QUADRATIC EQUATIONS Test

QUADRATIC EQUATIONS

This is QUADRATIC EQUATIONS Test-01 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A quadratic equation whose one root is 3 is
  • A
    \({x^2} + 6x - 5 = 0\)
  • B
    \({x^2} - 6x - 5 = 0\)
  • C
    \({x^2} - 5x - 6 = 0\)
  • D
    \({x^2} - 5x + 6 = 0\)
    Correct
2
One of the roots of the quadratic equation \({a^2}{x^2} - 3abx + 2{b^2} = 0\) is
  • A
    \(\frac{{2a}}{b}\)
  • B
    \(\frac{{ - 2a}}{b}\)
  • C
    \(\frac{{2b}}{a}\)
    Correct
  • D
    \(\frac{{ - 2b}}{a}\)
3
The quadratic equation whose roots are \(7 + \sqrt 3 \) and \(7 - \sqrt 3 \) is
  • A
    \({x^2} - 14x - 46 = 0\)
  • B
    \({x^2} - 14x + 46 = 0\)
    Correct
  • C
    \({x^2} + 14x - 46 = 0\)
  • D
    \({x^2} + 14x + 46 = 0\)
4
If x = 2 is a root of the quadratic equation 3x2 – px – 2 = 0, then the value of ‘p’ is
  • A
    3
  • B
    0
  • C
    1
  • D
    5
    Correct
5
\(5{x^2} + 8x + 4 = 2{x^2} + 4x + 6\) is a
  • A
    linear equation
  • B
    constant
  • C
    quadratic equation
    Correct
  • D
    cubic equation
6
The product of two consecutive integers is 240. The quadratic representation of the above situation is
  • A
    \(x(x + 1) = 240\)
    Correct
  • B
    \(5{x^2} + 8x + 4 = 2{x^2} + 4x + 6\)
  • C
    \({x^2} + (x + 1) = 240\)
  • D
    \(x{(x + 1)^2} = 240\)
7
The sum of two numbers is 17 and the sum of their reciprocals is \(\frac{{17}}{{62}}\). The quadratic representation of the above situation is
  • A
    \(\frac{1}{x} - \frac{1}{{17 - x}} = \frac{{17}}{{62}}\)
  • B
    \(\frac{1}{x} + \frac{1}{{x + 17}} = \frac{{17}}{{62}}\)
  • C
    \(\frac{1}{x} + \frac{1}{{17 - x}} = \frac{{17}}{{62}}\)
    Correct
  • D
    \(\frac{1}{{x(17 - x)}} = \frac{{17}}{{62}}\)
8
Which of the following is a quadratic equation?
  • A
    \((k + 1){x^2} + \frac{3}{2}x - 5 = 0\), where k = – 1
  • B
    \({x^3} - {x^2} = {(x - 1)^3}\)
    Correct
  • C
    \( - 2{x^2} = (5 - x)\left( {2x - \frac{2}{5}} \right)\)
  • D
    \({x^2} + 2x + 1 = {(4 - x)^2} + 3\)
9
Which of the following is not a quadratic equation?
  • A
    \(2{(x - 1)^2} = 4{x^2} - 2x + 1\)
  • B
    \({\left( {\sqrt 2 x + \sqrt 3 } \right)^2} + {x^2} = 3{x^2} - 5x\)
    Correct
  • C
    \({({x^2} + 2x)^2} = {x^4} + 3 + 4{x^3}\)
  • D
    \(2x - {x^2} = {x^2} + 5\)
10
If p = – 7 and q = 12 and \({x^2} + px + q = 0\), then the value of ‘x’ is
  • A
    – 3 and 4
  • B
    3 and – 4
  • C
    – 3 and – 4
  • D
    3 and 4
    Correct
11
The hypotenuse of a right triangle is 6m more than twice the shortest side. The third side is 2m less than the hypotenuse. The representation of the above situation in the form of a quadratic equation is
  • A
    none of these
  • B
    \({(2x + 6)^2} = {x^2} - {(2x + 4)^2}\)
  • C
    \({(2x + 6)^2} + {x^2} = {(2x + 4)^2}\)
  • D
    \({(2x + 6)^2} = {x^2} + {(2x + 4)^2}\)
    Correct
12
The roots of a quadratic equation \({x^2} - 4px + 4{p^2} - {q^2} = 0\) are
  • A
    2p – q, 2p – q
  • B
    2p + q, 2p – q
    Correct
  • C
    2p + q, 2p + q
  • D
    p + 2q, p – 2q
13
The two numbers whose sum is 27 and their product is 182 are
  • A
    12 and 13
  • B
    14 and 15
  • C
    12 and 15
  • D
    13 and 14
    Correct
14
If the sum of a number and its reciprocal is \({\text{2}}\frac{{\text{1}}}{{\text{2}}}\), then the numbers are
  • A
    \({\text{3 and }}\frac{{\text{1}}}{{\text{3}}}{\text{ }}\)
  • B
    none of these
  • C
    \({\text{2 and }}\frac{{\text{1}}}{{\text{2}}}{\text{ }}\)
    Correct
  • D
    \({\text{1 and }}\frac{{\text{3}}}{{\text{2}}}{\text{ }}\)
15
The common root of \(2{x^2} + x - 6 = 0\) and \({x^2} - 3x - 10 = 0\) is
  • A
    \(\frac{3}{2}\)
  • B
    – 2
    Correct
  • C
    2
  • D
    5