MCQ 11 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 : $(2 x-1)^2-4 x^2+5=0$ is not a quadratic equation.
Reason : An equation of the form $a x^2+b x+c=0, a \neq 0$, where $a, b, c \in R$ is called a quadratic equation.
- A
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
- ✓
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
- C
If Assertion is correct but Reason is incorrect.
- D
If Assertion is incorrect but Reason is correct.
AnswerCorrect option: B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
View full question & answer→MCQ 21 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 $(A) : (2 x-1)^2-4 x^2+5=0$ ota quadratic equation.
Reason $(R) : x=0,3$ are the roots of the equation $2 x^2-6 x=0$.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 31 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 : $3 y^2+17 y-30=0$ have distinct roots.
Reason : The quadratic equation $a x^2+b x+c=0$ have distinct roots $($real roots$)$ if $D>0$.
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: A. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
$\therefore D = b^2 - 4ac = (17)^2- 4 \times 3 (- 30)$
$= 289 + 360 = 649 > 0$
So, roots are real and distinct.
View full question & answer→MCQ 41 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 equation $ax^2 + bx + c = 0$, has two distinct real roots, if $b^2 - 4ac > 0$.
Reason : A quadratic equation can never be solved by using method of completing the squares.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 51 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 : $2\sqrt{2}$ is a root of the quadratic equation $\text{x}2−4\sqrt{2}\text{x}+8=0.$
Reason : The root of a quadratic equation satisfies it.
- ✓
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: A. If both assertion and reason are true and reason is the correct explanation of assertion.
Clearly, Reason is correct Now, We have,
$=\text{x}^2-4\sqrt{2}\text{x}+8=0$
Its root will be $2\sqrt{2}$, if it will satisfy the given equation.
Now ,$=\Big(2\sqrt{2}\Big)^2-4\sqrt{2}\Big(2\sqrt{2}\Big)+8$
$\Rightarrow=8-16+8$
$\Rightarrow=0$
Thus, $2\sqrt{2}$ is a root of the given equation.
Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
View full question & answer→MCQ 61 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 : Sum and product of roots of $2x^2 - 3x + 5 = 0$ are $\frac{3}{2}$ and $\frac{5}{2}$ respectively.
Reason : If $a$ and $b$ are the roots of $ax\ 2 + bx + c = 0, a \neq q0,$ then sum of roots $= \alpha + \beta = - \frac{\text{b}}{\text{a}}$ and product of roots $= \alpha \beta = \frac{\text{c}}{\text{a}}.$
- ✓
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: A. If both assertion and reason are true and reason is the correct explanation of assertion.
If both assertion and reason are true and reason is the correct explanation of assertion.
Assertion $2\text{x}^2-3\text{x}+5=0$ So $, \alpha +\beta$
$=-\frac{\text{b}}{\text{a}}=-\frac{-3}{2}=\frac{3}{2}$ and
$=\alpha \beta=\frac{\text{c}}{\text{a}}=\frac{5}{2}$
View full question & answer→MCQ 71 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 : $2x^2- 4x + 3 = 0$ is a quadratic equation.
Reason : All polynomials of degree $n,$ when $n$ is a whole number can be treated as quadratic equation.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
Assertion is correct statement but Reason is wrong statement.
View full question & answer→MCQ 81 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 : $3 x^2-6 x+3=0$ has repeated roots.
Reason : The quadratic equation $a x^2+b x+c=0$ have repeated roots if discriminant $D>0$.
- A
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
- B
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
- ✓
If Assertion is correct but Reason is incorrect.
- D
If Assertion is incorrect but Reason is correct.
AnswerCorrect option: C. If Assertion is correct but Reason is incorrect.
If Assertion is correct but Reason is incorrect.
View full question & answer→MCQ 91 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 : $4x^2 - 12x + 9 =$ has repeated roots.
Reason : The quadratic equation $ax^2 + bx + c = 0$ have repeated roots if discriminant $D>0$
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- ✓
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: C. If assertion is true but reason is false.
If assertion is true but reason is false.
Assertion $4 x^2-12 x+9=0$
So $D=b^2-4 a c$
$\Rightarrow D=(-12)^2-4(4)(9)$
$\Rightarrow D=144-144=0$
Roots are repeated.
View full question & answer→MCQ 101 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 value of $k = 2,$ if one root of the quadratic equation $6x^2 - x - k = 0$ is $\frac{3}{2}$
Reason : The quadratic equation $ax^2+ bx + c =0$ has two roots.
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- ✓
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: B. If both assertion and reason are true but reason is not the correct explanation of assertion.
If both assertion and reason are true but reason is not the correct explanation of assertion.
As one root is $\frac{2}{3}$, so $\text{x}=\frac{2}{3}$
Hence, substituring the value of $x,$ we get
$=6\times\Big(\frac{2}{3}\Big)^2-\frac{2}{3}-\text{k}=0$
$\Rightarrow6\times\frac{4}{9}-\frac{2}{3}=\text{k}$
$\Rightarrow\text{x}=\frac{8}{3}-\frac{2}{3}$
$\Rightarrow\text{k}=\frac{6}{3}=2$
$\text{k}=2$
View full question & answer→MCQ 111 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 :$ 2x^2 - 4x + 3 = 0$ is a quadratic equation.
Reason : All polynomials of degree $n,$ when $n$ is a whole number can be treated as quadratic equation.
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- ✓
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: C. If assertion is true but reason is false.
If assertion is true but reason is false.
View full question & answer→MCQ 121 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 value of $kk$ for which the equation $kx^2 - 12x + 4 = 0$ has equal roots, is $9.$
Reason : The equation $ax^2+ bx + c = 0,(a \neq q)$ has equal roots, if $b^2 - 4ac > 0.$
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- ✓
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: C. If assertion is true but reason is false.
Clearly, Reason is wrong.
Now, the given equation is $kx ^2-12 x +4=0$
If the roots are equal, then $(-12)^2-4( k )(4)=0$
$\Rightarrow144-16\text{k}=0$
$\Rightarrow\text{k}=\frac{144}{16}=9$
Assertion is correct.
View full question & answer→MCQ 131 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 equation $x^2+3 x+1=(x$ $-2)^2$ is a quadratic equation.
Reason : Any equation of the form $a x^2+b x+c=0$ where $a \neq 0$, is called a quadratic equation.
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- ✓
If both assertion and reason are false.
AnswerCorrect option: D. If both assertion and reason are false.
We have, $x^2+3 x+1=(x-2)^2$
$\Rightarrow x^2+3 x+1$
$=x^2-4 x+4$
$\Rightarrow 7 x-3=0$
it is not of the form $a x^2+b x+c=0$
View full question & answer→MCQ 141 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 roots of the quadratic equation $x ^2+2 x +2=0$ are imaginary.
Reason : If discriminant $D = b ^2-4 ac <0$ then the roots of quadratic equation $ax + bx + c =0$ are imaginary.
- ✓
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 $(A)$.
$x^2+2 x+2=0$
Discriminant, $D = b ^2-4 ac$
$=(2)^2-4 \times 1 \times 2$
$=4-8=-<04$
View full question & answer→MCQ 151 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 roots of the equation $x^2$ $b x+c=0$ are two consecutive integers, then $b^2-4 c=1$
Reason: If $a, b, c$ are odd integer then the roots of the equation $4 a b c\ x^2+\left(b^2-4 a c\right) x-b=0$ are real and distinct.
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- ✓
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: B. If both assertion and reason are true but reason is not the correct explanation of assertion.
Assertion : Given equation
$x^2-b x+c=0$
Let $\alpha, \beta$ be two roots such that
$|\alpha-\beta|=1$
$\Rightarrow(\alpha+\beta)^2-4 \alpha \beta=1$
$\Rightarrow b^2-4 c=1$
Reason: Given equation
$4 a b c \ x^2+\left(b^2-4 a c\right) x-b=0$
$\Rightarrow D=\left(b^2-4 a c\right)^2+16 a b^2 c$
$\Rightarrow D=\left(b^2-4 a c\right)^2>0$
View full question & answer→MCQ 161 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 : $2\sqrt{2}$ is a root of the quadratic equation $\text{x}^2-4\sqrt{2}\text{x}+8=0.$
Reason : The root of a quadratic equation satisfies it.
- ✓
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: A. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Clearly, Reason is correct
Now, We have, $\text{x}^2-4\sqrt{2}\text{x}+8=0.$
$2\sqrt{2}$ will be the root, if it will satisfy the given equation.
Now, $(2\sqrt{2})^2-4\sqrt{2}(2\sqrt{2})+8$
$=8-16+8=0$
Thus, $2\sqrt{2}$ is a root of the given equation.
View full question & answer→MCQ 171 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 equation $9x^2 + 3kx + 4 = 0$ has equal roots for $\text{k}=\pm4.$
Reason : If discriminant $'D'$ of a quadratic equation is equal to zero then the roots of equation are real and equal.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 $(R)$ isthe correct explanation of assertion $(A)$.
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe correct explanation of assertion $(A)$.
Assertion $9x^2 + 3kx + 4 = 0$
$D = b2 - 4ac$
$= (3k)2 - 4(9) (4)$
$= 9k - 144$
For equal roots $D = 0$
$= 9k^2 = 144$
$=\text{k}=\pm\frac{12}{3}$
$=\text{k}=\pm4$
View full question & answer→MCQ 181 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 value of $k=2$, if one root of the quadratic equation $6 x^2-x-k=0$ is $\frac{2}{3}$
Reason: The quadratic equation $ax ^2+ bx + c =0, a \neq 0$ has two roots.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 $(A)$.
As one root
$\text{a}=\frac{2}{3}$
$\text{x}=\frac{2}{3}$
$=6\times\Big(\frac{2}{3}\Big)-\frac{2}{3}-\text{k}=0$
$=6\times\frac{4}{9}-\frac{2}{3}=\text{k}$
$=\text{k}=\frac{8}{3}-\frac{2}{3}=\frac{6}{3}=2$
$=\text{k}=2$
So, both $A$ and $R$ are correct but $R$ does not explain $A$.
View full question & answer→MCQ 191 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 equation $x^2 + 3x + 1 = (x - 2)^2$ is a quadratic equation.
Reason : Any equation of the form $ax^2 + bx + c = 0$ where $\text{a}\neq0,$ is called a quadratic equation.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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
We have $, x^2+3 x^2+1=(x-2)^2=x^2-4 x+4$
$\Rightarrow x^2+3 x^2+1=x^2-4 x+4$
$\Rightarrow 7 x-3=0$
it is not of the form $a x^2+6 x+c=0$
So $,A$ is incorrect but $R$ is correct.
View full question & answer→MCQ 201 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 value of $k$ for which the equation $kx^2 - 12x + 4 = 0$ has equal roots, is $9.$
Reason: The equation $ax^2 + bx + c = 0 , (0\neq\text{a})$ has equal roots, if $(b^2 - 4ac) > 0.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
Clearly, Reason is wrong.
Now, the given equation is $k x^2-12 x+4=0$
If the roots are equal, then $(-12)^2-4(k)(4)=0$
$\Rightarrow 144-6 k=0$
$\Rightarrow k=\frac{144}{16}=9$
View full question & answer→MCQ 211 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 equation $8x^2 + 3kx + 2 = 0$ has equal roots then the value of $k$ is $\pm\frac{8}{3}$
Reason : The equation $ax^2+ bx + c = 0$ has equal roots if $D = b^2- 4ac = 0$
- A
If both assertion and reason are true and reason is the correct explanation of assertion.
- ✓
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: B. If both assertion and reason are true but reason is not the correct explanation of assertion.
If both assertion and reason are true but reason is not the correct explanation of assertion.
$8 x^2+3 k x+2=0$
Discriminant, $D=b^2-4 a c$
$\Rightarrow D=(3 k)^2-4(8)(2)=(9 k)^2-64$
For equal roots, $D=0$
$\Rightarrow(9\text{k})^2-64=0$
$\Rightarrow(9\text{k)}^2=64$
$\Rightarrow\text{k}^2=\frac{64}{9}$
$\Rightarrow\text{k}=\pm\frac{8}{3}$
So, $A$ and $R$ both are correct and $R$ explains $A$.
View full question & answer→MCQ 221 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: $\frac{1}{(\text{x-1)}\text{(x-2)}}+\frac{1}{(\text{x-2)}\text{(x-3)}}=\frac{2}{3} (x \neq 1,2,3)$ is a quadratic equation.
Reason: An equation of the form $ax^2 + bx + c = 0$, where $a, b,c, € R$ is a quadratic equation.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓
Assertion is correct statement but Reason is wrong statement.
- D
Assertion is wrong statement but Reason is correct statement
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
Assertion is correct statement but Reason is wrong statement.
View full question & answer→MCQ 231 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: $4 x^2-12 x+9=0$ has repeated roots.
Reason: The quadratic equation $a x^2+b x+c=0$ have repeated roots if discriminant $D>0$.
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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.
Assertion $4 x^2-12 x+9$
$D=b^2-4 a c$
$=(=127)^2-4(4)(9)$
$=144-144=0$
Roots are repeated.
View full question & answer→MCQ 241 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 equation $9 x^2+3 k x+4=0$ has equal roots for $k= \pm 4$.
Reason : If discriminant $'D\ ’$ of a quadratic equation is equal to zero then the roots of equation are real and equal.
- ✓
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: A. If both assertion and reason are true and reason is the correct explanation of assertion.
Assertion $9 x ^2+3 kx +4=0$
$\Rightarrow D=b 2-4 a c$
$\left.\Rightarrow D=(3 k)^2-4(9)(4)\right)$
$\Rightarrow D=9 k^2-144$
For equal roots $D =0$
$\Rightarrow9\text{k}^2=144$
$\Rightarrow \text{k}=\pm\frac{12}{3}$
$\Rightarrow \text{k}=\pm4$
View full question & answer→MCQ 251 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 values of $x$ are $-\frac{a}{2},$ a for a quadratic equation $2 x^2+a x-a^2=0$.
Reason : For quadratic equation $a x^2+b x+c=0$
$x=\frac{-b \pm \sqrt{b^2-4 ac}}{2 a}$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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
$2\text{x}^2 + \text{ax} - \text{a}^2 = 0$
$\text{x}=\frac{-\text{a}\pm\sqrt{\text{a}^2-8\text{a}^2}}{4}$
$=\frac{-\text{a+3}\text{a}}{4}=2\text{a},\frac{-4\text{a}}{4}$
$\text{x}=\frac{\text{a}}{2},-\text{a}$
So, $A$ is incorrect but $R$ is correct.
View full question & answer→MCQ 261 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: $9 x^2-3 x-20=0\Rightarrow(3 x-5)(3 x+4)=0$ If the roots are calculated by splitting the middle term.
Reason: To factorise $a x^2+b x+c=0$, we write it in the form $a x^2+b_1 x+b_2 x+c=0$ such that $b_1+b_2-b$ and $b_1 b_2=a e$.
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
We have $, 9 x^2-3 x-20=0$
$\Rightarrow 9 x^2-15 x+12 x-20=0$
$\Rightarrow 3 x(a x-5)+4(3 x-5)=0$
$\Rightarrow(3 x+4)(3 x-5)=0$
View full question & answer→MCQ 271 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 $(A)$ : The equation $8 x^2+3 k x+2=0$ has equal roots, then the value of $k$ is $\pm \frac{8}{3}$
Reason $(R)$ : The equation $a x^2+b x+c=0$ has equal roots if $D=b^2-4 a c=0$.
- ✓
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 $(R)$ isthe 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 281 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 equation $x ^2+(2 m+1) x +(2 n +1)=0$, where $m$ and $n$ are integers, cannot have any rational roots.
Reason : The quantity $(2 m+1)^2-4(2 n+1)$, where $m, n \in I$, can never be a perfect square.
- ✓
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
- C
Assertion is correct but Reason is incorrect.
- D
Assertion is incorrect but Reason is correct.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
$x^2+(2 m+1) x+(2 n+1)=0$
$D=(2 m+1)^2-4(2 n+1)$
For $D$ to be a perfect square the expression $4 m^2+4 m+(1-8 n-4)$ which is a quadratic in must have discriminant zero.
$\Rightarrow 4^2-(4)(4)(1-8 n-4)=0$
But $n$ is an integer.
Therefore, when $m \ n$ are integers $D$ cannot be perfect square.
Therefore, roots are irrational.
View full question & answer→MCQ 291 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 : Both the roots of the equation $x^2 - x +1 = 0$ are real.
Reason : The roots of the equation $ax^2+ bx + c = 0$ are real if and only if $b^2 - 4ac = 0.$
- A
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- B
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- C
Assertion is correct statement but Reason is wrong statement.
- ✓
Assertion is wrong statement but Reason is correct statement.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
Assertion is wrong statement but Reason is correct statement.
Clearly, Reason is Correct.
Now, given quadratic equation is $x^2-x+1=0$
$\therefore b^2-4 ac=(-1)^2-4(1)(1)=-3 < 0$
Hence, the given quadratic equation has no real roots.
View full question & answer→MCQ 301 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 : $9 x^2-3 x-20=0 \Rightarrow(3 x-5)(3 x+4)$ If the roots are calculated by splitting the middle term. Reason : To factorise $a x^2+b x+c$, we write it in the form $a x^2+b_1 x+b_2 x+c=0$ such that $b_1+b_2=b$ and $b_1 b_2= ac.$
- ✓
If both assertion and reason are true and reason is the correct explanation of assertion.
- B
If both assertion and reason are true but reason is not the correct explanation of assertion.
- C
If assertion is true but reason is false.
- D
If both assertion and reason are false.
AnswerCorrect option: A. If both assertion and reason are true and reason is the correct explanation of assertion.
If both assertion and reason are true and reason is the correct explanation of assertion.
We have, $9 x^2-3 x-20=0$
$\Rightarrow 9 x^2-15 x+12 x-20=0$
$[$By splitting the middle term$]$
$\Rightarrow 3 x(3 x-5)+4(3 x-5)=0$
$\Rightarrow(3 x+4)(3 x-5)=0$
Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
View full question & answer→MCQ 311 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 $(A)$ : The values of $x$ are $-\frac{a}{2}$, a for a quadratic equation $2 x^2+a x-a^2=0$
Reason $(R)$ : For quadratic equation $ax ^2+ bx + c =0, x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a }$
- A
Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ isthe 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 321 Mark
Statement $A\ ($Assertion$)$ :
$\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}=\frac{2}{3}(x \neq 1,2,3)$ is a quadratic equation.
Statement $R\ ($Reason$)$ : An equation of the form $a x^2+b x+c=0$, where $a, b, c \in R$ is a quadratic equation.
- 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.
$\Rightarrow \frac{x-3+x-1}{(x-1)(x-2)(x-3)}=\frac{2}{3}$
$\Rightarrow \frac{2 x-4}{(x-1)(x-2)(x-3)}=\frac{2}{3}$
$\Rightarrow \frac{2(x-2)}{(x-1)(x-2)(x-3)}=\frac{2}{3}$
$\Rightarrow \quad(x-1)(x-3)=3 $
$\Rightarrow x^2-4 x+3=3$
$\Rightarrow x^2-4 x=0$, which is of the form $a x^2+b x+c=0$, where $a \neq 0$
$\therefore x^2-4 x=0$ is a quadratic equation.
Also, an equation of the form $a x^2+b x+c=0, a, b, c \in R$ and $a \neq 0$ is a quadratic equation.
Thus, assertion is true but reason is false.
View full question & answer→MCQ 331 Mark
Statement A (Assertion) : $2 \sqrt{2}$ is a root of the quadratic equation $x^2-4 \sqrt{2} x+8=0$.
Statement R (Reason) : The roots of a quadratic equation satisfy it.
- ✓
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.
Now, we have, $x^2-4 \sqrt{2} x+8=0$
$2 \sqrt{2}$ will be the root, if it will satisfy the given equation.
Now, $(2 \sqrt{2})^2-4 \sqrt{2}(2 \sqrt{2})+8=8-16+8=0$
Thus, $2 \sqrt{2}$ is a root of the given equation.
$\therefore \quad$ Both assertion and reason are true and reason is the correct explanation of assertion.
View full question & answer→MCQ 341 Mark
Statement A (Assertion) : Both the roots of the equation $x^2-x+1=0$ are real.
Statement $R$ (Reason): The roots of the equation
$a x^2+b x+c=0$ are real if and only if $b^2-4 a c \geq 0$.
- 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) : Clearly, reason is true.
Now, given quadratic equation is $x^2-x+1=0$
$
\therefore \quad b^2-4 a c=(-1)^2-4(1)(1)=-3<0
$
Hence, the given quadratic equation has no real roots.
$\therefore \quad$ Assertion is false.
View full question & answer→MCQ 351 Mark
Statement A (Assertion) : The value of $k$ for which the equation $k x^2-12 x+4=0$ has equal roots is 9 .
Statement R (Reason): The equation $a x^2+b x+c=0,(a \neq 0)$ has equal roots, if $b^2-4 a c>0$
- 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.
Now, the given equation is $k x^2-12 x+4=0$
If the roots are equal, then $(-12)^2-4(k)(4)=0$
$\Rightarrow 144-16 k=0 \Rightarrow k=144 / 16=9$
$\therefore \quad$ Assertion is true.
View full question & answer→MCQ 361 Mark
Statement $A ($Assertion$)$ : If the roots are calculated by splitting the middle term, then $9 x^2-3 x-20=0\Rightarrow(3 x-5)(3 x+4)=0$
Statement $R ($Reason$)$: To factorise $a x^2+b x+c=0$, we write it in the form $a x^2+b_1 x+b_2 x+c=0$ such that $b_1+b_2=b$ and $b_1 b_2=a c$.
- ✓
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 $(A)$.
We have, $9 x^2-3 x-20=0$
$\Rightarrow 9 x^2-15 x+12 x-20=0 [$ By splitting the middle term $]$
$\Rightarrow 3 x(3 x-5)+4(3 x-5)=0$
$\Rightarrow(3 x+4)(3 x-5)=0$
$\therefore$ Both assertion and reason are true and reason is the correct explanation of assertion.
View full question & answer→MCQ 371 Mark
Statement $A\ ($Assertion$)$ : $3 y^2+17 y-30=0$ have distinct roots.
Statement $R\ ($Reason$)$ : The quadratic equation $a x^2+b x+c=0$ have distinct roots $($real roots$)$ if $D>0$.
- ✓
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 $(A)$.
$3 y^2+17 y-30=0$
$\therefore D=b^2-4 a c$
$ =(17)^2-4 \times 3(-30)$
$ =289+360=649>0$
So, roots are real and distinct.
Both assertion and reason are true and reason is the correct explanation of assertion.
View full question & answer→MCQ 381 Mark
Statement A (Assertion): $2 x^2-4 x+3=0$ is a quadratic equation.
Statement R (Reason) : All polynomials of degree $n$, when $n$ is a whole number can be treated as quadratic equation.
- 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) : Assertion $(A)$ is true but reason $(R)$ is false.
View full question & answer→