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 if line segments PQ and RS intersect at point T, such that anglePRT = 40^(@), angleRPT = 95^(@) and angleTSQ = 75^(@) , find angleSQT

In the given figure triangle ABC side AC has been produced to D. angleBCD = 125^(@) and angleA:angleB= 2 : 3 , find the measure of angleA and angleB

In the adjoining figure, square P Q R S is a cyclic quadrilateral. Side PQ ~= side RQ. anglePSR = 110^(@) . Find (i) anglePQR (ii) m (arc PQR) (iii) m (arc QR) (iv) anglePRQ

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 .

Find the slopes of lines passing through the given point. T(0,-3) and S(0,4)

Find the value of lambda so that the points P ,Q ,R and S on the sides O A ,O B ,OC and A B , respectively, of a regular tetrahedron O A B C are coplanar. It is given that (O P)/(O A)=1/3,(O Q)/(O B)=1/2,(O R)/(O C)=1/3 and (O S)/(A B)=lambdadot (A) lambda=1/2 (B) lambda=-1 (C) lambda=0 (D) for no value of lambda

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of A B Cdot

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of A B Cdot

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

From the veloicty time graph of a particle given in figure describe the motion of the particle qualitively int eh interval 0 to 4s. Find a. the distance travelled during first two seconds, b. during the time 2s to 4s, c. during the time 0 to 4s d. displacement during 0 to 4 s. e. acceleration at t=1/2 and f. acceleration at t=2s .