TS 10th Class Maths Bits Chapter 5 Quadratic Equations

Solving these TS 10th Class Maths Bits with Answers Chapter 5 Quadratic Equations Bits for 10th Class will help students to build their problem-solving skills.

Quadratic Equations Bits for 10th Class

Question 1.
The roots of the equation 3x² – 2 \(\sqrt{6}\)x + 2 = 0 are
A) \(\frac{2}{\sqrt{3}}\), \(\frac{-2}{\sqrt{3}}\)
B) \(\frac{1}{\sqrt{3}}\), \(\frac{-1}{\sqrt{3}}\)
C) \(\sqrt{\frac{2}{3}}\), \(\sqrt{\frac{2}{3}}\)
D) \(\frac{1}{\sqrt{3}}\), \(\frac{5}{\sqrt{3}}\)
Answer:
C) \(\sqrt{\frac{2}{3}}\), \(\sqrt{\frac{2}{3}}\)

Question 2.
One solution of the Q.E. 2x² – 5x
A) x = 2
B) x = – 1
C) x = -3
D) x = 3
Answer:
D) x = 3

Question 3.
The positive root of \(\sqrt{3 x^2+6}\) = 9 is
A) 3
B) 5
C) 4
D) \(\frac{2}{5}\)
Answer:
B) 5

Question 4.
Which of the following Q.E. has real and equal roots ?
A) x² – 4x + 4 = 0
B) 2x² – 4x + 3 = 0
C) 3x² – 5x + 2 = 0
D) x² – 2\(\sqrt{2}\)x – 6 = 0
Answer:
A) x² – 4x + 4 = 0

Question 5.
Which of the following is a Q.E. ?
A) (x + 1)² = 3(x + 7)
B) (x – 1) (x + 3) = (x – 2) (x + 1)
C) x² + 5x – 7 = (x – 4)²
D) x³ – 9 = 0
Answer:
A) (x + 1)² = 3(x + 7)

Question 6.
The sum of a number and its reciprocal is \(\frac{5}{2}\) then the number is
A) 2 or \(\frac{1}{3}\)
B) 3 or \(\frac{1}{2}\)
C) 2 or \(\frac{1}{2}\)
D) 5 and \(\frac{1}{5}\)
Answer:
C) 2 or \(\frac{1}{2}\)

Question 7.
If the equation x² – kx + 1 = 0 has equal roots, then
A) k = 1
B) k = – 1
C) k = 2
D) k = – 4
Answer:
C) k = 2

Question 8.
The Q.E. whose one root is 2 – \(\sqrt{3}\) is
A) x² – 4x + 1 = 0
B) x² + 4x – 1 = 0
C) x² – 4x – 1 = 0
D) x² – 2x – 3 = 0
Answer:
A) x² – 4x + 1 = 0

Question 9.
The roots of a quadratic equation \(\frac{x}{p}\) = \(\frac{p}{x}\)
A) ± p
B) p, 2p
C) -p, 2p
D) -p, -2p
Answer:
A) ± p

Question 10.
\(\sqrt{2}\)x² – 3x + 5\(\sqrt{2}\) = 0, sum of the root is ……….
A) \(\sqrt{2}\)
B) \(\frac{-3}{\sqrt{2}}\)
C) 3
D) 5
Answer:
A) \(\sqrt{2}\)

Question 11.
The quadratic equation whose roots are -3 and -4 is ……..
A) 7x² + x + 1 = 0
B) x² + 7x + 12 = 0
C) x² – 3x + 1 = 0
D) none
Answer:
B) x² + 7x + 12 = 0

Question 12.
The nature of the roots of a quadratic equation 4x² – 12x + 9 = 0 is ……….
A) real and equal
B) real and distinct
C) imaginary
D) none
Answer:
A) real and equal

Question 13.
The roots of the quadratic equation \(\frac{x^2-8}{x^2+20}\) = \(\frac{1}{2}\) are….
A) ±2
B) ±6
C) ±13
D) ±7
Answer:
B) ±6

Question 14.
If b² – 4ac = 0 then the roots of the quadratic equations are
A) real and distinct
B) real and equal
C) imaginary
D) none
Answer:
B) real and equal

Question 15.
The nature of roots of 3x² + 6x – 2 = 0 is
A) real and distinct
B) real and equal
C) complex
D) none
Answer:
A) real and distinct

Question 16.
Product of the roots of ax² + bx + c = 0 is
A) \(\frac{c}{a}\)
B) \(\frac{-b}{a}\)
C) \(\frac{-c}{a}\)
D) none
Answer:
A) \(\frac{c}{a}\)

