An LPP defined by the objective function Z = 2x + 2y has to be maximized.
The corner points are (0,0), (5, 0), (8, 2), (4, 6) and (0,8).
The maximum value occurs at :

If A and B are square matrices of order 3 such that \(|A|=-1,|B|=3\) then \(|3 A B|\) is:

In what ratio, water must be added to dilute honey costing ₹ 320 per liter so that the resulted syrup would be worth ₹ 280 per liter?

If \(\int_0^1 \frac{e^x}{1+x} d x=K\), then \(\int_0^1 \frac{e^x}{(1+x)^2} d x\) is equal to:

A vector of magnitude 8 units in the direction perpendicular to both the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{k}\) is

Match List - I with List - II

List - I	List - II
(A) Line: x = 2y + 1 = z - 1	(I) Crosses xz-plane at (1,0,1)
(B) Line: x + 1 = 2y + 1 = z	(II) Crosses xz-plane at (0,0,1)
(C) Line: x - 1 = 2y = z + 1	(III) Crosses xz-plane at (1,0,-1)
(D) Line: x - 1 = 2y = z - 1	(IV) Crosses xz-plane at (1,0,2)

Choose the correct answer from the options given below:

The function \(f(x)=\frac{x}{(x-2)(x-3)(x-5)}, x \in R\) is :

In a series LCR circuit, \( C = 5 \text{ }\mu\text{F} \) and \( \omega = 1000 \text{ rad/s} \). The value of inductance L for which the current is maximum in this circuit will be :

The distance between the y-axis and the point (1, 2, 3) is:

If \(I=\int \frac{x^4+x^2+1}{x^2-x+1} d x=a x+\beta x^2+\gamma x^3+\delta\), where \(\delta\) is the constant of integration, then \((a+2 \beta+3 \gamma)\) equals

Match List-l with List-II

List-l (Terms)	List-II (Features)
(A) Selectable marker	(I) Site that commonly used for cutting the DNA by restriction enzyme
(B) Origin of replication	(II) Removes nucleotides from the ends of the DNA
(C) Exonuclease	(III) Helps in identification and elimination of non- transformants
(D) Recognition site	(IV) The sequence responsible for controlling the copy number of linked DNA

Choose the correct answer from the options given below:

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, ns, np 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.
Which among the following are diamagnetic complexes?
\(\left[Ni(CN)_4\right]^{2-},\left[Co\left(C_2 O_4\right)_3\right]^{3-},\left[Fe(CN)_6\right]^{4-},\left[CoF_6\right]^{3-},\left[Mn(CN)_6\right]^{3-}\)

The figure shows an arrangement of bar magnets in different configurations. Each bar magnet has a magnetic dipole moment m. The figure which has the maximum magnetic dipole moment _______ .