List of practice Questions

If \( A(-1, 0), B(5, -2) \), and \( C(8, 2) \) are the vertices of a triangle, the coordinates of its centroid are
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = \frac{1}{10} \, \text{cm}, AC = 14 \, \text{cm}, BC = 6 \, \text{cm} \), then the value of \( DC \) is
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \, \text{cm} \), then \( AE \)= ?
The 2nd term of an A.P. is 13 and its 5th term is 25. The common difference of the A.P. is
The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) are
The graphs of the equations \( 2x + 3y = 4 \) and \( 4x + 6y = 12 \) are which type of straight lines?
How many solutions does the system of linear equations \( 2x - 3y + 1 = 0 \) and \( 3x + y + 2 = 0 \) have?
For what value of \( k \) has the system of linear equations \( x + 2y = 3 \) and \( 5x + ky = 15 \) infinite solutions?
Which of the following is an A.P.?
For what value of \( p \), the terms \( (2p + 1), 13, (5p - 3) \) are in A.P.?
If \( a_n \) is the \( n \)-th term of A.P. \( 3, 8, 13, 18, \dots \), then what is the value of \( a_{25} - a_{10} \)?
If the product of zeroes of the polynomial \( x^2 - 9x + a \) is 8, then the value of \( a \) is
Which of the following quadratic polynomials has zeroes 4 and -2?
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( p(x) = x^2 + 3x - 4 \), then the value of \( \frac{\alpha \beta}{4} \) is
If one zero of the polynomial \( q(x) \) is -3, then one factor of \( q(x) \) is
If \( f(x) = x^4 - 2x^3 - x + 2 \) is divided by \( g(x) = x^2 - 3x + 2 \), the degree of the quotient is
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 - 3(x+1) - 5 \), then the value of \( (\alpha + 1)(\beta + 1) \) is
If \( 2a + 3b = 8 \) and \( 3a - 4b = -5 \), then
The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower, which are in the same straight line, are complementary. Prove that the height of the tower is 6 m.
Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.
Find the median of the following data:
\[ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Frequency} \\ \hline 40-45 & 2 \\ 45-50 & 3 \\ 50-55 & 8 \\ 55-60 & 6 \\ 60-65 & 6 \\ 65-70 & 3 \\ 70-75 & 2 \\ \hline \end{array} \]
Which of the following is not a polynomial?
The degree of the polynomial \( (x^5 + x^2 + 3x) (x^6 + x^5 + x^2 + 1) \) is:
The zeroes of the polynomial \( x^2 - 11 \) are:
If -2 and -3 are the zeroes of the quadratic polynomial \( x^2 + (a+1)x + b \), then