MCQ 511 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the graph of polynomial intersect the $x -$ axis at only pont it be a quadratic polynomial.
Reason : Because every quadratic has at most two zeroes.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→MCQ 521 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $x^2 + x$ is a quadratic polynomial.
Reason: In this polynomial the highest power of $x$ is $2$.
Hence, the given polynomial is quadratic.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 531 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $− 1$ and $4$ are the zeros of the polynomial $x^2 − 3x − 4.$
Reason: A real number $k$ is said to be a zero of a polynomial $p(x)$, if $p(k) = 0.$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 541 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $x^2+ 4x + 5$ has two zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
Assertion $(A)$ is false but reason $(R)$ is true.
View full question & answer→MCQ 551 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The sum of the zeroes of the given quadratic polynomial $-3x^2 + k$ is $0$.
Reason: Sum of zeroes $=\frac{-\text{b}}{\text{a}}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 561 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Zeroes of $f(x) = x^2 - 4x - 5$ are $5, -1.$
Reason: The polynomial whose zeroes are $2+\sqrt{3},$ $2-\sqrt{3},$ is $x^2 - 4x = 7.$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
Assertion $(A)$ is true but reason $(R)$ is false.
View full question & answer→MCQ 571 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If both zeros of the quadratic polynomial $x^2 - 2kx + 2$ are equal in magnitude but opposite in sign then value of k is $\frac{1}{2}.$
Reason: Sum of zeros of a quadratic polynomial $ax^2 + bx + c$ is $\frac{-\text{b}}{\text{a}}.$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
As the polynomial is $x^2 - 2kx + 2$ and its zeros are equal but opposition sign
sum of zeros = 0 $=\frac{-(-2\text{k})}{1}=0$
$\Rightarrow2\text{k}=0$
$\Rightarrow\text{k}=0$
So, $A$ is incorrect but $R$ is correct.
View full question & answer→MCQ 581 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $ (s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : $(2-\sqrt{3}) $ is one zero of the quadratic polynomial then other zero will be $(2+\sqrt{3}).$
Reason : Irrational zeros $($roots$)$ always occurs in pairs.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
As irrational roots/ zeros always occurs in pairs therefore, when one zero is $(2-\sqrt{3}) $ then other will be $(2+\sqrt{3}).$
So, both $A$ and $R$ are correct and $R$ explains $ A.$
View full question & answer→MCQ 591 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : $x + 1$ is a Linear Polynomial.
Reason : The polynomials of degree $1$ are called linear polynomials.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→MCQ 601 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:Assertion: If one zero of polynomial $p(x)=\left(k^2+4\right) x^2+13 x+4 k$ is reciprocal of the other, then $k =2$.
Reason: If $(x-a)$ is a factor of $p(x)$, then $p(a)=0$ i.e., $a$ is a zero of $p(x)$.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A).$
View full question & answer→MCQ 611 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $t^2$ is a quadratic polynomial.
Reason: The degree of the given expression is $2$. So, it is a quadratic polynomial.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 621 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $( s )( R )$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:Assertion: $\left(a^2-b^2\right)=(a-b)(a+b)$.
Reason: $\left(5^2-4^2\right)=9$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 631 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : A polynomial having variable with two constant value is called constant polynomial
Reason : A constant polynomial has highest degree is $2.$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
View full question & answer→MCQ 641 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The cofficent of $x$ in the expansion of $(x + 3)^3$ is $27$.
Reason: $(\text{a}+\text{b})^{3}=\text{a}^{3}+\text{b}^{3}+3\text{a}^{2}+3\text{ab}^{2}$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A).$
View full question & answer→MCQ 651 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s) \ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : If the sum of the zeroes of the quadratic polynomial $x^2 - 2kx + 8$ is $2$ then value of $k$ is $1$.
Reason : Sum of zeroes of a quadratic polynomial $ax^2 + bx + c$ is $\frac{-\text{b}}{\text{a}}.$
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→MCQ 661 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion : A quadratic polynomial, sum of whose zeroes is $8$ and their product is $12$ is $x^2 - 20x + 96.$
Reason : If $\alpha$ and $\beta$ be the zeroes of the polynomial $f(x),$ then polynomial is given by $\text{f}(\text{x})=\text{x}^{2}-(\alpha+\beta)\text{x}+\alpha\beta.$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true but reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
Assertion $(A)$ is false but reason $(R)$ is true.
Reason is correct.
If $\alpha$ and $\beta$ be the zeroes of the required polynomial $f(x),$
then, $(\alpha+\beta)=8$ and $\alpha\beta=12$
$\therefore\text{f}(\text{x})=\text{x}^{2}-(\alpha+\beta)\text{x}+\alpha\beta$
$\Rightarrow\text{f}(\text{x})=\text{x}^{2}-8\text{x}+12$
So, Assertion is not correct
View full question & answer→MCQ 671 Mark
Statement A (Assertion): Zeroes of the polynomial $2 x^2-8 x+6$ are 1 and 3 .
Statement $R$ (Reason) : If $\alpha$ and $\beta$ are zeroes of quadratic polynomial $p(x)=a x^2+b x+c, a \neq$ 0 , then $p(x)=k\left[x^2-(\alpha+\beta) x+\alpha \beta\right]$, where $k$ is a constant.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
(b) : Clearly, Reason is true.
Let $p$
$\begin{aligned}
p(x) & =2 x^2-8 x+6 \\
& =2 x^2-2 x-6 x+6=2 x(x-1)-6(x-1) \\
& =(x-1)(2 x-6)
\end{aligned}$
So, the value of $p(x)$ is zero, when
$x-1=0 \text { or } 2 x-6=0$
i.e., when $x=1$ or $x=3$.
$\therefore \quad$ Zeroes of $p(x)$ are 1 and 3 .
$\therefore \quad$ Assertion and Reason both are true but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 681 Mark
Statement $A\ ($Assertion$)$ : If $-1$ is the zero of the polynomial $p(x)=x^2-3 a x+3 a-7,$ then value of $a$ is $3$ .
Statement $R\ ($Reason$)$ : The zeroes of polynomial $a x^2+b x+c, a \neq 0$ are the $x-$ coordinate of the points where the parabola representing $y$
$=a x^2+b x+c$ intersects the $x-$ axis.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion $(A)$ is false but reason $(R)$ is true.
We have $, -1$ is the zero of $p(x)=x^2-3 a x+3 a-7$.
$\therefore p(-1)=0$
$\Rightarrow (-1)^2-3 a(-1)+3 a-7=0$
$\Rightarrow 1+3 a+3 a-7=0$
$\Rightarrow 6 a-6=0 $
$\Rightarrow a=1$
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 691 Mark
Statement A (Assertion): If the sum and product of zeroes of a quadratic polynomial is 3 and -2 respectively, then the quadratic polynomial is $x^2-3 x-2$.
Statement R (Reason) : If $S$ is the sum of zeroes and $P$ is the product of zeroes of a quadratic polynomial, then the quadratic polynomial is given by $x^2-S x+P$.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
(a) : Let $\alpha$ and $\beta$ are the zeroes of quadratic polynomial.
Now, given $\alpha+\beta=3=S$ and $\alpha \beta=-2=P$
So, one of the quadratic polynomial is $x^2-3 x-2$.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 701 Mark
Statement A (Assertion) : One of the zeroes of the polynomial $f(x)=x^3-2 x^2-3 x+6$ is $\sqrt{3}$.
Statement R (Reason): A real number $k$ is said to be a zero of a polynomial $p(x)$, if $p(k)=0$.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
(a) : Clearly, Reason is true.
We have, $f(x)=x^3-2 x^2-3 x+6$
$\begin{aligned}
f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3 \sqrt{3}+6 \\
& =3 \sqrt{3}-6-3 \sqrt{3}+6=0
\end{aligned}$
$\therefore \quad \sqrt{3}$ is zero of $f(x)$.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 711 Mark
Statement A (Assertion) : A quadratic polynomial having 5 and -3 as zeroes is $x^2-2 x$ -15 .
Statement R (Reason): The quadratic polynomial having $\alpha$ and $\beta$ as zeroes is given by $p(x)=x^2-(\alpha+\beta) x+\alpha \beta$.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
(a) : Clearly, Reason is true.
Let $\alpha=5$ and $\beta=-3$.
Then, $\alpha+\beta=2$ and $\alpha \beta=-15$
$\therefore \quad$ Required polynomial is given by $p(x)=x^2-2 x-15$
$\therefore \quad$ Assertion and Reason both are true and Reason is the true explanation of Assertion.
View full question & answer→MCQ 721 Mark
Statement $A\ ($Assertion$)$ : If one zero of the polynomial $p(x)=\left(k^2+9\right) x^2+9 x+6 k$ is the reciprocal of the other zero, then $k=3$.
Statement $R \ ($Reason$)$ : If $(x-\alpha)$ is a factor of the polynomial $p(x),$ then $\alpha$ is a zero of $p(x)$.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A)$.
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion $(A)$ is false but reason $(R)$ is true.
AnswerCorrect option: B. Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion $(A)$.
Let $\alpha$ and $\frac{1}{\alpha}$ be the zeroes of polynomial
$p(x)=\left(k^2+9\right) x^2+9 x+6 k \text {. }$
Then, product of zeroes $=\alpha \times \frac{1}{\alpha}$
$=\frac{6 k}{k^2+9}$
$\Rightarrow \frac{6 k}{k^2+9}=1$
$\Rightarrow k^2+9=6 k $
$\Rightarrow k^2-6 k+9=0$
$\Rightarrow(k-3)^2=0 $
$\Rightarrow k-3=0 $
$\Rightarrow k=3$
$\therefore$ Assertion and Reason both are true but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 731 Mark
Statement A (Assertion): The polynomial $p(x)=x^3+x$ has one real zero.
Statement R (Reason) : A polynomial of $n^{\text {th }}$ degree has at most $n-1$ zeroes.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- ✓
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: C. Assertion $(A)$ is true but reason $(R)$ is false.
(c) : Clearly Reason is false.
We have, $p(x)=x^3+x=x\left(x^2+1\right)$
So, the value of $p(x)$ is zero when $x=0$ or $x^2+1=0$
But $x^2+1 \neq 0$ for any real value of $x \quad\left[\because x^2+1>0\right]$.
$\therefore \quad p(x)$ has one real zero, namely 0 .
So, Assertion is true.
View full question & answer→MCQ 741 Mark
StatementA(Assertion): $f(x)=2 x^3-\frac{3}{x}+7$ is a polynomial in the variable $x$ of degree 3 .
Statement R (Reason) : The highest power of $x$ in a polynomial $f(x)$ is called the degree of the polynomial $f(x)$.
- A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- ✓
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: D. Assertion (A) is false but reason $(R)$ is true.
(d) : $f(x)=2 x^3-\frac{3}{x}+7=2 x^3-3 x^{-1}+7$ is not a polynomial as one of the term is $-3 x^{-1}$.
$\therefore$ Assertion is false but Reason is true.
View full question & answer→MCQ 751 Mark
Statement A (Assertion) : $4 x+1$ is a linear polynomial.
Statement R (Reason): A polynomial of degree 1 is a linear polynomial.
- ✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
- B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
- C
Assertion $(A)$ is true but reason $(R)$ is false.
- D
Assertion (A) is false but reason $(R)$ is true.
AnswerCorrect option: A. Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
(a) : Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
View full question & answer→