In the method of least squares, we find trend values using:

A man wishes to ensure that he gets Rs. 75,000/- at the end of each year indefinitely. The amount that he invest now to produce the desired cash flow, if money is worth 2.5% compounded annually is:

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

The standard deviation of a sampling distribution of a statistic is also known as:

If \(f(x)=\left\{\begin{array}{ll}\frac{\tan \left(\frac{\pi}{4}-x\right)}{\cot 2 x}, & x \neq \frac{\pi}{4}, \\ 2 K+1, & x=\frac{\pi}{4},\end{array}\right.\) is continuous at \(x=\frac{\pi}{4}\), then the value of \(K\) is equal to

Area of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is equal to:

Let \(R\) be the relation in the set \(\{1,2,3\}\) given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\). Choose the correct answer.

The term "biodiversity" was popularised by:

Which transition metal ion is most stable against oxidation to its \(+3\) state?

Two coherent light sources have intensities in the ratio 25: 16. The ratio of the intensities of maxima to minima, in the interference pattern due to them would be

If \(\left(t_1, y_1\right),\left(t_2, y_2\right),\left(t_3, y_3\right), \ldots,\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variable \(y\), then \(\sum\left(y-y_t\right)\), the sum of deviations of \(y\) from their corresponding trend value is equal to :

Two capacitors of capacitances \(3 \mu F\) and \(6 \mu F\) are charged to potentials of \(2 V\) and \(3 V\), respectively. Now, if they are connected in parallel, the charge on each of the two capacitors, will be