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Process of indicating addition [3+2=5] at number system

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Updated On: Apr 19, 2024

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The Correct Option is B

The correct option is (B): B, A, C, D, E.

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\[ x - ny + z = 6 \\ x - (n - 2)y + (n + 1)z = 8 \\ (n - 1)y + z = 1 \] Let \( n \) be the number on the die when rolled randomly. Then \( P \) (that system equation has a unique solution) = \( \frac{k}{6} \). Then sum of value of \( k \) and all possible values of \( n \) is:
- JEE Main - 2026
- Mathematics
- Number Systems
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If \( a, b, c \) are in A.P. where \( a + b + c = 1 \) and \( a, 2b, c \) are in G.P., then the value of \( 9(a^2 + b^2 + c^2) \) is equal to:
- JEE Main - 2026
- Mathematics
- Number Systems
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Let \( \mathbf{a} = \sqrt{2} \hat{i} \) and \( \mathbf{b} = 5\hat{j} + \hat{k} \). If \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{c} \) lies in the \( y \)-\( z \) plane such that \( |\mathbf{c}| = 2 \), then the maximum value of \( |\mathbf{c} \cdot \mathbf{d}| \) is equal to:
- JEE Main - 2026
- Mathematics
- Number Systems
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If \[ \int_0^6 \left( x^3 + \lfloor x^{1/3} \rfloor \right) \, dx = \alpha \] and \[ \int_0^{\frac{\pi}{2}} \frac{\sin^2 x}{\sin^6 x + \cos^6 x} \, dx = \beta, \] then the value of \( ab^2 \) is equal to:
- JEE Main - 2026
- Mathematics
- Number Systems
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Let the domain of the function \[ f(x) = \log_3 \log_5 \left( 7 - \log_2 \left( x^2 - 10x + 15 \right) \right) + \sin^{-1} \left( \frac{3x - 7}{17 - x} \right) \] be \( (\alpha, \beta) \), then \( \alpha + \beta \) is equal to:
- JEE Main - 2026
- Mathematics
- Number Systems
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