Question 17.
The quadratic equation whose roots are 2, 3 is …………
A) x² – 5x + 1 = 0
B) x² – 5x – 6 = 0
C) x² – 3x + 1 = 0
D) x² – 5x + 6 = 0
Answer:
D) x² – 5x + 6 = 0

Question 18.
\(\frac{2 a^2+a-1}{a+1}\) + \(\frac{3 a^2+5 a+2}{3 a+2}\) + \(\frac{4-a^2}{a+2}\) + ……..
A) \(\frac{\mathrm{a}}{2}\)
B) \(\frac{a+1}{2}\)
C) 2(a + 1)
D) none
Answer:
C) 2(a + 1)

Question 19.

A) 1
B) x²
C) x
D) 0
Answer:
C) x

Question 20.
Sum of the roots of bx² + ax + c = 0 is ………
A) \(\frac{-b}{a}\)
B) \(\frac{c}{a}\)
C) \(\frac{c}{a}\)
D) \(\frac{-a}{b}\)
Answer:
D) \(\frac{-a}{b}\)

Question 21.
The nature of roots of 3x² + 13x – 2 = 0 is ……..
A) real and unequal
B) real and equal
C) complex
D) none
Answer:
A) real and unequal

Question 22.
Product of the roots of x² + 7x = 0 is ………
A) 1
B) -7
C) -3
D) 0
Answer:
D) 0

Question 23.
If α and β are the roots of x² – 2x + 3 = 0 then α² + β² = ………
A) 1
B) 4
C) 8
D) none
Answer:
D) none

Question 24.
If α and β are the roots of x² – 5x + 6 = 0 then the value of α – β = ……….
A) ±1
B) ±2
C) -3
D) none
Answer:
A) ±1

Question 25.
Form a quadratic equation from x³ – 4x² – x + 1 = (x – 2)³ = …….
A) 2x² – x + 1 = 0
B) 2x² – 13x + 9 = 0
C) x² + x + 1 = 0
D) none
Answer:
B) 2x² – 13x + 9 = 0

Question 26.
The product of two consecutive positive in¬teger is 306 then the smallest number is
A) 16
B) 13
C) 19
D) 17
Answer:
D) 17

Question 27.
x(x + 4) = 12 then x = …….
A) – 6 or 2
B) 6 or 7
C) 8 or – 9
D) none
Answer:
A) – 6 or 2

Question 28.
9 and 1 are the roots of ……
A) x² – 10x + 9 = 0
B) x² – x + 1 = 0
C) x² + 3x + 4 = 0
D) none
Answer:
A) x² – 10x + 9 = 0

Question 29.
The discriminant of 3x² – 2x = \(\frac{-1}{3}\) is ……..
A) 1
B) –\(\frac{-1}{3}\)
C) 8
D) 0
Answer:
D) 0

Question 30.
Which of the following is a quadratic equation ?
A) x² – 3x + 1
B) 8x³ + 7x² + 1
C) x² – x + 1 = 0
D) all
Answer:
C) x² – x + 1 = 0

Question 31.
(α + β)² – 2αβ = ………..
A) α² + β² + 1
B) α² + β²
C) α² + β²
D) αβ
Answer:
C) α² + β²

Question 32.
If α, β are the roots of x² – px + q = 0 then α³ + β³ = ………
A) p + q³
B) p – 3p³q
C) p³ – 3pq
D) p² – 3pq
Answer:
C) p³ – 3pq

Question 33.
(1 – 5x) (9x + 1) = …….
A) 3x² + 1 + x
B) 8x² – 5x + 1
C) 1 – 4x + 5x²
D) 1 + 4x – 45x²
Answer:
D) 1 + 4x – 45x²

Question 34.
The roots of x = \(\frac{1}{x}\) are ……..
A) 2 or -2
B) 2 or \(\frac{1}{2}\)
C) 1 or – 1
D) all
Answer:
C) 1 or – 1

Question 35.
If \(\frac{-7}{3}\) is a root of 6x² – 13x – 63 = 0 then other root is ……..
A) 8
B) \(\frac{1}{3}\)
C) \(\frac{2}{9}\)
D) \(\frac{9}{2}\)
Answer:
D) \(\frac{9}{2}\)

Question 36.
\(\sqrt{a \sqrt{a \sqrt{a \ldots \ldots \infty}}}\) = ………
A) a^1/2
B) a
C) a³
D) a/2
Answer:
B) a

Question 37.
If one root of x² – x – k = 0 is square of other then k =
A) 2
B) 3
C) -4
D) none
Answer:
D) none

Question 38.
The roots of 2x² + x – 4 = 0 are ………
A) \(\frac{-1 \pm \sqrt{33}}{4}\)
B) \(\frac{-1 \pm \sqrt{31}}{2}\)
C) \(\frac{-1 \pm \sqrt{29}}{2}\)
D) none
Answer:
A) \(\frac{-1 \pm \sqrt{33}}{4}\)

Question 39.
If b² < 4ac then shape of graph is …….

