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GRE FREE Mock exam for Students
Find the value of y for which the points (1, 4), (3, y), and (4, -y) lie on the same straight line.
(a) 2
(b) -2
(c) 3
(d) 4
(e) None of these
Option b – -2
Determine the x-intercept and y-intercept of the line 3x – 2y – 6 = 0.
(a) 2, -3
(b) 3, 2
(c) 2, 3
(d) -2, 3
(e) None of these
Option a – 2, -3
Write the equation of the line passing through (1, 1) that is perpendicular to the line 3x + 4y – 5 = 0.
(a) 3x + 4y – 7 = 0
(b) 3x + 4y + 7 = 0
(c) 4x – 3y + 1 = 0
(d) 4x – 3y – 1 = 0
(e) None of these
Option d – 4x – 3y – 1 = 0
The perpendicular PQ is drawn from the point P(-3, 1) to the line 7x – 24y – 15 = 0. Find its length.
(a) 1/5
(b) 10
(c) 12/5
(d) 14
(e) None of these
Option c – 12/5
Find the point on the x-axis that is equidistant from (7, 6) and (3, 4).
(a) (0, 3)
(b) (3, 0)
(c) (0, 4)
(d) (-4, 0)
(e) None of these
Option b – (3, 0)
AB is the diameter of a circle with center O. If A is at (2, 6) and B is at (6, 2), determine the coordinates of O.
(a) (4, 4)
(b) (4, -4)
(c) (2, -2)
(d) (0, 0)
(e) None of these
Option a – (4, 4)
The vertices of a triangle are (2, 1), (2, 5), and (5, 1). Calculate its area.
(a) 12
(b) 10
(c) 8
(d) 69
(e) None of these
Option d – 69
A circle has its center at (0, 0) and an area of 167. Which of the given points does not lie on it?
(a) (4, 4)
(b) (0, 4)
(c) (4, 0)
(d) (-4, 0)
(e) None of these
Option a – (4, 4)
Determine the distance between the points (2, -3) and (2, 2).
(a) 2
(b) 3
(c) 4
(d) 5
(e) None of these
Option d – 5
Find the coordinates of the point on the y-axis that is 6 units away from the x-axis.
(a) (0, 6)
(b) (6, 0)
(c) (6, 6)
(d) (-6, 6)
(e) None of these
Option a – (0, 6)
Identify the coordinates of a point in the 3rd or 4th quadrant, lying on the y-axis and 4 units away from the x-axis.
(a) (0, 4)
(b) (-4, 0)
(c) (0, -4)
(d) (4, -4)
(e) None of these
Option c – (0, -4)
Points A(0, 6), B(5, 3), and C(3, 1) form a triangle. Identify the type of triangle.
(a) Isosceles
(b) Right-angled
(c) Equilateral
(d) Scalene
(e) None of these
Option a – Isosceles
Determine the quadrant in which the point (-4, 3) lies.
(a) I
(b) II
(c) III
(d) IV
(e) Any quadrant
Option b – II
How many distinct squares can be formed if two vertices are given as (1, 0) and (2, 0)?
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of these
Option c – 3
Write the equation of the tangent to the circle x² + y² = 25 at the point (-3, -4).
(a) 3x + 4y + 25 = 0
(b) 3x + 4y – 25 = 0
(c) 4x + 3y + 25 = 0
(d) 4x + 3y – 25 = 0
(e) None of these
Option a – 3x + 4y + 25 = 0
Find the equation of the circle whose diameter endpoints are (3, 4) and (-3, 4).
(a) x² + y² + 25 = 0
(b) x² + y² = 16
(c) x² + y² = 25
(d) x² + y² = 64
(e) None of these
Option d – x² + y² = 64
Let A(3, 4), B(4, 4), and C(4, 5) be three points. Find the angle between AB and AC.
(a) 30°
(b) 60°
(c) 45°
(d) 90°
(e) None of these
Option c – 45°
Determine the length of the perpendicular from the point (4, 1) to the line 3x – 4y + 12 = 0.
(a) 4
(b) 4/3
(c) 3
(d) 1
(e) None of these
Option a – 4
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