10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank

done Pair of Lienear Equations in two variables and Quadratic Euqation Total Questions - 40

• question_answer1)
  Graphically, the pair of equations 3x + 2y = 16, 5x + y = 18 represents two lines which are _______
  A)
  intersecting at exactly one point done clear
  B)
  Parallel done clear
  C)
  Intersecting at exactly two points done clear
  D)
  Coincident done clear
  E)
  None of these done clear
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• question_answer2)
  If a pair of linear equations is consistent then the lines will _______
  A)
  Intersect             done clear
  B)
  Be coincident done clear
  C)
  Be parallel                     done clear
  D)
  Intersect or coincident done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  The pair of equations x = 2 and y = - 2 has _______
  A)
  One solution                   done clear
  B)
  Two solutions done clear
  C)
  Infinitely many solutions        done clear
  D)
  No solution done clear
  E)
  None of these done clear
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• question_answer4)
  If the lines given by \[\mathbf{ax}-\mathbf{y}=\mathbf{3}\] and \[\mathbf{21x}-\mathbf{3y}=\mathbf{9}\] will have infinitely many solutions, then the value of a is ______
  A)
  4                                                          done clear
  B)
  3            done clear
  C)
  7                                  done clear
  D)
  9 done clear
  E)
  None of these done clear
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• question_answer5)

  Find the values of p and q for which the pair of linear equations have infinitely many solutions.

  (3 p + 2q) x + (q + 2p) y = 3p - q + 14x + 7y = 29

  A)
  \[\frac{-5}{7},\,\,\frac{2}{7}\]                                                                 done clear
  B)
  \[\frac{2}{7},\,\,\frac{13}{14}\]   done clear
  C)
   \[\frac{-5}{7},\,\,\frac{13}{14}\]                                                            done clear
  D)
  \[\frac{-3}{7},\,\,\frac{11}{14}\] done clear
  E)
  None of these done clear
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• question_answer6)
  The equations given by the lines x = h and y = k represent_______
  A)
  coincident lines                                       done clear
  B)
  parallel lines done clear
  C)
   intersecting lines at point (h, k)                             done clear
  D)
  intersecting lines at (0, 0) done clear
  E)
  None of these done clear
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• question_answer7)
  Indetify which one among the following is the pair of linear equations having a unique solution x = - 3, y = 2.
  A)
  \[\frac{2}{3}x+\frac{7}{2}y=10\]\[~and\text{ }5x+3y=9\] done clear
  B)
  \[\sqrt{3}x-3y=3\sqrt{3}\,\,\,and\,\,\,x+7y=11\]  done clear
  C)
  \[3y=13x+45\,\,and\,\,-7x+3y=27\]                             done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer8)
  Prisha has only Rs. 1 and Rs. 2 coins with her. If she has a sum of Rs. 85 where total number of coins with her is 66, then the numbers of Rs. 1 and Rs. 2 Coins are, respectively ______
  A)
  35, 31                                                               done clear
  B)
  47, 19        done clear
  C)
  42, 24                                                               done clear
  D)
  50, 16 done clear
  E)
  None of these done clear
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• question_answer9)
  Find the values of x and y of the rectangle whose diagonals and breadths are shown below:
  A)
  4, 5                                                                   done clear
  B)
  2, 3 done clear
  C)
  1, 3                                                                   done clear
  D)
  5, 1 done clear
  E)
  None of these done clear
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• question_answer10)
  The angles of a cyclic quadrilateral PQRS are \[\angle P=(5x+3){}^\circ ,\] \[\angle Q=(4y+11){}^\circ ,\]\[\angle R=(7y+1){}^\circ ,\] \[\angle S=(6x+15){}^\circ \]. The values of x and y are respectively
  A)
  15, 16                                       done clear
  B)
  13, 14 done clear
  C)
  15, 17                                                   done clear
  D)
  17, 13 done clear
  E)
  None of these done clear
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• question_answer11)
  If (C, C) is the solution of system of equations \[\mathbf{mx}+\mathbf{n}\text{ }\mathbf{y}+\left( \mathbf{s}-\mathbf{t} \right)=\mathbf{0}\] and \[\mathbf{nx}+\mathbf{my}+\left( \mathbf{r}-\mathbf{s} \right)=\mathbf{0},\] \[\mathbf{(m}\ne \mathbf{n),}\] then
  A)
  2s = r + t     done clear
  B)
  2r = s + t done clear
  C)
  2t = r + s                                              done clear
  D)
  r = s + t done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer12)
  A two digit number is formed by either adding six to seven times the sum of its digits or by subtracting 2 from 17 times the difference of the digits Find the number
  A)
  83      done clear
  B)
  62 done clear
  C)
  60                                                                     done clear
  D)
  Cannot be determined done clear
  E)
  None of these done clear
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• question_answer13)
  The cost of 6 burgers, 12 sandwiches 5 cup of is Rs 525. of 3 burgres, 5 sandwiches 8 cup of is Rs 325. The of 2 Burgers, 3 sandwiches and 1 cup of It is of 1 cup of coffee is Rs 20 less than the burger.
  A)
  Rs 225                                                               done clear
  B)
  Rs 150        done clear
  C)
  Rs 145             done clear
  D)
  Rs 135 done clear
  E)
  None of these done clear
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• question_answer14)
  Amit can row 16 km downstream and 12 km upstream in 5 hours He row 24 km downstream and 4 km upstream in 4 hours. Find the of Amit in Still water.
  A)
  3 km/hr      done clear
  B)
  4 km/hr       done clear
  C)
  6 km/hr     done clear
  D)
  5 km/hr done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer15)
  A three digit number p q r is 378 more than the sum of its digits, the sum of the 1-digit number p and the two digit number pq.
  A)
  18                                                         done clear
  B)
   22           done clear
  C)
  42      done clear
  D)
  30 done clear
  E)
   None of these done clear
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• question_answer16)

