If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\) , then the possible values of x + y are:

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

If P and Q are non-singular square matrices of the same order, then \(\left(P Q^{-1}\right)^{-1}\) equals

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

A random sample of 100 individuals provides 25 positive responses.
Then the point estimate of the population proportion with positive responses is:

For any two non zero vectors \(\vec{a}\) and \(\vec{b}\)
A. If \(|\vec{a}| = |\vec{b}|\) then \(\vec{a} = \vec{b}\)
B. If \(\vec{a} = \vec{b}\) then \(|\vec{a}| = |\vec{b}|\)
C. \(\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}\)
D. \(\vec{a} \times \vec{b} = \vec{b} \times \vec{a}\)
E. area of the parallelogram = \(\frac{1}{2}|\vec{a} \times \vec{b}|\), where \(\vec{a}\) and \(\vec{b}\) represent the diagonals of the parallelogram.
Choose the correct answer from the options given below:

If \(A\) is a non-singular square matrix of order 3 such that \(A^3=4 A^2\), then the value of \(|A|\) is:

A semiconductor has an electron concentration of \( 8 \times 10^{13} \text{ m}^{-3} \) and hole concentration of \( 2 \times 10^3 \text{ m}^{-3} \). The semiconductor behaves as:

On warming an aldehyde with freshly prepared ammonical silver nitrate solution (Tollen's reagent) a bright silver mirror is produced due to formation of:

Match List - I with List - II.

List - I	List - II
(A) Cloning vector	(I) Sea weeds
(B) β-galactosidase	(II) Selectable marker
(C) Agarose	(III) Ti-plasmid of Agrobacterium tumifaciens
(D) \(a m p^{ R }\) in pBR322	(IV) Chromogenic screening

Choose the correct answer from the options given below :

Match List I with List II

List-I	List-II
A. Benzophenone \(\rightarrow\) Diphenylmethane	I. \(\text{LiAlH}_4\)
B. Benzaldehyde \(\rightarrow\) 1-phenylethanol	II. DIBAL-H
C. Cyclohexanone \(\rightarrow\) Cyclohexanol	III. \(\text{NH}_2\text{NH}_2\text{, KOH}\)
D. Methylbenzoate \(\rightarrow\) Benzaldehyde	IV. \(\text{CH}_3\text{MgBr, H}_2\text{O}\)

" Choose the correct answer from the options given below:

The standard reduction potentials of \(Mg^{2+}/Mg, Pb^{2+}/Pb\) and \(Sn^{2+}/Sn\)
are \(-2.36, -0.13\) and \(-0.14\) V respectively.
The reaction \(X + Y^{2+} \rightarrow X^{2+} + Y\) will be spontaneous when :

The zwitter ion formed in an aqueous solution of glycine is