List of top Questions asked in UP Board

Find the coordinates of the points which divide the line segment \( AB \) joining points \( A (-2, 2) \) and \( B (2, 8) \) into four equal parts.
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of new fraction and the original fraction is \( \frac{29}{20} \). Find the original fraction.
In the figure, AB and CD are two perpendicular diameters of a circle with center O. OD is the diameter of the smaller circle. If OA = 7 cm, find the ratio of the areas of the smaller and larger circles.
The roots of the quadratic equation $x^2 - 3x - 10 = 0$ are:
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:
The number of solid spheres, each of diameter $6$ cm, that can be made by melting a solid metal cylinder of height $45$ cm and diameter $4$ cm is:
If \( \triangle ABC \) is an equilateral triangle such that \( AD \perp BC \), then \( AD^2 \) is equal to:
Find the discriminant of the quadratic equation \( 4x^2 - 6x + 5 = 0 \) and hence find the nature of its roots.
Draw a circle of radius 3.0 cm. From a point 7.0 cm away from its centre, construct the pair of tangents to the circle. Write the steps of the construction in brief.
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:
Prime factors of the number 156 will be:
If mean and mode of a grouped data are 24 and 12 respectively, then its median is:
If the pair of linear equations $2x + 3y = 5$ and $4x + ky = 10$ has infinitely many solutions, then the value of $k$ 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 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:
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 mean of the numbers $7, 8, x, 11, 14$ is $x$, then the value of $x$ is:
If the roots of the quadratic equation \( ax^2 + bx + c = 0 \) are equal, then the value of \( c \) 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:
The arithmetic mean of the even positive numbers from 1 to 10 will be:
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.
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?