Mathematics Model Question Paper
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Mathematics Model Question Paper
Sample questions with model answers
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If f : R → R is defined by f(x) = 1 + x^2, then show that f is neither 1-1 nor onto.
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f is not 1-1 because f(x) = f(-x) and not onto because f(x) >= 1.
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For the matrices A = [2, 4; 1, 3; 6, 5], verify that (AB)' = B'A'.
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Use properties of transposes to verify.
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Solve the system of linear equations by matrix method: 2x + 3y + 3z = 5, x − 2y + z = −4, 3x − y − 2z = 3.
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x = 1, y = 2, z = 0.
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Integrate 1/(x^2 + 1) with respect to x and hence find ∫(x^2 + 2x + 10)dx.
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Integral = arctan(x) + x^2 + 10x + C.
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