The absolute maximum value of the function \(f(x) = \sin x + \cos x, x \in [0, \pi]\) is:

The order and degree of the differential equation \(\left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^3 + x^3 \left(\frac{dy}{dx}\right)^5 - \sqrt{x^2+1}\) are respectively:

If \(a>b\) and \(c<0\), then which of the following is NOT correct?
\(a c < b c\)
\(a+c<b+c\)
\(a-c < b-c\)
\(a c>b c\)
Choose the correct answer from the options given below :

A coin is biased so that head is 4 times as likely to occur as tails. If X represents the number of heads when coin is tossed 4 times then \(P(X=2)\) is equal to:

The angle between the vectors \(\hat{i}-2 \hat{j}+\hat{k}\) and \(3 \hat{i}+2 \hat{j}+\hat{k}\) is:

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4} \\ K, & x=\frac{\pi}{4}\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is :

Let \(A=\left[\begin{array}{cc}0 & 2 \alpha+1 \\ 1 & \beta\end{array}\right]\) and \(B=\left[b_{i j}\right]\) be a skew symmetric matrix of order 2 such that \(b_{12}=1\).
If \(A B=I_2\), where \(I_2\) is the identity matrix of order 2 , then :

A polythene piece rubbed with wool is found to have a negative charge of \( 8 \times 10^{-10} \, \text{C} \). What is the number of electrons transferred ?

Let the matrix \(A=\left[a_{i j}\right]_{3 \times 3}\) be defined by
\(a_{i j}=\left\{\begin{array}{ll}2 i+3 j, & i<j \\5, & i=j \\3 i-2 j, & i>j\end{array}\right.\)
The number of elements in the matrix \(A\) which are greater than 7 , is:

An electric source has an emf of 130 V and a terminal voltage of 110 V. If it supplies a terminal current of 20 A, its internal resistance will be

In a potentiometer arrangement for comparing emf of two cells, it was found that a cell of emf 1.25 V gives a balance point at 0.35 m length of the wire. On replacing the cell by another cell, the balance point shifted to 0.63 m. The emf of the second cell is :

The effective rate that is equivalent to a nominal rate of \(12 \%\) compounded quarterly is :

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
The rate constant of a reaction is 2.1 mol L-'s-¹. What is the order of the reaction?