  Solve:\[\frac{\mathbf{1}}{\sqrt{\mathbf{x}}}\mathbf{+}\frac{\mathbf{3}}{\sqrt{\mathbf{y}}}\mathbf{=1}\]

  \[\frac{\mathbf{3}}{\sqrt{\mathbf{x}}}\mathbf{+}\frac{\mathbf{15}}{\sqrt{\mathbf{y}}}\mathbf{=-1}\]

  A)
  \[x=3,\text{ }y=12\]                                          done clear
  B)
   \[x=4,\text{ }y=36\] done clear
  C)
  \[x=16,\text{ }y=25\]                                                    done clear
  D)
  \[x=9,\text{ }y=49\] done clear
  E)
  None of these done clear
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• question_answer17)
  The semiperimeter of a triangle exceeds each of its side by 8 units, 6 units and 5 units, respectively. Find the perimeter of the triangle.
  A)
  30 units                                                             done clear
  B)
   25 units        done clear
  C)
   38 units            done clear
  D)
  32 units done clear
  E)
  None of these done clear
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• question_answer18)
  The sum of a two digit number and the number obtained by reversing the order of its digits is 143. Also the difference between the two digits is 5. Find the number when sum of its digit is multiplied to it.
  A)
  1079                                                     done clear
  B)
   1022         done clear
  C)
  937 or 1022                                           done clear
  D)
  637 or 1222 done clear
  E)
  None of these done clear
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• question_answer19)
  A two digit number is formed by either subtracting 17 from eleven times the sum of the digit or by addling to 8 times the difference of the digit. Find the number.
  A)
  91                                                         done clear
  B)
   71 done clear
  C)
  63                                                                     done clear
  D)
  81 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer20)
  Point P and Q are 90 km apart on a highway. A car starts from P and another car starts from Q a. he same time. If they travel in the same direction, they meet in hour but if they travel towards each other, they meet in 1 hour. Find the speed of both the cars.
  A)
  30 km/hr and 60 km/hr        done clear
  B)
   25 km/hr and 65 km/hr done clear
  C)
   55 km/hr and 35 km/hr        done clear
  D)
  50 km/hr and 40 km/hr done clear
  E)
   None of these done clear
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• question_answer21)
  For a quadratic polynomial \[p(x)={{x}^{2}}-8x+15\] for all \[x\in r,\] which one among the following can be true?
  A)
  \[p(x)\ge 0,\] when \[3\le x\le 5\] and \[p(x)\le 0,\] when \[x\le 3\] or \[x\le 5\] done clear
  B)
  \[p(x)\ge 0,\] when \[-\,3\le x\le -\,5\] and \[p(x)\le 0,\] when \[x\le -3\] or \[x\ge -\,5\] done clear
  C)
  \[p(x)\ge 0,\] when \[x\le 3\] or \[x\ge 5\] and \[p(x)\le 0,\] when \[3\le x\le 5\] done clear
  D)
  \[p(x)\ge 0,\] when \[x\le -\,3\] or \[x\ge -\,5\] and \[p(x)\le 0,\] when \[-\,5\le x\le -\,3\] done clear
  E)
   None of these done clear
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• question_answer22)
  Solve form, m, \[{{\mathbf{m}}^{\mathbf{2}}}-\mathbf{4m}+\mathbf{3}\text{ }\ge \text{ }\mathbf{0}\]
  A)
  \[m\in (-\,\infty ,\,\,1]\,\,U\,[3,\,\,\infty )\]                done clear
  B)
  \[m\in (-\,\infty ,1)\,\,U\,(3,\infty )\] done clear
  C)
  \[m\in (1,2)\,\,U\,(2,\,\,3)\] done clear
  D)
  \[m\in (-\,\infty ,1]\,\,U\,[2,\infty )\] done clear
  E)
  None of these done clear
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• question_answer23)
  Find the solution set of \[{{a}^{2}}+21+8a>0\]
  A)
  \[(-\infty ,\infty )\]                        done clear
  B)
  \[(4,\infty )\]          done clear
  C)
  \[(-4,\infty )\]                                                                  done clear
  D)
  \[(-4,-4)\] done clear
  E)
  None of these done clear
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• question_answer24)
  If \[{{\mathbf{x}}^{\mathbf{4}}}-\text{ }\mathbf{26}{{\mathbf{x}}^{\mathbf{2}}}+\text{ }\mathbf{25}\text{ }=\text{ }\mathbf{0}\]then, find the sum of the squares of the roots
  A)
  52                     done clear
  B)
  48           done clear
  C)
  626                                                                   done clear
  D)
  320 done clear
  E)
  None of these         done clear
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• question_answer25)
                                                If roots of the equation \[\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+7x+6=0}\] are in the ratio m : n, then find the value of \[\sqrt{\frac{m}{n}}+\sqrt{\frac{n}{m}}\].
  A)
  \[\frac{-7\sqrt{2}}{2}\]                                                               done clear
  B)
  \[\frac{-7\sqrt{2}}{6}\]       done clear
  C)
  \[-\frac{7\sqrt{2}}{6}\]                                                               done clear
  D)
  \[\frac{\sqrt{2}}{2}\] done clear
  E)
  None of these done clear
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• question_answer26)
  In a right triangle, the base is 7 units more than the height. If the of the triangle is less than 72 sq units, the possible of the lie in the region will be ________.
  A)
  (7, 9)                 done clear
  B)
  (9, 16)        done clear
  C)
   (7, 16)              done clear
  D)
  (9, 12) done clear
  E)
  None of these done clear
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• question_answer27)
  For what value of m, the equation \[-\,2{{m}^{2}}+5m-12\] has maximum value?
  A)
  \[\frac{5}{2}\]                                                               done clear
  B)
  \[\frac{-5}{2}\]          done clear
  C)
  \[\frac{5}{4}\]               done clear
  D)
  \[\frac{-5}{4}\] done clear
  E)
  None of these done clear
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• question_answer28)
  Find the values of x which satisfies the equation. \[\sqrt{3x-5}+\frac{1}{\sqrt{3x-5}}=\frac{17}{4}\]
  A)
  4, 7                                                                   done clear
  B)
  \[7,\frac{27}{16}\]  done clear
  C)
  \[7,\frac{21}{16}\]                                                         done clear
  D)
  \[4,\frac{27}{16}\] done clear
  E)
  None of these done clear
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• question_answer29)
  If \[\mathbf{p}-\mathbf{q},\text{ }\mathbf{q}-\mathbf{r}\] are the roots of the equation \[p{{x}^{2}}+qx+r=0,\] then the value of \[\frac{\mathbf{(p-q)(q-r)}}{\mathbf{(r-q)}}\] is_______
  A)
  \[\frac{r}{q}\]            done clear
  B)
  \[\frac{p}{q}\]            done clear
  C)
  \[\frac{p}{r}\]                                                    done clear
  D)
  \[\frac{q}{r}\] done clear
  E)
  None of these done clear
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• question_answer30)
  Find the value of \[\sqrt{42+\sqrt{42+\sqrt{42+......\infty }}}\]
  A)
  7       done clear
  B)
  \[-\]6 done clear
  C)
  either 7 or \[-\]6                                                  done clear
  D)
  8 done clear
  E)
  None of these done clear
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• question_answer31)
  If \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{7x +4}\,\mathbf{m = 0}\] and \[{{x}^{2}}-8x+5m=0\] have a common root then the Possible values of m can be (where m is a contant)
  A)
  0, 2                                                       done clear
  B)
  0, 3          done clear
  C)
  0, 1                                                                   done clear
  D)
  0, 5 done clear
  E)
  None of these done clear
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• question_answer32)
  For a quadratic equation \[\alpha {{x}^{2}}+\beta x+\gamma =0\], if roots are In the ratio 3 : 4, then
  A)
  \[12{{\beta }^{2}}=49\alpha \gamma \]           done clear
  B)
  \[6{{\beta }^{2}}=7{{\alpha }^{2}}\gamma \] done clear
  C)
  \[15{{\beta }^{2}}=49\alpha \gamma \]                                                 done clear
  D)
  \[16{{\beta }^{2}}=7\alpha \gamma \] done clear
  E)
  None of these done clear
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• question_answer33)
  If one root of the equation \[a{{x}^{2}}-5x+16=0\] is 4 times the other, then the value of \[\alpha \] is
  A)
  0                                                          done clear
  B)
  \[\frac{1}{8}\]    done clear
  C)
  \[\frac{1}{4}\]               done clear
  D)
  \[\frac{1}{2}\] done clear
  E)
  None of these done clear
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• question_answer34)
  Find the value of m if the equation \[3{{p}^{2}}-2p+m=0\]and \[\mathbf{6}{{\mathbf{p}}^{\mathbf{2}}}-\mathbf{17p}+\mathbf{12}=\mathbf{0}\] have a common root.
  A)
  \[\frac{-8}{3},\frac{-15}{4}\]    done clear
  B)
  \[\frac{-3}{5},\frac{-15}{7}\]     done clear
  C)
  \[\frac{-7}{3},\frac{-12}{5}\]                                                      done clear
  D)
  \[\frac{-5}{3},\frac{7}{3}\] done clear
  E)
  None of these done clear
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• question_answer35)
  If p q, r belong to real number and equations \[p{{x}^{2}}+qx+r=0\] and \[{{x}^{2}}+3x+11=0\] have a common root, then p : q : r =
  A)
  1 : 3: 11        done clear
  B)
   2: 6: 7 done clear
  C)
  1: 2: 3                                                               done clear
  D)
  3: 2: 1 done clear
  E)
  None of these done clear
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• question_answer36)
  James opened his mathematics book and found that the product of the two pages in front of him was equal to 1406. What were the sum of these pages?
  A)
  79                                                                     done clear
  B)
  75           done clear
  C)
  69                                                                     done clear
  D)
  77 done clear
  E)
  None of these done clear
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• question_answer37)
  The length of a rectangle is 15 cm more that its width and the of the rectangle is 1134\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\]. Find the perimeter of the rectangle.
  A)
  88 cm                                                               done clear
  B)
  86 cm done clear
  C)
  84 cm             done clear
  D)
  92 cm done clear
  E)
  None of these done clear
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• question_answer38)
  The highest integral value of m for which the equation \[{{x}^{2}}-8x+m=0\] have two real and distinct roots?
  A)
  17                                                                     done clear
  B)
  15           done clear
  C)
  13                                                                     done clear
  D)
  12 done clear
  E)
  None of these done clear
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• question_answer39)
  For which value of m, the quadratic equation \[4{{x}^{2}}-mx+9=0\] have real and equal roots?
  A)
  -12                    done clear
  B)
  8            done clear
  C)
  16                                                                     done clear
  D)
  18 done clear
  E)
  None of these done clear
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• question_answer40)
  For a quadratic equation \[{{m}^{2}}+am+72=0,\] if roots are integers and distinct then how many such values are possible for ?a??
  A)
  6                                                                      done clear
  B)
  8            done clear
  C)
  12          done clear
  D)
  9 done clear
  E)
  None of these done clear
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