Which of the following can be an objective function for a Linear Programming problems in two variables x and y?

The corner points of the feasible region with the constraints \(x+y \leq 30, x+y \geq 15, y \leq 20, x \leq 15\), and \(x, y \geq 0\) are

If \(x=a t^2\) and \(y=2 a t\), then \(\frac{d^2 y}{d x^2}=\)

(A) The degree of differential equation \(\frac{d^2 y}{d x^2}+\sin \left(\frac{d y}{d x}\right)=0\) is 2
(B) The degree of differential equation \(\frac{d}{d x}\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3+\sin x=0\) is 1
(C) The order of differential equation \(2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0\) is 2
(D) The number of arbitrary constants in a particular solution of a differential equation of third order are 3
(E) The integrating factor of the differential equation \(\frac{d y}{d x}-y=\cos x\) is \(e^{-x}\)
Choose the correct answer from the options given below:

The value of the determinant \(\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}\) is:

If \(x y=e^{(x-y)}\), then \(\frac{d y}{d x}\) is equal to:

Let \(A\) be a non-singular square matrix of order \(n\) with \(|\operatorname{adj} A|=64\) and \(|A|=4\), then ' \(n\) ' is :

In some plants, the ovary develops into fruit without fertilization. This phenomenon is called:

Match List - I with List - II

List - I	List - II
(A) \([Ni(CN)_4]^{2-}\)	(I) \(EDTA^{4-}\)
(B) bidentate	(II) paramagnetic
(C) chelate ligand	(III) diamagnetic
(D) \([Ni(Cl)_4]^{2-}\)	(IV) oxalate

Choose the correct answer from the options given below:

The unit vector in the xy-plane, making an angle of \(60^{\circ}\) with the positive direction of x-axis is:

Answer the question on basis of passage given below :
P block elements are placed in groups 13 to 18 of the periodic table. Their valence shell electronic configuration is \(ns^2 np^{1-6}\). Group 16 of the p block elements are known as the group of chalcogens having \(ns^2 np^4\) as their general electronic configuration. They exhibit number of oxidation states but the stability of \(- 2\) oxidation state decreases down the group. They are sometimes also known as group of chalcogens as the name is derived from the Greek word for brass and points to the association of sulphur and its congeners with copper. Their ionisation enthalpy decreases down the group. Oxygen shows anomalous behaviour due to its small size and high electronegativity.
What will be the products formed in the following equation?

If \(x=4 t\) and \(y=\frac{4}{t}\), then \(\frac{d^2 y}{d x^2}\) is

GEAC is: