Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Assertion (A) : All trigonometric functions have their inverses over their respective domains.
Reason (R) : The inverse of $\tan ^{-1} x$ exists for some $x \in R$.
  • 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 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.
(d) : All trigonometric functions are periodic and hence not invertible over their respective domains but all trigonometric functions have inverse over their restricted domains.
Inverse of $\tan ^{-1} x$ is $\tan x$ which is defined for
$
x \in R-(2 n+1) \frac{\pi}{2}, n \in Z
$
$\therefore \quad$ Assertion is false and reason is true.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Assertion (A) : If $A=\left(\begin{array}{ccc}l & 0 & 0 \\ 0 & m & 0 \\ 0 & 0 & n\end{array}\right)$, then
$
A^{-1}=\left(\begin{array}{ccc}
1 / l & 0 & 0 \\
0 & 1 / m & 0 \\
0 & 0 & 1 / n
\end{array}\right)
$
Reason $( R )$ : The inverse of a diagonal matrix is a diagonal matrix.
→
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 linear programming problem, maximize Z = x + 2y subject to constraints $\text{x}-\text{y}\leq10,2\text{x}+3\text{y}\leq20$ and $\text{x}\geq0; \text{y}\geq0.$ It gives the maximum value of Z as $\frac{40}{3}.$
Reason (R): To obtain maximum value of Z, we need to compare value of Z at all the corner points of the shaded region.
  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.
→
Assertion (A) : If the points $\vec{P}=(\vec{a}+\vec{b}-\vec{c})$, $\vec{Q}=(2 \vec{a}+\vec{b})$ and $\vec{R}=(\vec{b}+t \vec{c})$ are collinear, where $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors, then the value of $t$ is -2 .
Reason (R) : If $P, Q, R$ are collinear, then
$
\overrightarrow{P Q} \| \overrightarrow{P R} \text { or } \overrightarrow{P Q}=\lambda \overrightarrow{P R}, \lambda \in R
$
→
Assertion (A) : Bag I contains 3 red and 4 black balls while another bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Then, the probability that it was drawn from bag II is $\frac{35}{68}$.
Reason (R) : By Bayes' theorem,
$
\begin{array}{r}
P\left(\frac{E_1}{A}\right)=\frac{P\left(E_1\right) \cdot P\left(A / E_1\right)}{P\left(E_1\right)\left(A \mid E_1\right)+P\left(E_1\right) \cdot P\left(A \mid E_2\right)+P\left(E_1\right) P\left(A \mid E_3\right)}
\end{array}
$
→
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.
  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
→
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{9}+\frac{\text{y}^2}{4}=1$ the line $\frac{\text{x}}{3}+\frac{\text{y}}{2}=1$ is $\frac{3}{2}(\pi-2)\text{ sq.units}$
Reason: Formula to calculate the area of the smaller region bounded by the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$ and the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ is $\frac{\text{ab}}{4}(\pi-2) \text{ sq.units}$ 
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
→
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 A is an invertible matrix of order 2, and det A = 3 then det( A -1) is equal to $\frac{1}{3}.$
Reason: If A is an invertible matrix of order 2 then det (A -1) = det A.
  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.
→
Assertion (A) : Let $A=\{-1,1,2,3\}$ and $B=\{1,4,9\}$, where $f: A \rightarrow B$ given by $f(x)=x^2$, then $f$ is not one-one function.
Reason (R): If $x_1 \neq x_2 \Rightarrow f\left(x_1\right) \neq f\left(x_2\right)$, for every $x_1, x_2 \in$ domain, then $f$ is one-one.
→
Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: $\int\sin3\text{x}\cos5\text{x}\text{ dx}=\frac{-\cos8\text{x}}{16}+\frac{\cos2\text{x}}{4}+\text{C}$
Reason: $2\cos\text{A}\sin\text{B}=\sin(\text{A+B})-\sin(\text{A-B})$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
→
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: A = {1, 2, 3}, B = {4, 5, 6, 7}, f = {(1, 4), (2, 5), (3, 6)} is a function from A to B.Then f is one - one.
Reason: A function f is one - one if distinct elements of A have distinct images in B.
  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 fals.
→