CBSE Class 12 Mathematics MCQs – Chapter Wise Practice Tests

Prepare smarter with CBSE Class 12 Mathematics MCQs – Online Practice Test designed chapter-wise as per the latest NCERT syllabus. Each quiz offers 30 multiple-choice questions with automatic scoring, instant per-question feedback, and a 30-minute timer to simulate real exam conditions. These CBSE Class 12 Mathematics MCQs – Online Practice Tests help students strengthen core concepts, improve problem-solving skills, and boost confidence for board exams. Ideal for self-assessment and quick revision, these MCQs cover every chapter comprehensively, making them a perfect study tool for CBSE board exam preparation and concept mastery.

Chapter 10 — Vector Algebra

1. If \(\mathbf{a} = \langle 2, -1, 3 \rangle\), its magnitude \(|\mathbf{a}|\) equals

2. The dot product \(\mathbf{a}\cdot\mathbf{b}\) is

3. The cross product \(\mathbf{i}\times\mathbf{j}\) equals

4. If \(\mathbf{a}\cdot\mathbf{b}=0\) (neither zero), then a and b are

5. The scalar triple product \(\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})\) represents

6. Vectors \(\mathbf{a}\) and \(\mathbf{b}\) are parallel if

7. The projection of \(\mathbf{a}\) on \(\mathbf{b}\) is given by

8. If \(\mathbf{a} = \langle 1,2,3\rangle\) and \(\mathbf{b} = \langle 2,-1,1\rangle\), then \(\mathbf{a}\cdot\mathbf{b} =\)

9. \(\mathbf{a}\times\mathbf{b}\) is a vector of magnitude \(|\mathbf{a}||\mathbf{b}|\sin\theta\) and direction

10. Two vectors are coplanar if their scalar triple product is

11. The unit vector in the direction of \(\mathbf{a}\) is

12. If \(\mathbf{a}\) and \(\mathbf{b}\) are perpendicular unit vectors, \(|\mathbf{a}+\mathbf{b}|^2\) equals

13. The area of the parallelogram formed by vectors \(\mathbf{a}\) and \(\mathbf{b}\) is

14. \(\mathbf{i}, \mathbf{j}, \mathbf{k}\) follow the cyclic product \(\mathbf{i}\times\mathbf{j}=\mathbf{k}\), \(\mathbf{j}\times\mathbf{k}=\mathbf{i}\), then \(\mathbf{k}\times\mathbf{i}=\)

15. If \(\mathbf{a} = \langle 1,0,0\rangle\) and \(\mathbf{b} = \langle 0,1,0\rangle\), then \((\mathbf{a}\times\mathbf{b})\cdot\mathbf{a} =\)

16. If position vectors of A and B are \(\mathbf{a}\) and \(\mathbf{b}\), the vector AB is

17. The angle \(\theta\) between vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfies \(\cos\theta =\)

18. If \(\mathbf{a}\times\mathbf{b} = \mathbf{0}\), then

19. The vector equation of a line through point with position vector \(\mathbf{a}\) and parallel to \(\mathbf{b}\) is

20. If \(\mathbf{a}=\langle 2,0,0\rangle\), \(\mathbf{b}=\langle 0,3,0\rangle\), area of parallelogram formed is

21. The scalar triple product is invariant under which operation?

22. If \(\mathbf{a}=\langle 1,1,1\rangle\), then unit vector along a is

23. Which is true: \((\mathbf{a}\times\mathbf{b})\cdot\mathbf{c} =\)

24. If \(\mathbf{a} = \langle 3,-3,1\rangle\), \(\mathbf{b} = \langle 4,9,2\rangle\), \(\mathbf{a}\cdot\mathbf{b} =\)

25. If \(\mathbf{a} = \langle 1,2,3\rangle\), \(\mathbf{b} = \langle 2,3,4\rangle\), then \(|\mathbf{a}\times\mathbf{b}|\) equals

26. The vector product is anti-commutative: \(\mathbf{a}\times\mathbf{b} =\)

27. If \(\mathbf{a}=\langle 2,3,4\rangle\), the component of a along unit vector \(\mathbf{u}\) is

28. The vector equation of a plane through point with position vector \(\mathbf{a}\) and normal \(\mathbf{n}\) is

29. If \(\mathbf{a}\cdot\mathbf{b} = |\mathbf{a}||\mathbf{b}|\), then the angle between a and b is

30. The volume of the parallelepiped formed by \(\mathbf{a},\mathbf{b},\mathbf{c}\) is

Chapter 10: Vector Algebra