Class 9 Mathematics MCQ Introduction to Euclid’s Geometry Mathematics

Question : The shape of base of Pyramid is:
(a) Triangle
(b) Square
(c) Rectangle
(d) Any polygon

Question : The first known proof that ‘the circle is bisected by its diameter’ was given by:
(a) Pythagoras
(b)Thales
(c) Euclid
(d) Hypatia

Question : How many lines do pass through two distinct points?
(a) 1
(b) 2
(c) 3
(d) 4

Question : The things which are double of same things are:
(a) halves of same thing
(b) double of the same thing
(c) Equal
(d) Unequal

Question : If a > b and b > c, then,
(a) a = c
(b) a < c (iii) a > c
(d) a ≤ c

Question : Three or more lines are called concurrent lines if they pass through …….. point.
(a) Two
(b) Three
(c) Same
(d) None of these

Question : Greeks emphasized on:
(a) Public worship
(b) Household rituals
(c) Both (i) and (ii)
(d) None of (i), (ii) and (iii)

Question : The things which coincide with one another are:
(a) equal
(b) unequal
(c) half of same thing
(d) triple of one another

Question : Lines are parallel if they do not intersect’ – is stated in the form of:
(a) A postulate
(b) An axiom
(c) A definition
(d) A proof

Question : The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
(a) 5, 3
(b) 7, 1
(c) 4, 4
(d) 2, 6

Question : The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.
(a) 57
(b) 75
(c) 85
(d) 58

Question : The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5 . Then the original number was _______.
(a) 7/11
(b) 3/5
(c) 5/8
(d) 4/7

Question : If am = bl and bn ≠ cm, then the system of equations
    ax + by = c
    lx + my = n
(a) Has a unique solution.
(b) Has no solution.
(c) Has infinitely many solutions.
(d) May or may not have a solution.

Question : The value of k, for which the system of equations kx – 3y + 6 = 0, 4x – 6y + 15 = 0 represent parallel lines, is _______.
(a) 1
(b) 2
(c) 3
(d) 4

Question : If the system of equations
    2x + 3y = 7
    2ax + (a + b)y = 28
has infinitely many solutions, then the values of a and b respectively are _______.
(a) 2, 5
(b) 5, 8
(c) 4, 8
(d) 3, 6

Question : In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B). The three angles will be _______.
(a) 20°, 40°, 120°
(b) 30°, 60°, 90°
(c) 45°, 45°, 90°
(d) 90°, 40°, 50°

Question : ax + by + c = 0 does not represent an equation of line when _______.
(a) a = c = 0, b ≠ 0
(b) b = c = 0, a ≠ 0
(c) a = b = 0
(d) a = b ≠ 0

Question : The ratio of a 2-digit number to the sum of digits of that number is 4 : 1. If the digit in the unit place is 3 more than the digit in the tens place, what is the number ?
(a) 63
(b) 36
(c) 24
(d) 40

Question : How many values of c, for which the systemof equations 6x + 3y = c – 3, 12x + cy = c has infinitely many solutions?
(a) 1
(b) 2
(c) 3
(d) Infinite

Question : Sum of two numbers is 64 and their difference is 22. Find the numbers.
(a) 42, 22
(b) 43, 21
(c) 40, 24
(d) 50, 28

Question : If a pair of linear equations in two variablesis consistent, then the lines represented by two equations are
(a) Always intersecting
(b) Parallel
(c) Always coincident
(d) Intersecting or coincident

Question : The solution of the system of equations 2x 5y/xy = and 4x – 5y/xy+ 3=0 (where x ≠ 0, y ≠ 0), is _______.
(a) 1, 2
(b) 0, 0
(c) –1, 2
(d) 1, –2

Question : Value of x in pair of linear equations 36x + 24y = 702 and 24x + 36y = 558 is
(a) 33/2
(b) 145/7
(c) 16
(d) 17

Question : Which of the following linear equation coincide with the line 4x + 5y = 15?
(a) 8x + 10y = 25
(b) 2x + 3y = 7
(c) 7x + 14y = 17
(d) 12x + 15y = 45

Question : Arun and Prabhat have some books with them. Once Prabhat said to Arun that, if Arun gives 3 books to Prabhat then Arun will have only 1/2 of the books that Prabhat will have with him. Then Arun asked frankly that if Prabhat gives him only two books (to Arun), then Prabhat will have as many books as Arun will have. The total number of books that Arun and Prabhat have with them is _______.
(a) 25
(b) 56
(c) 30
(d) Can’t be determined

Question : Places M and N are 90 km apart from each other on a national highway. A truck starts from M and another from N at the same time. If they go in the same direction, then they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. The speed of the trucks are _______.
(a) 90 km/hr, 40 km/hr
(b) 40 km/hr, 30 km/hr
(c) 20 km/hr, 60 km/hr
(d) 50 km/hr, 12 km/hr

Question : A boat goes 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can go 40 km upstream and 48 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then_______.
(a) x + y = 12, x – y = 8
(b) x + y = 5, x – y = 11
(c) x + y = 6, x – y = 10
(d) x + y = 10, x – y = 6

Question : At the end of the year 2002, Ram was half as old as his grandpa. The sum of the years in which they were born is 3854. Age of Ram at the end of year 2003 is _______.
(a) 50 years
(b) 35 years
(c) 51 years
(d) 36 years

Question : On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains ₹ 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains ` 13. Find the actual prices of the tea-set and the lemon-set.
(a) ₹ 100, ₹ 80
(b) ₹ 90,   ₹ 100
(c) ₹ 120, ₹ 60
(d) ₹ 150, ₹ 80

Question : Solve for x and y in the following question.

