If the money is worth \(8 \%\) per annum compounded semi-annually, then the present value of a sequence of payments of ₹ 1,000 made at the end of every 6 months and continuing forever, is:

The direction ratios of the line perpendicular to the lines \(\frac{x-5}{2}=\frac{y+11}{-3}=\frac{z+3}{1}\) and \(\frac{x-7}{1}=\frac{y+2}{2}=\frac{z-4}{-2}\) are proportional to :

If A and B are events such that \(P(A \mid B)=P(B \mid A)\), then :

Let \(f(x)=[x]\) and \(g(x)=|x|\). Then gof \(\left(\frac{-5}{3}\right)\) - fog \(\left(\frac{-5}{3}\right)\) where [x] is greatest integer valued function and |x| is modulus function.

The mean of the numbers obtained on throwing a die having 1 on three faces, 2 on two faces and 5 on one face is:

Choose the correct answer from the options given below:
A. Equation of the line passing through the point (1, 2, 3) and parallel to the vector \(3 \hat{i}+2 \hat{j}-2 \hat{k}\) is \(\frac{x-1}{3}=\frac{y-2}{2}=\frac{y-3}{-2}\)
B. Equation of line passing through (1, 2, 3) and parallel to the line given by \(\frac{x+3}{3}=\frac{4-y}{5}=\frac{z+8}{6}\) is \(\frac{x-1}{3}=\frac{y-2}{5}=\frac{z+3}{6}\).
C. Equation of line passing through the origin and (5, -2,3) is \(\frac{x}{5}=\frac{y}{-2}=\frac{z}{3}\).
D. Equation of plane passing through the point (1, 2, 3) and perpendicular to the line with direction ratio's 2, 3, -1 is 2(x - 1) + 3(y - 2) - (z - 3) = 0.
E. Equation of plane with intercepts 2, 3 and 4 on x, y and z-axis respectively is 2x + 3y + 4z = 1

Which of the following is incorrect about the Linear Programming Problem (LPP)?

The average power associated with an ideal capacitor of capacitance \( 5 \ \mu\text{F} \) connected to an alternating emf \( E = 200 \sin 100\pi t \) is:

The standard reduction potential \(\left(E^{\circ}\right)\) values of \(Ag ^{+}\left| Ag , K ^{+}\right| K , Mg ^{2+} \mid Mg\) and \(Cr ^{3+} \mid Cr\) are \(0.80 V,-2.93 V,-2.37 V\) and -0.74 V respectively. The decreasing order of reducing power of the following metals is:
(A)\(A g\)
(B)\(K\)
(C)\(Mg\)
(D)\(Cr\)
Choose the correct answer from the options given below:

\(\int_0^{\pi / 2} \frac{\sin ^8 x}{\sin ^8 x+\cos ^8 x} d x\) is equal to

For a random variable \(X, E(X)=3\) and \(E\left(X^2\right)=11\), then variance of \(X\) is :

The integrating factor of the differential equation \(x \frac{d y}{d x}-y=\sin x\) is :

In the following diagram, to prevent osmosis, if excess pressure is applied on one side of the semipermeable membrane (SPM), then I, II, III and IV are, respectively,

(A) Solution
(B) \(P_{\text {atm }}\)
(C) \(P_{\text {atm }}+\Pi\)
(D) Solvent
Choose the correct answer from the options given below: