Well defined nucleus is absent in

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ALOK_RAJ Asked Sep 24, 2023

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Write a Short Note on Nucleus.

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Double membrane is absent in

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A function f is defined by $f(x)=2+(x-1)^{2 / 3}$ in [0,2]. Which of the following is not correct?

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Show that the relation R in R defined as $R=\{(a, b): a \leq b\}$ is not symmetric.

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Is the binary operation * defined on set N, given by $a * b=\frac{a+b}{2}$ for all $a, b \in Q$, commutative?

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LEELADHAR YADAV Asked Sep 3, 2023

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It is given that $f(x)$ is a function defined on $N$, satisfying $f(1)=1$ and for any $x \in N$ $f(x+5) \geq f(x)+5 \quad \text { and } \quad f(x+1) \leq f(x)+1$ If $g(x)=f(x)+1-x$, then $g(2016)$ equals

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Show that the function $f$ in $A=R-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$ is one-one and onto. Hence find $f^{-1}$

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$, where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Show that $f$ is invertible. Find the inverse.

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Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Its inverse is -

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The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f(x)=4^{-x^2}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$ is defined, is

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Let $f:[0,4 \pi] \rightarrow[0, \pi]$ be defined by $f(x)=\cos ^{-1}(\cos x)$. The number of points $x \in[0,4 \pi]$ satisfying the equation $f(x)=\frac{10-x}{10}$ is

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LEELADHAR YADAV Asked Aug 22, 2023

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If the binary operation * on the set Z of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.

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LEELADHAR YADAV Asked Aug 22, 2023

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Consider the binary operations $*: R \times R \rightarrow R$ and $o: *: R \times R \rightarrow R$ defined as $a * b=|a-b|$ and $a \circ b=a$ for all $a, b \in R$. Show that ' $x$ ' is commutative but not associative ' $o$ ' is associative but not commutative.

LEELADHAR YADAV Asked Aug 22, 2023

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LEELADHAR YADAV Asked Aug 22, 2023

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Show that the relation S in the set R of real numbers, defined as $S=\left\{(a, b): a, b \in R\right.$ and $\left.a \leq b^2\right\}$ is neither reflexive, nor symmetric nor transitive.

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Let $Z$ be the set of all integers and R be the relation on Z defined as $R=\{(a, b): a, b \in Z$, and $(a-b)$ is divisible by 5} Prove that $R$ is an equivalence relation.

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Let * be a binary operation on Z defined by a * b=a+b−15 . The inverse of element 21 in Z, ) is

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Let * be a binary operation on Z defined by a∗b=a+b−15 for $a, b \in Z$. The identity element in Z, is

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Let * be a binary operation on $\mathrm{N}$ defined by $\mathrm{a}^* \mathrm{~b}=2^{5 \mathrm{ab}} ; \mathrm{a}, \mathrm{b} \in \mathrm{N}$. then the binary operation * is

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LEELADHAR YADAV Asked Aug 17, 2023

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Let * be a binary operation on Z defined by $x^* y=x^2+y^2+x y ; x, y \in Z$. The value of $\left[\left(1^* 2\right)+\left(0^* 3\right)\right]^2$ is

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LEELADHAR YADAV Asked Aug 16, 2023

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Let R be a relation on the set N be defined by $\{(x, y) \mid x, y \in N, 2 x+y=41\}$. Then $R$ is

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LEELADHAR YADAV Asked Aug 16, 2023

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Let L denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R \beta \Leftrightarrow \alpha \perp \beta, \alpha, \beta \in L$. The R is

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Let R_1 be a relation defined by $R_1=\{(a, b) \mid a \geq b ; a, b \in R\}$. Then $R_1$ is

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LEELADHAR YADAV Asked Aug 15, 2023

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The relation R defined in A={1,2,3} by a R b if $\left|a^2-b^2\right| \leq 5$. Which of the following is false :

LEELADHAR YADAV Asked Aug 15, 2023

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LEELADHAR YADAV Asked Aug 15, 2023

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In the set A={1,2,3,4,5} a relation R is defined by $R=\{(x, y) \mid x, y \in A$ and $x<y\}$. Then R is

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LEELADHAR YADAV Asked Aug 15, 2023

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The relation R defined in N as aRbb is divisible by a is

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