is	(q) 3
  C. H.C.F of 12, 15, 21	(r) 1
  D. H.C.F (306, 657)	(s) 2

  A)
            \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{q} \right),\text{D}-\left( \text{p} \right)\] done clear
  B)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{p} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{q} \right)\] done clear
  C)
  \[~\text{A}-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\] done clear
  D)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] done clear
  View Solution play_arrow

• question_answer113)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column ? I	Column - II
  A. 12 is a	(p) prime number
  B. 2, 7 are	(q) not a rational number
  C. 2 is a	(r) composite number
  D. \[\sqrt{2}\]	(s) coprime numbers

  A)
   \[\text{A}-\left( \text{s} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{q} \right),\text{D}-\left( \text{p} \right)\] done clear
  B)
   \[~\text{A}-\left( \text{r} \right),\text{B}-\left( \text{p} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{q} \right)\] done clear
  C)
   \[\text{A}-\left( \text{q} \right),\text{B}-\left( \text{r} \right),\text{C}-\left( \text{s} \right),\text{D}-\left( \text{p} \right)\] done clear
  D)
   \[\text{A}-\left( \text{r} \right),\text{B}-\left( \text{s} \right),\text{C}-\left( \text{p} \right),\text{D}-\left( \text{q} \right)\] done clear
  View Solution play_arrow

• question_answer114)
  DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): The H.C.F. of two numbers is 16 and their product is 3072. Then their L.C.M. = 162 Reason (R): If a, b are two positive integers, then \[H.C.F\times L.C.M.=a\times b\]
  A)
  Both A and R are individually true and R is the correct explanation of A: done clear
  B)
  Both A and R are individually true but R is not the correct explanation of. done clear
  C)
  A is true but R is false done clear
  D)
  A is false but R is true. done clear
  View Solution play_arrow

• question_answer115)
  DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion (A): 2 is a rational number. Reason (R): The square roots of all positive integers are irrationals.
  A)
  Both A and R are individually true and R is the correct explanation of A: done clear
  B)
  Both A and R are individually true but R is not the correct explanation of. done clear
  C)
  A is true but R is false done clear
  D)
  A is false but R is true. done clear
  View Solution play_arrow

• question_answer116)
  DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion: (3, 5) and (17, 19) are twin primes Reason: A pair of primes which differ by 2 are called twin primes
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true but R is not the correct explanation of. done clear
  C)
  A is true but R is false done clear
  D)
  A is false but R is true. done clear
  View Solution play_arrow

• question_answer117)
  DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion: LCM 404 and 96 is 9696 Reason: If a and b are two positive integers then LCM of a and b  \[\text{=}\frac{\text{HCF of a and b}}{\text{a }\!\!\times\!\!\text{ b}}\]
  A)
  Both A and R are individually true and R is the correct explanation of A: done clear
  B)
  Both A and R are individually true but R is not the correct explanation of. done clear
  C)
  A is true but R is false done clear
  D)
  A is false but R is true. done clear
  View Solution play_arrow

• question_answer118)
  DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion: \[5\sqrt{3}\] is an irrational number.                  Reason: For any two given integers a and b there exist unique integers q and r satisfying \[a=bq+r.0\le r<b\]
  A)
  Both A and R are individually true and R is the correct explanation of A. done clear
  B)
  Both A and R are individually true but R is not the correct explanation of. done clear
  C)
  A is true but R is false done clear
  D)
  A is false but R is true. done clear
  View Solution play_arrow

• question_answer119)
  Which one of the following is the correct definition of twin prime?
  A)
  The numbers which can be expressed in the form of p/q, where p, q are integers and\[q\ne 0\]. done clear
  B)
  Pair of prime numbers which have only one composite number between them. done clear
  C)
  Numbers having only one as common factor. done clear
  D)
  Natural numbers having more than two factors. done clear
  View Solution play_arrow

• question_answer120)
  Which one of the following is the correct definition of exponent?
  A)
  If the product of two surds is a rational number, then each surd is called a exponent of the other. done clear
  B)
  The set of rational and irrational numbers taken together. done clear
  C)
  The repeated multiplications of the same factor. done clear
  D)
  A surd which consists of three terms. done clear
  View Solution play_arrow

• question_answer121)
  Which one of the following explains correctly?
  A)
  A number is divisible by 11, if the difference of the sum of the alternative digits is zero or a multiple of 11. done clear
  B)
  A number is divisible by 11, if the last digit of that number is odd. done clear
  C)
  If the sum of the digits of a given number is divisible by 11, then that number is divisible by 11. done clear
  D)
  Given number is divisible by 11, if it is divisible by both 3 and 7. done clear
  View Solution play_arrow

• question_answer122)
  The L.C.M. of the fractions \[\frac{5}{16},\frac{15}{24}\] and \[\frac{25}{8}\] is    
  A)
   \[\frac{5}{48}\]                                  done clear
  B)
   \[\frac{5}{8}\] done clear
  C)
   \[\frac{75}{48}\]                                done clear
  D)
   \[\frac{75}{8}\]         done clear
  View Solution play_arrow

• question_answer123)
  The H.C.F. of the fractions \[\frac{8}{21},\frac{12}{35},\] and \[\frac{32}{7}\] is
  A)
   \[\frac{4}{105}\]                                done clear
  B)
   \[\frac{192}{7}\] done clear
  C)
   \[\frac{4}{7}\]                                    done clear
  D)
   \[\frac{5}{109}\] done clear
  View Solution play_arrow

• question_answer124)
  Consider the following statements. H.C.F of two numbers always divides their L.C.M. H.C.F of two co-prime numbers is 1. L.C.M of two co-prime numbers is product of the numbers. Which of the statement given above is/are correct?
  A)
  only (iii)                       done clear
  B)
  and (ii) done clear
  C)
  all (i), (ii) and (iii)        done clear
  D)
  none done clear
  View Solution play_arrow

• question_answer125)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. The least whole number is *-correct-answer-description-* Least whole number is 0. *-question-type-* 2 *-question-instructions-* 0
  View Solution play_arrow

• question_answer126)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. What least number should be added to 1330 to get a number exactly divisible by 43____? *-correct-answer-description-* Since, 1333 is exactly divisible by 43. *-question-type-* 2 *-question-instructions-* 0
  View Solution play_arrow

• question_answer127)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. Least prime number is ____ *-correct-answer-description-* Last prime Number is 2. *-question-type-* 2 *-question-instructions-* 0
  View Solution play_arrow

• question_answer128)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. The value of \[\left[ {{\left( \frac{1}{4} \right)}^{2}}-{{\left( \frac{1}{4} \right)}^{3}} \right]\times {{2}^{6}}\] is   *-correct-answer-description-* \[\left[ {{\left( \frac{1}{4} \right)}^{2}}-{{\left( \frac{1}{4} \right)}^{3}} \right]\times {{2}^{6}}={{\left( \frac{1}{4} \right)}^{2}}\left[ 1-\frac{1}{4} \right]\times {{2}^{6}}\] \[=\frac{1}{16}\times \frac{3}{4}\times 64=3\] *-question-type-* 2 *-question-instructions-* 0
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• question_answer129)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. If  \[\frac{p}{q}={{\left( \frac{2}{3} \right)}^{3}}\div {{\left( \frac{3}{2} \right)}^{-3}}\] then the value of \[{{\left( \frac{p}{q} \right)}^{-10}}=\_\_\_\_\_\_\_\_\] *-correct-answer-description-* \[\frac{p}{q}={{\left( \frac{2}{3} \right)}^{3}}\div {{\left( \frac{3}{2} \right)}^{-3}}={{\left( \frac{2}{3} \right)}^{3}}\div {{\left( \frac{2}{3} \right)}^{3}}=1\] \[\therefore \,\,\,{{\left( \frac{p}{q} \right)}^{-10}}={{(1)}^{-10}}=1\] *-question-type-* 2 *-question-instructions-* 0
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• question_answer130)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. If \[x*y=\sqrt{{{x}^{2}}+{{y}^{2}}},\]the value of \[(1*2\sqrt{2})(1*-2\sqrt{2})\] is _________ *-correct-answer-description-* \[1*2\sqrt{2}=\sqrt{{{(1)}^{2}}+{{(2\sqrt{2})}^{2}}}=\sqrt{1+8}=3\] \[1*-2\sqrt{2}=\sqrt{{{(1)}^{2}}+{{(-2\sqrt{2})}^{2}}}=\sqrt{1+8}=3\] \[\left( 1*2\sqrt{2} \right)\left( 1*-2\sqrt{2} \right)=(3)(3)=9\] *-question-type-* 2 *-question-instructions-* 0
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• question_answer131)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. The solution of \[{{3}^{3x-5}}=\frac{1}{{{9}^{x}}}\] is *-correct-answer-description-* \[{{3}^{3x-5}}=\frac{1}{{{9}^{x}}}\] \[{{3}^{3x-5}}={{3}^{-2x}}\] \[3x-5=-2x\] \[x=1\] *-question-type-* 2 *-question-instructions-* 0
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• question_answer132)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. \[{{(64)}^{\frac{-2}{3}}}\times {{\left( \frac{1}{4} \right)}^{-3}}\]equals to _________ *-correct-answer-description-* \[{{(64)}^{\frac{-2}{3}}}\times {{\left( \frac{1}{4} \right)}^{-3}}={{({{4}^{3}})}^{\frac{-2}{3}}}\times {{\left( \frac{1}{4} \right)}^{-3}}\] \[={{4}^{-2}}\times \frac{1}{{{4}^{-3}}}=4.\] *-question-type-* 2 *-question-instructions-* 0
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• question_answer133)
  DIRECTIONS: For the following questions write your answer in the given space in the answer sheet. Your answer would be only in single number. Do not write in word. If \[x=7+4\sqrt{3},\]then the value of\[\sqrt{x}+\frac{1}{\sqrt{x}}\]is _______ *-correct-answer-description-* Given \[x=7+4\sqrt{3}={{\left( 2+\sqrt{3} \right)}^{2}}\] \[\therefore \]  \[\sqrt{x}=2+\sqrt{3}\] Now, \[\sqrt{x}+\frac{1}{\sqrt{x}}=\frac{x+1}{\sqrt{x}}=\frac{4\left( 2+\sqrt{3} \right)}{2+\sqrt{3}}=4\] *-question-type-* 2 *-question-instructions-* 0
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