Let S = (1, 2, 3), R be (1, 1) (1, 2) (2, 2) (1, 3) (3, 1), what are the elements to-be included to make R reflexive ___________

(a)

(3, 3)

(b)

(2, 3)

(c)

(3, 2)

(d)

none of these

(x²-2x+2)(x²+2x+2) are the factors of the polynomial ___________

(a)

(x²-2x)²

(b)

x⁴-4

(c)

x⁴+4

(d)

(x²-2x+2)²

The product of r consecutive positive integers is divisible by _________

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

The middle term in the expansion of  is \((x- \frac{2}{x})^{12}\) is ______________

(a)

12C₆

(b)

12C₆2⁶

(c)

12C₇

(d)

12C₆2⁷

If \(\begin{bmatrix} 2x+y & 4x \\ 5x-7 & 4x \end{bmatrix}=\begin{bmatrix} 7 & 7y-13 \\ y & x+6 \end{bmatrix}\), then the value of x+y is _________ .

(a)

5

(b)

6

(c)

4

(d)

3

|adj A| =_________ where A is a square matrix of order

(a)

|A|

(b)

|A|²

(c)

|A|³

(d)

I

The rate of change of area A of a circle of radius r is

(a)

\(2\pi r\)

(b)

\(2\pi r\frac { dr }{ dt } \)

(c)

\(\pi { r }^{ 2 }\frac { dr }{ dt } \)

(d)

\(\pi \frac { dr }{ dt } \)

Choose the correct or the most suitable answer from the given four alternatives.
The derivative of \(\cos ^{ -1 }{ (2{ x }^{ 2 } } -1)\) with respect to \(\cos ^{ -1 }{ x } \) is _____

(a)

2

(b)

\(\frac { 1 }{ 2\sqrt { 1-{ x }^{ 2 } } } \)

(c)

\(\frac { 2 }{ x } \)

(d)

\(1-{ x }^{ 2 }\)

\(\int { \frac { { e }^{ x } }{ \left( 1+{ e }^{ x } \right) ^{ 2 } } } \) dx =_______+c

(a)

\(\frac { 1 }{ 1+{ e }^{ x } } \)

(b)

-\(\frac { 1 }{ 1+{ e }^{ x } } \)

(c)

1 + e^x

(d)

\(\frac { \left( 1+{ e }^{ x } \right) ^{ 3 } }{ 3 } \)

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

(a)

\(\frac { 64 }{ 64 } \)

(b)

\(\frac { 49 }{ 64 } \)

(c)

\(\frac { 40 }{ 64 } \)

(d)

\(\frac { 24 }{ 64 } \)