(A) x = 1, y = 2
(b) x = 2, y = 1
(c) x = 2 y = 1/2
(d) x = 1/2 y = 2

Question : Match the following.System of equations           Solutions
(P) 2x – 3y + 15 = 0             (i) x = 3, y = 5
3x – 5 = 0
(Q) 2x – y = 1                      (ii) x = 1, y = 4
4x + 3y = 27
(R) x + 2y – 3 = 0                (iii) x = 5/3 y = 55/9
3x – 2y + 7 = 0
(S) 4x + y/3 = 16/3              (iv) x =– 1,y = 2
x/2 + 2y/4 = 5/2
(a) (P) → (iii); (Q) → (iv); (R) → (i); (S) → (ii)
(b) (P) → (iii); (Q) → (i); (R) → (iv); (S) → (ii)
(c) (P) → (iii); (Q) → (ii); (R) → (iv); (S) → (i)
(d) (P) → (ii); (Q) → (i); (R) → (iv); (S) → (iii)

Question :Which of the following graphs represent the lines 2x + 4y = 8 and 3x – 4y = 12 ?

Question :Fill in the blanks.
(i) If pair of linear equations is consistent, then it has either P or Q solution(s).
(b) If the pair of linear equation is inconsistent, then it has R solution(s).
(c) If the graph of two linear equations coincide, then they have S solution(s).
        P             Q              R            S
(a) no          infinite      unique      infinite
(b) unique    infinite          no        infinite
(c) no          infinite      unique      unique
(d) unique    no            infinite      no

Question : Read the statements carefully and state ‘T’ for true and ‘F’ for false.
(i) The pair of linear equations x + 2y = 5 and 7x + 3y = 13 has unique solution x = 2, y = 1.
(b) √2x + √3y = 0, √3x − √8y = 0 has no solution.
(c) The values of p and q for which the following system of equations 2x – y = 5, (p + q)x + (2p – q)y = 15 has infinite number of solutions, is p = 1 and q = 5.
        (i)    (ii)   (iii)
(a)    T      F     T
(b)    T     T      F
(c)    F     T      T
(d)    F     F      T

Question : A solid has __________dimensions.
(a) One
(b) Two
(c) Three
(d) Zero

Question : A point has _______ dimension.
(a) One
(b) Two
(c) Three
(d) Zero

Question : The shape of the base of a Pyramid is:
(a) Triangle
(b) Square
(c) Rectangle
(d) Any polygon

Question : The line drawn from the center of the circle to any point on its circumference is called:
(a) Radius
(b) Diameter
(c) Sector
(d) Arc

Question : There are ________ number of Euclid’s Postulates
(a) Three
(b) Four
(c) Five
(d) Six

Question : Euclid’s fifth postulate is
(a) The whole is greater than the part
(b) All right angles are equal to one another.
(c) If a straight line falling on two straight lines makes the interior angles on the same
side of it taken together less than two right angles, then the two straight lines if
produced indefinitely, meet on that side on which the sum of angles is less than two
right angles
(d) A circle may be described with any centre and any radius

Question : The three steps from solids to points are: 
(a) Lines – points – surfaces – solids
(b) Lines – surfaces – points – solids
(c) Solids – lines – surfaces – points 
(d) Solids – surfaces – linepoint

Question : The boundaries of solid are called:
(a) Surfaces
(b) Curves
(c) Lines
(d) Points

Question : A surface of shape has:
(a) Length, breadth and thickness
(b) Length and breadth only
(c) Length and thickness only
(d) Breadth and thickness only

Question : The edges of the surface are :
(a) Points
(b) Curves
(c) Lines
(d) None of the above

Question : Which of these statements do not satisfy Euclid’s axiom?
(a) Things which are equal to the same thing are equal to one another
(b) If equals are added to equals, the wholes are equal.
(c) If equals are subtracted from equals, the remainders are equal.
(d) The whole is lesser than the part.

Question : Which of the following statements are true?
(a) Only one line can pass through a single point.
(b) There is an infinite number of lines that pass through two distinct points.
(c) A terminated line can be produced indefinitely on both sides
(d) If two circles are equal, then their radii are unequal.

Question : Axioms are assumed 
(a) Theorems
(b) Definitions
(c) Universal truths specific to geometry
(d) Universal truths in all branches of mathematics

Question : The things which are double of the same thing are 
(a) equal
(b) unequal
(c) double of the same thing
(d) halves of the same thing