List of top Mathematics Questions

If \( \sin x = \sin y \) and \( \cos x = \cos y \), then the value of \( x - y \) is:
Let \( Z \) be the set of all integers, and consider the set \( X = \{(x, y): x^2 + 2y^2 = 3, x, y \in Z \) and \( Y = \{(x, y): x>y, x, y \in Z\} \). Then the number of elements in \( X \cap Y \) is:
Let \( C \) denote the set of all tuples \( (x, y) \) which satisfy \( x^2 = 2^y \), where \( x \) and \( y \) are natural numbers. What is the cardinality of \( C \)?
If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
Sum of two numbers is 8 and sum of their inverses is \( \frac{8}{15} \). Find the numbers.
Find two consecutive positive integers whose sum of squares is 365.
Slant height of a right circular cone is 13 cm and its total surface area is 90\( \pi \) cm\(^2\). Find the diameter of its base.
Find the roots of the quadratic equation \( \sqrt{3}x^2 - 11x + 8\sqrt{3} = 0 \).
The angle of elevation of the top of a cable tower from the top of a building of height 7 metre is 60\(^\circ\) and the angle of depression of its bottom is 45\(^\circ\). Find the height of the cable tower.
Sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 18 more than original number. Find the number.
Find the median from the following data :
When the angle of elevation of sun becomes \( \theta \) from \( \phi \), then the shadow of a pillar situated in a horizontal plane increases by a metre. Find the height of the pillar.
A solid is of the cylindrical shape and its both ends are hemispherical. The total height of the solid is 19 cm and the radius of the cylinder is 3.5 cm. Find the volume and total surface area of the solid.
Volume of a cube is 729 cubic cm. Find its total surface area.
For which value of x the 2x, x + 8 and 3x + 1 will be in arithmetic progression ?
In which ratio, does the point (–4, 6) divides the line segment made by joining the points A(–6, 10) and B(3, –8)?
Prove that \( 2\sqrt{3} \) is an irrational number.
Find the mean from the following frequency distribution :
Prove that the line dividing any two sides of a triangle in a same ratio is parallel to the third side of the triangle.
The length of a tangent from a point A at a distance 7.5 cm from the centre of the circle is 6 cm. Find the radius of the circle.
Find the co-ordinates of the point dividing the line segment formed by joining the points (2, -3) and (-4, 6) in the ratio 1 : 2.
If \( \cot A = \frac{b}{a} \), then prove that \( \frac{b \sec A}{a \operatorname{cosec} A} = 1 \).
Area of the square which can be drawn in the circle of radius 4 cm will be
If mean of a frequency distribution is 20.5 and median is 21 then mode will be
Which of the following cannot be the probability of any event ?