Board of Secondary Education, Karachi, and Sindh all board Grade 10, Class 10th Mathematics Solved Past Papers read and pdf Download.

## Mathematics Solved Past Paper

Table of Contents

### i) The median of 2,8,6,10,4,12 is:

A. 6

B. 7

C. 8

D. 9**Answer:**

C. 8

### ii) Sin30^{o}=

A. √3/2

B. 1/√2

C. 1/√3

D. 1/2**Answer:**

D. 1/2

### iii) The multiplicative inverse of a-b is:

A. -a+b

B. a+b

C. 1/a-b

D. 1/a+b**Answer:**

C. 1/a-b

### iv) In 35,30,10,48,100,90 the range (R) is:

A. 10

B. 90

C. 100

D. 35**Answer:**

B. 90

### v) If (x^{3}+4x^{2}-7x+3)÷(x-1) then the remainder is:

A. 0

B. 1

C. 2

D. -1**Answer:**

B. 1

### vi) If x=2+√5, then x^{2} is:

A. 2√5

B. 9+4√5

C. 9

D. None of these**Answer:**

B. 9+4√5

Read more: Class 10 Physics Solved Past Papers

### vii) The characteristics of log 226.7 is:

_

A. 2

_

B. 3

C. 2

D. 3**Answer:**

C. 2

### viii) The point of concurrency of the medians of a triangle is called:

A. Centroid

B. Circum-centre

C. in-centre

D. None of these**Answer:**

A. Centroid

### ix) 8^{1/3} × 36 ^{1/2} =

A. 8

B. 36

C. 12

D. 24**Answer:**

C. 12

### x) The mean proportion of 14 and 56 is:

A. 14

B. 56

C. 28

D. 70**Answer:**

C. 28

### xi) (-5,-3) is in quadrant:

A. 1^{st}

B. 2^{nd}

C. 3^{rd}

D. 4^{th}**Answer:**

C. 3^{rd}

### xii) The solution set of 3x^{2}-10x=0

A. {10}

B. {10/3}

C. {0}

D. {0,10/3]**Answer:**

D. {0,10/3]

### xiii) If log_{7}x=2 then x=

A. 14

B. 128

C. 49

D. 64**Answer:**

C. 49

### xiv) If x+y=5 and x-y=5 then 4xy=:

A. 10

B. 25

C. 0

D. 5**Answer:**

C. 0

### xv) H.C.F of a^{3}+b^{3} and a^{2}-ab+b^{2} is:

A. a^{2}-ab+b^{2}

B. a+b

C. a-b

D. a^{2}+b^{2}**Answer:**

A. a^{2}-ab+b^{2}

### xvi) The cartesian product of sets A and B is written as:

A. A.B

B. A×B

C. AΔB

D. B×A**Answer:**

B. A×B

### xvii) If a:b=c:d the a:c=b:d this property of proportion is called:

A. Invertendo

B. Dividendo

C. Alternando

D. Componendo**Answer:**

C. Alternando

### xviii) The angle inscribed in a major arc is a/an:

A. Right angle

B. Obtuse angle

C. Acute angle

D. None of these**Answer:**

C. Acute angle

### xix) The sum of complementary angles is:

A. 180^{o}

B. 45^{o}

C. 90^{o}

D. 360^{o}**Answer:**

C. 90^{o}

### xx) If |A|=0 then matrix A is called:

A. Singular matrix

B. Non-singular matrix

C. Square matrix

D. None of these**Answer:**

A. Singular matrix

**Q.2 i) If A = {1,2,3,4,5,6,7,8} and B = {2,4,6,8,10} then prove that: ** **AΔB=(A∪B)-(A∩B) **

**Q.3 i) Find the value of x**^{3}+y^{3} when x+y=-5 and xy=8.

^{3}+y

^{3}when x+y=-5 and xy=8.

**Q.3 ii) Find the solution set of the following equation and also verify the answer:√25y-6=4√y+3**

**Q.3 iii) For what value of a and b, x ^{4}+4x^{3}+10x^{2}+ax+b will be a perfect square?**

**Q.3 iii) For what value of a and b, x**^{4}+4x^{3}+10x^{2}+ax+b will be a perfect square?

^{4}+4x

^{3}+10x

^{2}+ax+b will be a perfect square?

Solutions

**Q.4 i) Solve triangle ACB when m∠C=90**^{o}, c= 8cm, b = 4√3 cm

^{o}, c= 8cm, b = 4√3 cm

**Q.4 ii) Eliminate ‘x’ from the following equations: x+1/x=2p, x-1/x=2q+1**

**Q.5 i) If a transversal intersects two coplaner lines such that the pair of alternate angles are congruent, then the lines are parallel. Prove it.**

**Q.5 iii) Find the factors with help of Remainder Theorem : x**^{3} – 4x^{2} + 5x – 2.

^{3}– 4x

^{2}+ 5x – 2.

**Q.6 i) Find the variance of the following sets observations :** **X = 11,13, 25,15,12,18,17, 23, 20,16 **

### Q.6 iii) The measure of a central of a minor arc of a circle is double that of the inscribed angle of the corresponding major arc. Prove it.

### Q.9 b) One and only one circle can pass through three non-collinear points.

**Q.11) The distance between two points P and Q is 7.5cm. with the centre,** P draw a circle of radius 4.5cm. From the point Q, draw a tangent to the circle. Measure the segment of the tangent. Also,** write the steps of construction.**