List of top Mathematics Questions

In the figure given above, \( ABCD \) is a square, and a circle is inscribed in it. All sides of the square touch the circle. If \( AB = 14 \, \text{cm} \), find the area of the shaded region. 

Find the value of \( \sin^2 \theta + \cos^2 \theta \): 

In the above figure, \( \triangle ABC \) is inscribed in arc \( ABC \). If \( \angle ABC = 60^\circ \), find \( m\angle AOC \): 

If \( \triangle ABC \sim \triangle PQR \) and \( AB : PQ = 2 : 3 \), then find the value of \( \frac{A(\triangle ABC)}{A(\triangle PQR)} \):
\( ABCD \) is a trapezium, \( AB \parallel CD \), and the diagonals of the trapezium intersect at point \( P \). Write the answers to the following questions:
[(a)] Draw the figure using the given information.
[(b)] Write any one pair of alternate angles and opposite angles.
[(c)] Write the names of similar triangles with a test of similarity.
\( AB \) is a chord of a circle with center \( O \), \( AOC \) is the diameter of the circle, and \( AT \) is a tangent at \( A \). Write the answers to the following questions:
[(a)] Draw the figure using the given information.
[(b)] Find the measures of \( \angle CAT \) and \( \angle ABC \) with reasons.
[(c)] Determine whether \( \angle CAT \) and \( \angle ABC \) are congruent. Justify your answer.
Determine whether the points \( A(1, -3), B(2, -5), C(-4, 7) \) are collinear.
Prove that, "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion."
Segment \( PM \) is a median of \( \triangle PQR \), \( PM = 9 \), and \( PQ^2 + PR^2 = 290 \). Find \( QR \).
\( \triangle ABC \sim \triangle LMN \). In \( \triangle ABC \), \( AB = 5.5 \, \text{cm} \), \( BC = 6 \, \text{cm} \), \( CA = 4.5 \, \text{cm} \). Construct \( \triangle ABC \) and \( \triangle LMN \) such that \( \frac{BC}{MN} = \frac{5}{4} \).
Draw a circle with centre \( O \) having radius \( 3 \, \text{cm} \). Draw tangent segments \( PA \) and \( PB \) through the point \( P \) outside the circle such that \( \angle APB = 70^\circ \).
A cylinder of radius \( 12 \, \text{cm} \) contains water up to the height \( 20 \, \text{cm} \). A spherical iron ball is dropped into the cylinder, and thus the water level is raised by \( 6.75 \, \text{cm} \). What is the radius of the iron ball?
\( \frac{1}{\sin^2 \theta} - \frac{1}{\cos^2 \theta} - \frac{1}{\tan^2 \theta} - \frac{1}{\cot^2 \theta} - \frac{1}{\sec^2 \theta} - \frac{1}{\csc^2 \theta} = -3 \), then find the value of \( \theta \).
Find the slope of the line passing through the points \( A(2, 3) \) and \( B(4, 7) \).
Find the length of the hypotenuse of a right-angled triangle if the remaining sides are \( 9 \, \text{cm} \) and \( 12 \, \text{cm} \).
Find the surface area of a sphere of radius \( 7 \, \text{cm} \).
Radius of a sector of a circle is \( 3.5 \, \text{cm} \) and length of its arc is \( 2.2 \, \text{cm} \). Find the area of the sector.
A line makes an angle of \( 45^\circ \) with the positive direction of the X-axis. Find the slope of the line.
Find the side of a square whose diagonal is \( 10\sqrt{2} \, \text{cm} \):
A circle having radius \( 3 \, \text{cm} \), then the length of its largest chord is:
Two circles of radii \( 5 \, \text{cm} \) and \( 3 \, \text{cm} \) touch each other externally. Find the distance between their centres.
Find the value of \( \sin 0 \times \csc 0 \):
What is the slope of the X-axis?
Out of the dates given below, which date constitutes a Pythagorean triplet?
If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is: