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.

One of the factors of x³-2x²+2x -1 is

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

( )

One of the factors of x²- 3x -10 is

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

( )

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

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

( )

The zero of the polynomial 2x-5 is

1) 25 ' title="-

\frac{2}{5}

"/> -

\frac{2}{5}

2) 52 ' title="

\frac{5}{2}

"/>

\frac{5}{2}

3) 52 ' title=" -

\frac{5}{2}

"/> -

\frac{5}{2}

4) 25 ' title="

\frac{2}{5}

"/>

\frac{2}{5}

( )

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

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

\frac{b}{a}

)=0 "/> p(-

\frac{b}{a}

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

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
4) p(b)=0

( )

The polynomial 3x-2 is a

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

( )

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

( )

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}

)

( )

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

( )

10)

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) 1
4) 3

( )

One of the factors of x³-2x²+2x -1 is

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

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

One of the factors of x²- 3x -10 is

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

Answer: 2

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

.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

The zero of the polynomial 2x-5 is

1) 25 ' title="

\frac{2}{5}

"/>

\frac{2}{5}

2) 52 ' title="

\frac{5}{2}

"/>

\frac{5}{2}

3) 52 ' title=" -

\frac{5}{2}

"/> -

\frac{5}{2}

4) 25 ' title="-

\frac{2}{5}

"/> -

\frac{2}{5}

Answer: 2

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

1) p(b)=0
2) p(a)=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

Answer: 4

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

The polynomial 3x-2 is a

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

Answer: 2

SOLUTION 1 :

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

Ans = linear polynomial

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

Answer: 3

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

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

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

1) x = 1
2) x = 3
3) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

4) 13 ' title="x =

\frac{1}{3}

"/> x =

\frac{1}{3}

Answer: 4

SOLUTION 1 :

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

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

10)

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

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

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

Answer: 2

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

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