8th Class Mathematics Algebraic Expressions Question Bank

done Algebra Total Questions - 114

• question_answer1)
  The factors of \[{{x}^{2}}+xy-2xz-2yz\] are
  A)
   \[\Rightarrow \]           done clear
  B)
   \[P(-a)=0\] done clear
  C)
   \[P(x)={{x}^{3}}-3{{x}^{2}}+4x-12\]  done clear
  D)
   \[P(x)={{x}^{3}}-3{{x}^{2}}+4x-12\] done clear
  View Solution play_arrow

• question_answer2)
  The factors of \[P(3)=0\] are
  A)
    \[P(3)=0\] done clear
  B)
   \[P(3)={{3}^{3}}-{{3}^{2}}+4\times 3-12\] done clear
  C)
   \[27-27+12-12=0\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  The factors of \[P(3)=0\] are
  A)
   \[\therefore \] done clear
  B)
   \[(x-3)\] done clear
  C)
   \[\frac{4-x}{7-x}=\frac{2}{5}\] done clear
  D)
   \[20-5x=14-2x\] done clear
  View Solution play_arrow

• question_answer4)
  The value of\[3x=6\] is
  A)
   \[\Rightarrow \]                       done clear
  B)
  1 done clear
  C)
   \[x=2\]                                    done clear
  D)
  0.1 done clear
  View Solution play_arrow

• question_answer5)
  One of the factors of \[10x+x+3=11x+3\] is
  A)
   \[=x+x+3=2x+3\]               done clear
  B)
   \[\frac{11x+3}{2x+3}=\frac{4}{1}\] done clear
  C)
   \[11x+3=8x+12\]                 done clear
  D)
   \[3x=9\] done clear
  View Solution play_arrow

• question_answer6)
  If the factors of \[x=3\]\[28x-25x=36\] are \[\because \] and \[3x=36\] then the value of \[4{{x}^{2}}-20x+25=0\]is
  A)
  0                     done clear
  B)
  2 done clear
  C)
  4                                  done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer7)
  The factors of \[\frac{3}{2}\] are
  A)
   \[\left( x-3\sqrt{3} \right)\left( \sqrt{3x}+2 \right)\] done clear
  B)
   \[\frac{7}{2}\] done clear
  C)
   \[\frac{7}{2}\] done clear
  D)
   \[\frac{5}{2}\] done clear
  View Solution play_arrow

• question_answer8)
  If the digit 1 is placed after a two digit number whose tens digit is 'f and units digit is 'u?, the new number is
  A)
   \[\frac{5}{2}\]            done clear
  B)
   \[\frac{a+5}{3a-5}=\frac{a-8}{a+8}\] done clear
  C)
   \[2{{(a+b)}^{2}}-9(a+b)-5\]                     done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  The solution of \[a+b+5,2a+2b-1\] is
  A)
   \[a+b-5,2a+ab+1\]               done clear
  B)
   \[a-b+5,2a-2b+5\] done clear
  C)
   \[a+b+c=9\]                         done clear
  D)
   \[ab+bc+ca=26,\] done clear
  View Solution play_arrow

• question_answer10)
  In an examination a student was asked to find \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] th of a certain number. By mistake, he found \[x:\frac{x-a}{b+c}+\frac{x-b}{c+a}+\frac{x-c}{a+b}=3\] of it. His answer was 150 more than the correct answer. The number is
  A)
  290                              done clear
  B)
  280 done clear
  C)
  240                              done clear
  D)
  180 done clear
  View Solution play_arrow

• question_answer11)
  A man is 5 years older than his wife and the wife is now thrice as old as their daughter, who is 10 years old. How old was the man when his daughter was born?
  A)
  20 years                       done clear
  B)
  23 years done clear
  C)
  25 years        done clear
  D)
  30 years done clear
  View Solution play_arrow

• question_answer12)
  There were only two candidates in an election. One got 62% votes and was elected by a margin of 144 votes. The total number of voters were
  A)
  500                              done clear
  B)
  600 done clear
  C)
  700                              done clear
  D)
  800 done clear
  View Solution play_arrow

• question_answer13)
  A student has to secure 40% marks to pass. He got 40 marks and failed by 40 marks. The maximum number of marks is
  A)
  160                              done clear
  B)
  180 done clear
  C)
  200                      done clear
  D)
  320 done clear
  View Solution play_arrow

• question_answer14)
  The ratio of number of males to number of females in a club are 7:4. If there are 84 males in the club, the total number of members in the club are
  A)
  126                              done clear
  B)
  132 done clear
  C)
  136                              done clear
  D)
  148 done clear
  View Solution play_arrow

• question_answer15)
  If a number increased by 8% of itself gives 135, then that number is
  A)
  112                              done clear
  B)
  100 done clear
  C)
  125                    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  X and Y together can do a piece of work in 8 days, which X alone can do in 12 days. In how many days can Y do the same work alone?
  A)
  12 days                        done clear
  B)
  24 days done clear
  C)
  36 days                        done clear
  D)
  16 days done clear
  View Solution play_arrow

• question_answer17)
  A man can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48 minutes to row to a place and back. How far is the place?
  A)
  1km                done clear
  B)
  2km done clear
  C)
  3km                done clear
  D)
  4km done clear
  View Solution play_arrow

• question_answer18)
  If the angles of a triangle are in the ratio 2: 3: 4, then the difference between the greatest and smallest angles is
  A)
   \[1/2(a+b+c)\]                       done clear
  B)
   \[a+b+c\] done clear
  C)
   \[3(a+b+c)\]                          done clear
  D)
   \[2(abc)\]              done clear
  View Solution play_arrow

• question_answer19)
  What must be added to x/y to make y/x?
  A)
   \[x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\]               done clear
  B)
   \[{{x}^{3}}+\frac{1}{{{x}^{3}}}\] done clear
  C)
   \[3x-2=\frac{8}{x}.\]             done clear
  D)
   \[\left( -\frac{3}{4},2 \right)\] done clear
  View Solution play_arrow

• question_answer20)
  If \[(2,2)\] and y = 1, then the value of \[\left( -\frac{4}{3},2 \right)\] is:
  A)
   \[\frac{1}{x}-\frac{3}{4}+\frac{1}{2+x}=0\]                   done clear
  B)
   \[\left( 2,-\frac{3}{4} \right)\] done clear
  C)
   \[(5,4)\]                       done clear
  D)
   \[(-8,0)\] done clear
  View Solution play_arrow

• question_answer21)
  What is the reciprocal of \[\left( -\frac{4}{3},2 \right)\] when\[\frac{x}{x-1}+\frac{x-1}{x}=2\frac{1}{2}\] ?
  A)
   \[(5,4)\]                       done clear
  B)
  0 done clear
  C)
  1                                  done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer22)
  Evaluate \[\sqrt{\frac{0.36\times 0.72\times 0.049}{0.04\times 0.09\times 0.08}}\]
  A)
  27                                done clear
  B)
  27 done clear
  C)
  3.1                               done clear
  D)
  2.1 done clear
  View Solution play_arrow

• question_answer23)
  If \[x+y=2\]and \[x-y=1,\] then:
  A)
   \[P(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}\]                      done clear
  B)
   \[{{a}_{0}},{{a}_{1}},{{a}_{2}},.....,{{a}_{n}}\] done clear
  C)
   \[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}\]        done clear
  D)
   \[{{a}_{0}},{{a}_{1}},{{a}_{2}}......{{a}_{n}}\] done clear
  View Solution play_arrow

• question_answer24)
  If \[({{a}_{0}}\ne 0)\]and \[-9,\frac{15}{4},\frac{-13}{3}\] then the value of \[f(x)=ax+b\]is
  A)
   \[f(x)=a{{x}^{2}}+bx+c\ne 0\]     done clear
  B)
   \[3xy+7x{{y}^{2}}-8x{{y}^{3}}+7{{y}^{2}}{{x}^{2}}\] done clear
  C)
   \[\frac{{{a}^{3}}-3}{b}\]               done clear
  D)
   \[\therefore \] done clear
  View Solution play_arrow

• question_answer25)
  If \[{{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\], then the value of \[x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}\]is equal to
  A)
   \[{{(a+b)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}={{a}^{3}}+{{b}^{3}}+3ab(a+b)\]                        done clear
  B)
   \[{{(a-b)}^{3}}={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}={{a}^{3}}-{{b}^{3}}-3ab(a-b)\] done clear
  C)
   \[{{a}^{3}}+{{b}^{3}}=(a+b)({{a}^{2}}-ab+{{b}^{2}})\]                                done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer26)
  If \[{{2}^{2x-y}}=32\]and \[{{2}^{x+y}}=16\] then \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=(a+b+c)({{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca)\]is equal to
  A)
  9                                  done clear
  B)
  10 done clear
  C)
  11                                done clear
  D)
  13 done clear
  View Solution play_arrow

• question_answer27)
  If \[{{\text{a}}^{\text{3}}}\text{+}{{\text{b}}^{\text{3}}}\text{+}{{\text{c}}^{\text{3}}}\text{=3abc if a+b+c=0}\] then x is equal to
  A)
  1                                  done clear
  B)
  2 done clear
  C)
  3                                  done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer28)
  The value of \[P(x)={{x}^{3}}+{{x}^{2}}+2x+3\] is
  A)
   \[x+2=0\]                              done clear
  B)
   \[x=-2\] done clear
  C)
   \[P(x)={{x}^{3}}+{{x}^{2}}+2x+3\]                          done clear
  D)
   \[P(-2)={{(-2)}^{3}}+{{(-2)}^{2}}+2(-2)+3\] done clear
  View Solution play_arrow

• question_answer29)
  If two number differ by 3 and their product is 504, then the number are
  A)
  21, 24 or \[-\]24, \[-\]21 done clear
  B)
  30, 31 or \[-\]30, \[-\]31 done clear
  C)
  40, 41 or \[-\]40, \[-\]41 done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer30)
  The additive inverse of \[=-8+4-4+3=-12+7=-5\]is
  A)
   \[\Rightarrow \]           done clear
  B)
   \[P(-a)=0\] done clear
  C)
   \[P(x)={{x}^{3}}-3{{x}^{2}}+4x-12\]  done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer31)
  The sum of the reciprocals of \[P(x)={{x}^{3}}-3{{x}^{2}}+4x-12\] and \[P(3)=0\]is
  A)
   \[P(3)=0\]                   done clear
  B)
   \[P(3)={{3}^{3}}-{{3}^{2}}+4\times 3-12\] done clear
  C)
  1                                  done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer32)
  The equation for the statement: 'half of a number added to 10 is 15'.
  A)
   \[27-27+12-12=0\]                done clear
  B)
   \[P(3)=0\] done clear
  C)
   \[\therefore \]               done clear
  D)
   \[(x-3)\] done clear
  View Solution play_arrow

• question_answer33)
  In \[P(x)\]the value of a' is                  
  A)
   \[-\]1                           done clear
  B)
   \[ax+b=0\] done clear
  C)
   \[a\ne 0,x\]                              done clear
  D)
  +1          done clear
  View Solution play_arrow

• question_answer34)
  Ramu's father is thrice as old as Ramu. If father's age is 45 years then Ramu's age is
  A)
  45 years                       done clear
  B)
  30 years done clear
  C)
  15 years           done clear
  D)
  10 years done clear
  View Solution play_arrow

• question_answer35)
  The solution of \[ax=-b\]is
  A)
   \[x=-\frac{b}{a}\]                             done clear
  B)
   \[ax+by+c=0\] done clear
  C)
   \[ax+by+d=0\]                                 done clear
  D)
   \[a\ne 0,\] done clear
  View Solution play_arrow

• question_answer36)
  If 20% of 60% of a number is 144, then the number is
  A)
  1200 done clear
  B)
  2880 done clear
  C)
  8640 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer37)
  There were only two candidates who participated in an election. One contestant got 62% votes and was elected by a margin of 144 votes. The total number of votes were
  A)
  500                              done clear
  B)
  600 done clear
  C)
  700                              done clear
  D)
  800 done clear
  View Solution play_arrow

• question_answer38)
  What is the total number of candidates at an examination, if 31% fail and the number of those who passed exceeds the number of those who failed by 247?
  A)
  605                              done clear
  B)
  560 done clear
  C)
  650                  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer39)
  What must be subtracted from each term of the ratio 4: 7, so that the ratio becomes 2:5?                      
  A)
   \[-\]2                           done clear
  B)
   \[-\]1 done clear
  C)
  2                      done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer40)
  The ratio between a two digit number and the sum of digits of that number is 4 : 1. If the digit in the units place is 3 more than the digit in the tenth place. What is the number?
  A)
  63                                done clear
  B)
  36 done clear
  C)
  48                                done clear
  D)
  Data is not sufficient done clear
  View Solution play_arrow

• question_answer41)
  The ratio of number of boys to girls in a class is 1:25. If 36 more girls join, the ratio becomes 1:28. The number of boys in the class is
  A)
  24                                done clear
  B)
  32                      done clear
  C)
  12                    done clear
  D)
  48 done clear
  View Solution play_arrow

• question_answer42)
  The ratio of two numbers is a : b. If first of them is x, then second is
  A)
   \[b\ne 0\]                                 done clear
  B)
   \[3x-2y=4\] done clear
  C)
   \[x+y-3=0\]               done clear
  D)
   \[3x-2y=4\] done clear
  View Solution play_arrow

• question_answer43)
  Rs. 4800 are distributed among A, B and C in the ratio of 6:5:4. The difference between the shares of A and C is
  A)
  Rs. 450                        done clear
  B)
  Rs. 580 done clear
  C)
  Rs. 640                done clear
  D)
  Rs. 1260 done clear
  View Solution play_arrow

• question_answer44)
  One number is 3 less than the two times of the other. If their sum is increased by 7, the result is 37. Find the numbers.
  A)
  9, 11                            done clear
  B)
  11, 13 done clear
  C)
  11, 19            done clear
  D)
  9, 13 done clear
  View Solution play_arrow

• question_answer45)
  \[3(3-y)-2y=4\] of a flagpole is black, \[9-3y-2y=4\] is white and the remaining three meters is painted yellow. Find the length of the flagpole.
  A)
   \[\Rightarrow \]             done clear
  B)
   \[-5y=-5\] done clear
  C)
  5km                 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer46)
  In a two digit number, ten's digit is twice the unit's digit. The number formed by interchanging the digits is 36 less than the original number. Find the number.
  A)
  48                                done clear
  B)
  70 done clear
  C)
  72                                done clear
  D)
  84 done clear
  View Solution play_arrow

• question_answer47)
  In a two digit number, the ten's digit is 2 more than the unit's digit. Sum of the digits is \[y=1\] of the whole number. Find the number.
  A)
  24                                done clear
  B)
  42 done clear
  C)
  64                                done clear
  D)
  46 done clear
  View Solution play_arrow

• question_answer48)
  The three even consecutive integers whose sum is 90 are
  A)
  26, 30, 34              done clear
  B)
  24, 32, 34 done clear
  C)
  24, 28, 38              done clear
  D)
  28, 30, 32 done clear
  View Solution play_arrow

• question_answer49)
  Which of the following expressions is a polynomial?
  A)
   \[x+y-3=0\]               done clear
  B)
   \[x+1-3=0\] done clear
  C)
   \[x-2=0\]        done clear
  D)
   \[\Rightarrow \] done clear
  View Solution play_arrow

• question_answer50)
  The degree of the polynomial \[x=2\] is
  A)
  3                      done clear
  B)
  4 done clear
  C)
  2                                  done clear
  D)
  can't be determined done clear
  View Solution play_arrow

• question_answer51)
  The product of \[({{x}^{2}}+3x+5)\] and \[({{x}^{2}}-1)\] is
  A)
   \[a{{x}^{2}}+bx+c=0\] done clear
  B)
   \[a\ne 0\] done clear
  C)
   \[4{{x}^{2}}-4x-3=0\] done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer52)
  If quotient \[3{{y}^{2}}+4y-4=0\], remainder \[5{{x}^{2}}-2\sqrt{x}-4=0\] and divisor \[2{{x}^{2}}-3{{x}^{-1}}+6=0\] then the dividend is
  A)
   \[a{{x}^{2}}+bx+c=0\]      done clear
  B)
   \[a{{x}^{2}}\] done clear
  C)
   \[{{x}^{2}},b\]    done clear
  D)
   \[a{{x}^{2}}+bx+c=0\] done clear
  View Solution play_arrow

• question_answer53)
  The remainder obtained when \[a\ne 0\]is divided by \[b\ne 0\] is
  A)
   \[c\ne 0\]                     done clear
  B)
   \[a{{x}^{2}}+bx+c=0\] done clear
  C)
   \[a\ne 0\]         done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer54)
  What must be subtracted from \[{{x}^{4}}+2{{x}^{2}}-3x+7\] to get \[{{x}^{3}}+{{x}^{2}}+x-1?\]
  A)
   \[4{{x}^{2}}+3x=0,5{{x}^{2}}\] done clear
  B)
   \[a{{x}^{2}}+bx+c=0\] done clear
  C)
   \[a{{\alpha }^{2}}+b\alpha +c=0\] done clear
  D)
   \[5{{x}^{2}}-7x-6=0.\] done clear
  View Solution play_arrow

• question_answer55)
  If\[\because \] Then a = _____.
  A)
  1                                  done clear
  B)
   \[5{{(2)}^{2}}-7(2)-6=0\] done clear
  C)
   \[20-14-6=0\]                         done clear
  D)
  none of these done clear
  View Solution play_arrow

• question_answer56)
  The product of two factors with unlike signs is______.
  A)
  positive               done clear
  B)
  Negative done clear
  C)
  Cannot be determined   done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer57)
  The value of \[25{{x}^{2}}+16{{y}^{2}}+40xy\] at \[5{{x}^{3}}-7x-6=0.\]and\[y=-\,1\]is
  A)
  81                                done clear
  B)
   \[-\] 49 done clear
  C)
  1                     done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer58)
  If \[3x-7y=10\] and \[xy=-1,\] then the value of \[9{{x}^{2}}+49{{y}^{2}}\] is
  A)
  58                done clear
  B)
  142 done clear
  C)
  104                              done clear
  D)
   \[-\]104 done clear
  View Solution play_arrow

• question_answer59)
  \[{{x}^{2}}-36=0\]
  A)
   \[{{x}^{2}}-36=0\] done clear
  B)
   \[\Rightarrow \] done clear
  C)
   \[{{x}^{2}}-{{6}^{2}}=0\]                     done clear
  D)
  0 done clear
  View Solution play_arrow

• question_answer60)
  If \[\Rightarrow \], then the value of \[(x-6)(x+6)=0\] is
  A)
  Greater than 2           done clear
  B)
  less than 2 done clear
  C)
  Greater than 4           done clear
  D)
  less than 4 done clear
  View Solution play_arrow

• question_answer61)
  The value of\[\frac{{{(67.542)}^{2}}-{{(32.458)}^{2}}}{75.458-40.374}\]is
  A)
  1                                  done clear
  B)
  10 done clear
  C)
  100                  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer62)
  If \[x+y=6\] and \[3x-y=4,\]then \[x-y\] is equal to
  A)
   \[x=6\]                done clear
  B)
  0 done clear
  C)
  2                                  done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer63)
  The value of the product \[x=-6\] at \[{{x}^{2}}+5x+6=0\] is
  A)
  150                              done clear
  B)
  148 done clear
  C)
  152                              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer64)
  \[\Rightarrow \]
  A)
  0                                  done clear
  B)
   \[{{x}^{2}}+3x+2x+6=0\] done clear
  C)
  1                                  done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer65)
  \[11x+12y=58\]and \[12x+11y=57,\] the value of \[4(x+y)\] is...
  A)
  5                                  done clear
  B)
  12 done clear
  C)
  20                    done clear
  D)
  24 done clear
  View Solution play_arrow

• question_answer66)
  If \[\frac{2}{x}+3y=15\] and \[\frac{5}{x}-4y=3\] the value of x is
  A)
  1/2                               done clear
  B)
  2 done clear
  C)
  1/3           done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer67)
  The number 34 is divided into two parts such that the difference between them is 8. Find the larger one.
  A)
  20                                done clear
  B)
  35 done clear
  C)
  18                                done clear
  D)
  21 done clear
  View Solution play_arrow

• question_answer68)
  In 10 years A will be twice as old as B was 10 years ago. Find the age of A if he is now 9 years older than B.
  A)
  39yrs                            done clear
  B)
  48yrs done clear
  C)
  30yrs                            done clear
  D)
  45yrs done clear
  View Solution play_arrow

• question_answer69)
  From which number you subtract 40, the difference will be one third of the original number?
  A)
  48                                done clear
  B)
  60 done clear
  C)
  80                                done clear
  D)
  46 done clear
  View Solution play_arrow

• question_answer70)
  There are three consecutive numbers whose sum is 129. Find the square of the middle one.
  A)
  1849             done clear
  B)
  1764 done clear
  C)
  1829                            done clear
  D)
  1936 done clear
  View Solution play_arrow

• question_answer71)
  Ten years hence a man will be twice as old as his son, but two years ago he was four times as old as his son then was. Find the age of the father.
  A)
  26 years     done clear
  B)
  28 years done clear
  C)
  30 years                       done clear
  D)
  35 years done clear
  View Solution play_arrow

• question_answer72)
  A's present age is to B's present age as 7:9. Nine years ago, their ages were in the ratio of 2:3. Find the present age of A.
  A)
  27 years                       done clear
  B)
  21 years done clear
  C)
  25 years                       done clear
  D)
  22 years done clear
  View Solution play_arrow

• question_answer73)
  How old is a man now who, 20 years ago, was five times as old as his son who will be 41 years old 16 years after?
  A)
  40 years                       done clear
  B)
  45 years done clear
  C)
  48 years                       done clear
  D)
  50 years done clear
  View Solution play_arrow

• question_answer74)
  A number consists of two digits; the sum of the digits is 5 and if the left digit be increased by 1, it will be equal to 1/8 th of the number. Find the number.
  A)
  41                                done clear
  B)
  23 done clear
  C)
  14                                done clear
  D)
  32 done clear
  View Solution play_arrow

• question_answer75)
  If \[x+2=0\]find the value of\[\Rightarrow \].    
  A)
  3/4                               done clear
  B)
  2/3 done clear
  C)
  4/3                   done clear
  D)
  4/5 done clear
  View Solution play_arrow

• question_answer76)
  What are the roots of the equation \[x=-3\]
  A)
   \[x=-2\]                      done clear
  B)
  \[(x-y)(x+2z)\] done clear
  C)
   \[(x+y)(x-2z)\]            done clear
  D)
   \[(x-y)(x-2z)\] done clear
  View Solution play_arrow

• question_answer77)
  The solution set of \[(x+y)(y+2z)\] is
  A)
   \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}\]           done clear
  B)
   \[\left( \frac{x}{4}+\frac{y}{9} \right),\left( \frac{x}{4}-\frac{y}{9} \right)\] done clear
  C)
   \[\left( \frac{x}{2}+\frac{y}{9} \right),\left( \frac{x}{2}-\frac{y}{9} \right)\]                      done clear
  D)
   \[\left( \frac{x}{2}+\frac{y}{3} \right),\left( \frac{x}{2}-\frac{y}{3} \right)\] done clear
  View Solution play_arrow

• question_answer78)
  The roots of \[1-{{p}^{3}}\] are
  A)
  \[\frac{3}{2}\]and\[\frac{3}{2}\]                   done clear
  B)
   \[\frac{7}{2}\]and\[\frac{7}{2}\] done clear
  C)
  \[\frac{5}{2}\]and\[\frac{5}{2}\]              done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer79)
  The possible values of a in \[0.01\] are
  A)
  0 and 0                        done clear
  B)
  9 and 0 done clear
  C)
  0 and 21            done clear
  D)
  0 and 9 done clear
  View Solution play_arrow

• question_answer80)
  A boat goes downstream and covers the distance between two ports in 4 hrs while it covers the same distance upstream in 5 hrs. If the speed of the stream is 2 km ph, the speed of the boat in still water is
  A)
  15km/hr                       done clear
  B)
  20km/hr done clear
  C)
  24km/hr                       done clear
  D)
  18km/hr done clear
  View Solution play_arrow

• question_answer81)
  A farmer divides his herd of n cows among his four sons so that first son gets one half the herd, the second son gets one fourth, the third son gets one fifth, and the fourth son gets 7 cows, then n is:
  A)
  180                              done clear
  B)
  140 done clear
  C)
  240                              done clear
  D)
  100 done clear
  View Solution play_arrow

• question_answer82)
  If the difference of the squares of two numbers is 45, the square of the smaller number is 4 times the larger number, then the numbers are
  A)
  9,6 or 9,-6        done clear
  B)
  5,6 or 5,-6 done clear
  C)
  9,5 or 9,-5                    done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer83)
  Factors of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2-2x-\frac{2}{x}\] are
  A)
   \[x-\frac{1}{x}\]   done clear
  B)
   \[x+\frac{1}{x}-1\] done clear
  C)
   \[x+\frac{1}{x}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer84)
  In a piggy bank the number of 25 paise coins are five times the number of 50 paise coins. If there are 120 coins find the amount in the bank?
  A)
  Rs. 25                          done clear
  B)
  Rs. 10 done clear
  C)
  Rs. 35                done clear
  D)
  Rs. 40 done clear
  View Solution play_arrow

• question_answer85)
  The present age of a man is 3 times that of his son. Six years ago, the age of the man was four times that of his son. Find the ratio of their ages 6 years later.
  A)
  4:3                  done clear
  B)
  3:4 done clear
  C)
  2:5                  done clear
  D)
  5:2 done clear
  View Solution play_arrow

• question_answer86)
  If \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] and \[{{a}^{2}}+{{b}^{2}}+2\] then the value of \[(ab+bc+ca)\] is
  A)
  27             done clear
  B)
  29 done clear
  C)
  495                              done clear
  D)
  729 done clear
  View Solution play_arrow

• question_answer87)
  Solve for \[x:\frac{x-a}{b+c}+\frac{x-b}{c+a}+\frac{x-c}{a+b}=3\]
  A)
   \[(a+b+nc)\]  done clear
  B)
   \[m+n\] done clear
  C)
   \[\sqrt{3}{{x}^{2}}+11x+6\sqrt{3}\]                   done clear
  D)
   \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] done clear
  View Solution play_arrow

• question_answer88)
  A bag contains as many ruppes in it as there are 50 paise coins. Find the number of 50 paise coins if there be Rs. 30 in all.
  A)
  15                                done clear
  B)
  30 done clear
  C)
  16                                done clear
  D)
  20 done clear
  View Solution play_arrow

• question_answer89)
  Two numbers, whose sum is 39, are such that one-fifth of one of them is equal to one-eighth of the second. Find them.
  A)
  12,27                           done clear
  B)
  24,15 done clear
  C)
  15,24                 done clear
  D)
           27,12 done clear
  View Solution play_arrow

• question_answer90)
  A number consists of two digits whose sum is 5. If 9 be added to the number, the digits are reversed. Find the
  A)
  32                                done clear
  B)
  14 done clear
  C)
  41                                done clear
  D)
  23 done clear
  View Solution play_arrow

• question_answer91)
  A number consists of two digits whose sum is 10. If 72 be subtracted from the number, the digits are reversed. Find the number.
  A)
  91        done clear
  B)
  64 done clear
  C)
  55                                done clear
  D)
  82 done clear
  View Solution play_arrow

• question_answer92)
  A certain number of two digits is four times the sum of its digits. If 9 be added to the number, the digits are reversed. Find the number.
  A)
  15                                done clear
  B)
  12 done clear
  C)
  21                                done clear
  D)
  51 done clear
  View Solution play_arrow

• question_answer93)
  Father's age is equal to the sum of the ages of his five children. After 15 years his age will be only half of the sum of the children's ages. How old is the father?
  A)
  42 years                       done clear
  B)
  43 years done clear
  C)
  44 years                       done clear
  D)
  45 years done clear
  View Solution play_arrow

• question_answer94)
  If \[\left( x-3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\], find the value of \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x-2 \right)\].
  A)
  644                              done clear
  B)
  512 done clear
  C)
  488            done clear
  D)
  348 done clear
  View Solution play_arrow

• question_answer95)
  Find the roots of \[\left( x+3\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\]
  A)
   \[10t+u+1\]               done clear
  B)
   \[100t+10u+1\] done clear
  C)
   \[t+u+1\]                   done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer96)
  Choose the correct option for the roots of \[\frac{1}{x}-\frac{3}{4}+\frac{1}{2+x}=0\]
  A)
   \[x=1\]                        done clear
  B)
   \[x=-1\] done clear
  C)
   \[x=2\]                        done clear
  D)
   \[x=-3\] done clear
  View Solution play_arrow

• question_answer97)
  The roots of\[\frac{3}{14}\]are
  A)
   \[\frac{3}{14}\]                      done clear
  B)
   \[{{10}^{o}}\] done clear
  C)
   \[{{20}^{o}}\]                     done clear
  D)
   \[{{30}^{o}}\] done clear
  View Solution play_arrow

• question_answer98)
  Linear polynomials is
  A)
  A polynomial of degree two in one variable. done clear
  B)
  A polynomial of degree three. done clear
  C)
  A polynomial of degree 1 in one variable. done clear
  D)
  A polynomial of degree zero. done clear
  View Solution play_arrow

• question_answer99)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column - I	Column- II
  (A) Polynomial whose zeroes are \[{{40}^{o}}\]	(p) \[\frac{{{y}^{2}}-{{x}^{2}}}{yx}\]
  (B) Polynomial whose zeroes are 3 and -2 is	(q) \[\frac{xy}{x+y}\]
  (C) Polynomial whose zeroes are \[\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] is	(r) \[x=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\]
  (D) Polynomial whose zeroes \[\frac{x-y}{x-3y}\] and \[\frac{5}{\sqrt{6}-4}\] is	(s) \[\frac{5}{\sqrt{6}+4}\]

  A)
   \[\frac{\sqrt{6}-4}{5}\] done clear
  B)
   \[\frac{\sqrt{6}+4}{5}\] done clear
  C)
   \[\frac{1}{a-3b}\] done clear
  D)
   \[b=\frac{a}{3}\] done clear
  View Solution play_arrow

• question_answer100)
  Match column I with column II and select the correct answer using the code given below the columns:   

  Column - I	Column- II
  (A) Zeroes of \[f(x)=(x-1)\]\[(x-2)\,(x-3)\] are	(p) 1
  (B) Zeroes of \[x+y=2\]are	(q) 2
  (C) Zeroes of \[x-y=1,\] are	(r) 3
  (D) Zeroes of \[x=\frac{3}{2},y=\frac{1}{2}\] are	(s) -2

  A)
   \[x=0,y=3\] done clear
  B)
   \[x=1\frac{1}{2},y=6\] done clear
  C)
   \[y=0,x=6\] done clear
  D)
   \[x+y=a\] done clear
  View Solution play_arrow

• question_answer101)
  Match column I with column II and select the correct answer II using the code given below the columns:       

  Column - I	Column- II
  (A) \[xy=b,\]	(p) \[\frac{1}{{{x}^{3}}}+\frac{1}{{{y}^{3}}}\]
  (B) \[\frac{{{a}^{3}}-3ab}{{{b}^{3}}}\]	(q) \[\frac{{{a}^{3}}-3a}{{{b}^{3}}}\]
  (C) \[\frac{{{a}^{3}}-3}{h}\]	(r) \[\frac{{{a}^{3}}-3}{{{b}^{2}}}\]
  (D) \[x=\frac{1}{2}\]	(s) \[\begin{align}   & x+\overset{1}{\mathop{\_\_\_\_\_\_\_}}\, \\  & 1+\overset{1}{\mathop{\_\_\_\_}}\, \\  & 1+\frac{1}{x} \\ \end{align}\]
  (E) \[\frac{5}{4}\]	(t) \[\frac{4}{5}\]
  (F)  \[\frac{3}{4}\]	(u) \[{{2}^{2x-y}}=32\]

  A)
   \[{{2}^{x+y}}=16\]\[{{x}^{2}}+{{y}^{2}}\] done clear
  B)
            \[x-\frac{1}{x-2}=2-\frac{1}{x-2},\]\[(E)\to (t),\,(F)\to (p)\] done clear
  C)
  \[{{x}^{2}}\]\[{{x}^{a+b+c}}\] done clear
  D)
  \[{{x}^{abc}}\]\[{{x}^{0}}\] done clear
  View Solution play_arrow

• question_answer102)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column - I	Column - II
  (A) Solution of \[\frac{{{x}^{5}}-7{{x}^{2}}+18}{{{x}^{3}}-2}\]is	(p) ? 8
  (B) Solution of \[\frac{{{x}^{5}}+7{{x}^{2}}+18}{{{x}^{3}}-2}\]	(q) 0.6
  (C) Solution of \[\frac{-{{x}^{5}}-7{{x}^{2}}+18}{{{x}^{3}}-2}\] is	(r) \[-\frac{3}{4}\]
  (D) Solution of \[0.25(4t-3)\]\[=0.05(10t-9)\]	(s) 5
  (E) Solution of\[\frac{{{x}^{2}}-9}{{{x}^{2}}+3}\] is	(t) 2.4

  A)
   \[\frac{{{x}^{3}}+2{{x}^{2}}-x}{{{x}^{2}}-9}\]\[(D)\to (q),(E)\to (s)\] done clear
  B)
   \[\frac{x}{2}+10+5\]\[(D)\to (p),(E)\to (t)\] done clear
  C)
   \[\frac{x}{2}+15=10\]\[(D)\to (q),(E)\to (p)\] done clear
  D)
   \[6(2a-1)+8=14,\]\[(D)\to (q),(E)\to (p)\] done clear
  View Solution play_arrow

• question_answer103)
  Match column I with column II and select the correct answer using the code given below the columns:

  Column - I	Column- II
  (A) If \[2x-y-5\] and \[3x+2y=11,\]then \[x+y=\]	(p) no solution
  (B) If \[x+2y=5\]\[2x+3y=8,\] then \[x+y=\]	(q) 2
  (C) If \[2x+3y=7\] \[6x+9y=1,\]then there is	(r)  3
  (D)  If \[3x-4y=7\]\[5x+2y=3,\]then \[7x+5y=\]	(s) 4

  A)
   \[(A)\to (q),(B)\to (r),(C)\to (s),(D)\to (p)\] done clear
  B)
   \[(A)\to (s),(B)\to (r),(C)\to (p),(D)\to (q)\] done clear
  C)
   \[(A)\to (r),(B)\to (s),(C)\to (p),(D)\to (q)\] done clear
  D)
   \[(A)\to (s),(B)\to (r),(C)\to (q),(D)\to (p)\] done clear
  View Solution play_arrow

