If f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & ca \\1 & c & ab \end {vmatrix}\) = \(\begin{vmatrix}1 & a & a^2 \\1 & b & b^2 \\1 & c & c^2 \end {vmatrix}\) then which one among the following is correct?(a) (a – b)(b – c)(c – a)(b) a, b, c are in G.P(c) b, c, a are in G.P(d) a, c, b are in G.PI got this question by my college professor while I was bunking the class.This question is from Application of Determinants in portion Determinants of Mathematics – Class 12

If f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & ca \\1 & c & ab \end {

1.	If f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & ca \\1 & c & ab \end {vmatrix}\) = \(\begin{vmatrix}1 & a & a^2 \\1 & b & b^2 \\1 & c & c^2 \end {vmatrix}\) then which one among the following is correct?(a) (a – b)(b – c)(c – a)(b) a, b, c are in G.P(c) b, c, a are in G.P(d) a, c, b are in G.PI got this question by my college professor while I was bunking the class.This question is from Application of Determinants in portion Determinants of Mathematics – Class 12
Answer» Correct choice is (b) a, b, c are in G.P Easiest explanation: Here, f(x) = \(\begin{vmatrix}1 & a & bc \\1 & b & CA \\1 & c & AB \END {vmatrix}\) Multiplying and DIVING by abc, = (1/abc) \(\begin{vmatrix}a & a^2 & abc \\b & b^2 & abc \\c & c^2& abc \end {vmatrix}\) = \(\begin{vmatrix}1 & a & a^2 \\1 & b & b^2 \\1 & c & c^2 \end {vmatrix}\) = (a – b)(b – c)(c – a)

Discussion

No Comment Found

Related InterviewSolutions

Which of the following conditions holds true for a system of equations to be consistent?(a) It should have one or more solutions(b) It should have no solutions(c) It should have exactly one solution(d) It should have exactly two solutionsThe question was posed to me in homework.This intriguing question comes from Applications of Determinants and Matrices topic in portion Determinants of Mathematics – Class 12
If A=\(\begin{bmatrix}5&-8\\2&6\end{bmatrix}\), find A(adj A).(a) \(\begin{bmatrix}41&0\\0&46\end{bmatrix}\)(b) \(\begin{bmatrix}46&0\\1&46\end{bmatrix}\)(c) \(\begin{bmatrix}46&1\\0&46\end{bmatrix}\)(d) \(\begin{bmatrix}46&0\\0&46\end{bmatrix}\)I have been asked this question in an international level competition.Question is from Determinants in chapter Determinants of Mathematics – Class 12
For which of the following element in the determinant Δ=\(\begin{vmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{vmatrix}\) , the minor and the cofactor both are zero.(a) -5(b) 2(c) -6(d) 8The question was posed to me in an online interview.The doubt is from Determinants topic in division Determinants of Mathematics – Class 12
Find the minor of the element 1 in the determinant Δ=\(\begin{vmatrix}1&5\\3&8\end{vmatrix}\).(a) 5(b) 1(c) 8(d) 3The question was asked in an interview.The doubt is from Determinants in division Determinants of Mathematics – Class 12
Find the minor and cofactor respectively for the element 3 in the determinant Δ=\(\begin{vmatrix}1&5\\3&6\end{vmatrix}\).(a) M21=-5, A21=-5(b) M21=5, A21=-5(c) M21=-5, A21=5(d) M21=5, A21=5The question was asked during a job interview.The question is from Determinants in chapter Determinants of Mathematics – Class 12
Find the value of k for which the points (3,2), (1,2), (5,k) are collinear.(a) 2(b) 5(c) 4(d) 9I had been asked this question by my college professor while I was bunking the class.Enquiry is from Area of a Triangle in chapter Determinants of Mathematics – Class 12
What will be the value of the given determinant \(\begin{vmatrix}109 & 102 & 95 \\6 & 13 & 20 \\1 & -6 & 13 \end {vmatrix}\)?(a) constant other than 0(b) 0(c) 100(d) -1997I had been asked this question during an interview.This is a very interesting question from Application of Determinants in section Determinants of Mathematics – Class 12
Find the determinant of the matrix A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ &cos⁡θ \end{bmatrix}\).(a) sin^2⁡θ(b) sin⁡θ(c) -sin⁡θ(d) -sin^2⁡θI got this question in an online quiz.My question is based upon Determinant topic in division Determinants of Mathematics – Class 12
What is the value of \(\begin{vmatrix}sin^2 ⁡a & sina\, cosa & cos^2 ⁡a \\sin^2 ⁡b & sinb\, cosb & cos^2 ⁡b \\sin^2⁡ c & sinc\, cosc & cos^2⁡ c \end {vmatrix}\)?(a) -sin(a – b) sin(b – c) sin(c – a)(b) sin(a – b) sin(b – c) sin(c – a)(c) -sin(a + b) sin(b + c) sin(c + a)(d) sin(a + b) sin(b + c) sin(c + a)This question was addressed to me during an interview for a job.This is a very interesting question from Determinant in section Determinants of Mathematics – Class 12
For which of the elements in the determinant Δ=\(\begin{vmatrix}1&8&-6\\2&-3&4\\-7&9&5\end{vmatrix}\) the cofactor is -37.(a) 4(b) 1(c) -6(d) -3I had been asked this question during an interview for a job.This intriguing question comes from Determinants in chapter Determinants of Mathematics – Class 12

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment