Everything From Algebra To Physics! Only The Smartest Can Crack This Test.

Explanation
The magnitude of the vector product of a vector with itself is always zero. This is because the vector product of a vector with itself is a cross product, and the cross product of any vector with itself is always zero. Therefore, the correct answer is 0.

Explanation
The given polynomial equation, 3x^2 + 2√x + 7 = 0, is a polynomial over the set of natural numbers (N). This is because the equation contains only whole number coefficients (3, 2, and 7) and the variable x is not restricted to any specific set. Therefore, the equation can be solved using natural numbers as possible solutions.

Explanation
The inverse of a column matrix does not exist. Inverse matrices are only defined for square matrices, and a column matrix is not a square matrix. Therefore, the correct answer is "None of these".

Explanation
An infinite geometric sequence is defined as a sequence in which each term is obtained by multiplying the previous term by a constant factor. Since the given sequence contains all the numbers from the set of real numbers (R), it cannot be a geometric sequence because a geometric sequence has a common ratio between consecutive terms. In this case, there is no constant factor that can be multiplied to obtain the next term. Therefore, the given sequence cannot be a geometric sequence.

Explanation
To find the 15th term of an arithmetic progression (A.P.), we need to determine the common difference first. The difference between the 7th and 12th terms is 49 - 24 = 25. Since there are 5 terms between the 7th and 12th terms, the common difference is 25/5 = 5. Now, we can find the 15th term by adding 5 to the 12th term. Thus, the 15th term is 49 + 5 = 54. However, none of the given options match this result. Therefore, the correct answer is not available.

Explanation
A precise instrument should be used when measuring smaller physical quantities. Precision refers to the level of detail or exactness in a measurement. When dealing with smaller quantities, it is important to use an instrument that can provide a high level of precision in order to obtain accurate and reliable measurements. Therefore, the correct answer is "Precise".

Explanation
Green is not used in color printing because color printing typically uses a combination of cyan, magenta, yellow, and black inks to create a wide range of colors. Green can be created by mixing cyan and yellow inks, so there is no need for a separate green ink in the printing process.

Explanation
The rate of change of momentum is calculated by dividing the force applied on the body by the time duration for which the force is applied. In this case, a force of 2N is applied on the body for 4 seconds. Therefore, the rate of change of momentum would be 2N divided by 4 seconds, which equals 0.5Ns^-1.

Explanation
The correct answer is 1 min 20s. This is because light travels at a speed of approximately 299,792 kilometers per second. The average distance between the Moon and Earth is about 384,400 kilometers. Therefore, to calculate the time taken by light to reach Earth from the Moon, we can divide the distance by the speed of light. This gives us approximately 1 minute and 20 seconds.

Explanation
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is given as 2m with an absolute uncertainty of 1m, and the width is given as 5m with an absolute uncertainty of 2.5m. To find the maximum possible area, we add the length and width values with their absolute uncertainties: (2+1) * (5+2.5) = 3 * 7.5 = 22.5m². To find the minimum possible area, we subtract the length and width values with their absolute uncertainties: (2-1) * (5-2.5) = 1 * 2.5 = 2.5m². Therefore, the possible range for the area is 2.5m² to 22.5m², which is equivalent to 0m² to 20m².