Given that at x = 1, the function \(x^4-62 x^2+a x+90\) attains its maximum value on the interval [0, 2], the value of a is:

If A and B are independent events, then which of the following is/are true?
(A) \(\bar{A}\) and B are independent events
(B) \(P(A \cap B)=0\)
(C) \(\bar{A}\) and \(\bar{B}\) are independent events
(D) \(P(A \cap B)=P(A)+P(B)\)
Choose the correct answer from the options given below:

If \(f(x)=x^3 \log _e x\), Then \(f^{\prime \prime}\left(e^2\right)\) is equal to

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:

The function \(f(x)=\cos x\) is strictly decreasing in :

The foot of the perpendicular drawn from the point \((1,6,3)\) to the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) is :

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by r = k[CH₃OCH₃]^3/2. If the pressure is measured in bar and time in minutes, then the unit of rate constant will be

The normal distribution curve is symmetrical about[ \(\mu=\) mean, \(\sigma=\) standard deviation]

In an AC circuit, if the peak voltage is 20 V, then root mean square (rms) voltage will be

The value of \(\int_{0}^{\frac{\pi}{2}} \log \left( \frac{5 + 4 \sin x}{5 + 4 \cos x} \right) dx\) is:

The exine of pollen grains is made up of :