Assertion (A) & Reason (B) MCQ - MATHS STD 12 Science Questions - Vidyadip

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Assertion (A) & Reason (B) MCQ

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20 questions · timed · auto-graded

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 $(A) \frac{\text{dx}^{\sin\text{x}}}{\text{dx}}=\text{x}^{\sin\text{x}}[(\cos)\log\text{x}+\frac{\sin\text{x}}{\text{x}}]$
Reason $(R)$ if $y = x^{f(x)}$ then $\frac{\text{dy}}{\text{dx}}=\text{x}^\text{f(x)}[\text{f '(x)}\log\text{x}+\frac{\text{f(x)}}{\text{x}}]$

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$.
C
$A$ is true but $R$ is false
D
$A$ is false but $R$ is true

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$

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Question 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) f(x) = x - 1 + x - 2 is continuous but not differentiable at x = 1, 2.
Reason(R) Every differentiable function is continuous

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true but R is NOT the correct explanation of A.

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Question 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(A): $\text{f(x)}=\sin\text{x}$ is continuous x = 0.
Reason(R): $\sin\text{x}$ is differentiable at x = 0.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false.
A is false but R is true.

Answer

A is true but R is false.

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Question 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) f(x) = [x] greatest integer function is not differentiable at x = 2
Reason(R) The greatest integer function is not continuous at any integer

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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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 $(A): \text{f(x)}=\tan^2\text{x}$ is continuous at $\text{x}=\frac{\pi}{2}$
Reason $(R):\ ?$ is continuous at $\text{x}=\frac{\pi}{2}$

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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Question 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 (A) if $\text{y}=\tan^{-1}\Big(\frac{\cos\text{x}+\sin\text{x}}{\sin\text{x}-\cos\text{x}}\Big) ,\frac{-\pi}{4}<\text{x}<\frac{\pi}{4},\text{then}\frac{\text{dy}}{\text{dx}}=-1$
Reason(R) $\frac{\cos\text{x}+\sin\text{x}}{\sin\text{x}-\cos\text{x}}=\tan\Big(\text{x}+\frac{\pi}{4}\Big)$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

A is false but R is true

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Question 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 (A) The derivative of $\log\sin\text{x}\text{ w.r.t}\sqrt{\cos\text{x}}$ is $2\sqrt{\cos\text{x}} \cos\text{x } \text{cosec x}$
Reason(R) The derivative of u w.r.t. v is $\frac{\frac{\text{du}}{\text{dx}}}{\frac{\text{dv}}{\text{dx}}}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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Question 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(A): Acontinuous funection is always differentiable.
Reason(R): Adifferentiable function is always continuous.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false.
A is false but R is true.

Answer

A is false but R is true.

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Question 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 (A) If $\text{f(x)}=\cos,\text{then}\text{ f '}\Big(\frac{\pi}{4}\Big)=\frac{-1}{\sqrt{2}} \text{ and} \text{ f '}\Big(\frac{3\pi}{4}\Big)=\frac{1}{\sqrt{2}}$
Reason(R) $\text{f(x)}=\cos=\begin{cases}\cos\text{x },0\leq\text{x} \leq\frac{\pi}{2}\\-\cos\text{x },\text{if }\frac{\pi}{2}<\text{x}\leq\pi\end{cases}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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Question 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 (A) If $\text{f(x)}=\text{x}+\begin{vmatrix}\text{x}+2&\text{ab}\\\text{ab}&\text{x}+\text{b}^2\end{vmatrix}$ then $\text{f'(x)}=2\text{x}+\text{a}^2+\text{b}^2$
Reason(R) If $\triangle=\begin{vmatrix}\text{f(x)}&\text{g(x)} \\ \text{u(x)}&\text{g(x)} \end{vmatrix},$ Then $\frac{\text{d}\triangle}{\text{dx}}=\begin{vmatrix}\text{f'(x)}&\text{g'(x)} \\ \text{u(x)}&\text{g(x)} \end{vmatrix}+\begin{vmatrix}\text{f(x)}&\text{g(x)} \\ \text{u'(x)}&\text{g'(x)} \end{vmatrix}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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Question 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: $\text{u}=\text{f}(\cot\text{x})\&\text{f}(1)=\sqrt2$ and $\text{g}(\sqrt{2})=2$ then $\Big(\frac{\text{du}}{\text{dv}}\Big)_{\text{x}=\frac{\text{x}}{4}}=1.$
Reason: If u = f(x), v = g(x) then derivative of f w.r.t. to g is $\frac{\text{du}}{\text{dv}}=\frac{\frac{\text{du}}{\text{dx}}}{\frac{\text{dv}}{\text{dx}}}.$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
Assertion is correct but Reason is incorrect.
Both Assertion and Reason are incorrect.

Answer

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

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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 $(A)$ If $x = at^2$ and $y = 2$ at where $‘t’$ is the parameter and ‘a’ is a constant, then $\frac{\text{d}^2\text{y}}{\text{dy}^2}= \frac{-1}{\text{t}^2}.$
Reason $(R) \frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{\text{d}^2\text{y}}{\text{dt}^2}\div\frac{\text{d}^2\text{x}}{\text{dt}^2}$

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
✓
Both $A$ and $R$ are false
C
$A$ is true but $R$ is false
D
$A$ is false but $R$ is true

Answer

Correct option: B.

Both $A$ and $R$ are false

Both $A$ and $R$ are false

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Question 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 (A) if $\text{y}=\sin^{-1}\frac{2\text{x}}{1+\text{x}^2}$ then $\frac{\text{dy}}{\text{dx}}=\frac{2}{1+\text{x}^2}$
Reason(R) $\sin2\theta=\frac{2\tan\theta}{1+\tan^2\theta}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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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 $(A)$ If $x^2 + 2xy + y^3 = 42,$ Then $\frac{\text{dy}}{\text{dx}}=\frac{2(\text{x+y})}{(2\text{x+3}\text{y}^2)}$ Reason$(R) \frac{\text{dy}^\text{n}}{\text{dx}}=\text{ny}^{(\text{n-1})}$

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is $\ce{NOT}$ the correct explanation of $A.$
C
$A$ is true but $R$ is false
✓
$A$ is false but $R$ is true

Answer

Correct option: D.

$A$ is false but $R$ is true

Both $A$ and $R$ are false

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Question 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 (A) The function $\text{f(x)}=\begin{cases}12\text{x} -13 , \text{if x}\leq3\\2\text{x}^2+5,\text{if x}>3\end{cases}$ is differentiable at x = 3.
Reason(R) The function f(x) is differentiable at x = c of its domain if Left hand derivative of f at c = Right hand derivative of f at c.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

Both A and R are true and R is the correct explanation of A

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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: $\text{f}(\text{x})=\begin{cases}\text{x}^2\sin\big(\frac{1}{\text{x}}\big), &\text{x}=0\\0, &\text{x}=0\end{cases}$ is continuous at $x = 0.$
Reason: Both $\text{h}(\text{x})=\text{x}^2,\text{g}(\text{x})=\begin{cases}\text{x}^2\sin\big(\frac{1}{\text{x}}\big), &\text{x}=0\\0, &\text{x}=0\end{cases}$ are continuous at $x = 0.$

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
✓
Both $A$ and $R$ are true and $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$R$ is true but $A$ is false.

Answer

Correct option: B.

Both $A$ and $R$ are true and $R$ is not the correct explanation of $A.$

Assertion: $\text{f}(0)=0\lim\text{x}^2\sin\big(\frac{1}{\text{x}}\big)=0^2\times$ finite value $=0$
$\therefore$ It is continuous at $x = 0$
Reason: $h(x) = x^2$ is continuous but $g(x)$ is not continuous
$\lim\limits_{\text{x}\rightarrow0}\sin\big(\frac{1}{\text{x}}\big) =$ not defined $($value oscillates$)$
$\lim\limits_{\text{x}\rightarrow0}\sin\big(\frac{1}{\text{x}}\big)=0$
$\therefore$ not continuous.

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Question 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(A): :f(x) = [x] is not differentiableat x = 2.
Reason(R): f(x) = [x] is not continuous at x = 2.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false.
A is false but R is true.

Answer

Both A and R are true and R is the correct explanation of A

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Question 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 (A): $\text{f(x)}=\sin\text{x}$ is continuous for all $\text{x }\epsilon\text{ R}$
Reason (R): $\sin\text{x}$ and $\text{x}$ are continuous at on R.

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false.
A is false but R is true.

Answer

Both A and R are true and R is the correct explanation of A

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Question 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 (A) If $\text{y}=\log_7(\text{x}^2+7\text{x}+4),$ then $\frac{\text{dy}}{\text{dx}}=\frac{(2\text{x}+7)}{(\text{x}^2+7\text{x}+4),}$
Reason(R) $\log_\text{b}=\frac{\log_\text{e}}{\log_\text{e}\text{b}}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

A is false but R is true

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Question 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 (A) The value of the constant ‘k’ so that $\text{f(x)}=\begin{cases}\text{kx}^2,\text{if x}\leq2\\3,\text{if x}>2\end{cases}$ is continuous at x = 2 is $\text{k}=\frac{4}{3}$
Reason(R) A function f(x) is continuous at a point x= a of its domain if $\lim\limits_{\text{x}\rightarrow 0}\text{f(x)}=\text{f(x)}$

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A.
A is true but R is false
A is false but R is true

Answer

A is false but R is true

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Assertion (A) & Reason (B) MCQ - MATHS STD 12 Science Questions - Vidyadip