If \(V=\frac{4 \pi r^3}{3}\), at what rate in cubic units \(/ sec\) is V increasing when \(r=10\), and \(\frac{d r}{d t}=0.01 ?\)

The area bounded by the curve \(y=x^2|x|, x\)-axis and the ordinates \(x=-1\) and \(x=0\) is given by :

The area of the region given by \(\left\{(x, y): y \geq x^2, y \leq|x|+2\right\} \backslash-\backslash-\backslash-\backslash-\backslash-\) is

If \(A\) is an invertible matrix of order 2 , then \(\operatorname{det}\left((\operatorname{adj} A)^{-1}\right)\) is equal to

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:

If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are:

Which of the following matrix is not skew symmetric matrix?

A p-n junction can act basically as

Out of all isomers of \(\text{C}_4\text{H}_{11}\text{N}\), how many are primary amines?

The half-life of a given radioactive nucleus is 200 days. The mean life of this nucleus is

The secondary ecological succession begins in an area, where :

Enthalpy of atomisation of transition elements can be arranged in increasing order as:
A. \(V\)
B. \(Cr\)
C. \(Mn\)
D. \(Fe\)
E. \(Co\)
Choose the correct answer from the options given below:

The isotope \({ }^{42} K\) has a half life of about 12 hours. What fraction of the initial concentration remains after 48 hours?