Question
The diagram given below shows that
Image

Answer

(d) : As $f(a)$ is not unique, thus $f$ is not a function.

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Choose the correct answer from the given four options.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6,$ the probability of getting a sum $3,$ is:
The domain of $\sin ^{-1} x+\cos ^{-1} x+\tan ^{-1} x$ is
If $\cot^{-1}(\sqrt{\cos\alpha})-\tan^{-1}(\sqrt{\cos\alpha})=\text{x},$ then $\sin\text{x}$ is equal to:
  1. $\tan^2\Big(\frac{\alpha}{2}\Big)$
  2. $\cot^2\Big(\frac{\alpha}{2}\Big)$
  3. $\tan\alpha$
  4. $\cot\Big(\frac{\alpha}{2}\Big)$
The number of points in $(-\infty,\infty)$ for which $\text{x}^{2}-\text{x}\sin\text{x}-\cos\text{x}=0,$ is:
In linear programming, lack of points for a solution set is said to:
Find the value of $ {\sin ^{ - 1}}\left( 1 \right):$
  1. $ \dfrac{\pi}{7}$
  2. $ \dfrac{\pi}{6}$
  3. $ \dfrac{\pi}{4}$
  4. $ \dfrac{\pi}{2}$
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): Assertion (A):For an objective function Z= 15x + 20y, corner points are (0, 0), (10, 0), (0, 15) and (5, 5). Then optimal values are 300 and 0 respectively.
Reason (R): The maximum or minimum value of an objective function is known as optimal value of LPP. These values are obtained at corner points.
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$\int\frac{\text{x}}{4+\text{x}^4}\text{ dx}$ is equal to:
  1. $\frac{1}{4}\tan^{-1}\text{x}^2+\text{C}$
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