Let \(y=\sin \left(\cos x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to:

The set of points where the function given by \(f(x) = |x - 2|\) is differentiable is:

The value of \(\tan ^{-1} 5+\tan ^{-1} 3-\cot ^{-1} \frac{4}{7}\) is :

If three points \(A \left(a_1, b_1\right), B \left(a_2, b_2\right)\) and \(C \left(a_3, b_3\right)\) are collinear and D is the determinant of their coordinates with a column of 1s, then:

If \(y=a x^2+b x\) has minima at \(x=2\) and the minimum value is -12 , then which of the following are correct?
(A) \(a=3\)
(B) \(a=-3\)
(C) \(b=12\)
(D) \(b=-12\)
Choose the correct answer from the options given below :

The interval in which \(f(x)=2 x^3-9 x^2+12 x+1\) is decreasing is:

The value of \(\int_{-1}^1|x| d x\) is

A radioactive isotope has half-life of ' \(K\) ' years. How long will it take, so that activity reduces to \(6 . 2 5 \%\) of its original value?

For the given five values \(15,24,18,33,42\), the three years moving averages are :

Ravi's speed of rowing in still water is 6 km/hr
The speed of the stream is 3 km/hr
He rows between two points in a river and returns to the same point
He took 30 minutes more to cover the distance upstream than downstream
Find the distance between the two points

On what basis Scandium is considered as transition metal, but Zinc is not considered as transition metal?

If the solubility of the given gases in water decreases in the order of formaldehyde, methane, vinyl chloride, argon.
Match List-I with List-II.

List-I(Gas)	List-II(\((\mathrm{K})_{\mathbf{H}} / \mathrm{k}\) bar)
(A) Formaldehyde	(I) 40.3
(B) Vinyl Chloride	(II) 0.413
(C) Argon	(III) 1.83 x \(\mathrm{10}^{-5}\)
(D) Methane	(IV) 0.611

Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
Which one of the following statements is not a connotation of the theory of special creation?