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 polynomial 4x²+2x-2 is a

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

( )

.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

( )

One of the factors of x²- 3x -10 is

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

( )

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

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

( )

The zero of the polynomial 2x-5 is

1) 52 ' title="

\frac{5}{2}

"/>

\frac{5}{2}

2) 52 ' title=" -

\frac{5}{2}

"/> -

\frac{5}{2}

3) 25 ' title="-

\frac{2}{5}

"/> -

\frac{2}{5}

4) 25 ' title="

\frac{2}{5}

"/>

\frac{2}{5}

( )

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

1) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

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

\frac{1}{3}

"/> x =

\frac{1}{3}

4) x = 1

( )

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

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

( )

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

( )

The polynomial 3x-2 is a

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

( )

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) 3
4) 1

( )

The polynomial 4x²+2x-2 is a

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

Answer: 1

SOLUTION 1 :

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

Ans = quadratic polynomial

.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

One of the factors of x²- 3x -10 is

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

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 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 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: 4

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 = $\frac{5}{2}$

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

1) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

2) x = 3
3) x = 1
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 = $\frac{1}{3}$

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

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

Answer: 1

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) 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

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

The polynomial 3x-2 is a

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

Answer: 1

SOLUTION 1 :

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

Ans = linear polynomial

10)

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

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

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

Answer: 1

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