Mathematics For Class IX (Science) - MCQs Book 2022- By Ustani G

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Mathematics
For Class IX (Science)
MCQs Book 2022

By Ustani G
"According to prescribed syllabus of all board of secondary education, Sindh."
Team Of Ustani G, Free Educational Team, Karachi.(YouTube Channel)

MULTIPLE CHOICE QUESTIONS

CHAPTER 01
REAL AND COMPLEX NUMBERS

Choose the correct answer from the options given in each question.

CHAPTER 02
LOGARITHMS

Choose the correct answer from the options given in each question.

1. If 𝑎^𝑥 = 𝑛, then ______.
(a) 𝑎 = log_𝑥𝑛
(b) 𝑥 = log_n𝑎
(c) 𝑥 = log_a𝑛 ✓
(d) 𝑎 = log_n𝑥

2. The relation of 𝑦 = log_z𝑥 implies:
(a) 𝑦^𝑥=𝑧
(b) 𝑧^y=𝑥 ✓
(c) 𝑥^z=𝑦
(d) 𝑦^z=𝑥

3. The logarithm of unity to any base is:
(a) 1
(b) 10
(c) 𝑒
(d) 0 ✓

4. The logarithm to any number to itself as base is ______
(a) 1 ✓
(b) 0
(c) −1
(d) 10

5. log𝑒 = _______ where 𝑒 ≈ 2.718
(a) 0
(b) 0.4343 ✓
(c) ∞
(d) 1

CHAPTER 03
ALGEBRAIC EXPRESSION AND FORMULAS

Choose the correct answer from the options given in each question.

1. 4𝑥 + 3𝑦 − 2 is an algebraic _____
(a) expression ✓
(b) sentence
(c) equation
(d) inequation

2. The degree of polynomial 4𝑥⁴ + 2𝑥²𝑦 is _______
(a) 1
(b) 2
(c) 3
(d) 4 ✓

3. 𝑎³ + 𝑏³ is equal to ______
(a) (𝑎 − 𝑏)(𝑎² + 𝑎𝑏 + 𝑏²)
(b) (𝑎 + 𝑏)(𝑎² − 𝑎𝑏 + 𝑏²) ✓
(c) (𝑎 − 𝑏)(𝑎² − 𝑎𝑏 + 𝑏²)
(d) (𝑎 + 𝑏)(𝑎² + 𝑎𝑏 − 𝑏²)

4. (3 + √2)(3 − √2) is equal to _____
(a) 7 ✓
(b) −7
(c) −1
(d) 1

5. Conjugate of Surd 𝑎 + √𝑏 is ______
(a) − 𝑎 + √𝑏
(b) 𝑎 − √𝑏 ✓
(c) √a + √𝑏
(d) √a − √𝑏

18. (3 + √3)(3 − √2) = _______
(a) 12
(b) 9
(c) 6 ✓
(d) 3

19. Which of the following is not surd?
(a) √2
(b) √3
(c) √2 + 5
(d) √𝜋 ✓

20. In the polynomial with the variable 𝑥, all the powers of 𝑥 are _____ integers.
(a) non-negative ✓
(b) negative
(c) non-positive
(d) none of these

21. Polynomial means an expression with:
(a) one term
(b) two terms
(c) three terms
(d) many terms ✓

CHAPTER 04
FACTORIZATION

Choose the correct answer from the options given in each question.
1. The factor 𝑥² − 5𝑥 + 6 are ______
(a) 𝑥 + 1, 𝑥 − 6 ✓
(b) 𝑥 − 2, 𝑥 − 3
(c) 𝑥 + 6, 𝑥 − 1
(d) 𝑥 + 2, 𝑥 + 3

2. Factors 8𝑥³ + 27𝑦³ are ______
(a) (2𝑥 + 3𝑦)(4𝑥² − 9𝑦²)
(b) (2𝑥 − 3𝑦)(4𝑥² − 9𝑦²)
(c) (2𝑥 + 3𝑦)(4𝑥² − 6𝑥𝑦 + 9𝑦²) ✓
(d) (2𝑥 − 3𝑦)(4𝑥² + 6𝑥𝑦 + 9𝑦²)

3. Factors 3𝑥² − 𝑥 − 2 are ______
(a) (𝑥 + 1)(3𝑥 − 2)
(b) (𝑥 + 1)(3𝑥 + 2)
(c) (𝑥 − 1)(3𝑥 − 2)
(d) (𝑥 − 1)(3𝑥 + 2) ✓

4. Factors of 𝑎⁴−4𝑏⁴ are _____
(a) (𝑎 − 𝑏)(𝑎 + 𝑏)(𝑎²+4𝑏²)
(b) (𝑎² − 2𝑏²)(𝑎² + 2𝑏²) ✓
(c) (𝑎 − 𝑏)(𝑎 + 𝑏)(𝑎² − 4𝑏²)
(d) (𝑎 − 2𝑏)(𝑎² + 2𝑏²)

5. What will be added to complete the square of 9𝑎² − 12𝑎𝑏?
(a) − 16𝑏²
(b) 16𝑏²
(c) 4𝑏² ✓
(d) − 4𝑏²

6. Find 𝑚 so that 𝑥² + 4𝑥 + 𝑚 is a complete square:
(a) 8
(b) −8
(c) 4 ✓
(d) 16

7. Factors of 5𝑥² − 17𝑥𝑦 − 12𝑦² are _____
(a) (𝑥 + 4𝑦)(5𝑥 + 3𝑦)
(b) (𝑥 − 4𝑦)(5𝑥 − 3𝑦)
(c) (𝑥 − 4𝑦)(5𝑥 + 3𝑦) ✓
(d) (5𝑥 − 4𝑦)(𝑥 + 3𝑦)

19. How many factors of a cubic expression are there?
(a) zero
(b) 1
(c) 2
(d) 3 ✓

20. (𝑥 − 𝑦)(𝑥² + 𝑥𝑦 + 𝑦²) = ______
(a) 𝑥³ − 𝑦³ ✓
(b) 𝑥² + 𝑦²
(c) (𝑥 + 𝑦)²
(d) (𝑥 − 𝑦)²

CHAPTER 05
ALGEBRAIC MANIPULATION

Choose the correct answer from the options given in each question.
1. H.C.F. of 𝑝3𝑞−𝑝𝑞3 and 𝑝³𝑞² − 𝑝²𝑞⁵ is _________
(a) 𝑝𝑞(𝑝² − 𝑞²)
(b) 𝑝𝑞(𝑝 − 𝑞) ✓
(c) 𝑝²𝑞²(𝑝 − 𝑞)
(d) 𝑝𝑞(𝑝³ − 𝑞²)

2. H.C.F. of 5𝑥²𝑦² and 20𝑥³𝑦³ is:
(a) 5𝑥²𝑦² ✓
(b) 20𝑥³𝑦³
(c) 100𝑥⁵𝑦⁵
(d) 5𝑥𝑦

3. H.C.F. of (𝑥−2) and (𝑥² + 𝑥 − 6) is:
(a) 𝑥² + 𝑥 − 6
(b) 𝑥 + 2
(c) 𝑥 − 2 ✓
(d) 𝑥 + 3

4. H.C.F. of (𝑎³ +𝑏³) and (𝑎² − 𝑎𝑏 + 𝑏²) is
(a) 𝑎 + 𝑏
(b) 𝑎² − 𝑎𝑏 + 𝑏² ✓
(c) (𝑎 − 𝑏)²
(d) 𝑎² + 𝑏²

5. H.C.F. of (𝑥² − 5𝑥 + 6) and (𝑥² − 𝑥 − 6) is:
(a) 𝑥 − 3 ✓
(b) 𝑥 + 2
(c) 𝑥² − 4
(d) 𝑥 − 2

6. H.C.F. of (𝑎² − 𝑏²) and (𝑎³ − 𝑏³) is:
(a) 𝑎 − 𝑏 ✓
(b) 𝑎 + 𝑏
(c) 𝑎² + 𝑎𝑏 + 𝑏²
(d) 𝑎² − 𝑎𝑏 + 𝑏²

7. H.C.F. of (𝑥² + 3𝑥 + 2) and (𝑥²+ 4𝑥 + 3) is:
(a) 𝑥 + 1 ✓
(b) (𝑥 + 1)(𝑥 + 2)
(c) (𝑥 + 3)
(d) (𝑥 + 4)(𝑥 + 1)

8. L.C.M. of 15𝑥², 45𝑥𝑦 and 30𝑥𝑦𝑧 is:
(a) 90𝑥𝑦𝑧
(b) 90𝑥²𝑦𝑧 ✓
(c) 15𝑥𝑦𝑧
(d) 15𝑥2𝑦𝑧

CHAPTER 06
LINEAR EQUATION AND LINEAR INEQUALITIES

Choose the correct answer from the options given in each question.
1. Which of the following is the solution of the inequality 3 − 4𝑥 ≤ 11?
(a) 𝑥 ≥ −8
(b) 𝑥 ≥ −2 ✓
(c) 𝑥 ≥ −¹⁴/₃
(d) none of these

2. A statement involving any of the symbols <, >, ≤ or ≥ is called:
(a) equation
(b) identity
(c) inequality ✓
(d) linear equation

3. 𝑥 = ________ is a solution of the inequality −2 > 𝑥 > 32
(a) −5
(b) 3
(c) 0 ✓
(d) 52

4. If 𝑥 is no larger than 10, then:
(a) 𝑥 ≥ 8
(b) 𝑥 ≤ 10 ✓
(c) 𝑥 < 10
(d) 𝑥 > 10

5. If the capacity x of an elevator is at most 1600 pounds, then:
(a) 𝑐 < 1600
(b) 𝑐 ≥ 1600
(c) 𝑐 ≤ 1600 ✓
(d) 𝑐 > 1600

6. 𝑥 = 0 is a solution of the inequality:
(a) 𝑥 > 0
(b) 3𝑥 + 5 > 0
(c) 𝑥 + 2 < 0
(d) 𝑥 − 2 < 0 ✓

7. The linear equation in one variable 𝑥 is:
(a) 𝑎𝑥 + 𝑏 = 0 ✓
(b) 𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0
(c) 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0
(d) 𝑎𝑥² + 𝑏𝑦² + 𝑐 = 0

8. An inconsistent equation is that whose solution set is:
(a) empty ✓
(b) not empty
(c) zero
(d) positive

18. |𝑥| = 0 has only _______ solution:
(a) one ✓
(b) two
(c) three
(d) none of these

19. The equation |𝑥| = 2 is equivalent to:
(a) 𝑥 = 2 or 𝑥 = −2 ✓
(b) 𝑥 = −2 or 𝑥 = −2
(c) 𝑥 = 2 or 𝑥 = 12
(d) 𝑥 = 2 or 𝑥 = −12

20. A/an ________ is equation that is satisfied by every number for which both sides are defined:
(a) identity ✓
(b) conditional
(c) inconsistent
(d) inequation

21. A/an ________ equation is an equation whose solution set is the empty set:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

22. A/an ________ equation is an equation that is satisfied by at least one number but is not an identity:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

23. 𝑥 + 4 = 4 + 𝑥 is __________ equation:
(a) identity ✓
(b) conditional
(c) inconsistent
(d) none

24. 2𝑥 + 1 = 9 is __________ equation:
(a) identity
(b) conditional ✓
(c) inconsistent
(d) none

25. 𝑥 = 𝑥 + 5 is __________ equation:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

26. Equations having exactly the same solution are called _____ solution.
(a) equivalent ✓
(b) linear
(c) inconsistent
(d) inequation

27. A solution that does not satisfy the original equation is called ______ solution.
(a) extraneous ✓
(b) root
(c) general
(d) proper

CHAPTER 07
LINEAR GRAPH AND THEIR APPLICATION

Choose the correct answer from the options given in each question.
1. If (𝑥−1, 𝑦+1) = (0,0), then (𝑥, 𝑦) is:
(a) (1, −1) ✓
(b) (−1, 1)
(c) (1, 1)
(d) (−1, −1)

2. If (𝑥, 0) = (0, 𝑦), then (𝑥, 𝑦) is:
(a) (0, 1)
(b) (1, 0)
(c) (0, 0) ✓
(d) (1, 1)

3. Point (2, −3) lies in ________ quadrant.
(a) I
(b) II
(c) III
(d) IV ✓

4. Point (−3, −3) lies in ________ quadrant.
(a) I
(b) II
(c) III ✓
(d) IV

5. If 𝑦 = 2𝑥 + 1, 𝑥 = 2 then 𝑦 is:
(a) 2
(b) 3
(c) 4
(d) 5 ✓

6. Which ordered pair satisfy the equation 𝑦 = 2𝑥:
(a) (1, 2) ✓
(b) (2, 1)
(c) (2, 2)
(d) (0, 1)

7. The real number 𝑥, 𝑦 of the ordered pair (𝑥, 𝑦) are called ______ of point 𝑃(𝑥, 𝑦) in a plane.
(a) co-ordinate ✓
(b) 𝑥 co-ordinate
(c) 𝑦-co-ordinate
(d) ordinate

8. Cartesian plane is divided into _______ quadrants.
(a) two
(b) three
(c) four ✓
(d) five

9. The point of intersection of two coordinate axes is called:
(a) origin ✓
(b) centre
(c) 𝑥-coordinate
(d) ordinate

10. The 𝑥-coordinate of a point is called _______.
(a) origin
(b) abscissa ✓
(c) 𝑦-coordinate
(d) ordinate

11. The 𝑦-coordinate of a point is called _______.
(a) origin
(b) 𝑥-coordinate
(c) 𝑦-coordinate
(d) ordinate ✓

12. The set of points which lie on the same line are called _______ points.
(a) collinear ✓
(b) similar
(c) common
(d) none of these

13. The plane formed by two straight lines perpendicular to each other is called:
(a) cartesian plane ✓
(b) coordinate axes
(c) plane
(d) none of these

14. An ordered pair is a pair of elements in which elements are written in specific:
(a) order ✓
(b) array
(c) point
(d) none

15. Point (−1, 2) lies in quadrant.
(a) I
(b) II ✓
(c) III
(d) IV

16. Point (1, 1) lies in quadrant.
(a) I ✓
(b) II
(c) III
(d) IV

17. Point (1, −3) lies in quadrant.
(a) I
(b) II
(c) III
(d) IV ✓

18. Which of the following points is one the origin?
(a) (0, 0)
(b) (−2, −3)
(c) (0, 2) ✓
(d) (4, 0)

19. Which of the following lines is parallel to 𝑥-axis?
(a) 𝑥 = 0
(b) 𝑥 = −3
(c) 𝑥 = 3
(d) 𝑦 = −3 ✓

20. Which of the following lines is parallel to 𝑦-axis?
(a) 𝑦 = 2𝑥 ✓
(b) 𝑥 = −3
(c) 𝑦 = 3
(d) 𝑦 = 4𝑥 + 1

CHAPTER 08
QUADRATIC EQUATION

Choose the correct answer from the options given in each question.

CHAPTER 09
CONGRUENT TRIANGLES

Choose the correct answer from the options given in each question.
1. _______ triangle is an equiangular triangle.
(a) a scalene
(b) an isosceles
(c) an equilateral ✓
(d) a right triangle

2. A _______ has two end points.
(a) line
(b) line segment ✓
(c) ray
(d) angle

3. Three points are said to be collinear if they lie on the same:
(a) plane
(b) line ✓
(c) interior
(d) area

4. Two lines can intersect at:
(a) one point ✓
(b) two points
(c) no point
(d) infinite points

5. Two _______ lines cannot intersect each other:
(a) perpendicular
(b) parallel ✓
(c) non-parallel
(d) coplanar

6. All the medians of ______ triangle are equal in measure.
(a) a scalene
(b) an isosceles
(c) an equilateral ✓
(d) a right angled

7. If two angles of a triangle are congruent then the sides opposite to them are:
(a) congruent ✓
(b) equal
(c) non congruent
(d) similar

8. symbol for congruent is:
(a) ↔
(b) N
(c) ≅ ✓
(d) =

9. symbol for correspondence is:
(a) ↔ ✓
(b) N
(c) ≅
(d) =

10. How many end points does a ray have?
(a) 1 ✓
(b) 2
(c) 3
(d) 4

11. Symbolically two congruent triangles ABC and PQR are written as:
(a) ΔABC = ΔPQR
(b) ΔABC ∼ ΔPQR
(c) ΔABC ≅ ΔPQR ✓
(d) ΔABC ≠ ΔPQR

12. Which of the following is possible?
(a) S.S.S ≅ S.S.S
(b) S.A.A ≅ S.A.A
(c) H.S ≅ H.S
(d) S.A.S ✓

13. If sum of measures of two angles is 180° then angles are _______ angles.
(a) complementary
(b) supplementary ✓
(c) equal
(d) right

14. If sum of measures of two angles is 90° then angles are _______ angles.
(a) complementary ✓
(b) supplementary
(c) congruent
(d) acute

15. Hypotenuse is a side opposite to ________ in right angles triangle.
(a) 30°
(b) 60°
(c) 90° ✓
(d) 120°

16. In equilateral triangle each angle is of _________.
(a) 30°
(b) 60° ✓
(c) 90°
(d) 180°

17. Corresponding sides of congruent triangles are:
(a) equal ✓
(b) different
(c) perpendicular
(d) parallel

18. Median bisecting the base angle of an isosceles triangle bisects the _________ angle.
(a) base
(b) vertical ✓
(c) right
(d) acute

19. The median bisecting the base of an isosceles triangle is ________ to the base.
(a) parallel
(b) perpendicular ✓
(c) collinear
(d) adjacent

20. Corresponding angles of congruent triangles are:
(a) congruent ✓
(b) non- congruent
(c) unequal
(d) supplementary

21. Any two medians of an _______ triangle equal in measure.
(a) isosceles
(b) equilateral ✓
(c) acute
(d) obtuse

22. Sum of all the interior angles of a triangle is:
(a) 90°
(b) 150°
(c) 180° ✓
(d) 360°

CHAPTER 10
PARALLELOGRAMS AND TRIANGLES

Choose the correct answer from the options given in each question.

CHAPTER 11
LINE BISECTORS AND ANGLE BISECTORS

Choose the correct answer from the options given in each question.
1. Bisection means to divide into ________ equal parts.
(a) two ✓
(b) three
(c) four
(d) five

2. ______ of line segment means to draw perpendicular which passes through the midpoint of line segment.
(a) right bisection ✓
(b) bisection
(c) congruent
(d) mid-point

3. Any point on the _________ of a line segment is equidistant from its end points.
(a) right bisector ✓
(b) median
(c) angle bisector
(d) altitude

4. Any point equidistant from the end points of line segment is on the _________.
(a) right bisector ✓
(b) median
(c) angle bisector
(d) altitude

5. The bisectors of the angles of a triangle are:
(a) concurrent ✓
(b) congruent
(c) parallel
(d) none of these

6. Bisection of an angle means to draw a ray to divide the given angle into ________ equal parts.
(a) four
(b) three
(c) two ✓
(d) five

7. If CD is right bisector of line segment AB then 𝑚OA = ________
(a) 𝑚OQ
(b) 𝑚OB ✓
(c) 𝑚AQ
(d) 𝑚BQ

8. If CD is right bisector of line segment AB then 𝑚AQ = ________
(a) 𝑚OA
(b) 𝑚OB
(c) 𝑚BQ ✓
(d) 𝑚OD

9. The right bisectors of the sides of an acute triangle intersects each other ________ the triangle.
(a) inside ✓
(b) outside
(c) midpoint
(d) none

10. The right bisectors of the sides of a right triangle intersect each other on the ________.
(a) vertex
(b) midpoint
(c) hypotenuse ✓
(d) none

11. The right bisectors of the sides of an obtuse triangle intersect each other ________ the triangle.
(a) outside ✓
(b) inside
(c) midpoint
(d) none

12. The point of line segment through which the right bisector passes is called its _________ point.
(a) end
(b) mid ✓
(c) non-collinear
(d) trisection

13. The point of intersection of right bisectors of sides of a triangle is equidistant from the ________ of triangle.
(a) sides
(b) vertices
(c) centre ✓
(d) angles

14. The altitudes of a triangle are _________.
(a) congruent
(b) concurrent ✓
(c) equal
(d) parallel

CHAPTER 12
SIDES AND ANGLES OF A TRIANGLE

Choose the correct answer from the options given in each question.
1. Which of the following sets of lengths can be lengths of the sides of a triangle:
(a) 2cm, 3cm, 5cm
(b) 3cm, 4cm, 5cm ✓
(c) 2cm, 4cm, 7cm
(d) 1cm, 2cm, 3cm

2. Two sides of a triangle measure 10cm and 15cm. Which of the following measure is possible for the third side:
(a) 5 cm
(b) 20 cm ✓
(c) 25 cm
(d) 30 cm

3. The angle opposite to the longer side is:
(a) greater ✓
(b) shorter
(c) equal
(d) none

4. In right angle triangle greater angle of:
(a) 60°
(b) 30°
(c) 75°
(d) 90° ✓

5. In an isosceles right-angles triangle angles other than right angle are each of:
(a) 40°
(b) 45° ✓
(c) 50°
(d) 55°

6. A triangle having two congruent sides is called _________ triangle.
(a) equilateral
(b) isosceles ✓
(c) right
(d) none

7. Perpendicular to line from an angle of ___________.
(a) 30°
(b) 60°
(c) 90° ✓
(d) 120°

8. Sum of two sides of triangle is ________ than the third.
(a) greater ✓
b) smaller
(c) equal 
(d) none

9. The distance between a line and a point on it is _________.
(a) zero ✓
(b) one
(c) equal
(d) none

10. The difference of two sides of a triangle is ________ the third side.
(a) greater than
(b) smaller than ✓
(c) equal to
(d) congruent to

11. In a triangle, the side opposite to greater angle is __________.
(a) smaller
(b) greater ✓
(c) equal
(d) congruent

12. In a triangle the angles opposite to congruent sides are ________.
(a) congruent ✓
(b) concurrent
(c) unequal
(d) none

13. In a triangle, the side opposite to smaller angle is ________.
(a) smaller ✓
(b) greater
(c) congruent
(d) concurrent

14. An exterior angle of a triangle is ________ non-adjacent interior angle.
(a) equal to
(b) smaller than
(c) greater than ✓
(d) congruent to

15. For a ΔABC, which of the following is true? (a) 𝑚AB + 𝑚BC < 𝑚CA
(b) 𝑚AB − 𝑚BC > 𝑚CA
(c) 𝑚AB + 𝑚BC > 𝑚CA ✓
(d) 𝑚AB + 𝑚BC >/ 𝑚CA  (>/  is greater or not equal to sign)

16. What is the supplement of a right angle?
(a) 60°
(b) 90° ✓
(c) 120°
(d) 180°

17. The sum of the measures of two sides of a triangle is greater than ________ the measure of the median which bisects the third side.
(a) twice ✓
(b) thrice
(c) hypotenuse
(d) angles

18. In an obtuse angled triangle, the side opposite to the obtuse angle is ________ than each of the other two sides.
(a) smaller
(b) longer ✓
(c) twice
(d) thrice

CHAPTER 13
PRACTICAL GEOMETRY- TRIANGLES

Choose the correct answer from the options given in each question.
1. In a right angled triangle, the square of the length of hypotenuse is equal to the ________ of the squares of the lengths of the other two sides:
(a) sum ✓
(b) difference
(c) zero
(d) none of these

2. If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a ________ triangle.
(a) right angles ✓
(b) acute angled
(c) obtuse angles
(d) none of these

3. Let c be the longest of the sides a, b and c of a triangle. If 𝑎2+𝑏2=𝑐2, then the triangle is __________:
(a) right ✓
(b) acute
(c) obtuse
(d) none of these

4. Let c be the longest of the sides a, b and c of a triangle. If 𝑎2+𝑏2>𝑐2, then the triangle is __________:
(a) acute ✓
(b) right
(c) obtuse
(d) none of these

5. Let c be the longest of the sides a, b and c of a triangle. If 𝑎2+𝑏2 < 𝑐2, then the triangle is __________:
(a) acute
(b) right
(c) obtuse ✓
(d) none of these

6. If 3 cm and 4 cm are two sides of a right angled triangle, then hypotenuse is:
(a) 5cm ✓
(b) 3cm
(c) 4cm
(d) 2cm

7. In right triangle __________ is a side opposite to right angle.
(a) base
(b) perpendicular
(c) hypotenuse ✓
(d) none

8. In the figure, the value of 𝑥 is:
(a) 6cm
(b) 8cm ✓
(c) 10cm
(d) 16cm

9. In the figure, the value of 𝑥 is:
(a) 5cm
(b) 8cm
(c) 12cm ✓
(d) 18cm

10. In the figure, the value of 𝑥 is:
(a) 2cm
(b) 1cm ✓
(c) √2 cm
(d) 3cm

11. In right angles triangle greater angle is ___________.
(a) 30°
(b) 60°
(c) 90° ✓
(d) 120°

12. In right angled triangle on angle is 90° and other two angles are ___________.
(a) obtuse
(b) acute ✓
(c) right
(d) supplementary

13. If hypotenuse of an isosceles right angled triangle is √2 then each of other side is:
(a) 1cm ✓
(b) 2cm
(c) 3cm
(d) 4cm

14. In right angled triangle which side is the longest side?
(a) perpendicular
(b) base
(c) hypotenuse ✓
(d) none of these

15. In right angled triangle, if 𝑚∠B=90° then which of the following is true?
(a) 𝑎² + 𝑏² = 𝑐²
(b) 𝑎² + 𝑐² = 𝑏² ✓
(c) 𝑏² + 𝑐² = 𝑎²
(d) 𝑎² − 𝑐² = 𝑏²

16. In an isosceles right angled triangle two acute angles are equal to:
(a) 30°
(b) 45° ✓
(c) 60°
(d) 90°

CHAPTER 14
THEOREMS RELATED WITH AREA

Choose the correct answer from the options given in each question.

(c) A = L × W ✓
(d) A = L²

14. Area of parallelogram is _________.
(a) A = ½Base × Heigth
(b) A = Base × Heigth ✓
(c) A = L × W
(d) A = L²

15. If the length and breadth of a rectangle are ‘a’ and ‘b’ then its area will be:
(a) 𝑎 + 𝑏
(b) 𝑎 × 𝑏 ✓
(c) 𝑎 − 𝑏
(d) 𝑎 = 𝑏

16. In most cases similar figures have ________ areas.
(a) same
(b) different ✓
(c) equal
(d) congruent

17. All congruent figures have ________ areas.
(a) same ✓
(b) different
(c) zero
(d) non-congruent

18. Area of a geometrical figure is always _______ real number.
(a) zero
(b) positive ✓
(c) negative
(d) rational

CHAPTER 15
PROJECTION OF A SIDE OF A TRIANGLE

Choose the correct answer from the options given in each question.
1. A triangle having two sides congruent is called __________.
(a) scalene
(b) right angled
(c) equilateral
(d) isosceles ✓

2. A quadrilateral having each angle equal to 90° is called _______.
(a) parallelogram
(b) rectangle ✓
(c) trapezium
(d) rhombus

3. The right bisectors of the three sides of a triangle are _________.
(a) congruent
(b) collinear
(c) concurrent ✓
(d) parallel

4. The __________ altitudes of an isosceles triangle are congruent:
(a) two ✓
(b) three
(c) four
(d) none of these

5. A point equidistant from the end points of a line segment is on its _________.
(a) bisector
(b) right bisector ✓
(c) perpendicular
(d) median

6. ________ congruent triangles can be made by joining the midpoints of the sides of a triangle.
(a) three
(b) four ✓
(c) five
(d) two

7. The diagonals of a parallelogram __________ each other.
(a) bisect ✓
(b) bisect at right angle
(c) trisect
(d) none of these

8. The medians of a triangle cut each other in the ratio:
(a) 4:1
(b) 3:1
(c) 2:1 ✓
(d) 1:1

9. One angle on the base of an isosceles triangle is 30°. What is the measure of its vertical angle:
(a) 30°
(b) 60°
(c) 90°
(d) 120° ✓

10. If the three altitudes of a triangle are congruent then triangle is:
(a) equilateral ✓
(b) right angled
(c) isosceles
(d) acute angled

11. If two medians if a triangle are congruent then the triangle will be:
(a) isosceles ✓
(b) equilateral
(c) right angled
(d) acute angled

12. a line segment joining a vertex of a triangle to the midpoint of its opposite side is called a _________ of the triangle.
(a) altitude
(b) median ✓
(c) angle bisector
(d) right bisector

13. A line segment from a vertex of triangle perpendicular to the line containing the opposite side, is called an _______ of the triangle:
(a) altitude ✓
(b) median
(c) angle bisector
(d) right bisector

14. The point of concurrency of the three altitudes of a Δ is called its _________.
(a) ortho-centre ✓
(b) in-centre
(c) circum-centre
(d) none

15. The internal bisectors of the angles of a triangle meet at a point called the ________ of the triangle.
(a) in-centre ✓
(b) ortho-centre
(c) circum-centre
(d) none

16. The point of concurrency of the three perpendicular bisectors of the sides of:
(a) concurrent ✓
(b) congruent
(c) mid-point
(d) vertical angle

17. Point of concurrency of three medians of a triangle is called:
(a) in-centre
(b) ortho-centre
(c) centroid ✓
(d) circum-centre

18. sum of interior angles of a triangle is __________.
(a) 60°
(b) 120°
(c) 180° ✓
(d) 240°

19. The side opposite to right angle in right angled triangle is called ___________.
(a) base
(b) perpendicular
(c) hypotenuse ✓
(d) altitude

20. The altitudes of a right angled triangle are concurrent at the ________.
(a) mid-point of hypotenuse
(b) vertex of right angle ✓
(c) mid-point of base
(d) vertical

21. The triangle are said to be ________ if they are equiangular.
(a) congruent
(b) similar ✓
(c) equal
(d) scalene

22. All the _______ right bisectors of sides of triangle are concurrent.
(a) one
(b) two
(c) three ✓
(d) four

23. All the three bisectors of angles of a triangle are __________.
(a) congruent
(b) concurrent ✓
(c) parallel
(d) perpendicular

24. All the three medians of a triangle are __________.
(a) congruent
(b) concurrent ✓
(c) parallel
(d) perpendicular

25. All the three altitudes of a triangle are __________.
(a) congruent
(b) concurrent ✓
(c) parallel
(d) perpendicular

26. In-centre is the point of concurrency of three ________ of triangle.
(a) right bisectors
(b) angle bisectors ✓
(c) altitudes
(d) medians

27. Circum-centre is point of concurrency of three _____- of triangle.
(a) right bisectors ✓
(b) angle bisectors
(c) altitudes
(d) medians

28. Centroid is the point of concurrency of three ________ of triangle.
(a) right bisectors
(b) angle bisectors
(c) altitudes
(d) medians ✓

29. Three or more than three line passing through the same point are called ________ lines.
(a) congruent
(b) concurrent ✓
(c) parallel
(d) perpendicular

30. The common point of three or more than three lines is called ________.
(a) central point
(b) point of concurrency ✓
(c) vertex
(d) centroid

31. In right angled triangle if one angle is 30°, then other angle will be _________.
(a) 15°
(b) 30°
(c) 45°
(d) 60° ✓

32. In right angled triangle if one angle is 60°, then other angle will be _________.
(a) 15°
(b) 30° ✓
(c) 45°
(d) 60°

CHAPTER 16
INTRODUCTION TO COORDINATE GEOMETRY/ ANALYTICAL GEOMETRY

Choose the correct answer from the options given in each question.
1. Distance between points (0,0) and (1,1) is:
(a) 0
(b) 0
(c) √2 ✓
(d) 2

2. Distance between points (1,0) and (0,1) is:
(a) 0
(b) 0
(c) √2 ✓
(d) 2

3. Mid-point of the points (2,2) and (0,0) is:
(a) (1,1) ✓
(b) (1,0)
(c) (0,1)
(d) (−1,−1)

4. Mid-point of the points (2,−2) and (−2,2) is:
(a) (2,2)
(b) (−2,−2)
(c) (0,0) ✓
(d) (1,1)

5. A triangle having all sides equal is called:
(a) isosceles
(b) scalene
(c) equilateral ✓
(d) none of these

6. A triangle having all sides different is called:
(a) isosceles
(b) scalene ✓
(c) equilateral
(d) none of these

7. The points P, Q and R are collinear if:
(a) |PQ|+|QR|=|PR| ✓
(b) |PQ|−|QR|=|PR|
(c) |PQ|+|QR|=0
(d) none of these

8. The distance between points P(𝑥1,𝑦1) and P(𝑥2,𝑦2) in the coordinate plane is: 𝑑>0

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