MCQ(1M)

MCQ 11 Mark

If $p(x)=5 x-4 x^2+3$ then $p(-1)=$ ?

A
$2$
B
$-2$
C
$6$
✓
$-6$

Answer

Correct option: D.

$-6$

$P(x)=5 x-4 x^2+3$
$\Rightarrow p(-1)=5(-1)-4(-1)^2+3$
$=-5-4+3$
$=-6$

View full question & answer→

MCQ 21 Mark

Which of the following is a linear polynomial?

A
$x + x2$
✓
$x + 1$
C
$5x^2 - x + 3$
D
$\text{x}+\frac{1}{\text{x}}$

Answer

Correct option: B.

$x + 1$

A polynomial of degree $1$ is called a linear polynomial.
Options $(a),$ and $(c)$ have degree $2$,
so ther are quadratic polynomials.
option $(d)$ has a negative power,
so it is not a polynomial.
The degree of $x + 1$ is $1$,
so it is a linear polynomial.

View full question & answer→

MCQ 31 Mark

The zeros of the polynomial $p(x)=x^2-3 x$ are:

A
$0, 0$
✓
$0, 3$
C
$0, -3$
D
$3, -3$

Answer

Correct option: B.

$0, 3$

Let $p(x)$ be a polynomial. If $\text{p}(\alpha)=0,$ then we say that $\alpha$ is a zero of a polynomial.
$p(x)$ = $x^2 - 3x$
Now, $p(x) = 0$
$\Rightarrow x^2 - 3x$
$\Rightarrow x(x - 3) = 0$
$\Rightarrow x = 0$ or $(x - 3) = 0$
$\Rightarrow x = 0$ or $x = 3$
$\therefore$ $0$ and $3$ are the zeroes of the polynomial $p(x).$

View full question & answer→

MCQ 41 Mark

When $p(x)=x^3-a x^2+x$ is divided by $(x-a)$, the remainder is:

A
$0$
✓
$a$
C
$2a$
D
$3 a$

Answer

Correct option: B.

$a$

$p(x)=x^3-a x^2+x$
$x-a=0 \Rightarrow x=a$
By the remainder theorem,
we know that when $p(x)$ is divided by $( x - a ),$ the remainder is $p(a)$.
Now, $p(a)=a^3-a x^2+a$
$=a^3-a^3+a$
$=a$

View full question & answer→

MCQ 51 Mark

Where $p(x)=x^4+2 x^3-3 x^2-1$ is divided by $(x-2)$, the remainder is:

A
$0$
B
$-1$
C
$-15$
✓
$21$

Answer

Correct option: D.

$21$

$p(x)=x^4+2 x^3-3 x^2+x-1$
$x-2=0 \Rightarrow x=2$
By the remainder theorem,
we know that when $p(x)$ is divided by $(x-2)$, the remainder is $p(2)$.
Now, $p(2)=x^4+2 x^3-3 x^2+x-1$
$=(2)^4+2(2)^3-3(2)^2+2-1$
$=16+16-12+2-1$
$=21$

View full question & answer→

MCQ 61 Mark

When $p(x) = 4x^3 - 12x^2 + 11x - 5$ is divided by $(2x - 1)$, the remainder is:

A
$0$
B
$-5$
✓
$-2$
D
$2$

Answer

Correct option: C.

$-2$

$\text{p}(\text{x}) = 4\text{x}^3 - 12\text{x}^2 + 11\text{x} - 5$
$\text{x}-1=0\Rightarrow\text{x}=\frac{1}{2}$
By the remainder theorem, we know that when $p(x)$ is divided by $(2x - 1),$ the remainder is $\text{p}\Big(\frac{1}{2}\Big).$
Now, $\text{p}\Big(\frac{1}{2}\Big)= 4\text{x}^3 - 12\text{x}^2 + 11\text{x} - 5$
$=4\Big(\frac{1}{2}\Big)^3-12\Big(\frac{1}{2}\Big)^2+11\Big(\frac{1}{2}\Big)-5$
$=\frac{1}{2}-3+\frac{11}{2}-5$
$=-2$

View full question & answer→

MCQ 71 Mark

The zeros of the polynomial $p(x) = 2x^2 + 7x - 4$ are:

A
$4,\frac{-1}{2}$
B
$4,\frac{1}{2}$
✓
$-4,\frac{1}{2}$
D
$-4,\frac{-1}{2}$

Answer

Correct option: C.

$-4,\frac{1}{2}$

$p(x)=2 x^2+7 x-4$
Now, $p ( x )=0$
$\Rightarrow 2 x^2+7 x-4=0$
$\Rightarrow 2 x^2+8 x-x-4=0$
$\Rightarrow 2 x(x+4)-1(x+4)=0$
$\Rightarrow(x+4)(2 x-1)=0$
$\Rightarrow x+4=0 \text { and } 2 x-1=0$
$\Rightarrow x=-4 \text { and } x=\frac{1}{2}$

View full question & answer→

MCQ 81 Mark

For what value of $k$ is the polynomial $p(x)=2 x^3-k x^2+3 x+10$ exactly divisible by $(x+2) ?$

A
$-\frac{1}{3}$
B
$\frac{1}{3}$
C
$3$
✓
$-3$

Answer

Correct option: D.

$-3$

$p ( x )=2 x ^3-k x ^2+3 x +10$
$x+2=0 \Rightarrow x=-2$
By the factor theorem, we know that when $p(x)$ is divided by $(x+2)$, the remainder is $p(-2)$.
Now, $p (-2)=2(-2)^3+ k (-2)^2+3(-2)+10$
$\Rightarrow 0=-16-4 k -6+10$
$\Rightarrow 0=-12-4 k$
$\Rightarrow 4 k =-12$
$\Rightarrow k=-3$

View full question & answer→

MCQ 91 Mark

If $(x+2)$ and $(x-1)$ are factors of the polynomial $p(x)=x^3+10x^2+m x+n$ then:

A
$m = 5, n = -3$
✓
$m = 7, n = -18$
C
$m = 17, n = -8$
D
$m = 23, n = -19$

Answer

Correct option: B.

$m = 7, n = -18$

Let $f(x)=x^3+10 x^2+m x+n$
Now, $x+2=0 \Rightarrow x=-2$ and $x-1=0 \Rightarrow x=1$
By factor theorem,
$f(-2)=0$
$\Rightarrow(-2)^3+10(-2)^2+m(-2)+n$
$\Rightarrow-8+40-2 m+n=0$
$\Rightarrow 2 m-n=32 \ldots \text { (i) }$
By factor theorem,
$f(1)=0$
$\Rightarrow(1)^3+10(1)^2+m(1)+n=0$
$\Rightarrow m+n=-11 \ldots \text { (ii) }$
Adding $(i)$ and $(ii)$, we get
$3 m=21$
$\Rightarrow m=7$
Substituting in $(ii)$, we get
$n=-18$

View full question & answer→

MCQ 101 Mark

Which of the following expression is a polynomial in one variable?

A
$\text{x}+\frac{2}{\text{x}}+3$
B
$3\sqrt{\text{x}}+\frac{2}{\sqrt{\text{x}}}+5$
✓
$\sqrt2\text{x}^2-\sqrt3\text{x}+6$
D
$\text{x}^{10}+\text{y}^5+8$

Answer

Correct option: C.

$\sqrt2\text{x}^2-\sqrt3\text{x}+6$

Clearly, $\sqrt2\text{x}^2-\sqrt3\text{x}+6$ is a polynomial in one variable because it has only non $-$ negative integral powers of $x$ .

View full question & answer→

MCQ 111 Mark

$\sqrt3$ is a polynomial of degree:

A
$\frac{1}{2}$
B
$2$
C
$1$
✓
$0$

Answer

Correct option: D.

$0$

The degree of a constant polynomial is $0$.
So, $\sqrt3$ is a polynomial of degree $0$.

View full question & answer→

MCQ 121 Mark

Zero of the zero polynomial is :

A
$0$
B
$1$
C
Every real number.
✓
Not defined.

Answer

Correct option: D.

Not defined.

Let $p(x)$ be a polynomial. If $\text{p}(\alpha)=0,$ then we say that $\alpha$ is a zero of a polynomial.
A polynomial consisting of one term, namely zero only, is called a zero polynomoial.
So, the zero of a zero polynomial is not defined.

View full question & answer→

MCQ 131 Mark

Degree of the zero polynomial is:

A
$1$
B
$0$
✓
Not defined.
D
Non of these.

Answer

Correct option: C.

Not defined.

A polynomial consisting of one term, namely zero only, is called a zero polynomial.
So, a zero polynomial can be defined as $p(x) = 0.$
This can also be written as $p(x) = 0 = 0x = 0x^2 = 0x^3$ and so on.
So, it is not possible to determine the degree.
Hence, the degree of a zero polynomial is not defined.

View full question & answer→

MCQ 141 Mark

If $(x^{51} + 51)$ is divided by $(x + 1)$ then the remainder is:

A
$0$
B
$1$
C
$49$
✓
$50$

Answer

Correct option: D.

$50$

Let $f(x)=x^{51}+51$
By the remainder theorem, when $f(x)$ is divided by $(x+1)$, the remainder is $f(-1)$.
Now, $f(-1)=\left[(-1)^n+51\right]$
$=-1+51=50$

View full question & answer→

MCQ 151 Mark

Zero of the polynomial $p(x) = 2x + 5$ is:

A
$\frac{-2}{5}$
✓
$\frac{-5}{2}$
C
$\frac{2}{5}$
D
$\frac{5}{2}$

Answer

Correct option: B.

$\frac{-5}{2}$

$p(x) = 2x + 5$
Now $, p(x) = 0$
$\Rightarrow 2x + 5 = 0$
$\Rightarrow 2x = -5$
$\Rightarrow\text{x}=-\frac{5}{2}$

View full question & answer→

MCQ 161 Mark

If $\text{p}(\text{x})=\text{x}^2-2\sqrt2\text{x}+1$ then $\text{p}(2\sqrt2)=?$

A
$0$
✓
$1$
C
$4\sqrt2$
D
$-1$

Answer

Correct option: B.

$1$

$\text{p}(\text{x})=\text{x}^2-2\sqrt2\text{x}+1$
$\text{p}(2\sqrt2)=(2\sqrt2)^2-2\sqrt2(2\sqrt2)+1$
$=8-8+1$
$=1$

View full question & answer→

MCQ 171 Mark

When $p(x) = x^3 - 3x^2 + 4x + 32$ is divided by $(x + 2)$, the remainder is:

A
$0$
B
$32$
C
$36$
✓
$4$

Answer

Correct option: D.

$4$

$p(x)=x^3-3 x^2+4 x+32$
$x+2=0 \Rightarrow x=-2$
By the renainder theorem, we know that when $p(x)$ is divided by $(x+2)$, the remainder is $p(-2)$.
Now, $p(-2)=x^3-3 x^2+4 x+32$
$=(-2)^3-3(-2)^2+4(-2)+32$
$=-8-12-8+32$
$=4$

View full question & answer→

MCQ 181 Mark

Which of the following is a binomial?

A
$x^2+x+3$
✓
$x^2+4$
C
$2 x^2$
D
$x+3+\frac{1}{x}$

Answer

Correct option: B.

$x^2+4$

A polynomial with two non$-$zero terms is called a binomial.
$x^2+4$ is the polynomial that has two non$-$zero terms.
Hence is a binomial.

View full question & answer→

MCQ 191 Mark

Which of the following is a quadratic polynomial?

A
$x + 4$
B
$x^3 + x$
C
$x^3 + 2x + 6$
✓
$x^2 + 5x + 4$

Answer

Correct option: D.

$x^2 + 5x + 4$

A polynomial of degree $2$ is called a quadratic polynomial.
Options $(a), (b)$ and $(c)$ have degrees $1, 3$ and $3$ respectively,
so they are not quadratic polynomials.
The degree of $x^2 + 5x + 4$ is $2$,
so it is a quadratic polynomial.

View full question & answer→

MCQ 201 Mark

If $(x + 1)$ is a factor of the polynomial $(2x^2 + kx)$ then $k$ = ?

A
$4$
B
$-3$
✓
$2$
D
$-2$

Answer

Correct option: C.

$2$

Let $p(x) = 2x^2 + kx$
Since $(x + 1)$ is a factor of $p(x)$,
$= P(-1) = 0$
$\Rightarrow 2(-1)^2 + k(-1) = 0$
$\Rightarrow 2 - k = 0$
$\Rightarrow k = 2$

View full question & answer→

MCQ 211 Mark

The zeros of the polynomial p(x)$= 2x^2 + 5x -3$ are:

A
$\frac{1}{2},3$
✓
$\frac{1}{2},-3$
C
$\frac{-1}{2},3$
D
$1,\frac{-1}{2}$

Answer

Correct option: B.

