Disjoint

Q.

If $n\left(A\right)=3$ and $n\left(B\right)=6$ and $A\subseteq B$. Then the number of elements in $A\cap B$ is equal to

1. $3$

2. $9$

3. $6$

4. None of these.

Q. How many zeroes does the product of 100! Would contain?

Q.

By using properties of determinants, show that:

Q.

If $A,B$ and $C$are three sets, $A–(B\cap C)$is equal to

1. $(A–B)\cup (A–C)$

2. $(A–B)\cap (A–C)$

3. $(A–B)\cup C$

4. $(A–B)\cap C$

Q.

If A and B are sets, then prove that A - B, $A\cap B$ and B- A are pair wise disjoint.

Q. 22.Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a(ac)+b=0, then the acute angle between a and c is

Q.

If f: A→B and g:B→C are onto , then gof:A→C is:

1. a many-one and onto function

2. a bijective function

3. a many-one and onto function

4. an into function

Q. Let $A=\{1,2\},B=\{1,2,3,4\},C=\{5,6\}$ and $D=\{5,6,7,8\}.$ Verify that:
$\left(i\right)A\times (B\cap C)=(A\times B)\cap (A\times C)$
$\left(ii\right)A\times C$ is a subset of $B\times D$

Q. ntLet A be the set of all quadrilaterals in a plane and R+ be the set of positive real numbers. Prove that the function f:A→R+ defined by f(x) = area of quadrilateral x, is many-one and onto.n

Q. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq XandY\cap Z$ is empty is:

1. $5^2$
2. $3^5$
3. $5^3$
4. $2^5$

Q. 11. Vector a, b, c are coplannar then the value of [a+2b b+2c c+2a] is?

Q.

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

(i) A ∩ B

(ii) B ∩ C

(iii) A ∩ C ∩ D

(iv) A ∩ C

(v) B ∩ D

(vi) A ∩ (B ∪ C)

(vii) A ∩ D

(viii) A ∩ (B ∪ D)

(ix) (A ∩ B) ∩ (B ∪ C)

(x) (A ∪ D) ∩ (B ∪ C)

Q.

Using properties of sets show that

(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.

Q.

If A = {$(x,y):y=e^x,xϵR$} and B = {$x,y:y=e^{-x},xϵR$} , then write $A\cap B$.

Q.

If P (A|B) > P (A), then which of the following is correct:

(A) P (B|A) < P (B) (B) P (A ∩ B) < P (A).P (B)

(C) P (B|A) > P (B) (D) P (B|A) = P (B)

Q.

Assume that P (A) = P (B). Show that A = B.

Q.

If, for some prove that

is a constant independent of a and b.

Q. If A and B are not disjoint sets, then $n(A\cup B)$is equal to

1. n(A)+n(B)
2. n(A)+n(B)-n(A $\cap$ B)
3. n(A)+n(B)+n(A $\cap$ B)
4. n(A)-n(B)
5. n(A) n(B)

Q.

Show that the following four conditions are equivalent:

(i) A ⊂ B (ii) A – B = Φ

(iii) A ∪ B = B (iv) A ∩ B = A

Q. If A and B are disjoint, then $n(A\cup B)$ is equal to

1. n(A)+n(B)
2. n(A).n(B)
3. n(A)
4. n(B)

Q.

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

Q.

Which of the following pairs of sets are disjoint?

1. {3, 4, 5, 6, 7} and {x: x is a natural number and 7≤ x ≤ 10}

2. {x: x is an odd number} and {x: x is an even number}

3. {x: x is a prime number} and {x: x is an even number}

4. {x: x is an odd number} and {x:x is a multiple of 3}

Q.

The condition for 2 sets A and B to be disjoint is

1. A ∩ B = ∅

2. A ∪ B = ∅

3. A - B = ∅

4. B - A = ∅

Q. Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq XandY\cap Z$ is empty is:

1. $5^2$
2. $3^5$
3. $2^5$
4. $5^3$

Q. If $f\left(n\right)=2\cos nx\forall n\in N,$ then $f\left(1\right)f(n+1)-f\left(n\right)$ is equal to

1. $f(n+3)$
2. $f(n+2)$
3. $f(n+1)f\left(2\right)$
4. $f(n+2)f\left(2\right)$

Q. $A$ is a set containing $n$ elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ of $A$ is again chosen. Let ${}^n{C}_2\times k^{n-2}$ be the number of ways of choosing $P$ and $Q$ so that $P\cap Q$ contains exactly two elements.Find $k$ ?

Q. If the conjugate of (x + iy) (1- 2i) be 1 + i then x and y are

1. 3/5, 4/5
2. 3/5, 1/5
3. 3/5, -1/5
4. none of these

Q. Which of the following pairs is/are a disjoint set(s)?

1. A = {x : x is an even prime number}
   B = {x : x is an even number less than 10}
2. C = {x : x is a solution of $x^2-25=0$ }
   D = {x : x is an integer such that x < 5}
3. E = {x : x is a whole number and a multiple of 7 less than 20}
   F = {x : x is a natural number and a multiple of 3}
4. G = {x : x is a natural number}
   H = {x : x is not a positive integer}

Q.

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.

Q. find possible vqlues of a so that f(x) = x^3 - 3(7-a) x^2 - 3(9-a^2)x + 2 has negative point of local minima