JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The values of \(a\) and \(b\), for which the system of equations \(2 x+3 y+6 z=8\) ; \(x+2 y+a z=5\) ; \(3 x+5 y+9 z=b\) has no solution, are:
- A \(a=3, b=13\)
- B \(a \neq 3, b \neq 13\)
- C \(a \neq 3, b=3\)
- D \(a=3, b \neq 13\)
Answer & Solution
Correct Answer
(D) \(a=3, b \neq 13\)
Step-by-step Solution
Detailed explanation
\(D=\left|\begin{array}{lll} 2 & 3 & 6 \\ 1 & 2 & a \\ 3 & 5 & 9 \end{array}\right|=3-a\) \(D=\left|\begin{array}{lll}2 & 3 & 8 \\ 1 & 2 & 5 \\ 3 & 5 & b\end{array}\right|=b-13\) If \(a=3, b \neq 13\), no solution.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- For the system of equations \(x+y+z=6\) \(x+2 y+\alpha z=10\) \(x+3 y+5 z=\beta\), which one of the following is NOT true?JEE Mains 2023 Hard
- If for some \(p , q , r \in R\), not all have same sign, one of the roots of the equation \(\left(p^{2}+q^{2}\right) x^{2}-2 q(p+r) x\) \(+q^{2}+r^{2}=0\) is also a root of the equation \(x^{2}+2 x-8=0\), then \(\frac{q^{2}+r^{2}}{p^{2}}\) is equal to-JEE Mains 2022 Hard
- If \(a_1, a_2, a_3 …………\) an are in \(A.P\) and \(a_1 + a_4 + a_7 + …………… + a_{16} = 114\), then \(a_1 + a_6 + a_{11} + a_{16}\) is equal toJEE Mains 2019 Medium
- Among the statements:
I: If \( \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 0 \end{vmatrix} \), then \( \cos^{2}\alpha+\cos^{2}\beta+\cos^{2}\gamma=\frac{3}{2} \)
II: If \( \begin{vmatrix} x^{2}+x & x+1 & x-2 \\ 2x^{2}+3x-1 & 3x & 3x-3 \\ x^{2}+2x+3 & 2x-1 & 2x-1 \end{vmatrix} = px+q \), then \( p^{2}=196q^{2} \),JEE Mains 2026 Easy - The mean and variance of the marks obtained by the students in a test are \(10\) and \(4\) respectively. Later, the marks of one of the students is increased from \(8\) to \(12\) . If the new mean of the marks is \(10.2.\) then their new variance is equal to :JEE Mains 2023 Hard
- Let the sum of the first \(n\) terms of a non-constant \(A.P., a_1, a_2, a_3, ……\) be \(50\,n\, + \,\frac{{n\,(n\, - 7)}}{2}A,\) where \(A\) is a constant. If \(d\) is the common difference of this \(A.P.,\) then the ordered pair \((d,a_{50})\) is equal toJEE Mains 2019 Hard
More PYQs from JEE Mains
- The number of real roots of the equation \(\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}\), is:JEE Mains 2023 Hard
- The position vectors of the vertices \(A, B\) and \(C\) of a triangle are \(2 \hat{i}-3 \hat{j}+3 \hat{k}, \quad 2 \hat{i}+2 \hat{j}+3 \hat{k} \quad\) and \(-\hat{i}+\hat{j}+3 \hat{k}\) respectively. Let \(l\) denotes the length of the angle bisector \(\mathrm{AD}\) of \(\angle \mathrm{BAC}\) where \(\mathrm{D}\) is on the line segment \(\mathrm{BC}\), then \(2 l^2\) equals :JEE Mains 2024 Medium
- Let \(f :R \to R\) be defined by \(f(x)\,\, = \,\,\frac{x}{{1 + {x^2}}},\,x\, \in \,R.\) Then the range of \(f\) isJEE Mains 2019 Hard
- If \(x=\sum \limits_{n=0}^{\infty} a^{n}, y=\sum\limits_{n=0}^{\infty} b^{n}, z=\sum\limits_{n=0}^{\infty} c^{n}\), where \(a , b , c\) are in \(A.P.\) and \(|a| < 1,|b| < 1,|c| < 1\), \(abc \neq 0\), thenJEE Mains 2022 Medium
- Two vertical poles are \(150\, m\) apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) isJEE Mains 2021 Easy
- The sum of the absolute maximum and absolute minimum values of the function \(f(x)=\tan ^{-1}(\sin x-\cos x)\) in the interval \([0, \pi]\) is.JEE Mains 2022 Hard