The sum of the order and degree of the differential equation representing the family of curves \(y=m x+m^4\), where \(m\) is arbitrary constant, is

For fixed radii of curvature of a lens, power is proportional to :

The area of triangle with vertices \(P, Q, R\) is given by (where \(\overrightarrow{A B}=\) position vector of point \(B-\) position vector of point \(A\) )

The effective rate that is equivalent to a nominal rate of 16 % compounded semi-annually is :

If \(y=7 \sqrt{x}+3 e^x\), then \(\frac{d^2 y}{d x^2}\) is :

If the corner points of the bounded feasible region for a Linear Programming Problem (LPP) are \(A(0,2), B(3,0), C(2,3)\) and \(D(3,1)\), then the maximum value of the objective function \(Z=4 x+2 y\) occurs at

For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
Choose the correct answer from the options given below :

An object approaches a convex lens from distance with a uniform speed of 3 m/s and stops at the focus. The image

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), \(4 d\) series (Y to Cd), \(5 d\) series ( La and Hf to Hg ) and 6d series which has \(A c\) and elements from \(R f\) to \(C n\). The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and \(p\)-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
The highest oxidation states shown by V , Fe and Ni respectively are __________ .

Some strains of Bacillus thuringiensis produce toxic proteins that do not kill:

Identify the equation representing logistic growth of a population.

The half life of a radioactive nuclide is 20 hours. What fraction of original activity will remain after 80 hours ?

The value of \(\left|\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right|\) is: