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GATE2015139 Video Solution
Consider the operations $\textit{f (X, Y, Z) = X'YZ + XY' + Y'Z'}$ and $\textit{g (X, Y, Z) = X'YZ + X'YZ' + XY}$ Which one of the following is correct? Both $\left\{\textit{f} \right\}$ and $\left\{ \textit{g}\right\}$ ... $\left\{ \textit{g}\right\}$ is functionally complete Neither $\left\{ \textit{f}\right\}$ nor $\left\{\textit{g}\right\}$ is functionally complete
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Set Theory & Algebra
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gate20151
settheory&algebra
functions
difficult
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GATE2015240 Video Solution
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
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Apr 19
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Set Theory & Algebra
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gate20152
settheory&algebra
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GATE2016128 Video Solution
A function $f: \Bbb{N^+} \rightarrow \Bbb{N^+}$ , defined on the set of positive integers $\Bbb{N^+}$,satisfies the following properties: $f(n)=f(n/2)$ if $n$ is even $f(n)=f(n+5)$ if $n$ is odd Let $R=\{ i \mid \exists{j} : f(j)=i \}$ be the set of distinct values that $f$ takes. The maximum possible size of $R$ is ___________.
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Apr 19
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Set Theory & Algebra
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gate20161
settheory&algebra
functions
normal
numericalanswers
videosolution
0
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0
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GATE2015226 Video Solution
Let $f(x)=x^{\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the Xaxis, when $x$ varies from $1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[1, 1]$ $f$ is not bounded in $[1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
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Apr 19
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Calculus
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gate20152
continuity
functions
normal
videosolution
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0
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GATE2014349 Video Solution
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$. For each such function it must be the case that for every ... is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
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Apr 19
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Set Theory & Algebra
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gate20143
settheory&algebra
functions
normal
videosolution
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GATE201432 Video Solution
Let $X$ and $Y$ be finite sets and $f:X \to Y$ be a function. Which one of the following statements is TRUE? For any subsets $A$ and $B$ of $X, fA \cup B = f(A) + f(B)$ For any subsets $A$ and $B$ of $X, f(A \cap B) = f(A) \cap f(B)$ For any subsets $A$ ... $S$ and $T$ of $Y, f^{1}(S \cap T) = f^{1}(S) \cap f^{1}(T)$
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Apr 19
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Set Theory & Algebra
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gate20143
settheory&algebra
functions
normal
videosolution
0
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0
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GATE2014150 Video Solution
Let ܵ$S$ denote the set of all functions $f:\{0,1\}^4 \to \{0,1\}$. Denote by $N$ the number of functions from S to the set $\{0,1\}$. The value of $ \log_2 \log_2N $ is _______.
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Apr 19
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Set Theory & Algebra
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gate20141
settheory&algebra
functions
permutationandcombination
numericalanswers
videosolution
0
votes
0
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GATE20012.3 Video Solution
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S1: f(E \cup F) = f(E) \cup f(F)$ $S2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only S1 is correct Only S2 is correct Both S1 and S2 are correct None of S1 and S2 is correct
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Apr 19
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Set Theory & Algebra
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1
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gate2001
settheory&algebra
functions
normal
videosolution
0
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0
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GATE200625 Video Solution
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left  \left\{j \mid i\in X_j \right\} \right$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
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Apr 19
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Set Theory & Algebra
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gate2006
settheory&algebra
normal
functions
videosolution
0
votes
0
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GATE200337 Video Solution
Let \(f : A \to B\) be an injective (onetoone) function. Define \(g : 2^A \to 2^B\) as: \(g(C) = \left \{f(x) \mid x \in C\right\} \), for all subsets $C$ of $A$. Define \(h : 2^B \to 2^A\) as: \(h(D) = \{x \mid x \in A, f(x) \in D\}\), for all ... always true? \(g(h(D)) \subseteq D\) \(g(h(D)) \supseteq D\) \(g(h(D)) \cap D = \phi\) \(g(h(D)) \cap (B  D) \ne \phi\)
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Apr 19
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Set Theory & Algebra
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3.6k
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1
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gate2003
settheory&algebra
functions
normal
videosolution
0
votes
0
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GATE200543 Video Solution
Let $f: B \to C$ and $g: A \to B$ be two functions and let $h = f o g$. Given that $h$ is an onto function which one of the following is TRUE? $f$ and $g$ should both be onto functions $f$ should be onto but $g$ need not to be onto $g$ should be onto but $f$ need not be onto both $f$ and $g$ need not be onto
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Apr 19
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Set Theory & Algebra
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gate2005
settheory&algebra
functions
normal
videosolution
0
votes
0
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GATE2015254 Video Solution
Let $X$ and $Y$ denote the sets containing 2 and 20 distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being onetoone is ______.
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Apr 19
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Set Theory & Algebra
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gate20152
settheory&algebra
functions
normal
numericalanswers
videosolution
0
votes
0
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GATE201237 Video Solution
How many onto (or surjective) functions are there from an $n$element $(n ≥ 2)$ set to a $2$element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
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Apr 19
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Set Theory & Algebra
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gate2012
settheory&algebra
functions
normal
videosolution
0
votes
0
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GATE19962.1 Video Solution
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, xy)$. The inverse function of $f$ is given by $f^{1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{xy}\right)$ ... $f^{1}(x,y)=\left [ 2\left(xy\right),2\left(x+y\right) \right ]$
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Apr 19
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Set Theory & Algebra
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1
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gate1996
settheory&algebra
functions
normal
videosolution
0
votes
0
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GATE2005IT31 Video Solution
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ ... is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
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Set Theory & Algebra
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gate2005it
settheory&algebra
functions
normal
videosolution
0
votes
0
answers
GATE200339 Video Solution
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the ith prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a nonempty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$
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Apr 19
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Set Theory & Algebra
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3.6k
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1
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gate2003
settheory&algebra
functions
normal
videosolution
0
votes
0
answers
GATE20153GA5 Video Solution
A function $f(x)$ is linear and has a value of 29 at $x=2$ and 39 at $x=3$. Find its value at $x=5$. $59$ $45$ $43$ $35$
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Apr 19
in
Numerical Ability
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3.6k
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1
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gate20153
numericalability
normal
functions
videosolution
0
votes
0
answers
GATE20073 Video Solution
What is the maximum number of different Boolean functions involving $n$ Boolean variables? $n^2$ $2^n$ $2^{2^n}$ $2^{n^2}$
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Apr 19
in
Set Theory & Algebra
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3.6k
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2
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gate2007
permutationandcombination
functions
normal
videosolution
0
votes
0
answers
GATE19961.3 Video Solution
Suppose $X$ and $Y$ are sets and $X \text{ and } Y$ are their respective cardinality. It is given that there are exactly $97$ functions from $X$ to $Y$. From this one can conclude that $X =1, Y =97$ $X =97, Y =1$ $X =97, Y =97$ None of the above
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Apr 19
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Set Theory & Algebra
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3.6k
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2
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gate1996
settheory&algebra
functions
normal
videosolution
0
votes
0
answers
GATE20152GA9 Video Solution
If p, q, r, s are distinct integers such that: $f (p, q, r, s) = \text{ max } (p, q, r, s)$ $g (p, q, r, s) = \text{ min } (p, q, r, s)$ ... operations are valid with two variable functions of the form $f(p, q)$ What is the value of $fg \left(h \left(2, 5, 7, 3\right), 4, 6, 8\right)$?