Answer:
A)

Question 40.
One of the root of the Q.E. 6x² – x – 2 = 0 is
A) \(\frac{1}{3}\)
B) \(\frac{-1}{3}\)
C) \(\frac{-2}{3}\)
D) \(\frac{2}{3}\)
Answer:
D) \(\frac{2}{3}\)

Question 41.
The sum of a number and its reciprocal is \(\frac{50}{7}\), then the number is
A) \(\frac{1}{7}\)
B) 5
C) \(\frac{2}{7}\)
D) \(\frac{3}{7}\)
Answer:
A) \(\frac{1}{7}\)

Question 42.
If 5x² – kx + 11 = 0 has a root x = 3 then k =
A) \(\frac{16}{3}\)
B) \(\frac{56}{3}\)
C) \(\frac{-17}{3}\)
D) 15
Answer:
B) \(\frac{56}{3}\)

Question 43.
The value of p for which 4x² – 2px + 7 = 0 has a real root is
A) p > 2\(\sqrt{7}\)
B) p > \(\sqrt{7}\)
C) p > \(\sqrt{5}\)
D) p > \(\sqrt{3}\)
Answer:
A) p > 2\(\sqrt{7}\)

Question 44.
The standard form of a Q.E. is
A) ax + b = 0
B) ax² + bx + c = 0; a ≠ o
C) ax³ + bx² + cx + d = 0
D) a² x + b² y = c²
Answer:
B) ax² + bx + c = 0; a ≠ o

Question 45.
The roots of the Q.E. \(\frac{9}{x^2-27}\) = \(\frac{25}{x^2-11}\)
A) ±11
B) ± 3
C) ± 9
D) ± 6
Answer:
D) ± 6

Question 46.
The Q.E. whose roots are -2, -3 is
A) x² – 5x + 6 = 0
B) x² + 5x + 6 = 0
C) x² – 5x – 6 = 0
D) x² + 5x – 6 = 0
Answer:
B) x² + 5x + 6 = 0

Question 47.
Form a quadratic equation whose roots are k and \(\frac{1}{\mathbf{k}}\)
A) x² + (k + \(\frac{1}{\mathbf{k}}\)) x + 1 = 0
B) xk² – kx + 1 = 0
C) x² – (k + k) + 1 = 0
D) x² – (k + \(\frac{1}{\mathbf{k}}\)) x + 1 = 0
Answer:
D) x² – (k + \(\frac{1}{\mathbf{k}}\)) x + 1 = 0

Question 48.
The sum of the roots of the quadratic equation 5x² + 4 \(\sqrt{3}\)x – 11 = o is
A) \(\frac{-11}{5}\)
B) \(\frac{11}{4}\)
C) \(\frac{-4}{3}\)
D) \(\frac{-4}{5} \sqrt{3}\)
Answer:
D) \(\frac{-4}{5} \sqrt{3}\)

Question 49.
If one root of a quadratic equation is 7 – \(\sqrt{3}\) then the quadratic equation is ……..
A) x² – 7x + 3 = 0
B) x² – 4x + 6 = 0
C) x² – 7x + 1 = 0
D) x² – 14x + 46 = 0
Answer:
D) x² – 14x + 46 = 0

Question 50.
The roots of a quadratic equation (\(\sqrt{2}\)x + 3) (5x – \(\sqrt{3}\)) = 0 are ….
A) \(\frac{1}{3}\), \(\frac{1}{\sqrt{2}}\)
B) \(\frac{1}{2}\), \(\frac{3}{\sqrt{5}}\)
C) \(\frac{-3}{\sqrt{2}}\), \(\frac{1}{5}\)
D) \(\frac{-3}{\sqrt{2}}\), \(\frac{\sqrt{3}}{5}\)
Answer:
D) \(\frac{-3}{\sqrt{2}}\), \(\frac{\sqrt{3}}{5}\)

Question 51.
If b² – 4ac > 0 then the roots of the quadratic equations are ……..
A) real and distinct
B) real and equal
C) imaginary
D) none
Answer:
A) real and distinct

Question 52.
The roots of 7x² + 3x + 8 = 0 are
A) real
B) not real
C) real and equal
D) none
Answer:
B) not real

Question 53.
The quadratic equation whose roots are – 2 and -3 is
A) x² + 6x + 1 = 0
B) x² + 5x + 6 = 0
C) x² – 5x + 1 = 0
D) none
Answer:
B) x² + 5x + 6 = 0

Question 54.
\(\frac{1}{a+3}\) + \(\frac{1}{a-3}\) + \(\frac{6}{9-a^2}\) = ……….
A) \(\frac{1}{a+2}\)
B) \(\frac{3}{a+2}\)
C) \(\frac{2}{a+3}\)
D) \(\frac{2}{a+3}\)
Answer:
D) \(\frac{2}{a+3}\)

Question 55.
If (2x – 1) (2x + 3) = 0 then x = ……….
A) \(\frac{1}{2}\) or \(\frac{-1}{2}\)
B) \(\frac{1}{2}\) or \(\frac{-3}{2}\)
C) \(\frac{1}{2}\) or \(\frac{2}{3}\)
D) none
Answer:
B) \(\frac{1}{2}\) or \(\frac{-3}{2}\)

Question 56.
If α and β are the roots of the quadratic equation 2x² + 3x – 7 = 0 then \(\frac{a^2+b^2}{a b}\) = …………
A) \(\frac{-37}{16}\)
B) \(\frac{-37}{4}\)
C) \(\frac{-37}{14}\)
D) \(\frac{37}{8}\)
Answer:
C) \(\frac{-37}{14}\)

Question 57.
The degree of any quadratic equation is …………
A) 4
B) 1
C) 2
D) 3
Answer:
C) 2

Question 58.
The product of two consecutive positive integer is 306 then the largest number is ………..
A) 12
B) 16
C) 18
D) 10
Answer:
C) 18

Question 59.
3(x – 4)² – 5(x – 4) = 12 then x = ……….
A) 6, \(\frac{-1}{17}\)
B) 8, \(\frac{-1}{2}\)
C) 3, 4
D) 3, \(\frac{-4}{3}\)
Answer:
D) 3, \(\frac{-4}{3}\)

Question 60.
Discriminant of the quadratic equation
px² + qx + r = 0 is…… ( )
A) q² – pr
B) q – 4pr
C) q² – 4pr
D) none
Answer:
C) q² – 4pr

Question 61.
If a is a root of ax² + bx + c = 0 then aα² + bα + c = ………
A) -c
B) 0
C) 8
D) 1
Answer:
B) 0

Question 62.
Discriminant of the quadratic equation x + \(\frac{1}{x}\) = 3 is ………..
A) -10
B) 9
C) 6
D) 5
Answer:
D) 5

Question 63.
If the sum of the roots of kx² – 3x + 1 = 0 is \(\frac{-4}{3}\) then k = …………
A) \(\frac{-4}{9}\)
B) \(\frac{9}{5}\)
C) \(\frac{-9}{4}\)
D) none
Answer:
C) \(\frac{-9}{4}\)

Question 64.
If ax² – 4x + 3 = 1 then x = ………., a ≠ 0
A) 1 or 3
B) 2 or 7
C) 8 or \(\frac{1}{2}\)
D) 2 or -3
Answer:
A) 1 or 3

Question 65.

A) \(\frac{1+\sqrt{1+4 a}}{2}\)
B) \(\frac{1-\sqrt{4 a-2}}{3}\)
C) \(\frac{1+\sqrt{2}}{2}\)
D) none
Answer:
A) \(\frac{1+\sqrt{1+4 a}}{2}\)

Question 66.
If \(\frac{1}{x-2}\) + \(\frac{2}{x-1}\) = \(\frac{6}{x}\) then x = ………
A) 3 or \(\frac{4}{3}\)
B) 3 or \(\frac{-1}{3}\)
C) 1 or \(\frac{2}{3}\)
D) 8 or \(\frac{7}{2}\)
Answer:
A) 3 or \(\frac{4}{3}\)

Question 67.
Sum of the roots of a pure quadratic equation is ……..
A) -13
B) 12
C) -9
D) 0
Answer:
D) 0

Question 68.
If the sum of the squares of two consecutive odd numbers is 74; then the smaller number is
A) 11
B) 3
C) 7
D) 5
Answer:
D) 5

Question 69.
The roots of the Q.E. \(\sqrt{3}\)x² – 2x – \(\sqrt{3}\) = 0 are
A) Real and distinct
B) Real and equal
C) Not real
D) Can’t be determined
Answer:
A) Real and distinct

Question 70.
The roots of 5x² – x + 1 = 0 are
A) Real and equal
B) Real and unequal
C) Imaginary
D) None
Answer:
C) Imaginary

Question 71.
The roots of the Q.E. (7x – 1) (2x + 3) = 0 are
A) 1, 3
B) \(\frac{1}{7}\), \(\frac{3}{2}\)
C) \(\frac{1}{7}\), \(\frac{-3}{2}\)
D) \(\frac{-1}{7}\), \(\frac{-3}{2}\)
Answer:
C) \(\frac{1}{7}\), \(\frac{-3}{2}\)

Question 72.
The roots of the Q.E. (x – \(\frac{1}{3}\))² = 9 are
A) 10, 8
B) \(\frac{-10}{8}\), \(\frac{8}{3}\)
C) \(\frac{10}{3}\), \(\frac{-8}{3}\)
D) (-3, 3)
Answer:
C) \(\frac{10}{3}\), \(\frac{-8}{3}\)

Question 73.
If(x – 3) (x + 3) = 16 then the value of x is
A) ± 4
B) ± 3
C) ± 6
D) ± 5
Answer:
D) ± 5

Question 74.
The product of the roots of the quadratic equation \(\sqrt{2}\)x² – 3x + 5\(\sqrt{2}\) = 0 is ………
A) \(\frac{-5}{3}\)
B) \(\sqrt{2}\)
C) 5
D) 3
Answer:
C) 5

Question 75.
The nature of the roots of quadratic equation 3x² + x + 8 = 0 is ……….
A) real and distinct
B) real and equal
C) Imaginary
D) none
Answer:
C) Imaginary

Question 76.
If b² – 4ac < 0 then the roots of the quadratic equations are ………..
A) distinct
B) equal
C) imaginary
D) none
Answer:
C) imaginary

Question 77.
Sum of the roots of ax² + bx + c = 0 is ………….
A) \(\frac{c}{a}\)
B) \(\frac{b}{a}\)
C) \(\frac{a}{b}\)
D) none
Answer:
D) none

Question 78.
\(\frac{x}{x-y}\) – \(\frac{y}{x+y}\) = …………
A) \(\frac{x^2+y^2}{x^2-y^2}\)
B) \(\frac{x^2+y^2}{x+y}\)
C) \(\frac{x^2 y^2}{x+y}\)
D) none
Answer:
A) \(\frac{x^2+y^2}{x^2-y^2}\)

Question 79.
(x + \(\frac{1}{x}\))² – (y + \(\frac{1}{y}\))² – (xy – \(\frac{1}{x y}\)) . (\(\frac{x}{y}\) – \(\frac{y}{x}\)) = ………..
A) 0
B) 1
C) xy
D) \(\frac{1}{x y}\)
Answer:
A) 0

Question 80.
The roots of (x – a) (x – b) = b² are ……….
A) real
B) not real
C) complex
D) none
Answer:
A) real

Question 81.
Form a quadratic equation from
x(2x + 3) = x² + 1
A) x² + 3x – 1 = 0
B) x² – 3x – 2 = 0
C) x² + x + 1 = 0
D) none
Answer:
A) x² + 3x – 1 = 0

Question 82.
The roots of \(\sqrt{2}\)x² + 7x + 5\(\sqrt{2}\) = 0 are
A) \(\frac{-5}{\sqrt{2}}\) or 7
B) -1 or -5
C) –\(\sqrt{2}\) or \(\frac{5}{\sqrt{3}}\)
D) all
Answer:
B) -1 or -5

Question 83.
On solving x² + 5 = -6x we get x = …………….
A) 5 or – 2
B) -1 or – 5
C) -3 or – 7
D) none
Answer:
B) -1 or – 5

Question 84.
If kx(x – 2) + 6 = 0 has equal roots then k = ………..
A) 3
B) -6
C) 7
D) 6
Answer:
D) 6

Question 85.
If one root of x² – (p – 1) x + 10 = 0 is 5 then p = ……..
A) 8
B) 7
C) -3
D) none
Answer:
A) 8

Question 86.
\(\sqrt{k+1}\) = 3 then k = ………
A) 24
B) 16
C) 19
D) none
Answer:
D) none

