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With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite.
Two boysM and N start from the same point. M walks 5 km south, then turns to his left and walks 6 km, then turns to his right and walks 5 km, and then again turns to his right and walks 6 km. At the same time, N walks 5 km north, then turns to his left and walks 6 km, then turns to his left and walks 10 km, and then again turns to his left and walks 3 km and then turns to his right and walks 5 km.What is the position of N with respect to M?
Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?
From point P, Vikas walks towards the west for 2m, he then turns left and walks for 3m and then turns left and walks for 5m. He then turns left and walks for 4m and then turns left and walks for 2m. He then turns right and walks for 2m and then turns right and walks for 3m till point Q. What is the shortest distance between point P and point Q?
Two girls A and B start walking from the same point. A walks 3 km east, then turns to his right and walks 3 km, then turns to his left and walks 5 km, and then again turns to his left and walks 10 km. At the same time, B walks 3 km west, then turns to his left and walks 3 km, then turns to his right and walks 5 km, and then again turns to his right and walks 10 km. What is the position of B with respect to A now?
Ashita starts from home at 7: 00 am and walk straight from 8 km facing the sun. Then she takes a right turn and walks from 3 km. Then she turns right again and walks for 2 km and then turns left and walks for 1 km and then turn right to walk for 1 km. Then she turns right and travels for 4 km straight. How far is she from the starting point?
Two boys S and T start from the same point. S walks 7 km south, then turns to his right and walks 7 km, then turns to his left and walks 7 km, and then again turns to his left and walks 7 km. At the same time, T walks 7 km north, then turns to his right and walks 7 km, then turns to his right and walks 21 km.What is the position of T with respect to S?
It is said that development follows a definite pattern. A child starts gaining control over his head first then hands and last legs and feet. Which concept of development is referred by this?
In which of the following a strip of definite width and of length suitable for studying vegetation is marked out and plotted, then plants occurring along the strip are recorded?