Mathematics Solved Past Paper 10th Class 2015 Karachi Board

MCQs

MCQs

MCQs

MCQs

SECTION “B” (SHORT-ANSWER QUESTIONS)

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

ANSWER

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

Simplify

ANSWER:

ANSWER

ANSWER

4 With the help of logarithmic table find the

value of

value of

value of

ANSWER:

Using laws of logarithms

ANSWER

ANSWER

5. Find the value of a3 + b3 + c3 – 3abc when a + b + c = 15 and ab + bc + ca = 74

ANSWER:

ANSWER

ANSWER

6. Resolve into factors:
4a2 (3b – 4c) + 9b² (4c – 2a) + 16c² (2a – 3b)

ANSWER:

ANSWER

7. Find the solution set of: -6 + 5x – 3 = 3

ANSWER:

ANSWER

Question

Question

ANSWER

 

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.

ANSWER

angels

angels

ANSWER

proof

proof

10. Eliminate “a” from the following equation:

equation

equation

ANSWER

ANSWER

11. Congruent chords of a circle (or congruent circles) are equidistant from its (or their) centre (s). Prove it.

ANSWER:

ANSWER

12. If in 0 = 3/5 find the remaining trigonometric ratios, using trigonometric identities.

ANSWER:

ANSWER

ANSWER

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

ANSWER:

ANSWER

14. What should be added to x4 + 4×3 + 10×2 + 5 so that it may be a perfect square?

ANSWER:

ANSWER

Question

Question

ANSWER:

ANSWER

ANSWER

16. Find the solution set of the following in equation

equation

equation

ANSWER:

ANSWER

ANSWER

SECTION’C’ (DETAILED- ANSWER QUESTION)

(17) Factorize the following:

equation

equation

ANSWER:

ANSWER

ANSWER

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.

ANSWER:

ANSWER

20.(a) A set of data contains the values as 148, 145, 160, 157, 156, 160, 160, 165, show that the mode> median> Mean

ANSWER:

ANSWER

(b) .Findthe factors of x3 – 21x + 20 by means of the remainder theorem.

ANSWER:

ANSWER

ANSWER

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.

ANSWER:

ANSWER

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

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