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Maths Assertion (A) & Reason (B) MCQ

INVERSE TRIGNOMETRIC FUNCTIONS · Gujarat Board (GSEB) STD 12 Science (GSEB - English Medium). 14 questions.

Questions

Assertion (A) & Reason (B) MCQ

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14 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The solution of $\sin^{-1}(6\text{x})+\sin^{-1}(6\sqrt{3}\text{x})=\frac{-\pi}{2}$ is $\text{x}=\frac{1}{12}.$
Reason: $\cot^{-1}\text{x}$ is increasing function for $0\leq\text{x}\leq1.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
Answer
  1. A is false but R is true.
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Question 21 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If $0<\text{x}\leq\frac{\pi}{2},$ then $\sin^{-1}(\cos\text{x})+\cos^{-1}(\sin\text{x})=\pi-2\text{x}.$
Reason: $\cos^{-1}\text{x}=\frac{\pi}{2}-\sin^{-1}\text{x} $ for all $\text{x}\in[-1,1].$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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Question 31 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\big[\text{x}+\sqrt{1+\text{x}^{2}}\big]=\frac{\pi}{2}-\frac{1}{2}\cot^{-1}.$
Reason: $\sin^{2}\Big[2\tan^{-1}\sqrt{\frac{1+\text{x}}{1-\text{x}}}\Big]=1-\text{x}^{2}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true but R is not the correct explanation of A.
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Question 41 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cos^{-1}\text{x}=2\sin^{-1}\sqrt{\frac{1-\text{x}}{2}}=2\cos^{-1}\sqrt{\frac{1+\text{x}}{2}}.$
Reason: $1+\cos\text{A}=2\cos^{2}\big(\frac{\text{A}}{2}\big)$ and $1-\cos\text{A}=2\sin^{2}\big(\frac{\text{A}}{2}\big).$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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Question 51 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cot\big[\frac{\pi}{2}-2\cot^{-1}3\big]=7.$
Reason: $\sin^{-1}\big(\frac{4}{5}\big)+2\tan^{-1}\big(\frac{1}{3}\big)=\frac{\pi}{2}.$ 
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
Answer
  1. Both A and R are true but R is not the correct explanation of A.
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Question 61 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The value of $\cos^{-1}\text{x}+\cos^{-1}\Big\{\frac{\text{x}}{2}+\frac{\sqrt{2-3\text{x}^{2}}}{2}\Big\}=\frac{\pi}{3}$ when $\frac{1}{2}\leq\text{x}\leq1.$
Reason: $\cot^{-1}\text{x}$ is increasing function for $0\leq\text{x}\leq1.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
Answer
  1. A is true but R is false.
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Question 71 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\sin^{-1}\frac{8}{17}+\sin^{-1}\frac{3}{5}=\sin^{-1}\frac{77}{85}.$
Reason: $\sin^{-1}\text{x}+\sin^{-1}\text{y}=\sin^{-1}\big(\text{x}\sqrt{1-\text{y}^{2}}+\text{y}\sqrt{1-\text{x}^{2}}\big)$ for $-1\leq\text{x},\text{y}\leq1,\text{x}^{2}+\text{y}^{2}\leq1.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. 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, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\text{cosec}^{-1}\Big(\frac{1}{2}+\frac{1}{\sqrt{2}}\Big)>\sec^{-1}\Big(\frac{1}{2}+\frac{1}{\sqrt{2}}\Big).$
Reason: $\text{cosec}^{-1}(\text{x})>\sec^{-1}(\text{x})$ if $1<\text{x}<\sqrt{2}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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Question 91 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\text{cosec}^{-1}\text{x}>\sin^{-1}\text{x},$ for all $\text{x}\in[-1,1].$
Reason: $\text{cosec}^{-1}\text{x}$ is decreasing function in [-1, 1].
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true but R is not the correct explanation of A.
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Question 101 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\text{x}+\tan^{-1}\big(\frac{1}{\text{x}}\big)=\frac{\pi}{2}.$
Reason: $\tan^{-1}\text{x}+\cot^{-1}\text{x}=\frac{\pi}{2}$ for all $\text{x}\in\text{R}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
Answer
  1. 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, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\cos^{-1}\text{x}-\sin^{-1}\text{x}=0,$ then $\text{x}=\frac{1}{\sqrt{2}}.$
Reason: $\cot^{-1}\text{x}+\sin^{-1}\text{x}=\frac{\pi}{2}.$ 
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false. 
Answer
  1. Both A and R are true and R is the correct explanation of A.
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Question 121 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\big(\frac{2}{5}\big)+\tan^{-1}\big(\frac{3}{7}\big)=\frac{\pi}{4}.$
Reason: $\tan^{-1}\big(\frac{\text{x}}{\text{y}}\big)+\tan^{-1}\big(\frac{\text{y}-\text{x}}{\text{y}+\text{x}}\big)=\frac{\pi}{4}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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Question 131 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If $\text{x}=\frac{1}{5\sqrt{2}}$ then $\{\text{x}\cos(\cot^{-1}\text{x})+\sin(\cot^{-1}\text{x})\}^{2}=\frac{51}{50}.$
Reason: $\tan\Big[\cos^{-1}\Big(\frac{1}{5\sqrt{2}}\Big)-\sin^{-1}\Big(\frac{4}{\sqrt{17}}\Big)\Big]=\frac{29}{3}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true but R is not the correct explanation of A.
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Question 141 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\big(\frac{3}{4}\big)+\tan^{-1}\big(\frac{1}{7}\big)=\frac{\pi}{4}.$
Reason: For x > 0, y > 0, xy < 1, $\tan^{-1}\text{x}+\tan^{-1}\text{y}=\tan^{-1}\Big(\frac{\text{x}+\text{y}}{1-\text{xy}}\Big).$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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