If A and B are non-singular matrix then, which of the following is incorrect?

(a)

A² = I Iimplies A^-1 = A

(b)

I^-1 = I

(c)

If AX = B, then X = B^-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|²

If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is ________.

(a)

-5

(b)

-125

(c)

-25

(d)

0

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

2

(b)

3

(c)

4

(d)

5

The possible out comes when a coin is tossed five times _________.

(a)

2⁵

(b)

5²

(c)

10

(d)

\(\frac { 5 }{ 2 } \)

The angle between the pair of straight lines x² - 7xy + 4y² = 0 _______.

(a)

\(tan^{-1}\left(1\over 3\right)\)

(b)

\(tan^{-1}\left(1\over 2\right)\)

(c)

\(tan^{-1}\left(\sqrt{33}\over 5\right)\)

(d)

\(tan^{-1}\left(5\over\sqrt{33}\right)\)

If kx² + 3xy - 2y² = 0 represent a pair of lines which are perpendicular then k is equal to _______.

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

The degree measure of \(\frac{\pi}{8}\) is ______.

(a)

20^o60^'

(b)

22^o30^'

(c)

20^o60^'

(d)

20^o30^'

\(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\) ______.

(a)

\(\frac{-\pi}{2}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\pi\)

(d)

\(-\pi\)

The minimum value of the function f(x) = |x| is _______.

(a)

0

(b)

-1

(c)

+1

(d)

\(-\infty \)

\(\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =\)________.

(a)

1

(b)

\(\infty\)

(c)

\(-\infty\)

(d)

\(\theta\)

Average fixed cost of the cost function C(x) = 2x³ +5x² - 14x +21 is _______.

(a)

\(\frac { 2 }{ 3 } \)

(b)

\(\frac { 5}{ x } \)

(c)

\(\frac { 14 }{ x } \)

(d)

\(\frac { 21 }{ x } \)

The maximum value of f(x) = sinx is ________.

(a)

1

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

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

(d)

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

A person brought 100 shares of 9% stock of face value Rs. 100, at a discount of 10%, then the stock purchased is _______.

(a)

Rs. 9000

(b)

Rs. 6000

(c)

Rs. 5000

(d)

Rs. 4000

The present value of the perpetual annuity of Rs. 2000 paid monthly at 10 % compound interest is _______.

(a)

Rs. 2,40,000

(b)

Rs. 6,00,000

(c)

Rs. 20,40,000

(d)

Rs. 2,00,400

If median = 45 and its coefficient is 0.25, then the mean deviation about median is _________.

(a)

11.25

(b)

180

(c)

0.0056

(d)

45

The two events A and B are mutually exclusive if _________.

(a)

\(P\left( A\cap B \right) =0\)

(b)

\(P\left( A\cap B \right) =1\)

(c)

\(P\left( A\cup B \right) =0\)

(d)

\(P\left( AUB \right) =1\)

The regression coefficient of X on Y ________.

(a)

b_xy = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(b)

b_yx = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(c)

b_xy = \(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

(d)

b_y =\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma y^{ 2 }-(\Sigma y)^{ 2 } } } } \)

If two variables moves in decreasing direction then the correlation is ________.

(a)

positive

(b)

negative

(c)

perfect negative

(d)

no correlation

One of the conditions for the activity (i, j) to lie on the critical path is_______.

(a)

E_j - E_i = L_j - L_i = t_ij

(b)

E_i - E_j = L_j - L_i = t_ij

(c)

E_j - E_i = L_i - L_j = t_ij

(d)

E_j - E_i = L_j - L_i ≠ t_ij

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is ______.

(a)

10

(b)

20

(c)

0

(d)

5