MCQ Test of Chapter – Coordinate Geometry, Linear Equations in two Variables, Herons Formula
Q 1 – The sides of a triangle are 35 cm, 54 cm and 61 cm. The length of its longest altitude is
(a) 16√5 cm
(b) 10√5 cm
(c) 24√5 cm
(d) 28 cm
Q 2 – The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm is
(a) √15 cm²
(b) √5 / 2 cm²
(c 2 √5 cm²
(d) 4√15 cm
Q 3 – If x = 3 and y = -2 is a solution of the equation 4px – 3y = 12, then the value of p is
(a) 0
(b) 1/2
(c) 2
(d) 3
Q 4 – The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is :
(a) 10√3 cm2
(b) 100√3 cm2
(c) 300 cm2
(d) 50√3 cm2
Q 5 – The area of a triangle with base 8 cm and height 10 cm is
(a) 20 cm2
(b) 18 cm2
(c) 80 cm2
(d) 40 cm2
Q 6 – Solutions of the equation 2x + 5y = 0 is:
(a) 3,0
(b) – 3,2
(c) 0,0
(d) 0,4
Q 7 – Which of the following is the equation of a line parallel to y-axis?
(a) y = 0
(b) x + y = z
(c) y = x
(d) x = a
Q 8 – The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 70 paise per cm2 is
(a) Rs. 17
(b) Rs. 16.80
(c) Rs. 7
(d) Rs. 16
Q 9 – The Coordinates of point Q are
(a) (3, 3.5)
(b) (3.5, 3)
(c) (–3, 3.5)
(d) (–3, –3.5)
Q 10 – The base of a right triangle is 48 cm and its hypotenuse is 50 cm. The area of the triangle is
(a) 168 cm²
(b) 252 cm²
(c) 336 cm²
(d) 504 cm²
Q 11 – If the area of an equilateral triangle is 16√3 cm², then the perimeter of the triangle is
(a) 48 cm
(b) 24 cm
(c) 12 cm
(d) 36 cm
Q 12 – Cost of book (x) exceeds twice the cost of pen (y) by Rs 10. This statement can be expressed as linear equation.
(a) x – 2y – 10 = 0
(b) 2x – y – 10 = 0
(c) 2x + y – 10 = 0
(d) x – 2y + 10 = 0
Q 13 – The point M lies in the IV quadrant. The coordinates of point M are
(a) (a, b)
(b) (–a, b)
(c) (a, –b)
(d) (–a, –b)
Q 14 – The area of an equilateral triangle of side 6 cm is
(a) 18 cm2
(b) 9√3 cm2
(c) 56√3 cm2
(d) 58√3 cm2
Q 15 – Point (0, 4) lies
(a) in I quadrant
(b) on x-axis
(c) on y-axis
(a) in IV quadrant
Q 16 – Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).
(a) (12, 3)
(b) (11, 2)
(c) (10, 2)
(d) (11, 3)
Q 17 – The name of vertical line in the cartesian plane which determines the position of a point is called:
a) Origin
b) X-axis
c) Y-axis
d) Quadrants
Q 18 – If the abscissa of a point is y and the ordinate is x then the coordinates of the point are _______
(a) (x, 0)
(b) (y, x)
(c) (x, y)
(d) (0, y)
Q 19 – The graph of x = 3 is a line:
(a) Parallel to x-axis at a distance of 3 units from the origin
(b) Parallel to y-axis at a distance of 3 units from the origin
(c) Makes an intercept 3 on x-axis
(d) Makes an intercept 3 on y-axis
Q 20 – The point of intersection of horizontal and vertical lines determining the position of point in a cartesian plane is called:
a) Origin
b) X-axis
c) Y–axis
d) Quadrants
Q 21 – The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the
point from the:
(a) y–axis
(b) x–axis
(c) (0, 1)
(d) (1, 0)
Q 22 – Ordinate of all the points in the x-axis is:
a) 0
b) 1
c) –1
d) Any natural number
Q 23 – Find the ratio in which the line joining the points (6, 4) and (1, –7) is divided by x-axis.
(a) 1 : 3
(b) 2 : 7
(c) 4 : 7
(d) 6 : 7
Q 24 – The lengths of a triangle are 6 cm, 8 cm and 10 cm. Then the length of perpendicular from the opposite vertex to the side whose length is 8cm is:
(a) 4 cm
(b) 6 cm
(c) 5 cm
(d) 2 cm
Q 25 – If x coordinate of a point is zero, then the point lies on:
(a) First quadrant
(b) Second quadrant
(c) X-axis
(d) Y-axis
Q 26 – A point (x + 2, x + 4) lies in the first quadrant, the mirror image for which for x-axis is (5, –7). What is the value of x?
a) (–5, –7)
b) (–5, 7)
c) (5, –7)
d) (5, 7)
Q 27 – The area of quadrilateral PQRS, in which PQ = 7 cm, QR = 6 cm, RS = 12 cm, PS = 15 cm and PR = 9 cm:
(a) 74.98 cm2
(b) 25.25 cm2
(c) 75 cm2
(d) 68.25 cm2
Q 28 – The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. The length of the other diagonal and area of the rhombus
are
(a) 48 cm, 2320 cm2
(b) 48 cm, 1820 cm2
(c) 88 cm, 1320 cm2
(d) 48 cm, 1320 cm2
Q 29 – Length of perpendicular drawn on smallest side of scalene triangle is
(a) Smallest
(b) Largest
(c) No relation
(d) None
Q 30 – The equation of a line parallel to x-axis and 3 units above the origin is
(a) x = –3
(b) x = 3
(c) y = –3
(d) y = 3
Q 31 – To which equation does the graph represent?
(a) 3x – 7y = 10
(b) y – 2x = 3
(c) 8y – 6x = 4
(d) 5x + 35/2 y = 25
Q 32 – Any point of the form (a, – a) always lie on the graph of the equation
(a) x = – a
(b) y = a
(c) y = x
(d) x + y = 0
Q 33 – The area of a triangle whose sides are 12 cm, 16 cm and 20 cm is
(a) 96 cm2
(b) 320 cm2
(c) 240 cm2
(d) 72 cm2
Q 34 – Solution of linear equation 2x + 0.y + 9 = 0 is
Q 35 – Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.
(a) 20
(b) 50
(c) 60
(d) 40
Q 36 – If x = a, y = b is the solution of the pair of equation x-y = 2 and x+y = 4 then what will be value of a and b
(a) 2,1
(b) 3,1
(c) 4,6
(d) 1,2
Q 37 – The condition that the equation ax + by + c = 0 represents a linear equation in two variables is
(a) a ≠ 0, b = 0
(b) b ≠ 0, a = 0
(c) a = 0, b = 0
(d) a ≠ 0, b ≠ 0
Q 38 – The point lying on the equation 2x – y = 5 is:
(a) (3, 4)
(b) (–3, 1)
(c) (6, 1)
(d) (2, –1)
Q 39 – The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first
number. Find the first number.
(a) 46
(b) 48
(c) 64
(d) 84
Q 40 – Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?
(a) 6 km/hr
(b) 4 km/hr
(c) 3 km/hr
(d) 7 km/hr
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