Question 87.
The quadratic inequation with 2 < x < 3 is
A) x² + 6x + 5 < 0
B) x² – 5x + 6 > 0
C) x² – 5x + 6 < 0
D) none
Answer:
C) x² – 5x + 6 < 0

Question 88.
\(\frac{1}{x+4}\) – \(\frac{1}{x-7}\) = \(\frac{11}{30}\), x ≠ -4 or 7 then x = ………
A) -2 or 1
B) 2 or 1
C) -1 or 3
D) 7 or \(\frac{1}{2}\)
Answer:
B) 2 or 1

Question 89.
The roots of the equation 4x² + 4\(\sqrt{\mathbf{3}}\) x + 3 = 0 are
A) \(\frac{\sqrt{3}}{2}\)
B) \(\frac{-\sqrt{3}}{2}\)
C) -4
D) -2
Answer:
B) \(\frac{-\sqrt{3}}{2}\)

Question 90.
The sum of the roots of the equation 3x² – 7x + 11 = 0
A) \(\frac{11}{3}\)
B) \(\frac{-7}{3}\)
C) \(\frac{7}{3}\)
D) \(\frac{3}{7}\)
Answer:
C) \(\frac{7}{3}\)

Question 91.
The roots of the Q.E. (\(\sqrt{5} x\)x – 3)(\(\sqrt{5} x\)x – 3) = 0 are
A) \(\frac{3}{\sqrt{5}}\), \(\frac{3}{\sqrt{5}}\)
B) \(\frac{-3}{\sqrt{5}}\), \(\frac{-3}{\sqrt{5}}\)
C) \(\frac{3}{\sqrt{5}}\), \(\frac{-3}{\sqrt{5}}\)
D) \(\frac{\sqrt{3}}{\sqrt{5}}\), \(\frac{\sqrt{3}}{\sqrt{5}}\)
Answer:
A) \(\frac{3}{\sqrt{5}}\), \(\frac{3}{\sqrt{5}}\)

Question 92.
The roots of the Q.E. (3x + 4)² – 49 = 0 are
A) 1, \(\frac{-11}{3}\)
C) \(\frac{-1}{3}\), \(\frac{-11}{3}\)
D) 1, -11
Answer:
A) 1, \(\frac{-11}{3}\)

Question 93.
If the sum of the roots of the Q.E. 3x² + (2k + 1)x – (k + 5) = 0 is equal to the product of the roots, then the value of k is
A) 3
B) 4
C) 2
D) 6
Answer:
B) 4

Question 94.
The product of roots of the quadratic equation 5x² + 4\(\sqrt{3}\)x – 11 = 0 is
A) \(\frac{5}{-11}\)
B) \(\frac{1}{5}\)
C) \(\frac{-11}{5}\)
D) \(\frac{1}{5}\)
Answer:
C) \(\frac{-11}{5}\)

Question 95.
The discriminant of 5x² – 3x – 2 = 0 is …………
A) 49
B) 89
C) 20
D) none
Answer:
A) 49

Question 96.
The roots of 4x² – 20x + 25 = 0 are ….
A) real and equal
B) imaginary
C) real and distinct
D) none
Answer:
A) real and equal

Question 97.
4x² + kx – 2 = 0 has no real roots if ………….
A) k > – \(\sqrt{32}\)
B) k = 10
C) k < – \(\sqrt{32}\)
D) none
Answer:
C) k < – \(\sqrt{32}\)

Question 98.
(x – α)(x – β) = 0 then …….
A) x² – (α)x + βα = 0
B) x² – (α + β)x + αβ = 0
C) ax² – xβ + αβ = 0
D) none
Answer:
B) x² – (α + β)x + αβ = 0

Question 99.
For what values of m are the roots of the equation mx² + (m + 3) x + 4 = 0 are equal ?
A) 1 or 5
B) -1 or 2
C) 8 of 1
D) 9 or -7
Answer:
A) 1 or 5

Question 100.
If x + \(\frac{1}{x}\) = 2 then x² + \(\frac{1}{x^2}\) = …………
A) 8
B) 0
C) 4
D) 2
Answer:
D) 2

Question 101.
1 and \(\frac{3}{2}\) are the roots of ………..
A) 2x² – 5x + 3 = 0
B) x² – 5x + 1 = 0
C) 2x² – x + 3 = 0
D) all
Answer:
A) 2x² – 5x + 3 = 0

