Polynomials CBSE Questions & Answers

Polynomials

This is Mathematics Class 09 Polynomials CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(x + {1 \over x} = 7\) , then the value of \({x^3} + {1 \over {{x^3}}}\) is
  • A
    231
  • B
    320
  • C
    322
    Correct
  • D
    233
2
The value of \({{0.75 \times 0.75 \times 0.75 + 0.25 \times 0.25 \times 0.25} \over {0.75 \times 0.75 - 0.75 \times 0.25 + 0.25 \times 0.25}}\) is
  • A
    1
    Correct
  • B
    2
  • C
    -1
  • D
    0
3
If \({p^2} + 4{q^2} + 9{r^2} = 2pq + 6qr + 3pr\) , then the value of \({p^3} + 8{q^3} + 27{r^3}\) is
  • A
    9pqr
  • B
    12pqr
  • C
    10pqr
  • D
    18pqr
    Correct
4
The value of \({x^3} + {y^3} + 15xy - 125\) when \(x + y = 5\) is
  • A
    0
    Correct
  • B
    1
  • C
    2
  • D
    3
5
The value of \({({a^2} - {b^2})^3} + {({b^2} - {c^2})^3} + {({c^2} - {a^2})^3}\) is
  • A
    none of these
  • B
    \(3(a - b)(b - c)(c - a)\)
  • C
    \(3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)\)
    Correct
  • D
    \(3(a + b)(b + c)(c + a)\)
6
The value of \({{{{({a^2} - {b^2})}^3} + {{({b^2} - {c^2})}^3} + {{({c^2} - {a^2})}^3}} \over {{{(a - b)}^3} + {{(b - c)}^3} + {{(c - a)}^3}}}\) is
  • A
    \(3(a + b)(b + c)(c + a)\)
    Correct
  • B
    none of these
  • C
    \(3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)\)
  • D
    \(3(a - b)(b - c)(c - a)\)
7
If = \({x^3} - 23{x^2} + kx - 120\) , then the value of ‘k’ is
  • A
    120
  • B
    140
  • C
    124
  • D
    142
    Correct
8
If \({a^2} + {b^2} + {c^2} = 30\) and\(a + b + c = 10\), then the value of \(ab + bc + ca\) is
  • A
    35
    Correct
  • B
    25
  • C
    40
  • D
    30
9
If \(f(x) = {x^2} - 5x + 1\) , then the value of f(2) + f(-1) is
  • A
    -1
  • B
    2
    Correct
  • C
    -2
  • D
    1
10
The value of \(\left( {\sqrt x + \sqrt y } \right)\left( {\sqrt x - \sqrt y } \right)\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)\) is
  • A
    \(({x^4} - {y^4})\)
    Correct
  • B
    \({(x - y)^4}\)
  • C
    \({(x + y)^4}\)
  • D
    \(({x^4} + {y^4})\)
11
If \({x^2} + 3mx + 6\) , then the value of ‘m’ is
  • A
    1
  • B
    0
  • C
    3
  • D
    \(\sqrt 3 \)
    Correct
12
The degree of the polynomial \(({x^3} - 2)({x^2} - 11)\) is
  • A
    2
  • B
    3
  • C
    0
  • D
    5
    Correct
13
The possible expressions for the length and breadth of the rectangle whose area is given by \(4{a^2} + 4a - 3\) is
  • A
    none of these
  • B
    (2a – 1) and (2a + 3)
    Correct
  • C
    (2a – 1) and (2a – 3)
  • D
    (2a + 1) and (2a + 3)
14
The possible expressions for the length, breadth and height of the cuboid whose volume is given by \(3{x^3} - 12x\) is
  • A
    x, (x + 2) and (3x – 2)
  • B
    3x, (x + 2) and (x – 2)
    Correct
  • C
    none of these
  • D
    x, (3x + 2) and (x – 2)
15
If p(x) = (x – 1)(x + 1), then the value of p(2) + p(1) – p(0) is
  • A
    3
  • B
    1
  • C
    2
  • D
    4
    Correct