If \(A\) is a square matrix such that \(A^2=A\), then \((I+A)^3-8 A\) is equal to:

Which of the following are normal equations to fit a straight line trend \(y=a+b x\) by the method of least squares?

Let \(f: R \rightarrow R\) be defined as \(f(x)=5 x^2\). Choose the correct answer :

Solution of the inequality \(\frac{2 x+3}{4 x-5} \geq 0\) is

The inverse of the matrix \(A=\left[\begin{array}{cc}a & b \\ c & \frac{1+b c}{a}\end{array}\right]\) is:

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

In a 700 m race, the ratio of speeds of two participants A and B is 5: 6. If A has a start of 150 m, then the distance by which A wins the race is :

In a double slit experiment, if the distance between the slits be reduced to half, then the new fringe width will be

In eukaryotes, the regulation could be exerted at -
(A) Transcriptional level (formation of primary transcript)
(B) Processing level (regulation of splicing)
(C) Transport of mRNA from nucleus to the cytoplasm
(D) Translational level

For the following reaction, which is correct statement \(2 H ^{+}( aq )+2 e^{-} \rightarrow H _2(g)\)
under non-standard conditions.

Phytophagous insects feed on :

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties ?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds vix. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1\) )d, ns np or ns, np, nd 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.
Predict the type of hybridisation state in \(\left[ CoF _6\right]^{3-}\)

Which of the following is/are not the characteristics of wind pollinated flowers ?
A. Light and non-sticky
B. Possess well exposed stamens
C. Large and often feathery stigma
D. Often have many ovules in each ovary.
Choose the correct answer from the options given below :