List of practice Questions

For what value of \( m \), \( -4 \) is one of the zeros of the polynomial \( x^2 - x - (2m+2) \)?
If 1 is one zero of the polynomial \( p(x) = ax^2 - 3(a-1)x - 1 \), then the value of \( a \) is:
Which of the following quadratic polynomials has zeros \( \frac{3}{5} \) and \( -\frac{1}{2} \)?
If \( \alpha \) and \( \beta \) are the zeros of the polynomial \( p(x) = x^2 - 3x - 4 \), then the value of \( \frac{4}{3} (\alpha + \beta) \) is:
If one zero of the polynomial \( p(x) \) is 5, then one factor of \( p(x) \) is:
If \( p(x) = x^4 + 2x^3 - 17x^2 - 4x + 30 \) is divided by \( q(x) = x^2 + 2x - 15 \), then the degree of the quotient is:
If \( \alpha \) and \( \beta \) are the zeros of the polynomial \( x^2 + 5x + 8 \), then the value of \( \alpha^2 + \beta^2 + 2\alpha\beta \) is:
If \( TP \) and \( TQ \) are two tangents drawn from an external point \( T \) to a circle whose centre is \( O \) such that \( \angle POQ = 120^\circ \), then the value of \( \angle OTP \) is:
If \( \tan 2A = \cot (A - 18^\circ) \) where \( 2A \) is an acute angle, then the value of \( A \) is:
If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:
Which of the following is not a polynomial
What is the degree of the polynomial \( (3x^2 - 7x + 2)(2x^4 + 3x^3 - 5x + 2) \)?
The zeros of the polynomial \( x^2 - 13 \) are:
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle ABC \), \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \). Find the value of \( DC \).
In triangle ABC, DE || BC such that \(\frac{AD}{DB} = \frac{4}{x-4}\) and \(\frac{AE}{EC} = \frac{8}{3x-19}\), then the value of x is:
If \( \triangle ABC \) has \( AB = 13 \) cm, \( BC = 12 \) cm, and \( AC = 5 \) cm, then \( \angle C \) is:
If the ratio of areas of two equilateral triangles is \( 9:4 \), then the ratio of their perimeters is:
If \( \triangle ABC \sim \triangle DEF \) and \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), then the ratio of the areas of \( \triangle ABC \) and \( \triangle DEF \) is:
If one side of an equilateral triangle is \( a \), then its height is:
72. If two circles touch each other internally, then the number of common tangents is:
The HCF of two numbers is 15 and their LCM is 105. If one of the numbers is 5, the other number is:
If the Euclidean algorithm equation is given as \( a = bq + r \) where \( b = 43 \), \( q = 31 \), and \( r = 32 \), then the value of \( a \) is:
If \( q \) is a positive integer, which of the following is an even positive integer?
Which of the following has a terminating decimal expansion?
The midpoint of the line segment joining the points \( A(-2, 8) \) and \( B(-6, -4) \) is: