The matrix \(A = \begin{bmatrix} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{bmatrix}\) is a

The second order derivative of \(x^3\) log x is:

Consider the following hypothesis test :
\(H_0: \mu=15\)
\(H_a: \mu \neq 15\)
A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is

A random variable X has the following probability distribution :

X	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Then the values of ' \(a\) ' and \(P(0<X<5)\) respectively are :

Let \(\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{ll}-4 & -2 \\ -8 &-4\end{array}\right|\). Then :
(A) \(x=-4\)
(B) \(x=-6\)
(C) \(x=4\)
(D) \(x=6\)
Choose the correct answer from the options given below :

The function \(f:[0, \infty) \rightarrow R\) defined by, \(f(x)=2 x^2+3\), is:

The corner points of the feasible region of a LPP with the constraints \(x+2 y \leq 40,3 x+y \geq 30,4 x+3 y \geq 60, x, y \geq 0\) are

Which of the following are not involved in intra uterine devices?
(A) Lippes Loop
(B) LNG-20
(C) Saheli
(D) Implants
Choose the correct answer from the options given below:

\( P_1, P_2, P_3 \) are three Polaroid sheets; \( P_1 \) and \( P_3 \) are two crossed polaroids. What should be the angle between Polaroids \( P_1 \) and \( P_2 \), so that the value of \( I' = I_0/4 \)? (Where \( I' \) is intensity after \( P_2 \))

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance that absorbs. In physiosorption the attractive forces are mainly van der Waal's forces while in chemisorption ionic/covalent bonds are formed between particles of adsorbent and adsorbate. The catalytic activity of finely divided iron in Haber's process of ammonia manufacture can be explained by adsorption theory. Adsorption being an exothermic process, the heat of adsorption is utilised in enhancing the rate of the reaction. Adsorption has many applications being used in gas masks, control of humidity, chromatograph separation, curing diseases etc.
Which of the following is not a surface phenomenon?

Speed of Electromagnetic wave is not the same :

A pure inductor of 70 mH is connected to a source of 220 V. The frequency of the source is 50 Hz. The current in the circuit is:

The angle between the planes whose equations are \(4 x+8 y+z=8\) and \(y+z=4\) is: