The value of the determinant \(\left|\begin{array}{ccc}a+b & b+c & c+a \\ c & a & b \\ 1 & 1 & 1\end{array}\right|\) 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 :

The value of the integral \(\int\left(x^6+x^4\right) d\left(x^2\right)\) is equal to:

The area bounded by the curve \(y=\log x, y=0\) and \(x=e\), is

For \(x>y>0\), if \(x^5 y^6=(x+y)^{11}\), then \(\frac{d^{2} y}{d x^2}\) is

A vector of magnitude 8 units in the direction perpendicular to both the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{k}\) is

A runs 5 times faster than B . If A gives B a start of 100 m , how far must the goal be so that A and B reach there at the same time.

Observe the given figures and answer the question

The conditions created by Miller in his experiment were:

Which of the following material is a semiconductor?

Correct order of the following acids in order of their increasing acidic strength is
(A) \(CCl _3 COOH\)
(B) \(ClCH _2 COOH\)
(C) \(CH _3 COOH\)
(D) \(CHCl _2 COOH\)
Choose the correct answer from the options given below:

Two large plane parallel sheets with equal but opposite surface charge densities \(+\sigma\) and \(-\sigma\). A point charge q placed at points P1, P2, and P3 experiences forces F1, F2, and F3 respectively. Then :

According to Arrhenius equation \(k=A e^{-\frac{E_a}{R T}}\). If In k vs 1/T graph plotted, what will be the intercept of this plot?

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is: