10th Class Mathematics Related to Competitive Exam Question Bank

done Algebra Total Questions - 242

• question_answer1)
  If the equation \[4{{x}^{2}}+x(p+1)=0\] has exactly two equal roots, then one of the values of p is
  A)
  5                                              done clear
  B)
  - 3 done clear
  C)
  0                              done clear
  D)
         3   done clear
  View Solution play_arrow

• question_answer2)
  If a and b are the roots of the equation \[5{{x}^{2}}-x-2=0\], then the equation for which roots are\[\frac{2}{\alpha }\] and\[\frac{2}{\beta }\] is
  A)
  \[{{x}^{2}}-x+10=0\]    done clear
  B)
         \[{{x}^{2}}-x-10=0\] done clear
  C)
  \[{{x}^{2}}+x+10=0\]    done clear
  D)
          \[{{x}^{2}}+x-10=0\]   done clear
  View Solution play_arrow

• question_answer3)
  The sum of the coefficients of even powers of\[x\]a polynomial \[f(x)\] is
  A)
  \[f(1)\]                                 done clear
  B)
  \[f(0)\] done clear
  C)
  \[\frac{f(1)+f(-1)}{2}\]     done clear
  D)
  \[\frac{f(1)-f(-1)}{2}\] done clear
  View Solution play_arrow

• question_answer4)
  The G.C.D. of \[{{x}^{3}}-{{x}^{2}}-4x-6\] and \[{{x}^{2}}-2x-3\] is
  A)
  \[3x+2\]               done clear
  B)
         \[x-3\]   done clear
  C)
  \[-x-3\]                 done clear
  D)
         \[-2x-3\] done clear
  View Solution play_arrow

• question_answer5)
  The remainder when \[{{x}^{4}}-{{y}^{4}}\]is divided by x -y is
  A)
  0                                                done clear
  B)
  \[x-3\] done clear
  C)
  \[{{x}^{2}}-{{y}^{2}}\]           done clear
  D)
         \[2{{y}^{4}}\] done clear
  View Solution play_arrow

• question_answer6)
  If \[{{x}^{3}}-5x+7\] is divisible by \[(x+2)\], then the remainder is
  A)
  -21                            done clear
  B)
         -20 done clear
  C)
  - 17                         done clear
  D)
         - 25 done clear
  View Solution play_arrow

• question_answer7)
  H.C.F. of \[{{x}^{3}}-1\] and \[{{x}^{4}}+{{x}^{2}}+1\] will be
  A)
  \[x-1\]                                  done clear
  B)
  \[{{x}^{2}}+x+1\]   done clear
  C)
  \[{{x}^{2}}-x+1\]              done clear
  D)
         \[{{x}^{2}}-x-1\] done clear
  View Solution play_arrow

• question_answer8)
  The L.C.M. of \[xy+yz+zx+{{y}^{2}}\] and \[{{x}^{2}}+xy+yz+zx\] is
  A)
   \[x+y\]                done clear
  B)
         \[y+z\] done clear
  C)
  \[(x+y)(y+z)(z+x)\]           done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  The solution of \[\frac{2x+3}{2x-1}=\frac{3x-1}{3x+1}\]is
  A)
  \[\frac{1}{8}\]                    done clear
  B)
         \[-\frac{1}{8}\]   done clear
  C)
  \[\frac{8}{3}\]                    done clear
  D)
         \[-\frac{8}{3}\] done clear
  View Solution play_arrow

• question_answer10)
  If \[x-\frac{1}{x}=2\], then the value of \[{{x}^{4}}+\frac{1}{{{x}^{4}}}\] is
  A)
   4                                             done clear
  B)
   8 done clear
  C)
  12                           done clear
  D)
         34   done clear
  View Solution play_arrow

• question_answer11)
  The equation whose roots are 4 and 5 is
  A)
  \[{{x}^{2}}+9x+20=0\] done clear
  B)
  \[{{x}^{2}}-9x-20=0\] done clear
  C)
  \[{{x}^{2}}-9x+20=0\]   done clear
  D)
  \[{{x}^{3}}+9x+20=0\] done clear
  View Solution play_arrow

• question_answer12)
  The value .of   \[{{\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)}^{\frac{1}{bc}}}.{{\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right)}^{\frac{1}{ca}}}.{{\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right)}^{\frac{1}{ab}}}\] on simplifying is
  A)
  \[x\]                                      done clear
  B)
  \[\frac{1}{x}\] done clear
  C)
  1                                done clear
  D)
         - 1 done clear
  View Solution play_arrow

• question_answer13)
  The value of \[x\], y and z respectively on simplifying the equations \[2x+3y=0,\]\[3y+4z=14,\]\[2x+4z=26,\] is
  A)
  3,-2, 5                                      done clear
  B)
  -3,2,5 done clear
  C)
  - 3, 2, - 5         done clear
  D)
          3, 2, 5 done clear
  View Solution play_arrow

• question_answer14)
  If \[{{a}^{m}}.{{a}^{n}}={{a}^{mn}}\], then \[m(n-2)+n(m-2)\] is
  A)
  1                              done clear
  B)
         - 1 done clear
  C)
  0                                                done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer15)
  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_answer16)
  The value of \[{{x}^{2}}-6x+13\]can never be less than
  A)
  4                                                done clear
  B)
  5 done clear
  C)
  4.5                          done clear
  D)
         7 done clear
  View Solution play_arrow

• question_answer17)
  In n is a whole number greater than 1, then n \[\left( {{\text{n}}^{\text{2}}}\text{ }-\text{ 1} \right)\]is always divisible by
  A)
  12                                             done clear
  B)
  12 and 24 done clear
  C)
  24                           done clear
  D)
         36 done clear
  View Solution play_arrow

• question_answer18)
  In solving an equation of the form \[ax+b=0\] (a, b having only 1 as the common factor). A made a mistake in copying 6 and got \[\frac{7}{3}\] as the root whereas B made a mistake in copying a and got \[\frac{8}{5}\] as the root. The correct root is
  A)
  \[\frac{7}{5}\]                                    done clear
  B)
  \[\frac{3}{8}\] done clear
  C)
  \[\frac{8}{3}\]                      done clear
  D)
         \[\frac{8}{5}\] done clear
  View Solution play_arrow

• question_answer19)
  The polynomial (in \[x\]):\[{{x}^{6}}+18{{x}^{3}}+125\], admits
  A)
  No factor of degree between 2 and 5 done clear
  B)
  \[{{x}^{2}}-3x+5\] as a factor   done clear
  C)
  \[x+1\] as a factor done clear
  D)
  \[x-125\] as a factor done clear
  View Solution play_arrow

• question_answer20)
  If \[{{a}^{x}}=b,\,{{b}^{y}}=c,\,{{c}^{z}}=a\], then the value of \[xyz\] is
  A)
  0                              done clear
  B)
         1   done clear
  C)
  \[\frac{1}{abc}\]              done clear
  D)
          abc done clear
  View Solution play_arrow

• question_answer21)
  If the index of any power function is zero, then the value of that function is
  A)
   0                             done clear
  B)
          1   done clear
  C)
   - 1                          done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer22)
  If \[f:R\to R,f(x)={{x}^{2}}+8\], then \[f(-3)\] is
  A)
   1                             done clear
  B)
          - 17 done clear
  C)
   - 1                          done clear
  D)
          17   done clear
  View Solution play_arrow

• question_answer23)
  If \[f(x)={{x}^{2}},x>0\] then the function is
  A)
   not one to one function done clear
  B)
   one to one function   done clear
  C)
   into function done clear
  D)
   none of these done clear
  View Solution play_arrow

• question_answer24)
  Five tables and eight chairs cost Rs. 7,350 three tables and five chairs cost Rs. 4,475. The price of a table is
  A)
   Rs. 950                   done clear
  B)
   Rs. 325 done clear
  C)
   Rs. 925           done clear
  D)
          Rs. 350 done clear
  View Solution play_arrow

• question_answer25)
  If sum and difference of two expressions is \[5{{x}^{2}}-x-4\] and \[{{x}^{2}}+9x-10\] respectively, then the expressions are
  A)
   \[(4{{x}^{2}}+8x-6),(4{{x}^{2}}-10x+2)\] done clear
  B)
   \[(2{{x}^{2}}+4x-3),(3{{x}^{2}}-10x-6)\] done clear
  C)
   \[(3{{x}^{2}}+4x-7),(2{{x}^{2}}-5x+3)\]   done clear
  D)
   \[(3{{x}^{2}}+4x+7),(2{{x}^{2}}-5x-3)\] done clear
  View Solution play_arrow

• question_answer26)
  If the sum and the product of two numbers are 25 and 144 respectively, then the difference of the numbers must be
  A)
   3                             done clear
  B)
          5 done clear
  C)
   7                               done clear
  D)
          11 done clear
  View Solution play_arrow

• question_answer27)
  Range of function \[f(x)=\frac{1}{1-x}\]is
  A)
   set of rational numbers done clear
  B)
   set of real numbers except zero   done clear
  C)
   set of natural numbers done clear
  D)
   set of integers done clear
  View Solution play_arrow

• question_answer28)
  If \[f(x)=|x|\,\,\,\forall x\in R\], then the function is
  A)
   not one to one function done clear
  B)
   one to one function done clear
  C)
   into function   done clear
  D)
   not into function done clear
  View Solution play_arrow

• question_answer29)
  If l\[\log (x+1)+\log (x-1)=\log 3\], then value of x is
  A)
   3                             done clear
  B)
          2   done clear
  C)
   1                             done clear
  D)
          none of these done clear
  View Solution play_arrow

• question_answer30)
  \[{{3}^{x-y}}=27\] and \[{{3}^{x+y}}=243\], then \[x\] is equal to
  A)
   0                                             done clear
  B)
   4   done clear
  C)
   2                             done clear
  D)
          6 done clear
  View Solution play_arrow

• question_answer31)
  If \[p+q=1\] and the ordered pair (p, q) satisfies \[3x+2y=1\], then it also satisfies
  A)
   \[3x+3y=3\]          done clear
  B)
          \[5x+4y=4\] done clear
  C)
   \[5x+4y=4\]        done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer32)
  The age of a father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference of ages of the two sons is 15 years, the age of the father is
  A)
   100 years         done clear
  B)
          70 years done clear
  C)
   60 years          done clear
  D)
          50 years   done clear
  View Solution play_arrow

• question_answer33)
  If \[{{\log }_{10}}a+{{\log }_{10}}b={{\log }_{10}}(a+b)\], then
  A)
   \[a=b=2\]          done clear
  B)
  \[~\text{a}=\text{b}=\text{1}\] done clear
  C)
   \[a=\frac{{{b}^{2}}}{1-b}\]          done clear
  D)
          \[a=\frac{b}{b-1}\]   done clear
  View Solution play_arrow

