Sasi Math (Revised for 1024)

Scroll:Algebra >> Multiple Choice Questions: >> mcq (4180)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

The roots of the polynomial equation x² +2x = 0 are

1) X = 0,2
2) x = 1,2
3) x =0,-2
4) x = 1,-2

( )

The polynomial 3x-2 is a

1) linear polynomial
2) quadratic polynomial
3) cubic polynomial
4) constant polynomial

( )

If a polynomial p(x) is divided by (ax+b), then the remainder is

1) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

)
2) ba) ' title="p(-

\frac{b}{a}

) "/> p(-

\frac{b}{a}

)
3) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)
4) ab) ' title="p(-

\frac{a}{b}

) "/> p(-

\frac{a}{b}

)

( )

The polynomial 4x²+2x-2 is a

1) linear polynomial
2) quadratic polynomial
3) constant polynomial
4) cubic polynomial

( )

One of the factors of x²- 3x -10 is

1) x-5
2) x+2
3) x-2
4) x-3

( )

One of the factors of x³-2x²+2x -1 is

1) x+1
2) x-1
3) x+2
4) x-2

( )

The degree of the polynomial 4x²-7x³+ 6x + 1 is

1) 2
2) 0
3) 3
4) 1

( )

If ( ax- b) is a factor of p(x), then

1) p(a)=0
2) p(b)=0
3) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
4) ba)=0 ' title="p(-

\frac{b}{a}

)=0 "/> p(-

\frac{b}{a}

)=0

( )

If the polynomial x³ –ax²+2x-a is divided (x-a), then remainder is

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

1) 4
2) 1
3) 3
4) 2

( )

10)

.The coefficients of x² and x in 2x³ -3x²- 2x + 3 are respectively

1) -2,-3
2) -3,-2
3) 2,-3
4) -2,3

( )

The roots of the polynomial equation x² +2x = 0 are

1) X = 0,2
2) x =0,-2
3) x = 1,2
4) x = 1,-2

Answer: 2

SOLUTION 1 :

Hint: [ [x² +2x = 0 ⇒ x(x+2)=0 ⇒ x = 0 (or) x + 2 = 0 ⇒ x=0 (or) x = -2 ⇒ x = 0,-2]

Ans = x = 0, -2

The polynomial 3x-2 is a

1) constant polynomial
2) cubic polynomial
3) quadratic polynomial
4) linear polynomial

Answer: 4

SOLUTION 1 :

Hint: [ The degree of 3x-2 is 1, It is a linear polynomial]

Ans = linear polynomial

If a polynomial p(x) is divided by (ax+b), then the remainder is

1) ab) ' title="p(-

\frac{a}{b}

) "/> p(-

\frac{a}{b}

)
2) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)
3) ba) ' title="p(-

\frac{b}{a}

) "/> p(-

\frac{b}{a}

)
4) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

)

Answer: 3

SOLUTION 1 :

Ans = $\frac{p(-b}{a)}$

The polynomial 4x²+2x-2 is a

1) linear polynomial
2) quadratic polynomial
3) constant polynomial
4) cubic polynomial

Answer: 2

SOLUTION 1 :

Hint: [ The degree of 4x²+2x-2 is 2, It is a quadratic polynomial]

Ans = quadratic polynomial

One of the factors of x²- 3x -10 is

1) x-3
2) x-2
3) x+2
4) x-5

Answer: 4

SOLUTION 1 :

Hint : [ x²- 3x -10 = x²-5x + 2x -10 ⇒ x(x-5) + 2(x-5)

The factor of x²-3x -10 are (x-5) and (x+2) ]

Ans = x - 5

One of the factors of x³-2x²+2x -1 is

1) x+2
2) x-1
3) x+1
4) x-2

Answer: 2

SOLUTION 1 :

Hint:[ (x³-2x²+ 2x -1 = x³-x²-x² + x + x -1 = x²(x-1) – x(x-1) + 1(x-1) = (x-1) (x²-x + 1) ]

Ans = x - 1

The degree of the polynomial 4x²-7x³+ 6x + 1 is

1) 1
2) 3
3) 2
4) 0

Answer: 2

SOLUTION 1 :

Hint: [The term having the highest degree is -7x³, The degree is 3]

Ans =3

If ( ax- b) is a factor of p(x), then

1) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
2) p(a)=0
3) p(b)=0
4) ba)=0 ' title="p(-

\frac{b}{a}

)=0 "/> p(-

\frac{b}{a}

)=0

Answer: 1

SOLUTION 1 :

Hint: [ ax-b is a factor of p(x) ⇒ The zero of ax-b is $\frac{(b}{a)}$ ⇒ p $\frac{(b}{a)}$ =0]

Ans = p $\frac{(b}{a)}$ =0

If the polynomial x³ –ax²+2x-a is divided (x-a), then remainder is

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

1) 2
2) 4
3) 3
4) 1

Answer: 4

SOLUTION 1 :

Hint:[ [ p(x) = x³ – ax²+ 2x- a ⇒ The zero of x - a is a

p(a) = a³-a(a)²+2(a)-a ⇒ a³ - a³ + 2a - a = 2 ]

Ans = a

10)

.The coefficients of x² and x in 2x³ -3x²- 2x + 3 are respectively

1) -2,-3
2) 2,-3
3) -3,-2
4) -2,3

Answer: 3

SOLUTION 1 :

Hint:[The co-efficient of x² is- 3 and The co-efficient of x is -2]

Ans = -3,-2

Scroll:Algebra >> Multiple Choice Questions: >> mcq (4180)

One of the factors of x3 -2x2 +2x -1 is

One of the factors of x3 -2x2 +2x -1 is

One of the factors of x³-2x²+2x -1 is

One of the factors of x³-2x²+2x -1 is