It is given that `angleXYZ= 64^(@)` and XY is produced to point P. A ray YQ bisects `angleZYP`. Draw a figure from the given information. Find `angleXYQ` and reflex `angleQYP`.

In the given figure sides QP and RQ of ΔPQR are produced to points S and T respectively. If angleSPR = 135^(@) and anglePQT = 110^(@) , find anglePRQ.

In the given figure angle PQR=100^(@) , where P,Q and R are points on a circle with centre 'O' Find angleOPR .

A Charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii r_1 and r_2 (figure 30-E4). Find the electric field at a point P at a distance x away from the centre for r_1ltxltr_2 . Draw a rough graph showing the electric field as a function of x for 0ltx lt2r_2 .

In the adjoining figure, line PR touches the circle at point Q . Using the information given in the diagram, answer the following questions. (i) What is the sum of angleTAQ and angleTSQ ? (ii) Write names of angles congruent to angleAQP . (iii) Write names of angles congruent to angleQTS . (iv) If angleTAS= 65^@ , then find angleTQS and arc TS . (v) It angleAQR=42^(@) and angleSQR=58^(@) , then find angleATS .

In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is angleP ) measures 45^(@) and the distance to the tree is 60 metres. Find the height of the tree.

A tangent is drawn at any point P(t) on the parabola y^(2)=8x and on it is takes a point Q(alpha,beta) from which a pair of tangent QA and QB are drawn to the circle x^(2)+y^(2)=8 . Using this information, answer the following questions : The point from which perpendicular tangents can be drawn both the given circle and the parabola is

In the above fig. square ABCD is a trapezium AB |\| CD and its area is 33 cm^(2) . From the information given in the figure, find the lengths of all sides of the square ABCD. Fill in the empty boxes to get the solution.

A crane has an arm length of 20 m inclined at 30° with the vertical. It carries a container of mass of 2 ton suspended from the top end of the arm. Find the torque produced by the gravitational force on the container about the point where the arm is fixed to the crane. [Given: 1 ton = 1000 kg, neglect the weight of the arm. g-10 m s^(-2)]