List of top Mathematics Questions asked in UP Board X

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

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

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

Prime factors of the number 156 will be:

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

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:

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:

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:

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

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

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 angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45°. Find the height of the tower PQ and the distance PX.

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:

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

If a line intersects sides \( AB \) and \( AC \) of a triangle \( ABC \) at \( D \) and \( E \) respectively and is parallel to \( BC \), prove that \( \frac{AD}{AB} = \frac{AE}{AC} \).

If the median of the frequency distribution given is 28.5, find the values of \( x \) and \( y \) while the total of frequencies is 60.

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

A fraction becomes \( \frac{1}{3} \) when 1 is subtracted from the numerator and it becomes \( \frac{1}{4} \) when 8 is added to its denominator. Find the fraction.