List of practice Questions

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:
If the points \( (1, 2) \), \( (0, 0) \), and \( (a, b) \) are collinear, then:
Two vertices of a triangle ABC are A(2, 3) and B(1, -3), and the centroid is at C(3, 0), then the coordinates of the third vertex C are:
The given number \( 2:1311311311113 \dots \) is:
The product of a rational number and an irrational number is:
The simplest form of \( 0.57 \) is:
If \( 140 = 2^x \times 5^y \times 7^z \), then the value of \( x + y - z \) is:
The value of \( (6 + \sqrt{125}) - (3 + \sqrt{5}) + (1 - 4\sqrt{5}) \) is:
In the form \( \frac{p}{q} \) of 0.375, the form of \( q \) is:
If the product of the roots of the quadratic equation \( x^2 - 5x + p = 10 \) is -4, then the value of \( p \) is:
If \( (x - 2) \) is a factor of \( px^2 - x - 6 \), then the value of \( p \) is:
What is the nature of the roots of the quadratic equation \( \frac{4}{3}x^2 - 2x + \frac{3}{4} = 0 \)?
If one root of the quadratic equation \( y^2 + 3y - 18 = 0 \) is -6, then its other root is:
The roots of the quadratic equation \( ax^2 - bx - c = 0 \) are:
If \( x = 2 \) is a common root of the equations \( 2x^2 + 2x + p = 0 \) and \( qx + qx + 18 = 0 \), then the value of \( (q - p) \) is: