Which of the following tests cannot be used for identifying amino acids?

Let A = \left[ {\matrix{ 1 & 0 & 0 \cr 1 & 1 & 0 \cr 1 & 1 & 1 \cr } } \right] and B = A20. Then the sum of the elements of the first column of B is :

If \left| {\matrix{ {x - 4} & {2x} & {2x} \cr {2x} & {x - 4} & {2x} \cr {2x} & {2x} & {x - 4} \cr } } \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2} then the ordered pair (A, B) is equal to :

If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then {{xz} \over {{y^2}}} is equal to

Let $$A$$ be a matrix such that A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right] is a scalar matrix and |3A| = 108. Then A2 equals :

The number of values of k for which the system of linear equations, (k + 2)x + 10y = k kx + (k +3)y = k -1 has no solution, is :

Let S be the set of all real values of k for which the systemof linear equations x + y + z = 2 2x + y $$-$$ z = 3 3x + 2y + kz = 4 has a unique solution. Then S is :

Suppose A is any 3$$\times$$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I3 and O = O3. If $$\alpha$$A + $$\beta$$A-1 = 4I, then $$\alpha$$ + $$\beta$$ is equal to :

If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is {1 \over {12}}, then the number of children in each family is :

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3$$ black balls. If two balls are drawn at random, without eplacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is :

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of 'p' is :

Let A, B and C be three events, which are pair-wise independent and $$\overrightarrow{E}$$ denotes the completement of an event E. If $$P\left(A\cap B\cap C\right)=0$$ and $$P\left(C\right)>0,$$ then $$P\left[\left(\overline{A}\cap \overline{B}\right)|C\right]$$ is equal to :

If f(x) = sin-1 \left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right), then f'\left( { - {1 \over 2}} \right) equals :

If $$x=\sqrt{2^{\cos e{c}^{-1}}}$$ and $$y=\sqrt{2^{se{c}^{-1}t}}\left(\left|t\right|\ge 1\right),$$ then {{dy} \over {dx}} is equal to :

If x2 + y2 + sin y = 4, then the value of {{{d^2}y} \over {d{x^2}}} at the point ($$-$$2,0) is :

If f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|, then \mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}

The curve satifying the differeial equation, (x2 $$-$$ y2) dx + 2xydy = 0 and passing through the point (1, 1) is :

Let y = y(x) be the solution of the differential equation {{dy} \over {dx}} + 2y = f\left( x \right), where f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right. If y(0) = 0, then y\left( {{3 \over 2}} \right) is :