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Apr 19
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Set Theory & Algebra
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gate20152
settheory&algebra
functions
normal
numericalanswers
videosolution
0
votes
0
answers
GATE20152GA3 Video Solution
Consider a function $f(x) = 1 x \text{ on } 1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the maximum value of the function are: $0, 1$ $1, 0$ $0, 1$ $1, 2$
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Apr 19
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Calculus
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gate20152
settheory&algebra
functions
normal
maximaminima
videosolution
0
votes
0
answers
GATE199713 Video Solution
Let $F$ be the set of onetoone functions from the set $\{1, 2, \dots, n\}$ to the set $\{1, 2,\dots, m\}$ where $m\geq n\geq1$. How many functions are members of $F$? How many functions $f$ in $F$ satisfy the property $f(i)=1$ for some $i, 1\leq i \leq n$? How many functions $f$ in $F$ satisfy the property $f(i)<f(j)$ for all $i,j \ \ 1\leq i \leq j \leq n$?
asked
Apr 19
in
Set Theory & Algebra
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3
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gate1997
settheory&algebra
functions
normal
descriptive
videosolution
0
votes
0
answers
GATE19968 Video Solution
Let $F$ be the collection of all functions $f: \{1, 2, 3\} \to \{1, 2, 3\}$. If $f$ and $g \in F$, define an equivalence relation $\sim$ by $f\sim g$ if and only if $f(3) = g(3)$. Find the number of equivalence classes defined by $\sim$. Find the number of elements in each equivalence class.
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Apr 19
in
Set Theory & Algebra
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2
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gate1996
settheory&algebra
relations
functions
normal
descriptive
videosolution
0
votes
0
answers
GATE20062 Video Solution
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
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Apr 19
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Set Theory & Algebra
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1
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gate2006
settheory&algebra
normal
functions
videosolution
0
votes
0
answers
GATE2006IT6 Video Solution
Given a boolean function $f (x_1, x_2, \ldots, x_n),$ which of the following equations is NOT true? $f (x_1, x_2, \ldots, x_n) = x_1'f(x_1, x_2, \ldots, x_n) + x_1f(x_1, x_2, \ldots, x_n)$ ... $f (x_1, x_2, \ldots , x_n) = f(0, x_2, , x_n) + f(1, x_2, \ldots, x_n)$
asked
Apr 19
in
Set Theory & Algebra
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2
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gate2006it
settheory&algebra
functions
normal
videosolution
0
votes
0
answers
GATE20153GA8 Video Solution
Choose the most appropriate equation for the function drawn as thick line, in the plot below. $x=yy$ $x=(yy)$ $x=y+y$ $x=(y+y)$
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Apr 19
in
Numerical Ability
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3.6k
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1
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gate20153
numericalability
normal
functions
videosolution
0
votes
0
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GATE19981.8 Video Solution
The number of functions from an $m$ element set to an $n$ element set is $m + n$ $m^n$ $n^m$ $m*n$
asked
Apr 19
in
Set Theory & Algebra
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1
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gate1998
settheory&algebra
permutationandcombination
functions
easy
videosolution
0
votes
0
answers
GATE201515 Video Solution
If $g(x) = 1  x$ and $h(x) = \frac{x}{x1}$, then $\frac{g(h(x))}{h(g(x))}$ is: $\frac{h(x)}{g(x)}$ $\frac{1}{x}$ $\frac{g(x)}{h(x)}$ $\frac{x}{(1x)^{2}}$
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Apr 19
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Set Theory & Algebra
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gate20151
settheory&algebra
functions
normal
videosolution
0
votes
0
answers
GATE19938.6 Video Solution
Let $A$ and $B$ be sets with cardinalities $m$ and $n$ respectively. The number of oneone mappings from $A$ to $B$, when $m < n$, is $m^n$ $^nP_m$ $^mC_n$ $^nC_m$ $^mP_n$
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Apr 19
in
Set Theory & Algebra
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3.6k
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1
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gate1993
settheory&algebra
functions
easy
videosolution
0
votes
0
answers
GATE19871II Video Solution
The total number of Boolean functions which can be realised with four variables is: $4$ $17$ $256$ $65, 536$
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Apr 19
in
Digital Logic
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gate1987
digitallogic
booleanalgebra
functions
permutationandcombination
videosolution
0
votes
0
answers
GATE19879b Video Solution
How many onetoone functions are there from a set $A$ with $n$ elements onto itself?
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Apr 19
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Set Theory & Algebra
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3.6k
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gate1987
settheory&algebra
functions
descriptive
videosolution
0
votes
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GATE2018 CH: GA3 Video Solution
For $0\leq{x}\leq{2\pi}$, $\sin x \text{ and } \cos x$ are both decreasing functions in the interval _________ . $\left(0,\dfrac{\pi}{2}\right)$ $\left(\dfrac{\pi}{2},\pi\right)$ $\left(\pi,\dfrac{3\pi}{2}\right)$ $\left(\dfrac{3\pi}{2},2\pi\right)$
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Apr 19
in
Numerical Ability
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gate2018ch
numericalability
functions
trigonometry
videosolution
0
votes
0
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GATE2016 ME2: GA10 Video Solution
Which of the following curves represents the function $y=\ln \left( \mid e^{\left[\mid \sin \left( \mid x \mid \right) \mid \right]} \right)$ for $\mid x \mid < 2\pi$? Here, $x$ represents the abscissa and $y$ represents the ordinate.
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Apr 19
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Numerical Ability
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gate2016me2
functions
numericalability
videosolution
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votes
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GATE198913c Video Solution
Find the number of single valued functions from set A to another set B, given that the cardinalities of the sets A and B are $m$ and $n$ respectively.
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Apr 19
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Set Theory & Algebra
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gate1989
descriptive
functions
videosolution
0
votes
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GATE198813ii Video Solution
If the set $S$ has a finite number of elements, prove that if $f$ maps $S$ onto $S$, then $f$ is onetoone.
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Apr 19
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Set Theory & Algebra
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gate1988
descriptive
settheory&algebra
functions
videosolution
0
votes
0
answers
GATE20014 Video Solution
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b  1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (oneone). Prove that it is also a Surjection (onto)
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Apr 19
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Set Theory & Algebra
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gate2001
functions
settheory&algebra
normal
descriptive
videosolution
0
votes
0
answers
GATE2012 AR: GA7 Video Solution
Let $f(x) = x – [x],$ where $x\geq 0$ and $[x]$ is the greatest integer not larger than $x.$ Then $f(x)$ is a monotonically increasing function monotonically decreasing function linearly increasing function between two integers linearly decreasing function between two integers
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Apr 19
in
Numerical Ability
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gate2012ar
numericalability
functions
normal
videosolution
0
votes
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answers
GATE2015 EC3: GA5 Video Solution
If $x > y > 1,$ which of the following must be true$?$ $\ln x > \ln y$ $e^{x} > e^{y} $ $y^x > x^y $ $\cos x > \cos y$ (i) and (ii) (i) and (iii) (iii) and (iv) (ii) and (iv)
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Apr 19
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Numerical Ability
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gate2015ec3
generalaptitude
numericalability
functions
videosolution
0
votes
0
answers
GATE2018 EE: GA5 Video Solution
Functions $F(a, b)$ and $G(a, b)$ are defined as follows: $F(a, b) = (a − b)^2$ and $G(a, b) = \mid a − b\mid$, where $\mid x \mid$ represents the absolute value of $x$. What would be the value of $G(F(1, 3), G(1, 3))$? $2$ $4$ $6$ $36$
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Apr 19
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Numerical Ability
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gate2018ee
generalaptitude
numericalability
easy
functions
videosolution
0
votes
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GATE2018 ME1: GA9 Video Solution
Which of the following functions describe the graph shown in the below figure? $y=\mid \mid x \mid + 1 \mid 2$ $y=\mid \mid x \mid  1 \mid 1$ $y=\mid \mid x \mid + 1 \mid 1$ $y=\mid \mid x  1 \mid 1 \mid$
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Numerical Ability
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gate2018me1
generalaptitude
numericalability
functions
absolutevalue
videosolution
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