$\frac{1}{2},-3$

Let $p(x)$ be a polynomial. If $\text{p}(\alpha)=0,$
then we say that $\alpha$ is a zero of a polynomial.
p(x) = $2x^2 + 5x -3$
Now $,p(x) = 0$
$\Rightarrow 2x^2 + 5x -3 = 0$
$\Rightarrow 2x^2 + 6x - x - 3 = 0$
$\Rightarrow 2x(x + 3) - 1(x + 3) = 0$
$\Rightarrow (2x - 1)(x + 3) = 0$
$\Rightarrow (2x - 1) = 0$ or $(x + 3) = 0$
$\Rightarrow\text{x}=\frac{1}{2}$ or $x = -3$
$$$\therefore\frac{1}{2}$ and $-3$ are the zeroes of the polynomial $p(x).$

View full question & answer→

MCQ 221 Mark

Which of the following is a polynomial?

A
$\text{x}-\frac{1}{\text{x}}+2$
B
$\frac{1}{\text{x}}+5$
C
$\sqrt{\text{x}}+3$
✓
$-4$

Answer

Correct option: D.

$-4$

A polynomial is an algebraic expression in which the variables involved have only non $-$ negative integrals powers.
Option $(a), (b)$ and $(c)$ have negative and non-integral powers,
So they are not polynomials.
We know that, exery real number is a constant polynomial.
So $, -4$ being a real number is a polynomial.

View full question & answer→

MCQ 231 Mark

Which of the following expression is a polynomial?

A
$\sqrt{\text{x}}-1$
B
$\frac{\text{x}-1}{\text{x}+1}$
C
$\text{x}^2-\frac{2}{\text{x}^2}+5$
✓
$\text{x}^2+\frac{2\text{x}^\frac{3}{2}}{\sqrt{\text{x}}}+6$

Answer

Correct option: D.

$\text{x}^2+\frac{2\text{x}^\frac{3}{2}}{\sqrt{\text{x}}}+6$

A polynomial is an algebraic expression in which the variables involved have only non$-$negative integrals powers.
Option $(a), (b)$ and $(c)$ have negative and non-integral powers,
So they are not polynomials.
In option $(d),$
$\text{x}^2+\frac{2\text{x}^\frac{3}{2}}{\sqrt{\text{x}}}+6=\text{x}^2+2\text{x}^{\frac{3}{2}-\frac{1}{2}}+6$
$x^2 + 2x^1 + 6$ Which is a polynomial.

View full question & answer→

MCQ 241 Mark

If $p(x) = x + 4$ then $p(x) + p(-x) =$ ?

A
$0$
B
$4$
C
$2x$
✓
$8$

Answer

Correct option: D.

$8$

$p(x) = x + 4$
$p(-x) = -x + 4$
$p(x) + p(-x) = (x + 4) + (-x + 4)$
$= x + 4 - x + 4$
$= 8$

View full question & answer→

MCQ 251 Mark

If $\left(x^{100}+2 x^{99}+k\right)$ is divisible by $(x+1)$ then the value of $k$ is:

✓
$1$
B
$2$
C
$-2$
D
$-3$

Answer

Correct option: A.

$1$

$p(x)=x^{100}+2 x^{99}+k$
$x+1=0 \Rightarrow x=-1$
By the factor theorem, we know that when $p(x)$ is divided by $(x+1)$, the remainder is $p(-1)$.
Now, $p(-1)=(-1)^{100}+2(-1)^{99}+k$
$\Rightarrow 0=1-2+k \ldots ($Given that $p(x)$ is divisible by $x+1.)$
$\Rightarrow k=1$

View full question & answer→

MCQ 261 Mark

The zeros of the polynomial $p(x) = 3x^2 - 1$ are:

A
$\frac{1}{3}\ \text{and}\ 3$
B
$\frac{1}{\sqrt3}\ \text{and}\ \sqrt3$
C
$\frac{-1}{\sqrt3}\ \text{and}\ \sqrt3$
✓
$\frac{1}{\sqrt3}\ \text{and}\ \frac{-1}{\sqrt3}$

Answer

Correct option: D.

