The value of integral \(I=\int \frac{1-\sin x}{\cos ^2 x} d x\) is:

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is

Which of the following are correct?
(A) If \(A\) and \(B\) are symmetric matrices such that \(A B=B A\), then \(A B\) is symmetric.
(B) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A+B)\) is a symmetric matrix.
(C) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B-B A)\) is a symmetric matrix.
(D) If \(A\) and \(B\) are symmetric matrices of the same order, then \((A B+B A)\) is a skew-symmetric matrix.
Choose the correct answer from the options given below :

The corner points of the bounded feasible region for an LPP are (0,4), (4, 4), (6, 6), (0, 12).
If the objective function is \(Z=p x+q y, p>0, q>0\) then the condition on p and q so that the maximum of Z occurs at (6, 6) and (0, 12) is

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

Mr. X wishes to purchase a flat for Rs. 44, 60, 800 with a down payment of Rs. 10,00,000 and the balance in equal monthly instalments (EMI) for 20 years. If the bank charges 7.5% per annum compounded monthly, then the EMI is :
[Given that \((1.00625)^{240}=4.4608\) ]

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^5+x^3+x+2\right) d x\) is:

A sample of HCl gas is placed in an electric field of \(3 \times 10^4 \mathrm{~N} \mathrm{C}^{-1}\). The dipole moment of each HCl molecule is \(6 \times 10^{-30} \mathrm{C} \mathrm{m}\). The maximum torque that can act on this molecule is :

In a typical test cross:

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The standard Oxidation potential \(E^0\) for the half cell reactions are
\(Zn \rightarrow Zn ^{2+}+2 e^{-}: E^0=+0.76 V\)
\(Fe \rightarrow Fe ^{2+}+2 e^{-}: E^0=+0.41 V\)
The emf of cell \(Fe ^{2+}+ Zn \rightarrow Zn ^{2+}+ Fe\) is

Chromosomal theory of inheritance was given by:

If a sample has \(n\) observations \(x_1, x_2, \ldots, x_n\) with \(m\) constraints on these values, then the degree of freedom of the sample statistic is:

Which of the following combinations are correct?

Enzyme	Final product formed
A. Maltase	Glucose
B. Pepsin	Ammonia and \(CO _2\)
C. Urease	Amino acid
D. Zymase	Ethanol and \(CO _2\)
E. Diastase	Glucose

Choose the correct answer from the options given below :