Consider the following hypothesis test:
\(H _0: \mu \leq 3432\)
\(H _{ a }: \mu>3432\)
A sample of 96 provided a sample mean \(\bar{x}\) = 3648 and sample standard deviation s = 802 then the degree of freedom of t-distribution is:

The value of the integral \(\int_{-1}^1|x| d x\) is :

If \(\vec{a}\) and \(\vec{b}\) represent the diagonals of a square, then

The planes 2x - y + 4z = 5 and \(5 x-\frac{5}{2} y+10 z=6\) are

Let \(A=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right]\),where \(0 \leq \theta \leq 2 \pi\).
Then \(\operatorname{det}(A)\) lies in the interval :

Arrange the following as per statistical inferences :
(A) Data Analysis
(B) Population
(C) Making Inferences
(D) Data Collection
Choose the correct answer from the options given below :

\(\int \frac{d x}{\sqrt{5-4 x-x^2}}\) is equal to :

Match List - I with List - II.

List I (Disease)	List ll (Causal organism)
(A) Pneumonia	(I) Protozoan
(B) Common cold	(II) Roundworm
(C) Malaria	(III) Bacteria
(D) Ascariasis	(IV) Virus

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
The decomposition of \(N_2O_5\ (g)\) is given as
\(N_2O_5(g) \rightarrow 2NO_2(g) + \frac{1}{2}O_2(g)\)
The above reaction is found to be of first order.
Select the correct statement for the half life of the given reaction

The backbone of a polynucleotide chain is formed by:

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/ion. 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.
The spin only magnetic moment of \(\left[ MnBr _4\right]^{2-}\) is 5.9 BM. Predict the geometry of the complex ion?

Identify the incorrect statement about the genetic modification.

The charge flowing in a conductor varies with time as \(q(t) = (8t^2 - 4t + 5)C\). Then the current changes at the rate of :