• question_answer34)
  If \[x=\frac{1}{5+\frac{1}{5+\frac{1}{5}}}\] , then
  A)
   \[{{x}^{2}}+5x-1=0\]       done clear
  B)
   \[{{x}^{2}}-5x-1=0\] done clear
  C)
   \[{{x}^{2}}-5x+1=0\] done clear
  D)
          \[{{x}^{2}}+5x+1=0\] done clear
  View Solution play_arrow

• question_answer35)
  The values of \[x\] and y satisfying the two equations \[32x+33y=31,33x+32y=34\] respectively will be
  A)
   -1,2                       done clear
  B)
          2, - 1   done clear
  C)
   0, 0                        done clear
  D)
          2, 3 done clear
  View Solution play_arrow

• question_answer36)
  If \[2{{x}^{3}}+4{{x}^{2}}+2ax+b\] is exactly divisible by \[{{x}^{2}}-1\],then the value of a and b respectively will be
  A)
   1, 2                        done clear
  B)
          - 1, 4 done clear
  C)
   1, - 2                     done clear
  D)
          -1, - 4   done clear
  View Solution play_arrow

• question_answer37)
  The sum of \[\frac{1}{x+y}\]and \[\frac{1}{x-y}\]is
  A)
   \[\frac{2y}{{{x}^{2}}-{{y}^{2}}}\]                              done clear
  B)
   \[\frac{2x}{{{x}^{2}}-{{y}^{2}}}\]   done clear
  C)
   \[\frac{2x}{{{y}^{2}}-{{x}^{2}}}\]              done clear
  D)
          \[\frac{-2y}{{{x}^{2}}-{{y}^{2}}}\] done clear
  View Solution play_arrow

• question_answer38)
  The greatest value assumed by the function \[f(x)=5-|x-3|\] is
  A)
   3                                             done clear
  B)
   8 done clear
  C)
   6                             done clear
  D)
          5   done clear
  View Solution play_arrow

• question_answer39)
  The value of  \[\frac{{{2}^{m+3}}\times {{3}^{2m-n}}\times {{5}^{m+n+3}}\times {{6}^{n+1}}}{{{6}^{m+1}}\times {{10}^{n+3}}\times {{15}^{m}}}\]is equal to
  A)
   0                             done clear
  B)
          1   done clear
  C)
   \[{{2}^{m}}\]                     done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer40)
  If \[x=2,\,y=1\] and \[z=-3\] then \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\]is equal to
  A)
   6                             done clear
  B)
          0   done clear
  C)
   2                             done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer41)
  If \[{{3}^{4x-2}}=729\], then the value of \[x\] is
  A)
   3                             done clear
  B)
          1.2 done clear
  C)
   2                               done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer42)
  \[{{x}^{3}}+a{{x}^{2}}-7x-6\] can be factorised into 3 linear factors when
  A)
   a = 0                                        done clear
  B)
   a = 1 done clear
  C)
   a = 2                      done clear
  D)
          a = 3 done clear
  View Solution play_arrow

• question_answer43)
  The number of prime numbers between 0 and 20 is
  A)
   7                             done clear
  B)
          8   done clear
  C)
   6                             done clear
  D)
          9 done clear
  View Solution play_arrow

• question_answer44)
  The equation \[\frac{(x+2)(x-5)}{(x-3)(x+6)}=\frac{x-2}{x+4}\] has
  A)
   3 roots                 done clear
  B)
   2 roots done clear
  C)
   1 root               done clear
  D)
          no root done clear
  View Solution play_arrow

• question_answer45)
  The sum of two numbers is 9 and the sum of their squares is 41. The numbers are
  A)
   4 and 5                   done clear
  B)
   1 and 8 done clear
  C)
   3 and 6                 done clear
  D)
          2 and 7 done clear
  View Solution play_arrow

• question_answer46)
  If the sum of the squares of roots of the equation \[{{x}^{2}}+2x-p=0\] is 10, then the value of p will be
  A)
   - 3                                            done clear
  B)
   3 done clear
  C)
   6                             done clear
  D)
          - 6 done clear
  View Solution play_arrow

• question_answer47)
  lf \[h(x)={{x}^{2}}-2\], then the value of \[\frac{1}{2}h\left( \frac{1}{2} \right)\] his
  A)
   0                             done clear
  B)
          1 done clear
  C)
   \[-\frac{7}{8}\]                   done clear
  D)
          \[\frac{7}{8}\] done clear
  View Solution play_arrow

• question_answer48)
  If \[{{2}^{2x-y}}=32\] and \[{{2}^{x+y}}=16\] then \[{{x}^{2}}+{{y}^{2}}\] is equal to
  A)
   9                                             done clear
  B)
   10   done clear
  C)
   11                          done clear
  D)
          13 done clear
  View Solution play_arrow

• question_answer49)
  Factors of \[\text{2}\left( \text{a }+\text{ b} \right)\text{2}-\text{9}\left( \text{a }+\text{ b} \right)-\text{5}\] are
  A)
   \[a+b+5,2a+2b-1\] done clear
  B)
   \[\text{a}+\text{b}-\text{5},\text{2a}+\text{2b}+\text{1}\]   done clear
  C)
   \[a-b+5,2a-2b+5\] done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer50)
  If \[x-\frac{1}{x-2}=2-1\frac{1}{x-2}\] , then x is equal to
  A)
   1                                             done clear
  B)
   2 done clear
  C)
   1                                             done clear
  D)
   None of these   done clear
  View Solution play_arrow

• question_answer51)
  If\[\frac{1}{x}+\frac{1}{y}=\frac{1}{2z}\] then z is equal to
  A)
   \[\frac{x+y}{2xy}\]                         done clear
  B)
   \[\frac{xy}{2(x+y)}\]   done clear
  C)
   \[\frac{xy}{(x+y)}\]        done clear
  D)
          \[\frac{x+y}{xy}\] done clear
  View Solution play_arrow

• question_answer52)
  If \[{{a}^{x}}={{b}^{y}}\]and \[{{b}^{2}}=ac\], then \[\frac{1}{x}+\frac{1}{z}\]
  A)
   \[\frac{2}{y}\]                                     done clear
  B)
   \[\frac{1}{y}\] done clear
  C)
   \[\frac{1}{2}y\]                done clear
  D)
          \[2y\] done clear
  View Solution play_arrow

• question_answer53)
   If re, ,y, z are positive real numbers and a, b, c are rational numbers, then the value of \[\frac{1}{1+{{x}^{b-a}}+{{x}^{x-a}}}+\frac{1}{1+{{x}^{a-b}}+{{x}^{c-b}}}+\frac{1}{1+{{x}^{b-c}}+{{x}^{a-c}}}\]
  A)
   - 1                                          done clear
  B)
   1   done clear
  C)
   0                             done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer54)
  The product\[\left( 1-\frac{1}{n} \right)\left( 1-\frac{1}{n+1} \right)\left( 1-\frac{1}{n+2} \right)......\left( 1-\frac{1}{2n} \right)\] equals
  A)
   \[\frac{n-1}{2n}\]              done clear
  B)
          \[\frac{1}{2n}\] done clear
  C)
   \[\frac{2n}{n-1}\]            done clear
  D)
          \[\frac{1}{n}\] done clear
  View Solution play_arrow

• question_answer55)
  For which of the following function is : \[\frac{f-f}{a-b}\] Constant for all number a and b where \[a\ne b\]?
  A)
  \[f(x)=4x+7\]       done clear
  B)
   \[f(x)=x+{{x}^{2}}\] done clear
  C)
   \[f(x)=\cos x\]       done clear
  D)
          \[f(x)={{\log }_{e}}x\] done clear
  View Solution play_arrow

• question_answer56)
  After travelling for 30 minutes a train meets an accident, due to which it has to stop for 45 minutes. Due to the accident its speed is also reduced to \[\frac{2}{3}\] of its former value and the train reaches its destination 1 hour 30 minutes late. Had the accident occurred 60 km later, the train would have reached 30 minutes earlier. The length of journey is
  A)
   90 km                   done clear
  B)
          120 km   done clear
  C)
   150 km                 done clear
  D)
          180 km done clear
  View Solution play_arrow

• question_answer57)
  If p, q and r are in A.R, then which of the following statements is correct?
  A)
   \[pq+qr-2{{q}^{2}}=0\]   done clear
  B)
   \[pq+qr-2{{p}^{2}}=0\] done clear
  C)
   \[pq+qr-pqr=0\] done clear
  D)
   \[pq+qr-2{{r}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer58)
  The value of \[{{1}^{2}}+{{2}^{2}}+{{3}^{2}}+.....+{{n}^{2}}\]is
  A)
   \[\frac{n(n+1)}{2}\]          done clear
  B)
          \[\frac{n(n+1)(2n+1)}{6}\]   done clear
  C)
   \[\frac{n(n+1)(2n-1)}{6}\] done clear
  D)
          \[{{\left[ \frac{n(n+1)}{2} \right]}^{2}}\] done clear
  View Solution play_arrow

• question_answer59)
  \[f(x),g(x)\] are two polynomial with integer coefficient such that their HCF is 1 and LCM is \[({{x}^{2}}-4)({{x}^{4}}-1)\]lf \[f(x)={{x}^{3}}-2{{x}^{2}}-x+2\] then \[g(x)\]is
  A)
   \[{{x}^{3}}-2{{x}^{2}}+x+2\] done clear
  B)
  \[{{x}^{3}}-2{{x}^{2}}+x-2\] done clear
  C)
   \[{{x}^{3}}+2{{x}^{2}}+x+2\]   done clear
  D)
   \[{{x}^{3}}-2{{x}^{2}}-x-2\] done clear
  View Solution play_arrow

• question_answer60)
  If \[x-\frac{1}{x}=5\]then \[{{x}^{3}}-\frac{1}{{{x}^{3}}}\]equals
  A)
   125                        done clear
  B)
          130 done clear
  C)
   135                        done clear
  D)
          140   done clear
  View Solution play_arrow

• question_answer61)
  If \[{{c}_{0}},{{c}_{1}},{{c}_{2}}....,{{c}_{n}}\]denote the binomial coefficients in the expression of \[{{(1+x)}^{n}}\], then find the value of \[{{c}_{0}},+{{c}_{1}},+{{c}_{2}}+....,{{c}_{n}}+:\]
  A)
   \[{{2}^{n-1}}\]                  done clear
  B)
         \[{{2}^{n}}\]   done clear
  C)
   \[{{2}^{n+1}}\]                 done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer62)
  The sum of the series\[1+{{\log }_{e}}2+\frac{{{({{\log }_{e}}2)}^{2}}}{2!}+\frac{{{({{\log }_{e}}2)}^{2}}}{3!}+.....\,\,\,to\,\,\infty \] is
  A)
   2                               done clear
  B)
          1 done clear
  C)
   0                             done clear
  D)
          - done clear
  View Solution play_arrow

• question_answer63)
  The expansion of log \[{{\log }_{e}}\frac{1}{(1-x)}\]is
  A)
   \[x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] done clear
  B)
          \[x+\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}+\,.....\]   done clear
  C)
   \[1-x+\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}+\,.....\] done clear
  D)
         \[1+x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] done clear
  View Solution play_arrow

• question_answer64)
  If \[x\] and y are positive with \[x-y=2\] and \[xy=24\], then \[\frac{1}{x}+\frac{1}{y}\]is equal to
  A)
   \[\frac{5}{12}\]                  done clear
  B)
          \[\frac{1}{12}\] done clear
  C)
   \[\frac{1}{6}\]                   done clear
  D)
          \[\frac{25}{6}\] done clear
  View Solution play_arrow

• question_answer65)
  If \[f(x)=\frac{2x+5}{{{x}^{2}}+x+5}\], then \[f[f(-1)]\] is equal to
  A)
   \[\frac{149}{155}\]                         done clear
  B)
          \[\frac{155}{147}\] done clear
  C)
   \[\frac{155}{149}\]                           done clear
  D)
          \[\frac{147}{155}\] done clear
  View Solution play_arrow

• question_answer66)
  If\[x+\frac{1}{x}=2\] then, \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] is equal to
  A)
   2                                               done clear
  B)
   0 done clear
  C)
   4                             done clear
  D)
          6 done clear
  View Solution play_arrow

• question_answer67)
  The expression \[\frac{5-x}{{{x}^{2}}-x-20}\]when simplified, equals
  A)
   \[\frac{1}{x+4}\]                              done clear
  B)
   \[\frac{1}{x-4}\] done clear
  C)
   \[\frac{1}{x+4}\]                done clear
  D)
          \[\frac{1}{x-5}\] done clear
  View Solution play_arrow

• question_answer68)
  The value of k, for which the system of equation \[kx+2y=5,3x+y=1\] has no solution, is
  A)
   5                             done clear
  B)
          \[\frac{2}{3}\] done clear
  C)
   6                               done clear
  D)
          \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer69)
  Mohan gets 3 marks for each correct sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums solved correctly is
  A)
   10                                          done clear
  B)
   15 done clear
  C)
   20                            done clear
  D)
          25 done clear
  View Solution play_arrow

• question_answer70)
  If \[x\] satisfies \[|x-1|+|x-2|+|x-3|\,\,\,\ge 6\], then
  A)
   \[0\le 0\le 4\]                   done clear
  B)
          \[x\le 0\,\,or\,\,x\ge 4\]   done clear
  C)
   \[x\le -2\,\,or\,\,x\ge 4\]  done clear
  D)
          \[x\ge -2\,\,or\,\,x\le 4\] done clear
  View Solution play_arrow

• question_answer71)
  If \[a+b+c=0\], the value of \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\]is
  A)
   1                                             done clear
  B)
   0 done clear
  C)
   - 1                          done clear
  D)
          3   done clear
  View Solution play_arrow

• question_answer72)
  Which one of the following statements is correct?
  A)
   The set of natural numbers has the distributive property of multiplication over subtraction   done clear
  B)
   The set of natural number is associative under subtraction done clear
  C)
   The set of integers is not distributive under multiplication done clear
  D)
   The set of natural number is finite done clear
  View Solution play_arrow

• question_answer73)
  If \[{{2}^{x}}-{{2}^{x-1}}=4\], then \[{{x}^{x}}\] is equal to
  A)
   7                             done clear
  B)
          3 done clear
  C)
   27                            done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer74)
  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)
   comprise number           done clear
  D)
   none of these done clear
  View Solution play_arrow

• question_answer75)
  If \[x=2,\,y=3\], then \[{{x}^{2}}+{{y}^{3}}\]is equal to
  A)
   30                          done clear
  B)
          37 done clear
  C)
   33                          done clear
  D)
          31   done clear
  View Solution play_arrow

• question_answer76)
  If \[f(x)=\frac{{{x}^{2}}-5x+6}{x-2}\] ,\[x\ne 2\]then \[f(3)\] is equal to
  A)
   8                                             done clear
  B)
   6 done clear
  C)
   2                             done clear
  D)
          0   done clear
  View Solution play_arrow

• question_answer77)
  The value of \[k\] for which the roots of equation \[(x-1)(x-5)+k=0\] differ by 2 is
  A)
   3                               done clear
  B)
          6 done clear
  C)
   \[-3\]                    done clear
  D)
          \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer78)
  The value of the expression\[\sqrt{6+\sqrt{6+\sqrt{6+....+upto\,\,\infty \,\,}}}\] is
  A)
   2                             done clear
  B)
          3   done clear
  C)
   30                          done clear
  D)
          5 done clear
  View Solution play_arrow

• question_answer79)
  A lady has only 25 paise and 50-paise coins in her purse. She has a total of 120 coins and the total amount is Rs. 50. The number of coins of each type in her purse, respectively, is
  A)
   90, 30                   done clear
  B)
          60, 60 done clear
  C)
   40, 80   done clear
  D)
   70, 50 done clear
  View Solution play_arrow

• question_answer80)
  The largest angle of a triangle is twice the sum of the other two and the smallest one is one fourth of the largest. The agles are
  A)
  \[120{}^\circ ,\text{ }40{}^\circ ,\text{ }20{}^\circ \]    done clear
  B)
         \[120{}^\circ ,\text{ }30{}^\circ ,\text{ }30{}^\circ \]   done clear
  C)
  \[90{}^\circ ,\text{ }45{}^\circ ,\text{ }45{}^\circ \] done clear
  D)
         \[~90{}^\circ ,\text{ }60{}^\circ ,\text{ }30{}^\circ \] done clear
  View Solution play_arrow

• question_answer81)
  Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will start ringing together after
  A)
   6 minutes        done clear
  B)
          12 minutes   done clear
  C)
   18 minutes       done clear
  D)
          24 minutes done clear
  View Solution play_arrow

• question_answer82)
  A leap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of coconuts in the leap is
  A)
   11                          done clear
  B)
          21 done clear
  C)
   31                            done clear
  D)
          41 done clear
  View Solution play_arrow

• question_answer83)
  If one root of \[{{x}^{2}}-4x+k=0\] is 6, then the value of k is
  A)
   12                          done clear
  B)
          2 done clear
  C)
  -2                            done clear
  D)
         -12   done clear
  View Solution play_arrow

• question_answer84)
  The number \[{{10}^{n}}-1\] is divisible by 11 for
  A)
   odd values of n done clear
  B)
   even values of n   done clear
  C)
   all values of n done clear
  D)
   n, a multiple of 11 done clear
  View Solution play_arrow

• question_answer85)
  It costs Rs. 10 a kilometer to fly and Rs. 2 a kilometer to drive. If one travels 200 km covering fi \[x\] km of the distance by flying and the rest by driving, then the cost of the trip is
  A)
   Rs. 2,000         done clear
  B)
          Rs. 24,000 done clear
  C)
   Rs. (8\[x\] + 400)      done clear
  D)
         Rs. (12\[x\] + 400) done clear
  View Solution play_arrow

• question_answer86)
  For the equation\[|x{{|}^{2}}+|x|-6=0\]
  A)
   there is only one root done clear
  B)
   the sum of the roots is 1 done clear
  C)
   the sum of the roots is 0   done clear
  D)
   the product of the roots is 4 done clear
  View Solution play_arrow

• question_answer87)
  If \[A=\{x:{{x}^{2}}-3x+2=0\}\]and \[B=\{x:{{x}^{2}}+4x-5=0\}\] then the value of A - B is
  A)
   \[\{1,2\}\]                          done clear
  B)
   {2}   done clear
  C)
   \[\{1\}\]                              done clear
  D)
          {5, 2} done clear
  View Solution play_arrow

• question_answer88)
  The value of\[\frac{{{x}^{a+b}}.{{x}^{b+c}}.{{x}^{c+a}}}{{{({{x}^{a}}.{{x}^{b}}.{{x}^{c}})}^{2}}}\]
  A)
   \[{{x}^{2}}\]                      done clear
  B)
         \[{{x}^{a+b+c}}\] done clear
  C)
   \[{{x}^{abc}}\]                  done clear
  D)
          \[{{x}^{0}}\]   done clear
  View Solution play_arrow

• question_answer89)
  The H.C.F. of 608, 544; 638, 783; and 425, 476 respectively is
  A)
   32,29, 17           done clear
  B)
          17,32, 29 done clear
  C)
   29,32, 17         done clear
  D)
          32,17,29 done clear
  View Solution play_arrow

• question_answer90)
  If one root of the equation \[3{{x}^{2}}-9x=kx-k\] is 2,then the value of k is
  A)
   4                             done clear
  B)
          3 done clear
  C)
   - 6                            done clear
  D)
          - 8 done clear
  View Solution play_arrow

• question_answer91)
  If the expression\[(125-{{x}^{3}}=(5-x)({{x}^{2}}+ax+b)\], then the value of 'a' is
  A)
   4                             done clear
  B)
          2 done clear
  C)
   - 7                          done clear
  D)
          5   done clear
  View Solution play_arrow

• question_answer92)
  The value of \[x\] satisfying the equation\[{{x}^{2}}+{{p}^{2}}={{(q-x)}^{2}}\] is
  A)
  \[\frac{{{p}^{2}}-{{q}^{2}}}{2}\] done clear
  B)
  \[\frac{{{q}^{2}}-{{p}^{2}}}{2q}\]   done clear
  C)
  \[\frac{{{q}^{2}}-{{p}^{2}}}{2}\] done clear
  D)
  \[\frac{{{p}^{2}}-{{q}^{2}}}{2q}\] done clear
  View Solution play_arrow

• question_answer93)
  The equations \[3x-5y+2=0\] and \[6x+4=10y\] have
  A)
   No solution(s) done clear
  B)
   A single solution done clear
  C)
   Two solutions done clear
  D)
   An infinite number of solutions   done clear
  View Solution play_arrow

• question_answer94)
  If \[\alpha \] and \[\beta \] be the roots of the equation \[{{x}^{2}}+px+q=0\], then the equation whose roots are \[{{\alpha }^{2}}+\alpha \beta \]and \[{{\beta }^{2}}+\alpha \beta \]is
  A)
   \[{{x}^{2}}+{{p}^{2}}x+{{P}^{2}}q=0\] done clear
  B)
   \[{{x}^{2}}-{{q}^{2}}x+{{P}^{2}}q=0\] done clear
  C)
   \[{{x}^{2}}+{{q}^{2}}x+{{P}^{2}}q=0\] done clear
  D)
   \[{{x}^{2}}-{{p}^{2}}x+{{P}^{2}}q=0\]   done clear
  View Solution play_arrow

• question_answer95)
  The solution set of the equation \[{{x}^{\frac{2}{3}}}+{{x}^{\frac{1}{3}}}=2\] is
  A)
   \[\{-8,1\}\]                           done clear
  B)
          {8,1} done clear
  C)
  \[\text{ }\!\!\{\!\!\text{ 1},-\text{1}\}\]                done clear
  D)
          \[\{2,-2\}\] done clear
  View Solution play_arrow

• question_answer96)
  A student walks from his house at 4 km per hour and reaches his school late by 5 minutes. If his speed has been 5 km per hour then he would have reached 10 minutes early. The distance of the school from his house is
  A)
   \[\frac{5}{3}\]km           done clear
  B)
          5 km   done clear
  C)
   6 km                                     done clear
  D)
   4 km done clear
  View Solution play_arrow

• question_answer97)
  The v.lu. of \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{1}{4} \right)\left( 1-\frac{1}{5} \right).......\left( 1-\frac{1}{n} \right)\] is equal to
  A)
   \[\frac{1}{n}\]                  done clear
  B)
          \[\frac{2}{n}\]   done clear
  C)
   \[\frac{3}{n}\]                    done clear
  D)
          \[\frac{4}{n}\] done clear
  View Solution play_arrow

• question_answer98)
  The equations representing in the adjoining graph are
  A)
   \[7x+2y=11;y-2x=3\] done clear
  B)
   \[2x+7y=11;\,5x+\frac{35}{2}y=25\] done clear
  C)
   \[3x-7y=10\,;8y-6x=4\] done clear
  D)
   \[3x-4y=1\,;8y-6x=4\]   done clear
  View Solution play_arrow

• question_answer99)
  Factors of \[4{{x}^{2}}-{{y}^{2}}+2x-2y-3xy\] are
  A)
   \[(x+y)(4x+y-2)\] done clear
  B)
  \[(x-y)(4x-y+2)\]   done clear
  C)
   \[(x+y)(4x-y-2)\] done clear
  D)
   \[(xy+2)\] done clear
  View Solution play_arrow

• question_answer100)
  If one factor of the expression \[{{x}^{3}}+7k{{x}^{2}}-4kx+12\]is \[(x+3)\], then the value of k is
  A)
   5                                             done clear
  B)
   \[\frac{1}{5}\]   done clear
  C)
   \[-\frac{13}{17}\]            done clear
  D)
          \[-\frac{17}{13}\] done clear
  View Solution play_arrow

• question_answer101)
  If  \[f(x)=5x-10\]is divided by \[x-\sqrt{2}\], then the remainder will be
  A)
   a non-zero rational number done clear
  B)
   an irrational number   done clear
  C)
   zero done clear
  D)
   \[f\left( \frac{1}{\sqrt{2}} \right)\] done clear
  View Solution play_arrow

• question_answer102)
  The value of m, in order that \[{{x}^{2}}-mx-2\] is the quotient when \[{{x}^{3}}+3{{x}^{2}}-4\]is divided by\[x+2\], is
  A)
   - 1                            done clear
  B)
          1 done clear
  C)
   0                             done clear
  D)
          - 2 done clear
  View Solution play_arrow

• question_answer103)
  The H.C.F. of two expressions is x and their L.C.M. is \[{{x}^{3}}-9x\]. If one of the expression is \[{{x}^{2}}+3x\], then the other expression is
  A)
   \[{{x}^{2}}-3x\]              done clear
  B)
          \[{{x}^{3}}-3x\] done clear
  C)
   \[{{x}^{2}}+9x\]               done clear
  D)
         \[{{x}^{2}}-9x\] done clear
  View Solution play_arrow

• question_answer104)
  If \[f(x)=2{{x}^{2}}-x+1\] and \[g(x)={{x}^{3}}-3x+1\] then the value of \[f(1)+g(-1)\] is
  A)
   2                             done clear
  B)
          3 done clear
  C)
   4                             done clear
  D)
          5   done clear
  View Solution play_arrow

• question_answer105)
  The smallest integral value of \[x\], for which \[\frac{5}{x}\] is an integer is
  A)
   1                             done clear
  B)
          - 1   done clear
  C)
   - 5                          done clear
  D)
          5 done clear
  View Solution play_arrow

• question_answer106)
  The factors of \[(2{{x}^{2}}-3x-2)(2{{x}^{2}}-3x)-63\]are
  A)
   \[(x-3)(2x+3)(x-1)(x-7)\] done clear
  B)
   \[(x+3)(2x-3)(x-1)(x-7)\] done clear
  C)
   \[(x+3)(2x+3)(2{{x}^{2}}-3x+7)\] done clear
  D)
   \[(x-3)(2x+3)(2{{x}^{2}}-3x+7)\]   done clear
  View Solution play_arrow

• question_answer107)
  A man's age is six times that of his son's age. In six years the father's age will be three times of the son's age. The age of the father and the son are respectively
  A)
   18, 3                      done clear
  B)
          30, 5 done clear
  C)
   24, 4                        done clear
  D)
          42, 7 done clear
  View Solution play_arrow

• question_answer108)
  The remainder when \[{{x}^{3}}-6{{x}^{2}}+11x-6\] is divided by\[x+2\] is
  A)
   - 60                          done clear
  B)
          - 39 done clear
  C)
   31                          done clear
  D)
          45 done clear
  View Solution play_arrow

• question_answer109)
  The remainder when \[{{x}^{6}}-3{{x}^{5}}+2{{x}^{2}}+8\] is divided by \[x+1\] is
  A)
   24                          done clear
  B)
          14   done clear
  C)
   8                             done clear
  D)
          18 done clear
  View Solution play_arrow

• question_answer110)
  The value of k for which (\[x+1\]) is a factor of\[{{x}^{3}}-k{{x}^{2}}+11x-6\]is
  A)
   - 5                          done clear
  B)
          2 done clear
  C)
    6                              done clear
  D)
          - 6 done clear
  View Solution play_arrow

• question_answer111)
  The value of k for which x + k is a factor of \[k{{x}^{2}}-2x+k+4\]is
  A)
  \[\frac{-4}{3}\]                                    done clear
  B)
   -5 done clear
  C)
   2                             done clear
  D)
          \[\frac{6}{7}\] done clear
  View Solution play_arrow

• question_answer112)
  The L.C.M. of \[2x+2,\,3{{x}^{2}}-12\] and \[4{{x}^{2}}+12x+8\] is
  A)
   \[12(x+1)(x-3)(x+2)\] done clear
  B)
   \[12(x+1)(x-2)(x+3)\] done clear
  C)
   \[12(x+1)(x-3)(x+3)\] done clear
  D)
  \[12(x+1)(x+2)(x+2)\]   done clear
  View Solution play_arrow

• question_answer113)
  If\[x-\frac{1}{x}=9\], the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\] is
  A)
   83                            done clear
  B)
          79 done clear
  C)
   11                          done clear
  D)
          7 done clear
  View Solution play_arrow

• question_answer114)
  The product of the reciprocal of \[\frac{x+3}{x+2}\]and \[\frac{{{x}^{2}}-4}{{{x}^{2}}-9}\] is
  A)
   \[\frac{1}{(x-3)(x-2)}\] done clear
  B)
          \[\frac{x-2}{x-3}\] done clear
  C)
   \[\frac{x-3}{x-2}\]             done clear
  D)
         \[(x-3)(x-2)\] done clear
  View Solution play_arrow

• question_answer115)
  The value of k, if the roots of the equation \[2k{{x}^{2}}+2kx+2=0\] are equal is
  A)
   \[\frac{4}{5}\]                   done clear
  B)
          4   done clear
  C)
   1                             done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer116)
  If one root of the equation \[{{x}^{2}}-12x+3k=0\]is square of the other, then k is
  A)
   3                             done clear
  B)
          9   done clear
  C)
   6                             done clear
  D)
          12 done clear
  View Solution play_arrow

• question_answer117)
  If one root of the quadratic equation is \[\sqrt{3}+1\] the equation is
  A)
   \[{{x}^{2}}-2x-\sqrt{3}=0\] done clear
  B)
          \[{{x}^{2}}-2\sqrt{3}x+2=0\] done clear
  C)
   \[{{x}^{2}}-2x-2=0\]      done clear
  D)
        \[{{x}^{2}}+2\sqrt{3}x+23=0\] done clear
  View Solution play_arrow

• question_answer118)
  It k be the ratio of the roots of the equation\[{{x}^{2}}-px+q=0\]the value of \[\frac{k}{1+{{k}^{2}}}\] is
  A)
   \[\frac{{{q}^{2}}-2p}{p}\]            done clear
  B)
          \[\frac{q}{{{p}^{2}}-2q}\]   done clear
  C)
   \[\frac{p}{{{q}^{2}}-2p}\]            done clear
  D)
          \[\frac{p}{{{p}^{2}}-2q}\] done clear
  View Solution play_arrow

• question_answer119)
  If sum of the roots is p and the sum of their squares is\[{{\text{q}}^{\text{2}}}\], the equation is
  A)
   \[{{x}^{2}}-px+{{p}^{2}}{{q}^{3}}=0\] done clear
  B)
  \[{{x}^{2}}-px+{{q}^{3}}=0\] done clear
  C)
   \[{{x}^{2}}-px+\frac{{{p}^{2}}-{{q}^{2}}}{2}=0\]   done clear
  D)
   none of these done clear
  View Solution play_arrow

• question_answer120)
  If \[a,b,c\in R\], then the roots of the equation\[(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0\] are equal if and only if
  A)
   \[a=0,b=1,c=1\] done clear
  B)
                                                                                          \[a=b=c\]   done clear
  C)
   a = 1, b = 0, c = 1 done clear
  D)
         \[a\ne 1,b=1,c=1\] done clear
  View Solution play_arrow

• question_answer121)
  A student divided a number by two when he was required to multiply it by 2. The answer he got was 2. The correct answer should have been
  A)
   8                               done clear
  B)
          12 done clear
  C)
   6                             done clear
  D)
          4 done clear
  View Solution play_arrow

• question_answer122)
  A number consists of two digits. The sum of the digits is 11, reversing the digits, the number decreases by 45. The number is
  A)
   38                          done clear
  B)
          65 done clear
  C)
   74                          done clear
  D)
          83   done clear
  View Solution play_arrow

• question_answer123)
  The perimeter of a rectangular plot is 48 m and its area is 108 m2. The dimensions of the plot are
  A)
   12 and 9              done clear
  B)
   18 and 6   done clear
  C)
   27 and 4         done clear
  D)
          36 and 3 done clear
  View Solution play_arrow

• question_answer124)
  For a journey the cost of a child ticket is \[\frac{1}{3}\]rd of the cost of an adult ticket. If the cost of tickets for 4 adults and 5 children is Rs. 85, the cost of a child ticket is
  A)
   Rs. 5                        done clear
  B)
          Rs. 6 done clear
  C)
   Rs. 10                   done clear
  D)
          Rs. 15 done clear
  View Solution play_arrow

• question_answer125)
  The equations \[3x-5y+2=0\] and \[6x+4=10y\] have
  A)
   an infinite number of solutions   done clear
  B)
   no solution done clear
  C)
   two solutions done clear
  D)
   a single solution done clear
  View Solution play_arrow

• question_answer126)
  The value of \[{{x}^{2}}-6x+13\]can never be less than
  A)
   5                             done clear
  B)
          4   done clear
  C)
   6                             done clear
  D)
          13 done clear
  View Solution play_arrow

• question_answer127)
  The value of \[18-|-7|-|11-22|\]is equal to
  A)
   58                          done clear
  B)
          0   done clear
  C)
   41                          done clear
  D)
          28 done clear
  View Solution play_arrow

• question_answer128)
  \[\frac{(\log x-\log y)(\log {{x}^{2}}+\log {{y}^{2}})}{(\log {{x}^{2}}-\log {{y}^{2}})(\log x+\log y)}\]
  A)
   0                             done clear
  B)
          1   done clear
  C)
   \[\log \frac{x}{y}\]              done clear
  D)
          \[\log xy\] done clear
  View Solution play_arrow

• question_answer129)
  If \[{{\log }_{10}}(2{{x}^{2}}+7x+16)=1\], the value of \[x\] is
  A)
   \[-2\,or\frac{3}{2}\]                       done clear
  B)
          \[-2\,or-\frac{3}{2}\]   done clear
  C)
   \[-2\,or\frac{2}{3}\]           done clear
  D)
          \[2\,or\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer130)
  Given log 6 and log 8, then the only logarithm that cannot be obtained without using the table is
  A)
   log 64                   done clear
  B)
          log 21   done clear
  C)
   \[\log \frac{8}{3}\]              done clear
  D)
          log 9 done clear
  View Solution play_arrow

• question_answer131)
   The value of x and y respectively in the simultaneous equations\[2x-\frac{3}{y}=12\,\,and\,\,5x+\frac{7}{y}=1,y\ne 0\] is
  A)
   \[2,-\frac{1}{3}\]             done clear
  B)
          \[3,-\frac{1}{2}\]   done clear
  C)
   \[-3,\frac{1}{2}\]             done clear
  D)
          \[-2,\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer132)
  For all \[a>0,b>0,c>0\]\[\log ({{a}^{a}}{{b}^{b}}{{c}^{c}})+\log \left( \frac{1}{abc} \right)\]is equal to
  A)
   \[\log ({{a}^{a+1}}{{b}^{b+1}}{{c}^{c+1}})\] done clear
  B)
   \[\log \left( {{a}^{a}}{{b}^{b}}{{c}^{c}}+\frac{1}{abc} \right)\] done clear
  C)
   \[\log ({{a}^{a-1}}{{b}^{b-1}}{{c}^{c-1}})\]   done clear
  D)
   \[\log a+\log b+\log c\] done clear
  View Solution play_arrow

• question_answer133)
  If \[{{\log }_{10}}[{{\log }_{10}}(\log _{10}^{x})]=0\], then
  A)
   \[x={{10}^{3}}\]           done clear
  B)
          \[x={{10}^{10}}\]   done clear
  C)
  \[x={{10}^{5}}\]                done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer134)
  If \[f(x)=\log \left( \frac{1+x}{1-x} \right)\], then \[f\left( \frac{2x}{1+{{x}^{2}}} \right)\]is equal to
  A)
   \[2f(x)\]                                done clear
  B)
   \[f(2x)\] done clear
  C)
   \[2f(-x)\]               done clear
  D)
          \[f(x)\] done clear
  View Solution play_arrow

• question_answer135)
  A farmer divides his herd of n cows among his four sons so that one son gets one-half the herd, the second, one-fourth, the third son, one-fifth and the fourth, 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_answer136)
  The sum of two numbers is 20; their product is 40. The sum of their reciprocals is
  A)
   \[\frac{1}{10}\]                                                done clear
  B)
   4 done clear
  C)
   2                             done clear
  D)
          \[\frac{1}{2}\]   done clear
  View Solution play_arrow

• question_answer137)
  Consider the following statements : The system of equations \[2x-y=4\] and \[px-y=q\]

  \[\text{I}\]has a unique solution if \[p\ne 2\].

  \[\text{II}\]has infinitely many solutions if p = 2, q = 4 of these statements :

  A)
   \[\text{I}\] alone is correct. done clear
  B)
   \[\text{II}\] alone is correct. done clear
  C)
   \[\text{I}\] and \[\text{II}\] are correct.   done clear
  D)
   \[\text{I}\] and \[\text{II}\] are false. done clear
  View Solution play_arrow

• question_answer138)
  If the roots of \[{{x}^{2}}-2mx+{{m}^{2}}-1=0\]lie between - 2 and 4, then
  A)
   \[-3\le m\le 4\] done clear
  B)
   \[-3\le m\le 5\] done clear
  C)
   \[-1\le m\le 5\]   done clear
  D)
   \[-1\le m\le 3\] done clear
  View Solution play_arrow

• question_answer139)
  The value of \[7{{\log }_{a}}\frac{16}{15}+5{{\log }_{a}}\frac{25}{24}+3{{\log }_{a}}\frac{81}{80}\] is
  A)
   \[\log _{a}^{3}\]                              done clear
  B)
          \[\log _{a}^{1}\] done clear
  C)
   \[\log _{a}^{2}\]                                done clear
  D)
          \[\log _{a}^{5}\] done clear
  View Solution play_arrow

• question_answer140)
  \[\log ({{x}^{2}})+\log ({{y}^{2}})\]is equal to
  A)
   \[\log ({{x}^{2}}+{{y}^{2}})\]       done clear
  B)
        \[2\log (xy)\]   done clear
  C)
   \[2\log (x+y)\]       done clear
  D)
          \[\log \frac{{{x}^{2}}}{{{y}^{2}}}\] done clear
  View Solution play_arrow

• question_answer141)
  If \[{{\log }_{8}}m+{{\log }_{8}}\frac{1}{6}=\frac{2}{3}\], then m is equal to
  A)
   12                          done clear
  B)
          48 done clear
  C)
   18                          done clear
  D)
          24   done clear
  View Solution play_arrow

• question_answer142)
  If \[{{\log }_{2}}({{x}^{3}}+{{x}^{2}})-{{\log }_{2}}(x+1)=5\], then \[{{\log }_{2}}x\] is
  A)
   \[\frac{5}{2}\]                     done clear
  B)
          \[\frac{2}{5}\] done clear
  C)
   5                             done clear
  D)
          2 done clear
  View Solution play_arrow

• question_answer143)
  What is the condition for the roots of \[a{{x}^{2}}+bx+c=0\]to be in the ratio of p : q ?
  A)
  \[{{a}^{2}}{{c}^{2}}(p+q)={{p}^{2}}{{q}^{2}}b\] done clear
  B)
   \[ac{{(p+q)}^{2}}=pq{{b}^{2}}\]   done clear
  C)
   \[pq{{(a+c)}^{2}}=pq{{b}^{2}}\] done clear
  D)
  \[{{p}^{2}}{{q}^{2}}(a+c)={{a}^{2}}{{c}^{2}}b\] done clear
  View Solution play_arrow

• question_answer144)
  The sum of the roots of \[\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\]is zero. The product of the roots is
  A)
   \[-\frac{1}{2}({{a}^{2}}+{{b}^{2}})\]         done clear
  B)
          0 done clear
  C)
   \[\frac{1}{2}(a+b)\]          done clear
  D)
          \[2({{a}^{2}}+{{b}^{2}})\] done clear
  View Solution play_arrow

• question_answer145)
  One root of the equation \[a{{x}^{2}}+bx+c=0\] is square of the other if
  A)
   \[{{a}^{2}}c+{{b}^{3}}+a{{c}^{2}}=3abc\]   done clear
  B)
   \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] done clear
  C)
   \[{{b}^{2}}c+{{c}^{2}}a+{{a}^{2}}b=abc\] done clear
  D)
   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca=0\] done clear
  View Solution play_arrow

• question_answer146)
  The ratio of the ages of A and B ten years before was 3 : 5. The ratio of their present ages is 2 : 3. Their ages are respectively
  A)
   30, 50 done clear
  B)
   20,30 done clear
  C)
   40, 60   done clear
  D)
   16, 24 done clear
  View Solution play_arrow

• question_answer147)
  If a and b are  any two such real numbers that ab = 0, then
  A)
   a =0, \[b\ne 0\] done clear
  B)
   b=0, \[a\ne 0\] done clear
  C)
   a = 0 or b = 0 or both   done clear
  D)
   a =b and b=0 done clear
  View Solution play_arrow

• question_answer148)
  The value of \[{{(256)}^{0.16}}\times {{(256)}^{0.09}}\] is
  A)
   64                          done clear
  B)
          256.25 done clear
  C)
   16                          done clear
  D)
          4   done clear
  View Solution play_arrow

• question_answer149)
  If the roots of the equation \[a{{x}^{2}}+bx+c=0\] are reciprocal of each other; then
  A)
   a = b               done clear
  B)
          a = c   done clear
  C)
   b = c                      done clear
  D)
          a = 0 done clear
  View Solution play_arrow

• question_answer150)
  The value of k for which \[{{x}^{2}}-4x+k=0\] has coincident roots, is
  A)
   4                                               done clear
  B)
   - 4 done clear
  C)
   0                             done clear
  D)
          - 2 done clear
  View Solution play_arrow

• question_answer151)
  \[{{9}^{\frac{3}{2}}}\div {{(243)}^{\frac{-2}{3}}}\]simplifies to
  A)
   \[{{3}^{\frac{10}{3}}}\]                 done clear
  B)
         \[{{3}^{\frac{19}{3}}}\]   done clear
  C)
   \[{{3}^{\frac{1}{3}}}\]                    done clear
  D)
          \[{{3}^{19}}\] done clear
  View Solution play_arrow

• question_answer152)
  The solution of \[{{(25)}^{x-2}}={{(125)}^{2x-4}}\] is
  A)
  \[\frac{3}{4}\]                                    done clear
  B)
   0 done clear
  C)
   2                               done clear
  D)
          \[-2\] done clear
  View Solution play_arrow

• question_answer153)
  If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\]and \[\frac{b}{a}=\frac{c}{b}\], then \[\frac{2z}{x+z}\]is equal to
  A)
   \[\frac{y}{x}\]                     done clear
  B)
          \[\frac{x}{y}\] done clear
  C)
   \[\frac{x}{z}\]                   done clear
  D)
          \[\frac{z}{x}\] done clear
  View Solution play_arrow

• question_answer154)
  The condition that the roots of the equation \[l{{x}^{2}}+mx+n=0\] may be in the ratio 3: 4 is
  A)
   \[14{{n}^{2}}=49ml\]                     done clear
  B)
   \[{{m}^{2}}=9nl\] done clear
  C)
   \[12{{m}^{2}}=49nl\]       done clear
  D)
          \[4{{l}^{2}}=49nl\] done clear
  View Solution play_arrow

• question_answer155)
  The condition for the roots of equation\[{{x}^{2}}-lx+m=0\] to differ by one is
  A)
   \[{{l}^{2}}=4m+1\]                            done clear
  B)
   \[{{l}^{2}}+{{m}^{2}}=1\] done clear
  C)
   \[{{m}^{2}}=4l+1\]       done clear
  D)
          \[l=m+1\] done clear
  View Solution play_arrow

• question_answer156)
  Find k if one root of the equation \[{{x}^{2}}-6kx+8=0\] is twice the other.
  A)
   2                             done clear
  B)
          ± 1   done clear
  C)
   \[\pm \frac{1}{2}\]                         done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer157)
  If \[\alpha ,\beta \] are the roots of \[3{{x}^{2}}-4x+1=0\] the equation whose roots are\[\frac{\alpha }{\beta },\frac{\beta }{\alpha }\] is
  A)
   \[3{{x}^{2}}+10x+3=0\] done clear
  B)
   \[3{{x}^{2}}+10x-3=0\] done clear
  C)
   \[3{{x}^{2}}-10x-3=0\] done clear
  D)
  \[3{{x}^{2}}-10x+3=0\]   done clear
  View Solution play_arrow

• question_answer158)
  The solution of the equation \[{{3}^{1+x}}+{{7}^{1-x}}=50\]is
  A)
   0                             done clear
  B)
          2 done clear
  C)
   ± 1                           done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer159)
  The value of \[\frac{x+y+z}{{{x}^{-1}}{{y}^{-1}}+{{y}^{-1}}{{z}^{-1}}+{{z}^{-1}}{{x}^{-1}}}\] is
  A)
  \[\frac{1}{xyz}\]              done clear
  B)
          \[\frac{1}{xy}+\frac{1}{yz}+\frac{1}{xz}\] done clear
  C)
   \[xyz\]                  done clear
  D)
          \[xy+yz+zx\] done clear
  View Solution play_arrow

• question_answer160)
  If \[x\] be real and positive, then the value of\[y=x+\frac{1}{x}\] satisfies
  A)
   \[0<y\le 0.5\]        done clear
  B)
          \[0.5<y\le 1\] done clear
  C)
   \[1<y<2\]           done clear
  D)
          \[y\ge 2\]   done clear
  View Solution play_arrow

• question_answer161)
  If \[2x+y=3,xy=1\], then the value of \[8{{x}^{3}}+{{y}^{3}}\]is
  A)
   16                                          done clear
  B)
   9   done clear
  C)
   4                             done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer162)
  a + b is a factor of
  A)
   \[{{a}^{4}}({{b}^{2}}-{{c}^{2}})+{{b}^{4}}({{c}^{2}}-{{b}^{2}})+{{c}^{4}}({{a}^{2}}-{{b}^{2}})\]   done clear
  B)
   \[a{{(b-c)}^{3}}+b{{(c-a)}^{3}}+c{{(a-b)}^{3}}\] done clear
  C)
   \[{{(a+b+c)}^{3}}-{{(b+c-a)}^{3}}-{{(c+a-b)}^{3}}-{{(a+b-c)}^{3}}\] done clear
  D)
   \[a({{b}^{4}}-{{c}^{4}})+b({{c}^{4}}-{{a}^{4}})+c({{a}^{4}}+{{b}^{4}})\] done clear
  View Solution play_arrow

• question_answer163)
  The roots of the equation \[\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}\]are
  A)
   \[\frac{3}{13},\frac{2}{13}\]             done clear
  B)
          \[\frac{13}{6},\frac{11}{6}\] done clear
  C)
   \[\frac{9}{13},\frac{4}{13}\]             done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer164)
  The roots of the equation \[{{x}^{-2}}+{{x}^{-1}}=12\] are
  A)
   \[\frac{1}{2},\frac{1}{3}\]                            done clear
  B)
    \[\frac{1}{3},-\frac{1}{4}\]   done clear
  C)
   3, - 3                     done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer165)
  The roots of the equation \[\sqrt{3y+1}=\sqrt{y-1}\] are
  A)
   0, - 1                                     done clear
  B)
   2, 3 done clear
  C)
   2, 1                        done clear
  D)
          None of these   done clear
  View Solution play_arrow

• question_answer166)
  State which of the following statements is true \[{{2}^{16}}-1\] is divisible by
  A)
   11                                          done clear
  B)
   13 done clear
  C)
   17                                            done clear
  D)
   19 done clear
  View Solution play_arrow

• question_answer167)
  State which of the following statements is true. For every integer \[n,(n+1)(n+2)\] is divisible by
  A)
   7                             done clear
  B)
          6   done clear
  C)
   9                             done clear
  D)
          12 done clear
  View Solution play_arrow

• question_answer168)
  \[a,b,c(a>c)\]are three digits from left to right, of a three digits number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digits 4 in its unit place. The other two digits from left to right are
  A)
   5 and 4          done clear
  B)
          5 and 9   done clear
  C)
   4 and 5                 done clear
  D)
          9 and 5 done clear
  View Solution play_arrow

• question_answer169)
  If \[x+2\] is factor of \[{{\{{{(x+1)}^{5}}+2x+K)}^{3}}\}\], then the value of 'K' is
  A)
   1                             done clear
  B)
          3 done clear
  C)
   4                             done clear
  D)
          5   done clear
  View Solution play_arrow

• question_answer170)
  The remainder obtained by dividing \[{{x}^{n}}-\frac{a}{b}\]by\[ax-b\] is
  A)
   \[\frac{{{b}^{n+1}}-{{a}^{n+1}}}{{{a}^{n-1}}.b}\]                done clear
  B)
          \[\frac{{{a}^{n}}-{{b}^{n}}}{ab}\] done clear
  C)
  \[\frac{{{a}^{n}}-{{b}^{n}}}{{{a}^{n}}{{b}^{n}}}\]               done clear
  D)
          \[\frac{{{a}^{n+1}}-{{b}^{n+1}}}{a{{b}^{n}}}\] done clear
  View Solution play_arrow

• question_answer171)
  HCF of\[6{{x}^{2}}y(x-y)({{x}^{2}}+xy+{{y}^{2}}),18x{{y}^{2}}{{(x-y)}^{2}}\] and \[12x(x-y)\]is
  A)
   \[6x(x-y)\]   done clear
  B)
  \[6(x-y)\] done clear
  C)
   \[6x\] done clear
  D)
  \[x(x-y)\] done clear
  View Solution play_arrow

• question_answer172)
  LCM of the polynomials \[{{x}^{3}}y-x{{y}^{3}},\]\[{{x}^{4}}-2{{x}^{2}}{{y}^{2}}+{{y}^{4}}\]and\[{{x}^{4}}-{{y}^{4}}\]
  A)
   \[xy({{x}^{2}}-{{y}^{2}}){{(x+y)}^{2}}(x-y)\] done clear
  B)
   \[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}{{(x+y)}^{2}}\]      done clear
  C)
   \[xy({{x}^{2}}+{{y}^{2}}){{(x-y)}^{2}}(x+y)\] done clear
  D)
  \[xy({{x}^{2}}+{{y}^{2}})(x-y)(x+y)\] done clear
  View Solution play_arrow

• question_answer173)
  The sum of a number and its reciprocal is \[\frac{125}{22}\]The number is                              
  A)
   \[\frac{2}{11}\]                  done clear
  B)
         \[\frac{1}{11}\] done clear
  C)
   \[\frac{3}{11}\]               done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer174)
  If \[x=\frac{y}{{{(1+p)}^{q}}}\],then o is equal to
  A)
   \[\log \left[ \frac{\frac{y}{x}}{1+p} \right]\]        done clear
  B)
          \[\frac{\log \left( \frac{y}{x} \right)}{\log (1+p)}\]   done clear
  C)
   \[\frac{\log (y-x)}{\log (1+p)}\]                 done clear
  D)
   \[\frac{\log (y-x)}{\log (1+p)}\] done clear
  View Solution play_arrow

• question_answer175)
  If \[x\] and y are any two positive real numbers then \[x<y\] implies,
  A)
   \[-x<-y\]               done clear
  B)
          \[-x>-y\] done clear
  C)
   \[\frac{1}{x}>\frac{1}{y}\]                           done clear
  D)
          \[-\frac{1}{x}>\frac{1}{y}\] done clear
  View Solution play_arrow

• question_answer176)
  If a and b are any two real numbers such that\[ab=0\]
  A)
   a = 0 and b=0 done clear
  B)
   a = 0 or b = 0 or both   done clear
  C)
   a = 0 and \[b\ne 0\] done clear
  D)
   \[a\ne 0\] and b = 0 done clear
  View Solution play_arrow

• question_answer177)
  \[{{x}^{2}}+4x>2x+8\] is true when
  A)
  \[x>\,or\,x<-2\]    done clear
  B)
          \[x>4\,\,or\,x<2\] done clear
  C)
   \[x>2\,\,or\,x<-4\]     done clear
  D)
         \[x>-2\,\,or\,x<4\] done clear
  View Solution play_arrow

• question_answer178)
  If \[y=\frac{{{x}^{2}}-2x+4}{{{x}^{2}}+2x+4}\]where \[x\]can take real values, then
  A)
   \[\frac{1}{3}\le y\le 3\]                                   done clear
  B)
   \[3<y\le 5\] done clear
  C)
   \[5<y\le 7\]           done clear
  D)
          \[7<y\le 9\] done clear
  View Solution play_arrow

• question_answer179)
  Solution of the equations\[\frac{x+3}{4}+\frac{2y+9}{3}=3\]and \[\frac{2x-1}{2}-\frac{y+3}{4}=4\frac{1}{2}\]
  A)
  \[x=-5,y=-3\] done clear
  B)
          \[x=-5,y=3\] done clear
  C)
  \[x=5,y=3\]         done clear
  D)
          \[x=5,y=-3\]   done clear
  View Solution play_arrow

• question_answer180)
  If \[{{(3)}^{x+y}}=81\] and \[{{(81)}^{x-y}}=3\], then the values of \[x\] and y are
  A)
   \[\frac{17}{8},\frac{9}{8}\]                                          done clear
  B)
   \[\frac{17}{8},\frac{11}{8}\] done clear
  C)
   \[\frac{17}{8},\frac{15}{8}\]                          done clear
  D)
          \[\frac{11}{8},\frac{15}{8}\] done clear
  View Solution play_arrow

• question_answer181)
  The value of \[{{(625)}^{0.16}}\times {{(625)}^{0.09}}\]is
  A)
   4                             done clear
  B)
          5   done clear
  C)
   25                                          done clear
  D)
   625 done clear
  View Solution play_arrow

• question_answer182)
  What must be added to \[\frac{x}{y}\] make it\[\frac{y}{x}\] ?
  A)
   \[\frac{y-x}{{{y}^{2}}{{x}^{2}}}\]              done clear
  B)
         \[\frac{{{y}^{2}}-{{x}^{2}}}{yx}\]   done clear
  C)
  \[\frac{xy}{x+y}\]            done clear
  D)
         \[\frac{{{x}^{2}}{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] done clear
  View Solution play_arrow

• question_answer183)
  \[{{(x+y)}^{3}}-{{(x-y)}^{3}}\] can be factorised as
  A)
   \[2y(3{{y}^{2}}+{{x}^{2}})\]      done clear
  B)
          \[2y(3{{x}^{2}}+{{y}^{2}})\]   done clear
  C)
   \[2x(3{{x}^{2}}+{{y}^{2}})\]      done clear
  D)
         \[2x{{({{x}^{2}}+3y)}^{2}}\] done clear
  View Solution play_arrow

• question_answer184)
  If\[x=\frac{\sqrt{2}+1}{\sqrt{2}-1},y=\frac{\sqrt{2}-1}{\sqrt{2}+1}\], then\[{{x}^{2}}+xy+{{y}^{2}}\]is equal to
  A)
   39                          done clear
  B)
          35   done clear
  C)
   38                          done clear
  D)
          36 done clear
  View Solution play_arrow

• question_answer185)
  If\[f(x)=\frac{2x+3}{x-2},x\ne 2\] and \[x\in R\], then \[\frac{f(6)}{f\left( \frac{1}{2} \right)}\]is equal to
  A)
   \[\frac{35}{45}\]                              done clear
  B)
          \[\frac{-35}{45}\] done clear
  C)
   \[\frac{-45}{32}\]                              done clear
  D)
          \[\frac{45}{35}\] done clear
  View Solution play_arrow

• question_answer186)
  The perimeter of a rectangle whose length is twice the breadth is 24 cm. Then the area of the rectangle is
  A)
   28 sq. cm         done clear
  B)
          32 sq. cm   done clear
  C)
   36 sq. cm         done clear
  D)
          42 sq. cm done clear
  View Solution play_arrow

• question_answer187)
  If 6 kg of sugar and 5 kg of tea together cost Rs. 209 and 4 kg of sugar and 3 kg of tea together cost Rs. 131, then the cost of 1 kg sugar and 1 kg tea are respectively
  A)
   Rs. 11 and Rs. 25 done clear
  B)
   Rs. 12 and Rs. 20   done clear
  C)
   Rs. 14 and Rs. 20 done clear
  D)
   Rs. 14 and Rs. 25 done clear
  View Solution play_arrow

• question_answer188)
  If \[\alpha ,\beta \] are the roots of the equation \[\alpha {{x}^{2}}+bx+c=\]0, then the value of \[\frac{1}{a\alpha +b}+\frac{1}{a\beta +b}\]is
  A)
   \[\frac{b}{ac}\]                  done clear
  B)
          \[\frac{a}{bc}\] done clear
  C)
   \[\frac{c}{ab}\]                done clear
  D)
          \[\frac{bc}{a}\] done clear
  View Solution play_arrow

• question_answer189)
  If \[{{x}^{2}}+7ax+40=0\] and \[{{x}^{2}}+2ax-60=0\] have a common root, then the value of a is
  A)
   ± 1                         done clear
  B)
          ± 2   done clear
  C)
   ± 3                         done clear
  D)
          ± 4 done clear
  View Solution play_arrow

• question_answer190)
  If \[x=\frac{y}{{{(1+a)}^{p}}}\], then p is equal to
  A)
   \[\frac{{{\log }_{e}}\left( \frac{y}{x} \right)}{{{\log }_{e}}(1+a)}\]               done clear
  B)
          \[\log \left\{ \frac{y}{x(1+a)} \right\}\] done clear
  C)
   \[\log \left\{ \frac{y-x}{1+a} \right\}\]   done clear
  D)
          \[\frac{\log y}{\log \{x(1+a)\}}\] done clear
  View Solution play_arrow

• question_answer191)
  If \[x\] and y are any two positive real numbers, then \[x\] > y implies
  A)
   \[-x>-y\]                             done clear
  B)
   \[-x<-y\]   done clear
  C)
   \[\frac{1}{x}>\frac{1}{y}\]           done clear
  D)
          \[-\frac{1}{x}>\frac{1}{y}\] done clear
  View Solution play_arrow

• question_answer192)
  10 years ago the age of the father was 5 times that of the son. 20 years hence the age of the father will be twice that of the son. The present age of the father (in years) is
  A)
   40                          done clear
  B)
          45 done clear
  C)
   60                            done clear
  D)
          70 done clear
  View Solution play_arrow

• question_answer193)
  If 14 is the maximum of- \[-\lambda {{x}^{2}}+\lambda x+8\], then the value of \[\lambda \] is
  A)
   24                            done clear
  B)
          \[6\sqrt{3}\] done clear
  C)
   \[-6\sqrt{3}\]                    done clear
  D)
          - 12 done clear
  View Solution play_arrow

• question_answer194)
  The expression\[{{x}^{2}}-x-30\]is positive for
  A)
   no value of \[x\] done clear
  B)
   all values of \[x\] between - 5 and 6 done clear
  C)
   all\[x\] done clear
  D)
   \[x>6\,\,or\,\,x<-5\]   done clear
  View Solution play_arrow

• question_answer195)
  If \[a={{2}^{\frac{2}{3}}}+{{2}^{\frac{1}{3}}}\],then
  A)
   \[{{a}^{3}}-6a-6=0\]     done clear
  B)
          \[{{a}^{3}}-6a+6=0\] done clear
  C)
   \[{{a}^{3}}+6a-6=0\]    done clear
  D)
          \[{{a}^{3}}+6a+6=0\] done clear
  View Solution play_arrow

• question_answer196)
  The system of equations \[3x-4y=12\]and \[6x-8y=48\]has
  A)
   2 solution done clear
  B)
   1 solution done clear
  C)
   infinite number of solutions done clear
  D)
   no solution   done clear
  View Solution play_arrow

• question_answer197)
  If \[{{56}^{2}}-{{51}^{2}}=5p\], then p is equal is
  A)
   106                        done clear
  B)
          107   done clear
  C)
   105                        done clear
  D)
          104 done clear
  View Solution play_arrow

• question_answer198)
  A farmer divides his herd of \[x\] cows among his 4 sons so that one son gets one half of the herd, the second gets one-fourth, the third son gets one-fifth and the fourth gets 7 cows. Then \[x\] is
  A)
   100                        done clear
  B)
          140   done clear
  C)
   0                             done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer199)
  The graph of \[x\] = 15 is a straight line
  A)
   intersecting both the axes done clear
  B)
   parallel to y-axis   done clear
  C)
   parallel to : \[x\]-axis done clear
  D)
   passing through the origin done clear
  View Solution play_arrow

• question_answer200)
  \[{{x}^{m}}={{x}^{n}}\Rightarrow m\]
  A)
   > n                         done clear
  B)
          = n   done clear
  C)
   <n                          done clear
  D)
          none of these done clear
  View Solution play_arrow

• question_answer201)
  If\[2x+y=3\]and \[xy=1\], the value of\[{{(x+y)}^{x-y}}\]is
  A)
   100                        done clear
  B)
          10 done clear
  C)
   0                             done clear
  D)
          1   done clear
  View Solution play_arrow

• question_answer202)
  The smaller value of n for which\[{{x}^{2}}-2x-3\]and\[{{x}^{3}}-2{{x}^{2}}-nx-3\]have an H.C.F. involving \[x\] is
  A)
   0                             done clear
  B)
          1 done clear
  C)
   2                               done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer203)
  If \[2{{x}^{2}}+xy-3{{y}^{2}}+x+ay-10=\]\[(2x+3y+b)\]\[(x-y-2)\],the value of a and b are
  A)
   11 and 5 done clear
  B)
   1 and - 5               done clear
  C)
   - 1 and - 5                            done clear
  D)
   - 11 and 5                              done clear
  View Solution play_arrow

• question_answer204)
  If a-b = 3 and \[{{a}^{3}}-{{b}^{3}}=117\] then a+b is equals
  A)
   5 done clear
  B)
   7   done clear
  C)
   9 done clear
  D)
   11 done clear
  View Solution play_arrow

• question_answer205)
  The value of n for which the expression \[9{{x}^{4}}-12{{x}^{2}}+n{{x}^{2}}-8x+4\]becomes a perfect square is
  A)
   12                          done clear
  B)
          16   done clear
  C)
   18                          done clear
  D)
          24 done clear
  View Solution play_arrow

• question_answer206)
  The solution of\[{{64}^{2x-5}}=4\times {{8}^{x-5}}\]is
  A)
   \[\frac{9}{17}\]                                done clear
  B)
   \[\frac{17}{9}\]   done clear
  C)
   \[\frac{17}{10}\]                              done clear
  D)
          \[\frac{20}{9}\] done clear
  View Solution play_arrow

• question_answer207)
  The value of \[\frac{{{\left( x+\frac{1}{y} \right)}^{a}}{{\left( x-\frac{1}{y} \right)}^{b}}}{{{\left( y+\frac{1}{x} \right)}^{a}}{{\left( y-\frac{1}{x} \right)}^{b}}}\]is equal to
  A)
   \[{{\left( \frac{x}{y} \right)}^{a+b}}\]       done clear
  B)
          \[{{\left( \frac{y}{x} \right)}^{a+b}}\] done clear
  C)
   \[{{(xy)}^{a+b}}\]           done clear
  D)
          \[\frac{{{x}^{n}}}{{{y}^{b}}}\] done clear
  View Solution play_arrow

• question_answer208)
  If U = Set of all triangles, X = Set of isosceles triangles, Y = Set of equilateral triangles, Z = Set of right-angled triangles, W = Set of acute- angled triangles. Then \[Y\cap W\] is
  A)
   U                                            done clear
  B)
   Y   done clear
  C)
   Z                             done clear
  D)
          X done clear
  View Solution play_arrow

• question_answer209)
  If X = (multiples of 2), Y = (multiples of 5), Z = (multiples of 10), then\[X\cap (Y\cap Z)\] is equal to
  A)
   multiples of 10   done clear
  B)
   multiples of 5 done clear
  C)
   multiples of 2 done clear
  D)
   multiples of 7 done clear
  View Solution play_arrow

• question_answer210)
  Three bells, toll at intervals of 36 sec, 40 sec and sec respectively. They start ringing toll at particular time. They next toll together after
  A)
   18 minutes       done clear
  B)
          12 minutes   done clear
  C)
   6 minutes        done clear
  D)
          24 minutes done clear
  View Solution play_arrow

• question_answer211)
  Factors of\[16{{x}^{2}}-9{{(y+2x)}^{2}}\]are
  A)
   \[(2x+3y)(10x+3y)\] done clear
  B)
   \[-(2x+3y)(10x+3y)\]   done clear
  C)
  \[(2x+10y)(x+3y)\] done clear
  D)
  \[-(2x+10y)(x+3y)\] done clear
  View Solution play_arrow

• question_answer212)
  The G.C.D. of two whole numbers is 5 and their L.C.M. is 60. If one of the number is 20, then the other number would be
  A)
   25                          done clear
  B)
          13 done clear
  C)
   16                          done clear
  D)
          15   done clear
  View Solution play_arrow

• question_answer213)
  The number of possible pairs of number, whose product is 5400 and the HCF is 30 is
  A)
   1                             done clear
  B)
          2 done clear
  C)
   3                             done clear
  D)
          4   done clear
  View Solution play_arrow

• question_answer214)
  Let\[f(x)=g(x)q(x)+r(x)\], where\[f(x)g(x)\]\[,g(x)\]and\[r(x)\]are polynomials, and degree of \[r(x)<\]deg.\[g(x)\]If deg.\[f(x)\]<deg\[g(x)\], then deg.\[g(x)\]is
  A)
   not defined         done clear
  B)
          0 done clear
  C)
  \[\deg .f(x)-\deg .g(x)\]                done clear
  D)
  \[\deg .f(x)+\deg .g(x)\] done clear
  View Solution play_arrow

• question_answer215)
  If\[{{\log }_{10}}m+{{\log }_{10}}n={{\log }_{10}}(m+n)\]and\[m=7\], then the value of n is
  A)
   5                             done clear
  B)
          \[\frac{2}{3}\] done clear
  C)
   \[\frac{7}{6}\]                    done clear
  D)
          \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer216)
  The value of\[\frac{{{(1.5)}^{2}}+{{(4.7)}^{3}}+{{(3.8)}^{3}}-3\times 1.5\times 4.7\times 3.8}{{{(1.5)}^{2}}+{{(4.7)}^{2}}+{{(3.8)}^{2}}-1.5\times 4.7\times -4.7\times 3.8-1.5\times 3.8}\]
  A)
   8                             done clear
  B)
          9 done clear
  C)
   10                            done clear
  D)
          11 done clear
  View Solution play_arrow

• question_answer217)
  Consider the following statements : 1. \[X-2\]is a factor of \[{{X}^{3}}-3{{X}^{2}}+4X-4\] 2.\[X+1\]is a factor of \[2{{X}^{3}}+4X+6\] 3. \[X-1\] is a factor of\[{{X}^{6}}-{{X}^{5}}+{{X}^{4}}-{{X}^{3}}+{{X}^{2}}-X+1\] Of these statements
  A)
   1 and 2 are correct   done clear
  B)
   1, 2 and 3 are correct done clear
  C)
   2 and 3 are correct done clear
  D)
   1 and 3 are correct done clear
  View Solution play_arrow

• question_answer218)
  L.C.M. of 125, 175 and 225 is
  A)
   7875   done clear
  B)
   7575 done clear
  C)
   7075 done clear
  D)
   1235 done clear
  View Solution play_arrow

• question_answer219)
  If\[{{2}^{X}}{{.3}^{2X}}=100\](Given log 2 = 0.3010 and log = 0.4771), then the value of \[X\]is
  A)
   1.49 done clear
  B)
   1.59   done clear
  C)
   1.69 done clear
  D)
   1.79 done clear
  View Solution play_arrow

• question_answer220)
  If\[{{\log }_{10}}a,{{\log }_{10}}b,{{\log }_{10}}c\]are in A.P., then a, b, c must be in
  A)
   A.P.                                       done clear
  B)
   G.P.   done clear
  C)
   h.p.                       done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer221)
  The smallest number, which must be added to 803642 in order to obtain a multiple ot 9, is
  A)
   1                             done clear
  B)
          2 done clear
  C)
   3                             done clear
  D)
          4   done clear
  View Solution play_arrow

• question_answer222)
  The given table shows the bank transaction of

  Month	June	July	August
  Deposit (Rs.)	\[2x+y+z\]	\[x+2y+3z\]	\[x+4z\]
  Withdrawal (Rs.)	\[x-y-z\]	\[x-2y+3z\]	\[2x-3z\]

  His balance for the month of September is
  A)
   2(3y + 4z)         done clear
  B)
          3(2y + 3z)   done clear
  C)
   \[2(3x+4y)\]        done clear
  D)
          \[8x+7z\] done clear
  View Solution play_arrow

• question_answer223)
  If \[a=\frac{1}{3-2\sqrt{2}},b=\frac{1}{3+2\sqrt{2}}\]. then the value of \[{{a}^{2}}+{{b}^{2}}\]is
  A)
   34                            done clear
  B)
          35 done clear
  C)
   36                          done clear
  D)
          37 done clear
  View Solution play_arrow

• question_answer224)
  If \[a=\frac{1}{3-2\sqrt{2}},b=\frac{1}{3+2\sqrt{2}}\], then the value of \[{{a}^{3}}+{{b}^{3}}\]3 - 2V2     3 + 2^2
  A)
   194                        done clear
  B)
          196 done clear
  C)
   198                          done clear
  D)
          200 done clear
  View Solution play_arrow

• question_answer225)
  If \[(7+4\sqrt{3})\]), then the value of\[{{x}^{2}}+\frac{1}{{{x}^{2}}}\]is
  A)
   193                        done clear
  B)
          194   done clear
  C)
   195                        done clear
  D)
          196 done clear
  View Solution play_arrow

• question_answer226)
  Which one of the following statements is correct?
  A)
   If \[g(x)(\ne 0)\] and \[f(x)\] are two polynomials\[\in F(x)\], then there exists unique polynomials q\[q(x)\]and\[r(x)\in F(x)\]such that\[f(x)=g(x)q(x)+r(x)\], where deg.\[\deg .r(x),\deg .g(x)\]. done clear
  B)
   If\[g(x)(\ne 0)\]and\[f(x)\]are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and\[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\]where deg. \[r(x)<\]: deg. \[g(x)\]. done clear
  C)
   If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\] done clear
  D)
   If \[g(x)(\ne ,0)\] and\[f(x)\] are two polynomials \[\in f(x)\], then there exists unique polynomials \[q(x)\] and \[r(x)\in F(x)\]such that \[f(x)=g(x)q(x)+r(x)\], where either \[r(x)=0\] or deg. \[r(x)<\]deg. \[g(x)\]   done clear
  View Solution play_arrow

• question_answer227)
  If \[X=7+4\sqrt{3}\], then the value of\[\sqrt{X}+\frac{1}{\sqrt{X}}\]is
  A)
   8                             done clear
  B)
          6 done clear
  C)
   5    done clear
  D)
   4   done clear
  View Solution play_arrow

• question_answer228)
  If \[\sqrt{5}\text{=2}.\text{236}\] and\[\sqrt{10}=\text{ 3}.\text{162}\], the value of\[\frac{\sqrt{10}-\sqrt{5}}{\sqrt{2}}\]on simplifying is
  A)
   0.455                    done clear
  B)
          0.855 done clear
  C)
   0.655                      done clear
  D)
          0.755 done clear
  View Solution play_arrow

• question_answer229)
  The equation\[{{x}^{3}}-3x+q=0\]will have two roots equal, if the value of q is
  A)
   ±2                          done clear
  B)
          ± 1   done clear
  C)
   ± 3                         done clear
  D)
          ± 4 done clear
  View Solution play_arrow

• question_answer230)
  Consider the following statements : Assertion : \[x-3\] is a factor of \[\text{P}\left( \text{x} \right)\text{ }=\text{ x3 }-\text{ 3}{{\text{x}}^{\text{2}}}\text{ }+\text{ 4x }-\text{ 12}\] Reason (R): \[P(2)\ne 0\]Of these statements :
  A)
   Both A and R are true and R is the correct explanation of A. done clear
  B)
   Both A and R are true but R is not a 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_answer231)
  The value of \[{{\log }_{10}}2+16{{\log }_{10}}\frac{16}{15}+12{{\log }_{10}}\frac{25}{24}\]\[+7{{\log }_{10}}\frac{81}{80}\] is
  A)
   3                             done clear
  B)
          2 done clear
  C)
   1                               done clear
  D)
          0 done clear
  View Solution play_arrow

• question_answer232)
  The value of\[5\sqrt{3}-3\sqrt{12}+2\sqrt{75}\]on simplify is
  A)
   \[5\sqrt{3}\]                      done clear
  B)
          \[6\sqrt{3}\] done clear
  C)
   \[\sqrt{3}\]                        done clear
  D)
          \[9\sqrt{3}\]   done clear
  View Solution play_arrow

• question_answer233)
  The product of \[\sqrt{3}\]and \[\sqrt[3]{5}\] is
  A)
   \[5\sqrt{3}\]      done clear
  B)
          \[6\sqrt{3}\]   done clear
  C)
   \[\sqrt{3}\]                        done clear
  D)
          \[9\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer234)
  The value of \[|-5-6|\times |-4+3|\]on simplification is
  A)
   13                          done clear
  B)
          12 done clear
  C)
   11                            done clear
  D)
          10 done clear
  View Solution play_arrow

• question_answer235)
  The value of \[x\] on simplifying  \[X-2|X|=-3\]
  A)
   -1 or 3                    done clear
  B)
          1 or -3 done clear
  C)
   -1 or - 3                done clear
  D)
          1, 3 done clear
  View Solution play_arrow

• question_answer236)
  The value of\[{{\log }_{3}}9+{{\log }_{5}}25+{{\log }_{2}}8\]is
  A)
   4                                             done clear
  B)
   5 done clear
  C)
   6                             done clear
  D)
          7   done clear
  View Solution play_arrow

• question_answer237)
  \[\left( 1-\frac{1}{3} \right)\left( 1-\frac{14}{{}} \right)\left( 1-\frac{1}{5} \right).....\left( 1-\frac{1}{n} \right)\]
  A)
   \[\frac{1}{n}\]                  done clear
  B)
          \[\frac{2}{n}\]   done clear
  C)
   \[\frac{3}{n}\]                  done clear
  D)
          \[\frac{4}{n}\] done clear
  View Solution play_arrow

• question_answer238)
  If \[\frac{X}{2}=\frac{Y}{3}\], then\[\left[ \frac{4}{5}+\frac{y-X}{y+X} \right]\]equals
  A)
   \[\frac{3}{5}\]                                   done clear
  B)
  \[\frac{4}{5}\] done clear
  C)
   1                               done clear
  D)
          \[\frac{6}{5}\] done clear
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• question_answer239)
  The value of\[\frac{{{(119)}^{2}}+(119)(111)+{{(111)}^{2}}}{{{(119)}^{3}}-{{(111)}^{3}}}\] is
  A)
   8                             done clear
  B)
          \[\frac{1}{8}\]   done clear
  C)
   230                        done clear
  D)
          \[\frac{1}{230}\] done clear
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• question_answer240)
  The exponential form of\[\sqrt{\sqrt{2}\times \sqrt{3}}\]is
  A)
   \[{{6}^{-\frac{1}{2}}}\]                  done clear
  B)
          \[{{6}^{\frac{1}{2}}}\] done clear
  C)
   \[{{6}^{\frac{1}{4}}}\]                      done clear
  D)
          \[6\] done clear
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• question_answer241)
  If\[\sqrt{5}=2.236\] and \[\sqrt{3}=1.732\].then ^e value of
  A)
   14                                          done clear
  B)
   14.39 done clear
  C)
   14.392                    done clear
  D)
   16 done clear
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• question_answer242)
  If \[\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}\], then the value of 'a' and 'b' is
  A)
   \[\text{a }=\text{2},\text{ b}=-\text{ 1}\]   done clear
  B)
   \[\text{a }=\text{2},\text{ b}=-\text{ 1}\] done clear
  C)
   \[\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ 1}\] done clear
  D)
  \[~\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ }-\text{ 1}\] done clear
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