Question 102.
The equation 5x² + 2x + 8 = 0 has ……….
A) no real roots
B) real roots
C) equal roots
D) none
Answer:
A) no real roots

Question 103.
Diagonal of a rectangle is …….
A) \(\sqrt{l}\) + b²
B) \(\sqrt{l}\) + b
C) \(\sqrt{l \mathrm{~b}}\)
D) \(\sqrt{l^2+\mathrm{b}^2}\)
Answer:
D) \(\sqrt{l^2+\mathrm{b}^2}\)

Question 104.
The coefficient of x in a pure quadratic equation is…
A) 2
B) 0
C) 8
D) none
Answer:
B) 0

Question 105.
If 2 is a root of x² + 5x + r = 0 then r = ……..
A) -4
B) -14
C) 16
D) 8
Answer:
B) -14

Question 106.
x² + (x + 2)² = 290 then x = ………
A) 9 or -13
B) 8 or -12
C) 11 or -13
D) all
Answer:
C) 11 or -13

Question 107.
If 3y² = 192 then y = ……..
A) 12
B) 6
C) 8
D) none
Answer:
D) none

Question 108.
If x² – 2x + 1 = 0, then x + \(\frac{1}{x}\) =
A) 0
B) 2
C) 1
D) None
Answer:
B) 2

Question 109.
Product of the roots of the Q.E.
3x² – 6x + 11 = 0 is
A) -2
B) \(\frac{-11}{3}\)
C) \(\frac{-11}{6}\)
D) \(\frac{11}{3}\)
Answer:
D) \(\frac{11}{3}\)

Question 110.
The roots of a quadratic equation ax² + bx + c = 0 is….

Answer:
\(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)

Question 111.
The nature of the roots of a quadratic equation 4x² + 5x + 1 = 0 is ……
A) real and distinct
B) real and equal
C) imaginary
D) none
Answer:
A) real and distinct

Question 112.
If the roots of a quadratic equation ax² + bx + c = 0 are real and equal then b² = …………….
A) 4ab
B) 4ac
C) \(\frac{\mathrm{ac}}{4}\)
D) a² c²
Answer:
B) 4ac

Question 113.
3x² + (-kx) + 8 = 0 has real roots of ………..
A) k < 4\(\sqrt{6}\) B) k > 4\(\sqrt{6}\)
C) k = 6
D) k = 0
Answer:
B) k > 4\(\sqrt{6}\)

Question 114.
If k² – 8k + 16 = 0 has equal roots then ………
A) k = ±\(\sqrt{2}\)
B) k = ±7
C) k = + 1
D) none
Answer:
C) k = + 1

Question 115.
Sum of the roots of -7x + 3x² – 1 = 0 ………..
A) \(\frac{3}{4}\)
B) \(\frac{1}{7}\)
C) \(\frac{7}{3}\)
D) \(\frac{1}{2}\)
Answer:
C) \(\frac{7}{3}\)

Question 116.
If α and β are the roots of x² – 2x + 3 = 0 the value of α³ + β³ = …….
A) -10
B) 10
C) 8
D) 12
Answer:
A) -10

Question 117.
In the quadratic equation x² + x – 2 = 0, a + b + c = …………
A) 7
B) 0
C) 8
D) 1
Answer:
B) 0

Question 118.
The roots of 2x² – x + \(\frac{1}{8}\) = 0 are……..
A) \(\frac{1}{4}\), \(\frac{1}{2}\)
B) \(\frac{1}{3}\), \(\frac{1}{7}\)
C) \(\frac{1}{2}\), \(\frac{1}{8}\)
D) \(\frac{1}{4}\), \(\frac{1}{4}\)
Answer:
D) \(\frac{1}{4}\), \(\frac{1}{4}\)

Question 119.
Number of distinct line segments that can be formed out of n – points is….
A) \(\frac{\mathrm{n}(\mathrm{n}-1)}{2}\)
B) \(\frac{\mathrm{n}}{2}\)
C) \(\frac{\mathrm{n}+1}{2}\)
D) \(\frac{n^2(n-1)}{2}\)
Answer:
A) \(\frac{\mathrm{n}(\mathrm{n}-1)}{2}\)

Question 120.
From the figure, x = ………
A) 7
B) 3
C) 10
D) none

Answer:
C) 10

Question 121.
P(x) = x² + 2x + 1 then P(x²) = …….
A) x⁴ + 2x² + 1
B) x⁴ + 2x + 1
C) x³ + 2x + 1
D) none
Answer:
A) x⁴ + 2x² + 1

Question 122.
If α and β are the roots of the quadratic equation x² – 3x + 1 = 0 then \(\frac{1}{\alpha^2}\) + \(\frac{1}{\beta^2}\) = …………
A) 7
B) 8
C) -3
D) none
Answer:
A) 7

Question 123.
\(\sqrt{x}\) = \(\sqrt{2 x-1}\) then x =
A) 1
B) 4
C) 2
D) none
Answer:
A) 1

Question 124.
A pentagon has ……… diagonals.
A) 6
B) 7
C) 9
D) none
Answer:
D) none

Question 125.
Product of the roots of 1 = x² is ……..
A) -1
B) 7
C) 0
D) 1
Answer:
A) -1

Question 126.
If α and β are the roots of
x² + x + 1 = 0 then α² and β² = ………
A) 8
B) -1
C) 12
D) 0
Answer:
B) -1

Question 127.
\(\frac{x}{a-b}\) = \(\frac{\mathbf{a}}{\mathbf{x}-\mathbf{b}}\) then x = ……….
A) b – a or \(\frac{\mathrm{a}}{2}\)
B) b – a or -a
C) b + a or -a
D) all
Answer:
B) b – a or -a

Question 128.
\(\frac{n(n+1)}{2}\) = 55 then n = ……….
A) 13
B) 16
C) 10
D) 12
Answer:
C) 10

Question 129.
If α and β are the roots of x² – 2x + 3 = 0 then α²β + β²α = ……..
A) -3
B) 8
C) 6
D) none
Answer:
C) 6

Question 130.
x² – 7x – 60 = 0 the x = …….. (A.P.Mar. 15)
A) 12, 17
B) 12, -5
C) 8, 11
D) 12, 16
Answer:
B) 12, -5

Question 131.
The general form of a quadratic equation in variable x is ……. (A.P. Mar. 15)
A) ax² + bx + c = 0 (a ≠ 0)
B) ax + bx² + c = 0 (b ≠ 0)
C) ax² + bx = 0 (a ≠ 0)
D) a²x + bx + c = 0 (b ≠ 0)
Answer:
A) ax² + bx + c = 0 (a ≠ 0)

Question 132.
The possible numbers of roots to a quadratic equation are …….. (A.P. Mar.15)
A) At a maximum of 3
B) At a maximum of 2
C) Infinite
D) At a maximum of 5
Answer:
B) At a maximum of 2

Question 133.
If the roots of a quadratic equation px² + qx + r = 0 are imaginary then ……… (A.P. June 15)
A) q² > 4pr
B) q² < 4pr
C) q² = 4pr
D) p = q + r
Answer:
B) q² < 4pr

Question 134.
The discriminant of quadratic equation 2x² + x – 4 = 0 is ………. (A.P.June’15)
A) 35
B) 36
C) 33
D) 38
Answer:
C) 33

Question 135.
The product of roots of quadratic equation ax² + bx + c = 0 is (A.P. June’15)
A) \(\frac{c}{a}\)
B) \(\frac{-b}{a}\)
C) \(\frac{-c}{a}\)
D) \(\frac{b}{c}\)
Answer:
A) \(\frac{c}{a}\)

Question 136.
For what positive value of x the quadratic equation 4x² – 9 = 0 (A.P. June’15)
A) \(\frac{2}{3}\)
B) \(\frac{-2}{3}\)
C) \(\frac{-3}{2}\)
D) \(\frac{3}{2}\)
Answer:
D) \(\frac{3}{2}\)

Question 137.
Which of the following quadratic equations the roots are equal? (A.P.Mar.16)
A) x² – 5 =0
B) x² – 10x + 25 = 0
C) x² + 5x + 6 = 0
D) x² – 1 = 0
Answer:
B) x² – 10x + 25 = 0

Question 138.
If x² + ax + b = 0; x² + bx + a = 0 have a common roots then
A) a + b = 0
B) ab = 1
C) a + b = 1
D) a + b + 1 = 0
Answer:
D) a + b + 1 = 0

Question 139.
A metal cuboid of dimensions 22 cm × 15 cm × 7.5 cm was melted and cast into a cylinder of height 14 cm. Its radius is …………
A) 15 cm
B) 7.5 cm
C) 22.5 cm
D) 7 cm
Answer:
B) 7.5 cm

Question 140.
Solution of x – y = 2; x + y = 0 lies in quadratic. (AP-SA-I:2016)
A) I
B) IV
C) II
D) III
Answer:
B) IV