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 root of the polynomial equation 3x-1 = 0 is

1) x = 1
2) 13 ' title="x =

\frac{1}{3}

"/> x =

\frac{1}{3}

3) x = 3
4) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

( )

The zero of the polynomial 2x-5 is

1) 52 ' title=" -

\frac{5}{2}

"/> -

\frac{5}{2}

2) 25 ' title="

\frac{2}{5}

"/>

\frac{2}{5}

3) 25 ' title="-

\frac{2}{5}

"/> -

\frac{2}{5}

4) 52 ' title="

\frac{5}{2}

"/>

\frac{5}{2}

( )

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

1) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)
2) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

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

\frac{a}{b}

) "/> p(-

\frac{a}{b}

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

\frac{b}{a}

) "/> p(-

\frac{b}{a}

)

( )

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) 0
2) 2
3) 3
4) 1

( )

.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

( )

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(b)=0
3) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
4) p(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) 2
3) 3
4) 1

( )

The polynomial 4x²+2x-2 is a

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

( )

10)

One of the factors of x²- 3x -10 is

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

( )

The root of the polynomial equation 3x-1 = 0 is

1) x = 1
2) 13 ' title="x =

\frac{1}{3}

"/> x =

\frac{1}{3}

3) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

4) x = 3

Answer: 2

SOLUTION 1 :

Hint: [3x -1 = 0 ⇒ 3x = 1 ⇒ x = $\frac{1}{3}$ ]

Ans = x = $\frac{1}{3}$

The zero of the polynomial 2x-5 is

1) 25 ' title="-

\frac{2}{5}

"/> -

\frac{2}{5}

2) 25 ' title="

\frac{2}{5}

"/>

\frac{2}{5}

3) 52 ' title="

\frac{5}{2}

"/>

\frac{5}{2}

4) 52 ' title=" -

\frac{5}{2}

"/> -

\frac{5}{2}

Answer: 3

SOLUTION 1 :

Hint: [ p(x) = 2x -5=2 ( $\frac{x-5}{2)}$ $\frac{p(5}{2)}$ = $\frac{2(5}{2-5}$ /2)=0. Hence x= $\frac{5}{2is}$ zero of p(x)

Ans = $\frac{5}{2}$

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

1) ba) ' title="p(-

\frac{b}{a}

) "/> p(-

\frac{b}{a}

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

\frac{a}{b}

) "/> p(-

\frac{a}{b}

)
3) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)
4) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

)

Answer: 1

SOLUTION 1 :

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

One of the factors of x³-2x²+2x -1 is

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

Answer: 1

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) 2
3) 3
4) 0

Answer: 3

SOLUTION 1 :

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

Ans =3

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

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

Answer: 4

SOLUTION 1 :

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

Ans = -3,-2

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) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
4) p(b)=0

Answer: 3

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) 4
2) 2
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

The polynomial 4x²+2x-2 is a

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

Answer: 4

SOLUTION 1 :

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

Ans = quadratic polynomial

10)

One of the factors of x²- 3x -10 is

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

Answer: 3

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

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