Let X = {a, b,c},y = (1, 2, 3) then \(f:x\rightarrow y\) given by (a, 1) (b, 1) (c, 1) is called ___________

(a)

onto

(b)

constant function

(c)

one one

(d)

bijective

Which one of the following is false?

(a)

(A')' = A

(b)

AUA' = A

(c)

A⋂A' = Ø

(d)

AUA' = U

The logarithmic form of 5² = 25 is ___________

(a)

\({ log }_{ 5 }^{ 2 }=25\)

(b)

\({ log }_{ 2 }^{ 5 }=25\)

(c)

\({ log }_{ 2 }^{ 25 }=2\)

(d)

\({ log }_{ 25 }^{ 5 }=2\)

If 15C_3r = 15 C_r+3 , then r is equal to _________

(a)

5

(b)

4

(c)

3

(d)

2

ⁿC_r + ²ⁿC_r-1 + ⁿC_r-2 =  _________

(a)

ⁿ⁺¹C_r

(b)

⁽ⁿ⁺¹⁾C_r+1

(c)

⁽ⁿ⁺²⁾C_r

(d)

ⁿ⁺²C_r+1

The sum of the digits in the unit's place of all the 4- digit numbers formed by 3, 4, 5 and 6, without repetition, is _______.

(a)

432

(b)

108

(c)

36

(d)

72

Which one of the following statements in false?

(a)

A point \((\alpha,\beta)\) will lie on origin side of the line ax+by+c=0 if a\(\alpha\)+b\(\beta\)+c and c have the same sign

(b)

A point \((\alpha,\beta)\)  will lie on non-origin side of the line ax+by+c=0 if a\(\alpha\)+b\(\beta\) +c and c have opposite sign

(c)

If \(\alpha=\frac{\pi}{2},p=0\) , then the equation xcos\(\alpha\)+ysin\(\alpha\)=p represents x-axis

(d)

If \(\alpha =0,p=0\), then the equation xcos\(\alpha\)+ysin\(\alpha\)=presents x-axis

Find the odd one out of the following:

(a)

\(\begin{bmatrix} 0 & 2 \\ -2 & 0 \end{bmatrix}\)

(b)

\(\begin{bmatrix} 0 & \frac { -7 }{ 2 } \\ \frac { 7 }{ 2 } & 0 \end{bmatrix}\)

(c)

\(\begin{bmatrix} 0 & 3.2 \\ -3.2 & 0 \end{bmatrix}\)

(d)

\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\)

Find the odd one out of the following

(a)

\(\hat { i } +2\hat { j } +3\hat { k } \)

(b)

\(2\hat { i } +4\hat { j } +6\hat { k } \)

(c)

\(7\hat { i } +14\hat { j } +21\hat { k } \)

(d)

\(\hat { i } +3\hat { j } +2\hat { k } \)

\(\lim _{ x\rightarrow \infty }{ \frac { 1+2+3+....+n }{ { 2n }^{ 2 }+6 } } \)

(a)

2

(b)

6

(c)

\(\frac { 1 }{ 4 } \)

(d)

\(\frac { 1 }{ 2 } \)