Class 11 Math - 3D Geometry - MERIT YARD
Class 11 Math - 3D Geometry - MERIT YARD
1 / 40In 3D geometry, the three coordinate planes divide the space into how many parts (octants)?
A) \( 4 \)
B) \( 6 \)
C) \( 8 \)
D) \( 12 \)
2 / 40What are the exact coordinates of the
Origin in 3D space?
A) \( (0, 0, 0) \)
B) \( (1, 1, 1) \)
C) \( (0, 0) \)
D) \( (x, y, z) \)
3 / 40Any given point on the \( x \)-axis is strictly of the form:
A) \( (0, y, 0) \)
B) \( (x, 0, 0) \)
C) \( (0, 0, z) \)
D) \( (x, y, 0) \)
4 / 40Any given point on the \( y \)-axis is strictly of the form:
A) \( (x, 0, 0) \)
B) \( (0, y, z) \)
C) \( (x, y, 0) \)
D) \( (0, y, 0) \)
5 / 40Any given point on the \( z \)-axis is strictly of the form:
A) \( (x, 0, 0) \)
B) \( (0, y, 0) \)
C) \( (0, 0, z) \)
D) \( (0, y, z) \)
6 / 40What is the standard algebraic equation of the
\( xy \)-plane?
A) \( z = 0 \)
B) \( y = 0 \)
C) \( x = 0 \)
D) \( x + y = 0 \)
7 / 40What is the standard algebraic equation of the
\( yz \)-plane?
A) \( y = 0 \)
B) \( x = 0 \)
C) \( z = 0 \)
D) \( y + z = 0 \)
8 / 40What is the standard algebraic equation of the
\( zx \)-plane?
A) \( z = 0 \)
B) \( x = 0 \)
C) \( x + z = 0 \)
D) \( y = 0 \)
9 / 40If a point lies perfectly in the \( xy \)-plane, what must its \( z \)-coordinate be?
A) \( 1 \)
B) \( \infty \)
C) \( 0 \)
D) \( -1 \)
10 / 40The perpendicular distance of point \( (x, y, z) \) from the \( xy \)-plane is given by:
A) \( |z| \)
B) \( |y| \)
C) \( |x| \)
D) \( \sqrt{x^2+y^2} \)
11 / 40The perpendicular distance of point \( (x, y, z) \) from the \( yz \)-plane is given by:
A) \( |z| \)
B) \( |x| \)
C) \( |y| \)
D) \( \sqrt{y^2+z^2} \)
12 / 40Find the distance of the point \( (1, 2, 3) \)
from the origin.
A) \( \sqrt{6} \)
B) \( 6 \)
C) \( 14 \)
D) \( \sqrt{14} \)
13 / 40In which specific octant does the point
\( (2, 3, 4) \) lie?
A) Second
B) Third
C) First
D) Fourth
14 / 40In which specific octant does the point
\( (2, -3, 4) \) lie?
A) Fourth
B) First
C) Fifth
D) Eighth
15 / 40In which specific octant does the point
\( (-2, 3, 4) \) lie?
A) First
B) Second
C) Third
D) Sixth
16 / 40In which specific octant does the point
\( (-2, -3, -4) \) lie?
A) First
B) Fifth
C) Eighth
D) Seventh
17 / 40What is the formula for the distance between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \)?
A) \( (x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2 \)
B) \( \sqrt{x_1^2 + y_1^2 + z_1^2} \)
C) \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)
D) \( |x_2-x_1| + |y_2-y_1| + |z_2-z_1| \)
18 / 40The mathematical distance of any point \( (x, y, z) \) from the origin \( (0,0,0) \) is:
A) \( \sqrt{x^2 + y^2 + z^2} \)
B) \( x^2 + y^2 + z^2 \)
C) \( |x| + |y| + |z| \)
D) \( \sqrt{x + y + z} \)
19 / 40Find the exact distance between the origin
\( (0,0,0) \) and the point \( (3,4,0) \).
A) \( 7 \)
B) \( 5 \)
C) \( 25 \)
D) \( 1 \)
20 / 40If \( M \) is the midpoint of \( A(x_1, y_1, z_1) \) and \( B(x_2, y_2, z_2) \), its coordinates are:
A) \( (x_1+x_2, y_1+y_2, z_1+z_2) \)
B) \( (\frac{x_1-x_2}{2}, \frac{y_1-y_2}{2}, \frac{z_1-z_2}{2}) \)
C) \( (x_1 x_2, y_1 y_2, z_1 z_2) \)
D) \( (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}, \frac{z_1+z_2}{2}) \)
21 / 40Find the exact midpoint of the line segment joining \( (2, 4, 6) \) and \( (4, 6, 8) \).
A) \( (6, 10, 14) \)
B) \( (1, 2, 3) \)
C) \( (3, 5, 7) \)
D) \( (2, 2, 2) \)
22 / 40The coordinates of the centroid of a triangle with vertices \( (x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3) \) are:
A) \( (\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}) \)
B) \( (\frac{x_1+x_2+x_3}{2}, \frac{y_1+y_2+y_3}{2}, \frac{z_1+z_2+z_3}{2}) \)
C) \( (x_1+x_2+x_3, y_1+y_2+y_3, z_1+z_2+z_3) \)
D) \( (0, 0, 0) \)
23 / 40The point \( (0, 5, 0) \) strictly lies on which axis in the 3D plane?
A) \( x \)-axis
B) \( y \)-axis
C) \( z \)-axis
D) Origin
24 / 40The point \( (0, 0, -4) \) strictly lies on which axis in the 3D plane?
A) \( x \)-axis
B) \( y \)-axis
C) Origin
D) \( z \)-axis
25 / 40The point \( (3, 0, 0) \) strictly lies on which axis in the 3D plane?
A) \( y \)-axis
B) \( z \)-axis
C) \( x \)-axis
D) Origin
26 / 40What is the exact \( z \)-coordinate of every point lying on the \( x \)-axis?
A) \( 0 \)
B) \( 1 \)
C) \( x \)
D) Not defined
27 / 40The section formula for dividing a line segment internally in the ratio \( m:n \) uses the denominator:
A) \( m - n \)
B) \( m + n \)
C) \( mn \)
D) \( 2 \)
28 / 40The section formula for dividing a line segment externally in the ratio \( m:n \) uses the denominator:
A) \( m + n \)
B) \( mn \)
C) \( 2 \)
D) \( m - n \)
29 / 40What are the coordinates of the image of the point \( (x, y, z) \) in the \( xy \)-plane?
A) \( (-x, y, z) \)
B) \( (x, -y, z) \)
C) \( (x, y, -z) \)
D) \( (-x, -y, -z) \)
30 / 40Find the image of the point \( (2, 3, 4) \)
when reflected in the \( xy \)-plane.
A) \( (2, 3, -4) \)
B) \( (-2, 3, 4) \)
C) \( (2, -3, 4) \)
D) \( (-2, -3, -4) \)
31 / 40Find the image of the point \( (1, 2, 3) \)
when reflected in the \( yz \)-plane.
A) \( (1, -2, 3) \)
B) \( (-1, 2, 3) \)
C) \( (1, 2, -3) \)
D) \( (-1, -2, -3) \)
32 / 40In a standard 3D coordinate system, the three coordinate axes are mutually:
A) Parallel
B) Intersecting at infinity
C) Coplanar
D) Perpendicular
33 / 40What is the exact distance between the points
\( (1,0,0) \) and \( (0,1,0) \)?
A) \( 2 \)
B) \( 1 \)
C) \( \sqrt{2} \)
D) \( 0 \)
34 / 40If a point lies perfectly in the \( yz \)-plane, what must its \( x \)-coordinate be?
A) \( 0 \)
B) \( 1 \)
C) \( \infty \)
D) \( -1 \)
35 / 40If the centroid of \( \Delta ABC \) is origin \( (0,0,0) \) and \( A(a,0,0), B(0,b,0) \), then \( C \) is:
A) \( (a, b, 0) \)
B) \( (-a, -b, 0) \)
C) \( (0, 0, c) \)
D) \( (1, 1, 1) \)
36 / 40Find the perpendicular distance of the point \( P(3, 4, 5) \) from the \( z \)-axis.
A) \( 3 \)
B) \( 4 \)
C) \( 25 \)
D) \( 5 \)
37 / 40How many mutually perpendicular planes are strictly formed by the three coordinate axes?
A) \( 1 \)
B) \( 2 \)
C) \( 3 \)
D) \( 8 \)
38 / 40What is the perpendicular distance of the point
\( (1, -2, 3) \) from the \( xy \)-plane?
A) \( 3 \)
B) \( -2 \)
C) \( 1 \)
D) \( 2 \)
39 / 40If a point lies perfectly in the \( zx \)-plane, what must its \( y \)-coordinate be?
A) \( 1 \)
B) \( 0 \)
C) \( -1 \)
D) Not defined
40 / 40Find the mathematical distance between the points \( (a, b, c) \) and \( (-a, -b, -c) \).
A) \( 0 \)
B) \( \sqrt{a^2+b^2+c^2} \)
C) \( a+b+c \)
D) \( 2\sqrt{a^2+b^2+c^2} \)
Test Analysis

Correct ✅ 0

Wrong ❌ 0

Unattempted ⚠️ 40

Accuracy 🎯 0%

Time Taken ⏱️ 00m 00s

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