List of top Questions asked in UP Board X

A solid is of the cylindrical shape and its both ends are hemispherical. The total height of the solid is 19 cm and the radius of the cylinder is 3.5 cm. Find the volume and total surface area of the solid.
Slant height of a right circular cone is 13 cm and its total surface area is 90\( \pi \) cm\(^2\). Find the diameter of its base.
The angle of elevation of the top of a cable tower from the top of a building of height 7 metre is 60\(^\circ\) and the angle of depression of its bottom is 45\(^\circ\). Find the height of the cable tower.
When the angle of elevation of sun becomes \( \theta \) from \( \phi \), then the shadow of a pillar situated in a horizontal plane increases by a metre. Find the height of the pillar.
For which value of x the 2x, x + 8 and 3x + 1 will be in arithmetic progression ?
Prove that \( 2\sqrt{3} \) is an irrational number.
Volume of a cube is 729 cubic cm. Find its total surface area.
Find the co-ordinates of the point dividing the line segment formed by joining the points (2, -3) and (-4, 6) in the ratio 1 : 2.
Find the mean from the following frequency distribution :
In which ratio, does the point (–4, 6) divides the line segment made by joining the points A(–6, 10) and B(3, –8)?
The length of a tangent from a point A at a distance 7.5 cm from the centre of the circle is 6 cm. Find the radius of the circle.
Prove that the line dividing any two sides of a triangle in a same ratio is parallel to the third side of the triangle.
Area of the square which can be drawn in the circle of radius 4 cm will be
The mean from the following table will be
A die is thrown once. The probability of getting a prime number will be
If mean of a frequency distribution is 20.5 and median is 21 then mode will be
Which of the following cannot be the probability of any event ?
If \( \cot A = \frac{b}{a} \), then prove that \( \frac{b \sec A}{a \operatorname{cosec} A} = 1 \).
The coordinates of the mid-point of the line segment made by joining the points (-2, 6) and (-2, 10) are
If AD \(\perp\) BC in an equilateral triangle ABC, then AD\(^2\) will be
The vertices of triangle ABC are (7, 5), (5, 7) and (-3, 3) respectively. If the mid-point of BC is D, then the measure of AD will be
If sec \(\theta\) = 2, then the value of \(\theta\) will be
The value of \( (\text{cosec}^2\theta - \cot^2\theta)(1 - \cos^2\theta) \) is
Area of the base of a right circular cylinder is 9\( \pi \) cm\(^2\). Radius of its base will be
Simplest form of \( \frac{148}{185} \) is