List of top Mathematics Questions asked in UP Board

Do the equations \( x + 2y - 4 = 0 \) and \( 2x + 4y - 12 = 0 \) represent two parallel lines? Express this by geometrical method.
Prove that the points \( (3, 2) \), \( (-2, -3) \), and \( (2, 3) \) are vertices of a right angled triangle.
Find the mean of the following data:
If a copper rod whose diameter is 1 cm and length 8 cm is melted and recasted into another rod whose length is 18 cm, then find the width of the rod.
In the figure \( OA \cdot OB = OC \cdot OD \), then prove that \( \angle A = \angle C \) and \( \angle B = \angle D \).
There is a frustum of a cone whose height is 45 cm. If the radii of its ends are 28 cm and 7 cm, find its volume, curved surface area, and total surface area. (Use \( \pi = \frac{22}{7} \))
The ratio of income of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them saves ₹ 2,000 per month, then find their monthly income.
The angle of elevation of the top of a 10 m high building from a point \( P \) on the ground is 30°. There is a flag on the top of the building. The angle of elevation of the top of the flag from \( P \) is 45°. Then find the length of the flagpole and distance of point \( P \) from the building.
Find the roots of the quadratic equation \( 4x^2 + 3x + 5 = 0 \).
Find the length of a line segment joining the points \( A(2, -2) \) and \( B(3, 7) \).
The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:
If the arithmetic mean of 7, 13, 20, 17, and \( 3x \) is 18, then the value of \( x \) will be:
If the area and perimeter of a circle are numerically the same, then the radius of that circle will be:
Prove that \( \sqrt{2} \) is not a rational number.
If ratio of sides of two similar triangles is 4:7, then ratio of their areas will be:
In \( \triangle PQR \), \( \angle Q = 90^\circ \), if \( \tan P = \frac{1}{\sqrt{3}} \), then find the value of \( \sin P \cos R + \cos P \sin R \).
The roots of the equation \( x^2 - 2x + 1 = 0 \) will be:
The mean of the following table will be:
The distance of the point \( (-3, 5) \) from the y-axis will be:
If mode and mean of some observations are 45 and 27 respectively, then median will be:
If ratio of volumes of two spheres is \( 27 : 64 \), then ratio of their surface areas will be:
Value of \( \frac{\sin 15^\circ}{\cos 75^\circ} \) will be:
If \( 3 \cot \theta = 4 \), then the value of \( \cos \theta \) will be:
If one root of the equation \( x^2 + kx - 6 = 0 \) is -2, then the value of \( k \) will be:
If \( C \left( \frac{\alpha}{8}, 4 \right) \) is the mid-point of the line joining the points \( A(-4, 2) \) and \( B(5, 6) \), then the value of \( \alpha \) will be: