QUADRATIC EQUATIONS Test-03

QUADRATIC EQUATIONS Test-03

This is QUADRATIC EQUATIONS Test-03 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
In a cricket matchKumble took three wickets less than twice the number of wickets taken by Srinath. The product of the number of wickets taken by these two is 20, then the number of wickets taken by Kumble is
  • A
    5
    Correct
  • B
    10
  • C
    4
  • D
    2
2
The angry Arjun carried some arrows for fighting with Bheeshma. With half the arrows, he cut down the arrows thrown by Bheeshma on him and with six other arrows he killed the rath driver of Bheeshma. With one arrow each he knocked down respectively the rath, flag and bow of Bheeshma. Finally with one more than four times the square root of arrows he laid Bheeshma unconscious on an arrow bed. The total number of arrows that Arjun had is
  • A
    100
    Correct
  • B
    96
  • C
    80
  • D
    120
3
The constant that must be added and subtracted to solve the quadratic equation \(9{x^2} + \frac{3}{4}x - \sqrt 2 = 0\) by the method of completing the square is
  • A
    \(\frac{9}{{64}}\)
  • B
    \(\frac{1}{4}\)
  • C
    \(\frac{1}{8}\)
  • D
    \(\frac{1}{{64}}\)
    Correct
4
If \(a{x^2} + bx + c = 0\) has equal roots, then c is equal to
  • A
    \(\frac{{ - {b^2}}}{{4a}}\)
  • B
    \(\frac{{{b^2}}}{{4a}}\)
    Correct
  • C
    \(\frac{{{b^2}}}{{2a}}\)
  • D
    \( - \frac{{{b^2}}}{{2a}}\)
5
Let b = a + c. Then the equation \(a{x^2} + bx + c = 0\) has equal roots if
  • A
    a = – c
  • B
    a = 2c
  • C
    a = – 2c
  • D
    a = c
    Correct
6
If α and β are the roots of \(a{x^2} + bx + c = 0\), then the wrong statement is
  • A
    \({\alpha ^2} + {\beta ^2} = \frac{{{b^2} - 2ac}}{{{a^2}}}\)
  • B
    \(\alpha + \beta = \frac{b}{a}\)
    Correct
  • C
    \(\alpha \beta = \frac{c}{a}\)
  • D
    \(\frac{1}{\alpha } + \frac{1}{\beta } = \frac{{ - b}}{c}\)
7
If \({x^2} + 5kx + 16 = 0\) has equal roots, then the value of ‘k’ is
  • A
    \( \pm \frac{5}{8}\)
  • B
    \( \pm \frac{{64}}{{25}}\)
  • C
    \( \pm \frac{8}{5}\)
    Correct
  • D
    \( \pm \frac{{25}}{{64}}\)
8
A quadratic equation \(a{x^2} + bx + c = 0\) has real and distinct roots, if
  • A
    none of these
  • B
    \({b^2} - 4ac = 0\)
  • C
    \({b^2} - 4ac > 0\)
    Correct
  • D
    \({b^2} - 4ac < 0\)
9
A quadratic equation \(a{x^2} + bx + c = 0\) has real and equal roots, if
  • A
    \({b^2} - 4ac > 0\)
  • B
    \({b^2} - 4ac = 0\)
    Correct
  • C
    none of these
  • D
    \({b^2} - 4ac < 0\)
10
A quadratic equation \(a{x^2} + bx + c = 0\) has non – real roots, if
  • A
    \({b^2} - 4ac = 0\)
  • B
    \({b^2} - 4ac > 0\)
  • C
    none of these
  • D
    \({b^2} - 4ac < 0\)
    Correct
11
_______ is called the Discriminant of the quadratic equation \(a{x^2} + bx + c = 0\).
  • A
    \({c^2} - 4ab\)
  • B
    none of these
  • C
    \({a^2} - 4bc\)
  • D
    \({b^2} - 4ac\)
    Correct
12
The roots of the quadratic equation \({x^2} - 11x - 10 = 0\) is
  • A
    not real roots
  • B
    real and equal
  • C
    real and distinct
    Correct
  • D
    none of these
13
The discriminant of 4x2 + 3x – 2 = 0 is
  • A
    39
  • B
    – 23
  • C
    – 31
  • D
    41
    Correct
14
A quadratic equation \(a{x^2} + bx + c = 0\) has coincident roots, if
  • A
    \({b^2} - 4ac < 0\)
  • B
    \({b^2} - 4ac = 0\)
    Correct
  • C
    \({b^2} - 4ac > 0\)
  • D
    none of these
15
The quadratic equation, sum of whose roots is \(3\sqrt 2 \) and their product is 5, is
  • A
    \({x^2} + 3\sqrt 2 x - 5 = 0\)
  • B
    \({x^2} - 3\sqrt 2 x - 5 = 0\)
  • C
    \({x^2} + 3\sqrt 2 x + 5 = 0\)
  • D
    \({x^2} - 3\sqrt 2 x + 5 = 0\)
    Correct