A pole 10 m long rests slantly against a vertical wall AB making an angle 30° with the horizontal (ground). Find how far the foot of the pole is from the wall (in metres).
The bar graph given below shows the sales of books from six schools during two consecutive years, 2013 and 2014.
What percentage of the average sales of the schools A, B, and C in 2014 is the average sales of schools A, C, and F in 2013?
If a right circular cone of height 24 cm has a volume of 1232 cm³, then the total surface area of the cone is (\(\text{(use } \pi = \frac{22}{7}\text{)}\)
Let 0° < t < 90°. Then which of the followings is true?
\(\sin(t) \ne \cos(t) \text{ when } t = 45^\circ\)
\(\sin(t) > \cos(t) \text{ when } t < 45^\circ\)
\(\sin(t) < \cos(t) \text{ when } t < 45^\circ\)
\(\sin(t) < \cos(t) \text{ when } t > 45^\circ\)
Find the gain percentage, given that Priya sold her scooter for ₹42,564, gaining \(\frac{1}{6}\) th of the selling price.
If \( a + \frac{1}{a} = 12, \) then find the value of \( a^{2} + \frac{1}{a^{2}} \)
The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is described with a radius equal to half the length of the side of the triangle. Find the area of that part of the triangle which is not included in the circles \(\text{(use } \pi = \frac{22}{7} \text{ and } \sqrt{3} = 1.73\text{)}\)