The function \(f(x)=\frac{x^2-25}{(x+5)}, x \neq-5\) is:

\(\int e^{(x \log 5)} e^x d x\), is :
Where \(c\) is the constant of integration.

If \(y=\sqrt{a x+b}\), then \(y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=\)

The order and degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+x^2\left(\frac{d y}{d x}\right)^3+y=\sin x\) respectively are:

Let \(A=\left[a_{i j}\right]_{2 \times 4}\) and \(B=\left[b_{i j}\right]_{4 \times 2}\), then \(|3 A B|\) is equal to

\(\int e^x\left(\frac{1-x}{1+x^2}\right)^2\) dx is equal to :

Consider the following hypothesis test :
\(H_0: \mu \leq 30\)
\(H_a: \mu>30\)
A sample of 81 provided a sample mean of 29.25 . The population standard deviation is 3 . The value of the test statistic is :

The general solution of the differential equation \((1+y) d x-2 x d y=0\) is :

Two dice are thrown simultaneously. If X denotes the number of sixes, then the variance of X is:

A coil with an inductance of 0.2 H has an inductive reactance of \( 62.8 \, \Omega \) at a certain frequency. The frequency is

Read the given passage and answer the following questions:
Secondary treatment or biological treatment: The primary effluent is passed into large tanks where air is pumped into it. This allows vigorous growth of aerobic microbes. While growing, these microbes consume the major part of the organic matter in the effluent. This significantly change the BOD (biochemical oxygen demand) of the effluent. The effluent in then passed into a tank a small part of the sludge is pumped back into the aeration tank to serve as the inoculum. The remaining major part of the sludge is pumped into large tanks called sludge digesters. Here, other kinds of bacteria grow anaerobically in the sludge. The biogas produced can be used source of energy as it is inflammable. The effluent from the secondary treatment plant is generally released into natural water bodies like rivers and streams.
The greater the BOD of water

Match List - I with List - II.

List - I (Organism)	List - II (Sex chromosomes)
(A) Male grasshopper	(I) XY
(B) Male Drosophila	(II) ZX
(C) Female bird	(III) XX
(D) Female grasshopper	(IV) XO
	(V) ZW

Choose the correct answer from the options given below:

Match List-I with List-II

List-I	List-II
(A) The current lags behind the emf by \( \pi/4 \) in phase	(I) A.C. circuit containing only an inductor
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase	(II) A.C. circuit with resistance and inductances in series
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \)	(III) A.C. circuit containing only as capacitor
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \)	(IV) A.C. circuit with resistance and capacitor in series

Choose the correct answer from the options given below :