Practice AP Inter 1st Year Maths Study Material Chapter 11 Introduction to 3D Geometry MCQ to identify your strengths and weak areas.
AP Inter 1st Year Maths Introduction to 3D Geometry MCQ
Question 1.
The co-ordinates of the foot of the perpendicular from a point P(6, 7, 8) on the Y-axis are
1) (6, 0, 0)
2) (0, 7, 0)
3) (0, 0, 8)
4) (0, 7, 8)
Answer:
2) (0, 7, 0)
Explanation:
On Y-axis, x and z-coordinates of every point are zero so the coordinates of the foot of the perpendicular are (0, 7, 0).
Question 2.
The length of the perpendicular drawn from the point P(13, 5, 12) on the X-axis is
1) 13
2) 2\(\sqrt{13}\)
3) \(\sqrt{194}\)
4) \(\sqrt{313}\)
Answer:
1) 13
Explanation:
The foot of the perpendicular from P(13, 5, 12) on the X-axis is (13, 0, 0).
Length of the perpendicular = \(\sqrt{(4-1)^2+(5-2)^2+(8-5)^2}=3 \sqrt{3}\)
Question 3.
If a parallelepiped is formed by planes drawn through the points (1, 2, 5) and (4, 5, 8) parallel to the coordinate planes, then the length of the diagonal of the parallelepiped is
1) 2√2
2) 3
3) √3
4) 3√3
Answer:
4) 3√3
Explanation:
The length of the diagonal = \(\sqrt{(4-1)^2+(5-2)^2+(8-5)^2}\) = 3√3
Question 4.
The Locus of the point for which y = 0 is
1) XY-plane
2) YZ-plane
3) ZX-plane
4) None of these
Answer:
3) ZX-plane
Explanation:
The y-coordinate of every point of ZX-plane is zero the locus of the point (x, y, z) for which y = 0 is the XZ-plane.
Question 5.
If the distance between the points P(0, a, 3) and Q(3, 0, 7) is \41, then a =
1) -4
2) 4
3) ±4
4) 4
Answer:
3) ±4
Explanation:
PQ = \(\sqrt{41}\)
⇒ \(\sqrt{(0-3)^2+(a-0)^2+(3-7)^2}=\sqrt{41}\)
⇒ 9 + a2 + 16 = 41
⇒ a2 = 16
⇒ a = +4
Question 6.
The ratio in which the line joining (2, 4, 5) and (3, 5, -9) is divided by the YZ-plane
1) 2 : 3
2) 3 : 2
3) -2 : 3
4) 4 : -3
Answer:
3) -2 : 3
Explanation:
YZ-plane divides in the ratio = \(\frac{-x_1}{x_2}=\frac{-2}{3}\)
Question 7.
The points (1, 1, 1), (4, 1, 1), (4, 5, 1) and (1, 5, 1) are the vertices of ( 1 ) .
1) a rectangle
2) a square
3) parallelogram
4) None of these
Answer:
1) a rectangle
Explanation:
A = (1, 1, 1), B(4, 1, 1), C = (4, 5, 1), D = (1, 5, 1)
AB = \(\sqrt{9+0+0}\) = 3, BC = \(\sqrt{0+16+0}\) = 4, CD \(\sqrt{9+0+0}\) = 3, DA = \(\sqrt{0+16+0}\) = 4,
AC = \(\sqrt{9+16+0}\) = 5, BD = \(\sqrt{9+16+0}\) = 5
AB CD, BC = AD, AC = BD
∴ABCD is a rectangle.
Question 8.
What is the locus of a point for which y = 0, z = 0?
1) X-axis
2) Y-axis
3) Z-axis
4) YZ-plane
Answer:
X-axis
Explanation:
X-axis
Question 9.
XZ-plane divides the line joining (2, 3, 1) and (6, 7, 1) in the ratio
1) 3 : 7
2) 2 : 7
3) -3 : 7
4)-2 : 4
Answer:
3) -3 : 7
Explanation:
XZ-plane divides in the ratio = \(\frac{-y_1}{y_2}=\frac{-3}{7}\)
Question 10.
The co-ordinatea of the foot of the perpendicular drawn from the point P(3, 4, 5) on the YZ-plane are ( 2 )
1) (3, 4, 0)
2) (0, 4, 5)
3) (3, 0, 5)
4) (3, 0, 0)
Answer:
2) (0, 4, 5)
Explanation:
The point on the YZ-plane becomes its x-co-ordinate must be zero (0, 4, 5)
Question 11.
Statement-1 (Assertion) : Point (3, a2 – 1, a2 – 3a + 2) lies on the X-axis if a = 1
Statement-2 (Reason) : On X-axis, y and z co-ordinates of every point are equal to zero.
1) Statement-1 and statement-2 are true, statement-2 is a correct explanation for statement -1.
2) Statement-1 and statement-2 are true, statement-2 is not a correct explanation for statement-1.
3) Statement-1 is true, statement-2 is false.
4) Statement-1 is false, statement-2 is true.
Answer:
1) Statement-1 and statement-2 are true, statement-2 is a correct explanation for statement -1.
Explanation:
Statement-1 (Assertion) : If a = 1 then a2 – 1 = 0, and a2 – 3a + 2 = 0 the point is (3, 0, 0) lies on X-axis.
Statement-2 (Reason) : It is a correct explanation of statement-I. Hence option 1 is correct.