Question
A set is said to be convex if

Answer

(c)

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Which of the following is true?
  1. * defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Z.
  2. * defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Q.
  3. All binary commutative operations are associative.
  4. Subtraction is a binary operation on N.
The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}+\text{y}}\text{is}$
  1. $\text{e}^{\text{x}}+\text{e}^{-\text{y}}=\text{C}$
  2. $\text{e}^{\text{x}}+\text{e}^{\text{y}}=\text{C}$
  3. $\text{e}^{-\text{x}}+\text{e}^{\text{y}}=\text{C}$
  4. $\text{e}^{-\text{x}}+\text{e}^{-\text{y}}=\text{C}$
Choose the correct answer from the given four option.
The general solution of $\text{e}^{\text{x}}\cos\text{ydx}-\text{e}^\text{x}\sin\text{ydy}=0$ is:
  1. $\text{e}^{\text{x}}\cos\text{y}=\text{k}$
  2. $\text{e}^{\text{x}}\sin\text{y}=\text{k}$
  3. $\text{e}^{\text{x}}=\text{k}\cos\text{y}$
  4. $\text{e}^{\text{x}}=\text{k}\sin\text{y}$
For the curve $\sqrt{\text{x}}+\sqrt{\text{y}}=1,\frac{\text{dy}}{\text{dx}}$ at $\Big(\frac{1}{4},\frac{1}{4}\Big)$ is:
  1. $\frac{1}{2}$
  2. 1
  3. -1
  4. 0
$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$ is equal to
The function f : R → Z defined by$f(x)=[x]$; where $[$.$]$ denotes the greatest integer function, is
Let $T$ be the set of all triangles in the Euclidean plane, and let a relation $R$ on $T$ be defined as $a R b$ if $a$ is congruent to $b \forall a, b \in T$. Then $R$ is
The function $f(x)=\left\{\begin{array}{cc}|x-3|, & x \geq 1 \\ \frac{x^2}{4}-\frac{3 x}{2}+\frac{13}{4}, & x<1\end{array}\right.$ is
The angle between the lines $\frac{\text{x}-1}{1}=\frac{\text{y}-1}{1}=\frac{\text{z}-1}{2}$ and $\frac{\text{x}-1}{-\sqrt{3}-1}=\frac{\text{y}-1}{\sqrt{3}-1}=\frac{\text{z}-1}{4}$ is:
The whole area of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is :