Cartesian Product

Q. Let A = { x , y , z} and B = {1, 2}. Find the number of relations from A to B.

Q. The function f:R→ R defined as f(x)=(x-2)(x-3)(x-4) is(a) one -one but not onto(b)bijective(c)onto but not one -one(d)neither one-one nor ont

Q. consider set A = {x1, x2, x3, x4, x5} and set B = {y1, y2, y3} function f is defined from A to B. 1.> number of onto functions from A to B such that f(x1)=y1

Q. ntlet f(x) =ax3+bx2 +cx +d, a not equal to 0.if f(x) is one one and onto which of following is correct n ntb2<3acn ntb2>3acn ntb2=3acn

Q. 28. The value of m in -3(m-2)>12 is

Q. If A × B = {( a , x ), ( a , y ), ( b , x ), ( b , y )}. Find A and B.

Q. Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Q. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

Q. Product of two odd functions is

1. Neither even nor odd
2. Cannot be determined
3. Even function
4. Odd function

Q.

$\left[12\times \left(-7\right)\right]\times 5=\_\_\_\times \left[\left(-7\right)\times \_\_\_\right]$

Q. If a, b, c are in A.P. and a2, b2, c2 are inGP. such that a < b < c and a + b +c=3/4then the value of a is

Q. What is the integral of 1/3x+5 wrt x?

Q. 149. If f(x)=ax+b/cx+d, then (fof)(x)=x, prove that d+a=0

Q. The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.

Q. If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

Q. Let A and B be two sets such that n (A) = 3 and n (B) = 2. If ( x , 1), ( y , 2), ( z , 1) are in A × B, find A and B, where x , y and z are distinct elements.

Q.

Product of two odd functions is

1. Even function
2. Odd function
3. Neither even nor odd
4. Cannot be determined

Q. 49. If a, b, c, d, e are in H.P. then find the value of. ab+bc+cd+de/ae

Q. State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly. (i) If P = { m , n } and Q = { n , m }, then P × Q = {( m , n ), ( n , m )}. (ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs ( x , y ) such that x ∈ A and y ∈ B. (iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ ) = Φ .

Q.

Product of two odd functions is

1. Even function

2. Odd function

3. Neither even nor odd

4. Cannot be determined

Q.

Let set A = {1, 2, 3}, set B = {2, 3, 4}, set C = {4, 5}. Find (A ∩ B) $\times$ C.

1. {(2, 4), (2, 5), (3, 4), (3, 5)}

2. {(4, 2), (5, 2), (4, 3), (5, 3)}

3. {(1, 2), (1, 3), (2, 3), (2, 4)}

4. {(2, 3), (2, 4), (3, 5), (3, 4)}

Q. If $A=\{x:x^2-3x+2=0\}$ and $R$ is a universal relation on $A,$ then $R$ is

1. $\left\{\right(1,1),(2,2\left)\right\}$
2. $\left\{\right(1,1\left)\right\}$
3. $\left\{\varphi \right\}$
4. $\left\{\right(1,1),(1,2),(2,1),(2,2\left)\right\}$

Q. The exradii $r_1,r_{2}and{r}_3$ of a $△$ABC are H.P , then its sides a, b, c are in

1. HP

2. AP

3. GP

4. None of these

Q. If the coordinates of the points $A$ and $B$ in a plane are $(1,1)$ and $(1,2)$ respectively, find the
coordinates of $C$ (in the plane) such that $\overrightarrow{AB}$ and $\overrightarrow{BC}$ are equal.

Q. If (n + 1)! = 90 [(n − 1)!], find n.

Q. S/r1+s/r2+s/r3-s/r is equal to

Q. Let z1, z2 and z3 be 3 distinct complex no.s.If |z1|=|z2|=|z3|=1 , then prove that |(z1 z2)+(z2 z3)+(z1 z3)|=|z1+z2+z3|

Q. If A = {–1, 1}, find A × A × A.

Q. If f:[0, infinity) to [0, infinity) and f(x)=x/(1+x), then f is

Q. If $(x+3,5)=(7,2x+y),$ then $x=$ and $y=$ .

1. -4
2. 4
3. -3
4. 3