Scholastic Aptitude Test - Mathematics - Quadratic Equation

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Question - 1

The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is

  • A \(\frac { 1 }{ 289 } \)
  • B \(\frac { 289 }{ 290 } \)
  • C \(\frac { 290 }{ 289 } \)
  • D 289

Question - 2

If, \(x+\frac { 1 }{ x } =3\) then the value of x6+\(\frac { 1 }{ { x }^{ 6 } } \) is

  • A 927
  • B 114
  • C 364
  • D 322

Question - 3

ax2+bx+c=0, where a,b and c are real roots, if

  • A c = 0
  • B b2>3ac
  • C a, b, c are integers
  • D ac>0, and b is zero

Question - 4

The number of real roots of quadratic equation x2-3|x|-10 = 0 is

  • A 1
  • B 2
  • C 3
  • D 4

Question - 5

If one root of the two quadratic equations x2+ax+b=0 and x2+bx+a=0 is common, then

  • A a + b = 1
  • B a + b = -1
  • C ab = 1
  • D ab = -1

Question - 6

If the equation x2 - kx + 1 = 0, has no real roots then

  • A -2<k<2
  • B -3<k<3
  • C -4<k<4
  • D none of these

Question - 7

If \(\alpha\) and \(\beta\) are the roots of quadratic equation x2-2x+1, then \(\alpha\)2+\(\beta\)2 is

  • A 1
  • B 3
  • C 2
  • D -2

Question - 8

Find the nature of the roots of the quadratic equation \({ 3x }^{ 2 }-4\sqrt { 3 } x+4=0\)

  • A \(2\frac { \sqrt { 3 } }{ 3 } ,2\frac { \sqrt { 3 } }{ 3 } \)
  • B \(2\frac { \sqrt { 3 } }{ \sqrt { 3 } } ,2\frac { \sqrt { 3 } }{ \sqrt { 3 } } \)
  • C \(2\frac { \sqrt { 3 } }{ 3 } ,-2\frac { \sqrt { 3 } }{ 3 } \)
  • D None of these

Question - 9

Solve 5(x+1) + 5(2-x) = 53+1

  • A 2, -1
  • B -2, 1
  • C -2, -1
  • D None of these

Question - 10

A total number of 324 coins of 20 paise and 25 paise makes a sum of Rs 71. The number of 25 paise coins

  • A 120
  • B 124
  • C 37
  • D 40
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