List of top Questions asked in UP Board

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
For which value of p, the equations 3x - y + 8 = 0 and 6x - py = 16 represents coincident lines?
If the lines represented by 3x + 2py = 2 and 2x + 5y + 1 = 0 are parallel, then the value of p will be