List of top Mathematics Questions

Find the relation between \( x \) and \( y \) such that the point \( (x, y) \) is equidistant from the points \( (3, 6) \) and \( (-3, 4) \).

Find two consecutive positive integers, the sum of whose squares is 365.

If \( A = 30^\circ \), then the value of \( \frac{1 + \tan^2 A}{1 + \cot^2 A} \) will be:

If the radius of a sphere is doubled, then the increase in percentage of its surface area will be:

The ratio between the diameters of two circles is \( 4 : 9 \). The ratio between their circumferences will be:

If \( \triangle ABC \) is an equilateral triangle of side \( 2a \), the length of each of its altitudes will be:

If $\sin A = \cos A$, then the value of $A$ will be:

The mean of a frequency distribution is \( 24.1 \) and the mode is \( 28 \). Its median will be:

In $\triangle ABC$, if $AB = 6\sqrt{3}$ cm, $AC = 12$ cm, and $BC = 6$ cm, then $\angle B$ will be:

One third of any number is equal to 21. Then the number will be:

The coordinate of the point on the $x$-axis and equidistant from the points $(2, -5)$ and $(-2, 9)$ will be:

The ratio of the areas of two triangles is equal to the square of the ratio of their corresponding sides. Then these triangles will be:

If \( \triangle ABC \) is an isosceles triangle with \( AB = AC \), then:

If one root of the quadratic equation $x^2 + 2x - p = 0$ is $-2$, then the value of $p$ will be:

For any two positive integers ‘a’ and ‘b’:

The equivalent rational numbers of any rational number will be:

If \( m = 5 \) and \( n = m + 7 \), then the value of \( \sqrt{m^2 + n^2} \) will be:

The quotient of a non-zero rational and irrational number will be:

If $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are two linear equations, and if $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$, then:

If \(f(x)=\begin{cases} \frac{1-\cos4x}{x^2} & x\ne0 \\ k & x=0 \end{cases}\) is continuous at x = 0, then the value of k is :

Prove that the function \[ f(x) = \begin{cases} x^3 - 3 & \text{if } x \leq 2 \\ x^2 + 1 & \text{if } x>2 \end{cases} \] is continuous at \( x = 2 \).

Solve the following linear programming problem by the graphical method, under the following constraints: \[ x + 3y \leq 60, \quad x + y \geq 10, \quad x \leq y, \quad x \geq 0, \quad y \geq 0. \] Find the minimum and maximum values of \[ Z = 3x + 9y. \]

Solve the differential equation: \[ \tan^{-1}(y - x) \, dy = (1 + y^2) \, dx. \]

Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x + \cos x}} \, dx. \]