In the given figure, `angleX = 62^(@), angleXYZ = 54^(@)`. In `DeltaXYZ ` If YO and ZO are the bisectors of `angleXYZ` and `angleXZY` respectively find `angleOZY` and `angleYOZ`

In the figure angleA = 64^(@), angleABC = 58^(@) . If BO and CO are the bisectors of angleABC and angleACB respectively of triangleABC , find x^(@) and y^(@) .

In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of anglePOS and angleSOQ respectively. Find angleROT .

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 figures given below AB || CD. EF is the transversal intersecting AB and CD at G and H respectively. Find the values of x and y. Give reasons

Figure shows three concentric thin spherical shells A, B and C of radii a, b and c respectively. The shells A and C are given charges q and -q respectively and the shell B is earthed. Find the charges appearing on the surfaces of B and C.

figure shows two blocks connected by a light string placed on the two inclined parts of a triangular structure. The coefficients of static and inetic friction are 0.28 and 0.25 respectively at each of the surface. a.Find the minimum and maximum values of m for which the system remains at rest, b. Find the acceleration of either block if m is given the minimu value calculated in teh first part and is gentluy pushed up the incline for a short while.

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=y(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is