InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
A unit vector is a vector whose magnitude is unity.(a) True(b) FalseI had been asked this question at a job interview.Query is from Types of Vectors topic in chapter Vector Algebra of Mathematics – Class 12 |
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Answer» RIGHT CHOICE is (a) TRUE The explanation is: The given STATEMENT is true. The vector whose magnitude is unity is CALLED a unit vector. The unit vector in the given direction of given vector \(\vec{b}\) is denoted by \(\hat{b}\). |
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| 52. |
Find the angle between the vectors if \(|\vec{a}|=|\vec{b}|=3\sqrt{2}\) and \(\vec{a}.\vec{b}=9\sqrt{3}\).(a) \(\frac{π}{6}\)(b) \(\frac{π}{5}\)(c) \(\frac{π}{3}\)(d) \(\frac{π}{2}\)This question was addressed to me in an interview.Asked question is from Product of Two Vectors-2 in section Vector Algebra of Mathematics – Class 12 |
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Answer» The CORRECT answer is (a) \(\frac{π}{6}\) |
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| 53. |
Which of the following vectors are equal in the figure given below?(a) \(\vec{a}\) and c(b) \(\vec{c}\) and \(\vec{b}\)(c) \(\vec{a}\) and \(\vec{b}\)(d) \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\)This question was addressed to me in an interview.This interesting question is from Types of Vectors topic in chapter Vector Algebra of Mathematics – Class 12 |
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Answer» Correct choice is (c) \(\vec{a}\) and \(\vec{b}\) |
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| 54. |
Which of the following holds true for a vector quantity?(a) It has only magnitude(b) It has only direction(c) A vector has both direction and magnitude(d) A vector can never be negativeThis question was addressed to me in exam.I'd like to ask this question from Vector Algebra Basics in portion Vector Algebra of Mathematics – Class 12 |
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Answer» The correct answer is (c) A vector has both DIRECTION and MAGNITUDE |
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| 55. |
Which of the following is a scalar quantity?(a) 80m^3(b) 5 Newton(c) 7 m/s towards east(d) 55m/s^2The question was asked in unit test.My question is from Vector Algebra Basics topic in section Vector Algebra of Mathematics – Class 12 |
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Answer» CORRECT choice is (a) 80m^3 The best EXPLANATION: 80 cm^3 is a scalar QUANTITY as it is denoting VOLUME. Volume is a scalar quantity and has only MAGNITUDE but no direction. |
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| 56. |
Evaluate the product \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\).(a) \(|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)(b) \(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\)(c) \(8|\vec{a}|^2-4\vec{a}.\vec{b}-15|\vec{b}|^2\)(d) \(|\vec{a}|^2+\vec{a}.\vec{b}-5|\vec{b}|^2\)The question was asked by my school principal while I was bunking the class.The query is from Product of Two Vectors-2 topic in chapter Vector Algebra of Mathematics – Class 12 |
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Answer» CORRECT answer is (b) \(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\) The BEST I can EXPLAIN: To EVALUATE: \((2\vec{a}+5\vec{b}).(4\vec{a}-5\vec{b})\) =\(2\vec{a}.4\vec{a}-2\vec{a}.5\vec{b}+3\vec{b}.4\vec{a}-3\vec{b}.5\vec{b}\) =\(8|\vec{a}|^2+2\vec{a}.\vec{b}-15|\vec{b}|^2\) |
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| 57. |
Find vector \(\vec{c}\), if \(\vec{a}\)–\(\vec{b}\)+\(\vec{c}\)=6\(\hat{i}\)+8\(\hat{j}\) where \(\vec{a}\)=7\(\hat{i}\)+2\(\hat{j}\) and \(\vec{b}\)=4\(\hat{i}\)-5\(\hat{j}\).(a) -3\(\hat{i}\)+\(\hat{j}\)(b) 3\(\hat{i}\)+\(\hat{j}\)(c) 3\(\hat{i}\)–\(\hat{j}\)(d) -3\(\hat{i}\)–\(\hat{j}\)The question was asked during an online interview.This interesting question is from Addition of Vectors in division Vector Algebra of Mathematics – Class 12 |
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Answer» The correct option is (b) 3\(\hat{i}\)+\(\hat{j}\) |
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| 58. |
Which of the following is the condition for two vectors to be Collinear?(a) The vectors should be parallel to the same line(b) The vectors should have the same initial point(c) The vectors should have the same magnitude(d) The vectors should have the magnitude 1 and 0 respectivelyI had been asked this question in an online quiz.My question is taken from Types of Vectors topic in portion Vector Algebra of Mathematics – Class 12 |
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Answer» RIGHT option is (a) The vectors should be PARALLEL to the same LINE The explanation is: If two or more vectors are parallel to the same line then they are called collinear vectors. It is not necessary that they should have the same MAGNITUDE and direction. |
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| 59. |
Which of the below given is a vector quantity?(a) 8 kg(b) 4 seconds(c) 6 Newton(d) 90 cm^3This question was addressed to me by my school teacher while I was bunking the class.My question comes from Vector Algebra Basics in chapter Vector Algebra of Mathematics – Class 12 |
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Answer» RIGHT choice is (c) 6 NEWTON Explanation: 6 Newton is a vector quantity as it is a FORCE. Force is a vector quantity which has both MAGNITUDE and direction. |
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| 60. |
Which of the given qualities is a vector?(a) Speed(b) Time(c) Weight(d) VolumeI have been asked this question during an interview for a job.Query is from Vector Algebra Basics in division Vector Algebra of Mathematics – Class 12 |
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Answer» The CORRECT answer is (a) Speed |
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