To determine the correct statements, we need to analyze each given statement:
(A) Weight of a substance is the amount of matter present in it.
This is incorrect. The weight of a substance refers to the force of gravity acting on its mass. The mass, on the other hand, is the amount of matter in a substance.
(B) Mass is the force exerted by gravity on an object.
This is incorrect. The force exerted by gravity on an object is referred to as its weight, not its mass.
(C) Volume is the amount of space occupied by a substance.
This statement is true. Volume is indeed the measure of the amount of three-dimensional space an object occupies.
(D) Temperatures below 0°C are possible in Celsius scale, but in Kelvin scale negative temperature is not possible.
This statement is true. In the Kelvin scale, 0 K is the absolute zero point, and temperatures cannot go below this value. In the Celsius scale, temperatures can go below 0°C.
(E) Precision refers to the closeness of various measurements for the same quantity.
This statement is true. Precision is defined as the degree to which repeated measurements under unchanged conditions show the same results.
After analyzing the statements, the correct option is:
(C), (D) and (E) Only
Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
|---|---|---|---|
| A. | Boltzmann constant | I. | \( \text{ML}^2\text{T}^{-1} \) |
| B. | Coefficient of viscosity | II. | \( \text{MLT}^{-3}\text{K}^{-1} \) |
| C. | Planck's constant | III. | \( \text{ML}^2\text{T}^{-2}\text{K}^{-1} \) |
| D. | Thermal conductivity | IV. | \( \text{ML}^{-1}\text{T}^{-1} \) |
Choose the correct answer from the options given below :
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to: