The sides of an equilateral triangle are increasing at the rate of \(5 cm / sec\). The rate at which the area increases when the side is 20 cm , is

The value of the determinant \(\left|\begin{array}{lll}a-b & b+c & a \\b-c & c+a & b \\c-a & a+b & c\end{array}\right| \text { is : }\)

If a function \(f: R _{+} \rightarrow[-5, \infty)\) given by \(f(x)=9 x^2+6 x-5\) is one-one and onto, then \(f^{-1}(y)\) is

If \(\int_0^1 \frac{e^x}{1+x} d x=K\), then \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is equal to:

If the matrix \(\left[\begin{array}{ccc}0 & 1 & 4 x \\ -1 & 0 & -5 \\ 2 & 5 & y\end{array}\right]\) is skew-symmetric, then :

\(\int \frac{x^3-1}{x^2} d x\) is equal to

If the random variable \(X\) follows the Poisson distribution such that \(P(X=k)=P(X=k+1)\), then the mean value of \(X\) is :

\(7 XeF _4\) and \(XeF _6\) are :

A tank is filled with water to a height of 15 cm. If the refractive index of water is 1.33, the apparent depth of a needle lying at the bottom of the tank will be

Read the passage carefully and answer the questions
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
A first order reaction is one-fifth completed in 40 minutes. Calculate the time required for its 100 % completion

The \(K H\) values of \(HCOOH > CH _4> Ar\) and CO _2 > at \(2 9 8 K\) are \(1 . 8 3 \times 1 0 - 5 ~ k b a r\), \(0.413 kbar , 40 kbar\) and 1.67 kbar respectively. Arrange them in the order of their decreasing solubility at constant pressure :

The property of a medium which determines the electric force between two charges situated in the medium is

In double-slits experiment using light of wavelength 550 nm, the angular width of a fringe formed on a distant screen is 0.2°, What is the spacing between the two slits?