CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Polynomials
Question 1
1.
Which of the following are not polynomials?
a)
    • (
      8
      x
      −
      7
      y
      		)
b)
    • √x
c)
    • 81
      x
      2
       
      +
      1
      81
      x
      2
       
d)
    • (
      3
      x
      +
      10
      y
      		)
e)
    • 81
      x
      2
       
  • {e,a,b}
  • {d,c}
  • {a,b}
  • {d,c,b}
  • {b,c}
Question 2
2.
    • The remainder when
    • (
      4
      g
      2
       
      +
      6
      g
      		)
    • is divided by
    • (
      g
      +
      3
      		)
    • is
  • 18
  • 19
  • 21
  • 17
  • 16
Question 3
3.
    • In which of the cases,
    •  
    • g
      (
      x
      )
    •  
    • is a factor of
    •  
    • f
      (
      x
      )
    • ?
  • f
    (
    x
    )
    =
    (
    9
    x
    3
     
    −
    51
    x
    2
     
    −
    38
    x
    +
    120
    		)
    ,
    g
    (
    x
    )
    =
    (
    x
    +
    2
    		)
  • f
    (
    x
    )
    =
    (
    −
    6
    x
    3
     
    +
    5
    x
    2
     
    +
    151
    x
    +
    210
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    3
    x
    +
    4
    		)
  • f
    (
    x
    )
    =
    (
    x
    3
     
    −
    8
    x
    2
     
    +
    4
    x
    +
    48
    		)
    ,
    g
    (
    x
    )
    =
    (
    3
    x
    +
    5
    		)
  • f
    (
    x
    )
    =
    (
    3
    x
    3
     
    −
    10
    x
    2
     
    −
    16
    x
    +
    32
    		)
    ,
    g
    (
    x
    )
    =
    (
    −
    x
    +
    4
    		)
  • f
    (
    x
    )
    =
    (
    −
    3
    x
    3
     
    +
    7
    x
    2
     
    +
    56
    x
    +
    60
    		)
    ,
    g
    (
    x
    )
    =
    (
    2
    x
    +
    7
    		)
Question 4
4.
Which of the following are polynomials?
a)
    • (
      x
      +
      y
      		)
      (
      x
      −
      y
      		)
b)
    • x
      2
       
      +
      1
      x
      2
       
c)
    • x
      2
       
d)
    • x
      +
      1
      x
e)
    • (
      x
      +
      y
      		)
  • {b,e}
  • {b,e,c}
  • {d,a,c}
  • {c,e}
  • {a,c}
Question 5
5.
    • Factorize and divide
    • (
      −
      4
      x
      4
       
      −
      31
      x
      3
       
      −
      47
      x
      2
       
      +
      55
      x
      +
      75
      		)
    • ÷
    • (
      −
      x
      2
       
      −
      6
      x
      −
      5
      		)
  • (
    4
    x
    2
     
    +
    17
    x
    +
    15
    		)
  • (
    −
    x
    2
     
    −
    4
    x
    −
    3
    		)
  • (
    4
    x
    2
     
    −
    7
    x
    −
    15
    		)
  • (
    4
    x
    2
     
    −
    17
    x
    +
    15
    		)
  • (
    4
    x
    2
     
    +
    7
    x
    −
    15
    		)
Question 6
6.
    • The remainder when
    • (
      −
      a
      3
       
      −
      a
      −
      2
      		)
    • is divided by
    • (
      a
      2
       
      −
      3
      a
      −
      18
      		)
    • is
  • (
    −
    29
    a
    −
    56
    		)
  • (
    −
    27
    a
    −
    56
    		)
  • (
    −
    28
    a
    −
    56
    		)
  • (
    −
    31
    a
    −
    56
    		)
  • (
    −
    25
    a
    −
    56
    		)
Question 7
7.
    • Find the quadratic equation, the sum of whose roots is
    • 2
    • and product is
    • 1
  • (
    x
    2
     
    −
    5
    x
    +
    1
    		)
    =
    0
  • (
    2
    x
    2
     
    −
    2
    x
    +
    1
    		)
    =
    0
  • (
    x
    2
     
    −
    2
    x
    +
    1
    		)
    =
    0
  • (
    x
    2
     
    +
    1
    		)
    =
    0
  • (
    −
    2
    x
    +
    1
    		)
    =
    0
Question 8
8.
    • Given
    • f
      (
      i
      )
    • =
    • (
      −
      2
      i
      4
       
      −
      i
      3
       
      +
      7
      i
      2
       
      +
      i
      −
      6
      		)
    • ,
    • find
    •  
    • f
      (
      0
      )
  • -7
  • -4
  • -5
  • -6
  • -8
Question 9
9.
    • Find the roots of the quadratic equation
    • (
      32
      x
      2
       
      +
      8
      x
      		)
      =
      0
  • (
    1
    ,
    (
    -1
    2
    		 )
    )
  • (
    0
    ,
    (
    -1
    4
    		 )
    )
  • (
    2
    ,
    (
    -3
    4
    		 )
    )
  • (
    1
    ,
    (
    -1
    4
    		 )
    )
  • (
    2
    ,
    (
    -1
    2
    		 )
    )
Question 10
10.
Which of the following algebraic expressions is a linear polynomial?
  • 4
  • (
    −
    3
    p
    3
     
    −
    6
    p
    2
     
    +
    6
    p
    −
    1
    		)
  • (
    −
    8
    p
    2
     
    +
    5
    p
    −
    1
    		)
  • (
    9
    p
    −
    2
    		)
  • (
    4
    p
    5
     
    +
    7
    p
    4
     
    −
    6
    p
    3
     
    −
    7
    p
    2
     
    +
    3
    		)