Find the maximum value of the function sin x(1 + cos x) is:

Slope of the tangent to the parabola \(y^2=x+2\) at a point in the 1st quadrant and lying on the line \(y=x\) is:

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

The general solution of the differential equation \(\frac{d y}{d x}=-4 x y^2\) is given by

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

If \(\vec{a}=2 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\vec{c}=-\hat{i}+\hat{k}\) are three vectors, then the area (in sq, units) of the parallelogram whose diagonals are \((\vec{b}+\vec{c})\) and \((\vec{a}+\vec{c})\) is

Using the concept of differentials,\(\sqrt{36.6}\) is approximately equal to:

Which of the following is NOT a characteristic of Down's Syndrome?

The area bounded by the curve \(y=x|x|, x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:

Arrange the given geological periods according to their occurrence from oldest to latest order?
(A) Devonian
(B) Cretaceous
(C) Triassic
(D) Carboniferous
Choose the correct answer from the options given below:

Statins are produced by:

The volume of a cube is increasing at the rate of \(27 cm^3 / s\). How fast is the surface area increasing when the length of the cube is 12 cm ?

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 viz. 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.
Which of the following pair of ions is colourless according to CFT ?