alleryStart learning →The direction ratios of the line joining the points $(1,2,3)$ and $(4,5,6)$ are:
- $4, 5, 6$
- $3, 3, 3$
- $1, 2, 3$
- $5, 7, 9$
Show answer and solution
Correct answer: B. $3, 3, 3$
Direction ratios = differences of coordinates: (4−1, 5−2, 6−3) = (3,3,3).
Indian Navy INET Surface Areas and Volumes — practice questions
Explore 6 free Surface Areas and Volumes questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Surface Areas and Volumes with Quill →Surface Areas and Volumes questions and exercises with answers
Showing questions 1–6 of 6.
The direction ratios of the line joining the points $(1,2,3)$ and $(4,5,6)$ are:Read the answer and worked solution →The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:Read the answer and worked solution →A cylindrical glass tube of radius 1 cm is filled with water to depth 14 cm. A sphere of radius 1 cm is dropped in. The new water level rises byRead the answer and worked solution →A bucket in the shape of a frustum has radii 22 cm and 12 cm and height 24 cm. The slant height isRead the answer and worked solution →Match each solid to its shapeRead the answer and worked solution →True or false: solidsRead the answer and worked solution →
Worked practice questions
The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:
- $\tfrac{4}{9}$
- $\tfrac{2}{3}$
- $\tfrac{1}{9}$
- $\tfrac{8}{9}$
Show answer and solution
Correct answer: D. $\tfrac{8}{9}$
We have cosθ = (1·2+2·2+2·1)/(√9·√9).
So cosθ = 8/9.
A cylindrical glass tube of radius 1 cm is filled with water to depth 14 cm. A sphere of radius 1 cm is dropped in. The new water level rises by
- 2 cm
- 2/3 cm
- 1 cm
- 4/3 cm
Show answer and solution
Correct answer: D. 4/3 cm
1. Sphere volume = (4/3) × pi × 1 cubed = (4/3) pi cu cm.
2. Cross-section = pi × 1 squared = pi.
3. Rise = (4/3) pi / pi = 4/3 cm.
_Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.3_
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