I Quiz With Brilliant Maths Friends

Explanation
The mnemonic "S-OH, C-AH, T-OA" is related to trigonometry. This mnemonic stands for "Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent." It is used to remember the ratios of the sides of a right triangle in trigonometry.

Explanation
The grade of a quadratic polynomial refers to the highest power of its variable. In this case, since the options given are the numbers 1, 2, 3, and 4, we can determine that the correct answer is 2. This is because a quadratic polynomial has a degree of 2, as it contains a term with the variable raised to the power of 2.

Explanation
To find the value of f(2), we substitute x=2 into the given function f(x)= x^3 +3x^2-2x+2. Plugging in x=2, we get f(2)= 2^3 +3(2)^2-2(2)+2 = 8+12-4+2 = 18. Therefore, the correct answer is 18.

Explanation
This pair of linear equations is not inconsistent because the two equations have the same slope (5/2) and the same y-intercept (3/2). Therefore, the lines represented by these equations are parallel and will never intersect. This means that there is no solution to the system of equations, but it does not make the system inconsistent.

Explanation
The given numbers are 35 and 14. To find the highest common factor (HCF) of these two numbers, we can list down their factors and identify the largest common factor. The factors of 35 are 1, 5, 7, and 35, while the factors of 14 are 1, 2, 7, and 14. The largest common factor between the two numbers is 7, which is the HCF.

Explanation
The exponent of 2 in the prime factorization of 144 is 4 because 144 can be expressed as 2^4 * 3^2. This means that there are four factors of 2 in the prime factorization of 144.

Explanation
The highest common factor (HCF) of two numbers is always a factor of both numbers. Since the LCM of the two numbers is 1200, both numbers must be divisible by 1200. However, 500 is not divisible by 1200, so it cannot be their HCF. Therefore, 500 is the correct answer.

Explanation
The expression a1^2 - a2^2 represents the difference between the squares of two odd prime numbers. When we subtract the square of an odd number from the square of another odd number, the result is always an even number. This is because the square of an odd number is always odd, and the difference of two odd numbers is always even. Therefore, a1^2 - a2^2 will always be an even number.

Explanation
The sum of the zeros of a polynomial is equal to the opposite of the coefficient of the second term divided by the coefficient of the first term. In this case, the sum of the zeros is given as 6. So, we have -(-3k)/2 = 6. Simplifying this equation, we get 3k/2 = 6. Multiplying both sides by 2/3, we find that k = 4. Therefore, the value of k is 4.

Explanation
If the system of equations is inconsistent, it means that there is no solution that satisfies both equations simultaneously. To determine the value of k, we can use the method of substitution. By solving the first equation for y, we get y = 1 - 3x. Substituting this into the second equation, we get (2k-1)x + (k-1)(1-3x) = 2k+1. Simplifying this equation, we get (k-1)x - 3(k-1)x = 2k+1 - (k-1). Further simplifying, we get (k-1-3(k-1))x = 2k+1 - (k-1). This simplifies to (-2k+2)x = k+2. Since the left side of the equation does not depend on k, the only way for the equation to be inconsistent is if the right side does not depend on k as well. Therefore, k+2 = 0, which implies k = -2. Hence, the correct answer is -2.

Explanation
It is not possible to provide an explanation for the given correct answer as the question does not provide any context or criteria for selecting a preferred option. Without any additional information, it is impossible to determine why Option 1 is the correct answer.