Cartesian Product

Q. If A = {1, 3, 5} and B = {2, 3} then find A × B and B × A

1. A × B = {(1, 2), (3, 2), (5, 2), (1, 3), (3, 3), (5, 3)}
   B × A = {(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)}
2. A × B = {(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)}
   B × A = {(2, 1), (2, 3), (2, 5), (3, 1), (3, 3), (3, 5)}
3. A × B = {(1, 2), (3, 2), (5, 2), (1, 3), (3, 3), (5, 3)}
   B × A = {(2, 1), (3, 1), (2, 3), (3, 3), (2, 5), (3, 5)}
4. A × B = {(2, 1), (2, 3), (2, 5), (3, 1), (3, 3), (3, 5)}
   B × A = {(1, 2), (1, 3), (3, 2), (3, 3), (5, 2), (5, 3)}
   

Q. If A and B are skew symmetric matrices then (AB - BA) is a matrix and (AB + BA) is a matrix.

1. skew - symmetric
2. symmetric matrix
3. null matrix
4. identity matrix

Q. If A × B = { (3, 2), (3, 4), (5, 2), (5, 4) } then find A and B.

1. A = {3, 5}
   B = {2, 4}
2. A = {5, 3}
   B = {4, 2}
3. A = {4, 2}
   B = {5, 3}
   
4. A = {5, 2}
   B = {4, 3}

Q. Given that the eqn 12x-4x-5x+2 has two zeros equal find all the zeros.

Q. If 3^2017 is divided by 10 then the remainder is

Q.

Let $A=\{1,2,3,......,10\}$ and$f:A\to A$ be defined as $f\left(k\right)=\left\{\begin{array}{l}k+1\\ k\end{array}\left.\begin{array}{r}ifkisodd\\ ifkiseven\end{array}\right\}\right.$. Then the number of possible functions $g:A\to A$ such that $gof=f$ is:

1. ${10}^5$

2. $C_5^{10}$

3. $5^5$

4. $5!$

Q.

If $\left(1,3\right),\left(2,5\right)$ are $\left(3,3\right)$ three elements of $\left(A\times B\right)$ and the total number of elements in $\left(A\times B\right)$ is $6$, then the remaining elements of $A\times B$ are

1. $(1,5);(2,3);(3,5)$

2. $(5,1);(3,2);(5,3)$

3. $(1,5);(2,3);(5,3)$

4. none of these

Q.

1. 2

2. 1

3. 0

4. -2

5. -1

Q. If 3 + 8 = 17; 5 – 2 = 23; 6 × 2 = 72, then 8 ÷ 4 = ?

Q. 38. a/ax-1 + b/bx-1 = a+b

Q. Cos a + cos b - cos ( a+ b) = 1.5 then which of the following is true ? 1] , a+ b = 0 2], a= 2b 3], a= b 4], 2a= b

Q. If 3 × 5 × 7 + a, 5 × 7 × 11 + b and 7 × 11 × 13 + c are composite numbers, where a, b, c are distinct prime numbers, then the number of possible pairs of (a, b, c) is

यदि 3 × 5 × 7 + a, 5 × 7 × 11 + b तथा 7 × 11 × 13 + c संयुक्त संख्याएं हैं, जहाँ a, b, c भिन्न अभाज्य संख्याएं हैं, तब (a, b, c) के संभावित युग्मों की संख्या हैं

1. 12
2. 15
3. 14
4. 13

Q.

Find the G.P. if

(a) T₃ : T₆ = 1 : 8 and T₅ = 64

(b) T₄ : T8 = 1 : 81 and T₆ = 486

(c) S₁₀ : S₅ = 33 : 1 and T₆ = 32

(d) S₈ : S₄ = 97 : 81 and T₅ = 16

Q. If a2+b2=1 then find the value of 1+b+ia/1+b-ia

Q. x+y=7 x+y=11

Q. $\frac{3}{5}$ $\frac{2}{3}$.

1. $<$
2. $>$
3. =

Q. If x+1/x=3 then x3 + 1/x3=?

Q. If $A\times B\subseteq C\times D\text{and}A\times B\ne \varphi$, then which of the following is/are must be true?

1. $A\subseteq C$
2. $C\subseteq A$
3. $B\subseteq D$
4. $D\subseteq B$

Q. If $A\times B=\left\{\right(a,1),(a,2),(a,3),(b,1),(b,2),(b,3\left)\right\},$ then $n\left(A\right)+n\left(B\right)=$ .

1. 4
2. 5
3. 6
4. 7

Q. If A = {a, b}, B = {b, c} and C = {b, c, d} ; then A $\times$ (B $\cup$ C) = _____ .

1. (A $\cup$ B) $\cup$ C
2. (A $\times$ B) $\cup$ (A $\times$ C)
3. (A $\cup$ B) $\times$ C
4. (A $\cap$ B) $\times$ C

Q.

Expand the following

(1)

(2)

(3)

(4)

(5)

(6)

Q. If P(AnB) =1/2, P(Abar n Bbar) = 1/2 & 2P(A)=P(B)=P, then value of P is equal to. 1. 1/2 2. 2/3 3. 1/4 4.1/3

Q.

7*8=54;5*3=16;2*7=?

Q. If A = {x $\in$ N | 1 < x < 4},
B = {x $\in$ W | 0 $\le$ x < 2}
and C = {x $\in$ N | x < 3}.
Find (A $\times$ B) $\cup$ (A $\times$ C)

1. {(0, 2), (1, 2), (2, 2), (0, 3), (1, 3), (2, 3)}
2. {(2, 0), (2, 1), (3, 0), (3, 1)}
3. {(2, 1), (2, 2), (3, 1), (3, 2)}
4. {(2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2)}

Q.

Find the G.P. if

(1) (a) T_n = 2 × 5⁽ⁿ⁻¹⁾

(b) T_n = 2 × 3⁽ⁿ⁻¹⁾

(c) T₇ = 243 and r = 3

(d)

(e)

Q.

Find the G.P. if

(1) (a) T_n = 2 × 5⁽ⁿ⁻¹⁾

(b) T_n = 2 × 3⁽ⁿ⁻¹⁾

(c) T₇ = 243 and r = 3

(d)

(e)

Q. A-(B∩C) = A∩(B∩C)' = _________ = (A∩B')∪(A∩C') = (A-B)∪(A-C)

1. A∩(B'∪C')
2. (A∩B')C'
3. A∩(B'-C')
4. A(B'∪C')

Q. x3=a+1 x+b/x=a find the value of

Q.

1. a = 4/3 , b = 0, c = 3/2

2. a = 3/4 , b = 3, c = 3/2

3. a = 3/4 , b = 3, c = 3/2

4. a = 4/3 , b = 2, c = 4/3

5. a = 4/3 , b = 2, c = 3/2

Q. ntIf (x+a)/(b+c) + (x+b)/(c+a) + (x+c)/(a+b) + 3 = 0, a>0, b>0, c>0, then the value of x isn