Practice Test Class X Maths

Explanation
The given system of equations has unique solutions because the two equations are not multiples of each other and their slopes are not equal. This means that the two lines represented by the equations intersect at a single point, resulting in a unique solution.

Explanation
In this question, we are given that there are 10 students in the XII class, and some are math students while others are bio students. We are also given that the number of bio students is 4 more than the number of math students. To find the number of math and bio students, we need to look for an option where the math students are 3 and the bio students are 7. This satisfies the given condition that the number of bio students is 4 more than the number of math students. Therefore, the correct answer is 3, 7.

Explanation
The given statement is true because if p(x) is a factor of g(x), it means that g(x) can be divided evenly by p(x) without leaving a remainder. In this case, when we divide g(x) by p(x), we get a quotient of x and a remainder of 0, indicating that p(x) is indeed a factor of g(x).

Explanation
To find the value of p for which the linear pair has infinite solutions, we need to determine when the two equations are dependent. This occurs when the ratio of the coefficients of x and y in both equations is the same. In the given equations, the ratio of the coefficients of x is 12/36 = 1/3, and the ratio of the coefficients of y is 14/p. To have infinite solutions, these ratios must be equal. Therefore, 1/3 = 14/p. Cross multiplying gives us 1p = 14 * 3, which simplifies to p = 42. Hence, the value of p for which the linear pair has infinite solutions is 42.

Explanation
The given quadratic equation has the zeroes 11 and 2. In a quadratic equation, the expression is of the form ax^2 + bx + c, where a, b, and c are constants. The sum of the zeroes is equal to the coefficient of the x term with the opposite sign, divided by the coefficient of the x^2 term. In this case, the sum of the zeroes is 11 + 2 = 13. Therefore, the coefficient of the x term should be -13. The constant term is found by multiplying the zeroes, which is 11 * 2 = 22. Therefore, the expression for the quadratic equation is x^2 - 13x + 22.

Explanation
When we divide the polynomial x^4 + x^3 - 2x^2 + x + 1 by x - 1 using synthetic division, we get a remainder of 2. Therefore, the correct answer is 2.

Explanation
The given pair of equations, 2x+3y=10 and 9x+11y=12, is consistent because it is possible to find values of x and y that satisfy both equations simultaneously.

Explanation
The given statement is false because the graph of the polynomial (x^2-1) meets the x-axis at two points. This can be determined by setting the polynomial equal to zero and solving for x, which yields x=1 and x=-1 as the x-intercepts. Therefore, the graph intersects the x-axis at two points, not one.

Explanation
Both equations, 4x+5y=0 and 11x+17y=0, can be rewritten in the form y = mx, where m is the slope. When x=0 (which is the origin), y=0 for both equations. This means that both lines pass through the origin (0,0). Therefore, the answer is true.