TS 10th Class Maths Bits with Answers<\/a> Chapter 5 Quadratic Equations Bits for 10th Class will help students to build their problem-solving skills.<\/p>\nQuadratic Equations Bits for 10th Class<\/h2>\n
Question 1.
\nThe roots of the equation 3x2<\/sup> – 2 \\(\\sqrt{6}\\)x + 2 = 0 are
\nA) \\(\\frac{2}{\\sqrt{3}}\\), \\(\\frac{-2}{\\sqrt{3}}\\)
\nB) \\(\\frac{1}{\\sqrt{3}}\\), \\(\\frac{-1}{\\sqrt{3}}\\)
\nC) \\(\\sqrt{\\frac{2}{3}}\\), \\(\\sqrt{\\frac{2}{3}}\\)
\nD) \\(\\frac{1}{\\sqrt{3}}\\), \\(\\frac{5}{\\sqrt{3}}\\)
\nAnswer:
\nC) \\(\\sqrt{\\frac{2}{3}}\\), \\(\\sqrt{\\frac{2}{3}}\\)<\/p>\nQuestion 2.
\nOne solution of the Q.E. 2x2<\/sup> – 5x
\nA) x = 2
\nB) x = – 1
\nC) x = -3
\nD) x = 3
\nAnswer:
\nD) x = 3<\/p>\n<\/p>\n
Question 3.
\nThe positive root of \\(\\sqrt{3 x^2+6}\\) = 9 is
\nA) 3
\nB) 5
\nC) 4
\nD) \\(\\frac{2}{5}\\)
\nAnswer:
\nB) 5<\/p>\n
Question 4.
\nWhich of the following Q.E. has real and equal roots ?
\nA) x2<\/sup> – 4x + 4 = 0
\nB) 2x2<\/sup> – 4x + 3 = 0
\nC) 3x2<\/sup> – 5x + 2 = 0
\nD) x2<\/sup> – 2\\(\\sqrt{2}\\)x – 6 = 0
\nAnswer:
\nA) x2<\/sup> – 4x + 4 = 0<\/p>\nQuestion 5.
\nWhich of the following is a Q.E. ?
\nA) (x + 1)2<\/sup> = 3(x + 7)
\nB) (x – 1) (x + 3) = (x – 2) (x + 1)
\nC) x2<\/sup> + 5x – 7 = (x – 4)2<\/sup>
\nD) x3<\/sup> – 9 = 0
\nAnswer:
\nA) (x + 1)2<\/sup> = 3(x + 7)<\/p>\nQuestion 6.
\nThe sum of a number and its reciprocal is \\(\\frac{5}{2}\\) then the number is
\nA) 2 or \\(\\frac{1}{3}\\)
\nB) 3 or \\(\\frac{1}{2}\\)
\nC) 2 or \\(\\frac{1}{2}\\)
\nD) 5 and \\(\\frac{1}{5}\\)
\nAnswer:
\nC) 2 or \\(\\frac{1}{2}\\)<\/p>\n
Question 7.
\nIf the equation x2<\/sup> – kx + 1 = 0 has equal roots, then
\nA) k = 1
\nB) k = – 1
\nC) k = 2
\nD) k = – 4
\nAnswer:
\nC) k = 2<\/p>\nQuestion 8.
\nThe Q.E. whose one root is 2 – \\(\\sqrt{3}\\) is
\nA) x2<\/sup> – 4x + 1 = 0
\nB) x2<\/sup> + 4x – 1 = 0
\nC) x2<\/sup> – 4x – 1 = 0
\nD) x2<\/sup> – 2x – 3 = 0
\nAnswer:
\nA) x2<\/sup> – 4x + 1 = 0<\/p>\nQuestion 9.
\nThe roots of a quadratic equation \\(\\frac{x}{p}\\) = \\(\\frac{p}{x}\\)
\nA) \u00b1 p
\nB) p, 2p
\nC) -p, 2p
\nD) -p, -2p
\nAnswer:
\nA) \u00b1 p<\/p>\n
Question 10.
\n\\(\\sqrt{2}\\)x2<\/sup> – 3x + 5\\(\\sqrt{2}\\) = 0, sum of the root is ……….
\nA) \\(\\sqrt{2}\\)
\nB) \\(\\frac{-3}{\\sqrt{2}}\\)
\nC) 3
\nD) 5
\nAnswer:
\nA) \\(\\sqrt{2}\\)<\/p>\n<\/p>\n
Question 11.
\nThe quadratic equation whose roots are -3 and -4 is ……..
\nA) 7x2<\/sup> + x + 1 = 0
\nB) x2<\/sup> + 7x + 12 = 0
\nC) x2<\/sup> – 3x + 1 = 0
\nD) none
\nAnswer:
\nB) x2<\/sup> + 7x + 12 = 0<\/p>\nQuestion 12.
\nThe nature of the roots of a quadratic equation 4x2<\/sup> – 12x + 9 = 0 is ……….
\nA) real and equal
\nB) real and distinct
\nC) imaginary
\nD) none
\nAnswer:
\nA) real and equal<\/p>\nQuestion 13.
\nThe roots of the quadratic equation \\(\\frac{x^2-8}{x^2+20}\\) = \\(\\frac{1}{2}\\) are….
\nA) \u00b12
\nB) \u00b16
\nC) \u00b113
\nD) \u00b17
\nAnswer:
\nB) \u00b16<\/p>\n
Question 14.
\nIf b2<\/sup> – 4ac = 0 then the roots of the quadratic equations are
\nA) real and distinct
\nB) real and equal
\nC) imaginary
\nD) none
\nAnswer:
\nB) real and equal<\/p>\nQuestion 15.
\nThe nature of roots of 3x2<\/sup> + 6x – 2 = 0 is
\nA) real and distinct
\nB) real and equal
\nC) complex
\nD) none
\nAnswer:
\nA) real and distinct<\/p>\nQuestion 16.
\nProduct of the roots of ax2<\/sup> + bx + c = 0 is
\nA) \\(\\frac{c}{a}\\)
\nB) \\(\\frac{-b}{a}\\)
\nC) \\(\\frac{-c}{a}\\)
\nD) none
\nAnswer:
\nA) \\(\\frac{c}{a}\\)<\/p>\nQuestion 17.
\nThe quadratic equation whose roots are 2, 3 is …………
\nA) x2<\/sup> – 5x + 1 = 0
\nB) x2<\/sup> – 5x – 6 = 0
\nC) x2<\/sup> – 3x + 1 = 0
\nD) x2<\/sup> – 5x + 6 = 0
\nAnswer:
\nD) x2<\/sup> – 5x + 6 = 0<\/p>\nQuestion 18.
\n\\(\\frac{2 a^2+a-1}{a+1}\\) + \\(\\frac{3 a^2+5 a+2}{3 a+2}\\) + \\(\\frac{4-a^2}{a+2}\\) + ……..
\nA) \\(\\frac{\\mathrm{a}}{2}\\)
\nB) \\(\\frac{a+1}{2}\\)
\nC) 2(a + 1)
\nD) none
\nAnswer:
\nC) 2(a + 1)<\/p>\n
Question 19.
\n
\nA) 1
\nB) x2<\/sup>
\nC) x
\nD) 0
\nAnswer:
\nC) x<\/p>\nQuestion 20.
\nSum of the roots of bx2<\/sup> + ax + c = 0 is ………
\nA) \\(\\frac{-b}{a}\\)
\nB) \\(\\frac{c}{a}\\)
\nC) \\(\\frac{c}{a}\\)
\nD) \\(\\frac{-a}{b}\\)
\nAnswer:
\nD) \\(\\frac{-a}{b}\\)<\/p>\nQuestion 21.
\nThe nature of roots of 3x2<\/sup> + 13x – 2 = 0 is ……..
\nA) real and unequal
\nB) real and equal
\nC) complex
\nD) none
\nAnswer:
\nA) real and unequal<\/p>\nQuestion 22.
\nProduct of the roots of x2<\/sup> + 7x = 0 is ………
\nA) 1
\nB) -7
\nC) -3
\nD) 0
\nAnswer:
\nD) 0<\/p>\nQuestion 23.
\nIf \u03b1 and \u03b2 are the roots of x2<\/sup> – 2x + 3 = 0 then \u03b12<\/sup> + \u03b22<\/sup> = ………
\nA) 1
\nB) 4
\nC) 8
\nD) none
\nAnswer:
\nD) none<\/p>\n<\/p>\n
Question 24.
\nIf \u03b1 and \u03b2 are the roots of x2<\/sup> – 5x + 6 = 0 then the value of \u03b1 – \u03b2 = ……….
\nA) \u00b11
\nB) \u00b12
\nC) -3
\nD) none
\nAnswer:
\nA) \u00b11<\/p>\nQuestion 25.
\nForm a quadratic equation from x3<\/sup> – 4x2<\/sup> – x + 1 = (x – 2)3<\/sup> = …….
\nA) 2x2<\/sup> – x + 1 = 0
\nB) 2x2<\/sup> – 13x + 9 = 0
\nC) x2<\/sup> + x + 1 = 0
\nD) none
\nAnswer:
\nB) 2x2<\/sup> – 13x + 9 = 0<\/p>\nQuestion 26.
\nThe product of two consecutive positive in\u00acteger is 306 then the smallest number is
\nA) 16
\nB) 13
\nC) 19
\nD) 17
\nAnswer:
\nD) 17<\/p>\n
Question 27.
\nx(x + 4) = 12 then x = …….
\nA) – 6 or 2
\nB) 6 or 7
\nC) 8 or – 9
\nD) none
\nAnswer:
\nA) – 6 or 2<\/p>\n
Question 28.
\n9 and 1 are the roots of ……
\nA) x2<\/sup> – 10x + 9 = 0
\nB) x2<\/sup> – x + 1 = 0
\nC) x2<\/sup> + 3x + 4 = 0
\nD) none
\nAnswer:
\nA) x2<\/sup> – 10x + 9 = 0<\/p>\nQuestion 29.
\nThe discriminant of 3x2<\/sup> – 2x = \\(\\frac{-1}{3}\\) is ……..
\nA) 1
\nB) –\\(\\frac{-1}{3}\\)
\nC) 8
\nD) 0
\nAnswer:
\nD) 0<\/p>\nQuestion 30.
\nWhich of the following is a quadratic equation ?
\nA) x2<\/sup> – 3x + 1
\nB) 8x3<\/sup> + 7x2<\/sup> + 1
\nC) x2<\/sup> – x + 1 = 0
\nD) all
\nAnswer:
\nC) x2<\/sup> – x + 1 = 0<\/p>\nQuestion 31.
\n(\u03b1 + \u03b2)2<\/sup> – 2\u03b1\u03b2 = ………..
\nA) \u03b12<\/sup> + \u03b22<\/sup> + 1
\nB) \u03b12<\/sup> + \u03b22<\/sup>
\nC) \u03b12<\/sup> + \u03b22<\/sup>
\nD) \u03b1\u03b2
\nAnswer:
\nC) \u03b12<\/sup> + \u03b22<\/sup><\/p>\nQuestion 32.
\nIf \u03b1, \u03b2 are the roots of x2<\/sup> – px + q = 0 then \u03b13<\/sup> + \u03b23<\/sup> = ………
\nA) p + q3<\/sup>
\nB) p – 3p3<\/sup>q
\nC) p3<\/sup> – 3pq
\nD) p2<\/sup> – 3pq
\nAnswer:
\nC) p3<\/sup> – 3pq<\/p>\nQuestion 33.
\n(1 – 5x) (9x + 1) = …….
\nA) 3x2<\/sup> + 1 + x
\nB) 8x2<\/sup> – 5x + 1
\nC) 1 – 4x + 5x2<\/sup>
\nD) 1 + 4x – 45x2<\/sup>
\nAnswer:
\nD) 1 + 4x – 45x2<\/sup><\/p>\nQuestion 34.
\nThe roots of x = \\(\\frac{1}{x}\\) are ……..
\nA) 2 or -2
\nB) 2 or \\(\\frac{1}{2}\\)
\nC) 1 or – 1
\nD) all
\nAnswer:
\nC) 1 or – 1<\/p>\n
Question 35.
\nIf \\(\\frac{-7}{3}\\) is a root of 6x2<\/sup> – 13x – 63 = 0 then other root is ……..
\nA) 8
\nB) \\(\\frac{1}{3}\\)
\nC) \\(\\frac{2}{9}\\)
\nD) \\(\\frac{9}{2}\\)
\nAnswer:
\nD) \\(\\frac{9}{2}\\)<\/p>\n<\/p>\n
Question 36.
\n\\(\\sqrt{a \\sqrt{a \\sqrt{a \\ldots \\ldots \\infty}}}\\) = ………
\nA) a1\/2<\/sup>
\nB) a
\nC) a3<\/sup>
\nD) a\/2
\nAnswer:
\nB) a<\/p>\nQuestion 37.
\nIf one root of x2<\/sup> – x – k = 0 is square of other then k =
\nA) 2
\nB) 3
\nC) -4
\nD) none
\nAnswer:
\nD) none<\/p>\nQuestion 38.
\nThe roots of 2x2<\/sup> + x – 4 = 0 are ………
\nA) \\(\\frac{-1 \\pm \\sqrt{33}}{4}\\)
\nB) \\(\\frac{-1 \\pm \\sqrt{31}}{2}\\)
\nC) \\(\\frac{-1 \\pm \\sqrt{29}}{2}\\)
\nD) none
\nAnswer:
\nA) \\(\\frac{-1 \\pm \\sqrt{33}}{4}\\)<\/p>\nQuestion 39.
\nIf b2<\/sup> < 4ac then shape of graph is …….
\n
\nAnswer:
\nA)
\n<\/p>\nQuestion 40.
\nOne of the root of the Q.E. 6x2<\/sup> – x – 2 = 0 is
\nA) \\(\\frac{1}{3}\\)
\nB) \\(\\frac{-1}{3}\\)
\nC) \\(\\frac{-2}{3}\\)
\nD) \\(\\frac{2}{3}\\)
\nAnswer:
\nD) \\(\\frac{2}{3}\\)<\/p>\nQuestion 41.
\nThe sum of a number and its reciprocal is \\(\\frac{50}{7}\\), then the number is
\nA) \\(\\frac{1}{7}\\)
\nB) 5
\nC) \\(\\frac{2}{7}\\)
\nD) \\(\\frac{3}{7}\\)
\nAnswer:
\nA) \\(\\frac{1}{7}\\)<\/p>\n
Question 42.
\nIf 5x2<\/sup> – kx + 11 = 0 has a root x = 3 then k =
\nA) \\(\\frac{16}{3}\\)
\nB) \\(\\frac{56}{3}\\)
\nC) \\(\\frac{-17}{3}\\)
\nD) 15
\nAnswer:
\nB) \\(\\frac{56}{3}\\)<\/p>\nQuestion 43.
\nThe value of p for which 4x2<\/sup> – 2px + 7 = 0 has a real root is
\nA) p > 2\\(\\sqrt{7}\\)
\nB) p > \\(\\sqrt{7}\\)
\nC) p > \\(\\sqrt{5}\\)
\nD) p > \\(\\sqrt{3}\\)
\nAnswer:
\nA) p > 2\\(\\sqrt{7}\\)<\/p>\nQuestion 44.
\nThe standard form of a Q.E. is
\nA) ax + b = 0
\nB) ax2<\/sup> + bx + c = 0; a \u2260 o
\nC) ax3<\/sup> + bx2<\/sup> + cx + d = 0
\nD) a2<\/sup> x + b2<\/sup> y = c2<\/sup>
\nAnswer:
\nB) ax2<\/sup> + bx + c = 0; a \u2260 o<\/p>\nQuestion 45.
\nThe roots of the Q.E. \\(\\frac{9}{x^2-27}\\) = \\(\\frac{25}{x^2-11}\\)
\nA) \u00b111
\nB) \u00b1 3
\nC) \u00b1 9
\nD) \u00b1 6
\nAnswer:
\nD) \u00b1 6<\/p>\n
Question 46.
\nThe Q.E. whose roots are -2, -3 is
\nA) x2<\/sup> – 5x + 6 = 0
\nB) x2<\/sup> + 5x + 6 = 0
\nC) x2<\/sup> – 5x – 6 = 0
\nD) x2<\/sup> + 5x – 6 = 0
\nAnswer:
\nB) x2<\/sup> + 5x + 6 = 0<\/p>\nQuestion 47.
\nForm a quadratic equation whose roots are k and \\(\\frac{1}{\\mathbf{k}}\\)
\nA) x2<\/sup> + (k + \\(\\frac{1}{\\mathbf{k}}\\)) x + 1 = 0
\nB) xk2<\/sup> – kx + 1 = 0
\nC) x2<\/sup> – (k + k) + 1 = 0
\nD) x2<\/sup> – (k + \\(\\frac{1}{\\mathbf{k}}\\)) x + 1 = 0
\nAnswer:
\nD) x2<\/sup> – (k + \\(\\frac{1}{\\mathbf{k}}\\)) x + 1 = 0<\/p>\nQuestion 48.
\nThe sum of the roots of the quadratic equation 5x2<\/sup> + 4 \\(\\sqrt{3}\\)x – 11 = o is
\nA) \\(\\frac{-11}{5}\\)
\nB) \\(\\frac{11}{4}\\)
\nC) \\(\\frac{-4}{3}\\)
\nD) \\(\\frac{-4}{5} \\sqrt{3}\\)
\nAnswer:
\nD) \\(\\frac{-4}{5} \\sqrt{3}\\)<\/p>\nQuestion 49.
\nIf one root of a quadratic equation is 7 – \\(\\sqrt{3}\\) then the quadratic equation is ……..
\nA) x2<\/sup> – 7x + 3 = 0
\nB) x2<\/sup> – 4x + 6 = 0
\nC) x2<\/sup> – 7x + 1 = 0
\nD) x2<\/sup> – 14x + 46 = 0
\nAnswer:
\nD) x2<\/sup> – 14x + 46 = 0<\/p>\nQuestion 50.
\nThe roots of a quadratic equation (\\(\\sqrt{2}\\)x + 3) (5x – \\(\\sqrt{3}\\)) = 0 are ….
\nA) \\(\\frac{1}{3}\\), \\(\\frac{1}{\\sqrt{2}}\\)
\nB) \\(\\frac{1}{2}\\), \\(\\frac{3}{\\sqrt{5}}\\)
\nC) \\(\\frac{-3}{\\sqrt{2}}\\), \\(\\frac{1}{5}\\)
\nD) \\(\\frac{-3}{\\sqrt{2}}\\), \\(\\frac{\\sqrt{3}}{5}\\)
\nAnswer:
\nD) \\(\\frac{-3}{\\sqrt{2}}\\), \\(\\frac{\\sqrt{3}}{5}\\)<\/p>\n
Question 51.
\nIf b2<\/sup> – 4ac > 0 then the roots of the quadratic equations are ……..
\nA) real and distinct
\nB) real and equal
\nC) imaginary
\nD) none
\nAnswer:
\nA) real and distinct<\/p>\nQuestion 52.
\nThe roots of 7x2<\/sup> + 3x + 8 = 0 are
\nA) real
\nB) not real
\nC) real and equal
\nD) none
\nAnswer:
\nB) not real<\/p>\n<\/p>\n
Question 53.
\nThe quadratic equation whose roots are – 2 and -3 is
\nA) x2<\/sup> + 6x + 1 = 0
\nB) x2<\/sup> + 5x + 6 = 0
\nC) x2<\/sup> – 5x + 1 = 0
\nD) none
\nAnswer:
\nB) x2<\/sup> + 5x + 6 = 0<\/p>\nQuestion 54.
\n\\(\\frac{1}{a+3}\\) + \\(\\frac{1}{a-3}\\) + \\(\\frac{6}{9-a^2}\\) = ……….
\nA) \\(\\frac{1}{a+2}\\)
\nB) \\(\\frac{3}{a+2}\\)
\nC) \\(\\frac{2}{a+3}\\)
\nD) \\(\\frac{2}{a+3}\\)
\nAnswer:
\nD) \\(\\frac{2}{a+3}\\)<\/p>\n
Question 55.
\nIf (2x – 1) (2x + 3) = 0 then x = ……….
\nA) \\(\\frac{1}{2}\\) or \\(\\frac{-1}{2}\\)
\nB) \\(\\frac{1}{2}\\) or \\(\\frac{-3}{2}\\)
\nC) \\(\\frac{1}{2}\\) or \\(\\frac{2}{3}\\)
\nD) none
\nAnswer:
\nB) \\(\\frac{1}{2}\\) or \\(\\frac{-3}{2}\\)<\/p>\n
Question 56.
\nIf \u03b1 and \u03b2 are the roots of the quadratic equation 2x2<\/sup> + 3x – 7 = 0 then \\(\\frac{a^2+b^2}{a b}\\) = …………
\nA) \\(\\frac{-37}{16}\\)
\nB) \\(\\frac{-37}{4}\\)
\nC) \\(\\frac{-37}{14}\\)
\nD) \\(\\frac{37}{8}\\)
\nAnswer:
\nC) \\(\\frac{-37}{14}\\)<\/p>\nQuestion 57.
\nThe degree of any quadratic equation is …………
\nA) 4
\nB) 1
\nC) 2
\nD) 3
\nAnswer:
\nC) 2<\/p>\n
Question 58.
\nThe product of two consecutive positive integer is 306 then the largest number is ………..
\nA) 12
\nB) 16
\nC) 18
\nD) 10
\nAnswer:
\nC) 18<\/p>\n
Question 59.
\n3(x – 4)2<\/sup> – 5(x – 4) = 12 then x = ……….
\nA) 6, \\(\\frac{-1}{17}\\)
\nB) 8, \\(\\frac{-1}{2}\\)
\nC) 3, 4
\nD) 3, \\(\\frac{-4}{3}\\)
\nAnswer:
\nD) 3, \\(\\frac{-4}{3}\\)<\/p>\nQuestion 60.
\nDiscriminant of the quadratic equation
\npx2<\/sup> + qx + r = 0 is…… ( )
\nA) q2<\/sup> – pr
\nB) q – 4pr
\nC) q2<\/sup> – 4pr
\nD) none
\nAnswer:
\nC) q2<\/sup> – 4pr<\/p>\nQuestion 61.
\nIf a is a root of ax2<\/sup> + bx + c = 0 then a\u03b12<\/sup> + b\u03b1 + c = ………
\nA) -c
\nB) 0
\nC) 8
\nD) 1
\nAnswer:
\nB) 0<\/p>\nQuestion 62.
\nDiscriminant of the quadratic equation x + \\(\\frac{1}{x}\\) = 3 is ………..
\nA) -10
\nB) 9
\nC) 6
\nD) 5
\nAnswer:
\nD) 5<\/p>\n
Question 63.
\nIf the sum of the roots of kx2<\/sup> – 3x + 1 = 0 is \\(\\frac{-4}{3}\\) then k = …………
\nA) \\(\\frac{-4}{9}\\)
\nB) \\(\\frac{9}{5}\\)
\nC) \\(\\frac{-9}{4}\\)
\nD) none
\nAnswer:
\nC) \\(\\frac{-9}{4}\\)<\/p>\nQuestion 64.
\nIf ax2<\/sup> – 4x + 3 = 1 then x = ………., a \u2260 0
\nA) 1 or 3
\nB) 2 or 7
\nC) 8 or \\(\\frac{1}{2}\\)
\nD) 2 or -3
\nAnswer:
\nA) 1 or 3<\/p>\nQuestion 65.
\n
\nA) \\(\\frac{1+\\sqrt{1+4 a}}{2}\\)
\nB) \\(\\frac{1-\\sqrt{4 a-2}}{3}\\)
\nC) \\(\\frac{1+\\sqrt{2}}{2}\\)
\nD) none
\nAnswer:
\nA) \\(\\frac{1+\\sqrt{1+4 a}}{2}\\)<\/p>\n
<\/p>\n
Question 66.
\nIf \\(\\frac{1}{x-2}\\) + \\(\\frac{2}{x-1}\\) = \\(\\frac{6}{x}\\) then x = ………
\nA) 3 or \\(\\frac{4}{3}\\)
\nB) 3 or \\(\\frac{-1}{3}\\)
\nC) 1 or \\(\\frac{2}{3}\\)
\nD) 8 or \\(\\frac{7}{2}\\)
\nAnswer:
\nA) 3 or \\(\\frac{4}{3}\\)<\/p>\n
Question 67.
\nSum of the roots of a pure quadratic equation is ……..
\nA) -13
\nB) 12
\nC) -9
\nD) 0
\nAnswer:
\nD) 0<\/p>\n
Question 68.
\nIf the sum of the squares of two consecutive odd numbers is 74; then the smaller number is
\nA) 11
\nB) 3
\nC) 7
\nD) 5
\nAnswer:
\nD) 5<\/p>\n
Question 69.
\nThe roots of the Q.E. \\(\\sqrt{3}\\)x2<\/sup> – 2x – \\(\\sqrt{3}\\) = 0 are
\nA) Real and distinct
\nB) Real and equal
\nC) Not real
\nD) Can’t be determined
\nAnswer:
\nA) Real and distinct<\/p>\nQuestion 70.
\nThe roots of 5x2<\/sup> – x + 1 = 0 are
\nA) Real and equal
\nB) Real and unequal
\nC) Imaginary
\nD) None
\nAnswer:
\nC) Imaginary<\/p>\nQuestion 71.
\nThe roots of the Q.E. (7x – 1) (2x + 3) = 0 are
\nA) 1, 3
\nB) \\(\\frac{1}{7}\\), \\(\\frac{3}{2}\\)
\nC) \\(\\frac{1}{7}\\), \\(\\frac{-3}{2}\\)
\nD) \\(\\frac{-1}{7}\\), \\(\\frac{-3}{2}\\)
\nAnswer:
\nC) \\(\\frac{1}{7}\\), \\(\\frac{-3}{2}\\)<\/p>\n
Question 72.
\nThe roots of the Q.E. (x – \\(\\frac{1}{3}\\))2<\/sup> = 9 are
\nA) 10, 8
\nB) \\(\\frac{-10}{8}\\), \\(\\frac{8}{3}\\)
\nC) \\(\\frac{10}{3}\\), \\(\\frac{-8}{3}\\)
\nD) (-3, 3)
\nAnswer:
\nC) \\(\\frac{10}{3}\\), \\(\\frac{-8}{3}\\)<\/p>\nQuestion 73.
\nIf(x – 3) (x + 3) = 16 then the value of x is
\nA) \u00b1 4
\nB) \u00b1 3
\nC) \u00b1 6
\nD) \u00b1 5
\nAnswer:
\nD) \u00b1 5<\/p>\n
Question 74.
\nThe product of the roots of the quadratic equation \\(\\sqrt{2}\\)x2<\/sup> – 3x + 5\\(\\sqrt{2}\\) = 0 is ………
\nA) \\(\\frac{-5}{3}\\)
\nB) \\(\\sqrt{2}\\)
\nC) 5
\nD) 3
\nAnswer:
\nC) 5<\/p>\nQuestion 75.
\nThe nature of the roots of quadratic equation 3x2<\/sup> + x + 8 = 0 is ……….
\nA) real and distinct
\nB) real and equal
\nC) Imaginary
\nD) none
\nAnswer:
\nC) Imaginary<\/p>\nQuestion 76.
\nIf b2<\/sup> – 4ac < 0 then the roots of the quadratic equations are ………..
\nA) distinct
\nB) equal
\nC) imaginary
\nD) none
\nAnswer:
\nC) imaginary<\/p>\nQuestion 77.
\nSum of the roots of ax2<\/sup> + bx + c = 0 is ………….
\nA) \\(\\frac{c}{a}\\)
\nB) \\(\\frac{b}{a}\\)
\nC) \\(\\frac{a}{b}\\)
\nD) none
\nAnswer:
\nD) none<\/p>\nQuestion 78.
\n\\(\\frac{x}{x-y}\\) – \\(\\frac{y}{x+y}\\) = …………
\nA) \\(\\frac{x^2+y^2}{x^2-y^2}\\)
\nB) \\(\\frac{x^2+y^2}{x+y}\\)
\nC) \\(\\frac{x^2 y^2}{x+y}\\)
\nD) none
\nAnswer:
\nA) \\(\\frac{x^2+y^2}{x^2-y^2}\\)<\/p>\n
Question 79.
\n(x + \\(\\frac{1}{x}\\))2<\/sup> – (y + \\(\\frac{1}{y}\\))2<\/sup> – (xy – \\(\\frac{1}{x y}\\)) . (\\(\\frac{x}{y}\\) – \\(\\frac{y}{x}\\)) = ………..
\nA) 0
\nB) 1
\nC) xy
\nD) \\(\\frac{1}{x y}\\)
\nAnswer:
\nA) 0<\/p>\nQuestion 80.
\nThe roots of (x – a) (x – b) = b2<\/sup> are ……….
\nA) real
\nB) not real
\nC) complex
\nD) none
\nAnswer:
\nA) real<\/p>\nQuestion 81.
\nForm a quadratic equation from
\nx(2x + 3) = x2<\/sup> + 1
\nA) x2<\/sup> + 3x – 1 = 0
\nB) x2<\/sup> – 3x – 2 = 0
\nC) x2<\/sup> + x + 1 = 0
\nD) none
\nAnswer:
\nA) x2<\/sup> + 3x – 1 = 0<\/p>\n<\/p>\n
Question 82.
\nThe roots of \\(\\sqrt{2}\\)x2<\/sup> + 7x + 5\\(\\sqrt{2}\\) = 0 are
\nA) \\(\\frac{-5}{\\sqrt{2}}\\) or 7
\nB) -1 or -5
\nC) –\\(\\sqrt{2}\\) or \\(\\frac{5}{\\sqrt{3}}\\)
\nD) all
\nAnswer:
\nB) -1 or -5<\/p>\nQuestion 83.
\nOn solving x2<\/sup> + 5 = -6x we get x = …………….
\nA) 5 or – 2
\nB) -1 or – 5
\nC) -3 or – 7
\nD) none
\nAnswer:
\nB) -1 or – 5<\/p>\nQuestion 84.
\nIf kx(x – 2) + 6 = 0 has equal roots then k = ………..
\nA) 3
\nB) -6
\nC) 7
\nD) 6
\nAnswer:
\nD) 6<\/p>\n
Question 85.
\nIf one root of x2<\/sup> – (p – 1) x + 10 = 0 is 5 then p = ……..
\nA) 8
\nB) 7
\nC) -3
\nD) none
\nAnswer:
\nA) 8<\/p>\nQuestion 86.
\n\\(\\sqrt{k+1}\\) = 3 then k = ………
\nA) 24
\nB) 16
\nC) 19
\nD) none
\nAnswer:
\nD) none<\/p>\n
Question 87.
\nThe quadratic inequation with 2 < x < 3 is
\nA) x2<\/sup> + 6x + 5 < 0
\nB) x2<\/sup> – 5x + 6 > 0
\nC) x2<\/sup> – 5x + 6 < 0
\nD) none
\nAnswer:
\nC) x2<\/sup> – 5x + 6 < 0<\/p>\nQuestion 88.
\n\\(\\frac{1}{x+4}\\) – \\(\\frac{1}{x-7}\\) = \\(\\frac{11}{30}\\), x \u2260 -4 or 7 then x = ………
\nA) -2 or 1
\nB) 2 or 1
\nC) -1 or 3
\nD) 7 or \\(\\frac{1}{2}\\)
\nAnswer:
\nB) 2 or 1<\/p>\n
Question 89.
\nThe roots of the equation 4x2<\/sup> + 4\\(\\sqrt{\\mathbf{3}}\\) x + 3 = 0 are
\nA) \\(\\frac{\\sqrt{3}}{2}\\)
\nB) \\(\\frac{-\\sqrt{3}}{2}\\)
\nC) -4
\nD) -2
\nAnswer:
\nB) \\(\\frac{-\\sqrt{3}}{2}\\)<\/p>\nQuestion 90.
\nThe sum of the roots of the equation 3x2<\/sup> – 7x + 11 = 0
\nA) \\(\\frac{11}{3}\\)
\nB) \\(\\frac{-7}{3}\\)
\nC) \\(\\frac{7}{3}\\)
\nD) \\(\\frac{3}{7}\\)
\nAnswer:
\nC) \\(\\frac{7}{3}\\)<\/p>\nQuestion 91.
\nThe roots of the Q.E. (\\(\\sqrt{5} x\\)x – 3)(\\(\\sqrt{5} x\\)x – 3) = 0 are
\nA) \\(\\frac{3}{\\sqrt{5}}\\), \\(\\frac{3}{\\sqrt{5}}\\)
\nB) \\(\\frac{-3}{\\sqrt{5}}\\), \\(\\frac{-3}{\\sqrt{5}}\\)
\nC) \\(\\frac{3}{\\sqrt{5}}\\), \\(\\frac{-3}{\\sqrt{5}}\\)
\nD) \\(\\frac{\\sqrt{3}}{\\sqrt{5}}\\), \\(\\frac{\\sqrt{3}}{\\sqrt{5}}\\)
\nAnswer:
\nA) \\(\\frac{3}{\\sqrt{5}}\\), \\(\\frac{3}{\\sqrt{5}}\\)<\/p>\n
Question 92.
\nThe roots of the Q.E. (3x + 4)2<\/sup> – 49 = 0 are
\nA) 1, \\(\\frac{-11}{3}\\)
\nC) \\(\\frac{-1}{3}\\), \\(\\frac{-11}{3}\\)
\nD) 1, -11
\nAnswer:
\nA) 1, \\(\\frac{-11}{3}\\)<\/p>\nQuestion 93.
\nIf the sum of the roots of the Q.E. 3x2<\/sup> + (2k + 1)x – (k + 5) = 0 is equal to the product of the roots, then the value of k is
\nA) 3
\nB) 4
\nC) 2
\nD) 6
\nAnswer:
\nB) 4<\/p>\nQuestion 94.
\nThe product of roots of the quadratic equation 5x2<\/sup> + 4\\(\\sqrt{3}\\)x – 11 = 0 is
\nA) \\(\\frac{5}{-11}\\)
\nB) \\(\\frac{1}{5}\\)
\nC) \\(\\frac{-11}{5}\\)
\nD) \\(\\frac{1}{5}\\)
\nAnswer:
\nC) \\(\\frac{-11}{5}\\)<\/p>\nQuestion 95.
\nThe discriminant of 5x2<\/sup> – 3x – 2 = 0 is …………
\nA) 49
\nB) 89
\nC) 20
\nD) none
\nAnswer:
\nA) 49<\/p>\nQuestion 96.
\nThe roots of 4x2<\/sup> – 20x + 25 = 0 are ….
\nA) real and equal
\nB) imaginary
\nC) real and distinct
\nD) none
\nAnswer:
\nA) real and equal<\/p>\n<\/p>\n
Question 97.
\n4x2<\/sup> + kx – 2 = 0 has no real roots if ………….
\nA) k > – \\(\\sqrt{32}\\)
\nB) k = 10
\nC) k < – \\(\\sqrt{32}\\)
\nD) none
\nAnswer:
\nC) k < – \\(\\sqrt{32}\\)<\/p>\nQuestion 98.
\n(x – \u03b1)(x – \u03b2) = 0 then …….
\nA) x2<\/sup> – (\u03b1)x + \u03b2\u03b1 = 0
\nB) x2<\/sup> – (\u03b1 + \u03b2)x + \u03b1\u03b2 = 0
\nC) ax2<\/sup> – x\u03b2 + \u03b1\u03b2 = 0
\nD) none
\nAnswer:
\nB) x2<\/sup> – (\u03b1 + \u03b2)x + \u03b1\u03b2 = 0<\/p>\nQuestion 99.
\nFor what values of m are the roots of the equation mx2<\/sup> + (m + 3) x + 4 = 0 are equal ?
\nA) 1 or 5
\nB) -1 or 2
\nC) 8 of 1
\nD) 9 or -7
\nAnswer:
\nA) 1 or 5<\/p>\nQuestion 100.
\nIf x + \\(\\frac{1}{x}\\) = 2 then x2<\/sup> + \\(\\frac{1}{x^2}\\) = …………
\nA) 8
\nB) 0
\nC) 4
\nD) 2
\nAnswer:
\nD) 2<\/p>\nQuestion 101.
\n1 and \\(\\frac{3}{2}\\) are the roots of ………..
\nA) 2x2<\/sup> – 5x + 3 = 0
\nB) x2<\/sup> – 5x + 1 = 0
\nC) 2x2<\/sup> – x + 3 = 0
\nD) all
\nAnswer:
\nA) 2x2<\/sup> – 5x + 3 = 0<\/p>\nQuestion 102.
\nThe equation 5x2<\/sup> + 2x + 8 = 0 has ……….
\nA) no real roots
\nB) real roots
\nC) equal roots
\nD) none
\nAnswer:
\nA) no real roots<\/p>\nQuestion 103.
\nDiagonal of a rectangle is …….
\nA) \\(\\sqrt{l}\\) + b2<\/sup>
\nB) \\(\\sqrt{l}\\) + b
\nC) \\(\\sqrt{l \\mathrm{~b}}\\)
\nD) \\(\\sqrt{l^2+\\mathrm{b}^2}\\)
\nAnswer:
\nD) \\(\\sqrt{l^2+\\mathrm{b}^2}\\)<\/p>\nQuestion 104.
\nThe coefficient of x in a pure quadratic equation is…
\nA) 2
\nB) 0
\nC) 8
\nD) none
\nAnswer:
\nB) 0<\/p>\n
Question 105.
\nIf 2 is a root of x2<\/sup> + 5x + r = 0 then r = ……..
\nA) -4
\nB) -14
\nC) 16
\nD) 8
\nAnswer:
\nB) -14<\/p>\nQuestion 106.
\nx2<\/sup> + (x + 2)2<\/sup> = 290 then x = ………
\nA) 9 or -13
\nB) 8 or -12
\nC) 11 or -13
\nD) all
\nAnswer:
\nC) 11 or -13<\/p>\nQuestion 107.
\nIf 3y2<\/sup> = 192 then y = ……..
\nA) 12
\nB) 6
\nC) 8
\nD) none
\nAnswer:
\nD) none<\/p>\nQuestion 108.