• question_answer104)
  Which of the following is not a polynomial?     (i) \[3{{x}^{\frac{1}{2}}}-4x+3\]              (ii) \[x=1\] (iii) \[y=0,x=6\]          (iv) \[x+y=a\]
  A)
  (i), (ii) and (iii) only done clear
  B)
  (iii) only done clear
  C)
  (i), (iv) only done clear
  D)
  (ii) only               done clear
  View Solution play_arrow

• question_answer105)
  Which of the following statement (s) is/are correct? (i) \[xy=b,\] is a polynomial (ii) \[\frac{1}{{{x}^{3}}}+\frac{1}{{{y}^{3}}}\] is polynomial. (iii) \[\frac{{{a}^{3}}-3ab}{{{b}^{3}}}\]is a polynomial (iv) \[\frac{{{a}^{3}}-3a}{{{b}^{3}}}\] is a polynomial
  A)
  (i) and (iv)                   done clear
  B)
  (ii) and (iii) done clear
  C)
  (i) and (iii)                   done clear
  D)
  (iii) and (iv) done clear
  View Solution play_arrow

• question_answer106)
  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: Degree of the polynomial \[\frac{{{a}^{3}}-3}{h}\] is 2. Reason: The degree of a polynomial of one variable is the highest value of the exponent of the variable.
  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 A. 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_answer107)
  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: Binomials and trinomials are multinomials. Reason: An algebraic expression having two or more terms is called a multinomial.
  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 A. 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_answer108)
  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: If 2, 3 are the zeroes of a quadratic polynomial, then polynomial is \[{{x}^{2}}-5x+8\] Reason: If \[\frac{{{a}^{3}}-3}{{{b}^{2}}}\]are the zeroes of a monic quadratic polynomial, then polynomial is\[x=\frac{1}{2}\]
  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 A. 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_answer109)
  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: Zeroes of \[\begin{align}   & x+\overset{1}{\mathop{\_\_\_\_\_\_\_}}\, \\  & 1+\overset{1}{\mathop{\_\_\_\_}}\, \\  & 1+\frac{1}{x} \\ \end{align}\] are 5, \[-\]1 Reason: The polynomial whose zeroes are \[\frac{5}{4}\] is \[\frac{4}{5}\]
  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 A. 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_answer110)
  DIRECTIONS: For the following questions write your answer would be only in single number. Do not write in word. If \[\frac{3}{4}\] and \[{{2}^{2x-y}}=32\], then the value of \[{{2}^{x+y}}=16\] is equal to ______ *-correct-answer-description-* \[a-b+5,2a-2b+5\] Now, \[{{(x-y)}^{3}}={{x}^{3}}-{{y}^{3}}-3xy\,(x-y)\] \[ab+bc+ca=26,\]  \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] \[x:\frac{x-a}{b+c}+\frac{x-b}{c+a}+\frac{x-c}{a+b}=3\] *-question-type-* 6 *-question-instructions-* 0
  View Solution play_arrow

• question_answer111)
  DIRECTIONS: For the following questions write your answer would be only in single number. Do not write in word. If \[x+\frac{1}{x}=2\] then \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] is equal to ______ *-correct-answer-description-* \[x+\frac{1}{x}=2\] Squaring both sides, we get             \[{{\left( x+\frac{1}{x} \right)}^{2}}=4\] \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}+2=4\]             \[\Rightarrow \] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=2\] *-question-type-* 6 *-question-instructions-* 0
  View Solution play_arrow

• question_answer112)
  DIRECTIONS: For the following questions write your answer would be only in single number. Do not write in word. In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x - 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, then x = _________ *-correct-answer-description-* \[\frac{(x+2)\times 60+x\times 120+(x-2)\times 180}{x+2+x+x-2}=100\] \[\Rightarrow \]  \[\frac{60x+120+120x+180x-360}{3x}=100\] \[\Rightarrow \] \[360x-240=300x\] \[\Rightarrow \] \[60x=240\] \[\Rightarrow \]\[x=4\] *-question-type-* 6 *-question-instructions-* 0
  View Solution play_arrow

• question_answer113)
  DIRECTIONS: For the following questions write your answer would be only in single number. Do not write in word. The difference of the degrees of the polynomials   \[p(x)=3{{x}^{2}}{{y}^{3}}+5x{{y}^{7}}-{{x}^{6}}\]and \[{{x}^{2}}\] is ___________ *-correct-answer-description-* Maximum degree of \[p(n)=1+7=8\] Maximum degree of \[q(n)=5\] Difference \[=8-5=3\] *-question-type-* 6 *-question-instructions-* 0
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• question_answer114)
  DIRECTIONS: For the following questions write your answer would be only in single number. Do not write in word. If \[x-\frac{1}{x}=\sqrt{6},\] then \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=\_\_\_\_\_\_\_\_\_\_\] *-correct-answer-description-* \[x-\frac{1}{x}=\sqrt{6}\] Squaring on both sides, we get \[{{\left( x-\frac{1}{x} \right)}^{2}}={{\left( \sqrt{6} \right)}^{2}}\] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2.x\frac{1}{x}=6\] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=6+3=8.\] *-question-type-* 6 *-question-instructions-* 0
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