If \(n\) is the sample size of the population, then degree of freedom in t-distribution is

If the matrix \(A=\left[\begin{array}{ccc}0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0\end{array}\right]\) is skew-symmetric, then:

Let \(f:[-2,2] \rightarrow[-2,2]\) be a function defined by \(f(x)=x|x|\), then \(f\) is:

Which of the following statements are TRUE ?
(A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends.
(B) The price of stocks in the share market repeats after a definite time interval.
(C) The rise and fall of the share market is an example of a cyclic trend.
(D) The rise in prices before festivals is an example of a irregular trend.
Choose the correct answer from the options given below :

If \(f:[3, \infty) \rightarrow A\) defined by \(f(x)=x^2\) is an onto function, then \(A\) is:

If \(2 P(A)=P(B)=\frac{5}{13}\) and \(P(A \mid B)=\frac{2}{5}\), then \(P(A \cap B)\) is

The shortest distance between the following lines :
\(\vec{r}=(\hat{i}+\hat{j}-\hat{k})+s(2 \hat{i}+\hat{j}+\hat{k})\)
\(\vec{r}=(\hat{i}+\hat{j}+2 \hat{k})+t(4 \hat{i}+2 \hat{j}+2 \hat{k})\), where \(s\) and \(t\) are scalars, is :

Which of the following is an example of 'Ex-situ Conservation' of threatened animals and plants?

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?

The corner points of the bounded feasible region of the LPP: Maximise \(Z = x + y\) subject to constraints \(2x + 5y ≤ 100, 8x + 5y ≤ 200 x ≥ 0 y ≥ 0\) are

Read the passage carefully and give the answers to the question :
Does the number of species in a community really matter to the functioning of the ecosystem? This is a question for which ecologists have not been able to give a definitive answer. For many decades, ecologists believed that communities with more species, generally, tend to be more stable than those with less species. According to the International Union for Conservation of Nature and Natural Resources (IUCN) (2004), the total number of plant and animal species described so far is more than 1.5 million.
The following are the various hypotheses proposed in explaining the greatest biological diversity in tropics except :

What will happen during the electrolysis of aqueous solution of \(CuSO_4\) by using platinum electrodes?
A. Copper will deposit at cathode.
B. Copper will deposit at anode.
C. Oxygen will be released at anode.
D. Copper will dissolve at anode.
Choose the correct answer from the options given below:

The integrated rate equation for a first order reaction is \(\frac{kt}{2.303} = \log R_0 - \log R_t\). The straight line graph is obtained by plotting :