List of practice Questions

If \( \sin \theta = \frac{\sqrt{3}}{2} \), \( 0^\circ<\theta<90^\circ \), then \( \tan^2 \theta - 1 = \) ?
Evaluate \( 9 \csc^2 22^\circ - 9 \cot^2 22^\circ + 1 = \):
If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:
If \( \sec \theta = \frac{13}{12} \), then \( \cot \theta = \):
For what value of \( k \), the roots of the quadratic equation \( x^2 + 6x + k = 0 \) are real and equal?
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:
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:
The roots of the quadratic equation \( ax^2 - bx - c = 0 \) are:
If \( x = 2 \) is a common root of both the equations \( 2x^2 + 2x + p = 0 \) and \( qx^2 + qx + 18 = 0 \), then the value of \( (q - p) \) is:
The perpendicular distance from the centre of a circle to a chord of length 8 cm is 3 cm. Then the radius of the circle is:
If \( A, B, C, D \) is a rectangle with vertices \( A(0, 0), B(8, 0), C(8, 6), D(0, 6) \), then one of the diagonals of the rectangle is:
If \( (0, 4) \), \( (0, 0) \), and \( (3, 0) \) are the vertices of a triangle, then the perimeter of the triangle is:
Which of the following is a quadratic equation?
If the product of the roots of the quadratic equation \( x^2 - 5x + p = 10 \), then the value of \( p \) is:
If \( (x - 2) \) is a factor of \( px^2 - x - 6 \), then the value of \( p \) is:
How many terms are in A.P. 3, 8, 13, 18, ..., 93?
The sum of the first 30 terms of the A.P. 1, 3, 5, 7, ... is:
The point \((-2/\sqrt{2}, -2)\) lies in which quadrant?
The distance between the points \((5 \cos \theta, 0)\) and \((0, 5 \sin \theta)\) is:
If from a point \( B \), the length of the perpendicular drawn to the x-axis is 10 and the length of the perpendicular drawn to the y-axis is 5, then the coordinates of the point \( B \) are:
The distance between the points \( (1, -3) \) and \( (4, -6) \) is:
The point on the y-axis which is equidistant from the points \( (5, -2) \) and \( (-3, 2) \) is:
The distance between the points \( (2\cos\theta, 0) \) and \( (0, 2\sin\theta) \) is:
The intersecting point of the straight lines \( x = -2 \) and \( y = 3 \) is: