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Class 10 - Mathematics- Bise Multan 2025 2nd Annual Group-I

Mathematics - Class 10

Student Name

Roll Number

Section

Time Allowed

2 hours

Total Marks

Chapters

Date

Examiner Signature

Bubble Sheet for Q.No.1 (MCQs) Fill the correct option bubble for each question number.

A B C D

10.

A B C D

11.

A B C D

12.

A B C D

13.

A B C D

14.

A B C D

15.

A B C D

MAXIMUM MARKS: 15	OBJECTIVE حصہ معروضی	15 = کل نمبر	سوال نمبر Q.No.1
For each objective question four options (A–D) are given. Fill the bubble of the correct option against the question number on the bubble sheet.

Sr. No.	Questions	A	B	C	D
(i)	An equation of the type \( 3^x + 3^{2-x} + 6 = 0 \) is a/an:	Exponential equation	Radical equation	Reciprocal equation	Linear equation
(ii)	Two linear factors of \( x^2 - 15x + 56 \) are:	\( (x - 7) \) and \( (x + 8) \)	\( (x + 7) \) and \( (x - 8) \)	\( (x - 7) \) and \( (x - 8) \)	\( (x + 7) \) and \( (x + 8) \)
(iii)	The discriminant of \( ax^2 + bx + c = 0 \) is:	\( b^2 + 4ac \)	\( b^2 - 4ac \)	\( -b^2 - 4ac \)	\( -b^2 + 4ac \)
(iv)	If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), then product of the roots \( 2\alpha \) and \( 2\beta \) is:	-2	2	4	-4
(v)	In a ratio \( x : y \), \( y \) is called:	Relation	Antecedent	Consequent	Proportion
(vi)	In a proportion \( a : b :: c : d \), \( a \) and \( d \) are called:	Means	Extremes	Third proportional	Consequent
(vii)	Partial fractions of \( \frac{x-2}{(x-1)(x+2)} \) are of the form:	\( \frac{A}{x-1} + \frac{B}{x+2} \)	\( \frac{Ax}{x-1} + \frac{B}{x+2} \)	\( \frac{A}{x-1} + \frac{Bx+C}{x+2} \)	\( \frac{Ax+B}{x-1} + \frac{C}{x+2} \)
(viii)	The number of elements in power set \( \{2, 3, 4\} \) is:	4	6	8	9
(ix)	If \( A \subseteq B \), then \( A \cup B \) is equal to:	A	C	\( \emptyset \)	B
(x)	The spread or scatterness of observations in a data set is called:	Average	Dispersion	Central tendency	Mode
(xi)	\( \frac{3\pi}{4} \) radians =	\( 135^\circ \)	\( 115^\circ \)	\( 150^\circ \)	\( 30^\circ \)
(xii)	Radii of a circle are:	All unequal	Double of diameter	Half of any chord	All equal
(xiii)	A line which has only one point in common with a circle is called:	Sine of a circle	Cosine of a circle	Tangent of a circle	Secant of a circle
(xiv)	The semi circumference and the diameter of a circle both subtend a central angle of:	\( 180^\circ \)	\( 90^\circ \)	\( 360^\circ \)	\( 270^\circ \)
(xv)	The measure of the external angle of a regular octagon is:	\( π/6 \)	\( π/4 \)	\( π/8 \)	\( π/3 \)

(i)

An equation of the type \( 3^x + 3^{2-x} + 6 = 0 \) is a/an:

(a) Exponential equation (b) Radical equation (c) Reciprocal equation (d) Linear equation

(ii)

Two linear factors of \( x^2 - 15x + 56 \) are:

(a) \( (x - 7) \) and \( (x + 8) \) (b) \( (x + 7) \) and \( (x - 8) \) (c) \( (x - 7) \) and \( (x - 8) \) (d) \( (x + 7) \) and \( (x + 8) \)

(iii)

The discriminant of \( ax^2 + bx + c = 0 \) is:

(a) \( b^2 + 4ac \) (b) \( b^2 - 4ac \) (c) \( -b^2 - 4ac \) (d) \( -b^2 + 4ac \)

(iv)

If \( \alpha, \beta \) are the roots of \( x^2 - x - 1 = 0 \), then product of the roots \( 2\alpha \) and \( 2\beta \) is:

(a) -2 (b) 2 (c) 4 (d) -4

(v)

In a ratio \( x : y \), \( y \) is called:

(a) Relation (b) Antecedent (c) Consequent (d) Proportion

(vi)

In a proportion \( a : b :: c : d \), \( a \) and \( d \) are called:

(a) Means (b) Extremes (c) Third proportional (d) Consequent

(vii)

Partial fractions of \( \frac{x-2}{(x-1)(x+2)} \) are of the form:

(a) \( \frac{A}{x-1} + \frac{B}{x+2} \) (b) \( \frac{Ax}{x-1} + \frac{B}{x+2} \) (c) \( \frac{A}{x-1} + \frac{Bx+C}{x+2} \) (d) \( \frac{Ax+B}{x-1} + \frac{C}{x+2} \)

(viii)

The number of elements in power set \( \{2, 3, 4\} \) is:

(a) 4 (b) 6 (c) 8 (d) 9

(ix)

If \( A \subseteq B \), then \( A \cup B \) is equal to:

(a) A (b) C (c) \( \emptyset \) (d) B

(x)

The spread or scatterness of observations in a data set is called:

(a) Average (b) Dispersion (c) Central tendency (d) Mode

(xi)

\( \frac{3\pi}{4} \) radians =

(a) \( 135^\circ \) (b) \( 115^\circ \) (c) \( 150^\circ \) (d) \( 30^\circ \)

(xii)

Radii of a circle are:

(a) All unequal (b) Double of diameter (c) Half of any chord (d) All equal

(xiii)

A line which has only one point in common with a circle is called:

(a) Sine of a circle (b) Cosine of a circle (c) Tangent of a circle (d) Secant of a circle

(xiv)

The semi circumference and the diameter of a circle both subtend a central angle of:

(a) \( 180^\circ \) (b) \( 90^\circ \) (c) \( 360^\circ \) (d) \( 270^\circ \)

(xv)

The measure of the external angle of a regular octagon is:

(a) \( π/6 \) (b) \( π/4 \) (c) \( π/8 \) (d) \( π/3 \)

Subjective Type (Part-I) / حصہ انشائیہ

Q. 2: Write short answers to any 6 questions. (2x6=12)

Max. Marks: 12

(i)

Write \( \frac{x^2+4}{3} - \frac{x}{7} = -1 \) in standard form of quadratic equation.

lines
(ii)

Solve \( 5x^2 = 15x \)

lines
(iii)

Define exponential equation.

lines
(iv)

Find discriminant. \( x^2 - 30x + 25 = 0 \)

lines
(v)

Evaluate. \( (8 + 3\omega + 3\omega^2)^2 \)

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(vi)

Write quadratic equation having roots 1 and 7.

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(vii)

Define proportion.

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(viii)

Find the value of 'K' if \( R \propto T^2 \) and \( R = 8 \) when \( T = 3 \).

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(ix)

Find mean proportion between 5 and 180.

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Q. 3: Write short answers to any 6 questions. (2x6=12)

Max. Marks: 12

(i)

Define Rational Fraction and give example.

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(ii)

Convert the improper fraction into proper fraction: \( \frac{3x^2 - 2x - 1}{x^2 - x + 1} \)

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(iii)

What is meant by intersection of two sets?

lines
(iv)

If \( X = \{2, 4, 6, \dots, 20\} \) and \( Y = \{4, 8, 12, \dots, 24\} \), then Find \( X - Y \)

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(v)

If \( L = \{a, b, c\}, M = \{3, 4\} \) then find a binary relation in \( L \times M \)

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(vi)

Find 'a' and 'b' if \( (a - 4, b - 2) = (2, 1) \)

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(vii)

Find the Geometric Mean of the observations 2, 4, 8.

lines
(viii)

Define Median and give a short example.

lines
(ix)

Find the Mean salary of workers: 11500, 12400, 14500, 14800, 15000

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Q. 4: Write short answers to any 6 questions. (2x6=12)

Max. Marks: 12

(i)

Verify that \( \tan^4 \theta + \tan^2 \theta = \tan^2 \theta \sec^2 \theta \)

lines
(ii)

Convert \( -225^\circ \) to radian.

lines
(iii)

Find \( r \) when \( l = 52 \text{ cm}, \theta = 45^\circ \)

lines
(iv)

Write two Pythagorean identities:

lines
(v)

Define circle and show its figure.

lines
(vi)

Define length of a tangent.

lines
(vii)

Define obtuse angle and make its figure.

lines
(viii)

The length of the side of a regular pentagon is 7 cm. What is its perimeter?

lines
(ix)

Define circumscribed circle.

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Section-II: Attempt any 3 questions. (8x3=24 marks)

Q. 5 (8 marks)
1. (i) Solve the equation \( (x-1)(x-2)(x-8)(x+5) + 360 = 0 \)
  lines
2. (ii) Find the cube roots of \( -1 \)
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Q. 6 (8 marks)
1. (i) Find \( x \) in the following proportion: \( p^2 + pq + q^2 : x :: \frac{p^3 - q^3}{p + q} : (p - q)^2 \)
  lines
2. (ii) Resolve into partial fraction: \( \frac{x^2}{(x + 2)(x^2 + 4)} \)
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Q. 7 (8 marks)

(i) If \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \), \( A = \{1, 3, 5, 7\} \), and \( B = \{2, 3, 5, 7\} \), then verify that \( (A \cup B)' = A' \cap B' \).
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(ii) Determine the variance for the following grouped data:

Length لمبائی	20 – 22	23 – 25	26 – 28	29 – 31	32 – 34
Frequency تعداد	3	6	12	9	2

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Q. 8 (8 marks)
1. (i) If \( \csc \theta = \frac{13}{12} \) and \( \sec \theta > 0 \), find the remaining trigonometric functions.
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2. (ii) Inscribe a circle in an equilateral triangle ABC with each side of length 5cm.
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Q. 9 (8 marks)
1. (i) Prove that two chords of a circle which are equidistant from the centre, are congruent. OR
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2. (ii) Prove that any two angles in the same segment of a circle are equal.
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