JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in R\). If \(x(\alpha, 1,2)+y(1, \beta, 2)\) \(+z(2,3, \gamma)=(0,0,0)\) for some \(x, y, z \in R, x y z \neq\) 0 , then \(6 \alpha+4 \beta+\gamma\) is equal to ..............
- A \(55\)
- B \(56\)
- C \(54\)
- D \(31\)
Answer & Solution
Correct Answer
(A) \(55\)
Step-by-step Solution
Detailed explanation
\( \alpha \beta \gamma=45, \alpha \beta \gamma \in R \) \( x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)=(0,0,0) \) \( x, y, z \in R, x y z \neq 0 \) \( \alpha x+y+2 z=0 \) \( x+\beta y+3 z=0 \) \( 2 x+2 y+\gamma z=0 \) \( x y z \neq 0 \Rightarrow\) non-trivial…
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
- If the projections of a line segment on the \(x, y\) and \(z-\) axes in \(3-\) dimensional space are \(2, 3\) and \(6\) respectively, then the length of the line segment isJEE Mains 2013 Easy
- If the three lines \(x - 3y = p, ax + 2y = q\) and \(ax + y = r\) form a right-angled triangle thenJEE Mains 2013 Hard
- If \(A\) is the area in the first quadrant enclosed by the curve \(C: 2 x^2-y+1=0\), the tangent to \(C\) at the point \((1,3)\) and the line \(x+y=1\), then the value of \(60 A\) isJEE Mains 2023 Hard
- Let integers \(\mathrm{a}, \mathrm{b} \in[-3,3]\) be such that \(\mathrm{a}+\mathrm{b} \neq 0\). Then the number of all possible ordered pairs
(a, b), for which \(\left|\frac{z-\mathrm{a}}{z+\mathrm{b}}\right|=1\) and \(\left|\begin{array}{ccc}z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega\end{array}\right|=1, z \in \mathrm{C}\), where \(\omega\) and \(\omega^2\) are the roots of \(x^2+x+1=0\), is equal to ________.JEE Mains 2025 Hard - The probability of selecting integers \(a \in[-5,30]\) such that \(x^{2}+2(a+4) x-5 a+64>0\), for all \(x \in R\), is:JEE Mains 2021 Hard
- Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and det \((( A + I )(\operatorname{Adj}( A )+ I ))=4\). Then the sum of the diagonal elements of \(A\) can be.JEE Mains 2022 Hard
More PYQs from JEE Mains
- A fair coin is tossed \(n\)-times such that the probability of getting at least one head is at least \(0.9 .\) Then the minimum value of \(n\) is \(....\)JEE Mains 2021 Easy
- Let the hyperbola \(H : \frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1\) pass through the point \((2 \sqrt{2},-2 \sqrt{2})\). A parabola is drawn whose focus is same as the focus of \(H\) with positive abscissa and the directrix of the parabola passes through the other focus of \(H\). If the length of the latus rectum of the parabola is e times the length of the latus rectum of \(H\), where \(e\) is the eccentricity of \(H\), then which of the following points lies on the parabola?JEE Mains 2022 Hard
- Let \(A=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right] .\) Then the number of \(3 \times 3\) matrices \(\mathrm{B}\) with entries from the set \(\{1,2,3,4,,5\}\) and satisfying \(A B=B A\) is \(....\)JEE Mains 2021 Hard
- Let \(y=y_{1}(x)\) and \(y=y_{2}(x)\) be two distinct solutions of the differential equation \(\frac{d y}{d x}=x+y\), with \(y _{1}(0)=0\) and \(y _{2}(0)=1\) respectively. Then, the number of points of intersection of \(y=y_{1}(x)\) and \(y=y_{2}(x)\) is.JEE Mains 2022 Hard
- The integral \(16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) is equal toJEE Mains 2023 Hard
- Let \(A, B\) and \(C\) be three events such that the probability that exactly one of \(A\) and \(B\) occurs is \((1-k)\), the probability that exactly one of \(B\) and \(C\) occurs is \((1-2 k)\), the probability that exactly one of \(C\) and \(A\) occurs is \((1-k)\) and the probability of all \(A, B\) and \(C\) occur simultaneously is \(k^{2}\), where \(0\,<\,\mathrm{k}\,<\,1\). Then the probability that at least one of \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) occur is:JEE Mains 2021 Hard