For the following questions answer them individually
ABC is a right angled triangle in which ∠B = 90°. If BD ⊥ AC, AB = 3 cm and BC = 4 cm, then what is the value of BD (in cm)?
In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR = 105°, then what is the value of ∠PAR (in degrees)?
If there are four lines in a plane, then what cannot be the number of points of intersection of these lines?
What is the simplified value of $$cosec2A + cot2A$$ ?
If A = 30°, B = 60° and C = 135°, then what is the value of $$sin^3A + cos^3B + tan^3C - 3sin A cos B tan C$$ ?
What is the least value of $$tan^2θ + cot^2θ + sin^2θ + cos^2θ + sec^2θ + cosec^2θ$$ ?
The pie chart given below shows the break-up of number of hours of teaching various subjects at an institute by Mr. Raghav.
If Mr. Raghav taught a total of 500 hours, then what is the difference in number of hours of teaching algebra and modern Maths?
Mr. Raghav taught Geometry for 36 hours. If the time taken in teaching Ratio consitutes one-fourth of the time for Arithmetic, then for how much time (in hours) did he taught the topic of Ratio?
If Data Interpretation and Modern Maths were taught for a combined time of 96 hours, then for how much time (in hours) were Number system and Geometry taught?
A new topic named Problem Solving was also introduced and it was decided that 10% time of all topics except Arithmetic will be devoted to it. What will be the central angle (in degrees) made by Problem Solving in the new pie chart?