$\frac{1}{\sqrt3}\ \text{and}\ \frac{-1}{\sqrt3}$

$\frac{1}{\sqrt3}\ \text{and}\ \frac{-1}{\sqrt3}$
p(x) $= 3x^2 - 1$
Now, $p(x) = 0$
$\Rightarrow 3x^2- 1 = 0$
\Rightarrow 3x^2 = 1
$\Rightarrow\text{x}^2=\frac{1}{3}$
$\Rightarrow\text{x}=\frac{1}{\sqrt3}\ \text{and}\ -\frac{1}{\sqrt3}$

View full question & answer→

MCQ 271 Mark

When $p(x) = x^3 + ax^2 + 2x$ +a is divided by $(x + a),$ the remainder is:

A
$0$
B
$a$
✓
$-a$
D
$2a$

Answer

Correct option: C.

$-a$

$-a$
$p(x)=x^3+a x^2+2 x+a$
$x+a=0 \Rightarrow x=-a$
By the remainder theorem, we know that when $p(x)$ is divided by $(x+a)$, the remainder is $p(-a)$.
Now,$p(-a)=x^3+a x^2+2 x+a$
$=(-a)^3+a(-a)^2+2(-a)+a$
$=-a^3+a^3-2 a+a$
$=-a$

View full question & answer→

MCQ 281 Mark

Which of the following is a polynomial?

A
$\sqrt[3]{\text{y}}+4$
B
$\sqrt{\text{y}}-3$
✓
$\text{y}$
D
$\frac{1}{\sqrt{\text{y}}}+7$

Answer

Correct option: C.

$\text{y}$

A polynomial is an algebraic expression in which the variables involved have only non $-$ negative integrals powers.
Option $(a), (b)$ and $(d) $ have negative and non $-$ integral powers,
So they are not polynomials.

View full question & answer→

MCQ 291 Mark

Which of the following is a polynomial?

A
$x^{-2} + x^{-1} + 3$
B
$x + x^{-1} + 2$
C
$x^{-1}$
✓
$0$

Answer

Correct option: D.

$0$

$0$
A polynomial is an algebraic expression in which the variables involved have only non-negative integrals powers.
Option (a), (b) and (c) have negative and non-integral powers,
So they are not polynomials.
We know that, exery real number is a constant polynomial.
So, 0 being a real number is a polynomial.

View full question & answer→

MCQ 301 Mark

If $(x + 5)$ is a factor of = $x^3 - 20x + 5k$ then $k$ =$ ?$

A
$-5$
✓
$5$
C
$3$
D
$-3$

Answer

Correct option: B.

$5$

$5$
$p(x)=x^3-20 x+5 k$
Now, $x+5=0 \Rightarrow x=(-5)$
By factor theorem,
$p(-5)=0$
$\Rightarrow(-5)^3-20(-5)+5 k=0$
$\Rightarrow-125+100+5 k=0$
$\Rightarrow-25+5 k=0$
$\Rightarrow 5 k=25$
$\Rightarrow k=5$

View full question & answer→

MCQ 311 Mark

The zeros of the polynomial $p(x) = x^2 + x - 6$ are:

A
$2, 3$
B
$-2, 3$
✓
$2, -3$
D
$-2, -3$

Answer

Correct option: C.

$2, -3$

$2, -3$
Let p(x) be a polynomial. If $\text{p}(\alpha)=0,$ then we say that $\alpha$ is a zero of a polynomial.
$p(x)=x^2+x-6$
Now, $p(x)=0$
$\Rightarrow x^2+x-6$
$\Rightarrow x^2+3 x-2 x-6=0$
$\Rightarrow x(x+3)-2(x+3)=0$
$\Rightarrow(x-2)(x+3)=0$
$\Rightarrow(x-2)=0 \text { or }(x+3)=0$
$\Rightarrow x=2 \text { or } x=-3$
$\therefore$ 2 and -3 are the zeroes of the polynomial p(x).

View full question & answer→

MCQ 321 Mark

$(x + 1)$ is a factor of the polynomial:

A
$x^3 + x^2 - x + 1$
✓
$x^3 + 2x^2 - x - 2$
C
$x^3 + 2x^2 - x + 2$
D
$x^4 + x^3 + x^2 + 1$

Answer

Correct option: B.

$x^3 + 2x^2 - x - 2$

Given, $x^3+2 x^2-x-2$
$\text { For } f(-1)$
$-1+2(-1)^2-(-1)-2$
$-1+2-1-2=0$
$x=-1$
$x+1=0$
So, $(x+1)$ is a factor of the polynomial $x^3+2 x^2-x-2$

View full question & answer→

Maths MCQ(1M)

Take a timed test