If \(f:R\rightarrow R\) is defined by \(f(x)=2x-3\) __________

(a)

\({1\over 2x-3}\)

(b)

\({1\over 2x+3}\)

(c)

\({x+3\over 2}\)

(d)

\({x-3\over 2}\)

The triangle of maximum area with constant perimeter 12m

(a)

is an equilateral triangle with side 4m

(b)

is an isosceles triangle with sides 2m, 5m, 5m

(c)

is a triangle with sides 3m, 4m, 5m

(d)

Does not exist

tan 70°- tan 20°= _____________ 

(a)

tan 50°

(b)

2 tan 50°

(c)

tan 70°

(d)

0

The product of first n odd natural numbers equals

(a)

²ⁿC_n\(\times\)ⁿP_n

(b)

\({ \left( \frac { 1 }{ 2 } \right) }^{ n }\times\)²ⁿC_n\(\times\)ⁿP_n

(c)

\({ \left( \frac { 1 }{ 4 } \right) }^{ n }\times \)²ⁿC_n\(\times\)²ⁿP_n

(d)

ⁿC_n \(\times\)ⁿP_n

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

(a)

12C₆

(b)

12C₆2⁶

(c)

12C₇

(d)

12C₆2⁷

If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then \(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

(a)

1 + \(\alpha ^2+\beta \gamma=0\)

(b)

1 - \(\alpha ^2-\beta \gamma=0\)

(c)

1 - \(\alpha ^2+\beta \gamma=0\)

(d)

1 + \(\alpha ^2-\beta \gamma=0\)

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)

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

Choose the incorrect pair?

(a)

330^o - \(\frac{11\pi}{6}\)radians

(b)

\(\frac{7\pi^c}{3}\) - 200^o

(c)

0^o - 0^c

(d)

2\(\pi\)^c - 360^o

\(\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } } \) dx = _______+C.

(a)

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

(b)

3 log ( 1 + log x)

(c)

2(1 + log x)

(d)

none of these

The probability that in a year of 22^nd century, chosen at random there will be 53 Sundays is

(a)

\(\frac { 3 }{ 28 } \)

(b)

\(\frac { 2 }{ 28 } \)

(c)

\(\frac { 7 }{ 28 } \)

(d)

\(\frac { 5 }{ 28 } \)