Consider the LPP, \(\operatorname{Min} Z=2 x-3 y\) subject to the conditions
\(x+y \leq 3\),
\(x \leq 3\),
\(x \geq 0, y \geq 0\)
then the minimum value of the objective function is at the point.

Match List-I with List-II

List - I	List - II
(A) Point of minima of \(f(x)=|x+1|\)	(I) 1
(B) Minimum value of \(f(x)=|x|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0

Choose the correct answer from the options given below :

Two cards are drawn without replacement. The probability distribution of number of aces is given by :

Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{c}=3 \hat{i}+\hat{j}\) be three vectors. If \((\vec{a}+\lambda \vec{b})\) is perpendicular to \(\vec{c}\), then the value of \(\lambda\) is

If \(e^y(x+1)=1\) and \(\frac{d^2 y}{d x^2}=k\left(\frac{d y}{d x}\right)^2\), then \(k\) is equal to

Let \(y=\sin \left(\cos x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to:

Which of the following statements about the Sinking Fund are correct?
(A) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future capital expense.
(B) It is a fund established by a business entity by setting aside revenue over a period of time to fund a future repayment of a long-term debt.
(C) It is set up for any purpose that it may serve.
(D) It is a fund that is accumulated for the purpose of paying off a financial obligation at some future designated date.
Choose the correct answer from the options given below :

Which of the following statements is not correct?

The equation of a plane passing through the points \((1,2,3),(4,2,3)\) and \((-1,0,6)\) is given by:

Answer the question on basis of passage given below :
A ketone \([A]\) which undergoes haloform reaction gives compound \([B]\) on reduction. Compound \([B]\) on heating with sulphuric acid gives compound \([C]\) which forms monozonide \([D]\). The compound [D] on hydrolysis in the presence of zinc dust gives compound [E].
Compound [E] on oxidation gives \(C _2 H _4 O _2\) [F]
The boiling point of \([ A ]\) observed is exceptionally high because of :

The dipole moment of a circular loop carrying a current I is m and the magnetic field at the centre of the loop is \( B_1 \). When the dipole moment is made three times by keeping the current I same, the magnetic field at the centre of the loop becomes \( B_2 \). The ratio of \( B_1 \) and \( B_2 \) is:

After ovulation, the remains of Graafian follicle are transformed into :

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
The product of complete hydrolysis of \(XeF _6\) in the following reaction is
\(XeF _6+ H _2 O \rightarrow ?+ HF\)