# Mathematics Solved Past Paper 10th Class 2015 Karachi Board

2. If A = {a, b, c} and B = {x , y} find only two binary relations in A x B.

A = {a, b, c} and B = {x , y}

Two binary relations in A x B = ?
Any subset of A x B is a Binary Relation:
A x B = {a, b, c} x {x, y}
A x 8 = {(a, x), (a, y), (b, x), (b, y), (c, x), (c, y)}
First Binary Relation = R1
R1= {(a, x) (b, x)}
Second Binary Relation = R2
R2= {(a, x) (b, y) (c, x)}

Simplify:  4 With the help of logarithmic table find the

value of

Using laws of logarithms

5. Find the value of a3 + b3 + c3 – 3abc when a + b + c = 15 and ab + bc + ca = 74  6. Resolve into factors:
4a2 (3b – 4c) + 9b² (4c – 2a) + 16c² (2a – 3b) 7. Find the solution set of: -6 + 5x – 3 = 3  9. If a side of a triangle is extended the exterior angle so formed is, in measure, greater than either of the two interior opposite angles. Prove it. 10. Eliminate “a” from the following equation: 11. Congruent chords of a circle (or congruent circles) are equidistant from its (or their) centre (s). Prove it. 12. If in 0 = 3/5 find the remaining trigonometric ratios, using trigonometric identities.  13. The line segment, joining the mid points of two sides of a triangle is parallel to the -third side and half as long. Prove it 14. What should be added to x4 + 4×3 + 10×2 + 5 so that it may be a perfect square?   16. Find the solution set of the following in equation  (17) Factorize the following:  19. In a correspondence of two triangles, if three sides of one triangle are congruent to the corresponding three sides of the other, the two triangles are congruent. Prove it. 20.(a) A set of data contains the values as 148, 145, 160, 157, 156, 160, 160, 165, show that the mode> median> Mean (b) .Findthe factors of x3 – 21x + 20 by means of the remainder theorem.  21. .Construct a triangle PQR in which mPQ=6cm, mQr=5cm,and mLQ = 70°. Draw the incircle of the triangle and write the steps of construction. STEPS OF CONSTRUCTION:

(i) Draw OR = 5 cm
(ii)At point 0 make ray OZ such that < ROZ = 70°
(iii)Cut off OP = 6 cm and join PR.
(vi)Draw the angular bisectors of LO and LR. Let these bisectors cross each other at point I.
(v) With centre I draw an arc of suitable radius intersecting
OR atC and D.
(vi) With points C and D draw two arcs of same radius inters~ting each oth~at I. Draw I T intersecting OR at S.
(vii) With centre I and radius =15 draw a circle. This is the inscribed circle .

Posted on December 15, 2015 in 10th Class 2015 Karachi Board Past Papers