HEC ETC 2026 USAT E Entry Test Mathematics Analytical Geometry in Three Dimensions Free Quiz 1

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HEC ETC 2026 USAT E Entry Test Mathematics Analytical Geometry in Three Dimensions Free Quiz 1

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HEC ETC 2026 USAT E Entry Test Mathematics Analytical Geometry in Three Dimensions Free Quiz 1

Practice HEC ETC 2026 USAT E Analytical Geometry in Three Dimensions MCQs. Get instant results with Explanation.

Practice Quiz 1 for "Analytical Geometry in Three Dimensions" (Mathematics). Total 18 MCQs available, split into 2 quizzes. Start with the fundamentals and build a strong base. Mastering these concepts is essential for securing a high percentile in HEC ETC.

General10 MCQs

1. How is a point represented in 3D space?

A. (x, y, z)B. (x, y)C. (x, y, z, w)D. (x, y, z, t)

2. What is the distance formula in 3D?

A. √[(x₂ - x₁)² + (y₂ - y₁)²]B. √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]C. (x₂ - x₁) + (y₂ - y₁) + (z₂ - z₁)D. √[(x₂ - x₁)² - (y₂ - y₁)² + (z₂ - z₁)²]

3. What is the midpoint formula in 3D?

A. ((x₁+x₂)/2, (y₁+y₂)/2)B. (x₁+x₂, y₁+y₂, z₁+z₂)C. ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)D. ((x₁-x₂)/2, (y₁-y₂)/2, (z₁-z₂)/2)

4. What is the distance between (1,2,3) and (4,6,8)?

A. 5B. 7C. √50D. 5√2

5. What are direction cosines?

A. Direction ratiosB. Direction cosinesC. AnglesD. Slopes

General10 MCQs

6. What is the relation for direction cosines l, m, n?

A. l + m + n = 1B. l² + m² + n² = 0C. l² + m² + n² = 1D. l × m × n = 1

7. What are the direction cosines for direction ratios (1, 2, 3)?

A. (1, 2, 3)B. (1/√6, 2/√6, 3/√6)C. (√14, 2√14, 3√14)D. (1/√14, 2/√14, 3/√14)

8. What is the general equation of a plane?

A. ax + by + cz + d = 0B. ax + by + cz = 0C. ax² + by² + cz² + d = 0D. ax + by = 0

9. What is the normal vector of 2x + 3y + 4z + 5 = 0?

A. (5, 0, 0)B. (2, 3, 4)C. (2, 3, 4, 5)D. (-2, -3, -4)

10. What is the distance from a point to a plane?

A. |ax₁ + by₁ + cz₁ + d| / (a + b + c)B. |ax₁ + by₁ + cz₁ + d| / √(a² + b²)C. |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c²)D. |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c² + d²)

📋 HEC ETC - Test Online Practice Quizzes

HEC ETC USAT

Conducting Body: Higher Education Commission (HEC)

Frequency: Quarterly | Time: 120 Minutes

Negative Marking: No

⚡ Test Pattern (Total: 100 MCQs):

Eng: 20 MCQs
Logical Reasoning: 20 MCQs
Quantitative Reasoning: 20 MCQs
Physics: 10 MCQs

Merit Formula: Merit Formula: There is no single HEC merit calculation formula for USAT. Universities determine their own merit criteria.

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