In \(\triangle A B C\), which of the following is not true is:
(A) \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=\overrightarrow{0}\)
(B) \(\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{A C}=\overrightarrow{0}\)
(C) \(\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{C A}=\overrightarrow{0}\)
(D) \(\overrightarrow{A B}-\overrightarrow{C B}+\overrightarrow{C A}=\overrightarrow{0}\)
(E) \(\overrightarrow{B A}-\overrightarrow{B C}-\overrightarrow{C A} \neq \overrightarrow{0}\)

The value of \(\int_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x\) is

A proton accelerated through potential difference V has de Broglie wavelength \(\lambda\). On doubling the potential, the de Broglie wavelength of the proton :

Let \(f: R \rightarrow R\) be defined as \(f(x)=10 x\). Then (Where R is the set of real numbers):

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

The cost of type 1 rice is Rs. 20 per kg and type 2 rice is Rs. 30 per kg. If both Type 1 and Type 2 are mixed in the ratio \(2: 3\), then the price per kg of the mixed variety is

The area of the parallelogram of which \(\hat{i}\) and \(\hat{i}+\hat{j}\) are adjacent sides is :

In gamma ray emission from a nucleus.

The common region determined by all constraints of a Linear programming problem is called:

If A and B are two square symmetric matrices of same order, then AB-BA is

Match List-I with List-II

List - I	List - II
(A) E is independent of r	(I) For a point charge
(B) \(E \propto \frac{1}{r}\)	(II) For a short dipole
(C) \(E \propto \frac{1}{r^2}\)	(III) For a linear charge distribution
(D) \(E \propto \frac{1}{r^3}\)	(IV) For a surface charge distribution on an infinite plane sheet

Choose the correct answer from the options given below :

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, 3d series (Sc to Zn), 4d series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has Ac and elements from Rf to Cn. The two series of the inner transition metals; 4f (Ce to Lu) and 5f (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.
Which of the following statements is correct?

A current carrying solenoid of cross-sectional area \( 2 \, cm^2 \) and 2000 turns has a magnetic moment of \( 0.80 \, Am^2 \). The current flowing through the solenoid is