If A, B and C are angles of a triangle, then the determinant
\(\left|\begin{array}{ccc}-1 & \cos C & \cos B \\ \cos C & -1 & \cos A \\ \cos B & \cos A & -1\end{array}\right|\) is equal to:

The area (in sq. units) of the region bounded by the parabola \(y^2=8 x\) and the line \(x=2\) is

If \(p\) is the probability of any event \(A\) then which one of the following statement is true?

The value of \(\int_0^{\pi / 2} \log _e\left(\frac{5+2 \sin x}{5+2 \cos x}\right) d x\) is

Given relation \(R =\{(x, y): y=x+5, x<4, x, y \in N\}\). Where N is a set of natural numbers then :

The maximum value of \(Z=3 x+4 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

\(\int\left(x+\frac{1}{x}\right)^2 d x\) equals :

Answer the question on basis of passage given below :
Molecular nitrogen is very little reactive chemically. During lightning discharge, atmospheric nitrogen and oxygen combines to form nitric oxide which also combines with oxygen to form nitrogen dioxide. Both NO and \(NO _2\) constitute smog which is very poisonous. It can cause burning sensation in the eyes and adversely affect respiratory system.
What are the constituents of photo chemical smog ?

Arrange the principal values of the following functions in ascending order
(A) \(\operatorname{cosec}^{-1}(2)\)
(B) \(\tan ^{-1}(-\sqrt{3})\)
(C) \(\tan ^{-1}(1)\)
(D) \(\tan ^{-1}\left(\cos \frac{3 \pi}{2}\right)\)
Choose the correct answer from the options given below:

Match List-I (vitamin) with List-II (deficiency disease)

List-l (Vitamin)	List-II (Deficiency disease)
(A) Thiamine	(I) Convulsions
(B) Pyridoxine	(II) Cheilosis
(C) Vitamin E	(III) Retarded Growth
(D) Riboflavin	(IV) Muscular weakness

Choose the correct answer from the options given below :

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

Read the passage carefully and answer the Questions:
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1\) )d, \(n s, n p\) or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/lon. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which of the following is not true about the limitations of VBT:

Choose the correct statements :
(A) If two non ideal batteries are connected in series, then equivalent emf is larger than either of the two
(B) If two non ideal batteries are connected in series, then the equivalent internal resistance is smaller than either of the two.
(C) If two non ideal batteries are connected in parallel, then the equivalent emf is smaller than either of the two
(D) If two non ideal batteries are connected in parallel then the equivalent internal resistance is smaller than the two internal resistances
Choose the correct answer from the options given below :