CUET PG PYQs for Three Dimensional Geometry with Solutions: Practice CUET PG Previous Year Questions

Content Writer | Journalism Graduate | J/hVSQ

Three Dimensional Geometry is an important topic in the Mathematics section in CUET PG exam. Practising this topic will increase your score overall and make your conceptual grip on CUET PG exam stronger.

This article gives you a full set of CUET PG PYQs for Three Dimensional Geometry with explanations for effective preparation. Practice of CUET PG Mathematics PYQs including Three Dimensional Geometry questions regularly will improve accuracy, speed, and confidence in the CUET PG 2026 exam.

CUET PG PYQs for Three Dimensional Geometry with Solutions

1.
The equation of cone with vertex at (0, 0, 0) and passing through the circle given by
\(x^2 + y^2 + z^2 + x - 2z + 3y - 4 = 0, x - y + z = 2\), is
- \( x^2 + 2y^2 + 3z^2 + xy + 2yz = 0 \)
- \( x^2 + 3y^2 + 3z^2 + 2xy + yz = 0 \)
- \( x^2 + 2y^2 + 3z^2 + xy - yz = 0 \)
- \( x^2 + 2y^2 + 3z^2 + xy - 3yz = 0 \)
View Solution
2.
The base of hexadecimal system is
- 2
- 6
- 8
- 16
View Solution
3.
The plane \(x + y + z = \sqrt{3}\lambda\) touches the sphere \(x^2 + y^2 + z^2 - 2x - 2y - 2z - 6 = 0\) if:
- \( \lambda = \sqrt{3} \pm 3 \)
- \( \lambda = \sqrt{3} + 3 - \sqrt{2} \)
- \( \lambda = \sqrt{3} \pm \frac{1}{3} \)
- \( \lambda = \frac{1}{\sqrt{3}} \pm 3 \)
View Solution
4.
The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x₁+3x₂+4x₃+5x₄= 6
- 2x₁+3x₂+4x₃+5x₄<6
- 2x₁+3x₂+4x₃+5x₄>6
- 2x₁+3x₂+4x₃+5x₄<62
- 2x₁+3x₂+4x₃+5x₄>62
View Solution
5.
Which of the following statements are true?
(A) The equations of the plane passing through the point (1, -1, 2) having 2, 3, 2 as direction ratios of normal to the plane is 2x + 3y + 2z = 3
(B) Angle between the normal to the plane 2x - y + z = 6 and x + y + 2z = 7 is \(\frac{\pi}{3}\)
(C) The angle at which the normal vectors to the plane 4x + 8y + z = 5 is inclined to the z-axis is \( \sin^{-1}(\frac{1}{9}) \)
(D) The equation of the plane passing through the point (3, -3, 1) and normal to the line joining the points (3, 4, -1) and (2, -1, 5) is x + 5y + 6z = -18
(E) A normal vector to the plane 2x - y + 2z = 5 is \( \frac{1}{3}(2\vec{i} - \vec{j} + 2\vec{k}) \)
Choose the correct answer from the options given below:
- (A), (B), (C) and (E) only
- (B), (C), (D) and (E) only
- (A), (B), (D) and (E) only
- (A), (B) and (E) only
View Solution

View more CUET PG Questions

gr54sW uqE+cS

Comments

No Comments To Show

CUET PG PYQs for Three Dimensional Geometry with Solutions

1.The equation of cone with vertex at (0, 0, 0) and passing through the circle given by \(x^2 + y^2 + z^2 + x - 2z + 3y - 4 = 0, x - y + z = 2\), is

2.The base of hexadecimal system is

3.The plane \(x + y + z = \sqrt{3}\lambda\) touches the sphere \(x^2 + y^2 + z^2 - 2x - 2y - 2z - 6 = 0\) if:

4.The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x1+3x2+4x3+5x4 = 6

Comments

dOGVmW

1.
The equation of cone with vertex at (0, 0, 0) and passing through the circle given by
\(x^2 + y^2 + z^2 + x - 2z + 3y - 4 = 0, x - y + z = 2\), is

2.
The base of hexadecimal system is

3.
The plane \(x + y + z = \sqrt{3}\lambda\) touches the sphere \(x^2 + y^2 + z^2 - 2x - 2y - 2z - 6 = 0\) if:

4.
The point (-1, 2, 7, 6) lies in which of the following half spaces corresponding to hyperplane 2x₁+3x₂+4x₃+5x₄= 6