The binary operation * defined on a set s is said to be commutative if ______

(a)

a*b \(\in \) S ∀ a, b \(\in \) S

(b)

a*b = b*a ∀ a, b \(\in \) S

(c)

(a*b) * c = a*(b*c) ∀ a, b \(\in \) S

(d)

a*b = e ∀ a, b \(\in \) S

If * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is _____________

(a)

20

(b)

40

(c)

400

(d)

445

The number of binary operations that can be defined on a set of 3 elements is _____________

(a)

3²

(b)

3³

(c)

3⁹

(d)

3¹

The identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x \(\in \) R, x ≠ 0} under matrix multiplication is __________

(a)

\(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \)

(b)

\(\left( \begin{matrix} \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \\ \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \end{matrix} \right) \)

(c)

\(\left( \begin{matrix} \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \\ \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \end{matrix} \right) \)

(d)

\(\left( \begin{matrix} \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \\ \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \end{matrix} \right) \)

Which one of the following is not a statement?

(a)

2 + 3 =5

(b)

How beautiful is this flower?

(c)

Delhi is the capital of Tamil Nadu

(d)

A triangle has found angles.

Which of the following is a tautology?

(a)

p ν q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

The identity element in the group {R - {1},x} where a * b = a + b - ab is __________

(a)

0

(b)

1

(c)

\(\frac { 1 }{ a-1 } \)

(d)

\(\frac { a }{ a-1 } \)

Define * on Z by a * b = a + b + 1 ∀ a,b \(\in \) Z. Then the identity element of z is ________

(a)

1

(b)

0

(c)

1

(d)

-1

A binary operation * is defined on the set of positive rational numbers Q⁺ by a*b = \(\frac { ab }{ 4 } \). Then 3 * \(\left( \frac { 1 }{ 5 } *\frac { 1 }{ 2 } \right) \) is _____________

(a)

\(\frac { 3 }{ 160 } \)

(b)

\(\frac { 5 }{ 160 } \)

(c)

\(\frac { 3 }{ 10 } \)

(d)

\(\frac { 3 }{ 40 } \)

If a * b = a²b² - ab then 3 * (1 * 1)

(a)

0

(b)

1

(c)

2

(d)

4

The number whose multiplication universe does not exist in C.

(a)

0

(b)

1

(c)

0

(d)

1

Let p: Kamala is going to school
q: There are 20 students in the class. Then Kamala is not going to school or there are 20 students in the class is represented by

(a)

p v q

(b)

p ∧ q

(c)

~ p

(d)

~ p v q

If p is true and q is unknown, then _________

(a)

~ p is true

(b)

p v (~p) is false

(c)

p ∧ (~p) is true

(d)

p v q is true

'+' is not a binary operation on ___________

(a)

~

(b)

z

(c)

c

(d)

Q- {0}