Match List - I with List - II

List - I (Matrix/Equations)	List - II (Values)
(A) \(\left[\begin{array}{cc}2 x+1 & 3 y \\ 0 & y^2-5 y\end{array}\right]=\left[\begin{array}{cc}x+3 & y^2+2 \\ 0 & -6\end{array}\right]\)	(I) \(x = 2, y = - 1\)
(B) \(\left[\begin{array}{ccc}1 & 2 & -1 \\ x & 0 & 3 \\ y & 3 & 4\end{array}\right]\) is symmetric	(II) \(x = 2, y = 2\)
(C) \(\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & -3\end{array}\right]\left[\begin{array}{ll}5 & 2 \\ 0 & y\end{array}\right]=0\)	(III) \(x = - 2, y = 2\)
(D) \(\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]=\left[\begin{array}{cc}4 & 0 \\ -1 & y / 2\end{array}\right]\)	(IV) \(x = 2, y = 0\)

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A boat covers a distance of 24 km upstream and returns to the same point in a total time of 4 hours. If the speed of the boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

The corner points of a bounded feasible region determined by the following system of linear inequalities \(x+3 y \leq 60, x+y \geq 10, x \leq y, x \geq 0, y \geq 0\) are \((0,10),(5,5),(15,15)\) and (0,20). Let \(z=2 p x+q y, p, q>0\). If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

The maximum value of \(\frac{\log x}{x}\) for \(x\) in \([2, \infty)\) is :

The coordinates of the image of the point \(\mathbf{P}(5,4,2)\) in the line \(\vec{r}=(-\hat{i}+3 \hat{j}+\hat{k})+\lambda(2 \hat{i}+3 \hat{j}-\hat{k})\), where \(\lambda\) is a parameter, is

Let \(\vec{a}, \vec{b}\) be two vectors such that \(|\vec{a}|=2,|\vec{b}|=3, \vec{a} \cdot \vec{b}=4\). Then \(|\vec{a}-\vec{b}|\) is equal to :

The remainder when (672 + 541 + 383 + 295 + 101 + 86) is divided by 3, is :

Which statement is/are true for Gabriel phthalimide synthesis?
A. It is used for the preparation of primary and secondary amines
B. It is only used for the preparation of primary amines
C. Aromatic primary amines can not be prepared by this method
D. Only tertiary amines can be prepared
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Three magnetic materials : (A) Paramagnetic, (B) Diamagnetic, (C) Ferromagnetic. The correct order of increasing magnetic susceptibility is :

Read the passage carefully and answer the questions
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, ar

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm. Its refractive index is

At what rate of interest will the present value of a perpetuity of ₹ 500 payable at the end of every 6 months be ₹ 20,000 ?

The current in a resistive series circuit is 7.0 A. On adding a resistance of 1.6 \( \Omega \) in the same circuit in series, the current drops to 5.0 A. The original resistance of the circuit is :