List of practice Questions

A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is 0.9 g/cm³, the mass of the wooden cube is:
If \( p(x) = x^4 - 5x + 6 \) and \( q(x) = 2 - x^2 \), then the degree of \( \frac{p(x)}{q(x)} \) is:
If \( \tan(\alpha + \beta) = \sqrt{3} \) and \( \tan \alpha = \frac{1}{\sqrt{3}} \), then the value of \( \tan \beta \) is:
Evaluate \( \frac{\sec(90^\circ - \theta) \csc\theta - \tan(90^\circ - \theta) \cot\theta + \cos^2 25^\circ + \cos^2 65^\circ}{3\tan 27^\circ \tan 63^\circ} \).
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - 8x + 5 = 0 \), then the value of \( \alpha^2 + \beta^2 \) is:
If \( p(y) = (y+1)(y^3+2)(y^4+6) \) and \( g(y) = y^2 - 3y +1 \), then the degree of \( \frac{p(y)}{g(y)} \) is:

Which of the following is not an A.P.?

If \( \tan(\alpha + \beta) = \sqrt{3} \) and \( \tan \alpha = \frac{1}{\sqrt{3}} \), then the value of \( \tan \beta \) is
If \( p(x) = x^4 - 5x + 6 \) and \( q(x) = 2 - x^2 \), then the degree of \( \frac{p(x)}{q(x)} \) is:
If \( p(y) = (y + 1)(y^3 + 2)(y^4 + 6) \) and \( g(y) = y^2 - 3y + 1 \), then the degree of \( \frac{p(y)}{g(y)} \) is:
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \). If \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \), then the value of \( DC \) is:
In triangle \( ABC \), \( DE \parallel BC \) such that
\[ \frac{AD}{DB} = \frac{4}{x - 4} \quad \text{and} \quad \frac{AE}{EC} = \frac{8}{3x - 19}, \] then the value of \( x \) is:
If in \( \triangle ABC \), \( AB = 13 \, \text{cm} \), \( BC = 12 \, \text{cm} \), and the value of \( \angle C \) is:
If the ratio of areas of two equilateral triangles is 9:4, then the ratio of their perimeters is:
In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), then the ratio of the areas of \( \triangle ABC \) and \( \triangle DEF \) is:
In \( \triangle ABC \) and \( \triangle PQR \), the area of \( \triangle ABC \) is to the area of \( \triangle PQR \) as \( 49:16 \), then the ratio of their corresponding sides is:
If one side of an equilateral triangle is \( a \), then its height is:
If the probability of occurrence of an event \( A \) is 0.35, then the probability of non-occurrence of \( A \) is:
In tossing three coins, the number of possible outcomes is:
Which of the following numbers cannot be the probability of an event?
In a throw of one die, the probability of occurrence of a number 5 or less than 5 is:
The mid-point 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 \( B(1, -3) \). If the centroid is \( (3, 0) \), then the coordinates of the third vertex \( C \) are:
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 + 5x + 8 \), then the value of \( \alpha^2 + \beta^2 + 2\alpha \beta \) is: