QUADRATIC EQUATIONS Test-05

QUADRATIC EQUATIONS Test-05

This is QUADRATIC EQUATIONS Test-05 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If the sum and product of the roots of the equation \(k{x^2} + 6x + 4k = 0\) are equal, then k =
  • A
    \(\frac{{ - 3}}{2}\)
    Correct
  • B
    \(\frac{{ - 2}}{3}\)
  • C
    \(\frac{3}{2}\)
  • D
    \(\frac{2}{3}\)
2
If ‘sin α’ and ‘cos α’ are the roots of the equation \(a{x^2} + bx + c = 0\), then \({b^2} = \)
  • A
    \({a^2} - ac\)
  • B
    \({a^2} + ac\)
  • C
    \({a^2} - 2ac\)
  • D
    \({a^2} + 2ac\)
    Correct
3
If ‘a’ and ‘b’ are the roots of the equation \({x^2} + ax + b = 0\), then \(a + b = \)
  • A
    – 2
  • B
    – \(a\)
    Correct
  • C
    \(a\)
  • D
    2
4
If one root of the equation \(a{x^2} + bx + c = 0\) is three times the other, then \({b^2}:ac = \)
  • A
    3 : 16
  • B
    16 : 3
    Correct
  • C
    3 : 1
  • D
    16 : 1
5
If one root of the equation \(4{x^2} - 2x + (\lambda - 4) = 0\) be the reciprocal of the other, then the value of is
  • A
    4
  • B
    – 8
  • C
    8
    Correct
  • D
    – 4
6
A quadratic equation whose one root is 3 and the sum of the roots is zero is
  • A
    \(9{x^2} + 1 = 0\)
  • B
    \(9{x^2} - 1 = 0\)
  • C
    \({x^2} + 9 = 0\)
  • D
    \({x^2} - 9 = 0\)
    Correct
7
If the sum of the roots of \({x^2} - (k + 6)x + 2(2k - 1) = 0\) is equal to half of their product, then k =
  • A
    7
    Correct
  • B
    6
  • C
    5
  • D
    1
8
If the quadratic equation \(b{x^2} - 2\sqrt {ac} x + b = 0\) has equal roots, then
  • A
    \({b^2} = ac\)
    Correct
  • B
    \(2{b^2} = ac\)
  • C
    \({b^2} = - ac\)
  • D
    \({b^2} = 2ac\)
9
If \(\alpha \;and\;\;\beta\) are the roots of \({x^2} - p(x + 1) - c = 0\), then \(\left( {\alpha + 1} \right)\left( {\beta + 1} \right)\) =
  • A
    c – 1
  • B
    c
  • C
    1 + c
  • D
    1 – c
    Correct
10
If \(\alpha \) and \(\beta \) are the roots of \(2{x^2} - 3x - 1 = 0\), then the value of \({\alpha ^2} + {\beta ^2}\) is
  • A
    \(\frac{{13}}{2}\)
  • B
    \(\frac{{ - 13}}{2}\)
  • C
    \(\frac{{ - 13}}{4}\)
  • D
    \(\frac{{13}}{4}\)
    Correct
11
\({\left( {x + 2} \right)^3} = 2x({x^2} - 1)\) is a
  • A
    quadratic equation
  • B
    bi – quadratic equation
  • C
    linear equation
  • D
    cubic equation
    Correct
12
The roots of the quadratic equation \(4{x^2} - 4{a^2}x + {a^4} - {b^4} = 0\) are
  • A
    \(\frac{{{a^2} - {b^2}}}{3}{\text{ }}and{\text{ }}\frac{{{a^2} + {b^2}}}{3}\)
  • B
    \(\frac{{{a^2} + {b^2}}}{2}{\text{ }}and{\text{ }}\frac{{{a^2} + {b^2}}}{2}\)
  • C
    \(\frac{{{a^2} - {b^2}}}{2}{\text{ }}and{\text{ }}\frac{{{a^2} - {b^2}}}{2}\)
  • D
    \(\frac{{{a^2} - {b^2}}}{2}{\text{ }}and{\text{ }}\frac{{{a^2} + {b^2}}}{2}\)
    Correct
13
If y = 1 is the common root of \(l{y^2} + ly + 3 = 0\)and \({y^2} + y + m = 0\), then the value of ‘\(lm\)’ is
  • A
    4
  • B
    3
    Correct
  • C
    – 3
  • D
    – 4
14
The roots of \(9{x^2} - 9(a + b)x + (2{a^2} + 5ab + 2{b^2}) = 0\) are
  • A
    \(\frac{{2a + b}}{2}{\text{ }}and{\text{ }}\frac{{a + 2b}}{2}\)
  • B
    \(\frac{{2a + 3b}}{3}{\text{ }}and{\text{ }}\frac{{3a + 2b}}{3}\)
  • C
    \(\frac{{2a - b}}{3}{\text{ }}and{\text{ }}\frac{{a - 2b}}{3}\)
  • D
    \(\frac{{2a + b}}{3}{\text{ }}and{\text{ }}\frac{{a + 2b}}{3}\)
    Correct
15
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Then the number of camels is
  • A
    48
  • B
    30
  • C
    60
  • D
    36
    Correct