NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

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NCERT Solutions for Class 12 Maths Chapter 11 Three-dimensional Geometry Miscellaneous Exercise is covered in this article. This exercise of Chapter 11 is based on Direction Cosines and Direction Ratios of a Line, Equation of a Line in Space, Angle between Two Lines, Shortest Distance between Two Lines, Plane, Coplanarity of Two Lines, Angle between Two Planes, Distance of a Point from a Plane, Angle between a Line and a Plane. NCERT Solutions for Class 12 Maths Chapter 11 will carry a weightage of around 7-14 marks in the CBSE Term 2 Exam 2022. NCERT has provided a total of 23 problems and solutions based on the important topics of the exercise.

Download PDF NCERT Solutions for Class 12 Maths Chapter 11 Integrals Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Important topics covered in the Three-dimensional Geometry Chapter are:

Angle between two lines

Plane

Angle between line and plane

Angle between two vectors

Coplanarity

Also check: NCERT Solutions for Class 12 Maths Chapter 11 Three-dimensional Geometry

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

Exercise 11.1 Solutions	5 Questions
Exercise 11.2 Solutions	17 Questions
Exercise 11.3 Solutions	14 Questions
Miscellaneous Exercise Solutions	23 Questions

Chapter 11 Three-dimensional Geometry:

Angle between a Line and a Plane	Equation Line	Angle Between Two Vectors
Angle between Two Planes	Geometry	Plane
Coplanarity two lines	Section formula 3 dimension	Section formula 3 dimension

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Maths MCQs	Maths Syllabus
Mathematics Notes	Trigonometry	Maths Study Material
Arithmetic	Calculus	Algebra

CBSE CLASS XII Related Questions

1.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

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2.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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3.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

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4.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).

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5.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.

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6.
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

CBSE CLASS XII Related Questions

1.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

2.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

3.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

CBSE CLASS XII Related Questions

1.Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

2.Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

3.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

2.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

3.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.