If \(x^2-y^2=1\), then which of the following is correct?
(A) \(\left(x^2-1\right)\left(\frac{d y}{d x}\right)^2=x^2\)
(B) \(\left(x^2-1\right)\left(\frac{d^2 y}{d x^2}\right)^2=x^2\)
(C) \(\left(x^2-1\right)^3\left(\frac{d^2 y}{d x^2}\right)^2=x^2\)
(D) \(\left(x^2-1\right)^3\left(\frac{d^2 y}{d x^2}\right)^2=1\)
Choose the correct answer from the options given below :

If A, B and C are angles of a triangle, then the determinant
\(\left|\begin{array}{ccc}-1 & \cos C & \cos B \\ \cos C & -1 & \cos A \\ \cos B & \cos A & -1\end{array}\right|\) is equal to:

\(\int \frac{x+e^{2 z}}{x^2+e^{2 x}} d x=\)

The integral \(\int e^x\left(\log x+\frac{1}{x^2}\right) d x\) equals for some arbitrary constant k

The area of the region bounded by the curve y = x + 1, x-axis and the lines x = 2 and x = 3 is

If \(x=a \cos \alpha+b \sin \alpha\) and \(y=a \sin \alpha-b \cos \alpha\), then \(\left(x \frac{d y}{d x}-y^2 \frac{d^2 y}{d x^2}\right)\) is equal to :

A small start-up started making wafers and distributing them to the retailers. After a week, average sales per week were found to be 150 packets. So, to increase the sales, a strategy was used to change the packaging and add a chocolate worth Rs. 5 as a free gift with the pack. After this, a sample of 17 shops was taken, which showed that sales went up with mean 165 and a standard deviation of 25. Check whether the strategy was effective \(5 \%\), level of significance? [Given \(\left.t_{16}(0.05)=2.12\right]\)

If we plot graph for first order reaction involving reactant \(R\), then it will be a straight line if plotted for :

During ice age between __________ modern Homo sapiens arose.

Arrange the following compounds in decreasing order of their acidity.
(A) Acetic acid
(B) Chloroacetic acid
(C) Dichloroacetic acid
(D) Trichloroacetic acid
Choose the correct answer from the options given below:

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively.
Both pipes A and B are opened together for some time and then pipe B is turned off.
If the tank is filled in 15 minutes, then after how many minutes is pipe B turned off?

In a photoelectric effect, the number of photo electrons emitted per second is directly proportional to

Answer the question on the basis of passage given below :
There are some deposits of nitrates and phosphates in the earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under laboratory conditions, but microbes do it easily. Ammonia forms a large number of complexes with transition metals. Hybridisation easily explains the ease of sigma donation capability of NH₃ and PH₃. Phosphine is an inflammable gas, prepared from white phosphorus.
Which of the following is the correct statement?
A. Between NH₃ and PH₃, NH₃ is a better electron donor because the lone pair of electrons occupy spherical 's' orbital and is less directional.
B. Between NH₃ and PH₃, NH₃ is a better electron donor because the lone pair of electrons occupies sp³ orbital and is more directional.
C. Between NH₃ & PH₃, PH₃ is a better electron donor because the lone pair of electrons occupies sp² orbital and is more directional.
D. Between NH₃ & PH₃, PH₃ is a better electron donor because the lone pair of electrons occupies 's' orbital and is less directional.
Choose the most appropriate answer from the options given below: