# Mathematics Solved Past Paper 10th Class 2015 Karachi Board

MCQs

MCQs

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:

Simplify

4 With the help of logarithmic table find the

value of

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

Question

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.

angels

proof

10. Eliminate “a” from the following equation:

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?

Question

16. Find the solution set of the following in equation

equation

(17) Factorize the following:

equation

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