The total number of local maxima and local minima of the function
$$f(x) = \left\{ {\matrix{
{{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr
{{x^{2/3}},} & { - 1 < x < 2} \cr
} } \right.$$ is
Consider the system of equations:
$$x-2y+3z=-1$$
$$-x+y-2z=k$$
$$x-3y+4z=1$$
Statement - 1 : The system of equations has no solution for $$k\ne3$$.
and
Statement - 2 : The determinant $$\left| {\matrix{ 1 & 3 & { - 1} \cr { - 1} & { - 2} & k \cr 1 & 4 & 1 \cr } } \right| \ne 0$$, for $$k \ne 3$$.
Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
| Student | Length of the pendulum (cm) |
No. of oscillations (n) |
Total time for(n) oscillations (s) |
Time periods (s) |
|---|---|---|---|---|
| I | 64.0 | 8 | 128.0 | 16.0 |
| II | 64.0 | 4 | 64.0 | 16.0 |
| III | 20.0 | 4 | 36.0 | 9.0 |
If EI, EII and EIII are the percentage errors in g, i.e., $$\left(\frac{\triangle g}g\times100\right)$$ for students I, II and III, respectively,then
Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
