List of top Mathematics Questions asked in UP Board

The roots of the quadratic equation $x^2 - 3x - 10 = 0$ are:

Find the discriminant of the quadratic equation \( 4x^2 - 6x + 5 = 0 \) and hence find the nature of its roots.

If \( \triangle ABC \) is an equilateral triangle such that \( AD \perp BC \), then \( AD^2 \) is equal to:

If the length of shadow of a tower on the plane ground is \( \sqrt{3} \) times of its height, the angle of elevation of the sun is:

If \( \cos(A - B) = \frac{\sqrt{3}}{2} \) and \( \sin(A + B) = \frac{\sqrt{3}}{2} \), where \( 0^\circ<(A + B) \leq 90^\circ \) and \( A>B \), then find the values of \( A \) and \( B \).

Find the median of the following frequency distribution:

If the pair of linear equations $2x + 3y = 5$ and $4x + ky = 10$ has infinitely many solutions, then the value of $k$ is:

Prime factors of the number 156 will be:

If the radii of two circles are 4 cm and 3 cm respectively, then the radius of the circle having area equal to the sum of the areas of these circles is:

ABC and BDE are two equilateral triangles such that D is the midpoint of BC. The ratio of the areas of the triangles ABC and BDE is:

If $\cos A = \dfrac{7}{25}$, then the value of $\tan A + \cot A$ is:

If mean and mode of a grouped data are 24 and 12 respectively, then its median is:

In the given figure, if $AD=(x+3)$ cm, $DB=(3x+19)$ cm, $AE=x$ cm, $EC=(3x+4)$ cm and $DE \parallel BC$, then the value of $x$ is:

For any positive even integer \( p \), every positive odd integer will be of the form:

If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, then the value of \( c \) is:

The value of $\sin^2 18^\circ - \cos^2 72^\circ$ is:

If the mean of the numbers $7, 8, x, 11, 14$ is $x$, then the value of $x$ is:

The arithmetic mean of the even positive numbers from 1 to 10 will be:

From a boat which is coming towards a bridge, at any instant the angle of elevation of the bridge is 30°. After travelling 4 minutes with the same velocity, the angle of elevation of the bridge becomes 60°. How much more time will be taken by the boat to reach the bridge?

The father is 7 times older than his son. Two years ago, the father was 13 times as old as his son. What are their present ages?

The solution of the pair of linear equations \( x + y = 10 \), \( x - y = 4 \) is:

In the following numbers, the rational number is:

The distance of the point $(5, 9)$ from the $y$-axis is:

If one side of an isosceles right triangle is \( 5\sqrt{2} \) cm, then the length of its hypotenuse is:

Solve the following pair of equations by reducing them to a pair of linear equations: \[ \frac{10}{x + y} + \frac{2}{x - y} = 4 \] \[ \frac{15}{x + y} - \frac{5}{x - y} = 2 \]