Image

Q. y(1+xy)dx=xdy

Q.

Let R be the relation in the set N given by R = {(a, b): a = b - 2, b > 6}. Choose the correct answer.
$\left(A\right)(2,4)\in R\left(B\right)(3,8)\in R\left(C\right)(6,8)\in R\left(D\right)(8,7)\in R$

Q.

Solution set of $x=3(mod7),p\in Z,$ is given by

1. $\left\{3\right\}$

2. $\left\{7p–3:p\in Z\right\}$

3. $\left\{7p+3:p\in Z\right\}$

4. None of these

Q. Let $f\left(x\right)=x^3-x^2+x+1$ and $g\left(x\right)=\{\begin{array}{c}max\text{{}f\left(t\right)\text{}},0\le t\le x,0\le x\le 1\\ 3-x,1<x\le 2\end{array},$
Then which among the following options is/are correct for $g\left(x\right)$ in $[0,2]$

1. $g\left(x\right)$ is continuous for all $x$
2. $g\left(x\right)$ is differentiable for all $x$
3. $g\left(x\right)$ is discontinuous at $x=1$
4. $g\left(x\right)$ is not differentiable at $x=1$

Q.

What should be the relation between range and codomain of a function, for a function to be an onto function -

1. Range > Co domain

2. Range = Co domain

3. None of the above

4. Range < Co domain

Q.

Jamey has $4$ quarters, some dimes, and some pennies. If the ratio of quarters to dimes is $8:6$ and the ratio of pennies to dimes is $7:3$, then how many pennies does Jamey have?

Q. If a function is defined from $A$ to $B$ as


then the number of preimages of $3$ is

Q. If $f:N\to R$ is a function defined as $f\left(x\right)=2x^2+1$, then the preimage of $9$ is

Q. Let A = {1, 2, 3} and B = {a, b} , which of the following subsets of A $\times$ B is a mapping From A to B?

1. {(1, a), (3, b), (2, a), (2, b)}
2. None of the above
3. {(1, a), (2, b)}
4. {(1, b), (2, a), (3, a)}

Q. If a function defined from $A$ to $B$ as follows


Then the correct options is/are

1. Image of $2$ under $f$ is $4$
2. Image of $5$ under $f$ is $10$
3. Preimage of $4$ under $f$ is $8$
4. Preimage of $6$ under $f$ is $3$

Q. If a function is defined from $A$ to $B$ as


then the image of $1$ is

Q.

If A = {1, 2, 3, 4, 5, 6, 7, 8, 9} Relation R from A to A by R = {(x, y):y = x + 3}. Find Domain, Co domain and Range of R.

1. Domain = {2, 3, 4, 5, 6}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {4, 5, 6, 7, 8, 9}

2. Domain = {1, 2, 3, 4, 5, 6}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {4, 5, 6, 7, 8, 9}

3. Domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Co-domain = {1, 2, 3, 4, 5, 6, 7, 8, 9}, Range = {1, 2, 3, 4, 5, 6, 7, 8, 9}

4. Domain = {1, 2, 3, 4, 5}, Co-domain = {6, 7, 8, 9}, Range = {6, 7, 8, 9}

Q. Fill in the blanks​:

(vi) ​$12\times 4=\underset{–}{}$ and $12a{x}^2\times 4ax=\underset{–}{}$

Q.

Number of ways of selecting four letters from proportion

Q. If a function is defined from $A$ to $B$ as


then the image of $1$ is

Q. If a function defined from $A$ to $B$ as follows


Then the correct options is/are

1. Image of $2$ under $f$ is $4$
2. Image of $5$ under $f$ is $10$
3. Preimage of $4$ under $f$ is $8$
4. Preimage of $6$ under $f$ is $3$

Q. Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and f , g : A → B be functions defined by f ( x ) = x 2 − x , x ∈ A and . Are f and g equal? Justify your answer. (Hint: One may note that two function f : A → B and g: A → B such that f ( a ) = g( a ) &mnForE; a ∈ A , are called equal functions).

Q.

If $f\left(x\right)=\{\begin{array}{c}{x}^2,whenx<0\\ x,when0\le x<1\\ \frac{1}{x},whenx>1\end{array}$
Find: (i) $f\left(\frac{1}{2}\right)$
(ii) $f(-2)$
(iii) $f\left(1\right)$
(iv) $f\left(\sqrt{3}\right)$
(v) $f\left(\sqrt{-3}\right)$

Q. If $X=\{1,2,3,4,5\}$ and $Y=\{1,3,5,7,9\}$ then which of the following sets are relation from $X$ to $Y$

1. $R_1=\left\{\right(x,a):a=x+2,x\in X,a\in Y\}$
2. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
3. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$
4. $R_4=\left\{\right(1,3),(2,5),(4,7),(5,9),(3,1\left)\right\}$

Q. What is difference between co domain and range

Q. Let $A$ be the set of first $10$ natural numbers and $R$ be a relation on $A$ defined by $(x,y)\in R\iff x+2y=10.$ Then the range of $R$ is

1. $\{1,2,3,\dots ,10\}$
2. $\{2,4,6,8\}$
3. $\{2,4,6,8,10\}$
4. $\{1,2,3,4\}$

Q.

Q. The function $f\left(x\right)=ax+b$ is strictly increasing for all real $x$, if

1. $a=0$
2. $a>0$
3. $a<0$
4. $a\le 0$

Q. The second component of all ordered pairs of a relation is

1. Range
2. Domain
3. none of these
4. mapping

Q. Let $R$ be the relation on $Z$ defined by $R=\left\{\right(a,b):a,b\in Z,a-b\text{is an integer}\}$. Find the domain and range of $R$.

Q. Let $X=\{1,2,3,4\}$ and $Y=\{1,2,3,4\}$. Which of the following is a relation from $X$ to $Y$.

1. $R_1=\left\{\right(x,y)|y=2+x,x\in X,y\in Y\}$
2. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
3. $R_4=\left\{\right(1,3),(2,5),(2,4),(7,9\left)\right\}$
4. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$

Q.

Which of the following is/are correct?

1. Domain of R = set of first components of all the ordered pairs which belong to R

2. Domain of R = set of second components of all the ordered pairs which belong to R

3. Range of R = set of second components of all the ordered pairs which belong to R

4. Range of R = set of first components of all the ordered pairs which belong to R

Q.

1. range f = f

2. range f = R

3. range f = constant

4. range f = {constant}

Q. { (a, 1), (b, 2), (c, 3), (b, 3), (b, 4) }

Q. Let $R$ be the relation on $Z$ defined by $R=\left\{\right(a,b):a,b\in z,a-b$ is an integer$\}$. Find the domain and Range of $R$.

1. $z,z$
2. $z^{+},z$
3. $z,z^{-}$
4. None of these